CBSE Class 10 Mathematics 2020 — Set 2

Questions in this 2020 Mathematics paper (Set 2)

All 40 questions from this set, exactly as asked. Try each one, then open the question-paper PDF above for the complete paper.

1. 1.
   The sum of exponents of prime factors in the prime factorisation of 196 is:

   • (a) 3
   • (b) 4
   • (c) 5
   • (d) 2
2. 2.
   Euclid's division Lemma states that for two positive integers a and b, there exists unique integers q and r satisfying a = bq + r, and:

   • (a) 0 < r < b
   • (b) 0 < r ≤ b
   • (c) 0 ≤ r < b
   • (d) 0 ≤ r ≤ b
3. 3.
   The zeroes of the polynomial x² − 3x − m(m + 3) are:

   • (a) m, m + 3
   • (b) −m, m + 3
   • (c) m, −(m + 3)
   • (d) −m, −(m + 3)
4. 4.
   The value of k for which the system of linear equations x + 2y = 3, 5x + ky + 7 = 0 is inconsistent is:

   • (a) −14/3
   • (b) 2/5
   • (c) 5
   • (d) 10
5. 5.
   The roots of the quadratic equation x² − 0.04 = 0 are:

   • (a) ± 0.2
   • (b) ± 0.02
   • (c) 0.4
   • (d) 2
6. 6.
   The common difference of the A.P. 1/p, (1 − p)/p, (1 − 2p)/p, ...... is:

   • (a) 1
   • (b) 1/p
   • (c) −1
   • (d) −1/p
7. 7.
   The n-th term of the A.P. a, 3a, 5a, ...... is:

   • (a) na
   • (b) (2n − 1)a
   • (c) (2n + 1)a
   • (d) 2na
8. 8.
   The point P on x-axis equidistant from the points A(−1, 0) and B(5, 0) is:

   • (a) (2, 0)
   • (b) (0, 2)
   • (c) (3, 0)
   • (d) (2, 2)
9. 9.
   The coordinates of the point which is the reflection of point (−3, 5) in the x-axis are:

   • (a) (3, 5)
   • (b) (3, −5)
   • (c) (−3, −5)
   • (d) (−3, 5)
10. 10.
    If the point P(6, 2) divides the line segment joining A(6, 5) and B(4, y) in the ratio 3 : 1, then the value of y is:

    • (a) 4
    • (b) 3
    • (c) 2
    • (d) 1
11. 11.
    In Fig. 1, MN ∥ BC and AM : MB = 1 : 2, then ar(△AMN)/ar(△ABC) = ______.
12. 12.
    In Fig. 2, two concentric circles have centre O. PA is a tangent to the outer circle and PB is a tangent to the inner circle. OA = 5 cm and OP = 3 cm is the radius of the inner circle. The length PB = ______ cm.
13. 13.
    In △ABC, AB = 6√3 cm, AC = 12 cm and BC = 6 cm, then ∠B = ______.
14. 14.
    The value of (tan 1° tan 2° ...... tan 89°) is equal to ______.
15. 15.
    In Fig. 3, the angles of depression from the observing positions O₁ and O₂ respectively of the object A are ______, ______.
16. 16.
    If sin A + cos² A = 1, then find the value of the expression (cos² A + cos⁴ A).
17. 17.
    In Fig. 4, a sector of a circle of radius 10.5 cm has angle 60°. Find the perimeter of the sector. (Take π = 22/7)
18. 18.
    If a number x is chosen at random from the numbers −3, −2, −1, 0, 1, 2, 3, then find the probability that x² < 4.
19. 19.
    Find the class marks of the classes 10–25 and 35–55.
20. 20.
    A die is thrown once. What is the probability of getting a prime number?
21. 21.
    A teacher asked 10 of his students to write a polynomial in one variable on a paper and then to handover the paper. The following were the answers given by the students: 2x + 3, 3x² + 7x + 2, 4x³ + 3x² + 2, x³ + √x + 7, 7x + √7, 5x³ − 7x + 2, 2x² + 3 − (5/x), 5x − 1/2, ax³ + bx² + cx + d (a ≠ 0), x + 1/x. Answer the following:

