Karnataka 1st PUC Question Bank for Statistics

Government of Karnataka
Department of School Education
(Pre-University)

QUESTION BANK

¥ÀæxÀªÀÄ ¦.AiÀÄÄ.¹. ¸ÀASÁå±Á¸ÀçÛ ¥Àæ±Éß PÉÆñÀ
Unit - I
¥ÀjZÀAiÀÄ – CxÀð ªÀÄvÀÄÛ ªÁå¦Û
¸ÀjAiÀiÁzÀ GvÀg
Û ÀªÀ£ÀÄß DAiÉÄ̪ÀiÁr §gɬÄj:

1. ¸ÀASÁå±Á¸ÀçÛ zÀ ¦vÁªÀĺÀ AiÀiÁgÀÄ?
a) Dgï J ¦ü±Àgï b) J J¯ï ¨Ë° c) ºÉÆgÁ¸É ¸ÉQæ¸ïÖ d) §Ä¢ÝAUïl£ï

2. “STATISTICS” JA§ ¥ÀzÀªÀ£ÀÄß ªÀÅåvÀàwÛ ªÀiÁrzÀ ¯ÁånÃ£ï ¥ÀzÀ AiÀiÁªÀÅzÁVzÉ.
a) Status b) Statista c) Statistik d) Statistique
3. “STATISTICS” JA§ ¥ÀzÀªÀ£ÀÄß ªÀÅåvÀàwÛ ªÀiÁrzÀ EmÁ°£ï ¥ÀzÀ AiÀiÁªÀÅzÁVzÉ.
a) Status b) Statista c) Statistik d) Statistique
4. “STATISTICS” JA§ ¥ÀzÀªÀ£ÀÄß ªÀÅåvÀàwÛ ªÀiÁrzÀ dªÀÄð£ï ¥ÀzÀ AiÀiÁªÀÅzÁVzÉ.
a) Status b) Statista c) Statistik d) Statistique
5. “STATISTICS” JA§ ¥ÀzÀªÀ£ÀÄß ªÀÅåvÀàwÛ ªÀiÁrzÀ ¥sÉæAZï ¥ÀzÀ AiÀiÁªÀÅzÁVzÉ.
a) Status b) Statista c) Statistik d) Statistique
6. ¸ÀASÁå±Á¸ÀçÛ ªÀ£ÀÄß JtÂPÉUÀ¼À «eÁÕ£ÀªÉAzÀÄ ªÁåSÁå¤zÀªÀgÀÄ AiÀiÁgÀÄ?
a) Dgï J ¦ü±Àgï b) J J¯ï ¨Ë° c) ºÉÆgÁ¸É ¸ÉQæ¸ïÖ d) §Ä¢ÝAUïl£ï

7. CzsÀåAiÀÄ£ÀPÉÌ M¼À¥ÀlÖ ªÀ¸ÀÄÛUÀ¼À UÀÄA¥À£ÀÄß »ÃUÉ£ÀÄߪÀgÀÄ.
a) ¸ÀªÀÄ¶× b) ¤zÀ±ÀðPÀ c) ZÀ®PÀ d) UÀÄtzsÀªÀÄð

8. ¸ÀªÀĶ×AiÀÄ£ÀÄß ¥Àæw¤¢ü¸ÀĪÀ ¨sÁUÀªÀ£ÀÄß »ÃUÉ£ÀÄߪÀgÀÄ.
a) ¤zÀ±ÀðPÀ b) ZÀ®PÀ c) UÀÄtzsÀªÀÄð d) ±Á©ÞPÀ C¼ÀvÉ

9. ªÀ¸ÀÄÛ«¤AzÀ ªÀ¸ÀÄÛ«UÉ §zÀ¯ÁUÀĪÀ ¥ÀjªÀiÁuÁvÀäPÀ ®PÀëtªÉÃ
a) ¸ÀªÀÄ¶× b) ¤zÀ±ÀðPÀ c) ZÀ®PÀ d) UÀÄtzsÀªÀÄð

10. ªÀ¸ÀÄÛ«¤AzÀ ªÀ¸ÀÄÛ«UÉ §zÀ¯ÁUÀĪÀ UÀÄuÁvÀäPÀ ®PÀëtªÉÃ
a) ¸ÀªÀÄ¶× b) ¤zÀ±ÀðPÀ c) ZÀ®PÀ d) UÀÄtzsÀªÀÄð

11. UÀÄA¥ÀÄUÀ¼À£ÀÄß UÀÄgÀÄw¸À®Ä CªÀÅUÀ½UÉ ¸ÀASÉåUÀ¼À£ÀÄß ºÀAaPɪÀiÁqÀĪÀÅzÀÄ
a) ±Á©ÞPÀ C¼ÀvÉ b) PÀæªÀÄ C¼ÀvÉ c) ZÀ®PÀ d) UÀÄtzsÀªÀÄð

12. KjPÉ CxÀªÁ E½PÉ PÀæªÀÄzÀ°è eÉÆÃr¸À®Ä ¥Áæ¥ÁÛAPÀUÀ½UÉ ¸ÀASÉåUÀ¼À£ÀÄß ºÀAaPɪÀiÁqÀĪÀÅzÀÄ
a) ±Á©ÞPÀ C¼ÀvÉ b) PÀæªÀÄ C¼ÀvÉ c) ZÀ®PÀ d) UÀÄtzsÀªÀÄð

DªÀgÀtzÀ°ègÀĪÀ ¸ÀjAiÀiÁzÀ GvÀg
Û ÀªÀ£ÀÄß Dj¹, ©lÖ ¸ÀܼÀ vÀÄA©j:
(d£À¸ÀASÁå±Á¸ÀçÛ , ZÀ®PÀ, ¸ÀªÀĶ×, UÀÄtzsÀªÀÄð, Statista, PÀæªÀÄ, Statistique, ¤zÀ±ÀðPÀ, ±Á©ÞPÀ, ¥ÀjªÀiÁuÁvÀäPÀ, UÀÄuÁvÀäPÀ,
Status, MlÄÖUÀÆr¹zÀ, Statistik, ¸ÀASÁåvÀäPÀªÁV, «aÒ£Àß)
1. “STATISTICS” JA§ ¥ÀzÀªÀ£ÀÄß ªÀÅåvÀàwÛ ªÀiÁrzÀ ¯ÁånÃ£ï ¥ÀzÀ _________
2. “STATISTICS” JA§ ¥ÀzÀªÀ£ÀÄß ªÀÅåvÀàwÛ ªÀiÁrzÀ EmÁ°£ï ¥ÀzÀ _________
3. “STATISTICS” JA§ ¥ÀzÀªÀ£ÀÄß ªÀÅåvÀàwÛ ªÀiÁrzÀ dªÀÄð£ï ¥ÀzÀ _________

3

¥ÀæxÀªÀÄ ¦.AiÀÄÄ.¹. ¸ÀASÁå±Á¸ÀçÛ ¥Àæ±Éß PÉÆñÀ
4. “STATISTICS” JA§ ¥ÀzÀªÀ£ÀÄß ªÀÅåvÀàwÛ ªÀiÁrzÀ ¥sÉæAZï ¥ÀzÀ _________
5. CzsÀåAiÀÄ£ÀPÉÌ M¼À¥ÀlÖ ªÀ¸ÀÄÛUÀ¼À UÀÄA¥À£ÀÄß _________ J£ÀÄߪÀgÀÄ.
6. ¸ÀªÀĶ×AiÀÄ£ÀÄß ¥Àæw¤¢ü¸ÀĪÀ ¨sÁUÀªÀ£ÀÄß _________ J£ÀÄߪÀgÀÄ.
7. ¸ÀASÁåvÀäPÀªÁV C¼ÀvɪÀiÁqÀ®Ä ¸ÁzsÀå«gÀĪÀ ®PÀëtUÀ¼À£ÀÄß __________ ®PÀëtUÀ¼É£ÀÄߪÀgÀÄ.
8. ¸ÀASÁåvÀäPÀªÁV C¼ÀvɪÀiÁqÀ®Ä ¸ÁzsÀå«®èzÀ ®PÀëtUÀ¼À£ÀÄß __________ ®PÀëtUÀ¼É£ÀÄߪÀgÀÄ.
9. ªÀ¸ÀÄÛ«¤AzÀ ªÀ¸ÀÄÛ«UÉ §zÀ¯ÁUÀĪÀ ¥ÀjªÀiÁuÁvÀäPÀ ®PÀëtªÉà _________ .
10. ªÀ¸ÀÄÛ«¤AzÀ ªÀ¸ÀÄÛ«UÉ §zÀ¯ÁUÀĪÀ UÀÄuÁvÀäPÀ ®PÀëtªÉà _________ .
11. ªÀiÁ£ÀªÀ d£ÁAUÀzÀ ¸ÀASÁå±Á¹ÛçÃAiÀÄ CzsÀåAiÀÄ£ÀªÀ£ÀÄß _________ J£ÀÄߪÀgÀÄ.
12. CAQCA±ÀUÀ¼ÀÄ __________ ¸ÀAUÀwUÀ¼ÁVgÀÄvÀÛªÉ.
13. CAQCA±ÀUÀ¼ÀÄ __________ ªÀåPÀÛ¥Àr¸À¯ÁVgÀÄvÀª
Û É.
14. UÀÄA¥ÀÄUÀ¼À£ÀÄß UÀÄgÀÄw¸À®Ä CªÀÅUÀ½UÉ ¸ÀASÉåUÀ¼À£ÀÄß ºÀAaPɪÀiÁqÀĪÀÅzÀ£ÀÄß _________ C¼ÀvÉ J£ÀÄߪÀgÀÄ.
15. KjPÉ CxÀªÁ E½PÉ PÀæªÀÄzÀ°è eÉÆÃr¸À®Ä ¥Áæ¥ÁÛAPÀUÀ½UÉ ¸ÀASÉåUÀ¼À£ÀÄß ºÀAaPɪÀiÁqÀĪÀÅzÀ£ÀÄß ________ C¼ÀvÉ
J£ÀÄߪÀgÀÄ.

ºÉÆA¢¹ §gɬÄj: (£ÉÃgÀªÁV GvÀÛgÀUÀ¼À£ÀÄß ¤ÃqÀ¯ÁVzÉ.)
Status ¯ÁånÃ£ï ¥ÀzÀ
Statista EmÁ°£ï ¥ÀzÀ
Statistik dªÀÄð£ï ¥ÀzÀ
Statistique ¥sÉæAZï ¥ÀzÀ
¸Àgï gÉÆ£Á¯ïØ J ¦ü±Àgï ¸ÀASÁå±Á¸ÀçÛ zÀ ¦vÁªÀĺÀ
¦ ¹ ªÀĺÀ®£ÉÆ©¸ï ¨sÁgÀwÃAiÀÄ ¸ÀASÁå±Á¸ÀçÛ zÀ ¦vÁªÀĺÀ
d£À¸ÀASÁå±Á¸ÀÛç ªÀiÁ£ÀªÀ d£ÁAUÀzÀ ¸ÀASÁå±Á¹ÛçÃAiÀÄ CzsÀåAiÀÄ£À
PÀȶ «eÁÕ£À fêÀ«ªÀiÁ PÉëÃvÀæzÀ°è ¸ÀASÁå±Á¸ÀçÛ
¥ÀjªÀiÁuÁvÀäPÀ zÀvÁÛA±À ¸ÀASÁåvÀäPÀªÁV ªÀåPÀÛ¥Àr¹gÀĪÀÅzÀÄ
JvÀgÛ À ZÀ®PÀ
ZÀªÀÄðzÀ §tÚ UÀÄtzsÀªÀÄð

MAzÀÄ CAPÀzÀ ¥Àæ±ÉßUÀ¼ÀÄ:
1. ¨sÁgÀwÃAiÀÄ ¸ÀASÁå±Á¸ÀçÛ zÀ ¦vÁªÀĺÀ AiÀiÁgÀÄ?
2. “STATISTICS” JA§ ¥ÀzÀ AiÀiÁªÀ ¯Áån£ï ±À§Ý¢AzÀ GvÀàwÛAiÀiÁVzÉ JAzÀÄ w½¹.
3. ¸ÀASÁå±Á¸ÀçÛ ªÀ£ÀÄß JtÂPÉUÀ¼À «eÁÕ£À JAzÀÄ AiÀiÁgÀÄ ªÁåSÁå¤zÁÝgÉ?
4. ¨Ë°AiÀĪÀgÀ ¸ÀASÁå±Á¸ÀçÛ zÀ ªÁåSÉå §gɬÄj.
5. ¨ÉÆ¢ÝAUïl£ïgÀªÀgÀ ¸ÀASÁå±Á¸ÀçÛ zÀ ªÁåSÉå PÉÆr.
6. PÉÆæPÁìl£ï ªÀÄvÀÄÛ PËqÀ£ïgÀªÀgÀ ¸ÀASÁå±Á¸ÀçÛ zÀ ªÁåSÉå §gɬÄj.
7. ¸ÀASÁå±Á¸ÀçÛ ªÀÅ ªÉÊAiÀÄQÛPÀ zÀvÁÛA±ÀzÉÆA¢UÉ ªÀåªÀºÀj¸ÀĪÀÅzÉÃ?
8. ¸ÀªÀĶÖAiÀÄ£ÀÄß ªÁåSÁ夹.
9. ¤zÀ±ÀðPÀ(¥ÀæwZÀAiÀÄ)ªÀ£ÀÄß ªÁåSÁ夹.
10. UÀÄuÁvÀäPÀ ®PÀëtªÀ£ÀÄß ªÁåSÁ夹.

4

¥ÀæxÀªÀÄ ¦.AiÀÄÄ.¹. ¸ÀASÁå±Á¸ÀçÛ ¥Àæ±Éß PÉÆñÀ
11. ¥ÀjªÀiÁuÁvÀäPÀ ®PÀëtªÀ£ÀÄß ªÁåSÁ夹.
12. UÀÄtzsÀªÀÄðªÀ£ÀÄß ªÁåSÁ夹.
13. UÀÄtzsÀªÀÄðPÉÌ MAzÀÄ GzÁºÀgÀuÉ PÉÆr.
14. ZÀ®PÀªÀ£ÀÄß ªÁåSÁ夹.
15. «aߣÀß ZÀ®PÀªÀ£ÀÄß ªÁåSÁ夹.
16. «aߣÀß ZÀ®PÀPÉÌ MAzÀÄ GzÁºÀgÀuÉ PÉÆr.
17. ¸ÀvÀvÀ ZÀ®PÀªÀ£ÀÄß ªÁåSÁ夹.
18. ¸ÀvÀvÀ ZÀ®PÀPÉÌ MAzÀÄ GzÁºÀgÀuÉ PÉÆr.
19. ±Á©ÝPÀ C¼ÀvÉAiÀÄ£ÀÄß ªÁåSÁ夹.
20. PÀæªÀÄ ¸ÀÆZÀPÀ C¼ÀvÉAiÀÄ£ÀÄß ªÁåSÁ夹.

JgÀqÀÄ CAPÀzÀ ¥Àæ±ÉßUÀ¼ÀÄ:
1. ¥ÉÆæ. ºÉÆgÉ¸ï ¸ÉQæ¸ïÖgÀªÀgÀ ¸ÀASÁå±Á¸ÀçÛ zÀ ªÁåSÉå §gɬÄj.
2. ¸ÀASÁå±Á¸ÀçÛ zÀ JgÀqÀÄ ®PÀëtUÀ¼À£ÀÄß w½¹.
3. ¸ÀASÁå±Á¸ÀçÛ zÀ JgÀqÀÄ PÁAiÀÄðUÀ¼À£ÀÄß w½¹.
4. ¸ÀASÁå±Á¸ÀçÛ zÀ JgÀqÀÄ Ew«ÄwUÀ¼À£ÀÄß w½¹.
5. ¸ÀASÁå±Á¸ÀçÛ ªÀÅ G¥ÀAiÉÆÃV¸À®àqÀĪÀ JgÀqÀÄ PÉëÃvÀæUÀ¼À£ÀÄß w½¹.
6. ¸ÀASÁå±Á¸ÀçÛ zÀ C¥À£ÀA©PÉUÉ JgÀqÀÄ PÁgÀtUÀ¼À£ÀÄß w½¹.
7. ¸ÀASÁå±Á¸ÀçÛ zÀ C¥À£ÀA©PÉUÀ¼À£ÀÄß ºÉÆÃUÀ¯Ár¸ÀĪÀ JgÀqÀÄ ¥ÀjºÁgÀUÀ¼À£ÀÄß w½¹.
8. ¸ÀªÀÄ¶Ö ªÀÄvÀÄÛ ¤zÀ±ÀðPÀUÀ¼À£ÀÄß ªÁåSÁ夹.
9. UÀÄuÁvÀäPÀ ªÀÄvÀÄÛ ¥ÀjªÀiÁuÁvÀäPÀ ®PÀëtUÀ¼À £ÀqÀÄ«£À ªÀåvÁå¸À w½¹.
10. UÀÄtzsÀªÀÄðªÀ£ÀÄß ªÁåSÁ夹. MAzÀÄ GzÁºÀgÀuÉ PÉÆr.
11. ZÀ®PÀªÀ£ÀÄß ªÁåSÁ夹. MAzÀÄ GzÁºÀgÀuÉ PÉÆr.
12. «a£Àß ZÀ®PÀªÀ£ÀÄß MAzÀÄ GzÁºÀgÀuÉAiÉÆA¢UÉ ªÁåSÁ夹.
13. ¸ÀvÀvÀ ZÀ®PÀªÀ£ÀÄß MAzÀÄ GzÁºÀgÀuÉAiÉÆA¢UÉ ªÁåSÁ夹.
14. E°è PÁtĪÀ ZÀ®PÀzÀ ¥ÀæPÁgÀªÀ£ÀÄß w½¹.
(a) ¢£ÀzÀ vÁ¥ÀªÀiÁ£À (b) ¥ÁzÀgÀPÉëUÀ¼À C¼ÀvÉ.
15. ±Á©ÝPÀ ªÀÄvÀÄÛ PÀæªÀÄ ¸ÀÆZÀPÀ C¼ÀvÉUÀ¼ÉAzÀgÉãÀÄ?

LzÀÄ CAPÀzÀ ¥Àæ±ÉßUÀ¼ÀÄ:
1. ¥ÉÆæ. ºÉÆgÉ¸ï ¸ÉQæ¸ïÖgÀªÀgÀ ¸ÀASÁå±Á¸ÀçÛ ªÀ£ÀÄß ªÁåSÁ夹. CªÀÅUÀ¼À°è JgÀqÀÄ ®PÀëtUÀ¼À£ÀÄß «ªÀj¹.
2. ¸ÀASÁå±Á¸ÀçÛ zÀ LzÀÄ ®PÀëtUÀ¼À£ÀÄß w½¹.
3. ¸ÀASÁå±Á¸ÀçÛ zÀ LzÀÄ PÁAiÀÄðUÀ¼À£ÀÄß w½¹.
4. ¸ÀASÁå±Á¸ÀçÛ zÀ ªÀÄÆgÀÄ PÁAiÀÄð ªÀÄvÀÄÛ JgÀqÀÄ Ew-«ÄwUÀ¼À£ÀÄß w½¹.
5. ¸ÀASÁå±Á¸ÀçÛ zÀ LzÀÄ Ew«ÄwUÀ¼À£ÀÄß w½¹.

5

¥ÀæxÀªÀÄ ¦.AiÀÄÄ.¹. ¸ÀASÁå±Á¸ÀçÛ ¥Àæ±Éß PÉÆñÀ
Unit - II
zÀvÁÛA±ÀzÀ ¸ÀAWÀl£É
¸ÀjAiÀiÁzÀ GvÀg
Û ÀªÀ£ÀÄß DAiÉÄ̪ÀiÁr §gɬÄj:

1. ¸ÁATåPÀ ¥Àj²Ã®£É £ÀqɸÀĪÀ ªÀåQÛ
a) ¥Àj²Ã®PÀ b) ¨ÁwäÃzÁgÀ c) ¥ÀæwQæ¬Ä¸ÀĪÀªÀ d) ªÀiÁ»zÁgÀ

2. ¸ÀªÀĶ×AiÀÄ ¥ÀæwAiÉÆAzÀÄ WÀlPÀzÀ ¸ÀA¥ÀÆtð UÀtwAiÀÄ£ÀÄß »ÃUÉAzÀÄ PÀgÉAiÀÄÄvÁÛgÉ.
a) ªÀiÁUÀðzÀ²ð ¸À«ÄÃPÉë b) UÀtw «zsÁ£À c) ¤zÀ±ÀðPÀ ¸À«ÄÃPÉë d) ¥ÀæwZÀAiÀÄ£À

3. ¥ÀæwAiÉÆAzÀÄ WÀlPÀªÀÅ ¤zÀ±ÀðPÀzÀ°è ¸ÉÃgÀĪÀ ¸ÀA¨sÀªÀ¤ÃAiÀÄvÉ ¸ÀªÀÄ£ÁVgÀĪÀ PÀæªÀĪÉÃ
a) ¸ÀgÀ¼À DPÀ¹äPÀ ¥ÀæwZÀAiÀÄ£À b) ªÀåªÀ¹ÜvÀ ¥ÀæwZÀAiÀÄ£À
c) ¸Àj
Û ÃPÀÈvÀ ¥ÀæwZÀAiÀÄ£À d) ¥ÀæwZÀAiÀÄ£À zÉÆõÀ

4. ¸ÀªÀÄ£ÁV ¥ÀævÉåÃQ¹zÀ WÀlPÀUÀ½AzÀ ¤zÀ±ÀðPÀUÀ¼À£ÀÄß DAiÉÄ̪ÀiÁrPÉƼÀÄîªÀ PÀæªÀĪÉÃ
a) ¸ÀgÀ¼À DPÀ¹äPÀ ¥ÀæwZÀAiÀÄ£À b) ªÀåªÀ¹ÜvÀ ¥ÀæwZÀAiÀÄ£À
c) ¸Àj
Û ÃPÀÈvÀ ¥ÀæwZÀAiÀÄ£À d) ¥ÀæwZÀAiÀÄ£À zÉÆõÀ

5. ¸ÁªÀÄå®PÀëtUÀ¼À ¥Àæw UÀÄA¥ÀĤAzÀ ¸ÀÆPÀÛ ¸ÀASÉåAiÀÄ ¤zÀ±ÀðPÀUÀ¼À£ÀÄß DAiÀÄÄÝPÉƼÀÄîªÀ «zsÁ£ÀªÉÃ
a) ¸ÀgÀ¼À DPÀ¹äPÀ ¥ÀæwZÀAiÀÄ£À b) ªÀåªÀ¹ÜvÀ ¥ÀæwZÀAiÀÄ£À
c) ¸Àj
Û ÃPÀÈvÀ ¥ÀæwZÀAiÀÄ£À d) ¥ÀæwZÀAiÀÄ£À zÉÆõÀ

DªÀgÀtzÀ°ègÀĪÀ ¸ÀjAiÀiÁzÀ GvÀg
Û ÀªÀ£ÀÄß Dj¹, ©lÖ ¸ÀܼÀ vÀÄA©j:
(¥ÁæxÀ«ÄPÀ, ¨ÁwäÃzÁgÀ, ¥ÀPÀë¥ÁvÀ, ªÀgÀ¢UÁgÀgÀgÀÄ, UÀtw, ¥Àæ±ÁߪÀ½, ¥Àj²Ã®PÀ, ªÀiÁ»zÁgÀgÀÄ(¥ÀæwQæ¬Ä¸ÀĪÀªÀgÀÄ),
¤µÀàPÀë¥ÁvÀ, vÀ¥À²Ã®Ä¥ÀnÖ, ¤gÀ¥ÉÃPÀë)
1. ¸ÁATåPÀ ¥Àj²Ã®£É £ÀqɸÀĪÀ ªÀåQÛAiÉÄà ________
2. ¥Àj²Ã®PÀ¤UÁV ªÀiÁ»w ¸ÀAUÀ滸ÀĪÀ ªÀåQÛAiÀÄ£ÀÄß _________ J£ÀÄߪÀgÀÄ.
3. AiÀiÁªÀ ªÀåQÛUÀ½AzÀ ªÀiÁ»w ¸ÀAUÀ滸À®àqÀĪÀÅzÉÆÃ, CªÀgÉà __________ .
4. ªÉÆlÖªÉÆzÀ®¨ÁjUÉ, £ÉÃgÀªÁV PÉëÃvÀæ¢AzÀ ¥Àj²Ã®PÀ£À ªÀÄÆ®PÀ ¸ÀAUÀ滹zÀ zÀvÁÛA±ÀªÀ£ÀÄß _________ zÀvÁÛA±À
J£ÀÄߪÀgÀÄ.
5. ªÀiÁ»wzÁgÀ¤AzÀ ªÀiÁ»wAiÀÄ£ÀÄß ¸ÀAUÀ滸ÀĪÀ zÀ¯Áè½UÀ¼À£ÀÄß ¸ÁªÀiÁ£ÀåªÁV _________ J£ÀÄߪÀgÀÄ.
6. ªÀiÁ»wzÁgÀgÀÄ GvÀÛgÀUÀ¼À£ÀÄß vÀÄA§¨ÉÃQgÀĪÀ ¥Àæ±ÉßUÀ¼À ¥ÀnÖAiÉÄà __________ .
7. ªÀiÁ»wzÁgÀgÀÄ ¥ÀÆgÉʹzÀ ªÁ¸ÀÛªÀ¸ÀAUÀwUÀ¼À£ÀÄß, ¨ÁwäÃzÁgÀgÀÄ zÁR¯É ªÀiÁrPÉƼÀî¨ÉÃQgÀĪÀ ¥Àæ±ÉßUÀ¼À ¥ÀnÖAiÉÄÃ
__________ .
8. ¸ÀªÀĶ×AiÀÄ ¥ÀæwAiÉÆAzÀÄ WÀlPÀzÀ ¸ÀA¥ÀÆtð ªÀiÁ»w ¸ÀAUÀæºÀuÉAiÀÄ£ÀÄß _________ J£ÀÄߪÀgÀÄ.
9. «±ÉÃè µÀuÁ ¸ÀAzÀ¨sÀðzÀ°èAiÀÄ zÉÆõÀªÀ£ÀÄß _________ zÉÆõÀ J£ÀÄߪÀgÀÄ.
10. ¥Àj²Ã®PÀ UÀªÀÄ£ÀPÉÌ §gÀ§ºÀÄzÁzÀ zÉÆõÀUÀ¼À£ÀÄß _________ zÉÆõÀUÀ¼É£ÀÄߪÀgÀÄ.
11. ¥Àj²Ã®PÀ UÀªÀÄ£ÀPÉÌ §gÀ¯ÁgÀzÀ zÉÆõÀUÀ¼À£ÀÄß _________ zÉÆõÀUÀ¼É£ÀÄߪÀgÀÄ.

6

¥ÀæxÀªÀÄ ¦.AiÀÄÄ.¹. ¸ÀASÁå±Á¸ÀçÛ ¥Àæ±Éß PÉÆñÀ
ºÉÆA¢¹ §gɬÄj: (£ÉÃgÀªÁV GvÀÛgÀUÀ¼À£ÀÄß ¤ÃqÀ¯ÁVzÉ.)
¥Àj²Ã®PÀ ¸ÁATåPÀ ¥Àj²Ã®£É(«ZÁgÀuÉ) £ÀqɸÀĪÀ ªÀåQÛ
ªÉÆlÖªÉÆzÀ®¨ÁjUÉ ¸ÀAUÀæ»zÀ zÀvÁÛA±À ¥ÁæxÀ«ÄPÀ zÀvÁÛA±À
£ÉÃgÀ ªÉÊAiÀÄQÛPÀ «ÃPÀëuÉ ¥ÁæxÀ«ÄPÀ zÀvÁÛA±À
¥ÀgÉÆÃPÀë ªÀiËQPÀ ¸ÀAzÀ±Àð£À ¥ÁæxÀ«ÄPÀ zÀvÁÛA±À
¸ÀA¸ÉÜUÀ¼À(¥Àæw¤¢üUÀ¼À) ªÀÄÆ®PÀ ªÀiÁ»w ¥ÁæxÀ«ÄPÀ zÀvÁÛA±À
¥Àæ±ÁߪÀ½UÀ¼À ªÀÄÆ®PÀ ¥ÁæxÀ«ÄPÀ zÀvÁÛA±À
¨ÁwäÃzÁgÀgÀ ªÀÄÆ®PÀ vÀ¥À²Ã®Ä¥ÀnÖ
¥ÁæxÀ«ÄPÀ zÀvÁÛA±À
PÀ¼ÀÄ»¸ÀĪÀÅzÀgÉÆA¢UÉ
ªÀgÀ¢UÁgÀ ªÀiÁ»wzÁgÀ¤AzÀ ªÀiÁ»wAiÀÄ£ÀÄß ¸ÀAUÀ滸ÀĪÀ zÀ¯Áè½
¤gÀ¥ÉÃPÀë zÉÆõÀ £ÉÊd ¨É¯É – CAzÁf¹zÀ ¨É¯É

MAzÀÄ CAPÀzÀ ¥Àæ±ÉßUÀ¼ÀÄ:
1. ¸ÁATåPÀ ¥Àj²Ã®£É JAzÀgÉãÀÄ?
2. ¥Àj²Ã®PÀ JAzÀgÉ AiÀiÁgÀÄ?
3. ¨ÁwäÃzÁgÀ JAzÀgÉ AiÀiÁgÀÄ?
4. ªÀiÁ»wzÁgÀ JAzÀgÉ AiÀiÁgÀÄ?
5. zÀvÁÛA±ÀzÀ ¸ÀAUÀæºÀuÉAiÀÄ£ÀÄß ªÁåSÁ夹.
6. ¥ÁæxÀ«ÄPÀ zÀvÁÛA±ÀªÀ£ÀÄß ªÁåSÁ夹.
7. ¥Àæ±ÁߪÀ½ JAzÀgÉãÀÄ?
8. vÀ¥À²Ã®Ä¥ÀnÖ JAzÀgÉãÀÄ?
9. ¢éwÃAiÀÄ zÀvÁÛA±ÀªÀ£ÀÄß ªÁåSÁ夹.
10. ¢éwÃAiÀÄ zÀvÁÛA±ÀzÀ ¥ÀæPÀnvÀ ªÀÄÆ®PÉÌ MAzÀÄ GzÁºÀgÀuÉ PÉÆr.
11. ¢éwÃAiÀÄ zÀvÁÛA±ÀzÀ C¥ÀæPÀnvÀ ªÀÄÆ®PÉÌ MAzÀÄ GzÁºÀgÀuÉ PÉÆr.
12. UÀtw ¸À«ÄÃPÉëAiÀÄ£ÀÄß ªÁåSÁ夹.
13. ¤zÀ±ÀðPÀ (¥ÀæwZÀAiÀÄ) ¸À«ÄÃPÉëAiÀÄ£ÀÄß ªÁåSÁ夹.
14. ªÀiÁUÀðzÀ²ð ¸À«ÄÃPÉë JAzÀgÉãÀÄ?
15. ¥ÀæwZÀAiÀÄ£ÀªÀ£ÀÄß ªÁåSÁ夹.
16. ¸ÀgÀ¼À DPÀ¹äPÀ ¥ÀæwZÀAiÀÄ£À JAzÀgÉãÀÄ?
17. ¥ÀæwZÀAiÀÄ£À (¸ÁATåPÀ) zÉÆõÀ JAzÀgÉãÀÄ?
18. ¤gÀ¥ÉÃPÀë zÉÆõÀ JAzÀgÉãÀÄ? (¤gÀ¥ÉÃPÀë zÉÆõÀªÀ£ÀÄß ªÁåSÁ夹).
19. ¸Á¥ÉÃPÀë zÉÆõÀ JAzÀgÉãÀÄ? (¸Á¥ÉÃPÀë zÉÆõÀªÀ£ÀÄß ªÁåSÁ夹).
20. ¥ÀæwZÀAiÀÄ£À zÉÆõÀUÀ¼ÀÄ AiÀiÁªÁUÀ PÀrªÉÄ DUÀĪÀªÀÅ?

JgÀqÀÄ CAPÀzÀ ¥Àæ±ÉßUÀ¼ÀÄ:
1. ¸ÁATåPÀ ¥Àj²Ã®£ÉAiÀÄ JgÀqÀÄ ºÀAvÀUÀ¼À£ÀÄß w½¹.
2. ¥ÁæxÀ«ÄPÀ zÀvÁÛA±À JAzÀgÉãÀÄ? EzÀ£ÀÄß ¸ÀAUÀ滸ÀĪÀ MAzÀÄ «zsÁ£ÀªÀ£ÀÄß w½¹.
3. ¥ÁæxÀ«ÄPÀ zÀvÁÛA±ÀªÀ£ÀÄß ¸ÀAUÀ滸ÀĪÀ JgÀqÀÄ «zsÁ£ÀUÀ¼À£ÀÄß w½¹.
4. ¢éwÃAiÀÄ zÀvÁÛA±ÀzÀ JgÀqÀÄ ªÀÄÆ®UÀ¼À£ÀÄß w½¹.

7

¥ÀæxÀªÀÄ ¦.AiÀÄÄ.¹. ¸ÀASÁå±Á¸ÀçÛ ¥Àæ±Éß PÉÆñÀ
5. d£ÀUÀtwAiÀÄ MAzÀÄ UÀÄt ªÀÄvÀÄÛ MAzÀÄ zÉÆõÀªÀ£ÀÄß w½¹.
6. ¤zÀ±ÀðPÀ ¸À«ÄÃPÉëAiÀÄ MAzÀÄ UÀÄt ªÀÄvÀÄÛ MAzÀÄ zÉÆõÀªÀ£ÀÄß w½¹.
7. ¥ÀæwZÀAiÀÄ£ÀzÀ JgÀqÀÄ «zsÁ£ÀUÀ¼À£ÀÄß w½¹.
8. ¥ÀæwZÀAiÀÄ£À zÉÆõÀUÀ½UÉ JgÀqÀÄ PÁgÀtUÀ¼À£ÀÄß w½¹.
9. C©ü£ÀvÀ ªÀÄvÀÄÛ C£À©ü£ÀvÀ zÉÆõÀUÀ¼À £ÀqÀÄ«£À ªÀåvÁå¸À w½¹.
10. zÉÆõÀUÀ¼À£ÀÄß C¼ÀvɪÀiÁqÀĪÀ «zsÁ£ÀUÀ¼À£ÀÄß w½¹.

LzÀÄ CAPÀzÀ ¥Àæ±ÉßUÀ¼ÀÄ:
1. ¥Àj²Ã®£ÉAiÀÄ AiÉÆÃd£É gÀƦ¸ÀĪÀ°è ¥ÀjUÀt¸À§ºÀÄzÁzÀ CA±ÀUÀ¼À£ÀÄß w½¹.
2. ¸À«ÄÃPÉëAiÀÄ£ÀÄß C£ÀĵÁ×£ÀUÉƽ¸ÀĪÀ°è ¥ÀjUÀt¸À§ºÀÄzÁzÀ CA±ÀUÀ¼À£ÀÄß w½¹.
3. ¥ÁæxÀ«ÄPÀ zÀvÁÛA±ÀªÀ£ÀÄß £ÉÃgÀ ªÉÊAiÀÄQÛPÀ «ÃPÀëuÁ «zsÁ£À¢AzÀ ¸ÀAUÀ滸ÀĪÀ UÀÄt-zÉÆõÀUÀ¼À£ÀÄß w½¹.
4. ¥Àæ±ÁߪÀ½ vÀAiÀiÁj¸ÀĪÁUÀ ¥ÀjUÀt¸ÀĪÀ ªÀiÁUÀð¸ÀÆaUÀ¼ÀÄ AiÀiÁªÀŪÀÅ?
5. UÀtw ¸À«ÄÃPÉëAiÀÄ JgÀqÀÄ UÀÄt ªÀÄvÀÄÛ ªÀÄÆgÀÄ zÉÆõÀUÀ¼À£ÀÄß w½¹.
6. ¤zÀ±ÀðPÀ ¸À«ÄÃPÉëAiÀÄ ªÀÄÆgÀÄ UÀÄt ªÀÄvÀÄÛ JgÀqÀÄ zÉÆõÀUÀ¼À£ÀÄß w½¹.
7. UÀtw ¸À«ÄÃPÉë ªÀÄvÀÄÛ ¤zÀ±ÀðPÀ ¸À«ÄÃPÉëUÀ¼À ªÀåvÁå¸À w½¹.
8. ¥ÀæwZÀAiÀÄ£ÀzÀ ªÀÄÆgÀÄ «zsÁ£ÀUÀ¼À£ÀÄß ¸ÀAQë¥ÀÛªÁV «ªÀj¹.

Unit - III
ªÀVðÃPÀgÀt ªÀÄvÀÄÛ ¸ÁgÀtÂAiÀÄ£É
¸ÀjAiÀiÁzÀ GvÀg
Û ÀªÀ£ÀÄß DAiÉÄ̪ÀiÁr §gɬÄj:
1. ZÀ®PÀªÀ£ÀÄß DzsÀj¹ ªÀVÃðPÀj¸ÀĪÀÅzÉÃ
a) PÁ¯Á£ÀÄPÀæªÀÄzÀ b) ¨sËUÉÆýPÀ c) UÀÄuÁvÀäPÀ d) ¥ÀjªÀiÁuÁvÀäPÀ
2. UÀÄtzsÀªÀÄðªÀ£ÀÄß DzsÀj¹ ªÀVÃðPÀj¸ÀĪÀÅzÉÃ
a) PÁ¯Á£ÀÄPÀæªÀÄzÀ b) ¨sËUÉÆýPÀ c) UÀÄuÁvÀäPÀ d) ¥ÀjªÀiÁuÁvÀäPÀ
3. ¸ÁATåPÀ zÀvÁÛA±ÀªÀ£ÀÄß ¸ÀªÀÄAiÀiÁ£ÀĸÁgÀ ªÀVÃðPÀgÀt ªÀiÁqÀĪÀÅzÀÄ
a) ¥ÀjªÀiÁuÁvÀäPÀ ªÀVÃðPÀgÀt b) UÀÄuÁvÀäPÀ ªÀVÃðPÀgÀt
c) PÁ¯Á£ÀÄPÀæªÀÄzÀ ªÀVÃðPÀgÀt d) ¨sËUÉÆýPÀ ªÀVÃðPÀgÀt
4. DªÀÈwÛ «vÀgÀuÉAiÀÄ£ÀÄß vÀAiÀiÁj¸ÀĪÁUÀ ªÀUÁðAvÀgÀUÀ¼À£ÀÄß ¥ÀjUÀt¸À¢zÀÝgÉ, CzÀÄ
a) J¯É-
è vÉgÉzÀ DªÀÈwÛ «vÀgÀuÉ b) ¸ÀvÀvÀ ZÀ®PÀzÀ DªÀÈwÛ «vÀgÀuÉ
c) «aÒ£Àß ZÀ®PÀzÀ DªÀÈwÛ «vÀgÀuÉ d) ¸ÀAavÀ DªÀÈwÛ «vÀgÀuÉ
5. MAzÀÄ ªÀUÀðzÀ°è, PɼÀ«Äw CzÀgÀAvÉ ªÉÄðäwAiÀÄÄ ¸ÀºÀ M¼ÀUÉÆArzÀÝgÉ, CAxÀºÀ ªÀUÀðªÀ£ÀÄß »ÃUÉ£ÀÄߪÀgÀÄ.
a) ¸ÀAªÀÈvÀ ªÀUÀð b) «ªÀÄÄPÀÛ ªÀUÀð c) J¯É-
è vÉgÉzÀ ªÀUÀð d) ªÀÄzsÀå©AzÀÄ

6. 10-19, 20-29, 30-39 ªÀUÁðAvÀgÀUÀ¼À wzÀÄÝ¥Àr CA±À
a) 0.25 b) 0.5 c) 0.75 d) 1
7. MAzÀÄ ªÀUÁðAvÀgÀzÀ UÁvÀæ EzÁVzÉ.
a) ªÉÄðäw + PɼÀ«Äw b) ªÉÄðäw ÷ PɼÀ«Äw c) ªÉÄðäw – PɼÀ«Äw d) ªÉÄðäw × PɼÀ«Äw

8

¥ÀæxÀªÀÄ ¦.AiÀÄÄ.¹. ¸ÀASÁå±Á¸ÀçÛ ¥Àæ±Éß PÉÆñÀ
8. 10-20 ªÀUÁðAvÀgÀzÀ ªÀÄzsÀå©AzÀÄ EzÁVzÉ.
a) 10 b) 12.5 c) 15 d) 20
9. 10-19 ªÀUÁðAvÀgÀzÀ ªÀÄzsÀå©AzÀÄ EzÁVzÉ.
a) 10.5 b) 14.5 c) 15.5 d) 19.5
10. MAzÀÄ ¸ÁgÀtÂAiÀÄ°è, PÀA§¸Á°£À vÀ¯É§gÀºÀUÀ¼À£ÀÄß »ÃUÉ£ÀÄߪÀgÀÄ.
a) ¥ÀAQÛ£ÁªÀÄ b) ¸ÀAÛ ¨sÀ£ÁªÀÄ c) ²gÉÆà n¥ÀàuÉ d) Cr n¥ÀàuÉ

11. MAzÀÄ ¸ÁgÀtÂAiÀÄ°è, CqÀظÁ°£À vÀ¯É§gÀºÀUÀ¼À£ÀÄß »ÃUÉ£ÀÄߪÀgÀÄ.
a) ¥ÀAQÛ£ÁªÀÄ b) ¸ÀAÛ ¨sÀ£ÁªÀÄ c) ²gÉÆà n¥ÀàuÉ d) Cr n¥ÀàuÉ

12. MAzÀÄ ¸ÁgÀtÂAiÀÄ ¥ÀAQÛ£ÁªÀÄ
a) ¸ÁgÀtÂAiÀÄ JqÀ¨sÁUÀªÁVzÀÄÝ, PÀA§¸Á°£À CA±ÀUÀ¼À£ÀÄß «ªÀj¸ÀÄvÀÛªÉ.
b) ¸ÁgÀtÂAiÀÄ §®¨sÁUÀªÁVzÀÄÝ, PÀA§¸Á°£À CA±ÀUÀ¼À£ÀÄß «ªÀj¸ÀÄvÀÛªÉ.
c) ¸ÁgÀtÂAiÀÄ §®¨sÁUÀªÁVzÀÄÝ, CqÀظÁ°£À CA±ÀUÀ¼À£ÀÄß «ªÀj¸ÀÄvÀÛªÉ.
d) ¸ÁgÀtÂAiÀÄ JqÀ¨sÁUÀªÁVzÀÄÝ, CqÀظÁ°£À CA±ÀUÀ¼À£ÀÄß «ªÀj¸ÀÄvÀÛªÉ.

