Karnataka 8th Model Question Paper 2023 Maths

Karnataka Board

SAMPLE
PAPER


2023

PÀ£ÁðlPÀ ±Á¯Á ¥ÀjÃPÉë ªÀÄvÀÄÛ ªÀiË®å¤tðAiÀÄ ªÀÄAqÀ°
PÉJ¸ïPÀÄåJJ¹, ªÀįÉèñÀégÀA, ¨ÉAUÀ¼ÀÆgÀÄ-560003.
KARNATAKA SCHOOL EXAMINATION AND ASSESSMENT BOARD
KSQAAC, Malleshwaram, Bengaluru-560003.
ªÀi˯ÁåAPÀ£À - ªÀiÁZïð 2023 - ªÀiÁzÀj ¥Àæ±ÉÆßÃvÀÛgÀ ¥ÀwæPÉ
Assessment - March 2023 Model Paper
Subject : Mathematics Marks : 40
Class : 8 Medium : English Time : 2 Hours
Information to be filled by the Student
Name of the Student : _____________________________________________________________

Student SATS No : Signature
of the Student :________________

Information to be filled by the Room Invigilator
School DISE Code :

School Name :____________________________________________________________________

Cluster :__________________ Block :______________________ District :__________________
School Type : Govt. Aided Un-aided
(Put “” mark for applicable information)
Signature of the Room Invigilator : ______________________
Information to be filled by the Evaluator at the time of evaluation
Question Obtained Question Obtained Question Obtained
Number marks Number marks Number marks
1 11 21
2 12 22
3 13 23
4 14 24
5 15 25
6 16 26
7 17 27
8 18 28
9 19 -
10 20 -
Total marks Total marks Total marks
Grand Total

Total marks obtained (in words) :____________________________________________________
Signature of the Evaluator : _______________________
Name of the Evaluator : _______________________

2
I Four alternatives are given for each of the following questions/incomplete statements.
Choose the correct alternative and write the complete answer along with the correct
option for question numbers 1 to 20. 20 x 1 = 20

1. Cube root of 125 is

A. 5 B. 53 C. ∛5 D. √5

Answer: ____________________

2. 'a' is non-zero integer, m and n are the natural numbers and m>n
am
then = ______________
an

A. am - n B. am + n C. am × n D.

Answer: ____________________

3. The digit in units place of cube of 27 is

A. 2 B. 7 C. 9 D. 3

Answer: ____________________

4. The shape of solid in the given figure is

A. Sphere

B. Cylinder

C. Cone

D. Triangle

Answer: ____________________

3
5. The formula to find curved surface area of cylinder is

A. 2πrh sq. units B. 2πr (r + h) sq. units

C. πrh sq. units D. πr2h sq. units

Answer: ____________________

6. The least number to be multiplied to 243 to make it a perfect cube is

A. 5 B. 4 C. 2 D. 3

Answer: ____________________

7. If the length, breadth and height of a cuboidal room are 12 m, 8 m and 4 m respectively,
then area of its four walls is

A. 16 sq. metre B. 24 sq. metre

C. 160 sq. metre D. 80 sq. metre

Answer: ____________________

8. The perfect cube 729 lies between the cubes of these numbers,

A. 7 and 9 B. 8 and 10 C. 6 and 8 D. 10 and 11

Answer: ____________________

9. The central angle of the sector representing one third region in a pie chart is

A. 60° B. 180° C. 120° D. 240°

Answer: ____________________
[ Turn over

4
10. Diameter (d) of cylinder is equal to height (h) of the cylinder, then its total surface area
is (sq units)

A. 4πr2 B. 6πr2 C. 8πr2 D. 12πr2

Answer: ____________________

11. 43 can be expressed with base 2 as

A. 23 B. 24 C. 25 D. 26

Answer: ____________________

12. If sum of 43 + 44 + 45 is divided by 7, then quotient will be

A. 191 B. 193 C. 192 D. 194

Answer: ____________________

13. Height and radius of a cylindrical shaped water storage tank are 3m and
7m respectively. The cost of painting its curved surface at the rate of
`5 per sq. m is

