CBSE Class 10 Mathematics Sample Paper Set R

SECTION – A

1. The value of ‘a’, if HCF (a, 18) = 2 and LCM (a, 18) = 36, is: (1)
(a) 2
(b) 5
(c) 7
(d) 4

Answer: D

2. The LCM of smallest two-digit composite number and smallest composite number is:
(a) 12
(b) 4
(c) 20
(d) 44

Answer: C

3. If r = 3 is a root of quadratic equation kr² – kr – 3 = 0, then the value of k is:
(a) 1/2
(b) 3
(c) 1/3
(d) 1/4

Answer: A

4. The solution of the following pair of equation is:
x – 3y = 2, 3x – y = 14
(a) x = 5, y = 1
(b) x = 2, y = 3
(c) x = 1, y = 2
(d) x = 1, y = 4

Answer: A

5. What is the positive real root of 64x² – 1 = 0?
(a) 1/8
(b) 1/4
(c) 1/2
(d) 1/6

Answer: A

6. In the figure, if OA/OD = OC/OB , then 

which pair of angles are equal?
(a) ∠A = ∠C, ∠B = ∠D
(b) ∠A = ∠B, ∠C = ∠D
(c) ∠C = ∠B, ∠A = ∠D
(d) None of these

Answer: A

7. In ΔABC and ΔDEF, ∠B = ∠E, ∠F = ∠C and AB = 3DE. Then, the two triangles are
(a) congruent but not similar
(b) similar but not congruent
(c) neither congruent nor similar
(d) congruent as well as similar

Answer: B

8. If cosec A = 13/12, then the value of 2sinA - 3cos A/4sin A - 9cos A
(a) 4
(b) 5
(c) 6
(d) 3

Answer: D

9. In the given figure, if TP and TQ are tangents to a circle with centre O, so that ∠POQ = 110°, then ∠PTQ is 

(a) 110°
(b) 90°
(c) 80°
(d) 70°

Answer: D

10. If the angle of elevation of the top of a tower from a point of observation at a distance of 100 m from its base is 45°, then the height of the tower is:
(a) 160 m
(b) 100 m
(c) 200 m
(d) 150 m

Answer: B

11. The ratio in which x-axis divides the join of (2, -3) and (5, 6) is:
(a) 1: 2
(b) 3 : 4
(c) 1: 3
(d) 1: 5

Answer: A

12. If tan θ = 1, then the value of sec θ + cosec θ is:
(a) 3√2
(b) 4√2
(c) 2√2
(d) √2

Answer: C

13. If the area of circle is numerically equal to twice its circumference, then the diameter of the circle is
(a) 4 units
(b) 6 units
(c) 8 units
(d) 12 units

Answer: C

14. If the perimeter of a circle is equal to that of a square, then the ratio of the area of circle to the area of the square is
(a) 14: 11
(b) 12: 13
(c) 11:14
(d) 13:12

Answer: A

15. The radii of 2 cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. Then, the ratio of their volumes is:
(a) 19 : 20
(b) 20 : 27
(c) 18:25
(d) 17:23

Answer: B

16. For the following distribution: 

the upper limit of the median class is
(a) 18.5
(b) 20.5
(c) 25.5
(d) 17.5

Answer:  D

17. If the mean of the following distribution is 2.6, then the value of y is 

(a) 3
(b) 8
(c) 13
(d) 24

Answer: B

18. Two different dice are thrown together. The probability of getting the sum of the two numbers less than 7 is:
(a) 5/12
(b) 7/12
(c) 12/5
(d) 3/11

Answer: A

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: The HCF of two numbers is 9 and their LCM is 2016. If the one number is 54, then the other number is 336.
Reason: Relation between numbers and their HCF and LCM is product of two numbers a, b = HCF (a, b) × LCM (a, 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 value of y is 3, if the distance between the points P(2, -3) and Q(10, y) is 10.
Reason (R): Distance between two points is given by √(x₂ - x₁)² + (y₂ - y₁)² 
(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

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