DªÀgÀtzÀ°ègÀĪÀ ¸ÀjAiÀiÁzÀ GvÀg
Û ÀªÀ£ÀÄß Dj¹, ©lÖ ¸ÀܼÀ vÀÄA©j:
(DªÀÈwÛ, ªÀÄÆ®, PÁ¯Á£ÀÄPÀæªÀÄ, ªÀÄzsÀå©AzÀÄ, ¥ÀAQÛ£ÁªÀÄ, ¢é¨sÁdPÀ, ¸ÀAavÀ, «aÒ£Àß, ¸ÀvÀvÀ, J¯Éè-vÉgÉzÀ, UÁvÀæ, ªÀÄÄRå
¨sÁUÀ, f/w, ¸ÀAÛ ¨sÀ£ÁªÀÄ, ªÀUÀð DªÀÈwÛ)

1. ¸ÁATåPÀ zÀvÁÛA±ÀªÀ£ÀÄß ¸ÀªÀÄAiÀiÁ£ÀĸÁgÀ ªÀVÃðPÀgÀt ªÀiÁqÀĪÀÅzÀ£ÀÄß ________ ªÀVÃðPÀgÀt J£ÀÄߪÀgÀÄ.
2. MAzÀÄ ®PÀëtªÀ£ÀÄß JgÀqÀÄ ªÀUÀðUÀ¼ÁV «AUÀqÀ£É ªÀiÁqÀĪÀÅzÀ£ÀÄß ________ ªÀVÃðPÀgÀt J£ÀÄߪÀgÀÄ.
3. MAzÀÄ ªÀUÀðPÉÌ ¸ÉÃjzÀ ¥Áæ¥ÁÛAPÀUÀ¼À ¸ÀASÉåAiÀÄ£ÀÄß _________ J£ÀÄߪÀgÀÄ.
4. MAzÀÄ ¥Áæ¥ÁÛAPÀ ¥ÀÄ£ÀgÁªÀvÀð£É DVgÀĪÀ ¸ÀASÉåAiÉÄà _________ .
5. DªÀÈwÛ «vÀgÀuÉAiÀÄ£ÀÄß vÀAiÀiÁj¸ÀĪÁUÀ ªÀUÁðAvÀgÀUÀ¼À£ÀÄß ¥ÀjUÀt¸À¢zÀÝgÉ, CzÀ£ÀÄß ________ ZÀ®PÀzÀ DªÀÈwÛ
«vÀgÀuÉ J£ÀÄߪÀgÀÄ.
6. DªÀÈwÛ «vÀgÀuÉAiÀÄ£ÀÄß vÀAiÀiÁj¸ÀĪÁUÀ ªÀUÁðAvÀgÀUÀ¼À£ÀÄß ¥ÀjUÀt¹zÀgÉ, CzÀ£ÀÄß ________ ZÀ®PÀzÀ DªÀÈwÛ «vÀgÀuÉ
J£ÀÄߪÀgÀÄ.
7. MAzÀÄ ªÀUÀðzÀ°è, PɼÀ«Äw CxÀªÁ ªÉÄðäw ¤¢ðµÀÖªÁVgÀ¢zÀÝgÉ, CAxÀºÀ ªÀUÀðªÀ£ÀÄß _______ ªÀUÀð J£ÀÄߪÀgÀÄ.
8. MAzÀÄ ªÀUÀðzÀ ªÀÄzsÀåzÀ ¨É¯ÉAiÀÄ£ÀÄß _______ J£ÀÄߪÀgÀÄ.
9. MAzÀÄ ªÀUÀðzÀ ªÉÄðäw ªÀÄvÀÄÛ PɼÀ«ÄwAiÀÄ CAvÀgÀªÀ£ÀÄß _______ J£ÀÄߪÀgÀÄ.
10. ¸ÉÃj¸À¯ÁzÀ DªÀÈwÛUÀ¼À£ÀÄß _______ DªÀÈwÛUÀ¼É£ÀÄߪÀgÀÄ.
11. DªÀÈwÛ ¸ÁAzsÀævÉ _______.
12. MAzÀÄ ¸ÁgÀtÂAiÀÄ°è, PÀA§¸Á°£À vÀ¯É§gÀºÀUÀ¼À£ÀÄß _______ UÀ¼É£ÀÄߪÀgÀÄ.
13. MAzÀÄ ¸ÁgÀtÂAiÀÄ°è, CqÀظÁ°£À vÀ¯É§gÀºÀUÀ¼À£ÀÄß _______ UÀ¼É£ÄÀ ߪÀgÀÄ.
14. ¸ÁgÀtÂAiÀÄ ________ ¸ÁATåPÀ zÀvÁÛA±ÀªÀ£ÀÄß M¼ÀUÉÆArgÀÄvÀz
Û É.
15. Crn¥Ààt CxÀªÁ ¸ÁgÀt PɼÀUÉ, NzÀÄUÀ¤UÉ vÁ¼É£ÉÆÃqÀĪÀ zÀȶ֬ÄAzÀ zÀvÁÛA±ÀzÀ _______ ªÀ£ÀÄß w½¹gÀÄvÁÛgÉ.

9

¥ÀæxÀªÀÄ ¦.AiÀÄÄ.¹. ¸ÀASÁå±Á¸ÀçÛ ¥Àæ±Éß PÉÆñÀ
ºÉÆA¢¹ §gɬÄj: (£ÉÃgÀªÁV GvÀÛgÀUÀ¼À£ÀÄß ¤ÃqÀ¯ÁVzÉ.)
¸ÀªÀÄAiÀiÁ£ÀĸÁgÀzÀ ªÀVÃðPÀgÀt PÁ¯Á£ÀÄPÀæªÀÄ
UÀÄtzsÀªÀÄðUÀ¼À£ÀÄß DzsÀj¹ ªÀVÃðPÀj¸ÀĪÀÅzÀÄ UÀÄuÁvÀäPÀ
ZÀ®PÀUÀ¼À£ÀÄß DzsÀj¹ ªÀVÃðPÀj¸ÀĪÀÅzÀÄ ¥ÀjªÀiÁuÁvÀäPÀ
ªÀUÁðAvÀgÀzÀ UÁvÀæ ªÉÄðäw – PɼÀ«Äw
ªÀUÀðzÀ ªÀÄzsÀåzÀ ¨É¯É ªÀÄzsÀå©AzÀÄ
10 – 30 gÀ ªÀÄzsÀå©AzÀÄ 20
10 – 19 gÀ ªÀÄzsÀå©AzÀÄ 14.5
ªÀUÀð 30 – 40 gÀ UÁvÀæ 10
¥ÉÆæ. ¸ÀÆÖeÉìðgÀªÀgÀ ¤AiÀĪÀÄ K = 1 + 3.322 log N
¸ÀAÛ ¨sÀ£ÁªÀÄ PÀA§¸Á°£À vÀ¯É§gÀºÀ
¥ÀAQÛ£ÁªÀÄ CqÀظÁ°£À vÀ¯É§gÀºÀ
¸ÁgÀtÂAiÀÄ ªÀÄÄRå ¨sÁUÀ ¸ÁATåPÀ zÀvÁÛA±ÀªÀ£ÀÄß M¼ÀUÉÆArgÀÄvÀz
Û É

MAzÀÄ CAPÀzÀ ¥Àæ±ÉßUÀ¼ÀÄ:
1. zÀvÁÛA±ÀzÀ ªÀVðÃPÀgÀt JAzÀgÉãÀÄ?
2. zÀvÁÛA±ÀzÀ ªÀVðÃPÀgÀtzÀ MAzÀÄ GzÉÝñÀªÀ£ÀÄß w½¹.
3. PÁ¯Á£ÀÄPÀæªÀÄzÀ ªÀVðÃPÀgÀtªÀ£ÀÄß ªÁåSÁ夹.
4. ¨sËUÉÆýPÀ ªÀVðÃPÀgÀtªÀ£ÀÄß ªÁåSÁ夹.
5. UÀÄuÁvÀäPÀ ªÀVðÃPÀgÀtªÀ£ÀÄß ªÁåSÁ夹.
6. ¥ÀjªÀiÁuÁvÀäPÀ ªÀVðÃPÀgÀtªÀ£ÀÄß ªÁåSÁ夹.
7. DªÀÈwÛAiÀÄ£ÀÄß ªÁåSÁ夹.
8. ¸ÀAªÀÈvÀ ªÀUÁðAvÀgÀªÀ£ÀÄß ªÁåSÁ夹.
9. «ªÀÄÄPÀÛ ªÀUÁðAvÀgÀªÀ£ÀÄß ªÁåSÁ夹.
10. DªÀÈwÛ «vÀgÀuÉAiÀÄ°è wzÀÄÝ¥Àr CA±ÀªÀ£ÀÄß AiÀiÁªÀ GzÉÝñÀPÉÌ §¼À¸ÀĪÀgÀÄ?
11. J¯Éè vÉgÉzÀ ªÀUÁðAvÀgÀªÀ£ÀÄß ªÁåSÁ夹.
12. ªÀUÀð ªÀÄzsÀå©AzÀÄ JAzÀgÉãÀÄ?
13. DªÀÈwÛ ¸ÁAzsÀævÉAiÀÄ£ÀÄß ªÁåSÁ夹.
14. ¸Á¥ÉÃPÀë DªÀÈwÛAiÀÄ£ÀÄß ªÁåSÁ夹.
15. ¢éZÀ®PÀzÀ DªÀÈwÛ «vÀgÀuÉ JAzÀgÉãÀÄ?
16. zÀvÁÛA±ÀzÀ ¸ÁgÀtÂAiÀÄ£É JAzÀgÉãÀÄ?
17. MAzÀÄ ¸ÁgÀtÂAiÀÄ ¥ÀAQÛ£ÁªÀÄ JAzÀgÉãÀÄ?
18. MAzÀÄ ¸ÁgÀtÂAiÀÄ ¸ÀÛA¨sÀ£ÁªÀÄ JAzÀgÉãÀÄ?

JgÀqÀÄ CAPÀzÀ ¥Àæ±ÉßUÀ¼ÀÄ:
1. ªÀVðÃPÀgÀtzÀ ªÀÄvÀÄÛ ¸ÁgÀtÂAiÀÄ£ÉUÀ¼À £ÀqÀÄ«£À ªÀåvÁå¸À w½¹.
2. ªÀVðÃPÀgÀtzÀ JgÀqÀÄ GzÉÝñÀUÀ¼À£ÀÄß w½¹.
3. PÁ¯Á£ÀÄPÀæªÀÄzÀ ªÀVðÃPÀgÀt JAzÀgÉãÀÄ? MAzÀÄ GzÁºÀgÀuÉ PÉÆr.
4. ¨sËUÉÆýPÀ ªÀVðÃPÀgÀt JAzÀgÉãÀÄ? MAzÀÄ GzÁºÀgÀuÉ PÉÆr.

10

¥ÀæxÀªÀÄ ¦.AiÀÄÄ.¹. ¸ÀASÁå±Á¸ÀçÛ ¥Àæ±Éß PÉÆñÀ
5. UÀÄuÁvÀäPÀ ªÀVðÃPÀgÀtªÀ£ÀÄß MAzÀÄ GzÁºÀgÀuÉ ¸À»vÀ ªÁåSÁ夹.
6. ¥ÀjªÀiÁuÁvÀäPÀ ªÀVðÃPÀgÀtªÀ£ÀÄß MAzÀÄ GzÁºÀgÀuÉ ¸À»vÀ ªÁåSÁ夹.
7. ¸ÀAªÀÈvÀ ªÀUÁðAvÀgÀªÀ£ÀÄß ªÁåSÁ夹. MAzÀÄ GzÁºÀgÀuÉ PÉÆr.
8. «ªÀÄÄPÀÛ ªÀUÁðAvÀgÀªÀ£ÀÄß ªÁåSÁ夹. MAzÀÄ GzÁºÀgÀuÉ PÉÆr.
9. F ¸ÀAªÀÈvÀ ªÀUÁðAvÀgÀUÀ¼À£ÀÄß «ªÀÄÄPÀÛ ªÀUÁðAvÀgÀUÀ¼ÁV ¥ÀjªÀwð¹.
C – I: 10 – 19 20 – 29 30 – 39 40 - 49
10. J¯Éè vÉgÉzÀ ªÀUÁðAvÀgÀªÀ£ÀÄß ªÁåSÁ夹. MAzÀÄ GzÁºÀgÀuÉ PÉÆr.
11. ¸ÁgÀtÂAiÀÄ JgÀqÀÄ ¨sÁUÀUÀ¼À£ÀÄß w½¹.
12. ¸ÁgÀtÂAiÀÄ ¥ÀAQÛ£ÁªÀÄ ªÀÄvÀÄÛ ¸ÀÛA¨sÀ£ÁªÀÄUÀ¼ÀÄ JAzÀgÉãÀÄ?

LzÀÄ CAPÀzÀ ¥Àæ±ÉßUÀ¼ÀÄ:
1. ««zsÀ E¥ÀàvÀÄÛ PÁ¯ÉÃdÄUÀ¼À°è ¸ÉÃªÉ ¸À°è¸ÀÄwÛgÀĪÀ ¨ÉÆÃzsÀPÀ ¹§âA¢UÀ¼À ¸ÀASÉå F jÃwAiÀiÁVzÉ:
15, 12, 18, 10, 15, 12, 20, 25, 18, 10, 15, 12, 15 20, 25, 15, 18, 20, 15, 18
DªÀÈwÛ «vÀgÀuÉ vÀAiÀiÁj¹.
2. £À®ªÀvÀÄÛ ««zsÀ D¸ÀàvÉæUÀ¼À°è ¸ÉêɸÀ°è¸ÀÄwÛgÀĪÀ ªÉÊzsÀågÀ ¸ÀASÉå F jÃw EªÉ.
6 7 5 7 6 3 9 8 6 7 5 7 6 8 5 8 5 9 5 6
5 9 6 6 4 4 7 5 5 8 5 3 3 8 4 4 3 4 4 3
«aÑ£Àß ZÀ®PÀzÀ «vÀgÀuÉ vÀAiÀiÁj¹.
3. MAzÀÄ ¥ÀæzÉñÀzÀ 40 PÀÄlÄA§UÀ¼À°è ¥Àæw PÀÄlÄA§zÀ°èAiÀÄ ªÀÄPÀ̼À ¸ÀASÉåUÉ MAzÀÄ ¸À«ÄÃPÉëAiÀÄ°è F zÀvÁÛA±À
zÉÆgÉwzÉ.
1, 0, 3, 2, 1, 5, 6, 2, 2, 1, 0, 3, 4, 2, 5, 6, 3, 2, 1, 1,
3, 3, 2, 4, 2, 2, 3, 0, 2, 1, 4, 5, 3, 3, 4, 4, 5, 2, 4, 1.
F zÀvÁÛA±ÀªÀ£ÀÄß «aߣÀß ZÀ®PÀzÀ DªÀÈwÛ «vÀgÀuÉAiÀÄ gÀÆ¥ÀzÀ°è ¤gÀƦ¹.
4. ªÀÄƪÀvÀÄÛ ««zsÀ ¢£ÀUÀ¼À°è «ÃQë¹zÀ ªÉÄmÉÆæÃUÀ¼À ¸ÀASÉåUÀ½UÉ F zÀvÁÛA±À ¸ÀA§A¢ü¹zÉ.
7, 4, 2, 5, 9, 7, 4, 3, 8, 6, 9, 10, 3, 3, 5, 9, 5, 7, 6, 3, 8, 4, 3, 7, 9, 8, 10, 6, 8, 7.
F zÀvÁÛA±ÀªÀ£ÀÄß ªÀVðÃPÀj¹.
5. ¸ÀASÁå±Á¸ÀçÛ ¥ÀĸÀÛPÀzÀ ªÉÆzÀ® 30 ¥ÀÄlUÀ¼À°è PÀAqÀħAzÀ ªÀÄÄzÀæt zÉÆõÀUÀ¼À ¸ÀASÉå EAwªÉ:
0 1 3 3 2 5 6 0 1 0 4 1 1 0 2
3 2 5 0 4 2 2 3 3 4 6 1 4 3 2
ªÀÄÄzÀæt zÉÆõÀUÀ¼À DªÀÈwÛ «vÀgÀuÉ vÀAiÀiÁj¹.
6. ±Á¯Á ªÀÄPÀ̼À ªÀAiÀĸÀÄì ªÀµÀðUÀ¼À°è EAwªÉ:
12 5 13 12 10 11 7 9 6 10 9 13 5 10 7
14 6 11 13 7 9 8 11 10 8 12 13 9 6 14
UÁvÀæ 3 EgÀĪÀ ¸ÀAªÀÈvÀ ªÀUÁðAvÀgÀUÀ¼À£ÀÄß §¼À¹ DªÀÈwÛ «vÀgÀuÉ vÀAiÀiÁj¹.
7. F zÀvÁÛA±ÀªÀÅ MAzÀÄ ±Á¯ÉAiÀÄ 30 ªÀÄPÀ̼À §Ä¢Þ®§ÞPÉÌ ¸ÀA§A¢ü¹zÉ.
106 118 112 120 103 105 99 139 65 113 108 116 93 100 120
100 108 100 112 110 109 117 98 103 99 110 95 101 105 98
< 90, 90-110, 110-120, ≥ 120 ªÀUÁðAvÀgÀUÀ¼À£ÀÄß §¼À¹ DªÀÈwÛ «vÀgÀuÉ vÀAiÀiÁj¹.

11

¥ÀæxÀªÀÄ ¦.AiÀÄÄ.¹. ¸ÀASÁå±Á¸ÀçÛ ¥Àæ±Éß PÉÆñÀ
8. MAzÀÄ PÉÊUÁjPÉAiÀÄ PÉ®¸ÀUÁgÀgÀ PÀÆ° (gÀÆ/UÀAmÉ) EAwªÉ. 40-49, 50-59 EvÁå¢ ªÀUÁðAvÀgÀUÀ¼À£ÀÄß §¼À¹ DªÀÈwÛ
«vÀgÀuÉ vÀAiÀiÁj¹.
76 63 83 75 61 41 115 82 60 40 74 42
78 95 56 77 78 65 67 50 84 76 100 53
100 81 59 73 54 79 79 80 104 69 68 79
72 80 70 69 64 42 76 84 90 77 49 66
73 71 94 78 86 51 96 103 52 79 50 72
9. MAzÀÄ PÁ¯ÉÃf£À 50 «zÁåyðUÀ¼À vÀÆPÀ PÉ.f.UÀ¼À°è EAwªÉ.
42 62 46 54 41 37 54 44 32 45
47 50 58 49 51 42 46 37 42 39
54 39 51 58 47 64 43 48 49 48
49 61 41 40 58 49 59 57 37 34
56 38 45 52 46 40 63 41 51 41
¸ÀÆPÀÛ ªÀUÁðAvÀgÀUÀ¼ÉÆA¢UÉ DªÀÈwÛ «vÀgÀuÉ vÀAiÀiÁj¹.
10. ¥Áè¹ÖPï GvÀà£ÀßUÀ¼À£ÀÄß vÀAiÀiÁj¸ÀĪÀ MAzÀÄ PÉÊUÁjPÉAiÀÄ 36 PÉ®¸ÀUÁgÀgÀ ¢£ÀzÀPÀÆ° (gÀÆUÀ¼À°è) EAwªÉ.
100 115 120 125 92 140 150 162 189
165 200 220 250 240 300 320 270 280
400 382 288 235 225 312 270 250 242
344 248 188 220 240 212 224 325 425
PÀ¤µÀ× ªÀUÀð 90-140 ªÀÄvÀÄÛ UÁvÀæ 50 §¼À¹ DªÀÈwÛ «vÀgÀuÉ vÀAiÀiÁj¹.
11. ºÀvÀÄÛ «zÁåyðUÀ¼ÀÄ UÀtÂvÀ±Á¸ÀÛç ªÀÄvÀÄÛ ¸ÀASÁå±Á¸ÀçÛ zÀ°è ¥ÀqÉzÀ CAPÀUÀ¼À£ÀÄß F PɼÀUÉ ¤ÃrzÉ.
ºÁdj ¸ÀASÉå 1 2 3 4 5 6 7 8 9 10
UÀtÂvÀ±Á¸ÀÛçzÀ CAPÀUÀ¼ÀÄ 53 54 52 52 50 53 54 54 52 50
¸ÀASÁå±Á¸ÀçÛ zÀ CAPÀUÀ¼ÀÄ 58 55 57 56 58 57 56 59 57 55
¢éZÀ®PÀzÀ DªÀÈwÛ «vÀgÀuÉ vÀAiÀiÁj¹.

12. F PɼÀV£À zÀvÁÛA±ÀªÀÅ ¥Àw ªÀÄvÀÄÛ ¥ÀwßAiÀÄgÀ ªÀAiÀĹìUÉ ¸ÀA§A¢ü¹zÉ. JgÀqÀÆ ZÀ®PÀUÀ½UÉ (20-25), (25-30),
EvÁå¢ ªÀUÁðAvÀgÀUÀ¼ÉÆA¢UÉ ¢éZÀ®PÀzÀ DªÀÈwÛ «vÀgÀuÉ vÀAiÀiÁj¹.
¥ÀwAiÀÄ ªÀAiÀĸÀÄì (ªÀµÀðUÀ¼À°è) 24 42 29 43 35 41 33 36 29 38
¥ÀwßAiÀÄ ªÀAiÀĸÀÄì (ªÀµÀðUÀ¼À°è) 25 37 25 37 23 39 23 32 24 38

13. MAzÀÄ PÁ¯ÉÃf£À «zÁåyðUÀ¼À F PɼÀV£À ªÀiÁ»w vÉÆÃj¸ÀĪÀ SÁ° ¸ÁgÀt gÀa¹.
i. vÀgÀUÀw: ¥ÀæxÀªÀÄ ¦AiÀÄĹ, ¢éwÃAiÀÄ ¦AiÀÄĹ.
ii. «¨sÁUÀ: PÀ¯Á, ªÁtÂdå, «eÁÕ£À.
iii. °AUÀ: UÀAqÀÄ, ºÉtÄÚ.

14. MAzÀÄ PÁ¯ÉÃf£À «zÁåyðUÀ¼À F PɼÀV£À ªÀiÁ»w vÉÆÃj¸ÀĪÀ SÁ° ¸ÁgÀt gÀa¹.
i. «¨sÁUÀ: ªÁtÂdå, «eÁÕ£À.
ii. °AUÀ: UÀAqÀÄ, ºÉtÄÚ.
iii. ªÀAiÉÆêÀUÀð(ªÀµÀðUÀ¼À°è): 18 QÌAvÀ PÀrªÉÄ, 18 - 20, 20 ªÀÄvÀÄÛ ºÉZÀÄÑ.

12

¥ÀæxÀªÀÄ ¦.AiÀÄÄ.¹. ¸ÀASÁå±Á¸ÀçÛ ¥Àæ±Éß PÉÆñÀ
15. MAzÀÄ PÁ¯ÉÃf£À «zÁåyðUÀ¼À F PɼÀV£À ªÀiÁ»w vÉÆÃj¸ÀĪÀ SÁ° ¸ÁgÀt gÀa¹.
i. PÁ¯ÉÃdÄ: ¸ÀgÀPÁj, C£ÀÄzÁ¤vÀ, C£ÀÄzÁ£À gÀ»vÀ.
ii. «¨sÁUÀ: «eÁÕ£,À ªÁtÂdå, PÀ¯Á.
iii. °AUÀ: UÀAqÀÄ, ºÉtÄÚ.

16. MAzÀÄ ¥ÀæzÉñÀzÀ ¤ªÁ¹UÀ½UÉ ¸ÀA§A¢ü¹zÀ F PɼÀV£À ªÀiÁ»w vÉÆÃj¸ÀĪÀ SÁ° ¸ÁgÀt gÀa¹.
i. GzÉÆåÃUÀ: PÀZÉÃj ¸ÀºÁAiÀÄPÀgÀÄ, ªÁå¥ÁgÀ¸ÀÜgÀÄ, ²PÀëPÀgÀÄ, ¨ÁåAPï GzÉÆåÃVUÀ¼ÀÄ.
ii. °AUÀ: ¥ÀÄgÀĵÀ, ¹ÛçÃ
iii. ªÉʪÁ»PÀ ¹Üw: «ªÁ»vÀgÀÄ, C«ªÁ»vÀgÀÄ.

17. MAzÀÄ PÉÊUÁjPÉAiÀÄ d£À¸ÀASÉåAiÀÄ «vÀgÀuÉ vÉÆÃj¸ÀĪÀ F ªÀiÁ»w C£ÀĸÁgÀ SÁ° ¸ÁgÀt gÀa¹.
i. °AUÀ: ¥ÀÄgÀĵÀ, ¹ÛçÃ
ii. ªÀUÀð: ¥ÀjtvÀ, C¥ÀjtvÀ.
iii. ªÉÃvÀ£À: gÀÆ. 5000 QÌAvÀ PÀrªÉÄ, gÀÆ. 5000-10000 ªÀÄvÀÄÛ gÀÆ. 10000 & ºÉZÀÄÑ.

18. MAzÀÄ ºÀ½îAiÀÄ ¸ÁPÀëgÀvÉAiÀÄ §UÉV£À MAzÀÄ ¤zÀ±ÀðPÀ ¸À«ÄÃPÉëAiÀÄ°è F zÀvÁÛA±À «ÃQë¹zÉ. 55% ¤ªÁ¹UÀ¼ÀÄ
¥ÀÄgÀĵÀgÀÄ, 85% ¤ªÁ¹UÀ¼ÀÄ ¸ÁPÀëgÀgÀÄ, PÉêÀ® 12% gÀµÀÄÖ ªÀÄ»¼Á ¸ÁPÀëgÀgÀÄ. F zÀvÁÛA±ÀªÀ£ÀÄß ¸ÁgÀtÂPÀj¹.

19. MAzÀÄ £ÀUÀgÀzÀ°Aè iÀÄ zsÀƪÀÄ¥Á£À ºÀªÁå¸ÀzÀ MAzÀÄ ¤zÀ±ÀðPÀ ¸À«ÄÃPÉëAiÀÄ°è F zÀvÁÛA±À zÉÆgÉwzÉ.
¥ÀÄgÀĵÀ d£À¸ÀASÉå: 58 %
zsÀƪÀÄ¥Á¤UÀ¼ÀÄ: 22 %
¥ÀÄgÀĵÀ zsÀƪÀÄ¥Á¤UÀ¼ÀÄ: 18 %
F ªÉÄð£À zÀvÁÛA±ÀªÀ£ÀÄß ¸ÁgÀtÂPÀj¹.

20. MAzÀÄ ¥ÀlÖtzÀ DºÁgÀ ¥ÀzÀÞwAiÀÄ §UÉV£À MAzÀÄ ¤zÀ±ÀðPÀ ¸À«ÄÃPÉëAiÀÄ°è F zÀvÁÛA±À zÉÆgÉwzÉ.
50% ªÀåQÛUÀ¼ÀÄ ¥ÀÄgÀĵÀgÀÄ
30% ªÀiÁA¸ÀºÁjUÀ¼ÀÄ
18% ¥ÀÄgÀĵÀ ªÀiÁA¸ÀºÁjUÀ¼ÀÄ
F ªÉÄð£À zÀvÁÛA±ÀªÀ£ÀÄß ¸ÁgÀtÂPÀj¹.

21. MAzÀÄ PÁ¯ÉÃf£À 2005 gÀ «zÁåyðUÀ¼À ¸ÀASÉå 510. EzÀgÀ°è 480 ºÀÄqÀÄUÀgÀÄ. 2005 PÉÌ ºÉÆð¹zÁUÀ 2010
gÀ°è ºÀÄqÀÄUÀgÀ ¸ÀASÉå ±Éà 10gÀµÀÄÖ ªÀÄvÀÄÛ ºÀÄqÀÄVAiÀÄgÀ ¸ÀASÉå ±Éà 30gÀµÀÄÖ ºÉZÁÑVzÉ. 2012 gÀ MlÄÖ «zÁåyðUÀ¼À
¸ÀASÉå 1200. ºÀÄqÀÄUÀgÀ ¸ÀASÉå ºÀÄqÀÄVgÀ ¸ÀASÉåAiÀÄ JgÀqÀgÀµÀÄÖ DVzÉ. F zÀvÁÛA±ÀªÀ£ÀÄß ¸ÁgÀtÂPÀj¹.

13

¥ÀæxÀªÀÄ ¦.AiÀÄÄ.¹. ¸ÀASÁå±Á¸ÀçÛ ¥Àæ±Éß PÉÆñÀ
Unit –IV
zÀvÁÛA±ÀzÀ avÀæ ªÀÄvÀÄÛ D¯ÉÃR ¤gÀÆ¥ÀuÉ

¸ÀjAiÀiÁzÀ GvÀg
Û ÀªÀ£ÀÄß DAiÉÄ̪ÀiÁr §gɬÄj:
1. ¸ÀgÀ¼À ¸ÀAÛ ¨sÀ £ÀPÉë, EzÀÄ
a) MAzÀÄ DAiÀiÁªÀÄzÀ avÀæ b) JgÀqÀÄ DAiÀiÁªÀÄzÀ avÀæ
c) ªÀÄÆgÀÄ DAiÀiÁªÀÄzÀ avÀæ d) £ÀPÁ±À avÀæUÀ¼ÀÄ
2. §ºÀÄ ¸ÀÛA¨sÀ £ÀPÉë, EzÀÄ
a) MAzÀÄ DAiÀiÁªÀÄzÀ avÀæ b) JgÀqÀÄ DAiÀiÁªÀÄzÀ avÀæ
c) ªÀÄÆgÀÄ DAiÀiÁªÀÄzÀ avÀæ d) £ÀPÁ±À avÀæUÀ¼ÀÄ
3. ¸ÀAWÀlPÀ ¸ÀAÛ ¨sÀ £ÀPÉë, EzÀÄ
a) MAzÀÄ DAiÀiÁªÀÄzÀ avÀæ b) JgÀqÀÄ DAiÀiÁªÀÄzÀ avÀæ
c) ªÀÄÆgÀÄ DAiÀiÁªÀÄzÀ avÀæ d) £ÀPÁ±À avÀæUÀ¼ÀÄ
4. ±ÉÃRqÁ ¸ÀAÛ ¨sÀ £ÀPÉë, EzÀÄ
a) MAzÀÄ DAiÀiÁªÀÄzÀ avÀæ b) JgÀqÀÄ DAiÀiÁªÀÄzÀ avÀæ
c) ªÀÄÆgÀÄ DAiÀiÁªÀÄzÀ avÀæ d) £ÀPÁ±À avÀæUÀ¼ÀÄ
5. ¥ÉÊ- £ÀPÉë, EzÀÄ
a) MAzÀÄ DAiÀiÁªÀÄzÀ avÀæ b) JgÀqÀÄ DAiÀiÁªÀÄzÀ avÀæ
c) ªÀÄÆgÀÄ DAiÀiÁªÀÄzÀ avÀæ d) £ÀPÁ±À avÀæUÀ¼ÀÄ
6. «vÀgÀuÉAiÀÄ §ºÀÄ®PÀ ¥ÀqÉAiÀÄ®Ä §¼À¸ÀĪÀ D¯ÉÃR
a) DªÀÈvÁÛöåPÀÈw b) DªÀÈwÛ ªÀPÀæ c) DªÀÈwÛ §ºÀĨsÀÄeÁPÀÈw d) NeÉʪïì
7. «vÀgÀuÉAiÀÄ ªÀÄzsÁåAPÀ ¥ÀqÉAiÀÄ®Ä §¼À¸ÀĪÀ D¯ÉÃR
a) DªÀÈvÁÛöåPÀÈw b) DªÀÈwÛ ªÀPÀæ c) DªÀÈwÛ §ºÀĨsÀÄeÁPÀÈw d) NeÉʪïì
8. «vÀgÀuÉAiÀÄ ¨sÁUÀ¨É¯ÉUÀ¼À£ÀÄß ¥ÀqÉAiÀÄ®Ä §¼À¸ÀĪÀ D¯ÉÃR
a) DªÀÈvÁÛöåPÀÈw b) DªÀÈwÛ ªÀPÀæ c) DªÀÈwÛ §ºÀĨsÀÄeÁPÀÈw d) NeÉʪïì

DªÀgÀtzÀ°ègÀĪÀ ¸ÀjAiÀiÁzÀ GvÀg Û ÀªÀ£ÀÄß Dj¹, ©lÖ ¸ÀܼÀ vÀÄA©j:
(¸ÀvÀvÀ, DªÀÈvÁÛöåPÀÈw, ¸ÀAavÀ, JgÀqÀÄ, MAzÀÄ, NeÉʪïì, ¥ÉÊ-£ÀPÉë)

1. §ºÀÄ ¸ÀÛA¨sÀ £ÀPÉë ________ DAiÀiÁªÀÄ jÃwAiÀÄ avÀæªÁVzÉ.
2. ¥ÉÊ-£ÀPÉë ________ DAiÀiÁªÀÄ jÃwAiÀÄ avÀæªÁVzÉ.
3. __________ §¼À¹ D¯ÉÃRzÀ ªÀÄÆ®PÀ §ºÀÄ®PÀ ¥ÀqÉAiÀħºÀÄzÁVzÉ.
4. __________ §¼À¹ D¯ÉÃRzÀ ªÀÄÆ®PÀ «vÀgÀuÉAiÀÄ ªÀÄzsÁåAPÀ ¥ÀqÉAiÀħºÀÄzÁVzÉ.
5. DªÀÈwÛ DPÀÈwAiÀÄ£ÀÄß ________ ZÀ®PÀzÀ DªÀÈwÛ «vÀgÀuÉUÉ gÀa¸ÀĪÀgÀÄ.
6. ________ DªÀÈwÛUÀ½UÉ ºÁUÀÆ ªÀUÀð«ÄwUÀ½UÉ J¼ÉzÀ ªÀPÀæUÀ¼À£ÀÄß NeÉʪïì (¸ÀAavÀ DªÀÈwÛ ªÀPÀæUÀ¼ÀÄ) J£ÀÄߪÀgÀÄ.

14

¥ÀæxÀªÀÄ ¦.AiÀÄÄ.¹. ¸ÀASÁå±Á¸ÀçÛ ¥Àæ±Éß PÉÆñÀ
ºÉÆA¢¹ §gɬÄj: (£ÉÃgÀªÁV GvÀÛgÀUÀ¼À£ÀÄß ¤ÃqÀ¯ÁVzÉ.)
¸ÀgÀ¼À ¸ÀAÛ ¨sÀ £ÀPÉë KPÀ DAiÀiÁªÀÄ(¢±É)
§ºÀÄ ¸ÀÛA¨sÀ £ÀPÉë KPÀ DAiÀiÁªÀÄ
¸ÀAWÀlPÀ(«¨sÀfvÀ) ¸ÀAÛ ¨sÀ £ÀPÉë KPÀ DAiÀiÁªÀÄ
±ÉÃRqÁ ¸ÀAÛ ¨sÀ £ÀPÉë KPÀ DAiÀiÁªÀÄ
¥ÉÊ-£ÀPÉë ¢é¢±É
DªÀÈvÁÛöåPÀÈwAiÀÄ PÉëÃvÀæ MlÄÖ DªÀÈwÛ
DªÀÈwÛ DPÀÈw «vÀgÀuÉAiÀÄ §ºÀÄ®PÀ
ªÀÄzsÁåAPÀ PÀAqÀÄ»rAiÀÄ®Ä §¼À¸ÀĪÀ D¯ÉÃR NeÉʪïì
¨sÁUÀ¨É¯ÉUÀ¼À£ÀÄß PÀAqÀÄ»rAiÀÄ®Ä §¼À¸ÀĪÀ D¯ÉÃR NeÉʪïì
¸ÀAavÀ DªÀÈwÛ «vÀgÀuÉ ªÉÄðäwVAvÀ PÀrªÉÄ ¸ÀAavÀ DªÀÈwÛ ªÀPÀæ
NeÉʪïì ¸ÀAavÀ DªÀÈwÛ ªÀPÀæUÀ¼ÀÄ

MAzÀÄ CAPÀzÀ ¥Àæ±ÉßUÀ¼ÀÄ:
1. MAzÀÄ DAiÀiÁªÀÄzÀ(¢±ÉAiÀÄ) avÀæ JAzÀgÉãÀÄ?
2. MAzÀÄ DAiÀiÁªÀÄzÀ(¢±ÉAiÀÄ) AiÀiÁªÀÅzÁgÉÆAzÀÄ avÀæªÀ£ÀÄß w½¹.
3. JgÀqÀÄ DAiÀiÁªÀÄzÀ(¢±ÉAiÀÄ) MAzÀÄ avÀæªÀ£ÀÄß w½¹.
4. ¥ÉÊ £ÀPÉë JAzÀgÉãÀÄ?
5. DªÀÈwÛ DPÀÈw JAzÀgÉãÀÄ?
6. DªÀÈwÛ DPÀÈwAiÀÄ ªÀÄÆ®PÀ UÀÄgÀÄw¸ÀĪÀ ¸ÀgÁ¸ÀjAiÀÄ£ÀÄß ºÉ¸Àj¹.
7. §ºÀÄ®PÀ UÀÄgÀÄw¸À®Ä G¥ÀAiÉÆÃV¸ÀĪÀ D¯ÉÃR AiÀiÁªÀÅzÀÄ?
8. ¸ÀAavÀ DªÀÈwÛ ªÀPÀæUÀ¼ÉAzÀgÉãÀÄ?
9. ¸ÀAavÀ DªÀÈwÛ ªÀPÀæUÀ¼À ªÀÄÆ®PÀ UÀÄgÀÄw¸ÀĪÀ ¸ÀgÁ¸ÀjAiÀÄ£ÀÄß ºÉ¸Àj¹.
10. ªÀÄzsÁåAPÀªÀ£ÀÄß UÀÄgÀÄw¸ÀĪÀ D¯ÉÃRªÀ£ÀÄß ºÉ¸Àj¹.

LzÀÄ CAPÀzÀ ¥Àæ±ÉßUÀ¼ÀÄ:
1. ¨sÀvz
ÀÛ À GvÁàzÀ£É(’000 l£ïß)UÉ ¸ÀA§A¢ü¹zÀ F zÀvÁÛA±ÀªÀ£ÀÄß ¸ÀgÀ¼À ¸ÀÛA¨sÀ £ÀPÉëAiÀÄ ªÀÄÆ®PÀ vÉÆÃj¹.
ªÀµÀð 2005 2006 2007 2008
GvÁàzÀ£É 90 85 100 105

2. F zÀvÁÛA±ÀªÀÅ ¥Àæw zÀ±ÀPÀzÀ°è §zÀ¯ÁzÀ ¨sÁgÀvÀzÀ d£À¸ÀASÉå vÉÆÃj¸ÀÄvÀz
Û É. ¸ÀgÀ¼À ¸ÀÛA¨sÀ £ÀPÉë gÀa¹.
ªÀµÀð 1971 1981 1991 2001 2011
d£À¸ÀASÉå («Ä°AiÀÄ£ï) 548 688 846 1028 1210

3. MAzÀÄ PÁ¯ÉÃf£À PÀ¼ÉzÀ ªÀÄÆgÀÄ ªÀµÀðUÀ¼À ¥sÀ°vÁA±ÀªÀ£ÀÄß PɼÀV£À PÉÆõÀÖPÀ vÉÆÃj¸ÀÄvÀÛzÉ. §ºÀÄ ¸ÀÛA¨sÀ £ÀPÉë gÀa¹.
ªÀµÀð ¥ÀæxÀªÀÄ zÀeÉð ¥ÀæxÀªÀÄ zÀeÉð GwÛÃtð C£ÀÄwÛÃtð
2010 25 32 28 5
2011 28 25 17 10
2012 32 30 15 3

15

¥ÀæxÀªÀÄ ¦.AiÀÄÄ.¹. ¸ÀASÁå±Á¸ÀçÛ ¥Àæ±Éß PÉÆñÀ

4. MAzÀÄ ¥ÀæzÉñÀzÀ UÉÆâü ªÀÄvÀÄÛ CQÌAiÀÄ GvÁàzÀ£ÉAiÀÄ£ÀÄß F PɼÀUÉ ¤ÃqÀ¯ÁVzÉ.
ªÀµÀð 2005 2006 2007 2008 2009 2010
GvÁàzÀ£É UÉÆâü 12 15 18 19 22 26
(ªÉÄlæPï l£ïß UÀ¼À°)è CQÌ 25 30 32 36 40 45
§ºÀÄ ¸ÀÛA¨sÀ £ÀPÉë gÀa¹.
5. MAzÀÄ PÁ¯ÉÃf£À ««zsÀ «¨sÁUÀUÀ¼À°èAiÀÄ «zÁåyðUÀ¼À ¸ÀASÉåAiÀÄ£ÀÄß F zÀvÁÛA±À vÉÆÃj¸ÀÄvÀz
Û É.
F zÀvÁÛA±À vÉÆÃj¸ÀĪÀ §ºÀÄ ¸ÀÛA¨sÀ £ÀPÉë gÀa¹.
««zsÀ ªÀµÀðUÀ¼À «zÁåyðUÀ¼À ¸ÀASÉå
«¨sÁUÀ
2008 2009 2010
PÀ¯Á 150 90 100
«eÁÕ£À 120 150 140
ªÁtÂdå 200 250 280
MlÄÖ 470 490 520

6. 2008-10gÀ ªÀgÉV£À MAzÀÄ «±Àé«zÁå®AiÀÄzÀ «zÁåyðUÀ¼À ¸ÀASÉåUÉ F zÀvÁÛA±À ¸ÀA§A¢ü¹zÉ. «¨sÀfvÀ ¸ÀAÛ ¨sÀ £ÀPÉë
gÀa¹.
«¨sÁUÀ
ªÀµÀð
PÀ¯Á «eÁÕ£À ªÁtÂdå EAf¤ÃAiÀÄjAUï ªÉÊzsÀåQÃAiÀÄ
2008 200 150 50 30 20
2009 250 200 80 50 40
2010 300 250 100 80 50

7. F zÀvÁÛA±ÀªÀÅ A ªÀÄvÀÄÛ B JA§ JgÀqÀÄ PÀÄlÄA§UÀ¼À RaðUÉ ¸ÀA§A¢ü¹zÉ. zÀvÁÛA±ÀªÀ£ÀÄß «¨sÀfvÀ ¸ÀAÛ ¨sÀ £ÀPÉëAiÀÄ
ªÀÄÆ®PÀ vÉÆÃj¹.
ªÀ¸ÀÄÛ DºÁgÀ §mÉÖ ¨ÁrUÉ ²PÀët EAzsÀ£À EvÀgÉ
PÀÄlÄA§ A 2580 880 2200 360 280 1800
RZÀÄð (gÀÆ.UÀ¼À°è)
PÀÄlÄA§ B 3350 1250 3100 1550 450 2000

8. PÀ£ÁðlPÀ gÁdåzÀ°è ªÀÄÄRåªÁV G¥À¨sÉÆÃV¸ÀĪÀ DºÁgÀ zsÁ£ÀåUÀ½UÉ F zÀvÁÛA±À ¸ÀA§A¢ü¹zÉ. zÀvÁÛA±ÀªÀ£ÀÄß
«¨sÀfvÀ ¸ÀAÛ ¨sÀ £ÀPÉëAiÀÄ ªÀÄÆ®PÀ vÉÆÃj¹.
G¥À¨sÉÆÃV¹zÀ ¥ÀæªÀiÁt
DºÁgÀ zsÁ£Àå
(«Ä°AiÀÄ£ï l£ïßUÀ¼À°è)
eÉÆüÀ 450
gÁV 320
UÉÆâü 150
CQÌ 400

16

¥ÀæxÀªÀÄ ¦.AiÀÄÄ.¹. ¸ÀASÁå±Á¸ÀçÛ ¥Àæ±Éß PÉÆñÀ
9. A ªÀÄvÀÄÛ B JA§ JgÀqÀÄ PÀÄlÄA§UÀ¼À ªÀiÁ¹PÀ RZÀÄð(gÀÆ.UÀ¼À°è) EAwªÉ.
RZÀÄð(gÀÆ.UÀ¼À°è)
ªÀ¸ÀÄÛ
PÀÄlÄA§ A PÀÄlÄA§ B
DºÁgÀ 2000 2500
§mÉÖ 1000 2000
¨ÁrUÉ 800 1000
EAzsÀ£À ªÀÄvÀÄÛ ¨É¼ÀPÀÄ 400 500
EvÀgÉ 800 2000
F zÀvÁÛA±ÀªÀ£ÀÄß ±ÉÃRqÁ ¸ÀAÛ ¨sÀ £ÀPÉëAiÀÄ ªÀÄÆ®PÀ vÉÆÃj¹.
10. MAzÀÄ ªÁ¶ðPÀ ¥ÀjPÉëAiÀÄ°è A ªÀÄvÀÄÛ B JA§ E§âgÀÄ «zÁåyðUÀ¼ÀÄ ¥ÀqÉzÀ CAPÀUÀ¼ÀÄ EAwªÉ.
F zÀvÁÛA±ÀªÀ£ÀÄß ±ÉÃRqÁ ¸ÀAÛ ¨sÀ £ÀPÉëAiÀÄ ªÀÄÆ®PÀ vÉÆÃj¹.
«zÁåyðUÀ¼À CAPÀUÀ¼ÀÄ
«µÀAiÀÄUÀ¼ÀÄ
«zÁåyð A «zÁåyð B
¨sÁµÉ 72 82
EAVèõÀ 85 92
¸ÀASÁå±Á¸ÀçÛ 97 95
CxÀð±Á¸ÀçÛ 88 90
ªÀåªÀºÁgÀ CzsÀåAiÀÄ£À 90 87
¯ÉPÀ̱Á¸ÀçÛ 94 98
MlÄÖ 526 544
11. ¨ÉAUÀ¼ÀÆj£À°èAiÀÄ ªÀÄ£É ¤ªÀiÁðtzÀ ±ÉÃRqÁ «¨sÀfvÀ ªÉZÀÑ (¨sÀÆ«Ä ¨É¯É ºÉÆgÀvÀÄ ¥Àr¹) F PɼÀV£ÀAwzÉ.
PÉ®¸ÀzÁ¼ÀÄ: 20%, EnÖUÉ: 12%, ¹ªÉÄAmï: 20%, PÀ©ât: 15%, PÀnÖUÉ: 13%, ªÉÄðéZÁgÀuÉ:15%, EvÀgÉ: 5%. ¥ÉÊ
£ÀPÉë gÀa¹.
12. ««zsÀ ªÀÄÆ®UÀ½AzÀ ¸ÀgÀPÁgÀPÉÌ §gÀĪÀ DzsÁAiÀÄ F jÃwAiÀiÁVzÉ. ¥ÉÊ £ÀPÉë gÀa¹.
ªÀÄÆ® ¸ÁA¥ÀæzÁAiÀÄPÀ C§PÁj DzÁAiÀÄ vÉjUÉ ¸ÁA¹ÜPÀ EvÀgÉ
PÀAzÁAiÀÄ
(«Ä°AiÀÄ£ï gÀÆ.UÀ¼À°è) 80 190 160 75 35