A. `330 B. `660 C. `2200 D. `2310

Answer: ____________________

3 2
14. The general form of 1 × 1000 + 4 × 100 + 2 × 1 + + is
100 1000
A. 1402.32 B. 1042.32

C. 1420.032 D. 1402.032

Answer: ____________________

5
15. Three cubes each of edges 4 cm are placed one adjacent to the other to form a Cuboid,
then the length, breadth and height of resulting Cuboid respectively are

A. 4 cm, 4 cm, 12 cm B. 12 cm, 4 cm, 4 cm

C. 12 cm, 8 cm, 4 cm D. 8 cm, 4 cm, 12 cm

Answer: ____________________

16. The graph that represents the relation between whole of a circle and its parts is
_____________

A. Bar chart B. Double bar chart

C. Histogram D. Pie chart

Answer: ____________________

17. Multiplicative inverse of 10-5 is

1 1 1
A. B. C. D. 105
5 105 510

Answer: ____________________

18. Expanded form of (2x + 3y)2 is

A. 4x2 + 9y2 B. 4x2 + 12xy + 9y2

C. 4x2 + 6xy + 9y2 D. 4x2 ˗ 9y2

Answer: ____________________

19. The value of (3-1 + 42 + 5-2)0

A. 0 B. 1 C. 21 D. 3

Answer: ____________________
[ Turn over

6
20. The monthly salary of a person is `50000. The amount spent on various activities is
shown in the pie chart. The amount saved by the person is

A. `3000 B. `300 C. `30 D. `30000

Answer: ____________________

II. Answer the questions from 21 to 28 in the space provided.

21. Write any two properties of rhombus. 2 Marks

OR

Name the point of intersection of vertical axis and horizontal axis in a cartesian plane.
Also write the co-ordinates of it.

7
22. Construct a square of side 6 cm. 2 Marks

OR

Locate and join the points A (1, 1), B (1, 3), C (3, 3) and D (3, 1) on the graph sheet
provided.

[ Turn over

8
23. If 4 is added to 8 times a number, we get 60. Find the number. 2 Marks
OR
If the weight of 12 sheets of thick paper is 40 grams, how many sheets of same paper
would weigh 2½ kilograms?

24. The base of a swimming pool, in front of girl's house is quadrilateral in shape. If 60°,
120°, 70° are the measures of angles of this quadrilateral, then find the measure of
remaining angle. 2 Marks

OR

Verify Euler's formula for the solid figure given below.

9

1 5
25. Find any two rational numbers between and 2 Marks
4 3
OR

On Sunday 845 people went to the zoo. On Monday only 169 people went. What is
the percent decrease in the people visiting the zoo on Monday?

10
26. Verify associative property for addition of rational numbers
3 2 1
, and 3 Marks
2 3 2
OR

If a person calculates compound interest on `10000 for 2 years at 10% per annum,
then find the compound interest.

27. Favourite colours of different people is given. Draw a pie chart for the given data.
3 Marks

Colours Number of people
Blue 18
Green 9
Red 6
Yellow 3
Total 36

11

OR
The marks scored by 40 students in Mathematics is as follows. Draw Histogram for
the given data.
CI 0-10 10-20 20-30 30-40 40-50
f 7 9 8 10 6

[ Turn over

12
28. Age of A is 5 more than 3 times B's age. If present age of 'A' is 44 years, then find the
present age of 'B'. 4 Marks

OR

Divide 44 (x4 - 5x3 - 24x2) by 11x (x-8)

PÀ£ÁðlPÀ ±Á¯Á ¥ÀjÃPÉë 1ªÀÄvÀÄÛ ªÀiË®å¤tðAiÀÄ ªÀÄAqÀ°
PÉJ¸ïPÀÄåJJ¹, ªÀįÉèñÀégÀA, ¨ÉAUÀ¼ÀÆgÀÄ-560003.
KARNATAKA SCHOOL EXAMINATION AND ASSESSMENT BOARD
KSQAAC, Malleshwaram, Bengaluru-560003.
ªÀi˯ÁåAPÀ£À - ªÀiÁZïð 2023 - ªÀiÁzÀj ¥Àæ±ÉÆßÃvÀÛgÀ ¥ÀwæPÉ
Assessment - March 2023 Model Paper
«µÀAiÀÄ : UÀtÂvÀ CAPÀUÀ¼ÀÄ : 40
vÀgÀUÀw : 8 ªÀiÁzsÀåªÀÄ : PÀ£ÀßqÀ ¸ÀªÀÄAiÀÄ : 2 UÀAmÉ
«zÁåyðUÀ¼ÀÄ ¨sÀwð ªÀiÁqÀ¨ÉÃPÁVgÀĪÀ ªÀiÁ»w
«zÁåyðAiÀÄ ºÉ¸ÀgÀÄ : _____________________________________________________________________

