CBSE Class 10 Mathematics (Basic) — MCQs

1. The HCF of 960 and 432 is : (a) 48 (b) 54 (c) 72 (d) 36

2. The natural number 2 is : (a) a prime number (b) a composite number (c) prime as well as composite (d) neither prime nor composite

3. For any natural number n, $6^n$ ends with the digit : (a) 0 (b) 6 (c) 3 (d) 2

4. The graph of $y = f(x)$ is given. The number of zeroes of $f(x)$ is : (a) 0 (b) 1 (c) 2 (d) 4

5. If a pair of linear equations in two variables is represented by two coincident lines, then the pair of equations has : (a) a unique solution (b) two solutions (c) no solution (d) an infinite number of solutions

6. The common difference of the AP : $\sqrt{2}, 2\sqrt{2}, 3\sqrt{2}, 4\sqrt{2}$, ..... is : (a) √2 (b) 1 (c) 2√2 (d) -√2

7. If $\triangle ABC$ and $\triangle DEF$ are similar such that $2AB = DE$ and $BC = 8\text{ cm}$, then EF is equal to : (a) 4 cm (b) 8 cm (c) 12 cm (d) 16 cm

8. The mid-point of the line segment joining the points $(5, -4)$ and $(6, 4)$ lies on : (a) x-axis (b) y-axis (c) origin (d) neither x-axis nor y-axis

9. Given that $\sin \theta = \frac{a}{b}$, then cos θ is equal to : (a) $\frac{b}{\sqrt{b^2-a^2}}$ (b) $\frac{b}{a}$ (c) $\frac{\sqrt{b^2-a^2}}{b}$ (d) $\frac{a}{\sqrt{b^2-a^2}}$

10. If $\cos A = \frac{1}{2}$, then the value of $\sin^2 A + 2\cos^2 A$ is : (a) 3/2 (b) 5/4 (c) -1 (d) 1/2

11. A car is moving away from the base of a 30 m high tower. The angle of elevation of the top of the tower from the car at an instant, when the car is $10\sqrt{3}$ m away from the base of the tower, is : (a) 30° (b) 45° (c) 90° (d) 60°

12. If TP and TQ are two tangents to a circle with centre O from an external point T so that $\angle POQ = 120°$, then ∠PTQ is equal to : (a) 60° (b) 70° (c) 80° (d) 90°

13. In the given figure, PA is a tangent from an external point P to a circle with centre O. If $\angle POB = 125°$, then ∠APO is equal to : (a) 25° (b) 65° (c) 90° (d) 35°

14. The length of the arc of the sector of a circle with radius 21 cm and of central angle 60°, is : (a) 22 cm (b) 44 cm (c) 88 cm (d) 11 cm

15. The hour hand of a clock is 7 cm long. The angle swept by it between 7:00 a.m. and 8:10 a.m. is : (a) $\left(\frac{35}{4}\right)°$ (b) $\left(\frac{35}{2}\right)°$ (c) $35°$ (d) $70°$

16. The total surface area of a solid hemisphere of diameter '2d' is : (a) $3\pi d^2$ (b) $2\pi d^2$ (c) $\frac{1}{2}\pi d^2$ (d) $\frac{3}{4}\pi d^2$

17. If the mean and mode of a data are 12 and 21 respectively, then its median is : (a) 6 (b) 13.5 (c) 15 (d) 14

18. A die is thrown once. Probability of getting a number other than 3 is : (a) $\frac{1}{6}$ (b) $\frac{3}{6}$ (c) $\frac{5}{6}$ (d) 1

19. Assertion (A) : The probability that a leap year has 53 Mondays is $\frac{2}{7}$. Reason (R) : The probability that a non-leap year has 53 Mondays is $\frac{5}{7}$. (a) Both, Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A). (b) Both, Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A). (c) Assertion (A) is true, but Reason (R) is false. (d) Assertion (A) is false, but Reason (R) is true.

20. Assertion (A) : The polynomial $p(y) = y^2 + 4y + 3$ has two zeroes. Reason (R) : A quadratic polynomial can have at most two zeroes. (a) Both, Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A). (b) Both, Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A). (c) Assertion (A) is true, but Reason (R) is false. (d) Assertion (A) is false, but Reason (R) is true.