13. ¨sÁgÀwÃAiÀÄ ºÉÆmÉïï GzsÀåªÀÄzÀ°èAiÀÄ ±ÉÃRqÁ ªÉZÀÑzÀ gÀZÀ£ÉAiÀÄ£ÀÄß F zÀvÁÛA±ÀªÀÅ vÉÆÃj¸ÀÄvÀÛzÉ.
DqÀ½vÀ PÉ®¸ÀUÁgÀgÀ zÀÄgÀ¹Û ªÀÄvÀÄÛ DºÁgÀ ªÀÄvÀÄÛ ªÀiÁgÁlzÀ
ªÉZÀÑzÀ ¨sÁUÀUÀ¼ÀÄ «zÀÄåvï
RZÀÄð ªÉÃvÀ£À ¤ªÀðºÀuÉ ¥Á¤ÃAiÀÄ RZÀÄð
MlÄÖ RZÀÄð (%) 30 20 12 16 14 8
F zÀvÁÛA±À vÉÆÃj¸ÀĪÀ ¥ÉÊ £ÀPÉë gÀa¹.
14. F zÀvÁÛA±ÀPÉÌ DªÀÈwÛ DPÀÈw gÀa¹, §ºÀÄ®PÀzÀ ¨É¯É UÀÄgÀÄw¹.
C.I 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50
f 13 17 15 13 10
15. F zÀvÁÛA±ÀPÉÌ DªÀÈwÛ DPÀÈw gÀa¹.
PÀÆ° (’000gÀÆ.) 2-4 5-7 8 - 10 11-13 14-16 17-19 20-22 23-25
PÉ®¸ÀUÁgÀgÀ ¸ÀASÉå 2 6 8 25 40 30 20 8

17

¥ÀæxÀªÀÄ ¦.AiÀÄÄ.¹. ¸ÀASÁå±Á¸ÀçÛ ¥Àæ±Éß PÉÆñÀ
16. F zÀvÁÛA±ÀPÉÌ DªÀÈwÛ DPÀÈw gÀa¹, §ºÀÄ®PÀzÀ ¨É¯É UÀÄgÀÄw¹.
CAPÀUÀ¼ÀÄ 0-5 5-10 10-20 20-30 30-40 40-50 50-70 70-80
«zÁåyðUÀ¼À ¸ÀASÉå 2 6 8 25 40 30 20 8
17. F zÀvÁÛA±ÀPÉÌ DªÀÈwÛ DPÀÈw gÀa¹, £ÀAvÀgÀ DªÀÈwÛ §ºÀĨsÀÄeÁPÀÈw J¼É¬Äj.
¢£ÀzÀ PÀÆ° (gÀÆ.UÀ¼À°è) 100-150 150-200 200-250 250-300 300-350 350-400
PÉ®¸ÀUÁgÀgÀ ¸ÀASÉå 7 19 27 15 12 8
18. F PɼÀV£À DªÀÈwÛ «vÀgÀuÉUÉ DªÀÈwÛ §ºÀĨsÀÄeÁPÀÈw J¼É¬Äj.
ªÀÄzsÀå-©AzÀÄUÀ¼ÀÄ 15 25 35 45 55 65 75
DªÀÈwÛ 5 12 25 18 10 6 2
19. F PɼÀV£À «vÀgÀuÉUÉ DªÀÈwÛ DPÀÈw gÀa¹, £ÀAvÀgÀ DªÀÈwÛ §ºÀĨsÀÄeÁPÀÈw ªÀÄvÀÄÛ DªÀÈwÛ ªÀPÀæ J¼É¬Äj.
C.I 10-20 20-30 30-40 40-50 50-60
f 2 7 10 8 4
20. F zÀvÁÛA±ÀPÉÌ DªÀÈwÛ ªÀPÀæ J¼É¬Äj.
CAPÀUÀ¼ÀÄ 0-10 10-20 20-30 30-40 40-50
«zÁåyðUÀ¼À ¸ÀASÉå 5 14 20 16 8
21. F «vÀgÀuÉUÉ ªÉÄðäwVAvÀ PÀrªÉÄ ¸ÀAavÀ DªÀÈwÛ ªÀPÀæ J¼ÉzÀÄ, ªÀÄzsÁåAPÀzÀ ¨É¯ÉAiÀÄ£ÀÄß UÀÄgÀÄw¹.
¢£ÀzÀ PÀÆ° gÀÆ.VAvÀ PÀrªÉÄ 250 260 270 280 290 300 310 320 330 340
PÉ®¸ÀUÁgÀgÀ ¸ÀASÉå 6 16 38 70 110 154 192 218 228 250
22. ªÉÄðäwVAvÀ PÀrªÉÄ ¸ÀAavÀ DªÀÈwÛ ªÀPÀæ J¼ÉzÀÄ, ªÀÄzsÁåAPÀzÀ ¨É¯ÉAiÀÄ£ÀÄß D¯ÉÃR¢AzÀ UÀÄgÀÄw¹.
CAPÀUÀ¼ÀÄ 0-10 10-20 20-30 30-40 40-50 50-60
«zÁåyðUÀ¼À ¸ÀASÉå 3 9 15 30 18 5
23. F zÀvÁÛA±ÀPÉÌ ªÉÄðäwVAvÀ PÀrªÉÄ ¸ÀAavÀ DªÀÈwÛ ªÀPÀæ J¼ÉzÀÄ, ªÀÄzsÁåAPÀzÀ ¨É¯ÉAiÀÄ£ÀÄß C¼ÀvÉ ªÀiÁr.
ªÀUÁðAvÀgÀUÀ¼ÀÄ 0-10 10-20 20-30 30-40 40-50
DªÀÈwÛ 5 11 21 16 10
24. F «vÀgÀuÉUÉ PɼÀ«ÄwVAvÀ ºÉaÑ£À ¸ÀAavÀ DªÀÈwÛ ªÀPÀæ J¼ÉzÀÄ, ªÀÄzsÁåAPÀzÀ ¨É¯ÉAiÀÄ£ÀÄß UÀÄgÀÄw¹.
ªÀUÁðAvÀgÀUÀ¼ÀÄ 10-20 20-30 30-40 40-50 50-60 60-70 70-80
DªÀÈwÛ 3 8 14 25 15 7 2
25. F «vÀgÀuÉUÉ ªÉÄðäwVAvÀ PÀrªÉÄ ªÀÄvÀÄÛ PɼÀ«ÄwVAvÀ ºÉaÑ£À ¸ÀAavÀ DªÀÈwÛ ªÀPÀæUÀ¼À£ÀÄß J¼É¬Äj.
ªÀUÁðAvÀgÀUÀ¼ÀÄ 20-24 24-28 28-32 32-36 36-40 40-44
DªÀÈwÛ 17 25 40 23 12 8
26. F zÀvÁÛA±ÀPÉÌ ªÉÄðäwVAvÀ PÀrªÉÄ ¸ÀAavÀ DªÀÈwÛ ªÀPÀæ J¼ÉzÀÄ, Q1 ªÀÄvÀÄÛ Q3 ¨É¯ÉUÀ¼À£ÀÄß D¯ÉÃR¢AzÀ UÀÄgÀÄw¹.
10 PÀÆÌ 20 PÀÆÌ 30 PÀÆÌ 40 PÀÆÌ 50 PÀÆÌ 60 PÀÆÌ
CAPÀUÀ¼ÀÄ
PÀrªÉÄ PÀrªÉÄ PÀrªÉÄ PÀrªÉÄ PÀrªÉÄ PÀrªÉÄ
«zÁåyðUÀ¼À ¸ÀASÉå 5 13 24 39 52 60

18

¥ÀæxÀªÀÄ ¦.AiÀÄÄ.¹. ¸ÀASÁå±Á¸ÀçÛ ¥Àæ±Éß PÉÆñÀ
Unit - V
KPÀZÀ®PÀ zÀvÁÛA±ÀzÀ «±ÉèõÀuÉ
PÉÃA¢æAiÀÄ ¥ÀæªÀÈwÛ ªÀiÁ¥À£À, ºÀgÀ«£À ªÀiÁ¥À£À, «µÀªÀÄvÉ ªÀÄvÀÄÛ ²RgÀvÉ
¸ÀjAiÀiÁzÀ GvÀg
Û ÀªÀ£ÀÄß DAiÉÄ̪ÀiÁr §gɬÄj:
1. zÀvÀÛ ¥Áæ¥ÁÛAPÀUÀ½UÉ CªÀÅUÀ¼À CAPÀUÀtÂvÀ ¸ÀgÁ¸Àj¬ÄAzÀ PÀAqÀÄ»rzÀ CAvÀgÀ(«ZÀ®£É)UÀ¼À ªÉÆvÀÛªÀÅ EzÁVgÀÄvÀÛzÉ.
a) 0 b) 1 c) 2 d) 3
2. 10, 12, 15, 17, 20 gÀ ªÀÄzsÁåAPÀ EzÁVzÉ.
a) 12 b) 15 c) 17 d) 19
3. 8, 9, 8, 7, 8 gÀ ªÀÄzsÁåAPÀ EzÁVzÉ.
a) 6 b) 7 c) 8 d) 9
4. ªÀÄzsÀåªÀÄ «µÀªÀÄvÉ ºÉÆA¢zÀ MAzÀÄ «vÀgÀuÉAiÀÄ°è ¸ÀgÁ¸Àj, ªÀÄzsÁåAPÀ ªÀÄvÀÄÛ §ºÀÄ®PÀ ¨É¯ÉUÀ¼À £ÀqÀÄ«£À ¸ÀA§AzsÀªÀÅ
EzÁVzÉ.
a) §ºÀÄ®PÀ = 2 ªÀÄzsÁåAPÀ – 3 ¸ÀgÁ¸Àj b) §ºÀÄ®PÀ = ªÀÄzsÁåAPÀ – 3 ¸ÀgÁ¸Àj
c) §ºÀÄ®PÀ = 2 ªÀÄzsÁåAPÀ – ¸ÀgÁ¸Àj d) §ºÀÄ®PÀ = 3 ªÀÄzsÁåAPÀ – 2 ¸ÀgÁ¸Àj
5. 4 ªÀÄvÀÄÛ 16 gÀ UÀÄuÉÆÃvÀg
Û À EzÁVzÉ.
a) 5 b) 6 c) 8 d) 10
6. 8, 4 ªÀÄvÀÄÛ 2 gÀ UÀÄuÉÆÃvÀg
Û À EzÁVzÉ.
a) 4 b) 2 c) 8 d) 6
7. 4, 0, 6 ªÀÄvÀÄÛ 8 gÀ UÀÄuÉÆÃvÀg
Û À EzÁVzÉ.
a) 4 b) 0 c) 6 d) 8
8. zÀvÁÛA±ÀªÀ£ÀÄß ¸ÀªÀÄ£ÁzÀ £Á®ÄÌ ¨sÁUÀªÀiÁqÀĪÀ C¼ÀvÉUÀ¼ÉÃ
a) ZÀvÀÄxÁðAPÀUÀ¼ÀÄ b) zÀ±ÁAPÀUÀ¼ÀÄ c) ±ÀvÁAPÀUÀ¼ÀÄ d) ªÀÄzsÁåAPÀ
9. zÀvÁÛA±ÀªÀ£ÀÄß ¸ÀªÀÄ£ÁzÀ ºÀvÀÄÛ ¨sÁUÀªÀiÁqÀĪÀ C¼ÀvÉUÀ¼ÉÃ
a) ZÀvÀÄxÁðAPÀUÀ¼ÀÄ b) zÀ±ÁAPÀUÀ¼ÀÄ c) ±ÀvÁAPÀUÀ¼ÀÄ d) ªÀÄzsÁåAPÀ
10. zÀvÁÛA±ÀªÀ£ÀÄß ¸ÀªÀÄ£ÁzÀ £ÀÆgÀÄ ¨sÁUÀªÀiÁqÀĪÀ C¼ÀvÉUÀ¼ÉÃ
a) ZÀvÀÄxÁðAPÀUÀ¼ÀÄ b) zÀ±ÁAPÀUÀ¼ÀÄ c) ±ÀvÁAPÀUÀ¼ÀÄ d) ªÀÄzsÁåAPÀ
11. MAzÀÄ ªÉÃ¼É Q2 = 40 DzÁUÀ, D5 ¨É¯É EzÁVgÀÄvÀÛzÉ.
a) 10 b) 20 c) 30 d) 40
12. MAzÀÄ ªÉÃ¼É D5 = 30 DzÁUÀ, P50 ¨É¯É EzÁVgÀÄvÀÛzÉ.
a) 10 b) 20 c) 30 d) 40
13. MAzÀÄ ªÉÃ¼É Q2 = 70 DzÁUÀ, P50 ¨É¯É EzÁVgÀÄvÀÛzÉ.
a) 50 b) 70 c) 80 d) 90
14. ¥Áæ¥ÁÛAPÀUÀ¼À «¸ÁÛgÀzÀ ¸ÀÆvÀæ EzÁVzÉ.
a) H – L b) H + L c) L – H d) H ÷ L
15. 10, 20, 15, 30, 35 gÀ «¸ÁÛgÀ EzÁVzÉ.
a) 10 b) 15 c) 20 d) 25

19

¥ÀæxÀªÀÄ ¦.AiÀÄÄ.¹. ¸ÀASÁå±Á¸ÀçÛ ¥Àæ±Éß PÉÆñÀ
DªÀgÀtzÀ°ègÀĪÀ ¸ÀjAiÀiÁzÀ GvÀg
Û ÀªÀ£ÀÄß Dj¹, ©lÖ ¸ÀܼÀ vÀÄA©j:
(ZÀvÀÄxÁðAPÀUÀ¼ÀÄ, PÀ¤µÀ×, 0, 3, ZÀvÀÄxÀðPÀ, ªÀÄzsÁåAPÀ, ±ÀvÁAPÀUÀ¼ÀÄ, UÀAmÉ, zÀ±ÁAPÀUÀ¼ÀÄ, §ºÀÄ®PÀ, ¸À«ÄävÀ,
¨sÁUÀ¨É¯ÉUÀ¼ÀÄ, 3M - 2𝐱̅)

1. zÀvÀÛ ¥Áæ¥ÁÛAPÀUÀ½UÉ CªÀÅUÀ¼À CAPÀUÀtÂvÀ ¸ÀgÁ¸Àj¬ÄAzÀ PÀAqÀÄ»rzÀ «ZÀ®£ÉUÀ¼À ªÉÆvÀÛªÀÅ _______ DVgÀÄvÀÛzÉ.
2. ¥Áæ¥ÁÛAPÀUÀ½UÉ CªÀÅUÀ¼À CAPÀUÀtÂvÀ ¸ÀgÁ¸Àj¬ÄAzÀ PÀAqÀÄ»rzÀ «ZÀ®£ÉUÀ¼À ªÀUÀðUÀ¼À ªÉÆvÀÛªÀÅ _____ DVgÀÄvÀÛzÉ.
3. zÀvÁÛA±ÀªÀ£ÀÄß MAzÀÄ PÀæªÀÄzÀ°è eÉÆÃr¹zÁUÀ, £ÀlÖ£ÀqÀÄ«£À ¨É¯ÉAiÉÄà __________
4. zÀvÀÛ ¥Áæ¥ÁÛAPÀUÀ¼À°è ºÉZÀÄѸÀ® ¥ÀÄ£ÀgÁªÀvÀð£ÉAiÀiÁzÀ ¨É¯ÉAiÉÄà __________
5. ¸ÀgÁ¸Àj, ªÀÄzsÁåAPÀ ªÀÄvÀÄÛ §ºÀÄ®PÀUÀ¼À £ÀqÀÄ«£À G¨sÀAiÀÄd£Àå ¸ÀA§AzsÀªÀÅ Z = _________
6. zÀvÁÛA±ÀªÀ£ÀÄß ¸ÀªÀÄ£ÁzÀ ¨sÁUÀUÀ¼À£ÁßV ªÀiÁqÀĪÀ ¨É¯ÉUÀ¼Éà _________ ¨É¯ÉUÀ¼ÀÄ.
7. zÀvÁÛA±ÀªÀ£ÀÄß ¸ÀªÀÄ£ÁzÀ £Á®ÄÌ ¨sÁUÀUÀ¼À£ÁßV ªÀiÁqÀĪÀ ¨É¯ÉUÀ¼Éà _________ ¨É¯ÉUÀ¼ÀÄ.
8. zÀvÁÛA±ÀªÀ£ÀÄß ¸ÀªÀÄ£ÁzÀ ºÀvÀÄÛ ¨sÁUÀUÀ¼À£ÁßV ªÀiÁqÀĪÀ ¨É¯ÉUÀ¼Éà _________ ¨É¯ÉUÀ¼ÀÄ.
9. zÀvÁÛA±ÀªÀ£ÀÄß ¸ÀªÀÄ£ÁzÀ £ÀÆgÀÄ ¨sÁUÀUÀ¼À£ÁßV ªÀiÁqÀĪÀ ¨É¯ÉUÀ¼Éà _________ ¨É¯ÉUÀ¼ÀÄ.
10. CAvÀgï ZÀvÀÄxÁðAPÀ «¸ÁÛgÀzÀ CzsÀðªÀ£ÀÄß _________ «ZÀ®£É J£ÀÄߪÀgÀÄ.
11. ¸À«ÄävÀ «vÀgÀuÉAiÀÄ£ÀÄß D¯ÉÃRzÀ°è J¼ÉzÁUÀ, £ÀªÀÄUÉ _______ DPÁgÀzÀ ªÀPÀæ zÉÆgÉAiÀÄÄvÀÛzÉ.
12. _______ «vÀgÀuÉAiÀÄ°è ¸ÀgÁ¸Àj, ªÀÄzsÁåAPÀ ªÀÄvÀÄÛ §ºÀÄ®PÀUÀ¼ÀÄ ¸ÀªÀÄ£ÁVgÀÄvÀÛªÉ.
13. ¸ÁªÀiÁ£Àå ²RgÀvÉAiÀÄ «vÀgÀuÉAiÀÄ°è, β2 ¨É¯É ________ DVgÀÄvÀÛzÉ.
14. GZÀÒ ²RgÀvÉAiÀÄ «vÀgÀuÉAiÀÄ°è, β2 ¨É¯É ________ QÌAvÀ ºÉZÁÑVgÀÄvÀz
Û É.
15. ¤ÃZÀ ²RgÀvÉAiÀÄ «vÀgÀuÉAiÀÄ°è, β2 ¨É¯É ________ QÌAvÀ PÀrªÉÄAiÀiÁVgÀÄvÀÛzÉ.

ºÉÆA¢¹ §gɬÄj: (£ÉÃgÀªÁV GvÀÛgÀUÀ¼À£ÀÄß ¤ÃqÀ¯ÁVzÉ.)
Σ (x - 𝐱̅) 0
Σ (x - 𝐱̅)2 »ÃUÁVgÀÄvÀÛzÉ PÀ¤µÀ×
§ºÀÄ®PÀ 3 ªÀÄzsÁåAPÀ – 2 ¸ÀgÁ¸Àj
¸ÀgÁ¸Àj ¨É¼ÀªÀtÂUÉAiÀÄ zÀgÀ UÀÄuÉÆÃvÀgÛ À ¸ÀgÁ¸Àj
¸ÀgÁ¸Àj ªÉÃUÀ ºÀgÁvÀäPÀ ¸ÀgÁ¸Àj
ZÀvÀÄxÁðAPÀUÀ¼ÀÄ zÀvÁÛA±ÀªÀ£ÀÄß ¸ÀªÀÄ£ÁzÀ 4 ¨sÁUÀUÀ¼À£ÁßV ªÀiÁqÀÄvÀÛªÉ.
zÀ±ÁAPÀUÀ¼ÀÄ zÀvÁÛA±ÀªÀ£ÀÄß ¸ÀªÀÄ£ÁzÀ 10 ¨sÁUÀUÀ¼À£ÁßV ªÀiÁqÀÄvÀÛªÉ.
±ÀvÁAPÀUÀ¼ÀÄ zÀvÁÛA±ÀªÀ£ÀÄß ¸ÀªÀÄ£ÁzÀ 100 ¨sÁUÀUÀ¼À£ÁßV ªÀiÁqÀÄvÀÛªÉ.
«¸ÁÛgÀ H–L
CAvÀgï ZÀvÀÄxÁðAPÀ «¸ÁÛgÀ Q3 – Q1
C¸À«ÄävÀvÉ (¸À«ÄävÀvÉ E®è¢gÀĪÀÅzÉÃ) «µÀªÀÄvÉ
²RgÀvÉ ²RgÀvÉUÀ¼À£ÀÄß ºÉÆA¢zÀ
β2 > 3 GZÀÒ²RgÀvÉAiÀÄ «vÀgÀuÉ
β2 = 3 ¸ÁªÀiÁ£Àå²RgÀvÉAiÀÄ «vÀgÀuÉ
β2 < 3 ¤ÃZÀ(PÀrªÉÄ)²RgÀvÉAiÀÄ «vÀgÀuÉ

20

¥ÀæxÀªÀÄ ¦.AiÀÄÄ.¹. ¸ÀASÁå±Á¸ÀçÛ ¥Àæ±Éß PÉÆñÀ
MAzÀÄ CAPÀzÀ ¥Àæ±ÉßUÀ¼ÀÄ:
1. PÉÃA¢æAiÀÄ ¥ÀæªÀÈwÛAiÀÄ CxÀðªÉãÀÄ?
1. PÉÃA¢æAiÀÄ ¥ÀæªÀÈwÛAiÀÄ ªÀiÁ¥À£ÀzÀ CxÀðªÉãÀÄ?
2. ¸ÀgÁ¸ÀjAiÀÄ MAzÀÄ GzÉÝñÀ w½¹.
3. CAPÀUÀtÂvÀ ¸ÀgÁ¸ÀjAiÀÄ£ÀÄß ªÁåSÁ夹.
4. ∑(𝐱 − 𝐱̅) ¨É¯É JµÀÄÖ?
5. CAPÀUÀtÂvÀ ¸ÀgÁ¸ÀjAiÀÄ PÀ¤µÀÖ UÀÄtzsÀªÀÄðªÀ£ÀÄß §gɬÄj.
6. ªÀÄzsÁåAPÀªÀ£ÀÄß ªÁåSÁ夹.
7. §ºÀÄ®PÀªÀ£ÀÄß ªÁåSÁ夹.
8. MAzÀÄ §ºÀÄ®PÀªÀżÀî «vÀgÀuÉ JAzÀgÉãÀÄ?
9. UÀÄuÉÆÃvÀg
Û À ¸ÀgÁ¸ÀjAiÀÄ£ÀÄß ªÁåSÁ夹.
10. ºÀgÁvÀäPÀ ¸ÀgÁ¸ÀjAiÀÄ£ÀÄß ªÁåSÁ夹.
11. F zÀvÁÛA±ÀzÀ §ºÀÄ®PÀªÀ£ÀÄß PÀAqÀÄ»r¬Äj: 3, 4, 5, 5, 6, 8, 5, 7, 5, 5, 8, 5, 5, 4, 5.
12. F «vÀgÀuÉAiÀÄ §ºÀÄ®PÀªÀ£ÀÄß ¯ÉQ̹.
X 10 12 15 22 25 35 45 50 60
f 4 6 10 14 20 18 10 6 3
13. 4, 25 gÀ UÀÄuÉÆÃvÀg
Û À ¸ÀgÁ¸ÀjAiÀÄ£ÀÄß PÀAqÀÄ»r¬Äj.
14. AM, GM, HM ºÉÃUÉ ¸ÀA§AzsÀ ºÉÆA¢gÀÄvÀª
Û É?
15. X , M , Z UÀ¼À £ÀqÀÄ«£À G¨sÀAiÀÄd£Àå ¸ÀA§AzsÀ w½¹.
16. UÀÄuÁvÀäPÀ zÀvÁÛA±ÀPÉÌ ¸ÀÆPÀÛªÁzÀ ¸ÀgÁ¸ÀjAiÀÄ£ÀÄß ºÉ¸Àj¹.
17. ¨sÁUÀ ¨É¯ÉUÀ¼ÀÄ JAzÀgÉãÀÄ?
18. ZÀvÀÄxÁðAPÀUÀ¼À£ÀÄß ªÁåSÁ夹.
19. zÀ±ÁAPÀUÀ¼À£ÀÄß ªÁåSÁ夹.
20. ±ÀvÁAPÀUÀ¼À£ÀÄß ªÁåSÁ夹.
21. ªÀÄzsÁåAPÀ 50 DzÀgÉ, Q2 ¨É¯É JµÀÄÖ?
22. ªÀÄzsÁåAPÀ, Q2, D5 ªÀÄvÀÄÛ P50 UÀ¼À £ÀqÀÄ«£À ¸ÀA§AzsÀªÉãÀÄ?
23. ºÀgÀ«£À ªÀiÁ¥À£À JAzÀgÉãÀÄ?
24. ªÁå¦ÛAiÀÄ£ÀÄß ªÁåSÁ夹.
25. X: 7, 12, 25, 18, 35 DzÁUÀ, ªÁå¦ÛAiÀÄ£ÀÄß PÀAqÀÄ»r¬Äj.
26. ZÀvÀÄxÀðPÀ «ZÀ®£ÉAiÀÄ£ÀÄß ªÁåSÁ夹.
27. ¸ÀgÁ¸Àj «ZÀ®£ÉAiÀÄ£ÀÄß ªÁåSÁ夹.
28. ¤AiÀÄvÀ (ªÀiÁ£ÀPÀ) «ZÀ®£ÉAiÀÄ£ÀÄß ªÁåSÁ夹.
29. ªÀiÁ¦ð£À UÀÄuÁAPÀ JAzÀgÉãÀÄ?
30. «ZÀ®£ÉAiÀÄ£ÀÄß ªÁåSÁ夹.
31. ¤AiÀÄvÀ «ZÀ®£É (SD) = 4 ¸ÉA.«ÄÃ. DzÁUÀ, «ZÀ®£ÉAiÀÄ£ÀÄß PÀAqÀÄ»r¬Äj.
32. «ZÀ®£É = 16 ªÀUÀð Cr DzÁUÀ, ¤AiÀÄvÀ «ZÀ®£ÉAiÀÄ£ÀÄß PÀAqÀÄ»r¬Äj.
33. «µÀªÀÄvÉAiÀÄ£ÀÄß ªÁåSÁ夹.

21

¥ÀæxÀªÀÄ ¦.AiÀÄÄ.¹. ¸ÀASÁå±Á¸ÀçÛ ¥Àæ±Éß PÉÆñÀ
34. MAzÀÄ ¸À«ÄävÀ ªÀPÀæzÀ°è ¸ÀgÁ¸Àj, ªÀÄzsÁåAPÀ ªÀÄvÀÄÛ §ºÀÄ®PÀUÀ¼À ¸ÀA§AzsÀ AiÀiÁªÀÅzÀÄ?
35. ²RgÀvÉAiÀÄ£ÀÄß ªÁåSÁ夹.
36. β2 > 3 DzÁUÀ, ²RgÀvÉAiÀÄ£ÀÄß ºÉ¸Àj¹.
37. β2 = 3 DzÁUÀ, ²RgÀvÉAiÀÄ£ÀÄß ºÉ¸Àj¹.
38. ªÀPÀæªÀÅ ¤ÃZÀ ²RgÀvÉ ºÉÆA¢zÁUÀ, β2 ¨É¯É JµÀÄÖ?

JgÀqÀÄ CAPÀzÀ ¥Àæ±ÉßUÀ¼ÀÄ:
1. ¸ÀgÁ¸ÀjAiÀÄ JgÀqÀÄ C¥ÉÃQëvÀ UÀÄtUÀ¼À£ÀÄß w½¹.
2. ¸ÀgÁ¸ÀjAiÀÄ £Á®ÄÌ C¼ÀvÉUÀ¼À£ÀÄß w½¹.
3. F PɼÀV£À ¥ÀæPÀgÀtUÀ¼À°è AiÀiÁªÀ ¸ÀgÁ¸ÀjAiÀÄÄ ¸ÀÆPÀÛªÁVzÉ?
a. ¹zÀÞ GqÀĦ£À ¸ÀgÁ¸Àj C¼ÀvÉ.
b. ¥Àæw zÀ±ÀPÀzÀ¯ÁèzÀ d£À¸ÀASÁå ¸ÀgÁ¸Àj ¨É¼ÀªÀtÂUÉAiÀÄ zÀgÀ.
4. F PɼÀV£À ¥ÀæPÀgÀtUÀ¼À°è AiÀiÁªÀ ¸ÀgÁ¸ÀjAiÀÄÄ ¸ÀÆPÀÛªÁVzÉ?
c. MAzÀÄ vÀgÀUÀwAiÀÄ°èAiÀÄ «zÁåyðUÀ¼À ¸ÀgÁ¸Àj CAPÀUÀ¼ÀÄ.
d. 4 x 100 «ÄÃ. jïÉAiÀÄ°è ¸ÀàzsÁð¼ÀÄUÀ¼À ¸ÀgÁ¸Àj ªÉÃUÀ.
5. CAPÀUÀtÂvÀ ¸ÀgÁ¸ÀjAiÀÄ UÀÄtzsÀªÀÄðUÀ¼À£ÀÄß w½¹.
6. CAPÀUÀtÂvÀ ¸ÀgÁ¸ÀjAiÀÄ MAzÀÄ UÀÄt ªÀÄvÀÄÛ MAzÀÄ zÉÆõÀªÀ£ÀÄß w½¹.
7. ªÀÄzsÁåAPÀzÀ MAzÀÄ UÀÄt ªÀÄvÀÄÛ MAzÀÄ zÉÆõÀªÀ£ÀÄß w½¹.
8. §ºÀÄ®PÀzÀ MAzÀÄ UÀÄt ªÀÄvÀÄÛ MAzÀÄ zÉÆõÀªÀ£ÀÄß w½¹.
9. 8, 5, 6, 4, 3, 7, 2 gÀ CAPÀUÀtÂvÀ ¸ÀgÁ¸Àj ¯ÉQ̹.
10. 15 ¥Áæ¥ÁÛAPÀUÀ¼À ªÉÆvÀÛ 450 DzÀgÉ, CAPÀUÀtÂvÀ ¸ÀgÁ¸Àj PÀAqÀÄ»r¬Äj.
11. 50 ¥Áæ¥ÁÛAPÀUÀ¼À CAPÀUÀtÂvÀ ¸ÀgÁ¸Àj 70 DzÀgÉ, ¥Áæ¥ÁÛAPÀUÀ¼À ªÉÆvÀÛªÀ£ÀÄß PÀAqÀÄ»r¬Äj.
̅1= 60, 𝐗
12. n1 = 50, n2 = 100, 𝐗 ̅2 = 70 JAzÀÄ PÉÆmÁÖUÀ, PÉÆæÃrüPÀÈvÀ CAPÀUÀtÂvÀ ¸ÀgÁ¸Àj PÀAqÀÄ»r¬Äj.
13. 80 ¨Á®PÀgÀ ªÉÆzÀ®£ÉAiÀÄ UÀÄA¦£À ªÀAiÀĹì£À ¸ÀgÁ¸Àj 10 ªÀµÀðUÀ¼ÀÄ ªÀÄvÀÄÛ 20 ¨Á®PÀgÀ JgÀqÀ£ÉAiÀÄ UÀÄA¦£À
ªÀAiÀĹì£À ¸ÀgÁ¸Àj 15 ªÀµÀðUÀ¼ÀÄ. JgÀqÀÄ UÀÄA¥ÀÄUÀ¼À MmÁÖgÉ ¸ÀgÁ¸Àj PÀAqÀÄ»r¬Äj.
14. F zÀvÁÛA±ÀzÀ ªÀÄzsÁåAPÀ PÀAqÀÄ»r¬Äj: 17, 32, 35, 33, 15, 21, 41, 32, 11, 18, 20.
15. F zÀvÁÛA±ÀzÀ ªÀÄzsÁåAPÀ PÀAqÀÄ»r¬Äj: 5, 9, 8, 6, 1, 4, 10, 8.
16. ¸Àé®à «µÀªÀÄvÉAiÀÄļÀî MAzÀÄ «vÀgÀuÉAiÀÄ ¸ÀgÁ¸Àj ªÀÄvÀÄÛ ªÀÄzsÁåAPÀUÀ¼ÀÄ PÀæªÀĪÁV 11 ¸ÉA.«ÄÃ. ªÀÄvÀÄÛ 11.7
¸ÉA.«ÄÃ. «vÀgÀuÉAiÀÄ §ºÀÄ®PÀªÀ£ÀÄß PÀAqÀÄ»r¬Äj.
17. MAzÀÄ «vÀgÀuÉAiÀÄ°è ¸ÀgÁ¸Àj = 24.6 ªÀÄvÀÄÛ §ºÀÄ®PÀ = 26.1 DzÀgÉ, ªÀÄzsÁåAPÀzÀ ¨É¯É PÀAqÀÄ»r¬Äj.
18. ¸Àé®à «µÀªÀÄvÉAiÀÄļÀî MAzÀÄ «vÀgÀuÉAiÀÄ §ºÀÄ®PÀ ªÀÄvÀÄÛ ªÀÄzsÁåAPÀ ¨É¯ÉUÀ¼ÀÄ PÀæªÀĪÁV 20 ªÀÄvÀÄÛ 24 DzÀgÉ,
¸ÀgÁ¸ÀjAiÀÄ£ÀÄß PÀAqÀÄ»r¬Äj.
19. 1, 4 ªÀÄvÀÄÛ 16 gÀ GM PÀAqÀÄ»r¬Äj.
20. 1, 2, 4 ªÀÄvÀÄÛ 5 gÀ HM PÀAqÀÄ»r¬Äj.
21. F zÀvÁÛA±ÀPÉÌ ªÁå¦ÛAiÀÄ ¸ÀºÀUÀÄtPÀ PÀAqÀÄ»r¬Äj:
Û À (¸ÉA.«ÄÃ): 160, 158, 159, 165, 148, 139, 142, 155.
JvÀg
22. ºÀgÀ«£À ªÀiÁ¥À£ÀzÀ ««zsÀ C¼ÀvÉUÀ¼À£ÀÄß w½¹.

22

¥ÀæxÀªÀÄ ¦.AiÀÄÄ.¹. ¸ÀASÁå±Á¸ÀçÛ ¥Àæ±Éß PÉÆñÀ
23. ºÀgÀ«£À ªÀiÁ¥À£ÀzÀ ¤gÀ¥ÉÃPÀë ªÀÄvÀÄÛ ¸Á¥ÉÃPÀë C¼ÀvÉUÀ¼ÁªÀŪÀÅ?
24. ZÀvÀÄxÀðPÀ «ZÀ®£ÉAiÀÄ JgÀqÀÄ zÉÆõÀUÀ¼À£ÀÄß §gɬÄj.
25. ¸ÀgÁ¸Àj «ZÀ®£ÉAiÀÄ JgÀqÀÄ zÉÆõÀUÀ¼À£ÀÄß §gɬÄj.
26. ZÀvÀÄxÀðPÀ «ZÀ®£É 7 ªÀÄvÀÄÛ Q1 = 21. Q3 PÀAqÀÄ»r¬Äj.
27. MAzÀÄ «vÀgÀuÉUÉ PɼÀ ªÀÄvÀÄÛ ªÉÄð£À ZÀvÀÄxÁðAPÀUÀ¼À ªÉÆvÀÛ 50 ªÀÄvÀÄÛ CªÀÅUÀ¼À ªÀåvÁå¸À 10 DzÀgÉ, ZÀvÀÄxÀðPÀ
«ZÀ®£É ¸ÀºÀUÀÄtPÀ PÀAqÀÄ»r¬Äj.
28. ¤AiÀÄvÀ «ZÀ®£ÉAiÀÄ JgÀqÀÄ UÀÄtUÀ¼À£ÀÄß §gɬÄj.
29. ¸ÀgÁ¸Àj 20 ªÀÄvÀÄÛ ¤AiÀÄvÀ «ZÀ®£É 5 DzÀgÉ, CV PÀAqÀÄ»r¬Äj.
30. CV = 10% ªÀÄvÀÄÛ ¤AiÀÄvÀ «ZÀ®£É 4 DzÀgÉ, ¸ÀgÁ¸Àj PÀAqÀÄ»r¬Äj.
31. ¤AiÀÄvÀ «ZÀ®£ÉAiÀÄ JgÀqÀÄ UÀÄtzsÀªÀÄðUÀ¼À£ÀÄß w½¹.
32. MAzÀÄ «vÀgÀuÉAiÀÄ ªÀiÁ¦ð£À UÀÄuÁAPÀ ªÀÄvÀÄÛ ¤AiÀÄvÀ «ZÀ®£ÉUÀ¼ÀÄ PÀæªÀĪÁV 75% ªÀÄvÀÄÛ 15 DzÀgÉ, EzÀgÀ ¸ÀgÁ¸Àj
PÀAqÀÄ»r¬Äj.
33. ¸Àé®à «µÀªÀÄvÉAiÀÄļÀî MAzÀÄ «vÀgÀuÉAiÀÄ CAPÀUÀtÂvÀ ¸ÀgÁ¸Àj = 160, §ºÀÄ®PÀ = 157 ªÀÄvÀÄÛ ¤AiÀÄvÀ «ZÀ®£É = 50
DzÀgÉ, «µÀªÀÄvÉAiÀÄ ¸ÀºÀUÀÄtPÀ PÀAqÀÄ»r¬Äj.
34. JgÀqÀÄ jÃwAiÀÄ ¨ÁæªÀÄPÀUÀ¼À£ÀÄß w½¹.

