CBSE Class 10 Mathematics Model Paper 2026: 20 Solved MCQs for Board Exam Success

Preparing for the CBSE Class 10 Mathematics board exam in 2026 requires a sharp focus on the objective section. Since Section A carries 20 marks and is entirely composed of Multiple Choice Questions (MCQs), it often determines whether a student can achieve a perfect score. This Mathematics Model Paper 2026 provides 20 high-probability questions that reflect the latest NCERT syllabus and the board's shift toward competency-based testing.

By practicing these problems, you will sharpen your speed and accuracy—two critical factors for exam day.

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Section A: Multiple Choice Questions (1 Mark Each)

Q1. The LCM of the smallest two-digit composite number and the smallest composite number is:

(a) 12

(b) 4

(c) 20

(d) 44

Q2. If one zero of the quadratic polynomial $x^2 + 3x + k$ is 2, then the value of $k$ is:

(a) 10

(b) -10

(c) 5

(d) -5

Q3. The lines representing the linear equations $2x - y = 3$ and $4x - y = 5$ will:

(a) Intersect at a point

(b) Be parallel

(c) Be coincident

(d) Intersect at two points

Q4. The nature of roots of the quadratic equation $9x^2 - 6x - 2 = 0$ is:

(a) Real and equal

(b) No real roots

(c) Real and distinct

(d) Imaginary roots

Q5. In an Arithmetic Progression, if $a = 3.5$, $d = 0$, and $n = 101$, then $a_n$ will be:

(a) 0

(b) 3.5

(c) 103.5

(d) 104.5

Q6. In $\triangle ABC$, $DE \parallel BC$. If $AD = x$, $DB = x - 2$, $AE = x + 2$, and $EC = x - 1$, then the value of $x$ is:

(a) 5

(b) 4

(c) 3

(d) 2

Q7. The distance of the point $P(3, -4)$ from the origin is:

(a) 3 units

(b) 4 units

(c) 5 units

(d) 7 units

Q8. If $\cos \theta = \frac{4}{5}$, then the value of $\tan \theta$ is:

(a) $3/5$

(b) $3/4$

(c) $4/3$

(d) $5/3$

Q9. From a point on the ground, $30 \text{ m}$ away from the foot of a tower, the angle of elevation of the top of the tower is $30^\circ$. The height of the tower is:

(a) $30 \text{ m}$

(b) $10\sqrt{3} \text{ m}$

(c) $30\sqrt{3} \text{ m}$

(d) $15\sqrt{3} \text{ m}$

Q10. At a point $P$ on a circle, a tangent $PQ$ is drawn. If $O$ is the center and $\angle OPQ$ is measured, what is its value?

(a) $45^\circ$

(b) $60^\circ$

(c) $90^\circ$

(d) $180^\circ$

Q11. The area of a sector of a circle of radius $7 \text{ cm}$ with a central angle of $90^\circ$ is:

(a) $38.5 \text{ cm}^2$

(b) $77 \text{ cm}^2$

(c) $154 \text{ cm}^2$

(d) $19.25 \text{ cm}^2$

Q12. If a metallic sphere of radius $6 \text{ cm}$ is melted and recast into a wire of cross-section radius $0.2 \text{ cm}$, the length of the wire is:

[Image showing the process of melting a sphere to recast it into a long cylinder/wire]

(a) $72 \text{ m}$

(b) $7.2 \text{ m}$

(c) $720 \text{ m}$

(d) $7200 \text{ m}$

Q13. In a frequency distribution, if $\text{Mean} = 26.4$ and $\text{Median} = 27.2$, then the Mode is:

(a) 28.8

(b) 25.6

(c) 28.4

(d) 24.8

Q14. Two dice are thrown together. The probability of getting the same number on both dice is:

(a) $1/2$

(b) $1/3$

(c) $1/6$

(d) $1/12$

Q15. The decimal expansion of $\frac{23}{2^3 \times 5^2}$ will terminate after how many places?