«zÁåyðAiÀÄ SATS ¸ÀASÉå : «zÁåyðAiÀÄ ¸À» :_______________

PÉÆoÀr ªÉÄðéZÁgÀPÀgÀÄ ¨sÀwð ªÀiÁqÀ¨ÉÃPÁVgÀĪÀ ªÀiÁ»w
±Á¯ÉAiÀÄ qÉʸï PÉÆÃqï :

±Á¯ÉAiÀÄ ºÉ¸ÀgÀÄ :_________________________________________________________________________

PÀè¸ÀÖgï :______________________ ¨ÁèPï :_______________________ f¯Éè :_______________________
±Á¯ÉAiÀÄ «zsÀ : ¸ÀPÁðj C£ÀÄzÁ¤vÀ C£ÀÄzÁ£À gÀ»vÀ
(C£Àé¬Ä¸ÀĪÀ ªÀiÁ»wUÉ “” UÀÄgÀÄvÀÄ ºÁQj)
PÉÆoÀr ªÉÄðéZÁgÀPÀgÀ ¸À» :______________________________
ªÀiË®åªÀiÁ¥À£À ¸ÀªÀÄAiÀÄzÀ°è ²PÀëPÀgÀÄ ¨sÀwð ªÀiÁqÀ¨ÉÃPÁzÀ ªÀiÁ»w
¥Àæ±Éß ¸ÀASÉå ¥ÀqÉzÀ CAPÀUÀ¼ÀÄ ¥Àæ±Éß ¸ÀASÉå ¥ÀqÉzÀ CAPÀUÀ¼ÀÄ ¥Àæ±Éß ¸ÀASÉå ¥ÀqÉzÀ CAPÀUÀ¼ÀÄ
1 11 21
2 12 22
3 13 23
4 14 24
5 15 25
6 16 26
7 17 27
8 18 28
9 19 -
10 20 -
MlÄÖ CAPÀUÀ¼ÀÄ MlÄÖ CAPÀUÀ¼ÀÄ MlÄÖ CAPÀUÀ¼ÀÄ
MlÄÖ UÀ½¹zÀ CAPÀ

MlÄÖ UÀ½¹zÀ CAPÀUÀ¼ÀÄ (CPÀëgÀUÀ¼À°è)___________________________________________________________

ªÀiË®åªÀiÁ¥ÀPÀgÀ ¸À» : _______________________

ªÀiË®åªÀiÁ¥ÀPÀgÀ ºÉ¸ÀgÀÄ : _______________________

2
I. 1 jAzÀ 20 gÀªÀgÉV£À ¥Àæ±ÉßUÀ½UÉ ¤ÃqÀ¯ÁVgÀĪÀ £Á®ÄÌ DAiÉÄÌUÀ¼À°è ¸ÀÆPÀÛªÁzÀ GvÀÛgÀªÀ£ÀÄß Dj¹ ¤UÀ¢¥Àr¹gÀĪÀ
¸ÀܼÀzÀ°è PÀæªÀiÁPÀëgÀzÉÆA¢UÉ GvÀÛgÀªÀ£ÀÄß §gɬÄj. (20 x 1 = 20)

1. 125gÀ WÀ£ÀªÀÄÆ®ªÀÅ

A. 5 B. 53 C. ∛5 D. √5

GvÀÛgÀ: ____________________

2. 'a' AiÀÄÄ ¸ÉÆ£ÉßAiÀÄ®èzÀ ¨ÉÃgÉ AiÀiÁªÀÅzÉà ¥ÀÇuÁðAPÀªÁzÁUÀ ºÁUÀÆ m ªÀÄvÀÄÛ n (m>n) ¸Áé¨sÁ«PÀ
am
¸ÀASÉåUÀ¼ÁzÀgÉ = ______________
an
A. am - n B. am + n C. am × n D.

