CBSE Class 10 Maths (Basic) 2026 — Paper 430/3/1

Question 1

Q1. The HCF of 2³ and 3² is: (a) 2⁰ × 3⁰ (b) 2¹ × 3¹ (c) 2³ × 3² (d) 2² × 3³

Accepted Answer

(a) 2⁰ × 3⁰

Question 2

Q2. The LCM of two consecutive natural numbers p and p + 1 is: (a) p (b) p² + p (c) 1 (d) 2p + 1

Accepted Answer

(b) p² + p

Question 3

Q3. The system of equations 2x + ky = 4 and 3x - 6y = 6 has infinitely many solutions, if: (a) k ≠ 4 (b) k = 4 (c) k = -4 (d) No value of k

Accepted Answer

(c) k = -4

Question 4

Q4. The value of ' m ' for which the quadratic equation x² - 2x + m = 0 has real and equal roots is: (a) -1 (b) 0 (c) 4 (d) 1

Accepted Answer

(d) 1

Question 5

Q5. Which of the following statements is true for the quadratic equation ax² + x + a = 0 (a ≠ 0)? (a) The roots of the given equation are reciprocal of each other. (b) The roots of the given equation are always real. (c) The roots of the given equation are always positive. (d) The sum of roots of the given equation is 0.

Accepted Answer

(a) The roots of the given equation are reciprocal of each other.

Question 6

Q6. The co-ordinates of the mid-point of the line segment joining points A(p - 1, q + 1) and B(p + 1, q - 1) are given by: (a) (p, q) (b) (2p, 2q) (c) ((p + 1)/2, (q + 1)/2) (d) ((p - 1)/2, (q - 1)/2)

Accepted Answer

(a) (p, q)

Question 7

Q8. Two isosceles triangles: (a) are always similar, but not congruent. (b) are always congruent, but not similar. (c) may or may not be similar. (d) are always similar and congruent.

Accepted Answer

(c) may or may not be similar.

Question 8

Q9. The number of solutions of the system of equations given by x = -2 and y = 2 is: (a) 0 (b) 1 (c) 2 (d) infinite

Accepted Answer

(b) 1

Question 9

Q11. If a, b and c are in A.P., then: (a) 2a, 3b and 4c are also in A.P. (b) a - 2, b - 2 and c - 2 are also in A.P. (c) a/2, b/3 and c/4 are also in A.P. (d) a + 2, b + 3 and c + 4 are also in A.P.

Accepted Answer

(b) a - 2, b - 2 and c - 2 are also in A.P.

Question 10

Q12. The value of (tan² 60° - 1)/(tan² 60° + 1) is equal to the value of which of the following? (a) tan 60° (b) cos 60° (c) sec 60° (d) sin 60°

Accepted Answer

(b) cos 60°

Question 11

Q13. Which of the following is not defined for x = 90°? (a) cot x (b) cosec x (c) tan(x/2) (d) sec x

Accepted Answer

(d) sec x

Question 12

Q15. The radius of the largest sphere that can be carved out from a solid cube of side 14 cm is: (a) 7 cm (b) 14 cm (c) 14√2 cm (d) 7√2 cm

Accepted Answer

(a) 7 cm

Question 13

Q16. Let ' a ' be the assumed mean and ' h ' be the class size for a grouped data. Which of the following is not the correct formula to find the mean of the grouped data? (a) x = (Σf_i x_i)/(Σf_i) (b) x = a + (Σf_i d_i)/(Σf_i), where d_i = x_i - a (c) x = a + (Σf_i u_i)/(Σf_i), where u_i = (x_i - a)/h (d) x = a + (Σf_i y_i)/(Σf_i) × h, where y_i = (x_i - a)/h

Accepted Answer

(c) x = a + (Σf_i u_i)/(Σf_i), where u_i = (x_i - a)/h

Question 14

Q17. Which of the following is affected by the extreme values in a given data? (a) Mean only (b) Median only (c) Mode only (d) Mean and Mode both

Accepted Answer

(a) Mean only

Question 15

Q18. From a bag containing yellow, red and green balls, the probability of drawing a yellow or red ball is equal to that of drawing a green ball. The probability of drawing a green ball from the bag is: (a) 1/3 (b) 1/2 (c) 1 (d) Not possible to find

Accepted Answer

(b) 1/2

Question 16

Q19. Assertion (A): The events “getting 2” and “not getting 2” in a single throw of an unbiased die are not equally likely events. Reason (R): The probability of getting 2 in a single throw of an unbiased die is 1/6. (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.

