CBSE Class 10 Mathematics Board Paper Set 2 — 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

   The pair of equations x + 2y = 5 and 3x + 6y = 15 has:

   A.exactly one solution

   B.no solution

   C.exactly two solutions

   D.infinitely many solutions✓ Correct

   Answer: D. infinitely many solutions

   Explanation: Comparing the ratios, 1/3 = 2/6 = 5/15, so all three ratios are equal and the two equations represent the same line. Coincident lines overlap at every point, which means infinitely many common solutions rather than a single point of intersection.

2. Q2Easy

   The sum of two numbers is 27 and their difference is 5. The larger of the two numbers is:

   A.11

   B.22

   C.16✓ Correct

   D.13.5

   Answer: C. 16

   Explanation: Let the numbers be x and y with x + y = 27 and x − y = 5. Adding the two equations gives 2x = 32, so x = 16 and then y = 11. Halving only the sum gives 13.5, which ignores the difference altogether.

3. Q3Easy

   The 11th term of the AP −3, −1/2, 2, 9/2, … is:

   A.25

   B.19.5

   C.−22

   D.22✓ Correct

   Answer: D. 22

   Explanation: The common difference is −1/2 − (−3) = 5/2. Using aₙ = a + (n − 1)d, a₁₁ = −3 + 10 × 5/2 = −3 + 25 = 22. Adding only the ten common differences and forgetting the first term gives 25.

4. Q4Medium

   Which of the following rational numbers has a terminating decimal expansion?

   A.17/8✓ Correct

   B.5/6

   C.7/15

   D.11/21

   Answer: A. 17/8

   Explanation: A rational number in its lowest form terminates only when its denominator is of the form 2ᵐ × 5ⁿ. Here 8 = 2³, so 17/8 terminates. The denominators 6 = 2 × 3, 15 = 3 × 5 and 21 = 3 × 7 each carry a prime other than 2 or 5, so those expansions are non-terminating and repeating.

5. Q5Medium

   If α and β are the zeroes of the polynomial x² − 6x + 8, then the value of 1/α + 1/β is:

   A.4/3

   B.3/4✓ Correct

   C.−3/4

   D.2/3

   Answer: B. 3/4

   Explanation: For x² − 6x + 8 the sum of the zeroes is 6 and the product is 8. Since 1/α + 1/β = (α + β)/(αβ), the value is 6/8 = 3/4. Writing the expression as (αβ)/(α + β) by mistake turns the answer upside down to 4/3.

6. Q6Medium

   The quadratic equation kx² − 6x + 1 = 0 has two equal roots when k equals:

   A.6

   B.9✓ Correct

   C.4

   D.36

   Answer: B. 9

   Explanation: Equal roots require the discriminant to be zero: b² − 4ac = 0. Here (−6)² − 4 × k × 1 = 36 − 4k = 0, so k = 9. Setting 36 − 4k equal to the coefficient 6 rather than to zero is what produces the answer 6.

7. Q7Hard

   The point on the x-axis which is equidistant from the points (2, −5) and (−2, 9) is:

   A.(−7, 0)✓ Correct

   B.(7, 0)

   C.(0, −7)

   D.(−3, 0)

   Answer: A. (−7, 0)

   Explanation: Any point on the x-axis has the form (x, 0). Equating the squared distances gives (x − 2)² + 25 = (x + 2)² + 81, which simplifies to −4x + 29 = 4x + 85, so 8x = −56 and x = −7. The required point is therefore (−7, 0); the point (0, −7) lies on the y-axis, not the x-axis.

8. Q8Hard

   If 3 cot θ = 4, then the value of (5 sin θ − 3 cos θ)/(5 sin θ + 3 cos θ) is:

   A.9

   B.1/9✓ Correct

   C.1/3

   D.3/5

   Answer: B. 1/9

   Explanation: From 3 cot θ = 4 we get cot θ = 4/3, so tan θ = 3/4 and the right triangle gives sin θ = 3/5 and cos θ = 4/5. Substituting, the expression becomes (3 − 12/5) ÷ (3 + 12/5) = (3/5) ÷ (27/5) = 1/9. Reading cot θ as 3/4 instead of 4/3 turns the value upside down to 9.

More Class 10 Mathematics board papers

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• Board Paper Set 1 — 20 questions
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• Board Paper Set 3 — 20 questions

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