Karnataka SSLC Model Question Paper 2025 Maths

ACADEMIC YEAR

2025

Karnataka
Board
Model Paper

PÜ®ÝìoPÜ ÍÝÇÝ ±ÜÄàûæ ÊÜáñÜᤠÊÜåèƯ|ì¿á ÊÜáívÜÈ
ÊÜáÇæÉàÍÜÌÃÜí, ¸æíWÜÙÜãÃÜá & 560 003
KARNATAKA SCHOOL EXAMINATION AND ASSESSMENT BOARD
Malleshwaram, Bengaluru – 560 003

2024-25 ÃÜ GÓ….GÓ….GÇ….Ô. ÊÜÞ¨ÜÄ ±ÜÅÍ氱ܣÅPæ-1
S.S.L.C. MODEL QUESTION PAPER-1 – 2024-25

…Œ⁄æ⁄fl : V⁄{}⁄
Subject : MATHEMATICS
( AMV⁄« »⁄·¤®⁄¥¿»⁄fl / English Medium )

ËÐÜ¿á ÓÜíPæàñÜ : 81-E Subject Code : 81-E
ÓÜÊÜá¿á : 3 WÜípæ 15 ¯ËáÐÜWÜÙÜá ] [ Time : 3 Hours 15 Minutes
WÜÄÐÜu AíPÜWÜÙÜá : 80 ] [ Max. Marks : 80

General Instructions to the Candidate :

1. This question paper consists of 38 questions.

2. Follow the instructions given against the questions.

3. Figures in the right hand margin indicate maximum marks for the questions.

4. The maximum time to answer the paper is given at the top of the question paper.

It includes 15 minutes for reading the question paper.

[ Turn over

81-E 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 its letter of alphabet. 8×1=8

1. The HCF of 5 2 × 2 and 25 × 5 is

(A) 2×5 (B) 25 × 5

(C) 52 × 26 (D) 25 × 52

2. The sum of first ‘n’ natural numbers is

n (n + 2 )
(A) n(n+1) (B)
2

n (n +1)
(C) (D) n(n–1)
2

3. In a pair of linear equations a1x + b1y + c1 = 0 and a 2 x + b 2y + c 2 = 0 ,

which of the following situations cannot arise ?
a1 b1
(A) ≠
a2 b2

a1 b1 c1
(B) = ≠
a2 b2 c2

a1 b1 c1
(C) = =
a2 b2 c2

(D) a1 = a 2 , b1 = b 2 , c1 = c 2

81-E 3

4. The number of zeroes of the polynomial y = P ( x ) in the given graph is

(A) 2 (B) 3

(C) 4 (D) 5

5. x ( x + 2 ) = 6 is a

(A) linear equation (B) quadratic equation

(C) cubic polynomial (D) quadratic polynomial

6. In the figure, ∆ PQR ~ ∆ ABC. The pair of corresponding sides in the

following is

(A) PQ and AB (B) PR and AB

(C) QR and AC (D) PR and BC

[ Turn over

81-E 4

7. sin 2 A – cos 2 A is equal to

(A) 1 (B) 1 – 2cos 2 A

(C) 1 + 2cos 2 A (D) –1

8. The sum of the probability of all elementary events of a random experiment

is

1
(A) 0 (B)
2

(C) 1 (D) –1

II. Answer the following questions : 8×1=8

9. Find the value of ‘b’ if the pair of linear equations 2x + by = 8 and

2 ( 2x + 3y ) = 16 has infinite solutions.

10. Write the degree of the polynomial P ( x ) = 5 x 3 − 3x 2 + 12x – 8.

3 1
11. If sin A = and cos A = , then find the value of tan A.
2 2

12. Write the empirical relation between the three measures of central tendency

Mean, Median and Mode.

x +1 3
13. Express the quadratic equation = in the standard form.
2 x

14. Find the distance of the point ( 6, 8 ) from the origin.

81-E 5

15. In the figure, ∆ POQ ~ ∆ ROS and PQ || SR. If PQ : SR = 1 : 2, then find

OS : OQ.

16. The circumference of the circular base of a cylinder is 44 cm and its height

is 10 cm. Find the curved surface area of the cylinder.

III. Answer the following questions : 8 × 2 = 16

17. Prove that 3 + 5 is an irrational number.

18. What is a composite number ? Which is the composite number among 23

and 24 ?

OR

State the fundamental theorem of arithmetic. Write the composite number

which has 7 and 3 as its only prime factors.

19. Find the 21st term of the arithmetic progression 5, 9, 13, ..... using

formula.

