Karnataka 2nd PUC Question Paper 2025 Statistics

Government of Karnataka
Karnataka Secondary Education Examination Board

Question Papers

£ÉÆÃAzÀt ¸ÀASÉå :
Registration No. :

X1 – 2025
«µÀAiÀÄ ¸ÀAPÉÃvÀ /
31 (NS)
Subject Code

¸ÀASÁå±Á¸ÀÛç / STATISTICS
(Kannada and English Versions)

[¸ÀªÀÄAiÀÄ: 3 UÀAmÉUÀ¼ÀÄ] [MlÄÖ ¥Àæ±ÉßUÀ¼À ¸ÀASÉå : 38] [UÀjµÀ× CAPÀUÀ¼ÀÄ : 80]
[Time : 3 Hours] [Total No. of questions : 38] [Max. Marks : 80]

(Kannada Version)
¸ÀÆZÀ£ÉUÀ¼ÀÄ : 1. ¸ÁATåPÀ PÉÆõÀÖPÀUÀ¼ÀÄ ªÀÄvÀÄÛ D¯ÉÃR PÁUÀzÀUÀ¼À£ÀÄß
«£ÀAwAiÀÄ ªÉÄÃgÉUÉ ¥ÀÆgÉʸÀ¯ÁUÀĪÀÅzÀÄ.
2. ªÉÊeÕÁ¤PÀ UÀtPÉÆÃ¥ÀPÀgÀtUÀ¼À£ÀÄß §¼À¸À§ºÀÄzÀÄ.
3. PÁAiÀÄðzÀ J¯Áè ºÀAvÀUÀ¼À£ÀÄß ¸ÀàµÀÖªÁV vÉÆÃj¸ÀvÀPÀÌzÀÄÝ.
4. ‘Ë»ÝWÜ -J’ zÀ°è£À ¥Àæ±ÉßUÀ½UÉ ¥ÀæxÀªÀĪÁV §gÉzÀ
GvÀÛgÀUÀ¼À£ÀÄß ªÀiÁvÀæ ªÀiË®åªÀiÁ¥À£ÀzÀ°è ¥ÀjUÀt¸À¯ÁUÀĪÀÅzÀÄ.
5. D¯ÉÃR ºÉÆA¢gÀĪÀ ¥Àæ±ÉßUÉ ¥ÀAiÀiÁðAiÀĪÁV ¥Àæ±Éß ¥ÀwæPÉAiÀÄ
PÉÆ£ÉAiÀÄ°è ¥ÀævåÉ ÃPÀ «¨sÁUÀz° À è zÀ馅 «PÀ®ZÉÃvÀ£À
«zÁåyðUÀ½UÉ «ªÀgÀuÁvÀäPÀ ¥Àæ±ÉßAiÀÄ£ÀÄß ¤ÃqÀ¯ÁVzÉ.
Ë»ÝWÜ – J
I. ¤ÃrgÀĪÀ DAiÉÄÌUÀ½AzÀ ºÉZÀÄÑ ¸ÀÆPÀÛªÁzÀ GvÀÛgÀªÀ£ÀÄß DAiÉÄÌ ªÀiÁr §gɬÄj.
(5 × 1 = 5)
1) M§â ªÀÄ»¼ÉAiÀÄ ªÀÄPÀ̼À£ÀÄß ºÉgÀĪÀ ¸ÁªÀÄxÀåðªÉÃ
a) ¥sÀ®ªÀAwPÉ b) ªÀÄÈvÀÄå¹Üw
c) ¢ÃWÁðAiÀÄĵÀå d) ¥sÀ®¨sÀjvÀvÉ

P.T.O.