LzÀÄ CAPÀzÀ ¥Àæ±ÉßUÀ¼ÀÄ:
1. F zÀvÁÛA±ÀzÀ CAPÀUÀtÂvÀ ¸ÀgÁ¸Àj ¯ÉQ̹.
X 2 3 4 5 6 7 8 9 10 11
f 3 8 10 12 16 14 10 8 7 5
2. F PɼÀV£À DªÀÈwÛ «vÀgÀuÉUÉ ¸ÀgÁ¸Àj PÀAqÀÄ»r¬Äj.
X 19 21 23 25 27 29 31
f 13 15 16 18 16 15 13
3. F PɼÀV£À DªÀÈwÛ «vÀgÀuÉUÉ ¸ÀgÁ¸Àj PÀAqÀÄ»r¬Äj.
CAPÀUÀ¼ÀÄ 10 - 25 25 - 40 40 - 55 55 - 70 70 - 85 85 - 100
«zÁåyðUÀ¼À ¸ÀASÉå 6 50 44 26 3 1
4. F PɼÀV£À DªÀÈwÛ «vÀgÀuÉUÉ ¸ÀgÁ¸Àj ¯ÉQ̹.
C.I 15-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64
f 6 14 12 10 10 9 9 10 6 4
5. F PɼÀV£À DªÀÈwÛ «vÀgÀuÉUÉ ¸ÀgÁ¸Àj ¯ÉQ̹.
20 PÀÆÌ 40 PÀÆÌ 60 PÀÆÌ 80 PÀÆÌ 100 PÀÆÌ
CAPÀUÀ¼ÀÄ
PÀrªÉÄ PÀrªÉÄ PÀrªÉÄ PÀrªÉÄ PÀrªÉÄ
«zÁåyðUÀ¼À ¸ÀASÉå 3 10 25 34 40

23

¥ÀæxÀªÀÄ ¦.AiÀÄÄ.¹. ¸ÀASÁå±Á¸ÀçÛ ¥Àæ±Éß PÉÆñÀ
6. F PɼÀV£À DªÀÈwÛ «vÀgÀuÉUÉ ¸ÀgÁ¸Àj ¯ÉQ̹
JvÀgÛ À 135 & 140 & 145 & 150 & 155 & 160 & 165 & 170 &
(¸ÉA.«ÄÃ.) ºÉZÀÄÑ ºÉZÀÄÑ ºÉZÀÄÑ ºÉZÀÄÑ ºÉZÀÄÑ ºÉZÀÄÑ ºÉZÀÄÑ ºÉZÀÄÑ
«zÁåyðUÀ¼À
¸ÀASÉå 100 96 87 69 41 17 7 2

7. F «vÀgÀuÉAiÀÄ ¸ÀgÁ¸Àj 20.5 DVzÉ. PÁuÉAiÀiÁzÀ DªÀÈwÛ PÀAqÀÄ»r¬Äj.
X 10 15 20 25 30
f 5 7 ̶ 12 6
8. F «vÀgÀuÉUÉ ¸ÀgÁ¸Àj 30.5 JAzÀÄ ¤ÃqÀ¯ÁVzÉ. PÁuÉAiÀiÁzÀ DªÀÈwÛ PÀAqÀÄ»r¬Äj.
X 10 20 30 40 50
f 8 10 - 15 7
9. F «vÀgÀuÉAiÀÄ ¸ÀgÁ¸Àj 50. PÁuÉAiÀiÁzÀ DªÀÈwÛ PÀAqÀÄ»r¬Äj.
C-I 0 - 20 20 - 40 40 - 60 60 - 80 80 - 100
f 19 28 32 ̶ 19
10. F «vÀgÀuÉUÉ 𝐱̅ = 45 DzÀgÉ, PÁuÉAiÀiÁzÀ DªÀÈwÛ PÀAqÀÄ»r¬Äj.
C.I 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80
f 5 8 7 - 28 20 10 10
11. MAzÀÄ ¥ÀjÃPÉëAiÀÄ°è M§â C¨sÀåyðAiÀÄÄ UÀ½¹zÀ CAPÀUÀ¼ÀÄ (±ÉÃRqÁzÀ°è); EAVèÃóµÀ (62), ¨sÁµÉ (74), UÀtÂvÀ (58),
«eÁÕ£À (61), ¸ÀªÀiÁd «eÁÕ£À (45). MAzÀÄ ªÉÃ¼É C£ÀÄPÀæªÀÄ ¨sÁgÀUÀ¼ÀÄ 3, 4, 4, 5 ªÀÄvÀÄÛ 2 DVzÀÝgÉ, ¨sÁjvÀ
¸ÀgÁ¸Àj PÀAqÀÄ»r¬Äj.
12. 50 ¥Áæ¥ÁÛAPÀUÀ¼À CAPÀUÀtÂvÀ ¸ÀgÁ¸Àj 100. ¯ÉQ̸ÀĪÀ ¸ÀAzÀ¨sÀðzÀ°è 40 ªÀÄvÀÄÛ 80 JA§ ¨É¯ÉUÀ¼À£ÀÄß vÀ¥ÁàV 14
ªÀÄvÀÄÛ 18 JAzÀÄ vÀUÉzÀÄ PÉƼÀî¯ÁVzÉ. ¸Àj¥Àr¹zÀ CAPÀUÀtÂvÀ ¸ÀgÁ¸Àj PÀAqÀÄ»r¬Äj.
13. MAzÀÄ vÀgÀUÀwAiÀÄ ‘A’ JA§ ‘B’ JgÀqÀÄ «¨sÁUÀUÀ¼À «zÁåyðUÀ¼À ¸ÀgÁ¸Àj CAPÀUÀ¼ÀÄ 62. ‘A’ «¨sÁUÀzÀ «zÁåyðUÀ¼À
¸ÀgÁ¸Àj CAPÀUÀ¼ÀÄ 70. MAzÀÄ ªÉÃ¼É ‘A’ ªÀÄvÀÄÛ ‘B’ «¨sÁUÀUÀ¼À «zÁåyðUÀ¼À ¸ÀASÉå PÀæªÀĪÁV 30 ªÀÄvÀÄÛ 35 DzÀgÉ,
‘B’ «¨sÁUÀzÀ «zÁåyðUÀ¼À ¸ÀgÁ¸Àj CAPÀ PÀAqÀÄ»r¬Äj.
14. MAzÀÄ PÀA¥À¤AiÀÄ £ËPÀgÀgÀ ¸ÀgÁ¸Àj ªÀiÁ¹PÀ ªÉÃvÀ£À gÀÆ. 20,000. ¥ÀÄgÀĵÀ ªÀÄvÀÄÛ ªÀÄ»¼ÉAiÀÄgÀ ¸ÀgÁ¸Àj ªÀiÁ¹PÀ
ªÉÃvÀ£À PÀæªÀĪÁV gÀÆ.20,800 ªÀÄvÀÄÛ gÀÆ.16,800. PÀA¥À¤AiÀÄ ¥ÀÄgÀĵÀ ªÀÄvÀÄÛ ªÀÄ»¼Á £ËPÀgÀgÀ ±ÉÃRqÁ ¸ÀASÉå
PÀAqÀÄ»r¬Äj.
15. MAzÀÄ vÀgÀUÀwAiÀÄ J¯Áè «zÁåyðUÀ¼À CAPÀUÀ¼À ¸ÀgÁ¸Àj 72. ºÀÄqÀÄUÀgÀ ¸ÀgÁ¸Àj CAPÀUÀ¼ÀÄ 75 ªÀÄvÀÄÛ ºÀÄqÀÄVAiÀÄgÀ
CAPÀUÀ¼À ¸ÀgÁ¸Àj 65. vÀgÀUÀwAiÀÄ ºÀÄqÀÄUÀ ªÀÄvÀÄÛ ºÀÄqÀÄVAiÀÄgÀ C£ÀÄ¥ÁvÀ PÀAqÀÄ»r¬Äj.
16. F zÀvÁÛA±À¢AzÀ ªÀÄzsÁåAPÀ PÀAqÀÄ»r¬Äj.
¢£ÀUÀÆ° (gÀÆ.) 120-140 140-160 160-180 180-200 200-220 220-240
£ËPÀgÀgÀ ¸ÀASÉå 8 12 20 25 22 13
17. ªÀiÁ«£À ºÀtÄÚUÀ¼À vÀÆPÀzÀ F PɼÀV£À DªÀÈwÛ «vÀgÀuÉUÉ ªÀÄzsÁåAPÀ PÀAqÀÄ»r¬Äj.
vÀÆPÀ (UÁæA) 410-419 420-429 430-439 440-449 450-459 460-469 470-479
ªÀiÁ«£À ºÀtÄÚUÀ¼À
¸ÀASÉå 10 20 40 50 45 23 12

24

¥ÀæxÀªÀÄ ¦.AiÀÄÄ.¹. ¸ÀASÁå±Á¸ÀçÛ ¥Àæ±Éß PÉÆñÀ
18. F PɼÀV£À PÉÆõÀÖPÀªÀÅ MAzÀÄ ¤¢ðµÀÖ PÉëÃvÀæzÀ ªÀåQÛUÀ¼À ªÀAiÀĹì£À «vÀgÀuÉAiÀÄ£ÀÄß vÉÆÃj¸ÀÄvÀÛzÉ. ªÀÄzsÁåAPÀ ªÀAiÀĸÀì£ÀÄß
PÀAqÀÄ»r¬Äj.
ªÀAiÀĸÀÄì 10 PÀÆÌ 20 PÀÆÌ 30 PÀÆÌ 40 PÀÆÌ 50 PÀÆÌ 60 PÀÆÌ 70 PÀÆÌ
(ªÀµÀðUÀ¼ÀÄ) PÀrªÉÄ PÀrªÉÄ PÀrªÉÄ PÀrªÉÄ PÀrªÉÄ PÀrªÉÄ PÀrªÉÄ
ªÀåQÛUÀ¼À ¸ÀASÉå (‘000) 2 7 16 28 38 45 48

19. F zÀvÁÛA±ÀzÀ ªÀÄzsÁåAPÀ 24 DzÁUÀ ©lÄÖºÉÆÃzÀ DªÀÈwÛAiÀÄ£ÀÄß PÀAqÀÄ»r¬Äj.
CI 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50
f 5 25 - 18 7
20. F PɼÀUÉ ¤ÃrzÀ zÀvÁÛA±À¢AzÀ §ºÀÄ®PÀ PÀAqÀÄ»r¬Äj.
X 5 10 15 20 25
f 3 2 8 6 1
21. F PɼÀV£À DªÀÈwÛ «vÀgÀuÉUÉ §ºÀÄ®PÀ£ÀÄß ¯ÉQ̹.
DzÁAiÀÄ (’000 gÀÆ.UÀ¼À°è) 1–2 2–3 3–4 4–5 5–6 6–7
PÉ®¸ÀUÁgÀgÀ ¸ÀASÉå 15 18 30 17 18 12
22. MAzÀÄ ±Á¯ÉAiÀÄ MAzÀÄ vÀgÀUÀwAiÀÄ 60 «zÁåyðUÀ¼À vÀÆPÀzÀ DªÀÈwÛ «vÀgÀuÉAiÀÄ£ÀÄß F PɼÀUÉ ¤ÃrzÉ. §ºÀÄ®PÀ vÀÆPÀ
PÀAqÀÄ»r¬Äj.
vÀÆPÀ (PÉ.f.UÀ¼À°)è 30 - 34 35 - 39 40 - 44 45 - 49 50 - 54 55 - 59 60 - 64
«zÁåyðUÀ¼À ¸ÀASÉå 3 5 12 18 14 6 2
23. F PɼÀV£À DªÀÈwÛ «vÀgÀuÉUÉ §ºÀÄ®PÀ£ÀÄß ¯ÉQ̹.
C -I 10 PÀÆÌ PÀrªÉÄ 10-12 12-14 14-16 16-18 18 & ºÉZÀÄÑ
f 3 15 27 20 3 2
24. MAzÀÄ ¸ÀA¸ÉÜAiÀÄ £ËPÀgÀgÀ ¥Àæw UÀAmÉAiÀÄ PÀÆ° (gÀÆ.UÀ¼À°è) EgÀĪÀ F PɼÀV£À «vÀgÀuɬÄAzÀ UÀAmÉAiÀÄ §ºÀÄ®PÀ
PÀÆ°AiÀÄ£ÀÄß PÀAqÀÄ»r¬Äj.
UÀAmÉAiÀÄ PÀÆ° (gÀÆ) < 10 < 20 < 30 < 40 < 50 < 60 < 70 < 80
£ËPÀgÀgÀ ¸ÀASÉå 2 15 60 82 95 122 140 150

25. F zÀvÁÛA±À¢AzÀ UÀÄuÉÆÃvÀÛgÀ ¸ÀgÁ¸ÀjAiÀÄ£ÀÄß ¯ÉQ̹.
ªÁå¸À («Ä.«Ä.) 130 135 140 145 146 148 149
¸ÀÆÌçUÀ¼À ¸ÀASÉå 3 4 6 6 3 5 2

26. F PɼÀUÉ ¤ÃrzÀ zÀvÁÛA±ÀPÉÌ UÀÄuÉÆÃvÀg
Û À ¸ÀgÁ¸ÀjAiÀÄ£ÀÄß ¯ÉQ̹.
C-I 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80
f 7 23 30 22 11 7

27. F zÀvÁÛA±ÀPÉÌ ºÀgÁvÀäPÀ ¸ÀgÁ¸ÀjAiÀÄ£ÀÄß ¯ÉQ̹.
X 12 14 16 18 20
f 3 5 9 4 2

25

¥ÀæxÀªÀÄ ¦.AiÀÄÄ.¹. ¸ÀASÁå±Á¸ÀçÛ ¥Àæ±Éß PÉÆñÀ
28. F zÀvÁÛA±ÀPÉÌ ºÀgÁvÀäPÀ ¸ÀgÁ¸ÀjAiÀÄ£ÀÄß PÀAqÀÄ»r¬Äj.
C–I 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50
f 5 8 10 7 4

29. MAzÀÄ PÉÊUÁjPÉAiÀÄ°è, MAzÀÄ ¨sÁUÀzÀ PÉ®¸ÀªÀ£ÀÄß A LzÀÄ ¤«ÄµÀzÀ°è, B DgÀÄ ¤«ÄµÀzÀ°è, C JAlÄ ¤«ÄµÀzÀ°è, D
MA¨sÀvÀÄÛ ¤«ÄµÀzÀ°è ªÀÄvÀÄÛ E ºÀ£ÉßgÀqÀÄ ¤«ÄµÀzÀ°è ¥ÀÆtðUÉƽ¸ÀĪÀgÀÄ. D ¨sÁUÀzÀ PÉ®¸À ¥ÀÆtðUÉƼÀÄîªÀ ¸ÀgÁ¸Àj
¸ÀªÀÄAiÀÄ PÀAqÀÄ»r¬Äj.
30. M§â ¸ÉÊPÀ¯ï ¸ÀªÁgÀ£ÀÄ ¥ÁægÀA¨sÀzÀ JgÀqÀÄ ªÉÄÊ®ÄUÀ¼À£ÀÄß ¥Àæw UÀAmÉUÉ 5 ªÉÄÊ°£À ªÉÃUÀzÀ°è PÀæ«Ä¸ÀĪÀ£ÀÄ. £ÀAvÀgÀzÀ
JgÀqÀÄ ªÉÄÊ®ÄUÀ¼À£ÀÄß ¥Àæw UÀAmÉUÉ 4 ªÉÄÊ°£ÀAvÉ, PÉÆ£ÉAiÀÄ JgÀqÀÄ ªÉÄÊ®ÄUÀ¼À£ÀÄß ¥Àæw UÀAmÉUÉ 3 ªÉÄÊ°£ÀAvÉ
PÀæ«Ä¸ÀĪÀ£ÀÄ. CªÀ£À ¥ÀÆtð ¥ÀæAiÀiÁtzÀ ¸ÀgÁ¸Àj ªÉÃUÀ PÀAqÀÄ»r¬Äj.
31. 1, 4 ªÀÄvÀÄÛ 16 PÉÌ AM > GM > HM JAzÀÄ vÉÆÃj¹.
32. MAzÀÄ ªÉÃ¼É X : 4, 4 DVzÀÝgÉ, AM = GM = HM JAzÀÄ vÉÆÃj¹.
33. F zÀvÁÛA±ÀPÉÌ PɼÀV£À ZÀvÀÄxÁðAPÀ, ªÉÄð£À ZÀvÀÄxÁðAPÀ ªÀÄvÀÄÛ 8£ÉAiÀÄ zÀ±ÁAPÀªÀ£ÀÄß ¯ÉQ̹.
22, 26, 14, 30, 18, 11, 35, 41, 12, 32.
34. F zÀvÁÛA±À¢AzÀ ªÉÆzÀ®£ÉAiÀÄ ZÀvÀÄxÁðAPÀ ªÀÄvÀÄÛ DgÀ£ÉAiÀÄ zÀ±ÁAPÀªÀ£ÀÄß ¯ÉQ̹.
X 58 59 60 61 62 63 64 65 66
f 2 3 6 15 10 5 4 3 2

35. F «vÀgÀuɬÄAzÀ 9£ÉAiÀÄ zÀ±ÁAPÀ, 55£ÉAiÀÄ ±ÀvÁAPÀªÀ£ÀÄß ¯ÉQ̹.
C.I. 1-3 3-5 5-7 7-9 9-11 11-13 13-15 15-17
f 6 53 85 56 21 16 4 4

36. F zÀvÁÛA±ÀPÉÌ ZÀvÀÄxÀðPÀ ªÁå¦Û ªÀÄvÀÄÛ CgÉ ZÀvÀÄxÀðPÀ ªÁå¦Û ¯ÉQ̹.
11, 15, 16, 9, 14, 19, 10, 12, 8, 17, 20, 23, 22.
37. F PɼÀUÉ ¤ÃrzÀ zÀvÁÛA±ÀPÉÌ ZÀvÀÄxÀðPÀ «ZÀ®£É ¯ÉQ̹.
X 2 4 6 8 10 12
f 3 5 10 12 6 4

38. F PɼÀUÉ ¤ÃrzÀ zÀvÁÛA±ÀPÉÌ CgÉ ZÀvÀÄxÀðPÀ ªÁå¦Û ªÀÄvÀÄÛ EzÀgÀ ¸Á¥ÉÃPÀë C¼ÀvÉAiÀÄ£ÀÄß ¯ÉQ̹.
ªÀAiÀĸÀÄì (ªÀµÀðUÀ¼À°è) 20 30 40 50 60 70 80
ªÀåQÛUÀ¼À ¸ÀASÉå 03 61 132 153 140 51 03
39. F «vÀgÀuÉUÉ ZÀvÀÄxÀðPÀ «ZÀ®£ÉAiÀÄ ¸ÀºÀUÀÄtPÀ ¯ÉQ̹.
PÀÆ° (gÀÆ.) 60-64 64-68 68-72 72-76 76-80 80-84 84-88
PÉ®¸ÀUÁgÀgÀ ¸ÀASÉå 12 18 16 14 12 8 8
40. F «vÀgÀuÉUÉ CgÉ ZÀvÀÄxÀðPÀ ªÁå¦Û PÀAqÀÄ»r¬Äj.
ªÀAiÀĸÀÄì (ªÀµÀðUÀ¼À°è) < 25 < 30 < 35 < 40 < 45 < 50 < 55
£ËPÀgÀgÀ ¸ÀASÉå 10 25 75 130 170 189 200
41. F zÀvÁÛA±ÀPÉÌ ¸ÀgÁ¸Àj¬ÄAzÀ ¸ÀgÁ¸Àj «ZÀ®£É ªÀÄvÀÄÛ EzÀgÀ ¸ÀºÀUÀÄtPÀ ¯ÉQ̹.
100, 150, 200, 360, 490, 500, 600.

26

¥ÀæxÀªÀÄ ¦.AiÀÄÄ.¹. ¸ÀASÁå±Á¸ÀçÛ ¥Àæ±Éß PÉÆñÀ
42. F zÀvÁÛA±ÀPÉÌ ¸ÀgÁ¸Àj¬ÄAzÀ ¸ÀgÁ¸Àj «ZÀ®£É ¯ÉQ̹.
ZÀ®PÀ 10 11 12 13
f 3 12 18 12
43. F «vÀgÀuÉUÉ ¸ÀgÁ¸Àj¬ÄAzÀ ¸ÀgÁ¸Àj «ZÀ®£É PÀAqÀÄ»¬Äj.
JvÀgÛ À (EAZÀÄ) 60 61 62 63 64 65 66 67 68
ªÀåQÛUÀ¼À ¸ÀASÉå 2 1 14 29 25 12 10 4 2
44. F MAzÀÄ ¤¢ðµÀÖ d£ÁAUÀPÉÌ ¸ÉÃjzÀ eÉÆÃrUÀ¼À ªÀAiÀĹì£À ªÀåvÁå¸ÀPÉÌ ¸ÀA§A¢ü¹zÀ F «vÀgÀuÉUÉ ¸ÀgÁ¸Àj¬ÄAzÀ
¸ÀgÁ¸Àj «ZÀ®£É PÀAqÀÄ»¬Äj.
ªÀåvÁå¸À (ªÀµÀðUÀ¼À°è) 0-2 2-4 4-6 6-8 8-10 10-12
eÉÆÃrUÀ¼À ¸ÀASÉå 220 345 452 280 63 10
45. F «vÀgÀuÉUÉ ¸ÀgÁ¸Àj¬ÄAzÀ ¸ÀgÁ¸Àj «ZÀ®£É ¯ÉQ̹.
C.I. 2–4 4–6 6–8 8 – 10 10 – 12
f 3 5 8 4 2
46. F zÀvÁÛA±ÀPÉÌ ªÀÄzsÁåAPÀ¢AzÀ ¸ÀgÁ¸Àj «ZÀ®£É ªÀÄvÀÄÛ EzÀgÀ ¸ÀºÀUÀÄtPÀ ¯ÉQ̹.
37, 45, 52, 46, 56, 40, 47, 55, 43.
47. F PɼÀV£À DªÀÈwÛ «vÀgÀuÉUÉ ªÀÄzsÁåAPÀ¢AzÀ ¸ÀgÁ¸Àj «ZÀ®£ÉAiÀÄ ¸ÀºÀUÀÄtPÀ ¯ÉQ̹.
X 5 6 7 8 9 10
f 8 12 18 8 2 1
48. F PɼÀV£À «vÀgÀuÉUÉ ªÀÄzsÁåAPÀ¢AzÀ ¸ÀgÁ¸Àj «ZÀ®£ÉAiÀÄ ¸ÀºÀUÀÄtPÀ ¯ÉQ̹.
ªÀAiÀĸÀÄì (ªÀµÀðUÀ¼À°è) 16 17 18 19 20 21 22 23 24
ªÀåQÛUÀ¼À ¸ÀASÉå 4 5 7 12 20 13 5 0 4
49. F PɼÀV£À «vÀgÀuÉUÉ ªÀÄzsÁåAPÀ¢AzÀ ¸ÀgÁ¸Àj «ZÀ®£ÉAiÀÄ ¸ÀºÀUÀÄtPÀ ¯ÉQ̹.
CAPÀUÀ¼ÀÄ 10 PÀÆÌ 20 PÀÆÌ 30 PÀÆÌ 40 PÀÆÌ 50 PÀÆÌ
PÀrªÉÄ PÀrªÉÄ PÀrªÉÄ PÀrªÉÄ PÀrªÉÄ
«zÁåyðUÀ¼À ¸ÀASÉå 3 8 17 20 25
50. MAzÀÄ ¤¢ðµÀÖ QgÀÄ ¥ÀjÃPÉëAiÀÄ°è ºÀvÀÄÛ «zÁåyðUÀ¼À CAPÀUÀ¼ÀÄ EAwªÉ. §ºÀÄ®PÀ¢AzÀ ¸ÀgÁ¸Àj «ZÀ®£É ªÀÄvÀÄÛ
CzÀgÀ ¸ÀºÀUÀÄtPÀªÀ£ÀÄß ¯ÉQ̹.
CAPÀUÀ¼ÀÄ (E¥ÀàÀvÀÛPÉÌ) : 7, 4, 10, 9, 15, 12, 7, 9, 7 ªÀÄvÀÄÛ 18.
51. F PɼÀUÉ ¤ÃrzÀ zÀvÁÛA±ÀPÉÌ §ºÀÄ®PÀ¢AzÀ ¸ÀgÁ¸Àj «ZÀ®£É ¯ÉQ̹.
X 0 1 2 3 4 5 6
f 18 22 35 25 20 12 2
52. ««zsÀ ¸ÀA¸ÉÜUÀ¼À ¯Á¨sÀUÀ½UÉ ¸ÀA§A¢ü¹zÀ F «vÀgÀuÉUÉ §ºÀÄ®PÀ¢AzÀ ¸ÀgÁ¸Àj «ZÀ®£É ¯ÉQ̹.
¯Á¨sÀ (‘000 gÀÆ.UÀ¼À°è) 20-40 40-60 60-80 80-100 100-120
¸ÀA¸ÉÜUÀ¼À ¸ÀASÉå 16 19 41 24 15
53. F zÀvÁÛA±ÀPÉÌ ¤AiÀÄvÀ «ZÀ®£ÉAiÀÄ£ÀÄß PÀAqÀÄ»r¬Äj: 25, 50, 45, 30, 70, 42, 36, 48, 34, 60.
54. ªÉÆzÀ® K¼ÀÄ ¸Áé¨sÁ«PÀ ¸Àj (¸ÀªÀÄ) ¸ÀASÉåUÀ¼À ¤AiÀÄvÀ «ZÀ®£ÉAiÀÄ£ÀÄß PÀAqÀÄ»r¬Äj.

27

¥ÀæxÀªÀÄ ¦.AiÀÄÄ.¹. ¸ÀASÁå±Á¸ÀçÛ ¥Àæ±Éß PÉÆñÀ
55. 100 ¨É¯ÉUÀ¼À MAzÀÄ «vÀgÀuÉAiÀÄ ¸ÀgÁ¸Àj ªÀÄvÀÄÛ ¤AiÀÄvÀ «ZÀ®£ÉUÀ¼ÀÄ PÀæªÀĪÁV 50 ªÀÄvÀÄÛ 5. 150 ¨É¯ÉUÀ¼À
ªÀÄvÉÆÛAzÀÄ «vÀgÀuÉAiÀÄ ¸ÀgÁ¸Àj ªÀÄvÀÄÛ ¤AiÀÄvÀ «ZÀ®£ÉUÀ¼ÀÄ PÀæªÀĪÁV 40 ªÀÄvÀÄÛ 4. MmÁÖgÉ 250 ¨É¯ÉUÀ¼À£ÀÄß
vÀUÉzÀÄPÉÆAqÁUÀ ¤AiÀÄvÀ «ZÀ®£É PÀAqÀÄ»r¬Äj.
56. F «vÀgÀuÉUÉ ¤AiÀÄvÀ «ZÀ®£ÉAiÀÄ£ÀÄß ¯ÉQ̹.
X 8 11 17 20 25 30 35
f 2 3 4 1 5 7 3
57. F «vÀgÀuÉUÉ «ZÀ®£ÉAiÀÄ£ÀÄß ¯ÉQ̹.
X 4 5 6 7 8 9 10
f 6 12 15 28 29 14 15
58. F zÀvÁÛA±ÀPÉÌ ¤AiÀÄvÀ «ZÀ®£É ªÀÄvÀÄÛ «ZÀ®£ÉUÀ¼À£ÀÄß PÀAqÀÄ»r¬Äj.
C.I. 0-6 6-12 12-18 18-24 24-30 30-36 36-42
f 19 25 36 72 51 43 28
59. F PÉÆõÀÖPÀ¢AzÀ PÉÆæÃrüPÀÈvÀ ¤AiÀÄvÀ «ZÀ®£É PÀAqÀÄ»r¬Äj.
¤zÀ±ÀðPÀ- I ¤zÀ±ÀðPÀ- II
¥Áæ¥ÁÛAPÀUÀ¼À ¸ÀASÉå 50 100
¸ÀgÁ¸Àj 54.1 50.3
¤AiÀÄvÀ «ZÀ®£É 8 7
60. MAzÀÄ ¥ÀjÃPÉëAiÀÄ°è A, B ªÀÄvÀÄÛ C JA§ ªÀÄÆgÀÄ «zÁåyðUÀ¼ÀÄ UÀ½¹zÀ ¸ÀgÁ¸Àj CAPÀUÀ¼ÀÄ PÀæªÀĪÁV 50, 44, 20.
CAPÀUÀ¼À ¤AiÀÄvÀ «ZÀ®£ÉUÀ¼ÀÄ PÀæªÀĪÁV 15, 11, 3. AiÀiÁgÀÄ ºÉZÀÄÑ ¹ÜgÀ?

ºÀvÀÄÛ CAPÀzÀ ¥Àæ±ÉßUÀ¼ÀÄ:
1. F PɼÀV£À «vÀgÀuÉUÉ ªÀÄzsÁåAPÀ ªÀÄvÀÄÛ §ºÀÄ®PÀ PÀAqÀÄ»r¬Äj.
C-I 200-400 400-600 600-800 800-1000 1000-1200 1200-1400
f 6 9 15 10 7 3
2. F zÀvÁÛA±ÀPÉÌ ¤AiÀÄvÀ «ZÀ®£É, «ZÀ®£É ªÀÄvÀÄÛ ªÀiÁ¦ð£À UÀÄuÁAPÀ PÀAqÀÄ»r¬Äj.
PÀÆ° (gÀÆ.) < 10 < 20 < 30 < 40 < 50 < 60 < 70 < 80
ªÀåQÛUÀ¼À ¸ÀASÉå 12 30 65 107 157 202 222 230
3. A ªÀÄvÀÄÛ B JA§ E§âgÀÄ ¨ÁåmïìªÀÄ£ÀßgÀÄ ««zsÀ E¤ßAUïìUÀ¼À°è UÀ½¹zÀ gÀ£ïßUÀ¼À ¸ÀASÉå F PɼÀV£ÀAwªÉ.
A 12 115 6 73 7 19 119 36 84 29
B 47 12 76 42 4 51 37 48 13 0
AiÀiÁgÀÄ GvÀÛªÀÄ gÀ£ïß UÀ½¹zÁÝgÉ? AiÀiÁgÀÄ ºÉZÀÄÑ ¹ÜgÀªÁVzÁÝgÉ?
4. «zÁåyðUÀ¼À vÀÆPÀUÀ¼À «vÀgÀuÉ F PɼÀV£ÀAwzÉ. CªÀgÀ ªÀiÁ¦ð£À UÀÄuÁAPÀUÀ¼À£ÀÄß ºÉÆðPÉ ªÀiÁr.
vÀÆPÀ (PÉ.f) 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70
vÀgÀUÀw A 7 10 20 18 7
«zÁåyðUÀ¼À ¸ÀASÉå
vÀgÀUÀw B 5 9 21 15 6

28

¥ÀæxÀªÀÄ ¦.AiÀÄÄ.¹. ¸ÀASÁå±Á¸ÀçÛ ¥Àæ±Éß PÉÆñÀ
5. F «vÀgÀuÉUÉ PÁ®ð ¦AiÀÄgï ¸À£ÀߣÀ «µÀªÀÄvÉAiÀÄ UÀÄtPÀ ¯ÉQ̹.
CAPÀUÀ¼ÀÄ >0 > 10 > 20 > 30 > 40 > 50 > 60 > 70 > 80
«zÁåyðUÀ¼À ¸ÀASÉå 150 140 100 80 80 70 30 14 0

6. F «vÀgÀuÉUÉ PÁ®ð ¦AiÀÄgï ¸À£ÀߣÀ «µÀªÀÄvÉAiÀÄ UÀÄtPÀ ¯ÉQ̹.

C.I. 70-80 60-70 50-60 40-50 30-40 20-30 10-20 0-10
f 11 12 30 35 21 11 6 5

7. F «vÀgÀuÉUÉ PÁ®ð ¦AiÀÄgï ¸À£ÀߣÀ «µÀªÀÄvÉAiÀÄ UÀÄtPÀ ¯ÉQ̹.
CAPÀUÀ¼ÀÄ 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80
«zÁåyðUÀ¼À ¸ÀASÉå 10 40 20 0 10 40 16 14

8. F PɼÀUÉ ¤ÃrzÀ zÀvÁÛA±ÀPÉÌ ¨Ë°AiÀÄ «µÀªÀÄvÉAiÀÄ UÀÄtPÀ ¯ÉQ̹.

C.I. 30-40 40-50 50-60 60-70 70-80 80-90 90-100
f 1 3 11 21 43 32 9

9. ZÀvÀÄxÁðAPÀ DzsÁjvÀ «µÀªÀÄvÉAiÀÄ UÀÄtPÀ ¯ÉQ̹.

C.I. 10-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89
f 5 9 14 20 25 15 8 4

10. F PɼÀUÉ ¤ÃrzÀ zÀvÁÛA±ÀPÉÌ ¨Ë°AiÀÄ «µÀªÀÄvÉAiÀÄ UÀÄtPÀ ¯ÉQ̹.
§AqÀªÁ¼À (®PÀë gÀÆ.) 1 – 5 6 – 10 10 – 15 16 – 20 20 – 25 26 – 30 31 – 35
PÀA¥À¤UÀ¼À ¸ÀASÉå 20 27 29 38 48 53 70

29

¥ÀæxÀªÀÄ ¦.AiÀÄÄ.¹. ¸ÀASÁå±Á¸ÀçÛ ¥Àæ±Éß PÉÆñÀ
Unit - VI
¢éZÀ®PÀ zÀvÁÛA±ÀzÀ «±ÉÃè µÀuÉ
¸ÀºÀ¸ÀA§AzsÀ ªÀÄvÀÄÛ ¸ÀªÀiÁ±ÀæAiÀÄt
MAzÀÄ CAPÀzÀ ¥Àæ±ÉßUÀ¼ÀÄ:
1. ¸ÀºÀ¸ÀA§AzsÀªÀ£ÀÄß ªÁåSÁ夹.
2. JgÀqÀÄ ZÀ®PÀUÀ¼À £ÀqÀÄ«£À IÄuÁvÀäPÀ ¸ÀºÀ¸ÀA§AzsÀPÉÌ MAzÀÄ GzÁºÀgÀuÉ PÉÆr.
3. JgÀqÀÄ ZÀ®PÀUÀ¼À £ÀqÀÄ«£À zsÀ£ÁvÀäPÀ ¸ÀºÀ¸ÀA§AzsÀPÉÌ MAzÀÄ GzÁºÀgÀuÉ PÉÆr.
4. ¸ÀºÀ¸ÀA§AzsÀ E®è¢gÀĪÀ MAzÀÄ GzÁºÀgÀuÉ PÉÆr.
5. ¸ÀgÀ¼À ¸ÀºÀ¸ÀA§AzsÀ JAzÀgÉãÀÄ?
6. ¸ÀgÀ¼À ¸ÀºÀ¸ÀA§AzsÀPÉÌ MAzÀÄ GzÁºÀgÀuÉ PÉÆr.
7. §ºÀÄ ¸ÀºÀ¸ÀA§AzsÀ JAzÀgÉãÀÄ?
8. PÁgÀt«zsÁ£À JAzÀgÉãÀÄ?
9. PÀÈvÀPÀ ¸ÀºÀ¸ÀA§AzsÀ CxÀðªÉãÀÄ?
10. ¸ÀA¥ÀÆtð (¥Àj¥ÀÆtð) ¸ÀºÀ¸ÀA§AzsÀ JAzÀgÉãÀÄ?
11. eÁ»gÁw£À RZÀÄð ªÀÄvÀÄÛ ¸ÀA¨sÀªÀ¤ÃAiÀÄ ªÀiÁgÁl JA§ ZÀ®PÀUÀ¼À £ÀqÀÄ«£À ¸ÀºÀ¸ÀA§AzsÀ AiÀiÁªÀ jÃwAiÀÄzÀÄÝ?
12. £ËPÀgÀgÀ ¸ÀASÉå ªÀÄvÀÄÛ ªÉÃvÀ£ÀzÀ RZÀÄð JA§ ZÀ®PÀUÀ¼À £ÀqÀÄ«£À ¸ÀºÀ¸ÀA§AzsÀ AiÀiÁªÀ jÃwAiÀÄzÀÄÝ?
13. zsÀ£À«¤AiÉÆÃUÀ ªÀÄvÀÄÛ ªÀiÁgÁl JA§ ZÀ®PÀUÀ¼À £ÀqÀÄ«£À ¸ÀºÀ¸ÀA§AzsÀ AiÀiÁªÀ ¥ÀæPÁgÀzÀÄÝ?
14. ªÉÃvÀ£À ªÀÄvÀÄÛ DzÁAiÀÄ vÉjUÉ JA§ ZÀ®PÀUÀ¼À £ÀqÀÄ«£À ¸ÀºÀ¸ÀA§AzsÀ AiÀiÁªÀ ¥ÀæPÁgÀzÀÄÝ?
15. PÀÈvÀPÀ ¸ÀºÀ¸ÀA§AzsÀPÉÌ MAzÀÄ GzÁºÀgÀuÉ PÉÆr.
16. ZÀzÀÄjPÉAiÀÄ avÀæ JAzÀgÉãÀÄ?
17. ZÀzÀÄjPÉAiÀÄ avÀæzÀ MAzÀÄ UÀÄtªÀ£ÀÄß w½¹.
18. ZÀzÀÄjPÉAiÀÄ avÀæzÀ MAzÀÄ zÉÆõÀªÀ£ÀÄß w½¹.
19. PÁ®ð¦AiÀÄgï ¸À£ÀߣÀ ¸ÀºÀ¸ÀA§AzsÀzÀ UÀÄtPÀªÀ£ÀÄß ªÁåSÁ夹.
20. JgÀqÀÄ ¸ÀévÀAvÀæ ZÀ®PÀUÀ½UÉ ‘r’ ¨É¯É JµÀÄÖ?
21. r = -1 DzÁUÀ, ¸ÀºÀ¸ÀA§AzsÀzÀ jÃwAiÀÄ£ÀÄß ºÉ¸Àj¹.
22. MAzÀÄ ªÉÃ¼É r = 1 DzÀgÉ, ¤ªÀÄä wêÀiÁð£ÀªÉãÀÄ?
23. PÁ®ð¦AiÀÄgï ¸À£ÀߣÀ ¸ÀºÀ¸ÀA§AzsÀzÀ UÀÄtPÀzÀ ªÁå¦Û JµÀÄÖ?
24. zÀvÁÛA±À UÀÄuÁvÀäPÀ jÃwAiÀÄzÁÝUÀ ¸ÀºÀ¸ÀA§AzsÀzÀ UÀÄtPÀ ¯ÉQ̸À®Ä G¥ÀAiÉÆÃV¸ÀĪÀ «zsÁ£À AiÀiÁªÀÅzÀÄ?
25. ¹àAiÀÄgï ªÀÄ£ÀߣÀ zÀeÁð ¸ÀºÀ¸ÀA§AzsÀ UÀÄtPÀzÀ MAzÀÄ «ÄwAiÀÄ£ÀÄß w½¹.
26. MAzÀÄ ªÉÃ¼É  d2  0 DzÁUÀ, ¹àAiÀÄgï ªÀÄ£ÀߣÀ zÀeÁð ¸ÀºÀ¸ÀA§AzsÀ UÀÄtPÀzÀ ¨É¯É JµÀÄÖ?
27. ¸ÀªÀiÁ±ÀæAiÀÄt (»AZÀ®£É) JAzÀgÉãÀÄ?
28. y ªÉÄð£À x ¸ÀªÀiÁ±ÀæAiÀÄt ¸À«ÄÃPÀgÀtªÀ£ÀÄß §gɬÄj.
29. x ªÉÄð£À y ¸ÀªÀiÁ±ÀæAiÀÄt ¸À«ÄÃPÀgÀtªÀ£ÀÄß §gɬÄj.
30. ¸ÀºÀ¸ÀA§AzsÀzÀ UÀÄtPÀ ªÀÄvÀÄÛ ¸ÀªÀiÁ±ÀæAiÀÄt ¸ÀºÀUÀÄtPÀUÀ¼À £ÀqÀÄ«£À ¸ÀA§AzsÀªÀ£ÀÄß §gɬÄj.
31. ¸ÀªÀiÁ±ÀæAiÀÄt gÉÃSÉUÀ¼ÀÄ ®A¨sÀªÁVzÁÝUÀ, ¤ªÀÄä wêÀiÁð£ÀªÉãÀÄ?
32. JgÀqÀÄ ¸ÀªÀiÁ±ÀæAiÀÄt ¸À«ÄÃPÀgÀtUÀ¼À bÉÃzÀ£À ©AzÀÄ«£À ¸ÁÜ£À(PÀæªÀÄ AiÀÄUÀä) §gɬÄj.
33. MAzÀÄ ¸ÀªÀiÁ±ÀæAiÀÄt gÉÃSÉ ªÀÄvÉÆÛAzÀgÀ ªÀÄÆ®PÀ ºÁzÀĺÉÆÃzÁUÀ, ¤ªÀÄä wêÀiÁð£ÀªÉãÀÄ?

30

¥ÀæxÀªÀÄ ¦.AiÀÄÄ.¹. ¸ÀASÁå±Á¸ÀçÛ ¥Àæ±Éß PÉÆñÀ
JgÀqÀÄ CAPÀzÀ ¥Àæ±ÉßUÀ¼ÀÄ:
1. JgÀqÀÄ jÃwAiÀÄ ¸ÀºÀ¸ÀA§AzsÀUÀ¼À£ÀÄß w½¹.
2. ¸ÀºÀ¸ÀA§AzsÀªÀ£ÀÄß ¯ÉQ̸ÀĪÀ ««zsÀ «zsÁ£ÀUÀ¼À£ÀÄß w½¹.
3. JgÀqÀÄ ZÀ®PÀUÀ¼À ªÀÄzsÀå zsÀ£ÁvÀäPÀ ¸ÀºÀ¸ÀA§AzsÀ vÉÆÃj¸ÀĪÀ ZÀzÀÄjPÉAiÀÄ avÀæ J¼É¬Äj.
4. JgÀqÀÄ ZÀ®PÀUÀ¼À ¸ÀA¥ÀÆtð IÄuÁvÀäPÀ ¸ÀºÀ¸ÀA§AzsÀ vÉÆÃj¸ÀĪÀ ZÀzÀÄjPÉAiÀÄ avÀæ J¼É¬Äj.
5. ¸ÀºÀ¸ÀA§AzsÀªÀ£ÀÄß ªÁåSÁ夹. MAzÀÄ GzÁºÀuÉ PÉÆr.
6. zsÀ£ÁvÀäPÀ ¸ÀºÀ¸ÀA§AzsÀ JAzÀgÉãÀÄ? MAzÀÄ GzÁºÀuÉ PÉÆr.
7. EªÀÅUÀ¼À ¸ÀºÀ¸ÀA§AzsÀ AiÀiÁªÀ ¥ÀæPÁgÀzÀÄÝ
a) vÀgÀPÁjAiÀÄ GvÁàzÀ£É ªÀÄvÀÄÛ ¨É¯É.
b) ºÀA¢AiÀÄ GvÁàzÀ£É ªÀÄvÀÄÛ ºÀA¢AiÀÄ UÉƧâgÀzÀ GvÁàzÀ£É.
8. ¸ÀºÀ¸ÀA§AzsÀªÀ£ÀÄß C¨sÁå¸À ªÀiÁqÀĪÀ JgÀqÀÄ G¥ÀAiÉÆÃUÀUÀ¼À£ÀÄß w½¹.
9. ZÀzÀÄjPÉAiÀÄ avÀæzÀ JgÀqÀÄ UÀÄtUÀ¼À£ÀÄß w½¹.
10. γ £À JgÀqÀÄ UÀÄtUÀ¼À£ÀÄß w½¹.
11. MAzÀÄ ¢éZÀ®PÀzÀ zÀvÁÛA±ÀzÀ°è Cov(x,y)=V(x)=V(y) DzÀgÉ, rxy PÀAqÀÄ»r¬Äj.
12. MAzÀÄ zÀeÉð ‘m’ ¸À® ¥ÀÄ£ÀgÁªÀvÀð£É DzÁUÀ, ¹àAiÀÄgï ªÀÄ£ÀߣÀ zÀeÁð ¸ÀºÀ¸ÀA§AzsÀ UÀÄtPÀzÀ ¸ÀÆvÀæ §gɬÄj.
13. ¹àAiÀÄgï ªÀÄ£ÀߣÀ zÀeÁð ¸ÀºÀ¸ÀA§AzsÀ UÀÄtPÀzÀ JgÀqÀÄ UÀÄtUÀ¼À£ÀÄß w½¹.
14. x ªÀÄvÀÄÛ y ªÉÄð£À MAzÀÄ ¢éZÀ®PÀzÀ zÀvÁÛA±ÀzÀ°è, Var(x) = 9 , Var(y) = 49 ªÀÄvÀÄÛ Cov(x , y) = 20. r
PÀAqÀÄ»r¬Äj.
15. Cov (x , y) = -100 , V(x) = 400 ªÀÄvÀÄÛ S.D(y) = 5 JAzÀÄ PÉÆmÁÖUÀ, r PÀAqÀÄ»r¬Äj.
16. MAzÀÄ ¢éZÀ®PÀzÀ zÀvÁÛA±ÀzÀ°è, ¸ÀºÀ«ZÀ®£É 20 ªÀÄvÀÄÛ «ZÀ®£ÉUÀ¼ÀÄ PÀæªÀĪÁV 25 ªÀÄvÀÄÛ 36 DzÀgÉ, r
PÀAqÀÄ»r¬Äj.

  
17.   x  x  = 1800,   y  y  = 200 ªÀÄvÀÄÛ  x  x y  y = 240 DzÁUÀ, r PÀAqÀÄ»r¬Äj.
2 2

18. x ªÀÄvÀÄÛ y ZÀ®PÀUÀ¼À £ÀqÀÄ«£À ¸ÀºÀ¸ÀA§AzsÀzÀ UÀÄtPÀ 0.4. CªÀÅUÀ¼À ¸ÀºÀ«ZÀ®£É 240. x £À ¤AiÀÄvÀ «ZÀ®£É 20
DzÀgÉ, y £À ¤AiÀÄvÀ «ZÀ®£É PÀAqÀÄ»r¬Äj.
19. n = 9 ªÀÄvÀÄÛ Σd2 = 24 DzÀgÉ, ¹àAiÀÄgï ªÀÄ£ÀߣÀ zÀeÁð ¸ÀºÀ¸ÀA§AzsÀ UÀÄtPÀ PÀAqÀÄ»r¬Äj.
20. ¸ÀªÀiÁ±ÀæAiÀÄt ¸ÀºÀUÀÄtPÀUÀ¼À JgÀqÀÄ UÀÄtzsÀªÀÄðUÀ¼À£ÀÄß w½¹.
21. 𝐫 = ±√𝐛𝐱𝐲 𝐛𝐲𝐱 JAzÀÄ ¸Á¢ü¹.
22. ¸ÀªÀiÁ±ÀæAiÀÄt «±ÉèõÀuÉAiÀÄ JgÀqÀÄ G¥ÀAiÉÆÃUÀ¼À£ÀÄß w½¹.
23. ¸ÀªÀiÁ±ÀæAiÀÄt gÉÃSÉUÀ¼À JgÀqÀÄ UÀÄtzsÀªÀÄðUÀ¼À£ÀÄß w½¹.
24. r = 0.4, 𝛔𝐱 = 12 ªÀÄvÀÄÛ 𝛔𝐲 = 15 DzÁUÀ, bxy ¨É¯É PÀAqÀÄ»r¬Äj.
25. r = 0.5, 𝛔𝐱 = 10 ªÀÄvÀÄÛ 𝛔𝐲 = 15 DzÁUÀ, byx ¨É¯É PÀAqÀÄ»r¬Äj.
26. bxy = 0.5, S.D (x) = 4 ªÀÄvÀÄÛ S.D(y) = 5 DzÁUÀ, r PÀAqÀÄ»r¬Äj.
27. bxy =0.6, r =0.75 ªÀÄvÀÄÛ S.D(x)= 3 DzÁUÀ, S.D(y) PÀAqÀÄ»r¬Äj.