GvÀÛgÀ: ____________________

3. 27gÀ WÀ£ÀzÀ ©r ¸ÁÜ£ÀzÀ CAQAiÀÄÄ

A. 2 B. 7 C. 9 D. 3

GvÀÛgÀ: ____________________

4. F WÀ£ÁPÀÈwAiÀÄ ºÉ¸ÀgÀÄ

A. UÉÆüÀ

B. ¹°AqÀgï

C. ±ÀAPÀÄ

D. wæ¨sÀÄd

GvÀÛgÀ: ____________________

3
5. ¹°AqÀgï£À ¥Á±Àéð ªÉÄïÉäöÊ «¹ÛÃtð PÀAqÀÄ»rAiÀÄ®Ä §¼À¸ÀĪÀ ¸ÀÆvÀæ

A. 2πrh ZÀ.ªÀiÁ£ÀUÀ¼ÀÄ B. 2πr (r + h) ZÀ.ªÀiÁ£ÀUÀ¼ÀÄ

C. πrh ZÀ.ªÀiÁ£ÀUÀ¼ÀÄ D. πr2h ZÀ.ªÀiÁ£ÀUÀ¼ÀÄ

GvÀÛgÀ: ____________________

6. 243 £ÀÄß ¥ÀÇtðWÀ£ÀªÀ£ÁßV ªÀiÁqÀ®Ä UÀÄt¸À¨ÉÃPÁzÀ PÀ¤µÀ× ¸ÀASÉå

A. 5 B. 4 C. 2 D. 3

GvÀÛgÀ: ____________________

7. DAiÀÄvÀ WÀ£ÁPÁgÀzÀ°ègÀĪÀ PÉÆoÀrAiÉÆAzÀgÀ GzÀÝ, CUÀ® ªÀÄvÀÄÛ JvÀÛgÀUÀ¼ÀÄ PÀæªÀĪÁV 12«ÄÃ, 8«ÄÃ
ªÀÄvÀÄÛ 4«Äà DzÀgÉ, F PÉÆoÀrAiÀÄ £Á®ÄÌ UÉÆÃqÉUÀ¼À «¹ÛÃtðªÀÅ

A. 16 ZÀ.«ÄÃ. B. 24 ZÀ.«ÄÃ.

C. 160 ZÀ.«ÄÃ. D. 80 ZÀ.«ÄÃ.

GvÀÛgÀ: ____________________

8. 729 F WÀ£À ¸ÀASÉåAiÀÄÄ F ¸ÀASÉåUÀ¼À WÀ£ÀUÀ¼À £ÀqÀÄªÉ EzÉ

A. 7 ªÀÄvÀÄÛ 9 B. 8 ªÀÄvÀÄÛ 10

C. 6 ªÀÄvÀÄÛ 8 D. 10 ªÀÄvÀÄÛ 11

GvÀÛgÀ: ____________________

9. ¥ÉÊ £ÀPÉëAiÀÄ°è, ªÀÈvÀÛzÀ ªÀÄÆgÀ£Éà MAzÀÄ ¨sÁUÀªÀ£ÀÄß ¥Àæw¤¢ü¸ÀĪÀ RAqÀzÀ PÉÆãÀªÀÅ

A. 60° B. 180° C. 120° D. 240°

GvÀÛgÀ: ____________________
[ Turn over

4
10. ¹°AqÀj£À ªÁå¸ÀªÀÅ (d) CzÀgÀ JvÀÛgÀPÉÌ (h) ¸ÀªÀÄ£ÁVzÉ. ºÁUÁzÀgÉ, ¹°AqÀgï£À ¥ÀÇtð ªÉÄïÉäöÊ
«¹ÛÃtðªÀÅ ZÀ.ªÀiÁ£ÀUÀ¼À°è