31 (NS) -2-

2) DzsÁgÀ ªÀµÀðzÀ°è ¸ÀÆZÁåAPÀzÀ ¨É¯É

a) 50 b) 100
c) 150 d) 200

3) ¥ÁAiÀÄì£ï «vÀgÀuÉAiÀÄ°è ¸ÀgÁ¸Àj ªÀÄvÀÄÛ «ZÀ®£É £ÀqÀÄ«£À ¸ÀA§AzsÀªÀÅ

a) ¸ÀgÁ¸Àj = «ZÀ®£É

b) ¸ÀgÁ¸Àj ≠ «ZÀ®£É

c) ¸ÀgÁ¸Àj > «ZÀ®£É

d) ¸ÀgÁ¸Àj < «ZÀ®£É

4) JgÀqÀ£ÉAiÀÄ vÀgÀºÀzÀ zÉÆõÀªÀÅ

a) ±ÀÆ£Àå ¥ÀjPÀ®à£É ¸ÀvÀå«zÁÝUÀ CzÀ£ÀÄß ¹éÃPÀj¸ÀĪÀÅzÀÄ

b) ±ÀÆ£Àå ¥ÀjPÀ®à£É ¸ÀvÀå«®èzÁUÀ CzÀ£ÀÄß ¹éÃPÀj¸ÀĪÀÅzÀÄ

c) ±ÀÆ£Àå ¥ÀjPÀ®à£É ¸ÀvÀå«zÁÝUÀ CzÀ£ÀÄß wgÀ¸ÀÌj¸ÀĪÀÅzÀÄ

d) ±ÀÆ£Àå ¥ÀjPÀ®à£É ¸ÀvÀå«®èzÁUÀ CzÀ£ÀÄß wgÀ¸ÀÌj¸ÀĪÀÅzÀÄ

5) MAzÀÄ ¸ÁUÁtÂPÁ ¸ÀªÀĸÉåAiÀÄÄ ¸ÀªÀÄvÉÆî£ÀªÁVzÉ JAzÀÄ ºÉüÀ¨ÉÃPÁzÀgÉ,
»ÃVgÀ¯ÉèÉÃPÀÄ.

a) ai = b j b) ai ≠ b j

c)  ai =  b j d)  ai ≠  b j

-3- 31 (NS)

II. DªÀgÀtUÀ¼À°è ¤ÃqÀ¯ÁzÀ ¸ÀÆPÀÛªÁzÀ GvÀÛgÀUÀ¼À£ÀÄß Dj¸ÀĪÀ ªÀÄÆ®PÀ
©lÖ ¸ÀܼÀUÀ¼À£ÀÄß ¨sÀwð ªÀiÁrj : (5 × 1 = 5)

(£ÀÆå£ÀvÉ, UÁvÀæ, a®ègÉ, C£ÀAwÃAiÀÄ, ¸ÁªÀÄxÀåðvÉ, CªÀ£ÀwAiÀiÁUÀĪÀ)
6) fêÀ£À ªÉZÀÑ ¸ÀÆZÁåAPÀªÀÅ «±ÉöÃPÀÈvÀ jÃwAiÀÄ __________ ¨É¯É
¸ÀÆZÁåAPÀ.
7) t - ªÀPÀæªÀÅ X- CPÀëPÉÌ ____________ ªÁVzÉ.

8) ±ÀÆ£Àå ¥ÀjPÀ®à£É ¸ÀvÀå«zÁÝUÀ CzÀ£ÀÄß wgÀ¸ÀÌj¸ÀĪÀ ¸ÀA¨sÀªÀ¤ÃAiÀÄvÉAiÀÄ£ÀÄß
¥ÀjÃPÁë _________ J£ÀÄߪÀgÀÄ.
9) MAzÀÄ ªÀ¸ÀÄÛ ¤¢ðµÀÖ¥Àr¹zÀ UÀÄtªÀÄlÖzÀ ®PÀët ºÉÆAzÀ¢gÀĪÀÅzÉÃ
__________.
10) MAzÀÄ ¸ÁUÁtÂPÁ ¸ÀªÀĸÉåAiÀÄ AiÀiÁªÀÅzÁzÀgÀÆ ªÀÄÆ® ±ÀPÀå ¥ÀjºÁgÀzÀ°è
zsÀ£ÁvÀäPÀ ºÀAaPÉUÀ¼À ¸ÀASÉåAiÀÄÄ m + n − 1 QÌAvÀ PÀrªÉÄ EzÀÝgÉ, DªÁUÀ
_________ ¥ÀjºÁgÀªÁVgÀÄvÀÛzÉ.