31

¥ÀæxÀªÀÄ ¦.AiÀÄÄ.¹. ¸ÀASÁå±Á¸ÀçÛ ¥Àæ±Éß PÉÆñÀ
LzÀÄ CAPÀzÀ ¥Àæ±ÉßUÀ¼ÀÄ:
1. F zÀvÁÛA±ÀPÉÌ ZÀzÀÄjPÉAiÀÄ avÀæ J¼ÉzÀÄ, «±Éèö¹.
x 15 18 20 19 14 12 22 11
y 14 16 13 15 18 18 11 20
2. F PɼÀUÉ ¤ÃrzÀ zÀvÁÛA±ÀPÉÌ ZÀzÀÄjPÉAiÀÄ avÀæ J¼ÉzÀÄ, «±Éèö¹.
x 50 100 150 200 250 300 350
y 12 14 13 14 16 18 19

3. F zÀvÁÛA±À¢AzÀ PÁ®ð ¦AiÀÄgï ¸À£ÀߣÀ ¸ÀºÀ¸ÀA§AzsÀzÀ UÀÄtPÀ ¯ÉQ̹.
x 12 9 8 10 11 13 7
y 14 8 6 9 11 12 3

4. F zÀvÁÛA±À¢AzÀ PÁ®ð ¦AiÀÄgï ¸À£ÀߣÀ ¸ÀºÀ¸ÀA§AzsÀzÀ UÀÄtPÀ ¯ÉQ̹.
x 40 42 46 48 50 56
y 10 12 15 23 27 30
5. F zÀvÁÛA±À¢AzÀ PÁ®ð ¦AiÀÄgï ¸À£ÀߣÀ ¸ÀºÀ¸ÀA§AzsÀzÀ UÀÄtPÀ ¯ÉQ̹.
x 36 41 46 59 46 65 31 68 41 70
y 48 60 53 36 50 42 66 44 58 65
6. RZÀÄð ªÀÄvÀÄÛ GvÁàzÀ£Á ªÉZÀÑPÉÌ ¸ÀA§A¢ü¹zÀ F zÀvÁÛA±À¢AzÀ PÁ®ð ¦AiÀÄgï ¸À£ÀߣÀ ¸ÀºÀ¸ÀA§AzsÀzÀ UÀÄtPÀ ¯ÉQ̹.
Overheads(‘000Rs) 80 90 100 110 120 130 140 150 160
ªÉZÀÑ (‘000gÀÆ.) 15 15 16 19 17 18 16 18 19

7. 8 «zÁåyðUÀ¼À ¸ÀASÁå±Á¸ÀçÛ ªÀÄvÀÄÛ UÀtÂvÀ±Á¸ÀÛçzÀ CAPÀUÀ¼ÀÄ EAwªÉ. ¹àAiÀÄgï ªÀÄ£ÀߣÀ zÀeÁð ¸ÀºÀ¸ÀA§AzsÀ UÀÄtPÀ
PÀAqÀÄ»r¬Äj.
¸ÀASÁå±Á¸ÀçÛ zÀ CAPÀUÀ¼ÀÄ 25 43 27 35 54 61 37 45
UÀtÂvÀ±Á¸ÀÛçzÀ CAPÀUÀ¼ÀÄ 35 47 20 37 63 54 28 40
8. ªÀtðavÀæ ¸ÀàzsÉðUÉ ¸ÀA§A¢ü¹zÀAvÉ E§âgÀÄ wÃ¥ÀÄðUÁgÀgÀÄ ¤ÃrzÀ zÀeÉðUÀ¼ÀÄ EAwªÉ. ¹àAiÀÄgï ªÀÄ£ÀߣÀ zÀeÁð
¸ÀºÀ¸ÀA§AzsÀ UÀÄtPÀ PÀAqÀÄ»r¬Äj.
ªÀtðavÀæ 1 2 3 4 5 6
wÃ¥ÀÄðUÁgÀ I 6 2 1 3 5 4
wÃ¥ÀÄðUÁgÀ II 4 1 3 5 6 2

9. F zÀvÁÛA±ÀPÉÌ zÀeÁð ¸ÀºÀ¸ÀA§AzsÀ UÀÄtPÀ ¯ÉQ̹.
x 80 78 75 75 68 67 60 59
y 12 13 14 14 14 16 15 17
10. F zÀvÁÛA±ÀªÀÅ ¯ÉPÀ̱Á¸ÀÛç ªÀÄvÀÄÛ ¸ÀASÁå±Á¸ÀçÛ zÀ CAPÀUÀ½UÉ ¸ÀA§A¢ü¹zÉ.
¯ÉPÀ̱Á¸ÀçÛ zÀ CAPÀUÀ¼ÀÄ 78 82 78 62 46 52 57 57 58 57
¸ÀASÁå±Á¸ÀçÛ zÀ CAPÀUÀ¼ÀÄ 68 81 73 64 52 56 48 68 73 78
¹àAiÀÄgï ªÀÄ£ÀߣÀ zÀeÁð ¸ÀºÀ¸ÀA§AzsÀ UÀÄtPÀ ¯ÉQ̹ F ¨É¯ÉAiÀÄ §UÉÎ «±ÉÃè ¶¹.
11. ¸ÀºÀ¸ÀA§AzsÀ ªÀÄvÀÄÛ ¸ÀªÀiÁ±ÀæAiÀÄt «±ÉèõÀuÉUÀ¼À £ÀqÀÄ«£À JgÀqÀÄ ªÀåvÁå¸ÀUÀ¼À£ÀÄß w½¹.

32

¥ÀæxÀªÀÄ ¦.AiÀÄÄ.¹. ¸ÀASÁå±Á¸ÀçÛ ¥Àæ±Éß PÉÆñÀ
12. F zÀvÁÛA±ÀªÀÅ ªÀµÀðUÀ¼À ¸ÉêÁªÀ¢ü ªÀÄvÀÄÛ DzÁAiÀÄ(¸Á«gÀ gÀÆ.)UÀ½UÉÉ ¸ÀA§A¢ü¹zÉ. DzsÀåvÉAiÀÄ zÀeÉðUÀ¼À£ÀÄß
¥ÀjUÀt¹ zÀeÁð ¸ÀºÀ¸ÀA§AzsÀ ¯ÉQ̹.
¸ÉêÁªÀ¢ü (ªÀµÀðUÀ¼À°è) 3 7 9 1 8 6 10 4 5 2
DzÁAiÀÄ(¸Á«gÀ gÀÆ.) 7 5 3 2 6 4 8 10 9 1

13. x ªÉÄð£À y ¸ÀªÀiÁ±ÀæAiÀÄt ¸À«ÄÃPÀgÀt PÀAqÀÄ»rzÀÄ, x ¨É¯É 9 DzÁUÀ y £À ªÀÄÄ£ÀÆìa ¨É¯É CAzÁf¹.

x 3 6 5 4 4 6 7 5
y 3 2 3 5 3 6 6 4

14. ¥Àw ªÀÄvÀÄÛ ¥ÀwßAiÀÄgÀ ªÀAiÀĹìUÉ ¸ÀA§A¢ü¹zÀ F zÀvÁÛA±À¢AzÀ ¥ÀwßAiÀÄ ªÀAiÀĸÀÄì 18 ªÀµÀð DzÁUÀ, ¥ÀwAiÀÄ
ªÀAiÀĸÀì£ÀÄß CAzÁf¹.
¥ÀwAiÀÄ ªÀAiÀĸÀÄì (ªÀµÀðUÀ¼À°è) 36 23 27 28 28 29 30 31 33 35
¥ÀwßAiÀÄ ªÀAiÀĸÀÄì (ªÀµÀðUÀ¼À°è) 29 19 20 22 27 21 29 27 29 28

15. eÁ»gÁw£À RZÀÄð ªÀÄvÀÄÛ ªÀiÁgÁlzÀ ªÀiÁ»w F PɼÀUÉ ¤ÃqÀ¯ÁVzÉ.
eÁ»gÁw£À RZÀÄð (PÉÆÃn gÀÆ.) ªÀiÁgÁl (PÉÆÃn gÀÆ.)
¸ÀgÁ¸Àj 20 120
¤.« 5 2
¸ÀºÀ¸ÀA§AzsÀzÀ UÀÄtPÀ = 0.8 ªÀÄvÀÄÛ eÁ»gÁw£À RZÀÄð gÀÆ.25 PÉÆÃn DzÁUÀ, ¸ÀA¨sÀªÀ¤ÃAiÀÄ ªÀiÁgÁlªÀ£ÀÄß
CAzÁf¹.
16. PÀ£ÀßqÀ ªÀÄvÀÄÛ EAVèõÀ ¥ÀjÃPÉëUÀ¼À°è «zÁåyðUÀ¼ÀÄ UÀ½¹zÀ CAPÀUÀ¼À «ªÀgÀUÀ¼ÀÄ EAwªÉ.
¸ÀºÀ¸ÀA§AzsÀzÀ UÀÄtPÀ = 0.3.
PÀ£ÀßqÀ EAVèõÀ
¸ÀgÁ¸Àj 40 50
¤.« 10 16

EAVèõÀ£À°è UÀ½¸ÀzÀ CAPÀUÀ¼ÀÄ 30 DzÁUÀ, PÀ£ÀßqÀzÀ°Aè iÀÄ CAPÀUÀ¼À£ÀÄß CAzÁf¹.
17. ¢éZÀ®PÀzÀ MAzÀÄ «vÀgÀuÉAiÀÄ°è ¸ÀªÀiÁ±ÀæAiÀÄt ¸À«ÄÃPÀgÀtUÀ¼ÀÄ:
x ªÉÄð£À y ¸ÀªÀiÁ±ÀæAiÀÄt ¸À«ÄÃPÀgÀt 4y = 9x+15

y ªÉÄð£À x ¸ÀªÀiÁ±ÀæAiÀÄt ¸À«ÄÃPÀgÀt 25x = 6y+7 DzÁUÀ, x , y ªÀÄvÀÄÛ r PÀAqÀÄ»r¬Äj.
18. ¸ÀºÀ¸ÀA§AzsÀzÀ ªÉÄð£À MAzÀÄ ¸ÀA±ÉÆÃzsÀ£Á ¥ÀæAiÉÆÃUÀzÀ°è JgÀqÀÄ ¸ÀªÀiÁ±ÀæAiÀÄt ¸À«ÄÃPÀgÀtUÀ¼ÀÄ 2x-y+1=0 ªÀÄvÀÄÛ
3x-2y+7=0. JAzÀÄ PÀAqÀÄ §A¢zÉ. x ªÀÄvÀÄÛ y UÀ¼À ¸ÀgÁ¸ÀjUÀ¼À£ÀÄß PÀAqÀÄ»r¬Äj. x ªÀÄvÀÄÛ y ZÀ®PÀUÀ¼À
¸ÀªÀiÁ±ÀæAiÀÄt ¸ÀºÀUÀÄtPÀUÀ¼À£ÀÄß ªÀÄvÀÄÛ CªÀÅUÀ¼À £ÀqÀÄ«£À ¸ÀºÀ¸ÀA§AzsÀzÀ UÀÄtPÀªÀ£ÀÄß ¸ÀºÀ PÀAqÀÄ»r¬Äj.

33

¥ÀæxÀªÀÄ ¦.AiÀÄÄ.¹. ¸ÀASÁå±Á¸ÀçÛ ¥Àæ±Éß PÉÆñÀ
ºÀvÀÄÛ CAPÀzÀ ¥Àæ±ÉßUÀ¼ÀÄ:
1. F zÀvÁÛA±À¢AzÀ UÀAqÀÄ ªÀÄPÀ̼À ªÀÄvÀÄÛ ºÉtÄÚ ªÀÄPÀ̼À ¸ÀASÉåUÀ¼À £ÀqÀÄ«£À ¸ÀºÀ¸ÀA§AzsÀzÀ UÀÄtPÀªÀ£ÀÄß ¯ÉQ̹.
UÀAqÀÄ ªÀÄPÀ̼À ºÉtÄÚ ªÀÄPÀ̼À ¸ÀASÉå
¸ÀASÉå 0 1 2 3 4
0 3 4 2 - -
1 4 8 8 2 -
2 - 7 12 8 4
3 - 3 8 8 5
4 - - 3 5 6

2. PÁ®ð ¦AiÀÄgï ¸À£ÀߣÀ ¸ÀºÀ¸ÀA§AzsÀzÀ UÀÄtPÀªÀ£ÀÄß ¯ÉQ̹.

x y 20 – 29 30 – 39 40 – 49 50 – 59
10 – 14 10 10 - -
14 – 18 - 20 8 -
18 – 22 - 10 25 6
22 – 26 - - 7 4

3. F PɼÀUÉ ¤ÃrzÀ zÀvÁÛA±À¢AzÀ PÁ®ð ¦AiÀÄgï ¸À£ÀߣÀ ¸ÀºÀ¸ÀA§AzsÀzÀ UÀÄtPÀªÀ£ÀÄß ¯ÉQ̹.
ªÀAiÀĸÀÄì (ªÀµÀðUÀ¼À°è)
CAPÀUÀ¼ÀÄ
18 19 20 21 22
20 – 25 3 2 - - -
15 – 20 - 5 4 - -
10 – 15 - - 7 10 -
5 – 10 - - - 3 2
0–5 - - - 3 1

4. 8 «zÁåyðUÀ¼À ¸ÀASÁå±Á¸ÀçÛ ªÀÄvÀÄÛ UÀtÂvÀ±Á¸ÀÛçzÀ CAPÀUÀ¼ÀÄ EAwªÉ. UÀtÂvÀ±Á¸ÀÛçzÀ°è 50 CAPÀ UÀ½¹zÀ M§â
«zÁåyðAiÀÄ ¸ÀASÁå±Á¸ÀçÛ zÀ CAPÀ ªÀÄvÀÄÛ ¸ÀASÁå±Á¸ÀçÛ zÀ°è 60 CAPÀ UÀ½¹zÀ M§â «zÁåyðAiÀÄ UÀtÂvÀ±Á¸ÀÛçzÀ CAPÀ
CAzÁf¹.
¸ÀASÁå±Á¸ÀçÛ zÀ CAPÀUÀ¼ÀÄ 25 43 27 35 54 61 37 45
UÀtÂvÀ±Á¸ÀÛçzÀ CAPÀUÀ¼ÀÄ 35 47 20 37 63 54 28 40

5. F zÀvÁÛA±À¢AzÀ JgÀqÀÆ ¸ÀªÀiÁ±ÀæAiÀÄt gÉÃSÉUÀ¼À£ÀÄß PÀAqÀÄ»r¬Äj.

x 3 6 5 4 4 6 7 5
y 3 2 3 5 3 6 6 4
rxy AiÀÄ£ÀÄß ¸ÀºÀ PÀAqÀÄ»r¬Äj.

34

¥ÀæxÀªÀÄ ¦.AiÀÄÄ.¹. ¸ÀASÁå±Á¸ÀçÛ ¥Àæ±Éß PÉÆñÀ
6. eÁ»gÁw£À RZÀÄð ªÀÄvÀÄÛ ªÀiÁgÁlzÀ ªÀiÁ»w F PɼÀUÉ ¤ÃqÀ¯ÁVzÉ.
eÁ»gÁw£À RZÀÄð (PÉÆÃn gÀÆ.) ªÀiÁgÁl (PÉÆÃn gÀÆ.)
¸ÀgÁ¸Àj 20 120
¤.« 5 2
¸ÀºÀ¸ÀA§AzsÀzÀ UÀÄtPÀ = 0.3
a) JgÀqÀÆ ¸ÀªÀiÁ±ÀæAiÀÄt ¸À«ÄÃPÀgÀt ¥ÀqɬÄj.
b) eÁ»gÁw£À RZÀÄð gÀÆ.25 PÉÆÃn DzÁUÀ, ¸ÀA¨sÀªÀ¤ÃAiÀÄ ªÀiÁgÁlªÀ£ÀÄß CAzÁf¹.
c) ªÀiÁgÁl gÀÆ.150 PÉÆÃn DzÁUÀ, eÁ»gÁw£À RZÀð£ÀÄß CAzÁf¹.
7. F PɼÀV£À ¢éZÀ®PÀzÀ PÉÆõÀÖPÀ¢AzÀ JgÀqÀÆ ¸ÀªÀiÁ±ÀæAiÀÄt ¸ÀºÀUÀÄtPÀUÀ¼À£ÀÄß ¯ÉQ̹, r ¨É¯É ¥ÀqɬÄj.

Y
0 – 10 10 – 20 20 – 30 30 – 40
X
10 – 20 5 4 3 -
20 – 30 7 6 7 6
30 – 40 - 5 - 7

8. F PɼÀV£À ¢éZÀ®PÀzÀ DªÀÈwÛ «vÀgÀuÉUÉ y ªÉÄð£À x ¸ÀªÀiÁ±ÀæAiÀÄt ¸À«ÄÃPÀgÀt ¥ÀqɬÄj.
ªÀiÁgÁlzÀ DzÁAiÀÄ eÁ»gÁw£À RZÀÄð (’000gÀÆ.UÀ¼À°è)
(’000gÀÆ.UÀ¼À°è) 5 – 15 15 – 25 25 – 35 35 – 45
75 – 125 4 1 - -
125 – 175 7 6 2 1
175 – 225 1 3 4 2
225 – 275 1 1 3 4

35

¥ÀæxÀªÀÄ ¦.AiÀÄÄ.¹. ¸ÀASÁå±Á¸ÀçÛ ¥Àæ±Éß PÉÆñÀ
Unit – VII

UÀÄtzsÀªÀÄðUÀ¼À ¸ÀºÀZÀAiÀÄð
JgÀqÀÄ CAPÀzÀ ¥Àæ±ÉßUÀ¼ÀÄ:
1. UÀÄtzsÀªÀÄðUÀ¼À ¸ÀºÀZÀAiÀÄð JAzÀgÉãÀÄ? EzÀ£ÀÄß C¼ÉAiÀÄĪÀ ««zsÀ C¼ÀvÉUÀ¼À£ÀÄß ºÉ¸Àj¹.
2. ¸ÀºÀ¸ÀA§AzsÀ ªÀÄvÀÄÛ UÀÄtzsÀªÀÄðUÀ¼À ¸ÀºÀZÀAiÀÄðUÀ¼À £ÀqÀÄ«£À ªÀåvÁå¸ÀªÉãÀÄ?
3. AiÀÄįÉãÀ ¸ÀºÀZÀAiÀÄð UÀÄtPÀzÀ ¸ÀÆvÀæªÀ£ÀÄß CzÀgÀ ªÁå¦ÛAiÉÆA¢UÉ §gɬÄj.

LzÀÄ CAPÀzÀ ¥Àæ±ÉßUÀ¼ÀÄ:
1. LzÀÄ £ÀÆgÁ E¥ÀàvÉÊzÀÄ «zÁåyðUÀ½UÉ ¸ÀA§A¢ü¹zÀ F zÀvÁÛA±À¢AzÀ ªÀÄzÀÄªÉ ªÀÄvÀÄÛ ¥sÀ°vÁA±ÀzÀ £ÀqÀÄ«£À
AiÀÄįÉãÀ ¸ÀºÀZÀAiÀÄð UÀÄtPÀzÀ ¯ÉQ̹.
GwÛÃtð C£ÀÄwÛÃtð
«ªÁ»vÀgÀÄ 90 65
C«ªÁ»vÀgÀÄ 260 110

2. MAzÀÄ ¸À«ÄÃPÉëAiÀÄ°è MAzÀÄ £ÀUÀgÀzÀ 88 ¤ªÁ¹UÀ¼À£ÀÄß ¸ÀAzÀ±Àð£À ªÀiÁr CªÀgÀ zsÀƪÀÄ¥Á£À ¸ÉêÀ£É ªÀÄvÀÄÛ ZÀºÀ
PÀÄrAiÀÄĪÀ ºÀªÁå¸ÀUÀ¼À C£ÀĸÁgÀ ªÀVðÃPÀj¸À¯ÁVzÉ. AiÀÄįÉãÀ ¸ÀºÀZÀAiÀÄð UÀÄtPÀ ¯ÉQ̹, ¨É¯ÉAiÀÄ §UÉÎ «ªÀIJð¹.
zsÀƪÀÄ¥Á£À ªÀiÁqÀĪÀªÀgÀÄ zsÀƪÀÄ¥Á£À ªÀiÁqÀzÀªÀgÀÄ
ZÀºÀ PÀÄrAiÀÄĪÀªÀgÀÄ 40 33
ZÀºÀ PÀÄrAiÀÄzÀªÀgÀÄ 3 12

3. F zÀvÁÛA±À¢AzÀ PÉæÃrmï PÁqÀ𠧼ÀPÉ ªÀÄvÀÄÛ Rað£À £ÀqÀÄªÉ ¸ÀºÀZÀAiÀÄð«zÉAiÉÄà JA§ÄzÀ£ÀÄß AiÀÄįÉãÀ UÀÄtPÀzÀ
ªÀÄÆ®PÀ PÀAqÀÄ»r¬Äj.
PÉæÃrmï PÁqÀ𠧼À¸ÀĪÀªÀgÀÄ PÉæÃrmï PÁqÀ𠧼À¸ÀzÀªÀgÀÄ
RZÀÄð ªÀiÁqÀĪÀªÀgÀÄ 225 50
RZÀÄð ªÀiÁqÀzÀªÀgÀÄ 75 I50

4. F zÀvÁÛA±ÀPÉÌ AiÀÄįÉãÀ ¸ÀºÀZÀAiÀÄð UÀÄtPÀ ¯ÉQ̹.
(AB) = 150, N = 1000, (A) = 200, (B) = 300.

5. F zÀvÁÛA±À¢AzÀ AiÀÄįÉãÀ ¸ÀºÀZÀAiÀÄð UÀÄtPÀ ¯ÉQ̹.
N = 250, (Aβ) = 70, (A) = 100, (B) = 50.

6. N = 500, (αβ) = 280, (A) = 160 ªÀÄvÀÄÛ (B) = 200 JAzÀÄ PÉÆmÁÖUÀ, AiÀÄįÉãÀ ¸ÀºÀZÀAiÀÄð UÀÄtPÀ ¯ÉQ̹.
7. N = 2500, (AB) = 400, (α) = 2100 ªÀÄvÀÄÛ (β) = 900 JAzÀÄ PÉÆmÁÖUÀ, AiÀÄįÉãÀ ¸ÀºÀZÀAiÀÄð UÀÄtPÀ ¯ÉQ̹.
8. PɼÀV£À ªÀiÁ»w¬ÄAzÀ ¸ÁgÀt vÀAiÀiÁj¹. AiÀÄįÉãÀ ¸ÀºÀZÀAiÀÄð UÀÄtPÀ ¯ÉQ̹, ¥sÀ°vÁA±ÀzÀ §UÉÎ «ªÀIJð¹.
(A) = 450, (B) = 600, (Aβ) = 100, N = 1000.

36

¥ÀæxÀªÀÄ ¦.AiÀÄÄ.¹. ¸ÀASÁå±Á¸ÀçÛ ¥Àæ±Éß PÉÆñÀ
9. F zÀvÁÛA±À¢AzÀ vÀAzÉ ªÀÄvÀÄÛ ªÀÄUÀ£À eÁtvÀ£ÀzÀ £ÀqÀÄ«£À ¸ÀºÀZÀAiÀÄð UÀÄtPÀ ¯ÉQ̹.

eÁt vÀAzÉ eÁt ªÀÄUÀ : 50

zÀqÀØ vÀAzÉ eÁt ªÀÄUÀ : 100

zÀqÀØ vÀAzÉ zÀqÀØ ªÀÄUÀ : 300

eÁt vÀAzÉ zÀqÀØ ªÀÄUÀ : 200

10. MAzÀÄ ¸ÀàzsÁðvÀäPÀ ¥ÀjÃPÉëUÉ 2000 C¨sÀåyðUÀ¼ÀÄ ºÁdgÁVzÁÝgÉ. 400 C¨sÀåyðUÀ¼ÀÄ ¥ÀjÃPÉëAiÀÄ°è GwÛÃtðgÁVzÁÝgÉ.

«±ÉõÀ vÀgÀ¨ÉÃw vÀgÀUÀwUÀ½UÉ ºÁdgÁzÀ 350 C¨sÀåyðUÀ¼À°è 200 C¨sÀåyðUÀ¼ÀÄ ¥ÀjÃPÉëAiÀÄ°è GwÛÃtðgÁVzÁÝgÉ.
AiÀÄįÉãÀ UÀÄtPÀ G¥ÀAiÉÆÃV¹ «±ÉõÀ vÀgÀ¨ÉÃwAiÀÄ ¥ÀjuÁªÀÄzÀ §UÉÎ ¤zsÀðj¹.

11. MAzÀÄ PÁ¯ÉÃf¤AzÀ ¥ÀjÃPÉëUÉ ºÁdgÁzÀ 200 «zÁåyðUÀ¼À°è 60 «zÁåyðUÀ¼ÀÄ G£ÀßvÀ zÀeÉðAiÀÄ°è

GwÛÃtðgÁVzÁÝgÉ. «±ÉõÀ vÀgÀ¨ÉÃw ¥ÀqÉzÀ 35 «zÁåyðUÀ¼À°è 20 «zÁåyðUÀ¼ÀÄ G£ÀßvÀ zÀeÉðAiÀÄ°è
GwÛÃtðgÁVzÁÝgÉ. AiÀÄįÉãÀ UÀÄtPÀ G¥ÀAiÉÆÃV¹ «±ÉõÀ vÀgÀ¨ÉÃw ¥ÀjuÁªÀÄPÁj CVzÉAiÉÄ CxÀªÁ E®èªÉ
JA§ÄzÀgÀ §UÉÎ ZÀað¹.

12. MAzÀÄ PÁ¯ÉÃf£À°è 200 «zÁåyðUÀ½zÁÝgÉ, EªÀgÀ°è 150 ºÀÄqÀÄUÀgÀÄ. MAzÀÄ ¥ÀjÃPÉëAiÀÄ°è 120 «zÁåyðUÀ¼ÀÄ

GwÛÃtðgÁVzÁÝgÉ. 10 ºÀÄqÀÄVAiÀÄgÀÄ C£ÀÄwÛÃtðgÁVzÁÝgÉ. AiÀÄįÉãÀ UÀÄtPÀ §¼À¹ °AUÀ ªÀÄvÀÄÛ ¥ÀjÃPÁë
¥sÀ°vÁA±ÀzÀ £ÀqÀÄ«£À ¸ÀºÀZÀAiÀÄð PÀAqÀÄ»r¬Äj.

37

¥ÀæxÀªÀÄ ¦.AiÀÄÄ.¹. ¸ÀASÁå±Á¸ÀçÛ ¥Àæ±Éß PÉÆñÀ
Unit - VIII
CAvÀgÉéñÀ£À ªÀÄvÀÄÛ §»gÉéñÀ£À
MAzÀÄ CAPÀzÀ ¥Àæ±ÉßUÀ¼ÀÄ:
1. CAvÀgÉéñÀ£À JAzÀgÉãÀÄ?
2. §»gÉéñÀ£À JAzÀgÉãÀÄ
3. CAvÀgÉéñÀ£ÀzÀ°èAiÀÄ MAzÀÄ PÀ®à£ÉAiÀÄ£ÀÄß §gɬÄj.
4. CAvÀgÉéñÀ£À ªÀiÁqÀĪÀ MAzÀÄ «zsÁ£ÀªÀ£ÀÄß w½¹.

LzÀÄ CAPÀzÀ ¥Àæ±ÉßUÀ¼ÀÄ:
1. F zÀvÁÛA±À¢AzÀ 2008gÀ°èAiÀÄ PÉʪÀÄUÀÎUÀ¼À gÀ¦£Û À CAvÀgÉéñÀ£À ªÀiÁr.
ªÀµÀð 1998 2000 2002 2004 2006 2008 2010
PÉʪÀÄUÀÎUÀ¼À gÀ¥ÀÄÛ (PÉÆÃn gÀÆ.UÀ¼À°è) 10 13 15 23 26 ̶ 32
2. F ¸ÁgÀt¬ÄAzÀ ©lÄÖºÉÆÃzÀ ¸ÀASÉåAiÀÄ£ÀÄß CAvÀgÉéñÀ£À ªÀiÁr.
ªÀµÀð 2001 2002 2003 2004 2005 2006 2007
ªÀiÁgÁl ('000 Rs.) 100 120 150 180 210 ̶ 320
3. PÉÆlÖ F zÀvÁÛA±À¢AzÀ MAzÀÄ ªÀ¸ÀÄÛ«£À ©lÄÖºÉÆÃzÀ ¨É¯ÉAiÀÄ£ÀÄß CAvÀgÉéñÀ£À ªÀiÁr.
ªÀµÀð 2006 2007 2008 2009 2010
¨É¯É (gÀÆ.) 278 281 ̶ 313 322
4. F zÀvÁÛA±À¢AzÀ 2007gÀ°èAiÀÄ ¹ªÉÄAmï GvÁàzÀ£ÉAiÀÄ£ÀÄß CAvÀgÉéñÀ£À ªÀiÁr.
ªÀµÀð 2005 2006 2007 2008 2009 2010
GvÁàzÀ£É (®PÀë l£ï) 44 90 ̶ 160 270 390
5. ¢é¥ÀzÀ «¸Àg
Û ÀuÁ «zsÁ£ÀzÀ ªÀÄÆ®PÀ F zÀvÁÛA±ÀzÀ°è ©lÄÖºÉÆÃzÀ ¨É¯É ¤zsÀðj¹.
ªÀµÀð 2011 2012 2013 2014 2015
¸ÀÆZÁåAPÀ 100 107 ? 157 212
6. ¤ÃrzÀ F zÀvÁÛA±À¢AzÀ 2015 PÉÌ ¸ÀA§A¢ü¹zÀ ªÀiÁgÁlªÀ£ÀÄß CAzÁf¹.
ªÀµÀð 2010 2011 2012 2013 2014 2015
ªÀiÁgÁl (000) 13 19 25 38 65 ?
7. MAzÀÄ PÀA¥À¤AiÀÄ ««zsÀ ªÀµÀðUÀ¼À ¯Á¨sÀªÀ£ÀÄß F zÀvÁÛA±ÀªÀÅ vÉÆÃj¸ÀÄvÀz
Û É. 2014gÀ°èAiÀÄ ¯Á¨sÀªÀ£ÀÄß CAvÀgÉéñÀ£À
ªÀiÁr.
ªÀµÀð 2006 2008 2010 2012 2014 2016
¯Á¨sÀ (PÉÆÃnUÀ¼À°è) 6 10 12 16 - 24
8. F zÀvÁÛA±À¢AzÀ 2005gÀ°èAiÀÄ ©lÄÖºÉÆÃzÀ ¨É¯É CAvÀgÉéñÀ£À ªÀiÁr.
ªÀµÀð 1995 2000 2005 2010 2015
ªÀiË®å 100 150 ? 175 200
9. X = 50 DzÁUÀ F zÀvÁÛA±À¢AzÀ Y ¨É¯É CAzÁf¹.
X 10 20 30 40 50
Y 110 90 80 60 ?
10. ¢é¥ÀzÀ «¸Àg
Û ÀuÁ «zsÁ£ÀzÀ ªÀÄÆ®PÀ F zÀvÁÛA±ÀzÀ°è ©lÄÖºÉÆÃzÀ ¨É¯É PÀAqÀÄ»r¬Äj.
wAUÀ¼ÀÄ d£ÉªÀj ¥sɧæªÀj ªÀiÁZïð K¦æÃ¯ï ªÉÄÃ
ªÀiË®å 230 260 350 ? 430

38

¥ÀæxÀªÀÄ ¦.AiÀÄÄ.¹. ¸ÀASÁå±Á¸ÀçÛ ¥Àæ±Éß PÉÆñÀ
Unit - IX
¸ÀA¨sÀªÀ ¹zÁÞAvÀ
¸ÀjAiÀiÁzÀ GvÀg
Û ÀªÀ£ÀÄß DAiÉÄ̪ÀiÁr §gɬÄj:
1. MAzÀÄ WÀl£ÉAiÀÄ ¸ÀA¨sÀªÀ¤ÃAiÀÄvÉAiÀÄÄ F ¨É¯ÉUÀ¼À£ÀÄß ºÉÆAzÀ§ºÀÄzÁVzÉ.
a) -∞ to ∞ b) -∞ to 1 c) -1 to 1 d) 0 to 1
2. ¸ÀA¨sÀªÀ¤ÃAiÀÄvÉAiÀÄÄ ªÁå¦Û EzÁVzÉ.
a) [0, 1] b) [0.5, 0] c) [0, 0.5] d) [0.5, 1]
3. MAzÀÄ DPÀ¹äPÀ ¥ÀæAiÉÆÃUÀ¢AzÀ GAmÁzÀ J¯Áè ¥sÀ°vÁA±ÀUÀ¼À UÀtzÀ ¸ÀA¨sÀªÀ¤ÃAiÀÄvÉAiÀÄÄ AiÀĪÁUÀ®Æ EzÀPÉÌ
¸ÀªÀÄ£ÁVgÀÄvÀÛzÉ.
a) C£ÀAvÀ b) ¸ÉÆ£Éß c) MAzÀÄ d) EzÁªÀÅzÀÄ C®è
4. JgÀqÀÄ ¥ÀgÀ¸ÀàgÀ «ªÀÄÄPÀÛ WÀl£ÉUÀ¼À bÉÃzÀ£ÀzÀ ¸ÀA¨sÀªÀ¤ÃAiÀÄvÉAiÀÄÄ AiÀĪÁUÀ®Æ EzÀPÉÌ ¸ÀªÀÄ£ÁVgÀÄvÀÛzÉ.
a) C£ÀAvÀ b) ¸ÉÆ£Éß c) MAzÀÄ d) EzÁªÀÅzÀÄ C®è
5. MAzÀÄ ¨sÀgÀtÂAiÀÄ°è 24 UÉÆðUÀ½ªÉ, CªÀÅUÀ¼À°è PÉ®ªÀÅ ºÀ¹gÀÄ ªÀÄvÀÄÛ PÉ®ªÀÅ ¤Ã°. ºÀ¹gÀÄ UÉÆðUÀ¼À
¸ÀA¨sÀªÀ¤ÃAiÀÄvÉAiÀÄÄ 2/3 DzÁUÀ, ¨sÀgÀtÂAiÀÄ°ègÀĪÀ ºÀ¹gÀÄ UÉÆðUÀ¼À ¸ÀASÉå JµÀÄÖ?
a) 16 b) 8 c) 2 d) 24
6. MAzÀÄ ¨sÀgÀtÂAiÀÄ°è 24 UÉÆðUÀ½ªÉ, CªÀÅUÀ¼À°è PÉ®ªÀÅ ºÀ¹gÀÄ ªÀÄvÀÄÛ PÉ®ªÀÅ ¤Ã°. ºÀ¹gÀÄ UÉÆðUÀ¼À
¸ÀA¨sÀªÀ¤ÃAiÀÄvÉAiÀÄÄ 2/3 DzÁUÀ, ¨sÀgÀtÂAiÀÄ°ègÀĪÀ ¤Ã° UÉÆðUÀ¼À ¸ÀASÉå JµÀÄÖ?
a) 16 b) 8 c) 2 d) 24
7. JgÀqÀÄ ¥ÀgÀ¸ÀàgÀ «ªÀÄÄPÀÛ WÀl£ÉUÀ¼À ¸ÀA¨sÀªÀvÉUÀ¼ÀÄ 0.2 ªÀÄvÀÄÛ 0.3 DzÁUÀ, F WÀl£ÉUÀ¼À°è PÀ¤µÀ× MAzÀÄ ¸ÀA¨sÀ«¸ÀĪÀ
¸ÁzsÀåvÉ JµÀÄÖ?
a) 0.2 b) 0.3 c) 0.4 d) 0.6
8. MAzÀÄ C¢üPÀ ªÀµÀðªÀÅ 53 gÀ«ªÁgÀUÀ¼À£ÀÄß ºÉÆA¢gÀĪÀ ¸ÀA¨sÀªÀvÉ EzÁVzÉ.
a) 1/7 b) 2/7 c) 2/53 d) 52/53
9. MAzÀÄ C¢üPÀªÀ®èzÀ ªÀµÀðªÀÅ 53 gÀ«ªÁgÀUÀ¼À£ÀÄß ºÉÆA¢gÀĪÀ ¸ÀA¨sÀªÀvÉ EzÁVzÉ.
a) 1/7 b) 2/7 c) 2/53 d) 52/53
10. A, B ªÀÄvÀÄÛ C ªÀÄÆgÀÄ ¸ÀévÀAvÀæ WÀl£ÉUÀ¼ÁzÁUÀ, CªÀÅUÀ¼À dAn ¸ÀA¨sÀªÀ¤ÃAiÀÄvÉ
𝟏
a) P(A)×P(B)×P(C) b) 𝐏(𝐀)×𝐏(𝐁)×𝐏(𝐂)
c) P(A)+P(B)+P(C) d) P(A)|P(B).P(C)

11. A JA§ MAzÀÄ WÀl£É ¸ÀA¨sÀ«¹zÉ JAzÀÄ UÉÆwÛzÁÝUÀ, A PÉÆmÁÖUÀ B JA§ WÀl£ÉAiÀÄ ¸ÀA¨sÀªÀ¤ÃAiÀÄvÉAiÀÄ£ÀÄß
»ÃUÉAzÀÄ PÀgÉAiÀÄÄvÁÛgÉ.
a) G¨sÀAiÀÄd£Àå ¸ÀA¨sÀªÀvÉ b) ¥ÀƪÀð ¸ÀA¨sÀªÀvÉ
c) £ÀAvÀgÀzÀ(C¥ÀgÀ) ¸ÀA¨sÀªÀvÉ d) C¢üãÀ ¸ÀA¨sÀªÀvÉ

39

¥ÀæxÀªÀÄ ¦.AiÀÄÄ.¹. ¸ÀASÁå±Á¸ÀçÛ ¥Àæ±Éß PÉÆñÀ
DªÀgÀtzÀ°ègÀĪÀ ¸ÀjAiÀiÁzÀ GvÀg
Û ÀªÀ£ÀÄß Dj¹, ©lÖ ¸ÀܼÀ vÀÄA©j:
(0, 0 ªÀÄvÀÄÛ 1, 0.3, 0.5, 0.6, 1, 4, 36, ¸ÀgÀ¼À, DPÀ¹äPÀ, ¤zÀ±ÀðPÀ, ¸ÁzsÀåvÉ, ¥sÀ°vÁA±ÀUÀ¼ÀÄ, ¸ÀA¨sÀ«¸À¢gÀĪÀÅzÉÃ,
WÀl£É, ¸ÀAAiÀÄÄPÀÛ, ±ÀÆ£Àå)

1. MAzÀÄ WÀl£ÉAiÀÄÄ £ÀqÉAiÀÄĪÀ _________ AiÀÄ£ÀÄß ¸ÀA¨sÀªÀ¤ÃAiÀÄvÉ ¸ÀASÁåvÀäPÀªÁV C¼ÀvÉ ªÀiÁqÀÄvÀÛzÉ.
2. AiÀiÁªÀ ¥ÀæAiÉÆÃUÀ¢AzÀ GAmÁzÀ ¥sÀ°vÁA±ÀUÀ¼ÀÄ MAzÉà DVgÀĪÀÅ¢®èªÉÇÃ, CzÀÄ _______ ¥ÀæAiÉÆÃUÀªÁVgÀÄvÀÛzÉ.
3. MAzÀÄ DPÀ¹äPÀ ¥ÀæAiÉÆÃUÀ¢AzÀ GAmÁzÀ J¯Áè ¥sÀ°vÁA±ÀUÀ¼À UÀtªÀ£ÀÄß ______ ªÀÇåªÀÄ J£ÀÄߪÀgÀÄ.
4. MAzÀÄ DPÀ¹äPÀ ¥ÀæAiÉÆÃUÀ¢AzÀ GAmÁzÀ __________ UÀtªÉà WÀl£É.
5. MAzÀÄ DPÀ¹äPÀ ¥ÀæAiÉÆÃUÀ¢AzÀ GAmÁzÀ ¥sÀ°vÁA±ÀUÀ¼À UÀtªÉà _____ .
6. AiÀiÁªÀÅzÉà ¥sÀ°vÁA±ÀUÀ¼À£ÀÄß ºÉÆA¢gÀzÀ WÀl£ÉAiÀÄÄ, ________ WÀl£ÉAiÀiÁVgÀÄvÀz
Û É.
7. AiÀiÁªÀ WÀl£É, PÉêÀ® MAzÉà ¥sÀ°vÁA±ÀªÀ£ÀÄß ºÉÆA¢gÀĪÀÅzÉÆà CzÀÄ, ________ WÀl£ÉAiÀiÁVgÀÄvÀz
Û É.
8. AiÀiÁªÀ WÀl£É, MAzÀQÌAvÀ ºÉZÀÄÑ ¥sÀ°vÁA±ÀUÀ¼À£ÀÄß ºÉÆA¢gÀĪÀÅzÉÆà CzÀÄ, ________ WÀl£ÉAiÀiÁVgÀÄvÀz
Û É.
9. ±ÀÆ£Àå WÀl£ÉAiÀÄ ¸ÀA¨sÀªÀ¤ÃAiÀÄvÉ _____ DVgÀÄvÀÛzÉ.
10. ¤²ÑvÀ WÀl£ÉAiÀÄ ¸ÀA¨sÀªÀ¤ÃAiÀÄvÉ _____ DVgÀÄvÀÛzÉ.
11. P(A) £À ¨É¯É _________ £ÀqÀÄªÉ EgÀÄvÀÛzÉ.
12. A WÀl£ÉAiÀÄ ¥ÀÆgÀPÀªÀÅ A £À _____ DVgÀÄvÀÛzÉ.
13. P(A) = 0.4 DzÁUÀ, P(Aˡ) £À _____ DVgÀÄvÀÛzÉ.
14. JgÀqÀÄ zÁ¼ÀUÀ¼À£ÀÄß J¸ÉzÁUÀ, ¸ÁzsÀå«gÀĪÀ ¥sÀ°vÁA±ÀUÀ¼À ¸ÀASÉå ______ DVgÀÄvÀÛzÉ.
15. JgÀqÀÄ £ÁtåUÀ¼À£ÀÄß a«ÄäzÁUÀ, ¸ÁzsÀå«gÀĪÀ ¥sÀ°vÁA±ÀUÀ¼À ¸ÀASÉå ______ DVgÀÄvÀÛzÉ.
16. UÀÄj vÀ®Ä¥ÀĪÀ ¸ÀA¨sÀªÀ¤ÃAiÀÄvÉ 0.7 DzÁUÀ, UÀÄj vÀ®Ä¥À¢gÀĪÀ ¸ÀA¨sÀªÀ¤ÃAiÀÄvÉ ______ DVgÀÄvÀz
Û É.
17. ¤µÀàPÀë¥ÁvÀzÀ MAzÀÄ zÁ¼ÀªÀ£ÀÄß GgÀĽ¹zÁUÀ, ¸ÀªÀÄ ¸ÀASÉå ¥ÀqÉAiÀÄĪÀ ¸ÀA¨sÀªÀ¤ÃAiÀÄvÉ ______ DVgÀÄvÀÛzÉ.

ºÉÆA¢¹ §gɬÄj: (£ÉÃgÀªÁV GvÀÛgÀUÀ¼À£ÀÄß ¤ÃqÀ¯ÁVzÉ.)
±ÀÆ£Àå WÀl£ÉAiÀÄ ¸ÀA¨sÀªÀ¤ÃAiÀÄvÉ 0
¤²ÑvÀ WÀl£ÉAiÀÄ ¸ÀA¨sÀªÀ¤ÃAiÀÄvÉ 1
P(A) = 0.4 P(Aˡ) = 0.6
P(AUAˡ) P(S)
P(A)+P(Aˡ) 1
P(A) ¨É¯É 0 ªÀÄvÀÄÛ 1ªÀÄzsÀå£ÀqÀÄªÉ EgÀÄvÀz
Û É
P(AB) = P(A).P(B) A ªÀÄvÀÄÛ B WÀl£ÉUÀ¼ÀÄ ¸ÀévÀAvÀæ
MAzÀÄ zÁ¼ÀªÀ£ÀÄß J¸ÉzÁUÀ ¨É¸À ¸ÀASÉå ªÉÄÃ¯É 𝟏
§gÀĪÀ ¸ÀA¨sÀªÀ¤ÃAiÀÄvÉ 𝟐
MAzÀÄ zÁ¼ÀªÀ£ÀÄß J¸ÉzÁUÀ ¸ÀªÀÄ ¸ÀASÉå ªÉÄÃ¯É 𝟏
§gÀĪÀ ¸ÀA¨sÀªÀ¤ÃAiÀÄvÉ 𝟐

40

¥ÀæxÀªÀÄ ¦.AiÀÄÄ.¹. ¸ÀASÁå±Á¸ÀçÛ ¥Àæ±Éß PÉÆñÀ
MAzÀÄ CAPÀzÀ ¥Àæ±ÉßUÀ¼ÀÄ:
1. ¥sÀ°vÁA±À(¥ÀjuÁªÀÄ)ªÀ£ÀÄß ªÁåSÁ夹.
2. DPÀ¹äPÀ ¥ÀæAiÉÆÃUÀ JAzÀgÉãÀÄ?
3. ¤zÀ±ÀðPÀ ªÀÇåªÀĪÀ£ÀÄß ªÁåSÁ夹.
4. JgÀqÀÄ £ÁtåUÀ¼À£ÀÄß MAzÀÄ ¸À® a«ÄäzÁUÀ GAmÁUÀĪÀ ¤zÀ±ÀðPÀ ªÀÇåªÀĪÀ£ÀÄß §gɬÄj.
5. MAzÀÄ zÁ¼ÀªÀ£ÀÄß J¸ÉzÁUÀ GAmÁUÀĪÀ ¤zÀ±ÀðPÀ ªÀÇåªÀĪÀ£ÀÄß §gɬÄj.
6. WÀl£É JAzÀgÉãÀÄ?
7. WÀl£ÉUÀ¼À ¸ÀAAiÉÆÃUÀ JAzÀgÉãÀÄ?
8. WÀl£ÉUÀ¼À bÉÃzÀ£À JAzÀgÉãÀÄ?
9. ¸ÀA¨sÀªÀ¤ÃAiÀÄvÉAiÀÄ ±Á¹ÛçÃAiÀÄ (UÀtÂvÀgÀÆ¥ÀPÀ) ªÁåSÉå PÉÆr.
10. ¸ÀA¨sÀªÀ¤ÃAiÀÄvÉAiÀÄ ¸ÀASÁå±Á¹ÛçÃAiÀÄ (C£ÀĨsÀªÀd£Àå) ªÁåSÉå PÉÆr.
11. ¸ÀA¨sÀªÀ¤ÃAiÀÄvÉAiÀÄ ¸Àé¥ÀæªÀiÁtÂÃPÀÈvÀ ªÁåSÉå PÉÆr.
12. ±ÀÆ£Àå WÀl£ÉAiÀÄ ¸ÀA¨sÀªÀ¤ÃAiÀÄvÉ JµÀÄÖ?
13. ¤²ÑvÀ WÀl£ÉAiÀÄ ¸ÀA¨sÀªÀ¤ÃAiÀÄvÉ JµÀÄÖ?
14. C¢üãÀ ¸ÀA¨sÀªÀvÉAiÀÄ£ÀÄß ªÁåSÁ夹.
15. P(A) = 1/4 DzÁUÀ, P(Aˡ) JµÀÄÖ?