[ Turn over

81-E 6

20. Solve the pair of linear equations by elimination method :

x+y= 4

2x + y = 6

21. If the quadratic equation x 2 + bx + 9 = 0 has two equal real roots, then find

the equation ( b < 1 ).

22. Find the coordinates of the point which divides the line segment joining the

points A ( 1, – 3 ) and B ( 8, 5 ) in the ratio 3 : 1 internally.

23. In the figure, XY is a tangent at the point P to a circle with centre O. Q is a

point on XY. Show that OQ > OP.

24. A toy is in the form of a cone of radius 3·5 cm mounted on a hemisphere of

same radius. The total height of the toy is 15·5 cm. Find the total surface

area of the toy.

OR

539
The volume of a sphere is cm 3 . Find its surface area.
3

81-E 7

IV. Answer the following questions : 9 × 3 = 27

25. One of the zeroes of a polynomial P ( x ) = x 2 – 5x + k is 1 more than the

other zero. Find the value of k.

26. Find the two numbers whose sum is 27 and the product is 182.

OR

The altitude of a right angled triangle is 7 cm less than its base. If the

hypotenuse is 13 cm, then find the other two sides.

27. Prove that

( sin A + cosec A ) 2 + ( cos A + sec A ) 2 = 7 + tan 2 A + cot 2 A.

28. Find a relation between x and y such that the point P ( x, y ) is equidistant

from the points A ( 7, 1 ) and B ( 3, 5 ). Also find the coordinates of the

point P, if A, P and B are collinear.

OR

If the points A ( 4, 5 ), B ( 7, y ), C ( 4, 3 ) and D ( x, 2 ) are the vertices of

a parallelogram, then find the values of x and y.

[ Turn over

81-E 8

29. Find the mean for the following frequency distribution table :

Class interval 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60

Frequency 2 3 5 7 3

OR

Find the median for the following frequency distribution table :

Class interval 15 – 20 20 – 25 25 – 30 30 – 35 35 – 40

Frequency 2 3 6 4 5

30. A boy and a girl are born in the month of September. Find the probability

that both will have

i) different birthdays

ii) the same birthday.

31. In a scalene triangle ABC, draw a line parallel to BC. Let this line intersect

AB at D and AC at E. If DE : BC = 2 : 5, AD = 2 cm, AE = 3 cm and

DE = 4 cm, then find the perimeter of the triangle ABC.

32. Prove that the lengths of tangents drawn from an external point to a circle

are equal.

81-E 9

33. The area of the sector OAYB shown in the figure is 462 cm 2 . Find the

length of the arc AYB if AOB = 120°.

OR

The area of the sector of a circle is numerically equal to the length of the
44
arc of the same sector. If the length of the arc is cm, then find the
21

radius of the circle and also the angle subtended by the arc at the centre.

V. Answer the following questions : 4 × 4 = 16

34. Find the solution of the given pair of linear equations by graphical method :

x+y=6

2x + y = 10

35. The ratio of 11th and 8th terms of an arithmetic progression is 3 : 2. Find

the ratio of the sum of the first 5 terms to the sum of the first 21 terms of it.

36. Prove that “If in two triangles, corresponding angles are equal, then their

corresponding sides are in the same ratio ( or in proportion ) and hence the

two triangles are similar”.

[ Turn over

81-E 10

37. A wooden article was made by scooping out a hemisphere from each end of

a solid cylinder, as shown in the figure. If the height of the cylinder is 10

cm, and the radius of its base is 3·5 cm, then find the total surface area of

the article.

OR

A juice seller was serving his customers using glass as shown in the figure.

The inner diameter of the cylindrical glass was 5 cm, but the bottom of the

glass had a hemispherical raised portion which reduced the capacity of the

glass. If the height of the glass was 10 cm, then find the apparent capacity

of the glass and its actual capacity. ( Take π = 3·14 )

81-E 11

VI. Answer the following question : 1×5=5

38. AB and RQ are two vertical towers standing on a level ground. The angle of

elevation of the top of the tower from a point P on the same ground and
from the foot of the tower QR are 30° as shown in the figure. If PQ = 24 m
and AR = 13 m, then find the heights of the towers AB and RQ. Also find

the length of AP.

