20 Must-Solve MCQs for CBSE Class 10 Maths (2026 Board Exam)

 Section A of the CBSE Class 10 Mathematics paper can be a "make or break" zone. With 20 marks on the line, these Multiple Choice Questions test your conceptual clarity rather than your ability to fill pages.

Below is a curated list of 20 high-probability MCQs covering the entire 2026 syllabus. Grab a pen, a notebook, and let's see how many you can get right!

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📝 The MCQ Challenge

Q1. The exponent of 2 in the prime factorization of 144 is:

(a) 4

(b) 5

(c) 6

(d) 3

Q2. If the zeroes of the quadratic polynomial $x^2 + (a + 1)x + b$ are 2 and -3, then:

(a) $a = -7, b = -1$

(b) $a = 5, b = -1$

(c) $a = 2, b = -6$

(d) $a = 0, b = -6$

Q3. The pair of equations $y = 0$ and $y = -7$ has:

(a) one solution

(b) two solutions

(c) infinitely many solutions

(d) no solution

Q4. The values of $k$ for which the quadratic equation $2x^2 - kx + k = 0$ has equal roots is:

(a) 0 only

(b) 4

(c) 8 only

(d) 0, 8

Q5. The $n^{th}$ term of an AP is given by $a_n = 3 + 4n$. The common difference is:

(a) 7

(b) 3

(c) 4

(d) 1

Q6. If $\triangle ABC \sim \triangle DEF$ such that $AB = 1.2 \text{ cm}$ and $DE = 1.4 \text{ cm}$, the ratio of the areas of $\triangle ABC$ and $\triangle DEF$ is:

(a) 9 : 49

(b) 36 : 49

(c) 6 : 7

(d) 144 : 196

Q7. The distance of the point $P(2, 3)$ from the x-axis is:

(a) 2 units

(b) 3 units

(c) 1 unit

(d) 5 units

Q8. If $\sin A = \frac{1}{2}$, then the value of $\cot A$ is:

(a) $\sqrt{3}$

(b) $\frac{1}{\sqrt{3}}$

(c) $\frac{\sqrt{3}}{2}$

(d) 1

Q9. The value of $\frac{\sin^2 22^\circ + \sin^2 68^\circ}{\cos^2 22^\circ + \cos^2 68^\circ} + \sin^2 63^\circ + \cos 63^\circ \sin 27^\circ$ is:

(a) 3

(b) 2

(c) 1

(d) 0

Q10. A ladder $10 \text{ m}$ long reaches a window $8 \text{ m}$ above the ground. The distance of the foot of the ladder from the base of the wall is:

(a) $8 \text{ m}$

(b) $2 \text{ m}$

(c) $6 \text{ m}$

(d) $4 \text{ m}$

Q11. At one end of a diameter $AB$ of a circle of radius $5 \text{ cm}$, tangent $XAY$ is drawn. The length of the chord $CD$ parallel to $XY$ at a distance $8 \text{ cm}$ from $A$ is:

(a) $4 \text{ cm}$

(b) $5 \text{ cm}$

(c) $6 \text{ cm}$

(d) $8 \text{ cm}$

Q12. If the perimeter and the area of a circle are numerically equal, then the radius of the circle is:

(a) 2 units

(b) $\pi$ units

(c) 4 units

(d) 7 units

Q13. It is proposed to build a single circular park equal in area to the sum of areas of two circular parks of diameters $16 \text{ m}$ and $12 \text{ m}$. The radius of the new park would be:

(a) $10 \text{ m}$

(b) $15 \text{ m}$

(c) $20 \text{ m}$

(d) $24 \text{ m}$

Q14. A metallic spherical shell of internal and external diameters $4 \text{ cm}$ and $8 \text{ cm}$ respectively, is melted and recast into the form of a cone of base diameter $8 \text{ cm}$. The height of the cone is:

(a) $12 \text{ cm}$

(b) $14 \text{ cm}$

(c) $15 \text{ cm}$

(d) $18 \text{ cm}$

Q15. The volume of the largest right circular cone that can be cut out from a cube of edge $4.2 \text{ cm}$ is:

(a) $9.7 \text{ cm}^3$

(b) $77.6 \text{ cm}^3$

(c) $58.2 \text{ cm}^3$

(d) $19.4 \text{ cm}^3$

Q16. If the mean of the first $n$ natural numbers is $\frac{5n}{9}$, then $n$ is:

(a) 5

(b) 4

(c) 9

(d) 10

Q17. The median of the following data: $33, 31, 35, 45, 72, 73, 36$ is:

(a) 33

(b) 35

(c) 36

(d) 45

Q18. Which of the following cannot be the probability of an event?

(a) $\frac{1}{3}$

(b) 0.1

(c) 3%

(d) $\frac{17}{16}$

Q19. A card is selected from a deck of 52 cards. The probability of its being a red face card is:

(a) $\frac{3}{26}$

(b) $\frac{3}{13}$

(c) $\frac{2}{13}$

(d) $\frac{1}{2}$

Q20. If $P(E) = 0.05$, then the probability of 'not E' is:

(a) -0.05

(b) 0.5

(c) 0.9

(d) 0.95

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✅ Answer Key & Solutions

Q.No	Ans	Explanation / Logic
1	(a)	$144 = 2^4 \times 3^2$. Exponent of 2 is 4.
2	(d)	Sum $= -1 = -(a+1) \implies a=0$. Product $= -6 = b$.
3	(d)	Lines $y=0$ (x-axis) and $y=-7$ are parallel.
4	(d)	$D = k^2 - 8k = 0 \implies k(k-8) = 0 \implies k = 0, 8$.
5	(c)	$d = a_2 - a_1 = 11 - 7 = 4$. (Or coeff. of $n$)
6	(b)	Ratio of areas $= (1.2/1.4)^2 = (6/7)^2 = 36/49$.
7	(b)	Distance from x-axis is $
8	(a)	If $\sin A = 1/2$, $A = 30^\circ$. $\cot 30^\circ = \sqrt{3}$.
9	(b)	Each term simplifies to 1 using complementary angles. $1+1=2$.
10	(c)	Using Pythagoras: $\sqrt{10^2 - 8^2} = \sqrt{36} = 6$.
11	(d)	Distance from center $= 8 - 5 = 3$. Chord $= 2 \times \sqrt{5^2 - 3^2} = 8$.
12	(a)	$2\pi r = \pi r^2 \implies r = 2$.
13	(a)	$R^2 = 8^2 + 6^2 = 100 \implies R = 10$.
14	(b)	Volume Sphere Shell = Volume Cone. $\frac{4}{3} \pi (4^3 - 2^3) = \frac{1}{3} \pi 4^2 h$.
15	(d)	$r = 2.1, h = 4.2$. $V = (1/3)\pi(2.1)^2(4.2) \approx 19.4$.
16	(c)	$(n+1)/2 = 5n/9 \implies 9n + 9 = 10n \implies n = 9$.
17	(c)	Arranged: $31, 33, 35, 36, 45, 72, 73$. Middle is 36.
18	(d)	Probability cannot be greater than 1 ($17/16 > 1$).
19	(a)	Red face cards (Jack, Queen, King of Hearts & Diamonds) $= 6$. $6/52 = 3/26$.
20	(d)	$1 - 0.05 = 0.95$.