JgÀqÀÄ CAPÀzÀ ¥Àæ±ÉßUÀ¼ÀÄ:
1. DPÀ¹äPÀ ¥ÀæAiÉÆÃUÀ JAzÀgÉãÀÄ? MAzÀÄ GzÁºÀgÀuÉ PÉÆr.
2. ±ÀÆ£Àå WÀl£ÉAiÀÄ£ÀÄß ªÁåSÁ夹. MAzÀÄ GzÁºÀgÀuÉ PÉÆr.
3. ¸ÀgÀ¼À WÀl£ÉAiÀÄ£ÀÄß ªÁåSÁ夹. MAzÀÄ GzÁºÀgÀuÉ PÉÆr.
4. ¸ÀAAiÀÄÄPÀÛ WÀl£ÉAiÀÄ£ÀÄß ªÁåSÁ夹. MAzÀÄ GzÁºÀgÀuÉ PÉÆr.
5. M®ªÀżÀî ¥ÀjuÁªÀÄUÀ¼À£ÀÄß GzÁºÀgÀuÉAiÉÆA¢UÉ ªÁåSÁ夹.
6. ¸ÁzsÀå«gÀĪÀ (¸ÀªÀðªÁå¦) ¥ÀjuÁªÀÄUÀ¼À£ÀÄß GzÁºÀgÀuÉAiÉÆA¢UÉ ªÁåSÁ夹.
7. ¸ÀªÀıÀPÀå WÀl£ÉUÀ¼À£ÀÄß GzÁºÀgÀuÉAiÉÆA¢UÉ ªÁåSÁ夹.
8. ¥ÀgÀ¸ÀàgÀ «ªÀÄÄPÀÛ WÀl£ÉUÀ¼À£ÀÄß GzÁºÀgÀuÉAiÉÆA¢UÉ ªÁåSÁ夹.
9. MAzÀÄ WÀl£ÉAiÀÄ ¥ÀÆgÀPÀ JAzÀgÉãÀÄ? GzÁºÀgÀuÉ PÉÆr.
10. 0 ≤ P(A) ≤ 1 JAzÀÄ vÉÆÃj¹.
11. A WÀl£ÉAiÀÄ Aˡ ¥ÀÆgÀPÀ DzÁUÀ, P(A) + P(Aˡ) = 1 JAzÀÄ vÉÆÃj¹.
12. ¸ÀévÀAvÀæ WÀl£ÉUÀ¼À£ÀÄß GzÁºÀgÀuÉAiÉÆA¢UÉ ªÁåSÁ夹.
13. CªÀ®A©üvÀ WÀl£ÉUÀ¼À£ÀÄß GzÁºÀgÀuÉAiÉÆA¢UÉ ªÁåSÁ夹.
14. MAzÀÄ £ÁtåªÀ£ÀÄß a«ÄäzÁUÀ, MAzÀÄ ¹AºÀ ªÀÄÄR ¥ÀqÉAiÀÄĪÀ ¸ÀA¨sÀªÀvÉ PÀAqÀÄ»r¬Äj.
15. MAzÀÄ £ÁtåªÀ£ÀÄß a«ÄäzÁUÀ, ¹AºÀ ªÀÄÄR CxÀªÁ vÀ£É ªÀÄÄR ¥ÀqÉAiÀÄĪÀ ¸ÀA¨sÀªÀvÉ PÀAqÀÄ»r¬Äj.
16. MAzÀÄ zÁ¼ÀªÀ£ÀÄß J¸ÉzÁUÀ, ¨É¸À ¸ÀASÉå ¥ÀqÉAiÀÄĪÀ ¸ÀA¨sÀªÀvÉ JµÀÄÖ?
17. JgÀqÀÄ £ÁtåUÀ¼À£ÀÄß a«ÄäzÁUÀ, JgÀqÀÄ ¹AºÀ ªÀÄÄRUÀ¼À£ÀÄß ¥ÀqÉAiÀÄĪÀ ¸ÀA¨sÀªÀvÉ PÀAqÀÄ»r¬Äj.
18. LªÀvÉÛqÀgÀÄ J¯ÉUÀ½gÀĪÀ MAzÀÄ E¸ÉàÃmï PÀnÖ¤AzÀ MAzÀÄ J¯ÉAiÀÄ£ÀÄß J¼ÉzÁUÀ, CzÀÄ gÁeÁ CxÀªÁ gÁtÂ
J¯ÉAiÀiÁVgÀĪÀ ¸ÀA¨sÀªÀvÉ JµÀÄÖ?

41

¥ÀæxÀªÀÄ ¦.AiÀÄÄ.¹. ¸ÀASÁå±Á¸ÀçÛ ¥Àæ±Éß PÉÆñÀ
19. LªÀvÉÛqÀgÀÄ J¯ÉUÀ½gÀĪÀ MAzÀÄ E¸ÉàÃmï PÀnÖ¤AzÀ MAzÀÄ J¯ÉAiÀÄ£ÀÄß J¼ÉzÁUÀ, CzÀÄ PÉA¥ÀÄ CxÀªÁ PÀj
J¯ÉAiÀiÁVgÀĪÀ ¸ÀA¨sÀªÀvÉ JµÀÄÖ?
20. P(A) = 1/13, P(B) =1/4 ªÀÄvÀÄÛ P(A∩B) = 1/52 DzÁUÀ, P(A∪B) ¨É¯É PÀAqÀÄ»r¬Äj.
21. If P(A) =1/2 , P(B) = 1/3 ªÀÄvÀÄÛ P(A∩B) =1/6 DzÁUÀ, P(A∪B) PÀAqÀÄ»r¬Äj.
22. If P(A∩B) = 1/3 ªÀÄvÀÄÛ P(B) = 2/3 DzÁUÀ, P(A|B) PÀAqÀÄ»r¬Äj.
23. If P(A) = 2/3 ªÀÄvÀÄÛ P(B|A) = 2/5 DzÁUÀ, P(A∩B) PÀAqÀÄ»r¬Äj.
24. A ªÀÄvÀÄÛ B ¸ÀévÀAvÀæ WÀl£ÉUÀ¼ÁVzÀÄÝ, P(A) = 0.6 ªÀÄvÀÄÛ P(B) = 0.5 DzÁUÀ, P(A∪B) PÀAqÀÄ»r¬Äj.

LzÀÄ CAPÀzÀ ¥Àæ±ÉßUÀ¼ÀÄ:
1. AiÀiÁªÀÅzÁzÀgÀÆ JgÀqÀÄ WÀl£ÉUÀ¼À ¸ÀAPÀ®£À ¸ÀA¨sÀªÀ ¥ÀæªÉÄÃAiÀĪÀ£ÀÄß ºÉý ¸Á¢ü¹.
2. JgÀqÀÄ ¥ÀgÀ¸ÀàgÀ «ªÀÄÄPÀÛ WÀl£ÉUÀ¼À ¸ÀAPÀ®£À ¸ÀA¨sÀªÀ ¥ÀæªÉÄÃAiÀĪÀ£ÀÄß ºÉý ¸Á¢ü¹.
3. JgÀqÀÄ CªÀ®A©üvÀ WÀl£ÉUÀ¼À UÀÄuÁPÁgÀ ¸ÀA¨sÀªÀ ¥ÀæªÉÄÃAiÀĪÀ£ÀÄß ºÉý ¸Á¢ü¹.
4. JgÀqÀÄ ¸ÀévÀAvÀæ WÀl£ÉUÀ¼À UÀÄuÁPÁgÀ ¸ÀA¨sÀªÀ ¥ÀæªÉÄÃAiÀĪÀ£ÀÄß ºÉý ¸Á¢ü¹.
5. LªÀvÉÛqÀgÀÄ J¯ÉUÀ½gÀĪÀ MAzÀÄ E¸ÉàÃmï PÀnÖ¤AzÀ MAzÀÄ J¯ÉAiÀÄ£ÀÄß J¼ÉzÁUÀ, CzÀÄ (i) gÁeÁ CxÀªÁ ¸ÉàÃqï
(ii) ¸ÉàÃqï CxÀªÁ PÉA¥ÀÄ (iii) ¸ÉàÃqï gÁeÁ DVgÀĪÀ ¸ÀA¨sÀªÀvÉ PÀAqÀÄ»r¬Äj.
6. MAzÀÄ ¥ÉnÖUÉAiÀÄ°è 1 jAzÀ 20 ¸ÀASÉåUÀ½gÀĪÀ J¯ÉUÀ½ªÉ. F ¥ÉnÖUɬÄAzÀ MAzÀÄ J¯ÉAiÀÄ£ÀÄß J¼ÉzÁUÀ, CzÀÄ
(i) ¨É¸À ¸ÀASÉå (ii) 4gÀ UÀÄtPÀzÀ ¸ÀASÉå (iii) ¥ÀÆtð ªÀUÀð ¸ÀASÉåAiÀÄ J¯ÉAiÀiÁVgÀĪÀ ¸ÀA¨sÀªÀvÉ PÀAqÀÄ»r¬Äj.
7. ªÀÄÆgÀÄ £ÁtåUÀ¼À£ÀÄß MAzÉà ¸À®PÉÌ a«ÄäzÁUÀ, (i) PÉêÀ® ¹AºÀ ªÀÄÄRUÀ¼ÀÄ ªÀiÁvÀæ (ii) PÀ¤µÀÖ JgÀqÀÄ ¹AºÀ
ªÀÄÄRUÀ¼ÀÄ zÉÆgÉAiÀÄĪÀ ¸ÀA¨sÀªÀvÉUÀ¼À£ÀÄß PÀAqÀÄ»r¬Äj.
8. 6 ºÀÄqÀÄUÀgÀÄ ªÀÄvÀÄÛ 4 ºÀÄqÀÄVAiÀÄgÀÄ EgÀĪÀ MAzÀÄ UÀÄA¦¤AzÀ, E§âgÀ£ÀÄß DPÀ¹äPÀªÁV DAiÀiÁÝUÀ, (a) CªÀj§âgÀÄ
ºÀÄqÀÄUÀgÀÄ (b) CªÀj§âgÀÄ ºÀÄqÀÄVAiÀÄgÀÄ (c) M§â ºÀÄqÀÄUÀ ªÀÄvÀÄÛ M§â ºÀÄqÀÄV DVgÀĪÀ ¸ÀA¨sÀªÀvÉUÀ¼À£ÀÄß
PÀAqÀÄ»r¬Äj.
9. MAzÀÄ ¥ÉnÖUÉAiÀÄ°è 5 PÉA¥ÀÄ ªÀÄvÀÄÛ 4 ºÀ¹gÀÄ ZÉAqÀÄUÀ½ªÉ. EzÀjAzÀ JgÀqÀÄ ZÉAqÀÄUÀ¼À£ÀÄß DPÀ¹äPÀªÁV DAiÀiÁÝUÀ, CªÀÅ
(a) MAzÉà §tÚzÀªÀÅUÀ¼ÀÄ (b) ¨ÉÃgÉ ¨ÉÃgÉ §tÚzÀªÀÅUÀ¼ÁVgÀĪÀ ¸ÀA¨sÀªÀvÉUÀ¼À£ÀÄß PÀAqÀÄ»r¬Äj.
10. MAzÀÄ ¥ÉnÖUÉAiÀÄ°è 6 ©½, 4 PÀj ªÀÄvÀÄÛ 5 ºÀ¹gÀÄ ZÉAqÀÄUÀ½ªÉ. F ¥ÉnÖUɬÄAzÀ ªÀÄÆgÀÄ ZÉAqÀÄUÀ¼À£ÀÄß DPÀ¹äPÀªÁV
DAiÀÄÄÝPÉƼÀî¯ÁVzÉ. CªÀÅ (a) JgÀqÀÄ ©½ ªÀÄvÀÄÛ MAzÀÄ PÀj (b) MAzÀÄ ©½ ªÀÄvÀÄÛ JgÀqÀÄ ºÀ¹gÀÄ
§tÚzÀªÀÅUÀ¼ÁVgÀĪÀ ¸ÀA¨sÀªÀvÉUÀ¼À£ÀÄß PÀAqÀÄ»r¬Äj.
11. MAzÀÄ ¥ÉnÖUÉAiÀÄ°è 5 PÉA¥ÀÄ, 4 ºÀ¹gÀÄ ªÀÄvÀÄÛ 3 ¤Ã° UÉÆðUÀ½ªÉ. F ¥ÉnÖUɬÄAzÀ ªÀÄÆgÀÄ UÉÆðUÀ¼À£ÀÄß
DPÀ¹äPÀªÁV DAiÀÄÄÝPÉƼÀî¯ÁVzÉ. CªÀÅ (a) ¨ÉÃgÉ ¨ÉÃgÉ §tÚzÀªÀÅUÀ¼ÀÄ (b) MAzÉà §tÚzÀªÀÅUÀ¼ÁVgÀĪÀ ¸ÀA¨sÀªÀvÉUÀ¼À£ÀÄß
PÀAqÀÄ»r¬Äj.
12. MAzÀÄ aîzÀ°è 1 jAzÀ 5 ¸ÀASÉåUÀ¼g
À ÀĪÀ 5 aÃnUÀ½ªÉ. JgÀqÀÄ aÃnUÀ¼À£ÀÄß DPÀ¹äPÀªÁV DAiÀÄÄÝPÉÆAqÁUÀ, D
aÃnUÀ¼À°è ¸ÀASÉåUÀ¼À ªÉÆvÀÛ (i) ¨É¸À (ii) ¸ÀªÀÄ DVgÀĪÀ ¸ÀA¨sÀªÀvÉUÀ¼ÀÄ JµÀÄÖ?
13. LzÀÄ ¨ÁåmïìªÀÄ£ïßgÀÄ, ªÀÄƪÀgÀÄ ¨Ë®gïUÀ¼ÀÄ ªÀÄvÀÄÛ E§âgÀÄ «PÉmï Q¥ÀgïUÀ¼ÀÄ EgÀĪÀ MAzÀÄ PÁ¯ÉÃf¤AzÀ E§âgÀÄ
DlUÁgÀgÀ£ÀÄß MAzÀÄ «±Àé«zÁå®AiÀÄzÀ QæPÉmï vÀAqÀPÉÌ DAiÉÄÌ ªÀiÁqÀ¨ÉÃPÁVzÉ. (i) M§â ¨ÁåmïìªÀÄ£ïß ªÀÄvÀÄÛ M§â
«PÉmï Q¥Àgï (ii) ¨Ë®gïUÀ¼ÀÄ ªÀiÁvÀæ DAiÉÄÌAiÀiÁUÀĪÀ ¸ÀA¨sÀªÀvÉ PÀAqÀÄ»r¬Äj.
14. ªÀÄƪÀgÀÄ ¥ÀzÀ«zsÀgÀgÀÄ, LªÀgÀÄ ¥ÀzÀ«¥ÀƪÀðzÀªÀgÀÄ ªÀÄvÀÄÛ JAlÄ ªÉÄnæPÀÄå¯ÉmïìUÀ½AzÀ ªÀÄÆgÀÄ C¨sÀåyðUÀ¼À£ÀÄß
MAzÀÄ ¸ÀA¸ÉÜAiÀÄÄ DAiÉÄÌ ªÀiÁrPÉƼÀî¨ÉÃPÁVzÉ. (a) M§â ¥ÀzÀ«zsÀgÀ ªÀÄvÀÄÛ E§âgÀÄ ªÉÄnæPÀÄå¯Émïì (b) E§âgÀÄ
¥ÀzÀ«¥ÀƪÀðzÀªÀgÀÄ ªÀÄvÀÄÛ M§â ªÉÄnæPÀÄå¯Émï DAiÉÄÌAiÀiÁUÀĪÀ ¸ÀA¨sÀªÀ¤ÃAiÀÄvÉ JµÀÄÖ?

42

¥ÀæxÀªÀÄ ¦.AiÀÄÄ.¹. ¸ÀASÁå±Á¸ÀçÛ ¥Àæ±Éß PÉÆñÀ
15. MAzÀÄ ªÀ¸Àw¤®AiÀÄzÀ°è 60% «zÁåyðUÀ¼ÀÄ ZÀºÀ PÀÄrAiÀÄÄvÁÛgÉ, 50% «zÁåyðUÀ¼ÀÄ PÁ¦ü PÀÄrAiÀÄÄvÁÛgÉ, 20%
«zÁåyðUÀ¼ÀÄ ZÀºÀ ªÀÄvÀÄÛ PÁ¦ü JgÀqÀ£ÀÆß PÀÄrAiÀÄÄvÁÛgÉ. DPÀ¹äPÀªÁV DAiÀÄÝ M§â «zÁåyðAiÀÄÄ ZÀºÀ CxÀªÁ PÁ¦ü
PÀÄrAiÀÄĪÀ ¸ÀA¨sÀªÀ¤ÃAiÀÄvÉ PÀAqÀÄ»r¬Äj.
16. M§â UÀÄwÛUÉzÁgÀ£ÀÄ PÉƼÁ¬Ä UÀÄwÛUÉ ¥ÀqÉAiÀÄĪÀ ¸ÀA¨sÀªÀvÉ 1/2. CªÀ£ÀÄ «zÀÄåwÛ£À UÀÄwÛUÉ ¥ÀqÉAiÀÄ¢gÀĪÀ ¸ÀA¨sÀªÀvÉ
2/3. CªÀ£ÀÄ PÀ¤µÀÖ MAzÀ£ÀÄß UÀÄwÛUÉ ¥ÀqÉAiÀÄĪÀ ¸ÀA¨sÀªÀvÉ 2/3. CªÀ£ÀÄ JgÀqÀ£ÀÆß UÀÄwÛUÉ ¥ÀqÉAiÀÄĪÀ ¸ÀA¨sÀªÀvÉ
JµÀÄÖ?
17. MAzÀÄ ¸ÀªÀĸÉåAiÀÄ£ÀÄß A ©r¸ÀĪÀ ¸ÀA¨sÀªÀvÉ 2/3 ªÀÄvÀÄÛ B CzÀ£ÀÄß ©r¸ÀĪÀ ¸ÀA¨sÀªÀvÉ 3/5. CªÀj§âgÀÆ ¸ÀévÀAvÀæªÁV
¥ÀæAiÀÄwß¹zÁUÀ, a) CªÀj§âgÀÆ CzÀ£ÀÄß ©r¸ÀĪÀ b) M§âgÀÆ CzÀ£ÀÄß ©r¸À¢gÀĪÀ ¸ÀA¨sÀªÀ¤ÃAiÀÄvÉ PÀAqÀÄ»r¬Äj.
18. A, B ªÀÄvÀÄÛ C JA§ ªÀÄÆgÀÄ ªÀåQÛUÀ¼ÀÄ UÀÄj vÀ®Ä¥ÀĪÀ ºÁUÉ ºÉÆqÉAiÀÄĪÀ ¸ÀA¨sÀªÀvÉUÀ¼ÀÄ PÀæªÀĪÁV 0.6, 0.5 ªÀÄvÀÄÛ
0.4 DVªÉ. CªÀgÀÄ ¸ÀévÀAvÀæªÁV UÀÄjAiÀÄvÀÛ ºÉÆqÉzÁUÀ, (i) M§âgÀÆ UÀÄj vÀ®Ä¥À¢gÀĪÀ (ii) UÀÄj vÀ®Ä¥ÀĪÀ ¸ÀA¨sÀªÀvÉ
PÀAqÀÄ»r¬Äj.
19. MAzÀÄ ¥ÉnÖUÉAiÀÄ°è 40 ªÉƼÉUÀ¼ÀÄ ªÀÄvÀÄÛ 20 ¸ÀÆÌçUÀ½ªÉ. 1/4£ÉAiÀÄ ¨sÁUÀzÀµÀÄÖ ªÉƼÉUÀ¼ÀÄ ªÀÄvÀÄÛ ±ÉÃ.20 gÀµÀÄÖ
¸ÀÆÌçUÀ¼ÀÄ vÀÄPÀÄÌ »r¢ªÉ. MAzÀÄ ªÀ¸ÀÄÛªÀ£ÀÄß DPÀ¹äPÀªÁV DAiÀiÁÝUÀ, CzÀÄ vÀÄPÀÄÌ »rzÀ ªÉÆ¼É CxÀªÁ ¸ÀÆÌç DVgÀĪÀ
¸ÀA¨sÀªÀvÉ JµÀÄÖ?
20. MAzÀÄ ¥À¸ïð£À°è 4 ¨É½îAiÀÄ ªÀÄvÀÄÛ 2 §AUÁgÀzÀ £ÁtåUÀ½ªÉ. ªÀÄvÉÆÛAzÀÄ ¥À¸ïð£À°è 3 ¨É½îAiÀÄ ªÀÄvÀÄÛ 4 §AUÁgÀzÀ
£ÁtåUÀ½ªÉ. F JgÀqÀÄ ¥À¸ïðUÀ¼À°è MAzÀjAzÀ MAzÀÄ £ÁtåªÀ£ÀÄß DPÀ¹äPÀªÁV DAiÀiÁÝUÀ, CzÀÄ ¨É½îAiÀÄ £Átå
DVgÀĪÀ ¸ÀA¨sÀªÀvÉ JµÀÄÖ?
21. aîUÀ¼ÀÄ F jÃw M¼ÀUÉÆArªÉ. aî I: 3 PÉA¥ÀÄ ªÀÄvÀÄÛ 2 ºÀ¹gÀÄ ZÉAqÀÄUÀ¼ÀÄ, aî II: 4 PÉA¥ÀÄ ªÀÄvÀÄÛ 3
ºÀ¹gÀÄ ZÉAqÀÄUÀ¼ÀÄ ªÀÄvÀÄÛ aî III: 2 PÉA¥ÀÄ ªÀÄvÀÄÛ 2 ºÀ¹gÀÄ ZÉAqÀÄUÀ¼ÀÄ. MAzÀÄ aîªÀ£ÀÄß DPÀ¹äPÀªÁV DAiÀÄÄÝ
£ÀAvÀgÀ CzÀjAzÀ MAzÀÄ ZÉAqÀ£ÀÄß vÀUÉAiÀįÁVzÉ. CzÀÄ PÉA¥ÀÄ ZÉAqÁVgÀĪÀ ¸ÀA¨sÀªÀ¤ÃAiÀÄvÉ PÀAqÀÄ»r¬Äj.
22. £ÀÆå£ÀvɬĮèzÀ JgÀqÀÄ zÁ¼ÀUÀ¼À£ÀÄß GgÀĽ¸À¯ÁVzÉ. (i) JgÀqÀÆ zÁ¼ÀUÀ¼ÀÄ MAzÉà ¸ÀASÉå vÉÆÃgÀĪÀ (ii) ¸ÀASÉåUÀ¼À
ªÉÆvÀÛ 7 CxÀªÁ 11 (iii) ¸ÀASÉåUÀ¼À ªÉÆvÀÛ 3 ªÀÄÆgÀjAzÀ ¨sÁUÀªÁUÀĪÀ (iv) ¸ÀASÉåUÀ¼À UÀÄt®§Þ 36 DVgÀĪÀ
¸ÀA¨sÀªÀ¤ÃAiÀÄvÉ PÀAqÀÄ»r¬Äj.
23. DPÀ¹äPÀªÁV DAiÀÄÝ MAzÀÄ i) ¸ÁªÀiÁ£Àå ii) C¢üPÀ ªÀµÀðzÀ°è 53 ¸ÉÆêÀĪÁgÀ EgÀĪÀ ¸ÀA¨sÀªÀvÉ JµÀÄÖ?
24. MAzÀÄ aîzÀ°è 3 ©½ ªÀÄvÀÄÛ 5 PÀj UÉÆðUÀ½ªÉ. F aî¢AzÀ MAzÀgÀ £ÀAvÀgÀ MAzÀgÀAvÉ JgÀqÀÄ UÉÆðUÀ¼À£ÀÄß
DAiÀÄÄÝPÉƼÀî¯ÁVzÉ. ªÁ¥Á¸Áw (i) ¸ÀÀ»vÀªÁzÁUÀ CªÀÅ JgÀqÀÆ ©½, (ii) gÀ»vÀªÁzÁUÀ CªÀÅ JgÀqÀÆ PÀj
UÉÆðUÀ¼ÁVgÀĪÀ ¸ÀA¨sÀªÀvÉUÀ¼ÀÄ JµÀÄÖ?

43

¥ÀæxÀªÀÄ ¦.AiÀÄÄ.¹. ¸ÀASÁå±Á¸ÀçÛ ¥Àæ±Éß PÉÆñÀ
Unit – X
DPÀ¹äPÀ ZÀ®PÀ
¸ÀjAiÀiÁzÀ GvÀg
Û ÀªÀ£ÀÄß DAiÉÄ̪ÀiÁr §gɬÄj:
1. X MAzÀÄ «aÒ£Àß DPÀ¹äPÀ ZÀ®PÀªÁVzÀÄÝ ªÀÄvÀÄÛ a MAzÀÄ ¹ÜgÀ ¸ÀASÉå DzÁUÀ, E(a) £À ¨É¯É EzÀPÉÌ ¸ÀªÀÄ£ÁVgÀÄvÀÛzÉ.
a) a b) a E(X) c) aE(X) + b d) b
2. X MAzÀÄ DPÀ¹äPÀ ZÀ®PÀªÁVzÀÄÝ ªÀÄvÀÄÛ a MAzÀÄ ¹ÜgÀ ¸ÀASÉå DzÁUÀ, E(aX) £À ¨É¯É EzÀPÉÌ ¸ÀªÀÄ£ÁVgÀÄvÀÛzÉ.
a) a b) a E(X) c) aE(X) + b d) b
3. X MAzÀÄ DPÀ¹äPÀ ZÀ®PÀªÁVzÀÄÝ, a ªÀÄvÀÄÛ b ¹ÜgÀ ¸ÀASÉåUÀ¼ÁzÁUÀ, E(aX+b) £À ¨É¯É EzÀPÉÌ ¸ÀªÀÄ£ÁVgÀÄvÀÛzÉ.
a) a b) a E(X) c) aE(X) + b d) b
4. X MAzÀÄ «aÒ£Àß DPÀ¹äPÀ ZÀ®PÀªÁVzÀÄÝ ªÀÄvÀÄÛ a MAzÀÄ ¹ÜgÀ ¸ÀASÉå DzÁUÀ, V(a) £À ¨É¯É EzÀPÉÌ ¸ÀªÀÄ£ÁVgÀÄvÀÛzÉ.
a) a b) a V(X) c) a2V(X) d) 0
5. X MAzÀÄ DPÀ¹äPÀ ZÀ®PÀªÁVzÀÄÝ ªÀÄvÀÄÛ a MAzÀÄ ¹ÜgÀ ¸ÀASÉå DzÁUÀ, V(aX) £À ¨É¯É EzÀPÉÌ ¸ÀªÀÄ£ÁVgÀÄvÀÛzÉ.
a) a V(X) b) a2V(X) c) a2V(X) + b d) a
6. X MAzÀÄ DPÀ¹äPÀ ZÀ®PÀªÁVzÀÄÝ ªÀÄvÀÄÛ a MAzÀÄ ¹ÜgÀ ¸ÀASÉå DzÁUÀ, V(aX+b) £À ¨É¯É EzÀPÉÌ ¸ÀªÀÄ£ÁVgÀÄvÀÛzÉ.
a) a V(X) b) a2V(X) c) a2V(X) + b d) a
7. E(X) = 5 DzÁUÀ, E(8) £À ¨É¯É EzÁVgÀÄvÀÛzÉ.
a) 5 b) 0 c) 40 d) 8
8. E(X) = 5 DzÁUÀ, E(-X) £À ¨É¯É EzÁVgÀÄvÀÛzÉ.
a) 5 b) - 5 c) 0 d) 10
9. E(X) = 5 DzÁUÀ, E(2X) £À ¨É¯É EzÁVgÀÄvÀÛzÉ.
a) 5 b) 2 c) 10 d) 20
10. E(X) = 5 DzÁUÀ, E(2X+4) £À ¨É¯É EzÁVgÀÄvÀÛzÉ.
a) 5 b) 14 c) 10 d) 20
11. V(X) = 5 DzÁUÀ, V(8) £À ¨É¯É EzÁVgÀÄvÀÛzÉ.
a) 5 b) 0 c) 40 d) 8
12. V(X) = 5 DzÁUÀ, V(-X) £À ¨É¯É EzÁVgÀÄvÀÛzÉ.
a) 5 b) - 5 c) 0 d) 10
13. V(X) = 5 DzÁUÀ, V(2X) £À ¨É¯É EzÁVgÀÄvÀÛzÉ.
a) 5 b) 2 c) 10 d) 20
14. V(X) = 5 DzÁUÀ, V(2X+4) £À ¨É¯É EzÁVgÀÄvÀÛzÉ.
a) 5 b) 14 c) 10 d) 20
𝐗
15. V(X) = 4 DzÁUÀ, V(𝟐) £À ¨É¯É EzÁVgÀÄvÀÛzÉ.
a) 0 b) 1 c) 2 d) 4
16. V(–X+b) £À ¨É¯É EzÀPÉÌ ¸ÀªÀÄ£ÁVgÀÄvÀÛzÉ.
a) –V(X) b) V(X) c) 0 d) V(X)+4

44

¥ÀæxÀªÀÄ ¦.AiÀÄÄ.¹. ¸ÀASÁå±Á¸ÀçÛ ¥Àæ±Éß PÉÆñÀ
DªÀgÀtzÀ°ègÀĪÀ ¸ÀjAiÀiÁzÀ GvÀg
Û ÀªÀ£ÀÄß Dj¹, ©lÖ ¸ÀܼÀ vÀÄA©j:
(¸ÀvÀvÀ, 0, 2, ¸ÀgÀ¼À, «aÒ£Àß, 0, 4)

1. E(2) ¨É¯É _____ DVgÀÄvÀÛzÉ.
2. V(2) ¨É¯É _____ DVgÀÄvÀÛzÉ.
3. AiÀiÁªÀ MAzÀÄ DPÀ¹äPÀ ZÀ®PÀªÀÅ ªÁå¦ÛAiÉƼÀV£À DAiÀÄÝ ¨É¯ÉUÀ¼À£ÀÄß ºÉÆAzÀÄvÀz
Û ÉAiÉÆÃ, CzÀ£ÀÄß _______ DPÀ¹äPÀ
ZÀ®PÀ J£ÀÄߪÀgÀÄ.
4. AiÀiÁªÀ MAzÀÄ DPÀ¹äPÀ ZÀ®PÀªÀÅ ªÁå¦ÛAiÉƼÀV£À J¯Áè ¨É¯ÉUÀ¼À£ÀÄß ºÉÆAzÀÄvÀÛzÉAiÉÆÃ, CzÀ£ÀÄß _______ DPÀ¹äPÀ
ZÀ®PÀ J£ÀÄߪÀgÀÄ.
5. X ªÀÄvÀÄÛ Y JA§ JgÀqÀÄ ¸ÀévÀAvÀæ DPÀ¹äPÀ ZÀ®PÀUÀ½UÉ Cov(X, Y) £À ¨É¯É _____ DVgÀÄvÀÛzÉ.

ºÉÆA¢¹ §gɬÄj: (£ÉÃgÀªÁV GvÀÛgÀUÀ¼À£ÀÄß ¤ÃqÀ¯ÁVzÉ.)
Σp(x) ¨É¯É 1 PÉÌ ¸ÀªÀÄ£ÁVgÀÄvÀÛzÉ
E(X) Σx p(x)
S.D.(X) √𝐕𝐚𝐫(𝐗)
E(a) a
E(aX) a E(X)
Var(a) 0
Cov(X,Y) E(XY) – E(X)E(Y)
X ªÀÄvÀÄÛ Y ¸ÀévÀAvÀæªÁVzÁÝUÀ Cov(X,Y) = 0

MAzÀÄ CAPÀzÀ ¥Àæ±ÉßUÀ¼ÀÄ:
1. DPÀ¹äPÀ ZÀ®PÀªÀ£ÀÄß ªÁåSÁ夹.
2. «aÒ£Àß DPÀ¹äPÀ ZÀ®PÀªÀ£ÀÄß ªÁåSÁ夹.
3. ¸ÀvÀvÀ DPÀ¹äPÀ ZÀ®PÀªÀ£ÀÄß ªÁåSÁ夹.
4. ¸ÀA¨sÀªÀ «vÀgÀuÉ JAzÀgÉãÀÄ?
5. ¸ÀA¨sÀªÀ gÁ² ¥sÀ®£ÉAiÀÄ£ÀÄß ªÁåSÁ夹.
6. UÀtÂvÀ ¤jÃPÉëAiÀÄ£ÀÄß ªÁåSÁ夹.
7. «ZÀ®£ÉAiÀÄ£ÀÄß UÀtÂvÀ ¤jÃPÉëAiÀÄ ¥ÀzÉÆÃQÛUÀ¼À°è ªÀåPÀ¥
Û Àr¹.
8. dAn ¸ÀA¨sÀªÀ gÁ² ¥sÀ®£ÉAiÀÄ£ÀÄß ªÁåSÁ夹.
9. E(8) £À ¨É¯É JµÀÄÖ?
10. V(4) £À ¨É¯É JµÀÄÖ?
11. ¸ÀºÀ«ZÀ®£ÉAiÀÄ£ÀÄß UÀtÂvÀ ¤jÃPÉëAiÀÄ ¥ÀzÉÆÃQÛUÀ¼À°è ªÀåPÀ¥
Û Àr¹.
12. X ªÀÄvÀÄÛ Y JgÀqÀÄ ¸ÀévÀAvÀæ ZÀ®PÀUÀ¼ÁzÁUÀ Cov(X Y) £À ¨É¯É JµÀÄÖ?
13. JgÀqÀÄ ¸ÀévÀAvÀæ ZÀ®PÀUÀ½UÉ ‘r’ £À ¨É¯É JµÀÄÖ?

45

¥ÀæxÀªÀÄ ¦.AiÀÄÄ.¹. ¸ÀASÁå±Á¸ÀçÛ ¥Àæ±Éß PÉÆñÀ
JgÀqÀÄ CAPÀzÀ ¥Àæ±ÉßUÀ¼ÀÄ:
1. ‘a’ MAzÀÄ ¹ÜgÀ ¸ÀASÉåAiÀiÁzÁUÀ, E(a) = a JAzÀÄ ¸Á¢ü¹.
2. X MAzÀÄ DPÀ¹äPÀ ZÀ®PÀ ªÀÄvÀÄÛ ‘a’ MAzÀÄ ¹ÜgÀ ¸ÀASÉåAiÀiÁzÁUÀ, E(aX) = a E(X) JAzÀÄ ¸Á¢ü¹.
3. X MAzÀÄ DPÀ¹äPÀ ZÀ®PÀ, a ªÀÄvÀÄÛ b JgÀqÀÄ ¹ÜgÀ ¸ÀASÉåUÀ¼ÁzÁUÀ, E(aX+b) = a E(X)+b JAzÀÄ ¸Á¢ü¹.
4. ‘a’ MAzÀÄ ¹ÜgÀ ¸ÀASÉåAiÀiÁzÁUÀ, V(a) = 0 JAzÀÄ ¸Á¢ü¹.
5. X MAzÀÄ DPÀ¹äPÀ ZÀ®PÀ ªÀÄvÀÄÛ ‘a’ MAzÀÄ ¹ÜgÀ ¸ÀASÉåAiÀiÁzÁUÀ, V(aX) = a2 V(X) JAzÀÄ ¸Á¢ü¹.
6. ¸ÀºÀ¸ÀA§AzsÀ UÀÄtPÀzÀ ¸ÀÆvÀæªÀ£ÀÄß UÀtÂvÀ ¤jÃPÉëAiÀÄ ¥ÀzÉÆÃQÛUÀ¼À°è §gɬÄj.
7. E(X) = 5 ªÀÄvÀÄÛ E(X2) = 36 DzÁUÀ, S.D(X) C£ÀÄß PÀAqÀÄ»r¬Äj.
8. E(X2) = 25 ªÀÄvÀÄÛ Var(X) = 16 DzÁUÀ, E(X) C£ÀÄß PÀAqÀÄ»r¬Äj.
9. E(X) = 10 ªÀÄvÀÄÛ S.D(X) = 12 DzÁUÀ, E(X2) C£ÀÄß PÀAqÀÄ»r¬Äj.
10. E(X) = 5 DzÁUÀ, E(6X) ¨É¯É JµÀÄÖ?
11. E(X) = 8 DzÁUÀ, E(4X+3) ¨É¯É JµÀÄÖ?
12. E(X) = 2 DzÁUÀ, E(-2X) ¨É¯É JµÀÄÖ?
13. V(X) = 6 DzÁUÀ, V(3X) ¨É¯É JµÀÄÖ?
14. V(X) = 4 DzÁUÀ, V(6X+7) ¨É¯É JµÀÄÖ?)
15. V(X) = 3 DzÁUÀ, Var(-X) PÀAqÀÄ»r¬Äj.
16. V(X) = 9 DzÁUÀ, Var(X/3) PÀAqÀÄ»r¬Äj.
17. V(X) = 16 DzÁUÀ, Var(3 - X) PÀAqÀÄ»r¬Äj.

LzÀÄ CAPÀzÀ ¥Àæ±ÉßUÀ¼ÀÄ:
1. M§â ªÀåQÛAiÀÄÄ MAzÀÄ £ÁtåªÀ£ÀÄß ªÀÄÆgÀÄ ¸À® aªÀÄÄävÁÛ£É. ¹AºÀ ªÀÄÄRUÀ¼À UÀtÂvÀ ¤jÃPÉëAiÀÄ£ÀÄß PÀAqÀÄ»r¬Äj.
2. X JA§ MAzÀÄ ZÀ®PÀªÀÅ -1, 0 ªÀÄvÀÄÛ 1 ¨É¯ÉUÀ¼À£ÀÄß C£ÀÄPÀæªÀÄ ¸ÀA¨sÀªÀvÉ 1/4, 1/2 ªÀÄvÀÄÛ 1/4 gÉÆA¢UÉ ºÉÆA¢zÉ.
¸ÀgÁ¸Àj ªÀÄvÀÄÛ «ZÀ®£É PÀAqÀÄ»r¬Äj.

3. F «vÀgÀuɬÄAzÀ k ªÀÄvÀÄÛ ¸ÀgÁ¸Àj PÀAqÀÄ»r¬Äj.
x 1 2 3 4 5 6
p(x) 0.1 0.15 k 0.25 0.18 0.12
4. MAzÀÄ ¥ÉnÖUÉAiÀÄ°è 8 ªÀ¸ÀÄÛUÀ½ªÉ, CªÀÅUÀ¼À°è 2 zÉÆõÀAiÀÄÄPÀÛªÁVªÉ. M§â ªÀåQÛAiÀÄÄ 3 ªÀ¸ÀÄÛUÀ¼À£ÀÄß DAiÉÄÌ
ªÀiÁrPÉƼÀÄîvÁÛ£É. DAiÉÄÌAiÀÄ°è zÉÆõÀAiÀÄÄPÀÛ ªÀ¸ÀÄÛUÀ¼À ¤jÃPÉëAiÀÄ£ÀÄß PÀAqÀÄ»r¬Äj.

5. F PɼÀUÉ ¤ÃrzÀ ¸ÀA¨sÀªÀ «vÀgÀuÉUÉ E(X) PÀAqÀÄ»r¬Äj.
x -2 -1 1 2
p(x) 1/5 2/10 3/10 2/5
6. F PɼÀV£À ¸ÀA¨sÀªÀ «vÀgÀuÉUÉ E(X+4) ¯ÉQ̹.
x 10 15 20
p(x) 1/6 2/6 3/6

46

¥ÀæxÀªÀÄ ¦.AiÀÄÄ.¹. ¸ÀASÁå±Á¸ÀçÛ ¥Àæ±Éß PÉÆñÀ
7. MAzÀÄ ¢éZÀ®PÀzÀ zÀvÁÛA±ÀzÀ°è E(X)= 4, E(Y) = 10, E(X2)= 25, E(Y2) = 136 ªÀÄvÀÄÛ E(XY) = 20. PÁ®ð¦AiÀÄgï
¸À£ÀߣÀ ¸ÀºÀ¸ÀA§AzsÀzÀ UÀÄtPÀ PÀAqÀÄ»r¬Äj.

8. MAzÀÄ ¢éZÀ®PÀzÀ zÀvÁÛA±ÀzÀ°è E(X) = 6 E(Y) = 9, E(X2)= 40 , E(Y2) = 130 ªÀÄvÀÄÛ E(XY) = 20.

rxy PÀAqÀÄ»rzÀÄ, «ªÀIJð¹.

9. MAzÀÄ ¢éZÀ®PÀzÀ zÀvÁÛA±ÀzÀ°è E(X) = 0 , E(Y) = 12 , E(X2) = 49, [E(X)]2 = 145 ªÀÄvÀÄÛ E(XY) = 3.5. Cov(X,
Y) ªÀÄvÀÄÛ rxy PÀAqÀÄ»r¬Äj.

10. F PɼÀV£À ¸ÀA¨sÀªÀ «vÀgÀuÉUÉ E(X), Var(X), S.D(X) ªÀÄvÀÄÛ E(2X-4) PÀAqÀÄ»r¬Äj.
X -1 0 1 2
p(x) 1/5 1/10 3/10 2/5
11. F PɼÀV£À «vÀgÀuÉUÉ ¸ÀgÁ¸Àj ªÀÄvÀÄÛ «ZÀ®£É PÀAqÀÄ»r¬Äj.
X 0 1 2 3 4
p(x) 3/8 1/4 1/8 3/16 1/16
12. F PɼÀV£À ¸ÀA¨sÀªÀ «vÀgÀuɬÄAzÀ PÁuÉAiÀiÁzÀ ¸ÀA¨sÀªÀvÉ, X £À ¸ÀgÁ¸Àj ªÀÄvÀÄÛ ¤AiÀÄvÀ «ZÀ®£ÉAiÀÄ£ÀÄß
PÀAqÀÄ»r¬Äj.
X -2 -1 0 1 2
p(x) 0.2 0.3 0.2 ? 0.1
13. F PɼÀV£À ¸ÀA¨sÀªÀ «vÀgÀuÉUÉ k, ¸ÀgÁ¸Àj ªÀÄvÀÄÛ «ZÀ®£ÉAiÀÄ£ÀÄß PÀAqÀÄ»r¬Äj.
X -3 -2 0 2 3
p(X) k/6 k/12 2k/3 k/2 k/6
14. X JA§ MAzÀÄ ZÀ®PÀªÀÅ 10 ªÀÄvÀÄÛ 20 JA§ ¨É¯ÉUÀ¼À£ÀÄß C£ÀÄPÀæªÀÄ ¸ÀA¨sÀªÀvÉ 1/3 ªÀÄvÀÄÛ 2/3 gÉÆA¢UÉ ºÉÆA¢zÉ.
¸ÀgÁ¸Àj ªÀÄvÀÄÛ «ZÀ®£É PÀAqÀÄ»r¬Äj.

15. X JA§ MAzÀÄ ZÀ®PÀªÀÅ 5 ªÀÄvÀÄÛ 10 JA§ ¨É¯ÉUÀ¼À£ÀÄß 0.6 ªÀÄvÀÄÛ 0.4 JA§ C£ÀÄPÀæªÀÄ ¸ÀA¨sÀªÀvÉUÀ¼ÉÆA¢UÉ
ºÉÆA¢zÉ. E(X), E(2X) ªÀÄvÀÄÛ V(X) PÀAqÀÄ»r¬Äj.