( Take 3 = 1·7 )

[ Turn over

PÜ®ÝìoPÜ ÍÝÇÝ ±ÜÄàûæ ÊÜáñÜᤠÊÜåèƯ|ì¿á ÊÜáívÜÈ
ÊÜáÇæÉàÍÜÌÃÜí, ¸æíWÜÙÜãÃÜá & 560 003
KARNATAKA SCHOOL EXAMINATION AND ASSESSMENT BOARD
Malleshwaram, Bengaluru – 560 003

2024-25 ÃÜ GÓ….GÓ….GÇ….Ô. ÊÜÞ¨ÜÄ ±ÜÅÍ氱ܣÅPæ -1
S.S.L.C. MODEL QUESTION PAPER-1 : 2024-25
ËÐÜ¿á : WÜ~ñÜ
Subject : MATHEMATICS
PܮܰvÜ ÊÜÞ«ÜÂÊÜá / Kannada Medium

ËÐÜ¿á ÓÜíPæàñÜ : 81-K Subject Code : 81-K
ÓÜÊÜá¿á 3 WÜípæ 15 ¯ËáÐÜWÜÙÜá ] [ Time : 3 Hours 15 Minutes
WÜÄÐÜu AíPÜWÜÙÜá 80 ] [ Max. Marks : 80

±ÜÄàûݦìWÝX ÓÝÊÜޮܠÓÜãaÜ®æWÜÙÜá

1. D ±ÜÅÍ氱ܣÅPæ¿áá Joár 38 ±ÜÅÍæ°WÜÙÜ®Üá° Öæãí©¨æ.

2. ±ÜÅÍæ°WÜÚWæ PæãqrÃÜáÊÜ ÓÜãaÜ®æWÜÙÜ®Üá° ±ÝÈÔ.

3. ŸÆ »ÝWܨÜÈÉ PæãqrÃÜáÊÜ AíQWÜÙÜá ¯ÜÅÍæ®WÜÚXÃÜáÊÜ ¯Üä|ì AíPÜWÜÙܬÜá® ÓÜãbÓÜáñܤÊæ.

4. ±ÜÅÍ氱ܣÅPæ¿á®Üá° K©PæãÙÜÛÆá 15 ¯ËáÐÜWÜÙÜ PÝÇÝÊÜPÝÍÜÊÜâ ÓæàĨÜíñæ, EñܤÄÓÜÆá ¯WÜ©±ÜwÓÜÇݨÜ
ÓÜÊÜá¿áÊÜ®Üá° ±ÜÅÍ氱ܣÅPæ¿á ÊæáàÇݽWܨÜÈÉ ¯àvÜÇÝX¨æ.

[ Turn over

81-K 2

I. PæÙÜX®Ü ±ÜÅÍæ°WÜÚWæ A¥ÜÊÝ A±Üä|ì ÖæàÚPæWÜÚWæ ®ÝÆáR ±Ü¿Þì¿á EñܤÃÜWÜÙÜ®Üá° ¯àvÜÇÝX¨æ. AÊÜâWÜÙÜÈÉ

ÓÜãPܤÊÝ¨Ü EñܤÃÜÊÜ®Üá° BÄÔ, A¨ÜÃÜ PÜÅÊÜÞûÜÃܨæãvÜ®æ ±Üä|ì EñܤÃÜÊÜ®Üá ° ŸÃæÀáÄ 8×1=8

1. 5 2  2 ÊÜáñÜᤠ25  5 ÃÜ ÊÜá.ÓÝ.A.ÊÜâ

(A) 2  5

(B) 2 5  5

(C) 5 2  2 6

(D) 2 5  5 2

2. Êæã¨ÜÆ ‘n’ ÓÝÌ»ÝËPÜ ÓÜíTæÂWÜÙÜ ÊæãñܤÊÜâ

(A) n ( n + 1 )

n (n  2)
(B)
2

n (n 1)
(C)
2

(D) n ( n – 1 )

81-K 3

3. a1x  b1y  c1  0 ÊÜáñÜᤠa 2 x  b2y  c 2  0 D hæãàw ÃæàTÝñܾPÜ ÓÜËáàPÜÃÜ|WÜÙÜÈÉ,

PæÙÜX®Ü ¿ÞÊÜ ÓÜí¨Ü»ÜìÊÜâ EípÝWÜáÊÜâ©ÆÉ

a1 b1
(A) 
a2 b2

a1 b1 c1
(B)  
a2 b2 c2

a1 b1 c1
(C)  
a2 b2 c2

(D) a1  a 2 , b1  b2 , c1  c 2

4. ®Üûæ¿áÈÉ PæãqrÃÜáÊÜ y = P ( x ) ŸÖÜá¯Ü¨æãàQ¤¿áá Öæãí©ÃÜáÊÜ ÍÜã¬ÜÂñæWÜÙÜ ÓÜíTæ¿áá

