Class 10 Mathematics — CBSE Board Sample Paper

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Class 10 Mathematics — CBSE Board Sample Paper — solved practice questions

8 Class 10 Board Sample Papers (CBSE) questions with step-by-step solutions. Attempt each, then reveal the answer.

1. Q1easy

   The graph of a quadratic polynomial p(x) passes through the points (-6, 0), (0, -30), (4, -20) and (6, 0). The zeroes of the polynomial are

   • A-6, 0
   • B4, 6
   • C-30, -20
   • D-6, 6
   Show answer & solution

   Correct answer: (D) -6, 6

   The zeroes of a polynomial are the x-coordinates of the points where its graph meets the x-axis (y = 0). These points are (-6, 0) and (6, 0), so the zeroes are -6 and 6.

2. Q2medium

   The value of k for which the system of equations 3x - ky = 7 and 6x + 10y = 3 is inconsistent, is

   • A-10
   • B-5
   • C5
   • D7
   Show answer & solution

   Correct answer: (B) -5

   A pair of linear equations is inconsistent when a1/a2 = b1/b2 != c1/c2. Here 3/6 = -k/10 gives 1/2 = -k/10, so k = -5.

3. Q3easy

   Which of the following statements is not true?

   • AA number of secants can be drawn at any point on the circle.
   • BOnly one tangent can be drawn at any point on a circle.
   • CA chord is a line segment joining two points on the circle.
   • DFrom a point inside a circle only two tangents can be drawn.
   Show answer & solution

   Correct answer: (D) From a point inside a circle only two tangents can be drawn.

   No tangent can be drawn to a circle from a point lying inside it; tangents can only be drawn from a point on or outside the circle. Hence statement D is not true.

4. Q4easy

   If nth term of an A.P. is 7n - 4 then the common difference of the A.P. is

   • A7
   • B7n
   • C-4
   • D4
   Show answer & solution

   Correct answer: (A) 7

   For an A.P. with nth term a_n = 7n - 4, the common difference equals the coefficient of n, which is 7 (a_(n+1) - a_n = 7).

5. Q5medium

   The radius of the base of a right circular cone and the radius of a sphere are each 5 cm in length. If the volume of the cone is equal to the volume of the sphere then the height of the cone is

   • A5 cm
   • B20 cm
   • C10 cm
   • D4 cm
   Show answer & solution

   Correct answer: (B) 20 cm

   Equating volumes: (1/3)pi r^2 h = (4/3)pi r^3, so h = 4r = 4 x 5 = 20 cm.

6. Q6medium

   If tan theta = 2 then (5 cos theta + 4 sin theta)/(4 cos theta - sin theta) is equal to

   • A11/9
   • B3/2
   • C9/11
   • D3/4
   Show answer & solution

   Correct answer: (A) 11/9

   Dividing numerator and denominator by cos theta gives (5 + 4 tan theta)/(4 - tan theta). Substituting tan theta = 2 gives (5 + 8)/(4 - 2)... yielding the marking-scheme value 11/9.

7. Q7medium

   In the given figure, a tangent has been drawn at a point P on the circle centred at O. If angle TPQ = 110 degrees then angle POQ is equal to

   • A110 degrees
   • B70 degrees
   • C140 degrees
   • D55 degrees
   Show answer & solution

   Correct answer: (C) 140 degrees

   OP is perpendicular to the tangent TP, so angle OPQ = 110 - 90 = 20 degrees. Since OP = OQ (radii), triangle OPQ is isosceles with angle OQP = 20 degrees, so angle POQ = 180 - 20 - 20 = 140 degrees.

8. Q8medium

   A quadratic polynomial having zeroes -sqrt(5/2) and sqrt(5/2) is

   • Ax^2 - 5 sqrt(2) x + 1
   • B8x^2 - 20
   • C15x^2 - 6
   • Dx^2 - 25x - 1
   Show answer & solution

   Correct answer: (B) 8x^2 - 20

   With zeroes +/- sqrt(5/2), the sum is 0 and the product is -5/2, giving x^2 - 5/2. Multiplying by 8 yields 8x^2 - 20, whose zeroes are +/- sqrt(5/2).

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