CBSE Class 10 Mathematics Sample Paper Set 19

SECTION – A

1. The vertices of a parallelogram in order are A(1, 2), B(4, y), C(x, 6) and D(3, 5). Then (x, y) is:
(a) (6, 3)
(b) (3, 6)
(c) (5, 6)
(d) (1, 4)

Answer: A

2. The ratio of LCM and HCF of the least composite and the least prime numbers is:
(a) 1: 2
(b) 2: 1
(c) 1: 1
(d) 1: 3 1

Answer: B

3. The value of k for which the lines 5x + 7y = 3 and 15x + 21y = k coincide is:
(a) 9
(b) 5
(c) 7
(d) 18

Answer: A

4. Write a quadratic polynomial whose sum of zeroes is -1/4 and product of zeroes is 1/4 .
(a) 4x² + x + 1
(b) x² + 4x – 1
(c) 2x² + 3x – 1
(d) x² – 2x + 1

Answer: A

5. ΔABC~ΔPQR. If AM and PN are altitudes of ΔABC and ΔPQR respectively and AB²: PQ² = 4: 9, then AM: PN =
(a) 16: 81
(b) 4: 9
(c) 3: 2
(d) 2: 3

Answer: D

6. In ΔABC right angled at B, if tanA = √3 , then then cosA cosC – sinAsinC =
(a) –1
(b) 0
(c) 1
(d) √3 / 2

Answer: B

7. If 2sin² β – cos² β = 2, then β is:
(a) 0°
(b) 90°
(c) 45°
(d) 30° 1

Answer: B

8. If LCM(x, 18) = 36 and HCF(x, 18) = 2, then x is:
(a) 2
(b) 3
(c) 4
(d) 5 1

Answer: C

9. ABCD is a trapezium with AD ∥ BC and AD = 4cm. If the diagonals AC and BD intersect each other at O such that AO/OC = DO/OB =1/2, then BC =
(a) 6cm
(b) 7cm
(c) 8cm
(d) 9cm

Answer: C

10. In the figure, if DE || BC, AD = 3 cm, BD = 4 cm and BC = 14 cm, then DE equals : 

(a) 7 cm
(b) 6 cm
(c) 4 cm
(d) 3 cm

Answer: B

11. In the given figure, PA and PB are tangents to the circle with centre O. If ∠APB = 60°, then ∠OAB is 

(a) 30°
(b) 60°
(c) 90°
(d) 15°

Answer: A

12. If the difference of Mode and Median of a data is 24, then the difference of median and mean is
(a) 8
(b) 12
(c) 24
(d) 36

Answer: B

13. A horse is tied to a pole with 28 m long rope. The perimeter of the field where the horse can graze is (Take π = 22/7)
(a) 60 cm
(b) 85 cm
(c) 124 cm
(d) 176 cm

Answer: D

14. Two dice are thrown at the same time. The probability of getting not doublet is
(a) 1/3
(b) 1/6
(c) 1/5
(d) 5/6

Answer: D

15. For the following distribution: 

the sum of lower limits of the median class and modal class is
(a) 15
(b) 25
(c) 30
(d) 35

Answer: B

16. If 5 tan θ = 4, then the value of 5sinθ - 3 cosθ/ 5sinθ + 2cosθ
(a) 1/6
(b) 1/7
(c) 1/4
(d) 1/5

Answer: A

17. The ratio of the volumes of two spheres is 8 : 27. The ratio between their surface areas is
(a) 2 : 3
(b) 4 : 27
(c) 8 : 9
(d) 4 : 9

Answer: D

18. The area of the circle that can be inscribed in a square of 6cm is
(a) 36π cm²
(b) 18π cm²
(c) 12 π cm²
(d) 9π cm²

Answer: D

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): The point (–1, 6) divides the line segment joining the points (–3, 10) and (6, –8) in the ratio 2 : 7 internally.
Reason (R): Given three points, i.e. A, B, C form an equilateral triangle, then AB = BC = AC.
(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: B

20. Assertion (A): The number 6ⁿ, n being a natural number, ends with the digit 5.
Reason (R): The number 9ⁿ cannot end with digit 0 for any natural number n.
(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: D

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