(A) 2 (B) 3

(C) 4 (D) 5

[ Turn over

81-K 4

5. x ( x + 2 ) = 6 C¨Üá Jí¨Üá

(A) ÃæàTÝñܾPÜ ÓÜËáàPÜÃÜ|

(B) ÊÜWÜìÓÜËáàPÜÃÜ|

(C) Z¬Ü ŸÖÜá¯Ü¨æãàQ¤

(D) ÊÜWÜìŸÖÜá¯Ü¨æãàQ¤

6. bñÜŨÜÈÉ  PQR ~  ABC BX¨æ. CÊÜâWÜÙÜÈÉ, £Å»ÜágWÜÙÜ A®ÜáÃÜã±Ü ¸ÝÖÜáWÜÙÜ hæãàw¿áá

(A) PQ ÊÜáñÜᤠAB (B) PR ÊÜáñÜᤠAB

(C) QR ÊÜáñÜᤠAC (D) PR ÊÜáñÜᤠBC

7. sin 2 A – cos 2 A C¨ÜPæR ÓÜÊÜáÊÝX¨æ

(A) 1 (B) 1 – 2cos 2 A

(C) 1 + 2cos 2 A (D) – 1

8. Jí¨Üá ¿Þ¨ÜêbfPÜ ±ÜÅÁãàWÜ¨Ü GÇÝÉ ±ÝÅ¥ÜËáPÜ Zo®æWÜÙÜ ÓÜí»ÜÊܯà¿áñæ¿á Êæãñܤ ÊÜâ

1
(A) 0 (B)
2

(C) 1 (D) – 1

81-K 5

II. PæÙÜX®Ü ±ÜÅÍæ°WÜÚWæ EñܤÄÔ 8×1=8

9. 2x + by = 8 ÊÜáñÜᤠ2 ( 2x + 3y ) = 16 D ÃæàTÝñܾPÜ ÓÜËáàPÜÃÜ|WÜÙÜ hæãàw¿áá A®æàPÜ

±ÜÄÖÝÃÜWÜÙÜ®Üá° Öæãí©¨ÜªÃæ, ‘b’ ¿á ¸æÇæ¿á®Üá° PÜívÜá×wÀáÄ.

10. P ( x ) = 5 x 3  3x 2  12x – 8 D ŸÖÜá¯Ü¨æãàQ¤¿á wXÅ¿á¬Üá® ÊÜáÖÜñܤÊÜá [ÝñÜ

ŸÃæÀáÄ.

11. sin A =
3
ÊÜáñÜᤠcos A = 1 B¨ÜÃæ, tan A ¸æÇæ¿á®Üá° PÜívÜá×wÀáÄ.
2 2

12. Pæàí©Åà¿á ±ÜÅÊÜ꣤¿á AÙÜñæWÜÙÝ¨Ü ÓÜÃÝÓÜÄ, ÊÜá«ÝÂíPÜ ÊÜáñÜᤠŸÖÜáÆPÜWÜÙÜ ¬ÜvÜáˬÜ

¯ÝÅÁãàXPÜ ÓÜíŸí«ÜÊܬÜá® ŸÃæÀáÄ.

x 1 3
13.  D ÊÜWÜìÓÜËáàPÜÃÜ|ÊܬÜá® B¨ÜÍÜìÃÜã¯Ü¨ÜÈÉ ŸÃæÀáÄ.
2 x

14. ÊÜáãƹí¨Üá˯í¨Ü ( 6, 8 ) D ¹í¨ÜáËXÃÜáÊÜ ¨ÜãÃÜÊÜ®Üá° PÜívÜá×wÀáÄ.

15. bñÜŨÜÈÉ  POQ ~  ROS ÊÜáñÜᤠPQ || SR BX¨æ. PQ : SR = 1 : 2 B¨ÜÃæ,

OS : OQ ®Üá° PÜívÜá×wÀáÄ.

16. Jí¨Üá ÔÈívÜÃ…¬Ü ÊÜêñݤPÝÃÜ¨Ü ¯Ý¨Ü¨Ü ¯ÜĘ¿áá 44 cm ÊÜáñÜᤠA¨ÜÃÜ GñܤÃÜÊÜâ 10 cm

BX¨æ. ÔÈívÜÃ…¬Ü ÊÜPÜÅÊæáàÇ澄 ËÔ¤à|ìÊܬÜá® PÜívÜá×wÀáÄ.

[ Turn over

81-K 6

III. PæÙÜX®Ü ±ÜÅÍæ°WÜÚWæ EñܤÄÔ 8 × 2 = 16

17. 3 + 5 Jí¨Üá A»ÝWÜÆŸœ ÓÜíTæ Gí¨Üá ÓݘÔ.

