CBSE Class 10 Mathematics Sample Paper Set 20

SECTION – A

1. If the distance between the points (4,p) and (1,0) is 5, then value of p is
(a) 4 only
(b) ±4
(c) -4 only
(d) 0

Answer: B

2. If p and q are positive integers such that p = a³b² and q = a²b, where ‘a’ and ‘b’ are prime numbers, then the LCM ( p, q) is 
(a) ab
(b) a²b²
(c) a³b²
(d) a³b³

Answer: C

3. 108 can be expressed as a product of its primes as ……………..
(a) 2³ x 3²
(b) 2³ x 3³
(c) 2² x 3²
(d) 2² x 3³

Answer: D

4. Two dice are thrown at the same time and the product of numbers appearing on them is noted.
The probability that the product is a prime number is
(a) 1/3
(b) 1/6
(c) 1/5
(d) 5/6

Answer: B

5. The pair of equations x + 2y + 5 = 0 and –3x – 6y + 1 = 0 have
(a) a unique solution
(b) exactly two solutions
(c) Infinitely many solutions
(d) no solution

Answer: D

6. If p and q are the zeroes of the quadratic polynomial f(x) = 2x² – 7x + 3, find the value of p + q – pq is
(a) 1
(b) 2
(c) 3
(d) None of these

Answer: B

7. If sin 2A = 1/2 tan² 45° where A is an acute angle, then the value of A is
(a) 60°
(b) 45°
(c) 30°
(d) 15°

Answer: D

8. In ΔABC right angled at B, if cotC = √3 , then then cos A sin C + sin A cos C =
(a) –1
(b) 0
(c) 1
(d) √3 / 2

Answer: C

9. If θ is an acute angle and tanθ + cotθ = 2, then the value of sin³ + cos³ is
(a) 1
(b) 1/2
(c) √2/2
(d) √2

Answer: C

10. A girl walks 200m towards East and then 150m towards North. The distance of the girl from the starting point is
(a) 350m
(b) 250m
(c) 300 m
(d) 325 m

Answer: B

11. In ABC, DE || AB, If CD = 3 cm, EC = 4 cm, BE = 6 cm, then DA is equal to
(a) 7.5 cm
(b) 3 cm
(c) 4.5 cm
(d) 6 cm

Answer: C

12. If angle between two radii of a circle is 130⁰, the angle between the tangents at the ends of the radii is :
(a) 90⁰
(b) 50⁰
(c) 70⁰
(d) 40⁰

Answer: B

13. The relationship between mean, median and mode for a moderately skewed distribution is
(a) mode = median – 2 mean
(b) mode = 3 median – 2 mean
(c) mode = 2 median – 3 mean
(d) mode = median – mean

Answer: B

14. For the following distribution: 

(a) 10 – 20
(b) 20 – 30
(c) 30 – 40
(d) 50 – 60

Answer: C

15. The area of a quadrant of a circle, whose circumference is 22 cm, is
(a) 11/8 cm²
(b) 77/8 cm²
(c) 77/2 cm²
(d) 77/4 cm²

Answer: B

16. If the quadratic equation x² + 4x + k = 0 has real and equal roots, then
(a) k < 4
(b) k > 4
(c) k = 4
(d) k ≥ 4

Answer: C

17. Volumes of two spheres are in the ratio 64 : 27. The ratio of their surface areas is
(a) 3 : 4
(b) 4 : 3
(c) 9 : 16
(d) 16 : 9

Answer: D

18. The area of the square that can be inscribed in a circle of radius 8 cm is
(a) 256 cm²
(b) 128 cm²
(c) 64√2 cm²
(d) 64 cm²

Answer: B

DIRECTION: In the question number 19 and 20, a statement of Assertion (A) is followed by a statement of Reason (R).
Choose the correct option

19. Assertion (A): If HCF ( 90, 144) = 18, then LCM (90, 144) = 720
Reason (R): HCF (a, b) x LCM (a, b) = a x b
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true.

Answer: A

20. Assertion (A): The point (0, 4) lies on y -axis.
Reason (R): The x co-ordinate on the point on y -axis is zero.
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A)
(b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of Assertion (A)
(c) Assertion (A) is true but reason(R) is false.
(d) Assertion (A) is false but reason(R) is true.

Answer: A

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