16. MAzÀÄ aîzÀ°è 4 ©½ ªÀÄvÀÄÛ 6 PÉA¥ÀÄ ZÉAqÀÄUÀ½ªÉ. F aî¢AzÀ JgÀqÀÄ ZÉAqÀÄUÀ¼À£ÀÄß DPÀ¹äPÀªÁV DAiÀiÁÝUÀ,
©½ ZÉAqÀÄUÀ¼À ¤jÃPÉë PÀAqÀÄ»r¬Äj.

17. MAzÀÄ aîzÀ°è 4 ºÀ¹gÀÄ ªÀÄvÀÄÛ 3 PÉA¥ÀÄ ZÉAqÀÄUÀ½ªÉ. M§â ªÀåQÛAiÀÄÄ F aî¢AzÀ ªÀÄÆgÀÄ ZÉAqÀÄUÀ¼À£ÀÄß
DPÀ¹äPÀªÁV DAiÀÄÄÝPÉƼÀÄîvÁÛ£É. CªÀ£ÀÄ DAiÀÄÄÝPÉÆAqÀ ¥Àæw ºÀ¹gÀÄ ZÉArUÉ gÀÆ.200 ªÀÄvÀÄÛ ¥Àæw PÉA¥ÀÄ ZÉArUÉ
gÀÆ.50 ¥ÀqÉAiÀÄĪÀ ºÁVzÀÝgÉ, CªÀ£À ¤jÃPÉë JµÀÄÖ?

18. M§â ªÀåQÛAiÀÄÄ £ÀÆå£ÀvÉAiÀÄļÀî MAzÀÄ £ÁtåªÀ£ÀÄß aªÀÄÄävÁÛ£É. MAzÀÄ ªÉÃ¼É ¹AºÀ ªÀÄÄR ªÉÄÃ¯É §AzÀgÉ, CªÀ£ÀÄ gÀÆ.
80 ¥ÀqÉAiÀÄÄvÁÛ£É E®èªÁzÀgÉ, gÀÆ.20 ¥ÀqÉAiÀÄÄvÁÛ£É. ¹AºÀ ªÀÄÄR ªÉÄÃ¯É §gÀĪÀ ¸ÀA¨sÀªÀvÉ 1/3 DzÀgÉ, CªÀ£À
¤jÃQëvÀ ºÀt PÀAqÀÄ»r¬Äj.

19. M§â ªÀåQÛAiÀÄÄ £ÀÆå£ÀvɬĮèzÀ MAzÀÄ zÁ¼ÀªÀ£ÀÄß J¸ÉAiÀÄÄvÁÛ£É. J¸ÉvÀzÀ°è ¸ÀªÀÄ ¸ÀASÉå ¥sÀ°vÁA±À zÉÆgÉvÀgÉ, CªÀ£ÀÄ
gÀÆ.500 ¥ÀqÉAiÀÄÄvÁÛ£É E®èªÁzÀgÉ, gÀÆ.100 PÀ¼z
É ÀÄPÉƼÀÄîvÁÛ£É. CªÀ£À ¤jÃPÉë PÀAqÀÄ»r¬Äj.

47

¥ÀæxÀªÀÄ ¦.AiÀÄÄ.¹. ¸ÀASÁå±Á¸ÀçÛ ¥Àæ±Éß PÉÆñÀ
20. M§â ªÀåQÛAiÀÄÄ £ÀÆå£ÀvɬĮèzÀ MAzÀÄ zÁ¼ÀªÀ£ÀÄß ¨Áj J¸ÉAiÀÄÄvÁÛ£É. ¥ÀqÉzÀ ¸ÀASÉå 3 UÀÄtPÀªÁVzÀÝgÉ, CªÀ£ÀÄ
gÀÆ.900 ¥ÀqÉAiÀÄÄvÁÛ£É E®èªÁzÀgÉ, gÀÆ.250 PÀ¼ÉzÀÄPÉƼÀÄîvÁÛ£É. CªÀ£À ¤jÃPÉë PÀAqÀÄ»r¬Äj.

21. M§â ªÀåQÛAiÀÄÄ gÀÆ.50 ¥ÀæªÉñÀ zsÀ£À ¤Ãr UÀÄjAiÀÄvÀÛ UÀÄAqÀÄ ºÉÆqÉAiÀÄĪÀ DlzÀ°è ¨sÁUÀªÀ»¸ÀÄvÁÛ£É. MAzÉÃ
UÀÄAr£À°è CªÀ£ÀÄ UÀÄj vÀ®Ä¦zÀgÉ, CªÀ¤UÉ gÀÆ.1000 zÉÆgÉAiÀÄĪÀÅzÀÄ. E®èªÁzÀgÉ, CªÀ¤UÉ K£ÀÄ zÉÆgÉAiÀÄĪÀÅ¢®è.
CªÀ£ÀÄ UÀÄjAiÀÄvÀÛ ºÉÆqÉAiÀÄĪÀ ¸ÀA¨sÀªÀvÉ 1/7 DzÀgÉ, CªÀ£À ¤jÃQëvÀ ºÀtªÀ£ÀÄß PÀAqÀÄ»r¬Äj.

22. MAzÀÄ ¯ÁljAiÀÄ°è ¥ÀæwAiÉÆAzÀPÉÌ gÀÆ.1 ¨É¯ÉAiÀÄļÀî 1000 nPÉmïUÀ½ªÉ. gÀÆ.100 gÀ 1 ªÉÆzÀ®£ÉAiÀÄ §ºÀĪÀiÁ£À,
gÀÆ.20 gÀ 2 ¢éwÃAiÀÄ §ºÀĪÀiÁ£ÀUÀ¼ÀÄ ªÀÄvÀÄÛ gÀÆ.10 gÀ 10 vÀÈwÃAiÀÄ §ºÀĪÀiÁ£ÀUÀ½ªÉ. MAzÀÄ nPÉmï
Rjâ¬ÄAzÀ DUÀĪÀ ¤jÃQëvÀ £ÀµÀÖ PÀAqÀÄ»r¬Äj.

23. MAzÀÄ aîzÀ°è MAzÀÄ gÀÆ¥Á¬ÄAiÀÄ 3, JgÀqÀÄ gÀÆ¥Á¬ÄAiÀÄ 4 ªÀÄvÀÄÛ LzÀÄ gÀÆ¥Á¬ÄAiÀÄ 2 £ÁtåUÀ½ªÉ. M§â
ºÀÄqÀÄUÀ£ÀÄ F aî¢AzÀ JgÀqÀÄ £ÁtåUÀ¼À£ÀÄß DPÀ¹äPÀªÁV DAiÀÄÄÝPÉƼÀÄîvÁÛ£É. £ÁtåUÀ¼À ºÀtzÀ ¤jÃPÉë JµÀÄÖ?

24. MAzÀÄ aîzÀ°è 1 jAzÀ 6 ¸ÀASÉåUÀ¼ÀgÀĪÀ 6 aÃnUÀ½ªÉ. M§â ªÀåQÛAiÀÄÄ JgÀqÀÄ aÃnUÀ¼À£ÀÄß DPÀ¹äPÀªÁV
DAiÀÄÄÝPÉƼÀÄîvÁÛ£É. aÃnUÀ¼À ªÉÄð£À ¸ÀASÉåUÀ¼À ªÉÆvÀÛ ¸ÀªÀÄ ¸ÀASÉåAiÀiÁzÀgÉ, CªÀ¤UÉ gÀÆ.100 zÉÆgÉAiÀÄĪÀÅzÀÄ.
E®èªÁzÀgÉ, gÀÆ.50 PÀ¼ÉzÀÄPÉƼÀÄîvÁÛ£É. CªÀ£À ¤jÃPÉëAiÀÄ£ÀÄß PÀAqÀÄ»r¬Äj.

25. £ÀÆå£ÀvɬĮèzÀ JgÀqÀÄ £ÁtåUÀ¼À£ÀÄß MAzÀÄ ¸À® aªÀÄÄä¯ÁVzÉ. JgÀqÀÆ £ÁtåUÀ¼ÀÄ ¹AºÀ ªÀÄÄR vÉÆÃjzÀgÉ M§â
ªÀåQÛAiÀÄÄ gÀÆ.10 ¥ÀqÉAiÀÄÄvÁÛ£É ªÀÄvÀÄÛ JgÀqÀÆ vÉ£É ªÀÄÄR vÉÆÃjzÀgÉ gÀÆ.5 ¥ÀqÉAiÀÄÄvÁÛ£É. E®èªÁzÀgÉ, CªÀ£ÀÄ
gÀÆ.8 PÀ¼ÉzÀÄPÉƼÀÄîvÁÛ£É. D ªÀåQÛAiÀÄ ¤jÃPÉëAiÀÄ£ÀÄß PÀAqÀÄ»r¬Äj.

26. M§â ªÀåQÛAiÀÄÄ UÀÄj vÀ®Ä¥ÀĪÀAvÉ ºÉÆqÉAiÀÄĪÀ ¸ÀA¨sÀªÀvÉ 2/3. UÀÄj vÀ®Ä¥ÀĪÀAvÉ ºÉÆqÉzÀgÉ CªÀ¤UÉ gÀÆ.150
zÉÆgÉAiÀÄĪÀÅzÀÄ. E®èªÁzÀgÉ, CªÀ£ÀÄ gÀÆ.50 PÀ¼ÉzÀÄPÉƼÀÄîvÁÛ£É. CªÀ£À ¤jÃPÉëAiÀÄ£ÀÄß PÀAqÀÄ»r¬Äj.

27. X ªÀÄvÀÄÛ Y UÀ¼À F PɼÀV£À ¢éZÀ®PÀzÀ zÀvÁÛA±À¢AzÀ (i) ‘k’ (ii) E(2X+3Y) PÀAqÀÄ»r¬Äj.
x\ y 0 10 20
1 0 0.1 0.1
2 0.1 0.2 0.1
3 0.2 k 0.1

28. X ªÀÄvÀÄÛ Y UÀ¼À F PɼÀV£À dAn ¸ÀA¨sÀªÀ «vÀgÀuÉUÉ k, E(X+Y) ªÀÄvÀÄÛ rxy PÀAqÀÄ»r¬Äj.
X Y 1 3 9
2 0.1 0.1 0.05
4 0.2 K 0.1
6 0.1 0.15 0.2

29. X ªÀÄvÀÄÛ Y UÀ¼À F PɼÀV£À dAn ¸ÀA¨sÀªÀ «vÀgÀuÉUÉ r ªÀÄvÀÄÛ E(3X+4Y) PÀAqÀÄ»r¬Äj.
X Y 1 2 3
-5 0 0.1 0.1
0 0.1 0.2 0.2
5 0.2 0.1 0

48

¥ÀæxÀªÀÄ ¦.AiÀÄÄ.¹. ¸ÀASÁå±Á¸ÀçÛ ¥Àæ±Éß PÉÆñÀ
30. F PɼÀV£À ¢éZÀ®PÀzÀ zÀvÁÛA±À¢AzÀ X ªÀÄvÀÄÛ Y UÀ¼À £ÀqÀÄ«£À ¸ÀºÀ¸ÀA§AzsÀzÀ UÀÄtPÀ PÀAqÀÄ»r¬Äj.
x\ y 0 10 20
1 0 0.1 0.1
2 0.1 0.2 0.1
3 0.2 0.1 0.1
31. F zÀvÁÛA±ÀPÉÌ rxy PÀAqÀÄ»r¬Äj.
x\ y 1 2 3
5 0 0.1 0.1
0 0.1 0.1 0.2
1 0.1 0.2 0.1

*****

49

I PU Statistics Question Bank
UNIT – I
INTRODUCTION – MEANING AND SCOPE
Choose the most appropriate answer from the choices given.
1. Who is the father of statistics?
a) R. A. Fisher b) A. L. Bowley c) Horace Secrist d) Boddington.

2. The Latin word from which the term ‘STATISTICS’ has been derived is:
a) Status b) Statista c) Statistik d) Statistique

3. The Italian word from which the term ‘STATISTICS’ has been derived is:
a) Status b) Statista c) Statistik d) Statistique

4. The German word from which the term ‘STATISTICS’ has been derived is:
a) Status b) Statista c) Statistik d) Statistique

5. The French word from which the term ‘STATISTICS’ has been derived is:
a) Status b) Statista c) Statistik d) Statistique

6. Who defined STATISTICS as “the science of counting”?
a) R. A. Fisher b) A. L. Bowley c) Horace Secrist d) Boddington.

7. The totality of units under consideration is called:
a) Population b) Sample c) Avariable d) Anattribute

8. The representative units of a population is called -
a) Sample b) A variable c) An attribute d) Nominal scale

9. A quantitative characteristic which varies from unit to unit is:
a) Population b) Sample c) A variable d) An attribute

10. A qualitative characteristic which varies from unit to unit is:
a) Population b) Sample c) A variable d) An attribute

11. A number assigned for every unit for identification of different categories is
called-
a) Anominal scale b) An ordinal scale c) A variable d) An attribute

12. Numbers assigned to observations that can be arranged in ascending or
descending order is called-
a) Anominal scale b) An ordinal scale c) A variable d) An attribute

13. The statistical study of human population is called –
a) Biometry b) Demography c) Econometrics d) Stylometry

3

I PU Statistics Question Bank
Fill in the blanks by choosing the appropriate word from those given in the
brackets.
(Demography, Variable, Population, Attribute, Statista, Ordinal, Statistique,
Sample, Nominal, Quantitative, Qualitative, Status, Aggregate, Statistik,
Numerically, Discrete)
1. The Latin word from which the term ‘STATISTICS’ has been derived is
____________.
2. The Italian word from which the term ‘STATISTICS’ has been derived is
___________.
3. The German word from which the term ‘STATISTICS’ has been derived is
___________.
4. The French word from which the term ‘STATISTICS’ has been derived is
____________.
5. The totality of units under consideration is called ____________.
6. The representative units of a population is called ____________.
7. Numerically measurable characteristics are called ______________ characteristics.
8. The characteristics which are not numerically measurable are _______________
characteristics.
9. A quantitative characteristic which varies from unit to unit is ____________.
10. A qualitative characteristic which varies from unit to unit is ____________.
11. The statistical study of human population is called ____________.
12. Statistics are ____________ of facts.
13. Statistics are ___________ expressed.
14. A number assigned for every unit for identification of different categories is called
a __________ scale.
15. Numbers assigned to observations that can be arranged in ascending or
descending order is called an __________ scale.

Match the following. (Direct answers are given)
Status Latin word
Statista Italian word
Statistik German word
Statistique French word
Sir Ronald A. Fisher Father of statistics
P. C. Mahalanobis Father of Indian statistics
Demography Statistical study of human population
Actuarial science Statistics in the field of insurance
Quantitative data Numerically expressed
Height Variable
Skin colour Attribute

4

I PU Statistics Question Bank
One mark questions
1. Who is the father of Indian Statistics?
2. Name the Latin word from which the term “STATISTICS” has been derived.
3. Who defined STATISTICS as “the science of counting”?
4. Define Bowley’s definition of Statistics.
5. Give Boddington’s definition of Statistics.
6. State Croxton and Cowden definition of Statistics.
7. Does Statistics deal with individual data?
8. Define population.
9. Define sample.
10. Define qualitative characteristic.
11. Define quantitative characteristic.
12. Define attribute.
13. Give an example for attribute.
14. Define variable.
15. Define discrete variable.
16. Give an example for discrete variable.
17. Define continuous variable.
18. Give an example for continuous variable.
19. Define nominal scale.
20. Define ordinal scale.

Two mark questions:
1. Write down Prof.Horace Secrist’s definition of Statistics.
2. Mention two characteristics of Statistics.
3. Mention two functions of Statistics.
4. Mention two limitations of Statistics.
5. Mention two fields where Statistics is used.
6. Mention two causes of distrust of Statistics.
7. Mention two remedies to remove distrust of Statistics.
8. Define population and sample.
9. Distinguish between qualitative and quantitative characteristics.
10. Define attribute. Give an example.
11. Define variable. Give an example.
12. Define discrete variable with the help of an example.
13. Define continuous variable with the help of an example.
14. Mention the type of variable seen in
(a) Daily temperature. (b) Size of shoes.
15. What is meant by nominal and ordinal scales?

Five mark questions:
1. Define Horace Secresit’s definition of Statistics. Explain any two of them.
2. Mention five characteristics of Statistics.
3. Mention five functions of Statistics.
4. Mention three functions and two limitations of Statistics.
5. Mention five limitations of Statistics.

5

I PU Statistics Question Bank
UNIT – II
ORGANIZATION OF DATA
Choose the most appropriate answer from the choices given.
1. The person who conducts the statistical enquiry is
a) Investigator b) Enumerator c) Respondent d) Informant

2. A complete enumeration of each and every unit of the population is called
a) Pilot Survey b) Census enumeration c) Sample survey d) Sampling

3. The procedure in which every unit has an equal chance of being included in the
sample is
a) Simple random sampling b) Systematic sampling
c) Stratified sampling d) Sampling error

4. Procedure of drawing samples by selecting equally separated units is
a) Simple random sampling b) Systematic sampling
c) Stratified sampling d) Sampling error

5. Procedure of drawing appropriate number of sample units from each
homogeneous stratum is
a) Simple random sampling b) Systematic sampling
c) Stratified sampling d) Sampling error

Fill in the blanks by choosing the appropriate word from those given in the
brackets.
(Primary, Enumerator, Biased, Correspondents, Census, Questionnaire,
Investigator, Respondents, Unbiased, Schedule, Manipulation, Absolute)
1. The ____________ is the person who conducts the statistical enquiry.
2. The person who collects the information for the investigator is called ___________.
3. The _____________ are the persons from whom the information will be collected.
4. Data which are collected for the first time, directly from the field by the
investigator is called ________ data.
5. 5. Agents who collect information from the informants are generally called
________________.
6. ___________ is a list of questions where the answers are filled by the informats.
7. ___________ is a list of questions where the facts will be supplied by informants
and recorded by enumerator.
8. A complete enumeration of each and every unit of the population is called
__________ enumeration.
9. The error that occurs at the time of analysis is called error of _____________.
10. The errors that occur with the notice of the investigator are called ____________
errors.
11. The errors that occur without the notice of the investigator are called
____________ errors.

6

I PU Statistics Question Bank
Match the following: (Direct answers are given)
Investigator The person who conducts statistical enquiry
The data collected for the first
Primary data
time(directly from the field)
Direct personal observation Primary data
Indirect oral interview Primary data
Information through agencies Primary data
Mailed questionnaire Primary data
Schedules sent through
Primary data
enumerator
Agents who collect information from the
Correspondents
informants
Absolute error Actual value – estimated value

One mark questions
1. What is meant by statistical enquiry?
2. Who is an investigator?
3. Who is enumerator?
4. Who is respondent?
5. Define collection of data.
6. Define primary data.
7. What is a questionnaire?
8. What is a schedule?
9. Define secondary data.
10. Give an example for published source of secondary data.
11. Give an example for unpublished source of secondary data.
12. Define census enumeration.
13. Define sample survey.
14. What is pilot survey?
15. Define sampling.
16. What is meant by simple random sampling?
17. What is meant by sampling (Statistical) error?
18. What is meant by absolute error? (Define absolute error).
19. What is meant by relative error? (Define relative error).
20. When the sampling errors are decreases?

7

I PU Statistics Question Bank
Two mark questions:
1. Mention the two stages of statistical enquiry.
2. What is primary data? Mention a method of collecting the same.
3. Mention two methods of collecting primary data.
4. Mention the sources of secondary data.
5. Define census enumeration and sample survey.
6. Mention a merit and demerit of census enumeration.
7. Mention a merit and demerit of sample survey.
8. Mention two methods of sampling.
9. Mention two causes of sampling errors.
10. Distinguish between biased and unbiased errors.
11. Mention the methods of measurement of errors.

Five mark questions:
1. Mention the points that are to be considered in planning an enquiry.
2. Mention the points that are to be considered in execution of the survey.
3. Mention the merits and demerits of direct personal observation method of
collecting primary data.
4. What are the guidelines for the construction of a questionnaire?
5. Mention any two merits and three demerits of census enumeration.
6. Mention any three merits and two demerits of sample survey.
7. Distinguish between census enumeration and sample survey.
8. Briefly explain the three methods of sampling.

8

I PU Statistics Question Bank
UNIT – III
CLASSIFICATION AND TABULATION
Choose the most appropriate answer from the choices given.
1. Classification on the basis of variable is
a) Chronological b) Geographical c) Qualitative d) Quantitative

2. Classification on the basis of attribute is
a) Chronological b) Geographical c) Qualitative d) Quantitative

3. Classification of statistical data according to time is called-
a) Quantitative classification b) Qualitative classification
c) Chronological classification d) Geographical classification.

4. While framing a frequency distribution, if class intervals are not considered, is
called
a) Open-end frequency distribution b) Continuous frequency distribution
c) Discrete frequency distribution d) Cumulative frequency distribution

5. In a class, if lower as well as upper limits are included in the same class, such a
class is called –
a) Inclusive class b) Exclusive class c) Open-end class d) Class mark

6. The correction factor of the class intervals: 10-19 20-29 30-39 is -
a) 0.25 b) 0.5 c) 0.75 d) 1

7. Width of the class interval is
a) UCL + LCL b) UCL ÷ LCL c) UCL - LCL d) UCL X LCL

8. The mid-point of the class interval 10 – 20 is-
a) 10 b) 12.5 c) 15 d) 20

9. The mid-point of the class interval 10 – 19 is-
a) 10.5 b) 14.5 c) 15.5 d) 19.5

10. In a table, column headings are called –
a) Stubs b) Captions c) Head note d) Foot note

11. In a table, row headings are called –
a) Stubs b) Captions c) Head note d) Foot note

12. ‘Stub’ of a table is the –
a) Left part of the table describing the columns
b) Right part of the table describing the columns
c) Right part of the table describing the rows
d) Left part of the table describing the rows.

9

I PU Statistics Question Bank
Fill in the blanks by choosing the appropriate word from those given in the
brackets.
(Frequency, Source, Chronological, Class mark, Stubs, Dichotomous,
Cumulative, Discrete, Continuous, Open-end, Width, Body, f/w, Captions)
1. Classification of statistical data according to time is called
_____________classification.
2. The classification of units on the basis of single characteristic into two classes is
called_____________ classification.
3. The number of observations belongs to a class is ___________.
4. _________refers to the number of times an observation repeated.
5. While framing a frequency distribution, if class intervals are not considered, is
called _______frequency distribution.
6. While framing a frequency distribution, if class intervals are considered, is called
__________frequency distribution.
7. In a class, if the lower or upper limit of the class is not specified such a class is
called ___________class.
8. The central value of a class is called ___________.
9. The difference between the upper and lower limits of a class is called __________of
the class.
10. The added up frequencies are called ____________frequencies.
11. Frequency density is __________.
12. In a table, column headings are called __________.
13. In a table, row headings are called __________.
14. The __________of the table contains numerical data.
15. Below foot note or below the table, ___________of the data may be mentioned for
verification to the reader.

Match the following. (Direct answers are given)
Classification according to time Chronological
Classification on the basis of attributes Qualitative
Classification on the basis of Variables Quantitative
Width of the class interval UCL – LCL
Central value of a class Class mark
Mid-point of the class 10 – 30 20
Mid-point of the class 10 – 19 14.5
Width of the class 30 – 40 10
Prof. Sturges’s rule K = 1 + 3.322 log N
Captions Column headings
Stubs Row headings
Body of the table Contains numerical data

10

I PU Statistics Question Bank
One mark questions
1. What is classification of the data?
2. Mention an objective of classification of data.
3. Define temporal classification.
4. Define spatial classification.
5. Define qualitative classification.
6. Define quantitative classification.
7. Define frequency.
8. Define inclusive class interval.
9. Define exclusive class interval.
10. For what purpose correction factor is used, in frequency distribution?
11. Define open-end class interval.
12. What is class midpoint?
13. Define frequency density.
14. Define relative frequency.
15. What is bi-variate frequency distribution?
16. What is tabulation of the data?
17. What is stub of a table?
18. What is caption of a table?

Five mark questions:
1. Number of teaching staff working in 20 different colleges was recorded as below:
15, 12, 18, 10, 15, 12, 20, 25, 18, 10, 15, 12, 15 20, 25, 15, 18, 20, 15, 18
Prepare a frequency table.

2. The number of doctors serving in forty different hospitals were recorded as
below:
6 7 5 7 6 3 9 8 6 7 5 7 6 8 5 8 5 9 5 6
5 9 6 6 4 4 7 5 5 8 5 3 3 8 4 4 3 4 4 3
Prepare a discrete frequency table.

3. In a survey of 40 families in a certain locality, the number of children per family
was recorded and the following data were obtained.
1 0 3 2 1 5 6 2 2 1 0 3 4 2 5 6 3 2 1 1
3 3 2 4 2 2 3 0 2 1 4 5 3 3 4 4 5 4 2 1
Represent the data in the form of a discrete frequency distribution.

4. Following is the data regarding the number of meteors observed in 30 different
days:
7, 4, 2, 5, 9, 7, 4, 3, 8, 6, 9, 10, 3, 3, 5, 9, 5, 7, 6, 3, 8, 4, 3, 7, 9, 8, 10, 6, 8, 7.
Classify the above observations.

11

I PU Statistics Question Bank
5. A review of the first 30 pages of a Statistics book reveals the following printing
mistakes:
0 1 3 3 2 5 6 0 1 0 4 1 1 0 2
3 2 5 0 4 2 2 3 3 4 6 1 4 3 2
Prepare a frequency distribution of printing mistakes.

6. Following are the ages (in years) of school children:
12 5 13 12 10 11 7 9 6 10 9 13 5 10 7
14 6 11 13 7 9 8 11 10 8 12 13 9 6 14
Prepare a frequency table using inclusive class interval of width 3 years.

7. Following is the data regarding the I.Q of 30 children of a school.
106 118 112 120 103 105 99 139 65 113
100 108 100 112 110 109 117 98 103 99
108 116 93 100 120 110 95 101 105 98
Prepare a frequency distribution with class intervals: < 90, 90-110, 110-120,
≥120.

8. From the following data of the hourly wages (in rupees) of workers employed in a
certain factory, construct a frequency table with classes 40-49, 50-59 and so on.
76 63 83 75 61 41 115 82 60 40 74 42
78 95 56 77 78 65 67 50 84 76 100 53
100 81 59 73 54 79 79 80 104 69 68 79
72 80 70 69 64 42 76 84 90 77 49 66
73 71 94 78 86 51 96 103 52 79 50 72

9. Weights in kg of 50 students of a college are as follows.
42 62 46 54 41 37 54 44 32 45
47 50 58 49 51 42 46 37 42 39
54 39 51 58 47 64 43 48 49 48
49 61 41 40 58 49 59 57 37 34
56 38 45 52 46 40 63 41 51 41
Prepare a frequency distribution table with suitable class intervals.

10. Given below are the daily wages in rupees of 36 workers in a factory
manufacturing plastic products.
100 115 120 125 92 140 150 162 189
165 200 220 250 240 300 320 270 280
400 382 288 235 225 312 270 250 242
344 248 188 220 240 212 224 325 425
Form a frequency distribution, taking first class-interval as 90-140 and width as
50.

12

I PU Statistics Question Bank
11. Below are given the marks obtained by a batch of 10 students in Mathematics
and Statistics:
Roll No. 1 2 3 4 5 6 7 8 9 10
Marks in Mathematics 53 54 52 52 50 53 54 54 52 50
Marks in Statistics 58 55 57 56 58 57 56 59 57 55
Prepare a bi-variate frequency table.

12. Beloware the ages of husbands and wives. Prepare a bi-variate frequency
distributionwith class intervals as (20-25), (25-30), … for both variables.
Age of Husband (in years) 24 42 29 43 35 41 33 36 29 38
Age of wife (in years) 25 37 25 37 23 39 23 32 24 38

13. Draw a blank table to show the students of a college according to
i. Class: I PUC, II PUC.
ii. Faculty: Arts, Commerce and Science.
iii. Sex: Boys, Girls.

14. Prepare a blank table showing the distribution of students of a college according
to :
i. Faculty: Commerce, Science.
ii. Sex: Boys and girls.
iii. Age group (in years): Below 18, 18 - 20, 20 and above.

15. Prepare a blank table to show the distribution of students according to
i. College: Government, Aided, Unaided.
ii. Faculty: Science, Commerce, Arts.
iii. Gender: Boys, Girls.

16. Prepare a blank table showing the particulars relating to the residents of a
certain locality according to:
i. Occupation: office assistants, business men, teachers, bank employees.
ii. Sex: men and women.
iii. Marital status: married, single.

17. Draft a blank table to show the distribution of employees of a factory according
to-
i. Sex: Men, Women
ii. Category: Skilled, Unskilled.
iii. Wages: Below Rs.5000, Rs.5000-10000 and Rs.10000 & above.

18. In a sample study about the literacy of residents of a village, the following data
were observed. 55% of the residents were males; 85% were literates; only 12%
were non-literate females. Tabulate the information.

13

I PU Statistics Question Bank
19. In a sample study regarding smoking habit in a town, the following data were
obtained:
Men population = 58%
Smokers = 22%
Men smokers = 18%
Tabulate the above data.

20. In a sample study about food habits of a town, the data was obtained:
50 % persons were males
30 % were non-vegetarians
18 % male non-vegetarians
Tabulate the above data.

21. The number of students in a college in 2005 was 510. Of these 480 were boys. In
2010 the number of boys increased by 10% and that of girls increased by 30% of
that of 2005.In 2012 the total number of students in the college was 1200, the
number of boys being double the number of girls. Tabulate the above
information.

14

I PU Statistics Question Bank
UNIT – IV
DIAGRAMMATIC AND GRAPHIC PRESENTATION OF DATA
Choose the most appropriate answer from the choices given.
1. Simple bar diagram is a type of,
a) One-dimensional diagram b) Two-dimensional diagram
c) Three-dimensional diagram d) Cartograms

2. Multiple bar diagram is a type of,
a) One-dimensional diagram b) Two-dimensional diagram
c) Three-dimensional diagram d) Cartograms

3. Component bar diagram is a type of,
a) One-dimensional diagram b) Two-dimensional diagram
c) Three-dimensional diagram d) Cartograms

4. Percentage bar diagram is a type of,
a) One-dimensional diagram b) Two-dimensional diagram
c) Three-dimensional diagram d) Cartograms

5. Pie-diagram diagram is a type of,
a) One-dimensional diagram b) Two-dimensional diagram
c) Three-dimensional diagram d) Cartograms

6. Mode of the distribution can be obtained graphically by using-
a) Histogram b) Frequency curve c) Frequency polygon d) Ogives

7. Median of the distribution can be obtained graphically by using-
a) Histogram b) Frequency curve c) Frequency polygon d) Ogives

8. Partition values of the distribution can be obtained graphically by using-
a) Histogram b) Frequency curve c) Frequency polygon d) Ogives

Fill in the blanks by choosing the appropriate word from those given in the
brackets.
(Continuous, histogram, cumulative, two, one, ogives, Pie-chart)
1. Multiple bar diagram is a type of ___________dimensional diagram.
2. Pie-chart is a type of __________dimensional diagram.
3. Mode can be obtained graphically by using______________.
4. Median of the distribution can be obtained graphically by using___________.
5. Histogram is constructed for a ____________frequency distribution.
6. The curves drawn for ___________frequencies against the class limits are called
ogives.

15

I PU Statistics Question Bank
Match the following. (Direct answers are given)
Simple bar diagram One dimensional
Multiple (Compound) bar diagram One dimensional
Component (Sub-divided) bar diagram One dimensional
Percentage bar diagram One dimensional
Pie-chart Two dimensional diagram
Area of the histogram Total frequency
Histogram Mode of the distribution
Graph used to find median Ogives
Graph used to find partition values Ogives
Cumulative frequency distribution Less than ogive
Ogives Cumulative frequency curves

One mark questions:
1. What is one dimensional diagram?
2. Mention a type of one dimensional diagram.
3. Mention a two dimensional diagram.
4. What is a pie diagram?
5. What is Histogram?
6. Name the graph used to locate mode.
7. Name the graph used to locate median.
8. Mention a merit of a diagram.
9. Mention a merit of graph.
10. Name the average located from Histogram.

Five mark questions:
1. Represent the following data regarding the production of paddy (in ’000 tons) by
simple bar diagram.
Year 2005 2006 2007 2008
Production 90 85 100 105

2. Following figures represent the decadal change of population of India. Draw a
simple bar diagram.
Year 1971 1981 1991 2001 2011
Population(Million) 548 688 846 1028 1210

3. The following table shows the results of II P.U.C. students of a college for the last
three years, Draw a multiple bar diagram.
Year 1st class 2nd class Pass class Failed
2010 25 32 28 5
2011 28 25 17 10
2012 32 30 15 3

16

I PU Statistics Question Bank

4. The production of wheat and rice of a region are given below:
Year 2005 2006 2007 2008 2009 2010
Production Wheat 12 15 18 19 22 26
(in Metric tons) Rice 25 30 32 36 40 45
Draw a multiple bar diagram to represent the data.

5. Following is the data showing the strength of a college in different faculties. Draw
a multiple bar diagram to represent the data.
Students in the year
Faculty
2008 2009 2010
Arts 150 90 100
Science 120 150 140
commerce 200 250 280
Total 470 490 520

6. Following is the data regarding the strength of students of a university during
2008-10. Construct a component bar diagram.
Faculty
Year
Arts Science Commerce Engineering Medical
2008 200 150 50 30 20
2009 250 200 80 50 40
2010 300 250 100 80 50

7. For the following data regarding the expenditure of families A and B. Represent
the data by sub-divided bar diagram.
Items Food Clothing House rent Education Fuel Others
Expenditure in Family A 2580 880 2200 360 280 1800
Rupees Family B 3350 1250 3100 1550 450 2000

8. Following data represents the major consumption of food grains in Karnataka
state. Represent the data by a subdivided bar diagram.
Food Quantity Consumed
Grains (In million Tons)
Jower 450
Ragi 320
Wheat 150
Rice 400

17

I PU Statistics Question Bank
9. The following data relates to the monthly expenditure (in Rs.) of two families A
and B.
Items of Expenditure (in Rs)
expenditure Family A Family B
Food 2000 2500
Clothing 1000 2000
Rent 800 1000
Light & Fuel 400 500
Miscellaneous 800 2000
Represent the data by a rectangular diagram on percentage basis.

10. Following are the marks obtained by two students A and B in an annual
examination. Represent the data by percentage bar diagram.
Marks of students
Subjects
Student A Student B
Language 72 82
English 85 92
Statistics 97 95
Economics 88 90
Business studies 90 87
Accountancy 94 98
Total 526 544

11. Percentage breakup of the cost of construction of a house in Bangalore
(Excluding land cost) is given below : Labour: 20% , Bricks:12%, Cement:20%,
Steel:15%, Wood:13%, Supervision:15%. Other expenses: 5%. Construct a pie
diagram.

12. For the following data regarding the income of the government from different
sources, draw a pie diagram:
Source Customs Excise Income tax Corporate tax Miscellaneous
Revenue
80 190 160 75 35
(in Million Rs.)

13. The following table shows the cost structure of Indian Hotel Industry in
percentages.
Cost Administrative Employees Repairs and Food and Selling
Electricity
components expense payments maintenance Beverages expenses
Total
30 20 12 16 14 8
expenses (%)
Draw a Pie diagram to represent the data.

14. Draw a histogram from the following data and locate mode:
C.I 0-10 10-20 20-30 30-40 40-50
f 13 17 15 13 10

15. Draw a histogram for the following data.
Wages (000’s Rs.) 2- 4 5 - 7 8 - 10 11 - 13 14 - 16 17 - 19 20 - 22 23 - 25
No. of workers 2 6 8 25 40 30 20 8

18

I PU Statistics Question Bank
16. Draw a histogram for the following data and hence locate the value of mode.
Marks 0-5 5 - 10 10-20 20-30 30-40 40-50 50-70 70-80
No. of students 2 6 8 25 40 30 20 8

17. Draw a histogram and then obtain frequency polygon from histogram.
Daily wages (in Rs.) 100-150 150-200 200-250 250-300 300-350 350-400
No. of workers 7 19 27 15 12 8

18. Draw a frequency polygon to the following frequency distribution.
Mid-points 15 25 35 45 55 65 75
Frequency 5 12 25 18 10 6 2

19. Draw histogram, frequency polygon and then obtain frequency curve from
thefollowing frequency distribution.
C.I 10-20 20-30 30-40 40-50 50-60
f 2 5 12 7 4

20. Draw frequency curve from the following frequency distribution.
Marks 0-10 10-20 20-30 30-40 40-50
No. of students 5 14 20 16 8

21. Draw a less than Ogive for the following distribution and locate the median from
the graph.
Daily wages
250 260 270 280 290 300 310 320 330 340
Below Rs.
No. of workers 6 16 38 70 110 154 192 218 228 250

22. Draw a less than Ogive and locate the median from the graph.
Marks 0-10 10-20 20-30 30-40 40-50 50-60
No. of students 3 9 15 30 18 5

23. Draw Ogive from the following data and measure the median value.
Class interval 0-10 10-20 20-30 30-40 40-50
Frequency 5 11 21 16 10

24. Draw less than and more than Ogives to the following frequency distribution and
hence, locate the value of median.
Classes 10-20 20-30 30-40 40-50 50-60 60-70 70-80
Frequencies 3 8 14 25 15 7 2

25. Draw less than and more than Ogives to the following frequency distribution.
Class 20-24 24-28 28-32 32-36 36-40 40-44
Frequency 17 25 40 23 12 8

26. From the following data, draw a less than ogive and locate the values of Q1 and
Q3 Graphically.
Less than Less than Less than Less than Less than Less than
Marks
10 20 30 40 50 60
No. of
5 13 24 39 52 60
students

19

I PU Statistics Question Bank
UNIT – V
ANALYSIS OF UNIVARIATE DATA
Choose the most appropriate answer from the choices given.
1. The algebraic sum of deviations of a given set of observations taken from their
mean is-
a) 0 b) 1 c) 2 d)3

2. The Median of the variate values 10, 12, 15, 18, 20 is:
a) 12 b) 15 c) 17 d) 19

3. The Mode of the variate values 8, 9, 8, 7, 8 is:
a) 6 b) 7 c) 8 d) 9

4. In a moderately skewed distribution, the relation among the value of mean,
median and mode is-
a) Mode = 2Median – 3Mean b) Mode = Median – 3Mean
c) Mode = 2Median – Mean d) Mode = 3Median – 2Mean

5. The geometric mean of 4 and 16 is,
a) 5 b) 6 c) 8 d) 10

6. The G.M. of 8, 4, 2 is,
a) 4 b) 2 c) 8 d) 6

7. Geometric mean of 4, 0, 6 and 8 is
a) 4 b) 0 c) 6 d) 8

8. Measures which divide the data into four equal parts are known as –
a) Quartiles b) Deciles c) Percentiles d) Median

9. Measures which divide the data into ten equal parts are known as –
a) Quartiles b) Deciles c) Percentiles d) Median

10. Measures which divide the data into 100 equal parts are known as –
a) Quartiles b) Deciles c) Percentiles d) Median

11. If Q2 = 40, the value of D5 is:
a) 10 b) 20 c) 30 d) 40

12. If D5 = 30, the value of P50 is:
a) 10 b) 20 c) 30 d) 40

13. If Q2 = 70, the value of P50 is:
a) 50 b) 70 c) 80 d) 90

14. Formula for range (R) of a set of values is –
a) H – L b) H + L c) L – H d) H ÷ L

15. The range of the variate values 10, 20, 15, 30, 35 is:
a) 10 b) 15 c) 20 d) 25

20

I PU Statistics Question Bank
Fill in the blanks by choosing the appropriate word from those given in the
brackets.
(Quartiles, Least, 0, 3, Quartile, Median, Percentiles, Bell, Deciles, Mode, Symmetric,
Partition, 3M - 2𝐱̅)
1. The algebraic sum of deviations of a given set of observations taken from their
mean is _______.
2. The sum of squares of deviations from their arithmetic mean is ________.
3. ___________is the middle most value of a data when they are arranged in an
order.
4. __________is a value which occurs most frequently in a set of observations.
5. Empirical relation between mean, median and mode is Z = __________
6. Measures which divide a given data into equal parts are known as
__________values.
7. Measures which divide the data into four equal parts are known as __________.
8. Measures which divide the data into ten equal parts are known as __________.
9. Measures which divide the data into 100 equal parts are known as _________.
10. _________deviation is known as half of the inter quartile range.
11. When the symmetric distribution is plotted on a graph, we get ______shaped
curve.
12. In a ___________ distribution, mean, median and mode are equal.
13. For a mesokurtic distribution, the value of β2 is _____.
14. For a leptokurtic distribution, the value of β2 is greater than ______.
15. For a platykurtic distribution, the value of β2 is lesser than ______.

Match the following. (Direct answers are given)
Σ (x - x̅) 0
Σ (x - x̅) is
2 Least
Mode 3Median – 2Mean
Average growth rate Geometric mean
Average speed Harmonic mean
Quartiles Divide the data into 4 equal parts
Deciles Divide the data into 10 equal parts
Percentiles Divide the data into 100 equal parts
Range H–L
Inter quartile range Q3 – Q1
Asymmetry (Lack of symmetry) Skewness
Kurtosis Peakedness
β2> 3 Leptokurtic distribution
β2 = 3 Mesokurtic distribution
β2< 3 Platykurtic distribution

21

I PU Statistics Question Bank
One Mark Questions:
1. What is meant by ‘central tendency’?
2. What is meant by ‘measure of central tendency’?
3. Mention any one objective of average.
4. Define arithmetic mean.
5. Define Median.
6. Define Mode.
7. What is uni-modal distribution?
8. Define geometric mean.
9. Define harmonic mean.
10. State the minimal property of mean.
11. What is the value of ∑(X-X ̅)?
12. Find mode for the following data: 3, 4, 5, 5, 6, 8, 5, 7, 5, 5, 8, 5, 5, 4, 5.
13. Calculate mode for the following distribution.
x 10 12 15 22 25 35 45 50 60
f 4 6 10 14 20 18 10 6 3
14. Find the geometric mean of 4, 25.
15. How AM, GM , HM are related?
16. Give the empirical relationship amongX ̅ , M , Z.
17. Name an average suitable for qualitative data.
18. What are partition values?
19. Define quartiles.
20. Define deciles.
21. Define percentiles.
22. If median is 50, what is the value of Q2?
23. What is the relationship between median, Q2, D5 and P50?
24. What is dispersion?
25. Define Range.
26. If X: 7, 12, 25, 18, 35 then find range.
27. Define Quartile deviation.
28. Define Mean deviation.
29. Define Standard deviation.
30. What is coefficient of variation?
31. Define variance.
32. If SD = 4 cms, find variance.
33. If variance = 16 Sq. feet, find SD.
34. Define Skewness?
35. What is the relationship among mean, Median and mode for a symmetrical
distribution?
36. Define Kurtosis.
37. Name the kurtosis if 2 > 3.
38. Name the kurtosis if 2 = 3.
39. What is the value of β2 if the curve is Platykurtic?

22

I PU Statistics Question Bank
Two Mark Questions:
1. Mention two desired qualities of average.
2. Mention the different measures of average.
3. Which average would be suitable in the following cases?
a. Average size of ready-made garments.
b. Average rate of growth of population per decade.
4. Which average would be suitable in the following cases?
a. Average marks of student in a class.
b. Average Speed of 4 participants in a 4 x 100 m relay race.
5. State the properties of Arithmetic mean.
6. Mention a merit and demerit of A.M.
7. Mention a merit and demerit of Median.
8. Mention a merit and demerit of Mode.
9. Find the AM of 8, 5, 6, 4, 3, 7, 2.
10. If mean of 50 observations is 70. Find the sum of observations.
11. If sum of 15 observations is 450. Find its mean.
12. Given n1=50, n2=100, ̅ X1= 60, ̅
X2 = 70, find combined mean.
13. The mean age of the first group of 80 boys is 10years and that of the second
group of 20 boys is 15years. Find the AM of the two groups together.
14. Find median for the following data. 17, 32, 35, 33, 15, 21, 41, 32, 11, 18, 20.
15. Find median for the following data: 5, 9, 8, 6, 1, 4, 10, 8.
16. The arithmetic mean and the median of a slightly skewed distribution are 11cms
and 11.7cms respectively. Find the mode of the distribution.
17. In a frequency distribution, if mean = 24.6 and mode = 26.1, find the value of
median.
18. In a moderately skewed distribution, the values of mode and median are 20 and
24 respectively. Find the mean.
19. Find GM of 1, 4 and 16.
20. Find the HM of 1,4,16.
21. For the following data compute coefficient of range.
Height (cms): 160, 158, 159, 165, 148, 139, 142, 155.
22. Mention the different measures of dispersion.
23. What are absolute and relative measures of dispersion?
24. State two merits of S.D.
25. State two demerits of Q.D.
26. State two demerits of M.D.
27. If quartile deviation is 7 and Q1=21. Find Q3.
28. For a distribution, if the sum of the lower and upper quartiles is 50 and their
difference is 10, find the relative measure of quartile deviation.
29. If mean is 20 and SD is 5, find CV.
30. Find mean if CV=10% and SD=4.
31. If coefficient of variation and standard deviation of a distribution are 75% and 15
respectively, find its mean.
32. Mention the two types of moments.
33. Mention two properties of standard deviation.
34. For a moderately skewed distribution, arithmetic mean = 160, mode = 157 and
standard deviation = 50, find coefficient of Skewness.