18. ÓÜí¿ááPܤ ÓÜíTæ Gí¨ÜÃæà®Üá 23 ÊÜáñÜᤠ24 CÊÜâWÜÙÜÈÉ ÓÜí¿ááPܤ ÓÜíTæ ¿ÞÊÜâ¨Üá

A¥ÜÊÝ

AíPÜWÜ~ñÜ¨Ü ÊÜáãÆ ±ÜÅÊæáà¿áÊÜ®Üá° ¯ÃÜã²Ô. 7 ÊÜáñÜᤠ3 ®Üá° ÊÜÞñÜÅ AË»ÝgÂ

A±ÜÊÜñÜì®ÜWÜÙܮݰX Öæãí©ÃÜáÊÜ ÓÜí¿ááPܤ ÓÜíTæ¿á¬Üá® ŸÃæÀáÄ.

19. 5, 9, 13, ..... D ÓÜÊÜÞíñÜÃÜ ÍæÅà{¿á 21 ®æà ±Ü¨ÜÊÜ®Üá° ÓÜãñÜÅÊÜ®Üá° E±ÜÁãàXÔ

PÜívÜá×wÀáÄ.

20. ÊÜiìÓÜáÊÜ Ë«Ý®Ü©í¨Ü D PæÙÜX®Ü ÃæàTÝñܾPÜ ÓÜËáàPÜÃÜ|WÜÙÜ®Üá° ¹wÔ

x+y= 4

2x + y = 6

21. x 2 + bx + 9 = 0 D ÊÜWÜìÓÜËáàPÜÃÜ|ÊÜâ GÃÜvÜá ÓÜÊÜáÊÝ¨Ü ÊÝÓܤÊÜ ÊÜáãÆWÜÙÜ®Üá°

Öæãí©¨ÜªÃæ, D ÓÜËáàPÜÃÜ|ÊÜ®Üá° PÜívÜá×wÀáÄ ( b < 1 ).

22. A ( 1, – 3 ) ÊÜáñÜᤠB ( 8, 5 ) D ¹í¨ÜáWÜÙÜ®Üá° ÓæàÄÓÜáÊÜ ÃæàTÝSívÜÊÜ®Üá° BíñÜÄPÜÊÝX

3 : 1 A®Üá±ÝñܨÜÈÉ Ë»ÝXÓÜáÊÜ ¹í¨Üá訆 ¯¨æàìÍÝíPÜWÜÙÜ®Üá° PÜívÜá×wÀáÄ.

81-K 7

23. bñÜŨÜÈÉ ‘O’ Pæàí¨ÜÅÊÝWÜáÙÜÛ ÊÜêñܤPæR ‘P’ ¹í¨ÜáË®ÜÈÉ XY ÓܳÍÜìPÜÊÜ®Üá° GÙæ¿áÇÝX¨æ. ‘Q’ XY
Êæáà騆 Jí¨Üá ¹í¨ÜáÊÝX¨æ. OQ > OP Gí¨Üá ñæãàÄÔ.

24. 3·5 cm £ÅgÂÊÜ®Üá° Öæãí©ÃÜáÊÜ Jí¨Üá ÍÜíPÜáÊÜ®Üá° AÐærà £ÅgÂÊÜ®Üá° Öæãí©ÃÜáÊÜ Jí¨Üá

A«ÜìWæãàÙÜ¨Ü ÊæáàÇæ hæãàwÔ Jí¨Üá BqPæ¿á®Üá° ñÜ¿ÞÄÓÜÇÝX¨æ. BqPæ¿á Joár GñܤÃÜ
15·5 cm BX¨æ. BqPæ¿á ¯Üä|ì ÊæáàÇ澄 ËÔ¤à|ìÊܬÜá® PÜívÜá×wÀáÄ.

A¥ÜÊÝ

Jí¨Üá WæãàÙÜ¨Ü Z®Ü¶ÜÆÊÜâ 539 cm 3 BX¨æ. ÖÝWݨÜÃæ A¨ÜÃÜ ÊæáàÇ澄 ËÔ¤à|ìÊܬÜá®
3

PÜívÜá×wÀáÄ.