III. PɼÀV£ÀªÀÅUÀ¼À£ÀÄß ºÉÆA¢¹ §gɬÄj : (5 × 1 = 5)

11) A B

a) MlÄÖ ¥sÀ®ªÀvÀÛvÉ zÀgÀ i) H0 : P1 = P2

b) P01 × Q01 = V01 ii) ¸ÀgÀPÀÄ zÁ¸ÁÛ£ÀÄ ªÀiÁzÀj – I

c) §£ÉÆÃð° «vÀgÀuÉAiÀÄ ªÁå¦Û iii)  ªÁ¶ðPÀ ASFR UÀ¼ÀÄ

d) H1 : P1 < P2 iv) ¸ÀgÀPÀÄ zÁ¸ÁÛ£ÀÄ ªÀiÁzÀj – II

e) PÉÆgÀvÉAiÀÄ£ÀÄß C£ÀĪÀÄw¸À¯ÁVzÉ v) x = 0, 1

vi) CA±ÀªÀåwjPÀÛ ¥ÀjÃPÉë

31 (NS) -4-

IV. F PɼÀV£À ¥Àæ±ÉßUÀ½UÉ GvÀÛj¹j : (5 × 1 = 5)

12) MAzÀÄ fêÀPÉÆõÀÖPÀzÀ°è ‘ªÀÄƯÁAPÀ’ªÀ£ÀÄß ªÁåSÁ夹.

13) PÁ®¸ÀgÀtÂAiÀÄ°è C¤AiÀÄ«ÄvÀ «ZÀ®£ÉUÉ MAzÀÄ PÁgÀtªÀ£ÀÄß w½¹.

14) t-«vÀgÀuÉAiÀÄ ¸ÀgÁ¸ÀjAiÀÄ£ÀÄß §gɬÄj.

15) ¤AiÀÄvÁAPÀªÀ£ÀÄß ªÁåSÁ夹.

16) MAzÀÄ DlzÀ ‘PÀ¤µÀÖzÀ°è-UÀjµÀÖ’ JAzÀgÉãÀÄ?

Ë»ÝWÜ & ©
V. D PæÙÜX®Ü ¿ÞÊÜâ¨Ý¨ÜÃÜã LzÀÄ ±ÜÅÍæ°WÜÚWæ EñܤÄÔÄ : (5 × 2 = 10)

17) F PɼÀV£À PÁ®¸ÀgÀt zÀvÁÛA±ÀPÉÌ CgÉ-¸ÀgÁ¸Àj «zsÁ£ÀzÀ ªÀÄÆ®PÀ ¥ÀæªÀÈwÛ
ªÀiË®åUÀ¼À£ÀÄß ¥ÀqɬÄj.
ªÀµÀð : 2014 2015 2016 2017 2018 2019

ªÀiÁgÁl : 110 105 115 110 120 130

18) CAvÀªÉÃð±À£À ªÀÄvÀÄÛ §»ªÉÃð±À£ÀzÀ JgÀqÀÄ PÀ®à£ÉUÀ¼À£ÀÄß §gɬÄj.

1
19) p = JA§ ¤AiÀÄvÁAPÀ ºÉÆA¢zÀ §£ÉÆÃð° «vÀgÀuÉAiÀÄ ¤AiÀÄvÀ
5
«ZÀ®£ÉAiÀÄ£ÀÄß PÀAqÀÄ»r¬Äj.

-5- 31 (NS)

20) ¸ÀévÀAvÁæAPÀ 10 EgÀĪÀ MAzÀÄ PÉʪÀUÀð (χ 2 ) ZÀ®PÀPÉÌ P (0 < χ 2 < 9.34 ) = 0.5
DzÁUÀ, ªÀÄzsÁåAPÀ ªÀÄvÀÄÛ §ºÀÄ®PÀUÀ¼À£ÀÄß PÀAqÀÄ»r¬Äj.

21) ¸ÁATåPÀ wêÀiÁð£ÀzÀ°è JgÀqÀÄ jÃwAiÀÄ CAzÁf¸ÀÄ«PÉUÀ¼À£ÀÄß w½¹.