(a) 1

(b) 2

(c) 3

(d) 4

Q16. If the zeroes of the polynomial $ax^2 + bx + c$ are reciprocal to each other, then:

(a) $a = c$

(b) $a = b$

(c) $b = c$

(d) $a = -c$

Q17. The coordinates of the midpoint of the line segment joining $A(2, 3)$ and $B(4, 7)$ are:

(a) $(3, 5)$

(b) $(1, 2)$

(c) $(6, 10)$

(d) $(5, 3)$

Q18. The value of $\frac{2 \tan 30^\circ}{1 + \tan^2 30^\circ}$ is:

(a) $\sin 60^\circ$

(b) $\cos 60^\circ$

(c) $\tan 60^\circ$

(d) $\sin 30^\circ$

Q19. Assertion (A): The value of $y$ is 6, for which the distance between the points $P(2, -3)$ and $Q(10, y)$ is 10.

Reason (R): Distance formula is given by $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.

(a) Both A and R are true and R is the correct explanation of A.

(b) Both A and R are true but R is not the correct explanation of A.

(c) A is true but R is false.

(d) A is false but R is true.

Q20. Assertion (A): If the probability of an event $E$ is 0.75, then $P(\text{not } E) = 0.25$.

Reason (R): $P(E) + P(\text{not } E) = 1$.

(a) Both A and R are true and R is the correct explanation of A.

(b) Both A and R are true but R is not the correct explanation of A.

(c) A is true but R is false.

(d) A is false but R is true.

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✅ Answer Key & Explanations

Q. No.	Answer	Quick Logic
1	(c) 20	Smallest 2-digit composite = 10; Smallest composite = 4. LCM(10, 4) = 20.
2	(b) -10	Put $x = 2$: $2^2 + 3(2) + k = 0 \Rightarrow 4 + 6 + k = 0$.
3	(a) Intersect	$a_1/a_2 = 2/4 = 1/2$; $b_1/b_2 = -1/-1 = 1$. Since $a_1/a_2 \neq b_1/b_2$.
4	(c) Real/Distinct	$D = b^2 - 4ac = (-6)^2 - 4(9)(-2) = 36 + 72 = 108 > 0$.
5	(b) 3.5	If $d = 0$, all terms are the same as $a$.
6	(b) 4	By BPT: $x/(x-2) = (x+2)/(x-1) \Rightarrow x^2 - x = x^2 - 4$.
7	(c) 5 units	$\sqrt{3^2 + (-4)^2} = \sqrt{9 + 16} = 5$.
8	(b) 3/4	$\sin \theta = \sqrt{1 - (4/5)^2} = 3/5$. $\tan \theta = \sin/\cos = 3/4$.
9	(b) $10\sqrt{3}$	$\tan 30^\circ = h/30 \Rightarrow 1/\sqrt{3} = h/30 \Rightarrow h = 30/\sqrt{3}$.
10	(c) $90^\circ$	Radius is perpendicular to the tangent at the point of contact.
11	(a) 38.5	Area $= (90/360) \times (22/7) \times 7^2 = 1/4 \times 154$.
12	(c) 720 m	Volume Sphere = Volume Wire. $(4/3)\pi(6^3) = \pi(0.2^2)L$.
13	(a) 28.8	$\text{Mode} = 3\text{Median} - 2\text{Mean} = 3(27.2) - 2(26.4)$.
14	(c) 1/6	Favorable: (1,1), (2,2), (3,3), (4,4), (5,5), (6,6). $6/36 = 1/6$.
15	(c) 3	Max power of 2 or 5 in the denominator is 3 ($2^3$).
16	(a) $a = c$	Product of zeroes $= c/a$. If reciprocals, product $= 1 \Rightarrow c/a = 1$.
17	(a) (3, 5)	$((2+4)/2, (3+7)/2) = (3, 5)$.
18	(a) $\sin 60^\circ$	This is the identity for $\sin 2\theta$, i.e., $\sin(2 \times 30^\circ)$.
19	(d) A is false	Solving distance gives $y = 3$ or $-9$, not 6. R is a true formula.
20	(a) Both true	Correct calculation and correct reasoning.