IV. PæÙÜX®Ü ±ÜÅÍæ°WÜÚWæ EñܤÄÔ 9 × 3 = 27

25. P ( x ) = x 2 – 5x + k D ŸÖÜá¯Ü¨æãàQ¤¿á Jí¨Üá ÍÜã¬ÜÂñæ¿á A¨ÜÃÜ ÊÜáñæã¤í¨Üá

ÍÜã®ÜÂñæXíñÜ ‘1’ ÖæaÝcX¨æ. ÖÝWݨÜÃæ ‘k’ ¿á ¸æÇæ¿á®Üá° PÜívÜá×wÀáÄ.

26. GÃÜvÜá ÓÜíTæÂWÜÙÜ Êæãñܤ 27 ÊÜáñÜᤠAÊÜâWÜÙÜ WÜá|ÆŸœ 182 B¨ÜÃæ, B ÓÜíTæÂWÜÙÜ®Üá°
PÜívÜá×wÀáÄ.

A¥ÜÊÝ

Jí¨Üá ÆíŸPæãà¬Ü £Å»Üág¨Ü GñܤÃÜÊÜâ A¨ÜÃÜ ¯Ý¨ÜQRíñÜ 7 cm PÜwÊæá C¨æ. A¨ÜÃÜ ËPÜ|ì¨Ü
E¨ÜªÊÜâ 13 cm B¨ÜÃæ, EÚ¨æÃÜvÜá ¸ÝÖÜáWÜÙÜ E¨ÜªWÜÙÜ®Üá° PÜívÜá×wÀáÄ.

[ Turn over

81-K 8

27. ( sin A + cosec A ) 2 + ( cos A + sec A ) 2 = 7 + tan 2 A + cot 2 A Gí¨Üá ÓݘÔ.

28. P ( x, y ) ¹í¨ÜáÊÜâ A ( 7, 1 ) ÊÜáñÜᤠB ( 3, 5 ) ¹í¨ÜáWÜÚí¨Ü ÓÜÊÜÞ®Ü ¨ÜãÃܨÜÈɨܪÃæ,

x ÊÜáñÜᤠy WÜÙÜ ¬ÜvÜáÊæ Jí¨Üá ÓÜíŸí«ÜÊܬÜá° PÜívÜá×wÀáÄ. ÖÝWÜã A, P ÊÜáñÜá¤
B ¹í¨ÜáWÜÙÜá ÓÜÃÜÙÜÃæàTÝWÜñÜÊÝX¨ÜªÃæ, ‘P’ ¹í¨Üá訆 ¯¨æàìÍÝíPÜWÜÙÜ®Üá° PÜívÜá×wÀáÄ.

A¥ÜÊÝ

A ( 4, 5 ), B ( 7, y ), C ( 4, 3 ) ÊÜáñÜᤠD ( x, 2 ) D ¹í¨ÜáWÜÙÜá ABCD

ÓÜÊÜÞíñÜÃÜ aÜñÜá»Üáìg¨Ü ÍÜêíWܹí¨ÜáWÜÙݨÝWÜ x ÊÜáñÜᤠy ¸æÇæ¿á®Üá° PÜívÜá×wÀáÄ.

29. PæÙÜX®Ü BÊÜ꣤ ËñÜÃÜOÝ ±ÜqrWæ ÓÜÃÝÓÜÄ¿á®Üá° PÜívÜá×wÀáÄ

ÊÜWÝìíñÜÃÜ BÊÜ꣤

10 — 20 2

20 — 30 3

30 — 40 5

40 — 50 7

50 — 60 3

A¥ÜÊÝ

PæÙÜX®Ü BÊÜ꣤ ËñÜÃÜOÝ ±ÜqrWæ ÊÜá«ÝÂíPÜÊÜ®Üá° PÜívÜá×wÀáÄ

ÊÜWÝìíñÜÃÜ BÊÜ꣤

15 — 20 2

20 — 25 3

25 — 30 6

30 — 35 4

35 — 40 5

81-K 9

30. JŸº ÖÜávÜáWÜ ÊÜáñÜᤠJŸºÙÜá ÖÜávÜáX¿áá Óæ¯æríŸÃ… £íWÜÚ¬ÜÈÉ ÖÜáqr¨ÝªÃæ. AÊÜÃÜ ÖÜáqr¨Ü

©®ÝíPÜÊÜâ

i) ¸æàÃæ ¸æàÃæ ©¬Ü¨ÜÈÉ ŸÃÜáÊÜ

ii) Jí¨æà ©¬Ü¨Üí¨Üá ŸÃÜáÊÜ ÓÜí»ÜÊÜ­à¿áñæ¿á¬Üá® PÜívÜá×wÀáÄ.