Accepted Answer

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

Question 17

Q20. Assertion (A): (√3 + 1)² is a rational number. Reason (R): (√3)² = 3 is a rational number. (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.

Accepted Answer

(d) Assertion (A) is false, but Reason (R) is true.

Question 18

Q21. An ant started moving from the point A(2, 3) and moved along the line segment AB. It covered three-fourth of the distance AB and reached at a point C(x, y). If the coordinates of the point B are (10, 15), find the coordinates of the point C.

Accepted Answer

The coordinates of the point C are (8, 12).

Question 19

Q22. Verify the relationship between the zeroes and the coefficients of the polynomial p(x) = 3x² - 5x.

Accepted Answer

The zeroes of p(x) = 3x² - 5x are 0 and 5/3; sum of zeroes = 5/3 = -b/a and product of zeroes = 0 = c/a. Hence the relationship between the zeroes and the coefficients is verified.

Question 20

Q26. Prove that √5 is an irrational number.

Accepted Answer

Assuming √5 = a/b with a, b coprime and b ≠ 0 leads to 5 dividing both a and b, contradicting that they are coprime. Hence the assumption is wrong and √5 is an irrational number.

Question 21

Q27. Each root of a quadratic equation ax² + bx + c = 0 is 2 more than each of the roots of the equation 3x² - 2x = 1. Find the roots of the quadratic equation ax² + bx + c = 0.

Accepted Answer

The roots of ax² + bx + c = 0 are 3 and 5/3.

Question 22

Q28(a). Show that the quadrilateral ABCD formed by joining the points A(-2, -1), B(1, -1), C(1, 2) and D(-2, 2) in order is a square.

Accepted Answer

AB = BC = CD = DA = 3 units and AC = BD = 3√2 units, so all four sides are equal and the diagonals are equal; hence ABCD is a square.

Question 23

Q29(a). Prove that: (sin A - cosec A)² + (cos A - sec A)² = tan² A + cot² A - 1

Accepted Answer

LHS = tan² A + cot² A - 1 = RHS, so the identity is proved.

Question 24

Q30. Prove that a rectangle circumscribing a circle is a square.

Accepted Answer

AB = BC = CD = DA and every angle is 90°, so the rectangle ABCD is a square. Hence proved.

Question 25

Q32. A fraction becomes 5/6 when 3 is added to both the numerator and the denominator. If 2 is added to both the numerator and the denominator, the fraction becomes 9/11. Express the given information algebraically as a system of linear equations in two variables. Hence, find the original fraction.

Accepted Answer

The given information is represented by the system 6x - 5y = -3 and 11x - 9y = -4, where x is the numerator and y is the denominator. Solving this pair gives x = 7 and y = 9, so the original fraction is 7/9.

Question 26

Q33(a). Sides AB, AC and altitude AD of △ABC are proportional to sides PQ, PR and altitude PS of another triangle PQR. Prove that △ABC ~ △PQR.

Accepted Answer

The altitudes give right angles at D and at S, and Pythagoras turns AB/(PQ) = AD/(PS) = k into BD = k QS, so △ABD ~ △PQS and likewise △ACD ~ △PRS. These give ∠B = ∠Q and ∠C = ∠R, hence △ABC ~ △PQR by the AA criterion.

Question 27

Q35. The following table shows the weight (in kg) of 40 students of class X: Find the mean weight and median weight. Table: Weight (in kg) | Number of students; 40 - 45 | 3; 45 - 50 | 4; 50 - 55 | 10; 55 - 60 | 8; 60 - 65 | 8; 65 - 70 | 4; 70 - 75 | 3.

Accepted Answer

The mean weight is 57.25 kg and the median weight is 56.875 kg.

CBSE Class 10 Maths (Basic) 2026 — Paper 430/3/1

Questions 1–20 · 1 mark each

Questions 21–25 · 2 marks each

Questions 26–31 · 3 marks each

Questions 32–35 · 5 marks each

Questions 36–38 · 4 marks each

Other 2026 papers