A. 4πr2 B. 6πr2 C. 8πr2 D. 12πr2

GvÀÛgÀ: ____________________

11. 43 EzÀ£ÀÄß DzsÁgÀ ¸ÀASÉå 2 DVgÀĪÀAvÉ ªÀåPÀÛ¥Àr¹zÁUÀ

A. 23 B. 24 C. 25 D. 26

GvÀÛgÀ: ____________________

12. 43 + 44 + 45 gÀ ªÉÆvÀÛªÀ£ÀÄß 7jAzÀ ¨sÁV¹zÁUÀ zÉÆgÉAiÀÄĪÀ ¨sÁUÀ®§ÞªÀÅ

A. 191 B. 193 C. 192 D. 194

GvÀÛgÀ: ____________________

13. ¹°AqÀj£ÁPÁgÀzÀ MAzÀÄ ¤ÃgÀÄ ¸ÀAUÀæºÀt vÉÆnÖAiÀÄ JvÀÛgÀ ªÀÄvÀÄÛ wædåUÀ¼ÀÄ PÀæªÀĪÁV 3«ÄÃ. ªÀÄvÀÄÛ
7«ÄÃ. DVzÉ. EzÀgÀ ¥Á±Àéð ªÉÄïÉäöÊUÉ §tÚ §½AiÀÄ®Ä ¥Àæw ZÀzÀgÀ «ÄÃlgïUÉ `5gÀAvÉ vÀUÀ®ÄªÀ RZÀÄð

A. `330 B. `660 C. `2200 D. `2310

GvÀÛgÀ: ____________________

3 2
14. 1 × 1000 + 4 × 100 + 2 × 1 + + zÀ ¸ÁªÀiÁ£Àå gÀÆ¥ÀªÀÅ
100 1000

A. 1402.32 B. 1042.32

C. 1420.032 D. 1402.032

GvÀÛgÀ: ____________________

5
15. CAa£À GzÀÝ 4 ¸ÉA.«Äà EgÀĪÀ ªÀÄÆgÀÄ WÀ£ÀUÀ¼À£ÀÄß MAzÀgÀ ¥ÀPÀÌ MAzÀ¤ßj¹ DAiÀÄvÀ WÀ£ÀªÀ£ÀÄß
ªÀiÁrzÉ. ºÁUÁzÀgÉ D DAiÀÄvÀ WÀ£ÀzÀ GzÀÝ, CUÀ® ªÀÄvÀÄÛ JvÀÛgÀUÀ¼ÀÄ PÀæªÀĪÁV

A. 4 ¸ÉA«ÄÃ, 4 ¸ÉA«ÄÃ, 12 ¸ÉA«Äà B. 12 ¸ÉA«ÄÃ, 4 ¸ÉA«ÄÃ, 4 ¸ÉA«ÄÃ

C. 12 ¸ÉA«ÄÃ, 8 ¸ÉA«ÄÃ, 4 ¸ÉA«Äà D. 8 ¸ÉA«ÄÃ, 4 ¸ÉA«ÄÃ, 12 ¸ÉA«ÄÃ

GvÀÛgÀ: ____________________

16. ¥ÀÇtð ªÀÈvÀÛ ªÀÄvÀÄÛ CzÀgÀ ¨sÁUÀUÀ¼À £ÀqÀÄ«£À ¸ÀA§AzsÀªÀ£ÀÄß vÉÆÃj¸ÀĪÀ £ÀPÉëAiÀÄ
«zsÀ _____________