31. Jí¨Üá AÓÜÊÜá¸ÝÖÜá £Å»Üág ABC ¿áÈÉ BC Wæ ÓÜÊÜÞíñÜÃÜÊÝX Jí¨Üá ÓÜÃÜÙÜÃæàTæ¿á®Üá°

GÙæÀáÄ. D ÓÜÃÜÙÜÃæàTæ¿áá AB ¿á®Üá° D ¹í¨ÜáË®ÜÈÉ ÊÜáñÜᤠAC ¿á®Üá° E ¹í¨ÜáË®ÜÈÉ

dæà©ÓÜÈ. DE : BC = 2 : 5, AD = 2 cm, AE = 3 cm ÊÜáñÜᤠDE = 4 cm B¨ÝWÜ,

£Å»Üág ABC ¿á ÓÜáñܤÙÜñæ¿á®Üá° PÜívÜá×wÀáÄ.

32. ¸ÝÖÜ ¹í¨Üá˯í¨Ü ÊÜêñܤPæR GÙæ¨Ü ÓܳÍÜìPÜWÜÙÜ E¨ÜªÊÜâ ÓÜÊÜáÊÝXÃÜáñܤ¨æ . Gí¨Üá ÓݘÔ.

33. bñÜŨÜÈÉ OAYB £ÅhÝÂíñÜÃÜ SívÜ¨Ü ËÔ¤à|ìÊÜâ 462 cm 2 BX¨æ. AOB = 120°

B¨ÜÃæ, AYB PÜíÓÜ¨Ü E¨ÜªÊÜ®Üá° PÜívÜá×wÀáÄ.

A¥ÜÊÝ

[ Turn over

81-K 10

Jí¨Üá ÊÜêñܤ¨Ü £ÅhÝÂíñÜÃÜ SívÜ¨Ü ËÔ¤à|ìÊÜâ A¨ÜÃÜ PÜíÓÜ¨Ü E¨ÜªPæR ÓÝíUÂPÜÊÝX ÓÜÊÜáÊÝX¨æ.

PÜíÓÜ¨Ü E¨ÜªÊÜâ 44 cm B¨ÜÃæ, ÊÜêñܤ¨Ü £ÅgÂÊÜ®Üá° ÖÝWÜã PÜíÓÜ©í¨Ü Pæàí¨ÜŨÜÈÉ EípݨÜ
21

Pæãà®Ü¨Ü AÙÜñæ¿á®Üá° PÜívÜá×wÀáÄ.

V. PæÙÜX®Ü ±ÜÅÍæ°WÜÚWæ EñܤÄÔ 4 × 4 = 16

34. PæãqrÃÜáÊÜ ÃæàTÝñܾPÜ ÓÜËáàPÜÃÜ|WÜÙÜ hæãàw¿á ±ÜÄÖÝÃÜÊÜ®Üá° ®Üûæ¿á ˫ݮܩí¨Ü

PÜívÜá×wÀáÄ

x+y=6

2x + y = 10

35. Jí¨Üá ÓÜÊÜÞíñÜÃÜ ÍæÅà{¿á 11®æà ÊÜáñÜᤠ8®æà ±Ü¨ÜWÜÙÜ A®Üá±ÝñÜ 3 : 2 BX¨æ. D ÍæÅà{¿á

Êæã¨ÜÆ 5 ±Ü¨ÜWÜÙÜ Êæãñܤ ÊÜáñÜᤠÊæã¨ÜÆ 21 ±Ü¨ÜWÜÙÜ ÊæãñܤWÜÙÜ A®Üá±ÝñÜÊÜ®Üá°

PÜívÜá×wÀáÄ.

36. GÃÜvÜá £Å»ÜágWÜÙÜÈÉ A®ÜáÃÜã±Ü Pæãà®ÜWÜÙÜá ÓÜÊÜáÊݨÜÃæ, AÊÜâWÜÙÜ A®ÜáÃÜã±Ü ¸ÝÖÜáWÜÙÜ

A®Üá±ÝñÜWÜÙÜá ÓÜÊÜá A¥ÜÊÝ ÓÜÊÜÞ®Üá±ÝñܨÜÈÉÃÜáñܤÊæ B¨ÜªÄí¨Ü B £Å»ÜágWÜÙÜá

ÓÜÊÜáÃÜã±ÜÊÝXÃÜáñܤÊæ Gí¨Üá ÓݘÔ.