22) eÉÆÃr t-¥ÀjÃPÁë ¤zÀ±Àðd ªÀÄvÀÄÛ ¸ÀévÀAvÁæAPÀUÀ¼À£ÀÄß §gɬÄj.

23) λ ′ = 4 DzÁUÀ, C-£ÀPÉëAiÀÄ ªÉÄð£À ¤AiÀÄAvÀæt «ÄwAiÀÄ£ÀÄß PÀAqÀÄ»r¬Äj.

24) R = 2500 ªÀ¸ÀÄÛUÀ¼ÀÄ/ªÀµÀðPÉÌ C1 = 2/ªÀ¸ÀÄÛ/ªÀµÀðPÉÌ ªÀÄvÀÄÛ C3 = 100/¸À®PÉÌ
DzÁUÀ, «ÄvÀªÀåAiÀÄ ¨ÉÃrPÉ ¥ÀæªÀiÁt (Q 0 ) ¯ÉQ̹.

Ë»ÝWÜ & ¹
VI. F PɼÀV£À AiÀiÁªÀÅzÁzÀgÀÆ £Á®ÄÌ ¥Àæ±ÉßUÀ½UÉ GvÀÛj¹j : (4 × 5 = 20)

25) F PɼÀV£À zÀvÁÛA±ÀPÉÌ PÀÄlÄA§ DAiÀÄ-ªÀåAiÀÄ «zsÁ£ÀªÀ£ÀÄß G¥ÀAiÉÆÃV¹
UÁæºÀPÀ ¨É¯É ¸ÀÆZÁåAPÀªÀ£ÀÄß ¯ÉQ̹.

¨É¯É ( UÀ¼À°è)
UÀÄA¥ÀÄ ¨sÁgÀ
DzsÁgÀ ªÀµÀð ¥ÀæZÀ°vÀ ªÀµÀð
DºÁgÀ 4000 4600 20

§mÉÖ 1400 1680 10

EAzsÀ£À 1500 1890 10

ªÀ¸Àw 2000 3000 20

EvÀgÉ 3000 3600 20

31 (NS) -6-

26) ¢é¥ÀzÀ «¸ÀÛgÀuÉ «zsÁ£ÀªÀ£ÀÄß G¥ÀAiÉÆÃV¹ F PɼÀV£À zÀvÁÛA±À¢AzÀ
2021 ªÀÄvÀÄÛ 2025 gÀ ªÀµÀðUÀ½UÉ CAvÀªÉÃð±À£À ªÀÄvÀÄÛ §»ªÉÃð±À£ÀzÀ
ªÀiË®åUÀ¼À£ÀÄß PÀAqÀÄ»r¬Äj.

ªÀµÀð : 2019 2020 2021 2022 2023 2024 2025

ªÀiË®å : 10 14 – 27 46 70 –

27) MAzÀÄ £ÀUÀgÀzÀ 40% d£ÀgÀÄ ¸À¸ÁåºÁjUÀ¼ÁVzÁÝgÉ. 4 ªÀåQÛUÀ¼À MAzÀÄ
DPÀ¹äPÀ ¤zÀ±ÀðPÀzÀ°è (a) E§âgÀÄ ¸À¸ÁåºÁjUÀ¼ÀÄ (b) PÀ¤µÀÖ M§â ¸À¸ÁåºÁj
DVgÀĪÀ ¸ÀA¨sÀªÀ¤ÃAiÀÄvÉUÀ¼À£ÀÄß PÀAqÀÄ»r¬Äj.

28) ¤AiÀÄvÁAPÀUÀ¼ÀÄ a = 6, b = 4 ªÀÄvÀÄÛ n = 5 DVgÀĪÀ MAzÀÄ CweÁå«Äw
«vÀgÀuÉAiÀÄ ¸ÀgÁ¸Àj ªÀÄvÀÄÛ «ZÀ®£ÉUÀ¼À£ÀÄß PÀAqÀÄ»r¬Äj.