A. ¸ÀÛA¨sÀ £ÀPÉë B. eÉÆÃr ¸ÀÛA¨sÀ £ÀPÉë

C. HvÀPÀ £ÀPÉë D. ¥ÉÊ £ÀPÉë

GvÀÛgÀ: ____________________

17. 10-5 gÀ UÀÄuÁPÁgÀzÀ «¯ÉÆêÀÄ

1 1 1
A. B. C. D. 105
5 105 510

GvÀÛgÀ: ____________________

18. (2x + 3y)2 £À «¸ÀÛöÈvÀ gÀÆ¥À

A. 4x2 + 9y2 B. 4x2 + 12xy + 9y2

C. 4x2 + 6xy + 9y2 D. 4x2 ˗ 9y2

GvÀÛgÀ: ____________________

19. (3-1 + 42 + 5-2)0 gÀ ¨É¯É

A. 0 B. 1 C. 21 D. 3

GvÀÛgÀ: ____________________
[ Turn over

6
20. M§â GzÉÆåÃVAiÀÄ wAUÀ¼À ªÉÃvÀ£À `50,000UÀ¼ÁVzÀÄÝ CªÀ£ÄÀ CzÀ£ÄÀ ß ««zsÀ PÁAiÀÄðUÀ½UÉ §¼À¸ÄÀ ªÀÅzÀ£ÄÀ ß
¥ÉÊ £ÀPA
ëÉ iÀÄ°è vÉÆÃj¸À¯ÁVzÉ. DvÀ G½vÁAiÀÄ ªÀiÁrzÀ ºÀt

A. `3000 B. `300 C. `30 D. `30000

GvÀÛgÀ: ____________________

II. 21 jAzÀ 28 gÀªÀgÉV£À ¥Àæ±ÉßUÀ½UÉ ¤UÀ¢¥Àr¹gÀĪÀ ¸ÀܼÀzÀ°è GvÀÛj¸ÀĪÀÅzÀÄ.

21. ªÀeÁæPÀÈwAiÀÄ JgÀqÀÄ UÀÄt®PÀëtUÀ¼À£ÀÄß §gɬÄj. 2 CAPÀ

CxÀªÁ

PÁnð¶AiÀÄ£ï ¸ÀªÀÄvÀ®zÀ°è ¨sÀÆ ®A§ CPÀë ªÀÄvÀÄÛ Qëwd CPÀëUÀ¼À bÉÃzÀ£À ©AzÀÄ«£À ºÉ¸ÀgÀÄ ªÀÄvÀÄÛ
CzÀgÀ ¤zÉÃð±ÁAPÀUÀ¼À£ÀÄß §gɬÄj.

7
22. ¨ÁºÀÄ«£À GzÀÝ 6 ¸ÉA«Äà C¼ÀvÉ ºÉÆA¢gÀĪÀ ZËPÀªÀ£ÀÄß gÀa¹. 2 CAPÀ

CxÀªÁ

PÉÆnÖgÀĪÀ £ÀPÁë ºÁ¼ÉAiÀÄ ªÉÄÃ¯É A (1, 1), B (1, 3), C (3, 3) ªÀÄvÀÄÛ D (3, 1) ©AzÀÄUÀ¼À£ÀÄß
UÀÄgÀÄw¹ ¸ÉÃj¹.

[ Turn over

8
23. MAzÀÄ ¸ÀASÉåAiÀÄ 8gÀµÀÖPÉÌ 4£ÀÄß PÀÆrzÁUÀ 60 zÉÆgÉAiÀÄÄvÀÛzÉ. ºÁUÁzÀgÉ D ¸ÀASÉå PÀAqÀÄ»r¬Äj.
2 CAPÀ
CxÀªÁ
zÀ¥Àà PÁUÀzÀzÀ 12 ºÁ¼ÉUÀ¼À vÀÆPÀªÀÅ 40 UÁæA UÀ¼ÁzÀgÉ EzÉà PÁUÀzÀzÀ JµÀÄÖ ºÁ¼ÉUÀ¼ÀÄ 2½ QUÁæA
vÀÆUÀÄvÀÛªÉ?

24. M§â ºÀÄqÀÄVAiÀÄ ªÀÄ£ÉAiÀÄ CAUÀ¼ÀzÀ°ègÀĪÀ FdÄPÉƼÀzÀ vÀ¼ÀªÀÅ ZÀvÀĨsÀÄðeÁPÀÈwAiÀÄ DPÁgÀzÀ°èzÉ.
F DPÀÈwAiÀÄ PÉÆãÀUÀ¼À C¼ÀvÉUÀ¼ÀÄ 60°, 120°, 70° DzÀgÉ G½zÀ PÉÆãÀzÀ C¼ÀvÉAiÀÄ£ÀÄß
PÀAqÀÄ»r¬Äj. 2 CAPÀ

CxÀªÁ

F PɼÀV£À avÀæzÀ°è ¤ÃrgÀĪÀ DPÀÈwUÉ DAiÀÄègï ¸ÀÆvÀæªÀ£ÀÄß ¥ÀjÃQë¹.

