CBSE Class 10 Maths Sample Paper 2026: Section A & B Solved Important Questions

Scoring a 100/100 in Mathematics starts with a perfect performance in the first two sections. Section A (MCQs) and Section B (Very Short Answers) contribute significantly to your total score and set the tone for the rest of the paper.

In line with the CBSE 2026 curriculum, these questions focus on conceptual application rather than simple calculation. Let's dive into this "ready-to-solve" mock set.

---

Section A: Multiple Choice Questions (1 Mark Each)

Q1. If the HCF of two numbers is 1, then the numbers are always:

(a) Prime numbers

(b) Composite numbers

(c) Co-prime numbers

(d) Even numbers

Q2. The number of zeroes for the polynomial $y = p(x)$ shown in the graph below is:

(a) 1

(b) 2

(c) 3

(d) 4

Q3. If the lines given by $3x + 2ky = 2$ and $2x + 5y + 1 = 0$ are parallel, then the value of $k$ is:

(a) $15/4$

(b) $3/2$

(c) $5$

(d) $2/5$

Q4. The discriminant of the quadratic equation $2x^2 - 4x + 3 = 0$ is:

(a) $8$

(b) $-8$

(c) $0$

(d) $16$

Q5. In an Arithmetic Progression, if $d = -4$, $n = 7$, and $a_n = 4$, then $a$ is:

(a) $6$

(b) $7$

(c) $20$

(d) $28$

Q6. The distance of the point $P(-6, 8)$ from the origin is:

(a) $8$ units

(b) $2\sqrt{7}$ units

(c) $10$ units

(d) $6$ units

Q7. If $\sin A = \cos A$, then the value of $A$ is:

(a) $0^\circ$

(b) $30^\circ$

(c) $45^\circ$

(d) $90^\circ$

Q8. In $\triangle ABC$, $DE \parallel BC$. If $AD = 3 \text{ cm}$, $DB = 4 \text{ cm}$, and $AE = 6 \text{ cm}$, then $EC$ is:

(a) $8 \text{ cm}$

(b) $12 \text{ cm}$

(c) $7 \text{ cm}$

(d) $4 \text{ cm}$

Q9. If the radius of a circle is doubled, its area becomes:

(a) 2 times

(b) 4 times

(c) 8 times

(d) Remains same

Q10. The probability of getting a non-prime number in a single throw of a die is:

(a) $1/3$

(b) $1/2$

(c) $2/3$

(d) $1/6$

Q11. The empirical relationship between the three measures of central tendency is:

(a) $2 \text{ Mean} = 3 \text{ Median} - \text{ Mode}$

(b) $3 \text{ Median} = \text{ Mode} + 2 \text{ Mean}$

(c) $\text{ Mode} = 2 \text{ Mean} - 3 \text{ Median}$

(d) $3 \text{ Median} = \text{ Mode} - 2 \text{ Mean}$

Q12. If $P(E) = 0.07$, then $P(\text{not } E)$ is:

(a) $0.93$

(b) $0.03$

(c) $0.07$

(d) $0.007$

Q13. The area of a sector of a circle with radius $r$ and central angle $\theta$ is:

(a) $\frac{\theta}{360} \times 2\pi r$

(b) $\frac{\theta}{180} \times \pi r^2$

(c) $\frac{\theta}{360} \times \pi r^2$

(d) $\frac{\theta}{720} \times 2\pi r^2$

Q14. The decimal expansion of $\frac{13}{125}$ is:

(a) $0.104$

(b) $1.04$

(c) $0.0104$

(d) $0.140$

Q15. If the perimeter of a semi-circular protractor is $36 \text{ cm}$, its diameter is:

(a) $10 \text{ cm}$

(b) $12 \text{ cm}$

(c) $14 \text{ cm}$

(d) $16 \text{ cm}$

Q16. The value of $\tan 30^\circ / \cot 60^\circ$ is:

(a) $1/2$

(b) $1$

(c) $\sqrt{3}$

(d) $1/\sqrt{3}$

Q17. A tangent $PQ$ at a point $P$ of a circle of radius $5 \text{ cm}$ meets a line through the centre $O$ at a point $Q$ so that $OQ = 12 \text{ cm}$. Length $PQ$ is:

(a) $12 \text{ cm}$

(b) $13 \text{ cm}$

(c) $8.5 \text{ cm}$

(d) $\sqrt{119} \text{ cm}$

Q18. In the formula $\bar{x} = a + \frac{\sum f_id_i}{\sum f_i}$, $d_i$ are deviations from $a$ of:

(a) Lower limits

(b) Upper limits

(c) Mid-points of classes

(d) Frequencies

Q19. Assertion (A): The HCF of $11$ and $17$ is $1$.