29) «zÁåyðUÀ¼À MAzÀÄ zÉÆqÀØ UÀÄA¦¤AzÀ 64 «zÁåyðUÀ¼À MAzÀÄ
¤zÀ±ÀðPÀªÀ£ÀÄß DAiÀÄÄÝPÉƼÀî¯ÁVzÉ. F «zÁåyðUÀ¼À ¸ÀgÁ¸Àj vÀÆPÀªÀÅ
56 PÉ.f. ªÀÄvÀÄÛ ¤AiÀÄvÀ «ZÀ®£ÉAiÀÄÄ 4 PÉ.f. DVzÉ. F zÉÆqÀØ UÀÄA¦£À
«zÁåyðUÀ¼À ¸ÀgÁ¸Àj vÀÆPÀªÀÅ 55 PÉ.f. JA§ÄzÀ£ÀÄß ±ÉÃPÀqÁ 5 gÀ
®PÁëöåºÀðvÉ ªÀÄlÖzÀ°è £ÁªÀÅ PÁgÀt ¸À»vÀ H»¸À§ºÀÄzÉÃ?

30) F PɼÀV£À DlªÀ£ÀÄß ¥Àæ¨sÀÄvÀé «zsÁ£À G¥ÀAiÉÆÃV¹ ©r¹. EzÀÄ
¤µÀàPÀë¥ÁvÀzÀ DlªÉÃ?

DlUÁgÀ - B
B1 B2 B3 B4
A1 3 0 2 5

DlUÁgÀ - A A2 – 6 0 1 –4
A3 – 2 –1 0 3
A4 6 –1 0 4

-7- 31 (NS)

31) MAzÀÄ AiÀÄAvÀæzÀ ªÉZÀÑ 30,000 ªÀÄvÀÄÛ «©ü£Àß ªÀµÀðUÀ¼À°è CzÀgÀ
¤ªÀðºÀuÁ ªÉZÀÑ ºÁUÀÆ ªÀÄgÀÄ ªÀiÁgÁl ªÀiË®å F PɼÀV£ÀAwªÉ :

ªÀµÀð : 1 2 3 4 5

¤ªÀðºÀuÁ ªÉZÀÑ ( UÀ¼À°è) : 1,000 2,000 3,100 4,500 6,000

ªÀÄgÀĪÀiÁgÁl ªÀiË®å ( UÀ¼À°è) : 20,000 16,000 13,000 10,000 8,000

AiÀÄAvÀæªÀ£ÀÄß §zÀ¯Á¬Ä¸ÀĪÀ ¸ÀªÀÄÄavÀ CªÀ¢üAiÀÄ£ÀÄß ¤±ÀѬĹ.

VII. F PɼÀV£À AiÀiÁªÀÅzÁzÀgÀÆ JgÀqÀÄ ¥Àæ±ÉßUÀ½UÉ GvÀÛj¹j : (2 × 5 = 10)

32) 400 PÉ®¸ÀUÁgÀgÀ ¢£ÀzÀ PÀÆ°AiÀÄÄ ¥Àæ¸ÁªÀiÁ£Àå «vÀgÀuÉAiÀÄ£ÀÄß ¸ÀgÁ¸Àj
600 ªÀÄvÀÄÛ ¤AiÀÄvÀ «ZÀ®£É 50 UÀ¼ÉÆA¢UÉ ºÉÆA¢zÉ. 550 ªÀÄvÀÄÛ 650

£ÀqÀÄªÉ PÀÆ° ¥ÀqÉAiÀÄĪÀ PÉ®¸ÀUÁgÀgÀ ¸ÀASÉåAiÀÄ£ÀÄß PÀAqÀÄ»r¬Äj.

33) MAzÀÄ gÁdåzÀ MAzÀÄ ªÁgÀzÀ°è ¸ÀA¨sÀ«¹zÀ 70 C¥ÀWÁvÀUÀ¼À£ÀÄß
F jÃwAiÀÄ°è ¸ÁgÀtÂÃPÀj¹zÉ.