9

1 5
25. ªÀÄvÀÄÛ UÀ¼À £ÀqÀÄ«£À JgÀqÀÄ ¨sÁUÀ®§Þ ¸ÀASÉåUÀ¼À£ÀÄß PÀAqÀÄ»r¬Äj. 2 CAPÀ
4 3
CxÀªÁ

¨sÁ£ÀĪÁgÀzÀAzÀÄ 845 d£ÀgÀÄ ªÀÄÈUÁ®AiÀÄPÉÌ ¨sÉÃn ¤ÃrzÀgÀÄ. ¸ÉÆêÀĪÁgÀzÀAzÀÄ PÉêÀ® 169 d£ÀgÀÄ
¨sÉÃn ¤ÃrzÀgÀÄ. ¸ÉÆêÀĪÁgÀzÀAzÀÄ ªÀÄÈUÁ®AiÀÄPÉÌ ¨sÉÃn ¤ÃrgÀĪÀ d£ÀgÀ ¸ÀASÉåAiÀÄ°è£À ±ÉÃPÀqÁ
E½PÉAiÀÄ£ÀÄß PÀAqÀÄ»r¬Äj.

10
3 2 1
26. , ªÀÄvÀÄÛ ¨sÁUÀ®§Þ ¸ÀASÉåUÀ½UÉ, ¸ÀAPÀ®£ÀzÀ ¸ÀºÀªÀvÀð¤ÃAiÀÄvÉ ¥ÀjÃQë¹. 3 CAPÀ
2 3 2
CxÀªÁ

ªÁ¶ðPÀ 10% §rØzÀgÀzÀ°è M§â ªÀåQÛAiÀÄÄ ¥Àæw ªÀµÀð ZÀPÀæ §rØ ¯ÉPÁÌZÁgÀ ªÀiÁrzÀgÉ `10,000 UÀ½UÉ
2 ªÀµÀðUÀ½UÉ DUÀĪÀ ZÀPÀæ §rØ PÀAqÀÄ»r¬Äj.

27. ««zsÀ d£ÀgÀÄ EµÀÖ¥ÀqÀĪÀ §tÚUÀ¼À£ÀÄß F PɼÀUÉ ¤ÃqÀ¯ÁVzÉ. F zÀvÁÛA±ÀUÀ½UÉ ¥ÉÊ £ÀPÉë gÀa¹.
3 CAPÀ

§tÚUÀ¼ÀÄ d£ÀgÀ ¸ÀASÉå
¤Ã° 18
ºÀ¹gÀÄ 9
PÉA¥ÀÅ 6
ºÀ¼À¢ 3
MlÄÖ 36

11

CxÀªÁ

40 «zÁåyðUÀ¼ÀÄ UÀtÂvÀ ¥ÀjÃPÉëAiÀÄ°è UÀ½¹zÀ CAPÀUÀ¼À DªÀvÀð£À «vÀgÀuÁ ¥ÀnÖ ¤ÃrzÉ. F zÀvÁÛA±ÀPÉÌ
(Histogram) HvÀPÀ £ÀPÉë gÀa¹.

ªÀUÁðAvÀgÀ 0-10 10-20 20-30 30-40 40-50
DªÀvÀð£À 7 9 8 10 6

[ Turn over

12
28. A £À ªÀAiÀĸÀÄì B £À ªÀAiÀĹì£À ªÀÄÆgÀgÀµÀÖQÌAvÀ 5 ªÀµÀðUÀ¼ÀÄ ºÉZÁÑVzÉ. A AiÀÄ FV£À ªÀAiÀĸÀÄì 44
ªÀµÀðUÀ¼ÁzÀgÉ, B AiÀÄ FV£À ªÀAiÀĸÀÄì PÀAqÀÄ»r¬Äj. 4 CAPÀ

CxÀªÁ

44 (x4 - 5x3 - 24x2) £ÀÄß 11x (x-8) jAzÀ ¨sÁV¹.