23

I PU Statistics Question Bank
Five Mark Questions:
1. Compute AM for the following data.
x 2 3 4 5 6 7 8 9 10 11
f 3 8 10 12 16 14 10 8 7 5

2. Find mean for the following frequency distribution.
x 19 21 23 25 27 29 31
f 13 15 16 18 16 15 13

3. Find mean for the following frequency distribution.
Marks 10 – 25 25 – 40 40 – 55 55 – 70 70 – 85 85 – 100
No. of students 6 50 44 26 3 1

4. Calculate mean for the following distribution.
15 – 20 – 25 – 30 – 35 – 40 – 45 – 50 – 55 – 60 –
C.I
19 24 29 34 39 44 49 54 59 64
f 6 14 12 10 10 9 9 10 6 4

5. Compute mean for the following distribution.
Marks Below 10 Below 20 Below 30 Below 40 Below 50
No. of students 3 8 17 20 22

6. Calculate AM for the following frequency distribution.
Height 135 & 140 & 145 & 150 & 155 & 160 & 165 & 170 &
(Cms) more more more more more more more more
No. of
100 96 87 69 41 17 7 2
students

7. The mean of the following data is 20.5. Find the missing frequency.
x 10 15 20 25 30
f 5 7 ̶ 12 6

8. Given mean = 30.5 for the following distribution, find the missing frequency.
x 10 20 30 40 50
f 8 10 - 15 7

9. The mean of the following distribution is 50. But frequency with respect to class
interval (60 – 80) is missing. Find the missing frequency.
C.I 0 – 20 20 – 40 40 – 60 60 – 80 80 – 100
f 19 28 32 ̶ 19

10. For the following distribution if x̅ = 45, find the missing frequency.
C.I 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80
f 5 8 7 - 28 20 10 10

11. In an examination, a candidate scores the following marks (in percentage).
Eng (62), Language (74), Mathematics (58), Science (61), Social Science (45). Find
the candidates weighted mean if the respective weights are 3, 4, 4, 5 and 2.

12. The AM of 50 observations was 100. At the time of calculations, two values were
wrongly taken as 14 and 18 instead of 40 and 80. Find the correct mean.

24

I PU Statistics Question Bank

13. The mean marks of students in 2 sections ‘A’ and ‘B’ of a class is 62. The mean
mark of students in section ‘A’ is 70. If the number of students in section ‘A’ and
section ‘B’ are 30 and 35 respectively, then find the mean marks of students in
section ‘B’.

14. The average monthly salary of employees of a company was Rs.20,000. The
average monthly salaries of male and female employees were Rs.20,800 and
Rs.16,800 respectively. Find the percentage of male and female employees of the
company.
15. The mean marks of all the students in a class are 72. If the mean marks of boys
are 75 and that of girls is 65. Find the proportion of boys and girls in the class.

16. From the following data find median.
120 – 140 – 160 – 180 – 200 – 220 – 240 –
Daily wage (Rs.)
140 160 180 200 220 240 260
No. of employees 8 12 20 30 22 18 10

17. For the following frequency distribution of weight of mangoes, find median.
410 – 420 – 430 – 440 – 450 – 460 – 470 –
Weight (gms)
419 429 439 449 459 469 479
No. of mangoes 10 20 42 54 45 18 7

18. The following table shows the age distribution of persons in a particular region.
Find median age.
Below Below Below Below Below Below Below
Age (years)
10 20 30 40 50 60 70
No. of persons
2 7 16 28 30 45 48
(‘000)

19. The median of the following distribution is 24, find the missing frequency.
C.I 0-10 10-20 20-30 30-40 40-50
f 5 25 - 18 7

20. Find the mode from the data given below.
x 05 10 15 20 25
f 3 2 8 6 1

21. Calculate mode for the following frequency distribution.
Income (in 000’s Rs.) 1 – 2 2 – 3 3 – 4 4 – 5 5 – 6 6 – 7
No. of workers 15 18 30 17 18 12

22. Below is given the frequency distribution of weights of a group of 60 students of
a class in a school. Find the modal weight.
Weight(in kg) 30-34 35-39 40-44 45-49 50-54 55-59 60-64
No of students 3 5 12 18 14 6 2

23. Calculate the mode for the following distribution.
C.I Below10 10-12 12-14 14-16 16-18 18 & above
f 3 15 27 20 3 2

25

I PU Statistics Question Bank
24. From the following distribution of hourly wage (in rupees) of firm employees, find
the modal hourly wage.
Hourly wage(Rs.) <10 <20 <30 <40 <50 <60 <70 < 80
No. of employees 2 15 60 82 95 122 140 150

25. Calculate the geometric mean from the following data.
Diameter (mm) 130 135 140 145 146 148 149
No. of screws 3 4 6 6 3 5 2

26. Calculate GM for the data given below:
C.I 20-30 30-40 40-50 50-60 60-70 70-80
f 7 23 30 22 11 7

27. Calculate the Harmonic mean for the following data.
x 12 14 16 18 20
f 3 5 9 4 2

28. Find HM for the following data.
C.I 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50
f 10 5 8 7 4

29. In a certain factory, a unit of work is completed by A in 5 minutes, B in 6
minutes, C in 8 minutes, D in 9 minutes and E in 12 minutes. Find the average
time to complete the unit of work?

30. A cyclist covers his first two miles at a speed of 5 miles per hour, another two
miles at 4 miles per hour and the last two miles at 3 miles per hour. Find the
average speed for entire journey.

31. For the values 1, 4 and 16 show that AM > GM > HM.

32. If X: 4, 4 . Show that AM = GM = HM.

33. Calculate lower quartile, upper quartile and 8th decile for the following data.
22, 26, 14, 30, 18, 11, 35, 41, 12, 32.

34. Calculate the first quartile and sixth decile from the following data.
x 58 59 60 61 62 63 64 65 66
f 2 3 6 15 10 5 4 3 2

35. Find the 9th decile and 55th percentile for the following distribution.
C.I 1-3 3-5 5-7 7-9 9-11 11-13 13-15 15-17
f 6 53 85 56 21 16 4 4

36. Calculate Inter quartile range and semi inter quartile range for the following data
11, 15, 16, 9, 14, 19, 10, 12, 8, 17, 20, 23, 22.

37. Compute coefficient of Q.D. from the data given below.
x 2 4 6 8 10 12
f 3 5 10 12 6 4

26

I PU Statistics Question Bank

38. Calculate semi-inter quartile range and its relative measure for the data given
below.
Age (Yrs) 20 30 40 50 60 70 80
No. of Persons 03 61 132 153 140 51 03

39. Calculate Coefficient of Q.D. for the following distribution.
Wages (Rs.) 60-64 64-68 68-72 72-76 76-80 80-84 84-88
No. of workers 12 18 16 14 12 8 8
40. Find semi-inter quartile range for the following distribution.
Less Less Less Less Less Less Less
Age (years) than than than than than than than
25 30 35 40 45 50 55
No. of
10 25 75 130 170 189 200
Employees

41. Calculate mean deviation from mean and its Coefficient for the following data.
100, 150, 200, 360, 490, 500, 600.

42. Calculate the mean deviation from mean from the following data.
Variable 10 11 12 13
f 3 12 18 12

43. Find mean deviation from mean for the following distribution.
Height(Inches) 60 61 62 63 64 65 66 67 68
No. of persons 2 1 14 29 25 12 10 4 2

44. Find M.D from mean for the following distribution regarding difference in age
(yrs) among couples of a particular community.
Difference (yrs) 0-2 2-4 4-6 6-8 8-10 10-12
No. of couples 220 345 452 280 63 10

45. Calculate the mean deviation from the mean for the following distribution.
C.I 2 – 4 4 – 6 6 – 8 8 – 10 10 – 12
f 3 5 8 4 2

46. Calculate M.D from median and its relative measure for the following data.
37, 45, 52, 46, 56, 40, 47, 55, 43.

47. Calculate coefficient of M.D from Median for the following frequency distribution.
x 5 6 7 8 9 10
f 8 12 18 8 2 1

48. Calculate coefficient of mean deviation from median for the following
distribution.
Age(Yrs) 16 17 18 19 20 21 22 23 24
No. of persons 4 5 7 12 20 13 5 0 4

49. Compute coefficient of M.D from median for the following distribution.
Marks Below 10 Below 20 Below 30 Below 40 Below 50
No. of students 3 8 17 20 25

27

I PU Statistics Question Bank

50. Marks of ten students in a certain test (out of 10) are as follows .compute M.D
and its Co-efficient from mode: 7, 4, 10, 9, 15, 12, 7, 9, 7, and 18.

51. Compute M.D from mode for the data given below:
x 0 1 2 3 4 5 6
f 18 22 35 25 20 12 2

52. Compute Mean deviation from mode for the following distribution regarding profit
(Rs.) of various firms.
Profit (in ‘000 Rs.) 20-40 40-60 60-80 80-100 100-120
No. of firms 16 19 41 24 15

53. Find standard deviation of the following data: 25, 50, 45, 30, 70, 42, 36, 48, 34,
60.

54. Find standard deviation of the first five even natural numbers.

55. The mean and standard deviation of a distribution of 100 and 150 items are 50,
5 and 40, 6 respectively. Find the standard deviation of all the 250 items taken
together.

56. Calculate standard deviation for the following distribution.
x 8 11 17 20 25 30 35
f 2 3 4 1 5 7 3

57. Calculate variance for the following distribution.
x 4 5 6 7 8 9 10
f 6 12 15 28 29 14 15

58. Find standard deviation and variance from the following data.
C.I. 0-6 6-12 12-18 18-24 24-30 30-36 36-42
f 19 25 36 72 51 43 28

59. Find the combined SD from the following table.
Sample I Sample II
No. of observations 50 100
Mean 54.1 50.3
SD 8 7

60. The arithmetic mean of marks scored by 3 students A, B &C in a examination
are 50, 44, 20 respectively. The standard deviations of marks are respectively 15,
11 and 3. Who is the most consistent scorer?

Ten mark questions
1. Find median and mode for the following distribution.
C.I 200-400 400-600 600-800 800-1000 1000-1200 1200-1400
f 6 9 15 10 7 3

28

I PU Statistics Question Bank
2. Find standard deviation, variance and coefficient of variation from the following
data.
Less Less Less Less Less Less Less Less
Wage
than than than than than than than than
(Rs)
10 20 30 40 50 60 70 80
No. of
12 30 65 107 157 202 222 230
persons

3. The number of runs scored by two batsmen A and B in different innings is as
follows:
A 12 115 6 73 7 19 119 36 84 29
B 47 12 76 42 4 51 37 48 13 0
Who is better run scorer? Who is more consistent?

4. Following is the distribution of weights of students. Compare their coefficient of
variations.
Weights (Kgs) 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70
Class A 7 10 20 18 7
No. of Students
Class B 5 9 21 15 6

5. Compute Karl Pearson’s coefficient of skewness for the following distribution.
Marks > 0 > 10 > 20 > 30 > 40 > 50 > 60 > 70 > 80
No. of students 150 140 100 80 80 70 30 14 0

6. Calculate Karl-Pearson’ s coefficient of skewness from the following data.
C.I. 70-80 60-70 50-60 40-50 30-40 20-30 10-20 0-10
f 11 12 30 35 21 11 6 5

7. Calculate Pearson’s coefficient of skewness from the following.
Marks 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80
No. of students 10 40 20 0 10 40 16 14

8. Calculate Bowley’s coefficient of skewness from the data given below.
C.I. 30-40 40-50 50-60 60-70 70-80 80-90 90-100
f 1 3 11 21 43 32 9

9. Compute the coefficient of skewness based on quartiles.
C.I. 10-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89
f 5 9 14 20 25 15 8 4

10. Calculate Bowley’s coefficient of skewness for the following data.
Capital (lakh Rs) 1 – 5 6 – 10 10 – 15 16 – 20 20 – 25 26 – 30 31 – 35
No.of companies 20 27 29 38 48 53 70

29

I PU Statistics Question Bank
UNIT – VI
ANALYSIS OF BIVARIATE DATA
Two mark questions:
1. Mention two types of correlation.
2. Mention various methods of computing correlation.
3. Draw a scatter diagram to show positive correlation between two variables.
4. Draw a scatter diagram to show that there exists perfect negative correlation
between two variables.
5. Define the term ‘correlation’. Give an example.
6. What is ‘positive correlation’? Give an example.
7. Mention which type of correlation is associated with
a) Production and price of vegetable.
b) Production of pigs and the production of the pig-iron.
8. Mention two uses of the study of correlation.
9. Mention two merits of scatter diagrams.
10. Mention two properties of γ.
11. In a bi-variate data, Cov(x,y)=V(x)=V(y). Find γxy and conclude.
12. Write the formula for Spearman’s coefficient of rank correlation when one
rankrepeats ‘m’ times.
13. Mention two merits of Spearman’s coefficient of rank correlation.
14. In a bi-variate data on x and y, Var(x) = 9, Var(y) = 49 and Cov(x, y) = 20. Find γ.
15. Given, Cov (X , Y) = -100 , V(x) = 400 and S.D(y) = 5 . Find γ.
16. In a bivariate data covariance is 20, variances are 25 and 36 respectively. Find γ.
17. If ∑(x − x̅)2 = 6000, ∑(y − y̅)2 = 920 and∑(x − x̅)(y − y̅) = 240, Find γ.
18. Coefficient of correlation between two variables ‘x’ and ‘y’ is 0.32. Their
covariance is 10.56. The variance of x is 9. Find Standard deviation of γ.
19. If n=9 and Σd2 = 24, find the coefficient of rank correlation.
20. Mention two properties of regression coefficients.
21. Prove that γ = ±√bxy byx .
22. Mention two uses of regression analysis.
23. Mention the properties of the regression lines.
24. If γ = 0.4, σx = 12, σy = 15, find the value of bxy.
25. If γ = 0.5, σx = 10, σy = 15, find the value of byx.
26. If bxy =0.5 S.D (x) =4 S.D(Y)=5, find γ.
27. If bxy =0.6, γ =0.75, S.D(X)= 3 find S.D(Y).

30

I PU Statistics Question Bank
Five mark questions:
1. Draw a scatter diagram for the data given below and interpret.
x 15 18 20 19 14 12 22 11
y 14 16 13 15 18 18 11 20

2. Draw a scatter diagram for the data given below and interpret.
x 50 100 150 200 250 300 350
y 12 14 13 14 16 18 19

3. Calculate Pearson’s coefficient of correlation from the following data.
x 12 9 8 10 11 13 7
y 14 8 6 9 11 12 3

4. Calculate Pearson’s coefficient of correlation from the following data.
x 40 42 46 48 50 56
y 10 12 15 23 27 30

5. Calculate Karl Pearson’s coefficient of correlation from the following data.
x 36 41 46 59 46 65 31 68 41 70
y 48 60 53 36 50 42 66 44 58 65

6. Calculate the coefficient of correlation by Karl Pearson’s method from the
following data relating to overhead expenses and cost of production.
Overheads(‘000Rs) 80 90 100 110 120 130 140 150 160
Cost(‘000Rs) 15 15 16 19 17 18 16 18 19

7. Following are the marks of 8 students in Statistics and Mathematics. Find
coefficient of rank correlation.
Marks in Statistics 25 43 27 35 54 61 37 45
Marks in Mathematics 35 47 20 37 63 54 28 40

8. Following are the ranks given by two Judges regarding exhibits of paintings. Find
the Spearman’s coefficient of rank correlation.
Paintings 1 2 3 4 5 6
I judge 6 2 1 3 5 4
II Judge 4 1 3 5 6 2
9. Calculate the coefficient of rank correlation from the following data.
x 80 78 75 75 68 67 60 59
y 12 13 14 14 14 16 15 17
10. The following data relate marks in Accountancy and Statistics.
Marks in Accountancy 78 82 78 62 46 52 57 57 58 57
Marks in Statistics 68 81 73 64 52 56 48 68 73 78
Calculate Spearman’s coefficient of correlation and interpret its value.

31

I PU Statistics Question Bank
11. Mention five differences between correlation and regression analysis.

12. The following figures relate to years of service and income (in thousands of
rupees) of the employees of an organization. Considering the preferential ranks,
compute the product moment rank correlation.
Length of service ( years) 3 7 9 1 8 6 10 4 5 2
Income (000’ of Rs.) 7 5 3 2 6 4 8 10 9 1

13. Find the regression equation of y on x and predict the average value of y when x
is 9.
x 3 6 5 4 4 6 7 5
y 3 2 3 5 3 6 6 4

14. From the following data regarding the age of husband and the age of wife,
estimate the age of husband when the age of wife is 16 years.
Husband’s age (Yrs.) 36 23 27 28 28 29 30 31 33 35
Wife’s age (Yrs.) 29 18 20 22 27 21 29 27 29 28

15. You are given with the following information about the expenditure on
advertisement and sales:
Advertisement
Sales (Crore Rs.)
Expenditure (Crore Rs.)
Mean 20 120
S.D 5 2
Correlation coefficient = 0.8
I. Obtain the two regression equations.
II. Find the likely sales when the expenditure on advertisement is Rs.25 crores.

16. Following are the details of the marks scored by students in kannada and
English examination. Coefficient of correlation = 0.3
kannada English
Mean 40 50
S.D 10 16
Estimate the marks in Kannada when the scores in English is 30.

17. The regression equations of a bi-variate distribution are:
Regression equation of y on x is 4y = 9x+15
Regression equation of x on y is 25x = 6y+7, FindX ̅,Y
̅ and γ.

18. In a laboratory experiment on correlation research study, the equation to the two
regression lines was found to be 2x-y+1=0 and 3x-2y+7=0. Find the means of x
and y. Also, workout the values of regression coefficients and the coefficient of
correlation between the two variables x and y.

32

I PU Statistics Question Bank
Ten mark questions:
1. Calculate the coefficient of correlation between the number of male children and
the number of female children from the following data.
No. of male No. of female children
children 0 1 2 3 4
0 3 4 2 - -
1 4 8 8 2 -
2 - 7 12 8 4
3 - 3 8 8 5
4 - - 3 5 6

2. Calculate Karl Pearson’s coefficient of correlation.
x y 20 – 29 30 – 39 40 – 49 50 – 59
10 – 14 10 10 - -
14 – 18 - 20 8 -
18 – 22 - 10 25 6
22 – 26 - - 7 4

3. Calculate Karl Pearson’s coefficient of correlation from the data given below :
Age in years
Marks
18 19 20 21 22
20 – 25 3 2 - - -
15 – 20 - 5 4 - -
10 – 15 - - 7 10 -
5 – 10 - - - 3 2
0–5 - - - 3 1

4. Following are the marks of 8 students in Statistics and Mathematics s and.
Estimate the marks of a student in statistics who has scored 50 marks in
Mathematic and estimate the marks of a student in mathematics who has scored
60 in statistics
Marks in Statistics 25 43 27 35 54 61 37 45
Marks in Mathematics 35 47 20 37 63 54 28 40

5. Find the two regression equations from the following data.
x 3 6 5 4 4 6 7 5
y 3 2 3 5 3 6 6 4
Also find correlation coefficient γxy.

6. Given the following information about expenditure on advertisement (crores) and
sales (crores)
Advertisement expenditure Sales
Mean 20 120
S.D 5 2
Correlation coefficient = 0.3
(a) Obtain the two regression equations
(b) Estimate the sales when the expenditure on advertisement is Rs.25 crores.
(c) Estimate the budget on advertisement if the sales are Rs. 150 crores.

33

I PU Statistics Question Bank

7. Calculate the two regression co-efficients from the following bi-variate table and
determine the value of γ.
Y
0 – 10 10 – 20 20 – 30 30 – 40
X
10 – 20 5 4 3 -
20 – 30 7 6 7 6
30 – 40 - 5 - 7

8. Obtain the regression line of x on y for the following bi-variate frequency
distribution.
Sales revenue Advertisement expenditure (in ‘000 Rs)
(in ’000 Rs) 5 – 15 15 – 25 25 – 35 35 – 45
75 – 125 4 1 - -
125 – 175 7 6 2 1
175 – 225 1 3 4 2
225 – 275 1 1 3 4

UNIT – VII
ASSOCIATION OF ATTRIBUTES
Two mark questions:
1. What is meant by association of attribute? Name the different methods of
measurement?
2. What is the difference between coefficient of correlation and association of
attributes?
3. Write the formula of Yule’s coefficient of Association with its range.

Five mark questions:
1. Calculate Yule’s coefficient of association between marriage and result of
students from the following data pertaining to 525 students.
Pass Fail
Married 90 65
Unmarried 260 110

2. Eighty eight residents of a city were interviewed during a sample survey and were
classified according to smoking and tea drinking habits. Calculate Yule’s
coefficient of association and comment on its value.
Smokers Non-smokers
Tea drinkers 40 33
Non tea drinkers 3 12

34

I PU Statistics Question Bank
3. From the following table find if there is any association between usage of credit
card and expenditure, using Yule’s coefficient.
Credit card No credit card
Expenses 225 50
No Expenses 75 I50

4. Compute Yule’s coefficient of Association from the following data.
(AB) = 150, N = 1000, (A) = 200, (B) = 300.

5. Compute Yule’s co-efficient of Association from the following data.
N = 250, (Aβ) = 70, (A) = 100, (B) = 50.

6. Given, N = 500, (αβ) = 280, (A) = 160 and (B) = 200. Calculate Yule’s coefficient of
Association.

7. Given, N = 2500, (AB) = 400, (α) = 2100 and (β) = 900. Calculate Yule’s coefficient
of Association.

8. Prepare a nine square with the following information. Calculate the Yule’s
Coefficient of Association and interpret the result. (A)=450, (B)=600, (Aβ)=100,
N=1000.

9. Find the association between intelligence of fathers and the intelligence of sons
from the following data :
Intelligent fathers with intelligent sons : 50
Dull fathers with intelligent sons : 100
Dull fathers with dull sons : 300
Intelligent fathers with dull sons : 200

10. 2000 candidates appeared for a competitive examination. 400 cleared the exam.
350 of them had attended a coaching class, out of which 200 had cleared the
exam. Conclude regarding the effectiveness of coaching classes, by using Yule’s
coefficient of Association.

11. 200 candidates appeared for II PUC Examination in a college and 60 of them
passed in distinction. 35 had received special coaching in college and out of them
20 candidates passed in distinction. Using Yule’s co-efficient, discuss whether
the Special coaching is effective or not.

12. In a collage there are 200 students, out of which 150 are boys. In an examination
120 of the students passed. 10 of the girls failed. Using Yule’s coefficient find if
there is any association between gender and passing of the examination.

35

I PU Statistics Question Bank
UNIT – VIII
INTERPOLATION AND EXTRAPOLATION
One mark questions
1. What is interpolation?
2. What is extrapolation?
3. Write an assumption made in interpolation.
4. Mention one method of interpolation.

Five mark questions:
1. From the following data interpolate the export of handlooms during 2008.
Year 1998 2000 2002 2004 2006 2008 2010
Export of handlooms
10 13 15 23 26 ̶ 32
(Rs. In crores)

2. Interpolate the missing figure from the following table.
Year 2001 2002 2003 2004 2005 2006 2007
Sales ('000 Rs.) 100 120 150 180 210 ̶ 320

3. From the given data interpolate the missing price of a commodity.
Year 2006 2007 2008 2009 2010
Price(Rs) 278 281 ̶ 313 322

4. From the following data interpolate the production of cement in 2007.
Year 2005 2006 2007 2008 2009 2010
Production (lakh tons) 44 90 ̶ 160 270 390

5. Using binomial expansion, ascertain the missing index number from the
following data.
Year 2011 2012 2013 2014 2015
Index No. 100 107 ? 157 212

6. Extrapolate the sales of a business concern for the year 2015 from the given
data.
Year 2010 2011 2012 2013 2014 2015
Sales (000) 13 19 25 38 65 ?

36

I PU Statistics Question Bank
7. Following data gives profit of a company for different years. Interpolate the profit
for 2014.
Year 2006 2008 2010 2012 2014 2016
Profit (crores) 6 10 12 16 - 24

8. Interpolate the missing value for the year 2005 from the following data.
Year 1995 2000 2005 2010 2015
Value 100 150 ? 175 200

9. Extrapolate the value of Y when X = 50 from the below data.
X 10 20 30 40 50
Y 110 90 80 60 ?

10. Using binomial expansion method, find the missing value from the following
data.
Month Jan Feb Mar April May
Value 230 260 350 ? 430

37

I PU Statistics Question Bank
UNIT – IX
PROBABILIY THEORY
Choose the most appropriate answer from the choices given.
1. Probability of an event can take values
a) -∞ to ∞ b) -∞ to 1 c) -1 to 1 d) 0 to 1

2. The range of probability is
a) [0, 1] b) [0.5, 0] c) [0, 0.5] d) [0.5, 1]

3. The probability of set of all possible outcomes of a random experiment is always
equal to
a) Infinity b) Zero c) One d) None of these.

4. The probability of the intersection of two mutually exclusive events is always
a) Infinity b) Zero c) One d) None of these.

5. A jar contains 24 marbles, in which some are green and some are blue. If the
2
probability of a green marble is 3 , what is the number of green marbles in the
jar?
a) 16 b) 8 c) 2 d) 24

6. A jar contains 24 marbles, in which some are green and some are blue. If the
2
probability of a green marble is 3 , what is the number of blue marbles in the jar?
a) 16 b) 8 c) 2 d) 24

7. If the probability of two mutually exclusive events are 0.2 and 0.4, the probability
of occurrence of at least one of these events is
a) 0.2 b) 0.3 c) 0.4 d) 0.6

8. The probability that a leap year will have 53 Sundays is
1 2 2 52
a) 7 b) 7 c) 53 d) 53

9. The probability that a non-leap year will have 53 Sundays is
1 2 2 52
a)7 b) 7 c) 53 d) 53

10. If A, B and C are three independent events, the probability of their joint
occurrence is
1
a) P(A)×P(B)×P(C) b)
P(A)×P(B)×P(C)
c) P(A)+P(B)+P(C) d) P(A)|P(B).P(C)

11. If it is known that an event A has occurred, the probability of an event ‘B given A’
is called
a) Empirical probability
b) A priori probability
c) Posteriori probability
d) Conditional probability

38

I PU Statistics Question Bank
Fill in the blanks by choosing the appropriate word from those given in the
brackets.
(0, 0 and 1, 0.3, 0.5, 0.6, 1, 4, 36, Simple, Random, Sample, Chance, Outcomes, Non-
occurrence, An event, Compound, Null)
1. Probability is a numerical measure of ________of occurrence of an event.
2. An experiment whose outcome is not always unique is a ________experiment.
3. The set of all possible outcomes of a random experiment is a _______space.
4. An event is a set of ________of a random experiment.
5. A set of outcomes of a random experiment is _______.
6. An event which does not contain any outcome is a _____event.
7. An event which has only one outcome is a ________event.
8. An event which has more than one outcome is a _________event.
9. The probability of a null event is _____.
10. The probability of a sure event is ______.
11. P(A) is the value between ________.
12. Complement of A is the event of _____________of A.
13. If P(A) = 0.4, the value of P(A’) is _________.
14. In throwing ‘2’ dice, total number of possible outcomes is ______.
15. In tossing of ‘2’ coins, total number of possible outcomes is _____.
16. If the probability of hitting the target is 0.7, the probability of missing the target
is _____.
17. If a fair die is rolled once, the probability of getting an even number is ______.

Match the following. (Direct answers are given)
The probability of null event 0
The probability of sure event 1
P(A) = 0.4 P(A’) = 0.6
P(AUA’) P(S)
P(A)+P(A’) 1
P(A) Value between 0 & 1
P(AB) = P(A).P(B) A & B are independent
When a die is thrown the probability 1
of obtaining even number is 2

When a die is thrown the probability 1
of obtaining odd number is 2

39

I PU Statistics Question Bank
One Mark Questions:
1. Define an outcome.
2. What is a random experiment?
3. Define sample space.
4. Write the sample space when two coins are tossed once.
5. Write a sample space when a die is thrown once.
6. What is an event?
7. What is union of events?
8. What is intersection of events?
9. Give the classical (Mathematical) definition of probability.
10. Give the statistical (empirical) definition of probability.
11. Give an axiomatic definition of probability.
12. What is probability of null event?
13. What is the probability of sample space?
14. Define conditional probability.
15. If P(A) = ¼, what is P(AC)?

Two mark questions:
1. What is a random experiment? Give an example.
2. Define null event. Give an example.
3. Define simple event. Give an example.
4. Define compound event. Give an example.
5. Define favourable outcomes with an example.
6. Define exhaustive outcomes with an example.
7. Define equally likely events with an example.
8. Define mutually exclusive events with an example.
9. What is complement of an event? Give an example.
10. Show that 0 ≤ P(A) ≤ 1.
11. If A′ is the complementary event of A, then show that P(A) + P(A′) = 1.
12. Define independent events with an example.
13. Define dependent events with an example.
14. A coin is tossed once. Find the probability of getting a head.
15. A coin is tossed once. Find the probability of getting head or tail.
16. A die is thrown once. What is the probability of getting an odd number?
17. When two coins are tossed, find the probability of getting 2 heads.
18. A card is drawn from a pack of cards. What is the probability that it is a king or a
queen card?
19. A card is drawn from a pack of cards .what is the probability that it is a red or
black card?
20. If P(A) = 1/13, P(B) =1/4 and P(A∩B) = 1/52 then, find the value of P(A∪B).
21. If P(A) =1/2, P(B) =1/3 and P(A∩B) =1/6 then , find P(A∪B).
22. If P(A∩B) = 1/3 and P(B) = 2/3 then, find P(A|B).If P(A) = 2/3 and P(B|A) = 2/5
then, find P(A∩B).
23. If A and B are two independent events and P(A) = 0.6, P(B) = 0.5 then, find
P(A∪B).

40

I PU Statistics Question Bank
Five mark questions:
1. State and prove addition theorem of probability for any two events.

2. State and prove addition theorem of probability for two mutually exclusive
events.

3. State and prove multiplication theorem of probability for two dependent events.

4. State and prove multiplication theorem of probability for two independent events.

5. A card is drawn randomly from a pack of 52 playing cards. Find the probability
that it is: (i) a King or a Spade (ii) a Spade or a Red. (iii) a spade king.

6. A box contains cards numbered from 1 to 20. A card is drawn randomly from it.
Find the probability of getting a card with: (i) an odd number (ii) a multiple of 4
(iii) a perfect square.

7. When three coins are tossed at a time. Find the probability of getting: (i) only
heads (ii) at least two heads.

8. From a group of 6 boys and 4 girls, two are selected at randomly. What is the
Probability that: (a) both are boys (b) both are girls (c) one is boy and other is a
girl.

9. A box contains 5 red and 4 green balls. Two balls are drawn at random from this
box. Find the probability that they are: (a) of different colours(b) of same colour.

10. A box contains 6 white, 4 black and 5 green balls. Three balls are drawn at
random from this box. Find the probability that they are: (a) two white and one
black (b) one white and two are green.

11. A box contains 5 red, 4 green and 3 blue marbles. Three marbles are drawn at
random from this box. Find the probability that they are of: (i) different colours
(ii) the same colour.

12. A bag contains 5 tickets numbered from 1 to 5. Two tickets are drawn at
random. What is the probability that the sum of obtained numbers is:
(i) odd (ii) even?

13. For a university cricket team 2 players are to be selected from a college having 5
batsmen,3 bowlers and 2 wicket-keepers. Find the probability of selecting-
(i) a batsman and a wicket-keeper (ii) bowlers only.

14. A firm wants to select three candidates among 3 graduates, 5 undergraduates
and 8 matriculates. What is the probability of selecting: (a) one graduate and
two matriculates, (b) two undergraduates and one matriculate?

41

I PU Statistics Question Bank

15. In a hostel 60% of students drink tea, 50% of students drink coffee and 20% of
students drink both tea and coffee. Find the probability that a randomly selected
student drinks either tea or coffee.

16. The probability that a contractor will get a plumbing contract is 1/2 and the
probability that he will not get an electrical contract is 2/3. If the probability of
getting at least one of these contracts is 2/3. What is the probability that he will
get both?

17. Probability that A solves a problem is 2/3 and that B solves it is 3/5. If a
randomly selected problem is given, find the Probability that: a) both of them
solve, b) none of them solves.

18. A, B and C hit a target with probabilities 0.6, 0.5 and 0.4 respectively. If they hit
at the target independently, find the probability that: (i) none of them hit the
target (ii) the target is hit.

19. A box contains 40 nails and 20 screws. 1/4th of nails and 20% of the screws are
rusted. If one item is selected at random, what is the probability that it is a
rusted nail or a screw?

20. A purse contains 4 silver and 2 gold coins. Another purse contains 3 silver and 4
gold coins. If a coin is selected at random from one of the two purses, what is the
probability that it is a silver coin?

21. Contents of the bags are are as follows - I bag: 3 red and 2 green balls, II bag: 4
red and 3 green balls, III bag: 2 red and 2 green balls. One bag is selected at
random and then a ball is drawn from it. Find the probability that it is red in
colour.

22. Two fair dice are rolled. Find the probability that : (i) both the dice show same
numbers, (ii) the sum of numbers is 7 or 11, (iii) the sum is divisible by 3 (iv)
product of numbers obtained is 36.

23. What is the probability that there will be 53 Mondays in a randomly selectedi)
Non-Leap year ii) Leap year?

24. A bag contains 3 white and 5 black marbles. Two marbles are drawn one after
another.
(i) What is the probability that both are white marbles under with replacement?
(ii) Both are black marbles under without replacement.

42

I PU Statistics Question Bank
UNIT – X
RANDOM VARIABLE
Choose the most appropriate answer from the choices given.
1. If ‘X’ is a random variable and ‘a’ is a constant then E(a) is equal to -
a) a b) a E(X) c) aE(X) + b d) b

2. If ‘X’ is a random variable and ‘a’ is a constantthen E(aX) is equal to –
a) a b) a E(X) c) aE(X) + b d) b

3. If ‘X’ is a random variable and ‘a’, ‘b’ are constants then E(aX+b) is equal to –
a) a b) a E(X) c) aE(X) + b d) b

4. If ‘X’ is a random variable and ‘a’ is a constant then V(a) is equal to –
a) a b) aV(X) c) a2V(X) d) 0

5. If ‘X’ is a random variable and ‘a’ is a constant then V(aX) is equal to –
a) aV(X) b) a2V(X) c) a2V(X) + b d) a

6. If ‘X’ is a random variable and ‘a’, ‘b’ are constants then V(aX+b) is equal to –
a) a V(X) b) a2 V(X) c) a2V(X) + b d) a

7. If E(X) = 5, the value of E(8) is –
a) 5 b) 0 c) 40 d) 8

8. If E(X) = 5, the value of E(-X) is –
a) 5 b) -5 c) 0 d) 10

9. If E(X) = 5, the value of E(2X) is –
a) 5 b) 2 c) 10 d) 20

10. If E(X) = 5, the value of E(2X+4) is –
a) 5 b) 14 c) 10 d) 20

11. If V(X) = 5, the value of V(8) is –
a) 5 b) 0 c) 40 d) 8

12. If V(X) = 5, the value of V(-X) is –
a) 5 b) -5 c) 0 d) 6

13. If V(X) = 5, the value of V(2X) is –
a) 5 b) 2 c) 10 d) 20

14. If V(X) = 5, the value of V(2X+4) is –
a) 5 b) 14 c) 10 d) 20

X
15. If V(X) = 4, the value of V(2) is –
a) 0 b) 1 c) 2 d) 4

16. V(–X+2) is equal to
a) –V(X) b) V(X) c) 0 d) V(X)+4

43

I PU Statistics Question Bank
Fill in the blanks by choosing the appropriate word from those given in the
brackets.
(Continuous, 0, 2, Discrete, 0, 4)
1. The value of E(2) is _____.
2. The value of V(2) is _____.
3. A random variable which takes the specified values in its range is called a
______random variable.
4. A random variable which assumes all the possible values in its range is called a
_________random variable.
5. For two independent random variables X and Y, the value of Cov(X,Y) is _______.

Match the following. (Direct answers are given)
Σp(x) Is equal to 1
E(X) Σx p(x)
S.D.(X) √Var(X)
E(a) a
E(aX) a E(X)
Var(a) 0
Cov(X,Y) E(XY) – E(X)E(Y)
X and Y are independent Cov(X,Y) = 0

One mark questions:
1. Define Random Variable.
2. Define Discrete Random Variable.
3. Define Continuous Random Variable.
4. What is meant by Probability Distribution?
5. Define Probability Mass Function.
6. Define Mathematical Expectation.
7. Express variance in terms of expectation.
8. Define a Joint Probability Mass Function.
9. What is the value of E(8) if 8 is a constant?
10. What is the value of V( 4) if 4 is a constant?
11. What is the value of Cov(X, Y) if X and Y are independent?
12. Express covariance in terms of expectation.
13. What is the value of γfor two independent random variables?

Two mark questions:
1. If X is a random variable and a is a constant then prove that E(a)=a.
2. If X is a random variable and a is a constant then prove that E(aX) = a E(X).
3. If X ia random variable and b are any two constants, then prove that
E(aX+b)=aE(X)+b.
4. If X is a random variable and a is a constant then prove that V(a) = 0.
5. If X is a random variable and a is a constant then prove that V(aX) = a2 V(X).
6. Write the formula for correlation coefficient in terms of expectation.

44

I PU Statistics Question Bank
7. If E(X) = 5 and E(X2) = 36, find S.D.(X).
8. If E(X2) = 25 and Var (X) = 16, find E(X).
9. If E(X) = 10 and S.D(X) = 12, find E (X2).
10. If E(X) = 5, what is E(6X)?
11. If E(X)= 8, what is E(4X+3)?
12. If E(X) = 2, what is E(-2X)?
13. If V(X) = 6, what is V(3X)?
14. If V(X) = 4, what is V(6X+7)?
15. If V(X) = 3, then find Var(-X).
16. If V(X) = 9, then find the values of Var(X/3).
17. If V(X) = 16, then find the values of Var(3 – X).

Five mark questions:
1. A person tosses a coin thrice. Find the expected number of heads.

2. A random variable X which assumes the values -1, 0 and 1 with respective
probabilities 1/4,1/2 and 1/4. Find the mean and variance.

3. Find the value of k and then find the mean of the following distribution.
x 1 2 3 4 5 6
p(x) 0.1 0.15 k 0.25 0.18 0.12

4. A box contains 8 items of which 2 are defective. A man selects 3 items. Find the
expected number of defective items in the selection.

5. Given the following probability distribution, find E(X).
x -2 -1 1 2
p(x) 1/5 2/10 3/10 2/5

6. Calculate E(X+4) for the following probability distribution.
x 10 15 20
p(x) 1/6 2/6 3/6

7. Prove addition theorem of expectation for two discrete random variables X and Y.

8. Prove multiplication theorem of expectation for two independent random
variables X and Y.

9. In a bi-variate data E(X)= 4, E(Y) = 10, E(X2)= 25, E(Y2) = 136 and E(XY) = 20.
Find Karl pearson’s correlation.

10. In a bi-variate data E(X) = 6 E(Y) = 9, E(X2)= 30 , E(Y2) = 120 and E(XY) = 20.
find γxy. Conclude.

11. In a bi-variate data, E(X) = 0, E(Y) = 12, E(X2) = 49, [E(X)]2 = 145 and E(XY) = 3.5.
Find Cov(X, Y) and γxy.

45

I PU Statistics Question Bank
12. For the following probability distribution, find E(X), Var(X) , S.D(X) and E(2X-4).
X -1 0 1 2
p(X) 1/5 1/10 1/13 2/5

13. Find the mean and variance of the following distribution.
X 0 1 2 3 4
p(X) 3/8 1/4 1/8 3/16 1/16
14. From the following probability distribution, find the missing probability, mean
and standard deviation of ‘X’.
X -2 -1 0 1 2
p(x) 0.2 0.3 0.2 ? 0.1

15. Find the mean, variance and the value of ‘k’ of the following probability
distribution.
X -3 -2 0 2 3
p(X) k/6 k/12 2k/3 k/2 k/6

16. A random variable ‘X’ assumes the values 10 and 20 with respective probabilities
1/3 and 2/3 Find its mean and variance.

17. A random variable ‘X’ assumes the values 5 and 10 with probabilities 0.6 and 0.4
respectively. Find E(X), E(2X), V(X).

18. A bag has 4 white and 6 red balls. Two balls are randomly drawn from the bag,
find the expected number of white balls.

19. A bag contains 4 green and 3 red balls. A man draws 3 balls at random from the
bag. If he is to receive Rs.200 for every green ball he draws and Rs.50 for every
red one. What is his expectation?

20. A person throws a biased coin. He gets Rs.80 if head appears otherwise he gets
Rs.20. If the probability of occurrence of head is 1/3, find his expected amount.

21. A man throws a fair die. If the throw results in an even number, he gets Rs500
otherwise he loses Rs.100, find his expectation.

22. A man throws a fair die once. If the number obtained is divisible by 3 he gets
Rs.900,otherwise he loses Rs250, find his expectation.

23. A person, by paying Rs.50 enters into a game of shooting a target. With one
shot, if he hits the target, he gets Rs 1000, otherwise he gets nothing If his
probability of hitting the target is 1/7. Find his expected amount.

24. In a lottery, there are 1000 tickets costing Re.1 each. There is one first prize
worth Rs.100, two second prizes worth Rs.20 each and ten third prizes worth
Rs.10 each. Find the expected loss in buying one ticket.

25. A bag has 3 one-rupee, 4 two rupees and 2 five rupees coins. A boy picks two
coins at random from the bag. What is the expectation of the amount of the
coins?

46

I PU Statistics Question Bank

26. A bag contains 6 tickets numbered 1 to 6. A person draws two tickets at random.
If the sum of the numbers on the tickets drawn is even, he gets Rs.100,
otherwise he loses Rs.50. What is his expectation?

27. Two fair coins are tossed once. A person receives Rs.10 if both head appears and
Rs.5 if both tail appears, otherwise he loses Rs. 8, find the expectation of a
person.
28. The probability of a person hitting a target is 2/3. If he hits the target he gets
Rs.150, otherwise he loses Rs. 50. Find his expectation.

29. From the following joint probability distribution of X and Y. Find the value of k,
E(X+Y) andγxy
X Y 1 3 9
2 0.1 0.1 0.05
4 0.2 K 0.1
6 0.1 0.15 0.2

30. For the following joint probability distribution of X and Y, find γ and E(3X+4Y) .
X
1 2 3
Y
-5 0 0.1 0.1
0 0.1 0.2 0.2
5 0.2 0.1 0

31. From the following bivariate data of X and Y find (i) ‘k’ (ii) E(2X+3Y)
x\ y 0 10 20
1 0 0.1 0.1
2 0.1 0.2 0.1
3 0.2 k 0.1

32. From the following bi-variate data of X and Y find co-efficient of correlation
between X and Y
x\ y 0 10 20
1 0 0.1 0.1
2 0.1 0.2 0.1
3 0.2 0.1 0.1

33. For the following data find γxy
x\ y 1 2 3
5 0 0.1 0.1
0 0.1 0.1 0.2
1 0.1 0.2 0.1

47

Study Materials
Notes

Model Papers Class 6 Notes

Sample Papers Class 7 Notes
Half Yearly Sample Papers Class 8 Notes

Class 9 Notes
Important Resources
Class 10 Notes
Periodic Table
Class 11 Notes
Writing Skills / Formats

Maps of India / World Class 12 Notes

Books and Solutions

NCERT Books
NCERT Book Solutions
HC Verma Chapter Wise Solutions
RD Sharma Solutions
CGBSE Solutions