ªÁgÀ : gÀ« ¸ÉÆêÀÄ ªÀÄAUÀ¼À §ÄzsÀ UÀÄgÀÄ ±ÀÄPÀæ ±À¤

C¥ÀWÁvÀUÀ¼ÀÄ : 5 9 12 10 6 13 15

C¥ÀWÁvÀUÀ¼ÀÄ ªÁgÀzÁzÀåAvÀ ¸ÀªÀÄ£ÁV ¸ÀA¨sÀ«¹ªÉAiÉÄà JA§ÄzÀ£ÀÄß
±ÉÃPÀqÁ 1 gÀ ®PÁëöåºÀðvÉ ªÀÄlÖzÀ°è ¥ÀjÃQë¹j.

31 (NS) -8-

34) F PɼÀV£À zÀvÁÛA±ÀPÉÌ R-£ÀPÉëAiÀÄ ¤AiÀÄAvÀæt «ÄwUÀ¼À£ÀÄß PÀAqÀÄ»r¬Äj.
( n = 4 JAzÀÄ ¤ÃrzÉ)
¤zÀ±ÀðPÀ ¸ÀASÉå : 1 2 3 4 5 6
ªÁå¦Û : 6 4 3 7 6 4

35) F PɼÀV£À gÉÃSÁvÀäPÀ PÀæªÀÄ«¢ü ¸ÀªÀĸÉåAiÀÄ£ÀÄß D¯ÉÃR «zsÁ£À¢AzÀ ©r¹.
UÀjµÀÖUÉƽ¹ Z = 4 x + 5y
¤§AzsÀ£ÉUÉƼÀ¥ÀlÄÖ : x + 2y ≥ 4
2 x + 3 y ≤ 12
ªÀÄvÀÄÛ x ≥ 0, y ≥ 0

Ë»ÝWÜ & r

VIII. F PɼÀV£À AiÀiÁªÀÅzÁzÀgÀÆ JgÀqÀÄ ¥Àæ±ÉßUÀ½UÉ GvÀÛj¹j : (2 × 10 = 20)

36) a) F PɼÀV£À zÀvÁÛA±À¢AzÀ MlÄÖ ¸ÀAvÁ£ÉÆÃvÀàwÛ zÀgÀªÀ£ÀÄß ¯ÉQ̹. (5)

ªÀAiÉÆÃUÀÄA¥ÀÄ ªÀÄ»¼Á ºÉtÄÚ
(ªÀµÀðUÀ¼À°è) d£À¸ÀASÉå d£À£ÀUÀ¼ÀÄ

15-19 14000 252
20-24 12000 780
25-29 11000 770
30-34 8000 336
35-39 7000 168
40-44 5000 70
45-49 4000 12

-9- 31 (NS)

b) F PɼÀV£À zÀvÁÛA±ÀPÉÌ ¤AiÀÄwÃPÀÈvÀ ªÀÄgÀtzÀgÀªÀ£ÀÄß ¯ÉQ̹. (5)

ªÀAiÉÆÃUÀÄA¥ÀÄ
d£À¸ÀASÉå ªÀÄgÀtUÀ¼ÀÄ DzÀ±Àð d£À¸ÀASÉå
(ªÀµÀðUÀ¼À°è)

0-21 11000 143 10000

21-40 16000 80 15000

40-60 12000 156 15000

60 ªÀÄvÀÄÛ ºÉZÀÄÑ 8000 240 10000

37) F PɼÀV£À zÀvÁÛA±ÀPÉÌ ¯Áå¸ÉàÃAiÀÄgï£À, ¥Á±ÉÑÃAiÀiï£À ªÀÄvÀÄÛ ¦ü±Àgï£À
¨É¯É ¸ÀÆZÁåAPÀUÀ¼À£ÀÄß ¯ÉQ̹.

2018 2024
ªÀ¸ÀÄÛ ¨É¯É ¥ÀjªÀiÁt ¨É¯É ¥ÀjªÀiÁt
( ) ( )
A 16 24 21 30
B 18 28 24 35
C 12 27 10 45
D 15 21 20 30

38) F PɼÀV£À PÁ®¸ÀgÀt zÀvÁÛA±ÀPÉÌ y = a + bx + cx 2 jÃwAiÀÄ ¢éWÁwÃAiÀÄ
¥ÀæªÀÈwÛAiÀÄ£ÀÄß ¤AiÉÆÃf¹ ªÀÄvÀÄÛ 2024 gÀ ¯Á¨sÀªÀ£ÀÄß CAzÁf¹.