81-K 11

37. ÊÜáÃÜ©í¨Ü ÊÜÞw¨Ü ÔÈívÜįí¨Ü GÃÜvÜá ÊÜêñݤPÝÃÜ¨Ü A«ÜìWæãàÙÜWÜÙÜ®Üá° bñÜŨÜÈÉ
ñæãàÄÔÃÜáÊÜíñæ PæãÃæ¨Üá Jí¨Üá ÊÜÓÜá¤ÊÜ®Üá° ñÜ¿ÞÄÔ¨æ. ÔÈívÜÄ®Ü GñܤÃÜ 10 cm ÊÜáñÜá¤
±Ý¨Ü¨Ü £Åg 3·5 cm B¨ÜÃæ, ÊÜÓÜá¤Ë¬Ü ¯Üä|ì ÊæáàÇ澄 ËÔ¤à|ìÊܬÜá® PÜívÜá×wÀáÄ.

A¥ÜÊÝ

ÖÜ~¡®Ü ÃÜÓÜ¨Ü ÊݱÝÄ¿áá bñÜŨÜÈÉ ñæãàÄÔÃÜáÊÜ BPÝÃܨÜÈÉÃÜáÊÜ WÝi®Ü Çæãào¨ÜÈÉ
WÝÅÖÜPÜÄWæ ÖÜ~¡®Ü ÃÜÓÜÊÜ®Üá° ¯àvÜᣤ¨Ýª®æ. ÔÈívÜÄ®ÝPÝÃÜ¨Ü WÝi®Ü Çæãào¨Ü JÙÜÊÝÂÓÜÊÜâ
5 cm C¨æ. B¨ÜÃæ Çæãào¨Ü PæÙÜ»ÝWܨÜÈÉ A«ÜìWæãàÙܨÜÐÜár GñܤÄst »ÝWÜ˨Üáª, C¨Üá

Çæãào¨Ü ÓÝÊÜá¥ÜÂìÊÜ®Üá° PÜwÊæá ÊÜÞvÜáñܤ¨æ. WÝi®Ü Çæãào¨Ü GñܤÃÜÊÜâ 10 cm B¨ÜÃæ,
Çæãào¨Ü WæãàaÜÃÜ ÓÝÊÜá¥ÜÂì ÊÜáñÜᤠ®æçg ÓÝÊÜá¥ÜÂìÊÜ®Üá° PÜívÜá×wÀáÄ.  = 3·14

Gí¨Üá ñæWæ¨ÜáPæãÚÛ

[ Turn over

81-K 12

VI. PæÙÜX®Ü ±ÜÅÍæ°Wæ EñܤÄÔ 1×5=5

38. AB ÊÜáñÜᤠRQ WÜÙÜá ÓÜÊÜáñÜpÝr¨Ü ¬æÆ¨Ü ÊæáàÇæ ­í£ÃÜáÊÜ GÃÜvÜá ¬æàÃÜÊÝ¨Ü PÜíŸWÜÙÝXÊæ.

C¨æà ®æÆ¨Ü Êæáà騆 ‘P’ ¹í¨Üá ÊÜáñÜᤠQR PÜíŸ¨Ü ¯Ý¨Ü©í¨Ü AB PÜíŸ¨Ü ñÜá©Wæ EípݨÜ

E®Ü°ñÜ Pæãà®ÜWÜÙÜá bñÜŨÜÈÉ ñæãàÄÔÃÜáÊÜíñæ 30° BXÊæ. PQ = 24 m ÊÜáñÜᤠAR = 13 m

B¨ÜÃæ, AB ÊÜáñÜᤠRQ PÜíŸWÜÙÜ E¨ÜªWÜÙܬÜá° PÜívÜá×wÀáÄ ÖÝWÜã AP E¨ÜªÊÜ®Üá°

PÜívÜá×wÀáÄ.

3 = 1·7 Gí¨Üá ñæWæ¨ÜáPæãÚÛ

Sample Papers

CBSE Sample Papers
ICSE / ISC Board Sample Papers
AP Board Sample Papers
Assam Board Sample Papers
Bihar Board Sample Papers
Chhattisgarh Board Sample Papers
Goa Board Sample Papers
Gujarat Board Sample Papers
Haryana Board Sample Papers
HP Board Sample Papers
J&K State Board Sample Papers
Jharkhand Board Sample Papers
Karnataka Board Sample Papers
Kerala Board Sample Papers

Sample Papers

MP Board Sample Papers
Maharashtra Board Sample Papers
Manipur Board Sample Papers
Mizoram Board Sample Papers
Orissa Board Sample Papers
Punjab Board Sample Papers
Rajasthan Board Sample Papers
Tamil Nadu Board Sample Papers
Telangana State Board Sample Papers
Tripura Board Sample Papers
UP Board Sample Papers
Uttarakhand Board Sample Papers
West Bengal Board Sample Papers