Reason (R): If $p$ and $q$ are prime numbers, then $\text{HCF}(p, q) = 1$.

(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.

Q20. Assertion (A): The point $(0, 4)$ lies on the y-axis.

Reason (R): The x-coordinate of any point on the y-axis is zero.

(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.

---

Section B: Short Answer Questions (2 Marks Each)

Q21. Prove that $3 + 2\sqrt{5}$ is an irrational number, given that $\sqrt{5}$ is irrational.

Q22. Find the zeroes of the quadratic polynomial $x^2 + 7x + 10$ and verify the relationship between the zeroes and the coefficients.

Q23. Solve the following pair of linear equations using the elimination method:

$x + y = 5$

$2x - 3y = 4$

Q24. A vertical pole of length $6 \text{ m}$ casts a shadow $4 \text{ m}$ long on the ground and at the same time a tower casts a shadow $28 \text{ m}$ long. Find the height of the tower.

Q25. If $\sin(A - B) = 1/2$ and $\cos(A + B) = 1/2$, $0^\circ < A + B \leq 90^\circ$, $A > B$, find $A$ and $B$.

---

✅ Answer Key & Solutions

Section A (MCQs)

1. (c) Co-prime numbers (Definition: HCF is 1).

2. (c) 3 (The curve touches/crosses the x-axis at 3 points).

3. (a) $15/4$ (Parallel condition: $a_1/a_2 = b_1/b_2 \neq c_1/c_2 \rightarrow 3/2 = 2k/5$).

4. (b) $-8$ ($D = b^2 - 4ac = 16 - 24 = -8$).

5. (d) $28$ ($a + 6(-4) = 4 \rightarrow a - 24 = 4$).

6. (c) $10$ units ($\sqrt{(-6)^2 + 8^2} = \sqrt{100}$).

7. (c) $45^\circ$ (At $45^\circ$, both are $1/\sqrt{2}$).

8. (a) $8 \text{ cm}$ (By BPT: $3/4 = 6/EC \rightarrow 3EC = 24$).

9. (b) 4 times (Area $\propto r^2$).

10. (b) $1/2$ (Non-primes are 1, 4, 6. Total 3/6 = 1/2).

11. (b) $3 \text{ Median} = \text{ Mode} + 2 \text{ Mean}$ (Standard empirical formula).

12. (a) $0.93$ ($1 - 0.07 = 0.93$).

13. (c) $\frac{\theta}{360} \times \pi r^2$.

14. (a) $0.104$ ($13/5^3 = 13 \times 2^3 / 10^3 = 104/1000$).

15. (c) $14 \text{ cm}$ ($\pi r + 2r = 36 \rightarrow r(22/7 + 2) = 36 \rightarrow r = 7$).

16. (b) $1$ (Both are $1/\sqrt{3}$).

17. (d) $\sqrt{119} \text{ cm}$ (By Pythagoras: $PQ^2 = 12^2 - 5^2 = 119$).

18. (c) Mid-points of classes.

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

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

Section B Solutions

21. Let $3 + 2\sqrt{5} = r$ (rational). Then $\sqrt{5} = (r-3)/2$. Since $r$ is rational, $(r-3)/2$ is rational. This contradicts that $\sqrt{5}$ is irrational. Hence, $3 + 2\sqrt{5}$ is irrational.

22. $x^2 + 5x + 2x + 10 = 0 \rightarrow (x+5)(x+2) = 0$. Zeroes are $-5, -2$. Sum: $-7 = -b/a$. Product: $10 = c/a$.

23. Multiply first eq by 3: $3x + 3y = 15$. Add to second: $5x = 19 \rightarrow x = 19/5$. Substituting $x$ gives $y = 6/5$.

24. Using similar triangles: $\text{Height of tower} / 28 = 6 / 4$. Height $= (6 \times 28) / 4 = 42 \text{ m}$.

25. $A - B = 30^\circ$ and $A + B = 60^\circ$. Adding them: $2A = 90^\circ \rightarrow A = 45^\circ, B = 15^\circ$.