ªÀµÀð : 2019 2020 2021 2022 2023

¯Á¨sÀ (PÉÆÃn UÀ¼À°è) : 32 20 30 22 26

31 (NS) -10-

«¨sÁUÀ – E

(zÀ馅 «PÀ®ZÉÃvÀ£À «zÁåyðUÀ½UÉ ªÀiÁvÀæ)

35) gÉÃSÁvÀäPÀ PÀæªÀÄ«¢ü ¸ÀªÀĸÉåAiÀÄ£ÀÄß D¯ÉÃR «zsÁ£À¢AzÀ ©r¸ÀĪÀ
PÁAiÀÄð«zsÁ£ÀªÀ£ÀÄß §gɬÄj.

———————

-11- 31 (NS)

(English Version)

Instructions : 1. Statistical tables and Graph sheets will be supplied on
request.

2. Scientific calculators are allowed.

3. All working steps should be clearly shown.

4. For ‘Section-A’ questions, only the first written answers
will be considered for evaluation.

5. For the question having graph, alternative question is given
at the end of the question paper in a separate section for
visually challenged students.

SECTION – A

I. Choose the most appropriate answer from the choices given : (5 × 1 = 5)

1) The capacity of a woman to bear children is

a) Fertility b) Mortality
c) Longevity d) Fecundity

2) The value of the index number for the base year is

a) 50 b) 100
c) 150 d) 200

3) The relationship between mean and variance of a Poisson distribution is

a) Mean = Variance b) Mean ≠ Variance
c) Mean > Variance d) Mean < Variance

31 (NS) -12-

4) Type – II error is

a) Accepting H0 when it is true

b) Accepting H0 when it is not true

c) Rejecting H0 when it is true

d) Rejecting H0 when it is not true

5) The transportation problem is said to be balanced if and only if

a) ai = b j b) ai ≠ b j

c)  ai =  b j d)  ai ≠  b j

II. Fill in the blanks by choosing the appropriate answers given in the brackets :
(5 × 1 = 5)

(Defect, Size, Retail, Asymptotic, Power, Degenerate)

6) The cost of living index is a specialised kind of ___________ price index.

7) The t-curve is ___________ to the X-axis.

8) The probability of rejecting the null hypothesis when it is true is called
___________ of the test.

9) A ___________ is a quality characteristic which does not conform to
specifications.

10) In a transportation problem, if the number of positive allocations in any
basic feasible solution is less than m + n − 1 , then the solution is
___________.

-13- 31 (NS)

III. Match the following : (5 × 1 = 5)

11) A B

a) Total Fertility Rate i) H 0 : P1 = P2

b) P01 × Q01 = V01 ii) Inventory model – I

c) Range of Bernoulli distribution iii)  Annual ASFRs

d) H1 : P1 < P2 iv) Inventory model – II

e) Shortages are allowed v) x = 0, 1

vi) Factor Reversal Test

IV. Answer the following questions : (5 × 1 = 5)

12) Define ‘Radix’ in a life table.

13) Mention a cause of irregular variation in a time series.

14) Write the mean of t-distribution.

15) Define parameter.

16) What is meant by ‘maximin’ of a game?

SECTION – B

V. Answer any five of the following questions : (5 × 2 = 10)

17) Obtain the trend values by semi-averages method for the following time
series data.
Year : 2014 2015 2016 2017 2018 2019
Sales : 110 105 115 110 120 130

18) Write two assumptions of interpolation and extrapolation.

31 (NS) -14-

19) Find the standard deviation of a Bernoulli distribution with parameter
1
p= .
5

20) For a chi-square (χ 2 ) variate with 10 degrees of freedom,
P (0 < χ 2 < 9.34 ) = 0.5 . Find its median and mode.

21) Mention two types of estimation in statistical inference.