    • (i) How many of the above ten are not polynomials?
    • (ii) How many of…
22. 22.
    In Fig. 5, ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, show that ar(△ABC)/ar(△DBC) = AO/DO.
23. 23.
    Prove that: 1 + cot²α/(1 + cosec α) = cosec α.
24. 24.
    The volume of a right circular cylinder with its height equal to the radius is 25 1/7 cm³. Find the height of the cylinder. (Use π = 22/7)
25. 25.
    A child has a die whose six faces show the letters A, B, C, D, E, A as shown. The die is thrown once. What is the probability of getting

    • (i) A,
    • (ii) D?
26. 26.
    Compute the mode for the following frequency distribution: Size of items (in cm): 0–4, 4–8, 8–12, 12–16, 16–20, 20–24, 24–28 Frequency: 5, 7, 9, 17, 12, 10, 6
27. 27.
    If 2x + y = 23 and 4x − y = 19, find the value of (5y − 2x) and (y/x − 2).
28. 28.
    Show that the sum of all terms of an A.P. whose first term is a, the second term is b and the last term is c, is equal to (a + c)(b + c − 2a) / [2(b − a)].
29. 29.
    In a flight of 600 km, an aircraft was slowed down due to bad weather. The average speed of the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. Find the duration of flight.
30. 30.
    If the mid-point of the line segment joining the points A(3, 4) and B(k, 6) is P(x, y) and x + y − 10 = 0, find the value of k.
31. 31.
    In Fig. 7, if △ABC ~ △DEF and their sides of lengths (in cm) are marked along them, then find the lengths of the sides of each triangle.
32. 32.
    If a circle touches the side BC of a triangle ABC at P and extended sides AB and AC at Q and R respectively, prove that AQ = 1/2 (BC + CA + AB).
33. 33.
    If sin θ + cos θ = √2, prove that tan θ + cot θ = 2.
34. 34.
    The area of a circular play ground is 22176 cm². Find the cost of fencing this ground at the rate of ₹50 per metre.
35. 35.
    Prove that √5 is an irrational number.
36. 36.
    It can take 12 hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for four hours and the pipe of smaller diameter for 9 hours, only half of the pool can be filled. How long would it take for each pipe to fill the pool separately?
37. 37.
    Draw a circle of radius 2 cm with centre O and take a point P outside the circle such that OP = 6.5 cm. From P, draw two tangents to the circle.
38. 38.
    From a point on the ground, the angles of elevation of the bottom and the top of a tower fixed at the top of a 20 m high building are 45° and 60° respectively. Find the height of the tower.
39. 39.
    Find the area of the shaded region in Fig. 8, if PQ = 24 cm, PR = 7 cm and O is the centre of the circle.
40. 40.
    The mean of the following frequency distribution is 18. The frequency f in the class interval 19–21 is missing. Determine f. Class interval: 11–13, 13–15, 15–17, 17–19, 19–21, 21–23, 23–25 Frequency: 3, 6, 9, 13, f, 5, 4

Class 10 Mathematics exam pattern (80 marks)

The theory paper carries 80 marks over 3 hours (38 questions, with internal choice in some). Section-wise structure:

Structure per the CBSE 2023-24 sample-paper design; question wording varies by set.

Prepare with

How to use these papers

1. 1Start chapter-wise early in the year — solve only the Mathematics questions from a chapter you have just finished.
2. 2Switch to full timed papers 2–3 months before the exam: one complete set in the real time limit, no notes.
3. 3Self-mark against the marking scheme, then fix every mistake with our free NCERT solutions.
4. 4Re-attempt your weakest chapters until the recurring question types feel routine.

CBSE Class 10 Mathematics 2020 paper — FAQ