CBSE Class 10 Mathematics Board Paper Set 3 — MCQs with Answers

8 solved questions from this paper

Answer and worked explanation shown for each. The remaining 12 are timed and scored when you sign in free.

1. Q1Easy

   A quadratic polynomial whose zeroes are 3 and −5 is:

   A.x² − 2x − 15

   B.x² + 2x + 15

   C.x² − 2x + 15

   D.x² + 2x − 15✓ Correct

   Answer: D. x² + 2x − 15

   Explanation: A quadratic polynomial with given zeroes is x² − (sum of zeroes)x + (product of zeroes). The sum is 3 + (−5) = −2 and the product is 3 × (−5) = −15, giving x² + 2x − 15. Missing the minus sign already built into the formula flips the middle term to −2x.

2. Q2Easy

   The roots of the equation x² − 3x − 10 = 0 are:

   A.−5 and 2

   B.5 and 2

   C.5 and −2✓ Correct

   D.−5 and −2

   Answer: C. 5 and −2

   Explanation: Factorising, x² − 3x − 10 = (x − 5)(x + 2), so the roots are 5 and −2. Both 5, −2 and −5, 2 give a product of −10, so check the sum: it must be −(−3) = 3, and 5 + (−2) = 3 while −5 + 2 = −3.

3. Q3Easy

   In ΔABC, AB = 6√3 cm, AC = 12 cm and BC = 6 cm. The measure of ∠B is:

   A.60°

   B.45°

   C.90°✓ Correct

   D.120°

   Answer: C. 90°

   Explanation: Test the Pythagoras relation: AB² + BC² = (6√3)² + 6² = 108 + 36 = 144, and AC² = 12² = 144. The square on AC equals the sum of the squares on the other two sides, so the angle opposite AC, which is ∠B, is a right angle.

4. Q4Medium

   The pair of equations 3x − y = 5 and 6x − 2y = k has no solution when:

   A.k ≠ 10✓ Correct

   B.k = 10

   C.k = 5

   D.k ≠ 5

   Answer: A. k ≠ 10

   Explanation: A pair of linear equations has no solution when a₁/a₂ = b₁/b₂ but c₁/c₂ is different. Here 3/6 = (−1)/(−2) = 1/2, so we need 5/k ≠ 1/2, that is k ≠ 10. At k = 10 the two equations describe the same line and would have infinitely many solutions instead of none.

5. Q5Medium

   Which term of the AP 21, 18, 15, … is −81?

   A.34th

   B.35th✓ Correct

   C.36th

   D.30th

   Answer: B. 35th

   Explanation: Here a = 21 and d = 18 − 21 = −3. Setting aₙ = a + (n − 1)d = −81 gives 21 − 3(n − 1) = −81, so n − 1 = 34 and n = 35. Stopping at n − 1 = 34 reports the number of gaps rather than the term number.

6. Q6Medium

   The diagonals of a rhombus measure 16 cm and 12 cm. The length of each side of the rhombus is:

   A.10 cm✓ Correct

   B.14 cm

   C.28 cm

   D.20 cm

   Answer: A. 10 cm

   Explanation: The diagonals of a rhombus bisect each other at right angles, so each side is the hypotenuse of a right triangle with legs 8 cm and 6 cm. The side is √(64 + 36) = √100 = 10 cm. Using the full diagonals 16 and 12 instead of their halves gives 20 cm.

7. Q7Hard

   Two positive integers are written as p = a²b³ and q = a³b, where a and b are prime numbers. Then HCF(p, q) is:

   A.a³b³

   B.a²b✓ Correct

   C.ab

   D.a²b³

   Answer: B. a²b

   Explanation: The HCF takes each common prime raised to the lower of the two powers. Comparing a² with a³ the lower power is a², and comparing b³ with b¹ the lower power is b, so the HCF is a²b. Taking the higher powers instead gives a³b³, which is the LCM.

8. Q8Hard

   The quadratic equation (k + 4)x² + (k + 1)x + 1 = 0 has equal roots for:

   A.k = −5 and k = 3

   B.k = 5 and k = 3

   C.k = −5 and k = −3

   D.k = 5 and k = −3✓ Correct

   Answer: D. k = 5 and k = −3

   Explanation: Equal roots mean the discriminant is zero, so (k + 1)² − 4(k + 4) = 0. Expanding gives k² + 2k + 1 − 4k − 16 = k² − 2k − 15 = 0, which factorises as (k − 5)(k + 3) = 0, so k = 5 or k = −3. Reversing the signs of the factors reverses both answers.

More Class 10 Mathematics board papers

• Board Paper — 31 questions
• Board Paper Set 1 — 20 questions
• Board Paper Set 2 — 20 questions
• Board Paper Set 3 — you are here

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