22) Write the test statistic and degrees of freedom of paired t-test.

23) If λ ′ = 4 , then find the upper control limit of C-chart.

24) Calculate the economic order quantity (Q 0 ) , when R = 2500 units/year,
C1 = 2/unit/year and C3 = 100/cycle.

SECTION – C

VI. Answer any four of the following questions : (4 × 5 = 20)

25) Calculate the consumer price index number by using family budget
method for the following data.

Price (in )
Group Weight
Base Year Current Year
Food 4000 4600 20
Clothing 1400 1680 10
Fuel 1500 1890 10
Housing 2000 3000 20
Others 3000 3600 20

-15- 31 (NS)

26) Interpolate and extrapolate the values for the years 2021 and 2025 by
using binomial expansion method from the following data.

Year : 2019 2020 2021 2022 2023 2024 2025
Value : 10 14 – 27 46 70 –

27) In a city 40% of the people are vegetarians. In a random sample of
4 persons, find the probability that (a) two are vegetarians (b) at least one
is a vegetarian.

28) Calculate the mean and variance of a hyper geometric distribution with
parameters a = 6, b = 4 and n = 5 .

29) A sample of 64 students is chosen from a large group of students.
The mean weight of these students is 56 kg and the standard deviation is
4 kg. At 5% level of significance can we reasonably assume that the
mean weight of large group of students is 55 kg?

30) Solve the following game by using dominance principle. Is the game fair?

Player – B
B1 B2 B3 B4
A1 3 0 2 5
A2 – 6 0 1 –4
Player – A
A3 – 2 –1 0 3
A4 6 –1 0 4

31) The cost of a machine is 30,000 and its maintenance cost and resale
value at different years are given below :
Year : 1 2 3 4 5
Maintenance cost (in ) : 1,000 2,000 3,100 4,500 6,000

Resale value (in ) : 20,000 16,000 13,000 10,000 8,000

Determine the optimal period for the replacement of the machine.

31 (NS) -16-

VII. Answer any two of the following questions. (2 × 5 = 10)

32) The daily wages of 400 workers are normally distributed with mean

600 and standard deviation 50. Find the number of workers whose

daily wages will be between 550 and 650.

33) 70 accidents occurred in a state in a week are tabulated as follows :

Day : Sun Mon Tue Wed Thu Fri Sat

Accidents : 5 9 12 10 6 13 15

Test whether accidents occur uniformly throughout the week at
1% level of significance.

34) Find the control limits for R-chart for the following data. (Given n = 4).

Sample number : 1 2 3 4 5 6

Range : 6 4 3 7 6 4

35) Solve the following linear programming problem graphically :

Maximize Z = 4 x + 5 y

Subject to constraints : x + 2y ≥ 4
2 x + 3 y ≤ 12
and x ≥ 0, y ≥ 0

-17- 31 (NS)

SECTION – D

VIII. Answer any two of the following questions : (2 × 10 = 20)

36) a) Compute gross reproduction rate from the following data. (5)

Age group Female Female
(in years) population births

15-19 14000 252

20-24 12000 780

25-29 11000 770

30-34 8000 336

35-39 7000 168

40-44 5000 70

45-49 4000 12

b) Calculate standardized death rate for the following data. (5)

Age group
(in years) Population Deaths Standard Population

0-21 11000 143 10000

21-40 16000 80 15000

40-60 12000 156 15000

60 and above 8000 240 10000

31 (NS) -18-

37) Calculate Laspeyre’s, Paasche’s and Fisher’s price index numbers for the
following data.

2018 2024
Item
Price Quantity Price Quantity
( ) ( )

A 16 24 21 30

B 18 28 24 35

C 12 27 10 45

D 15 21 20 30

38) Fit a quadratic trend equation of the form y = a + bx + cx 2 to the following
time series data and estimate the profit for the year 2024.

Year : 2019 2020 2021 2022 2023

Profit (in Crores ) : 32 20 30 22 26

SECTION – E

(For Visually Challenged Students only)

35) Write the procedure of solving linear programming problem graphically.

———————

-19- 31 (NS)

31 (NS) -20-

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