CBSE Class 10 Mathematics 2020 — Set 3

Questions in this 2020 Mathematics paper (Set 3)

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 HCF of 135 and 225 is

   • (a) 15
   • (b) 75
   • (c) 45
   • (d) 5
2. 2.
   The exponent of 2 in the prime factorization of 144 is

   • (a) 2
   • (b) 4
   • (c) 1
   • (d) 6
3. 3.
   The common difference of an AP, whose nth term is a_n = (3n + 7), is

   • (a) 3
   • (b) 7
   • (c) 10
   • (d) 6
4. 4.
   The value of λ for which (x² + 4x + λ) is a perfect square, is

   • (a) 16
   • (b) 9
   • (c) 1
   • (d) 4
5. 5.
   The value of k, for which the pair of linear equations kx + y = k² and x + ky = 1 have infinitely many solutions, is

   • (a) ±1
   • (b) 1
   • (c) −1
   • (d) 2
6. 6.
   The value of p for which (2p + 1), 10 and (5p + 5) are three consecutive terms of an AP is

   • (a) −1
   • (b) −2
   • (c) 1
   • (d) 2
7. 7.
   In the given figure, the graph of the polynomial p(x) is shown. The number of zeroes of the polynomial is

   • (a) 1
   • (b) 2
   • (c) 3
   • (d) 0
8. 8.
   If (a, b) is the mid-point of the line segment joining the points A(10, −6) and B(k, 4) and a − 2b = 18, the value of k is

   • (a) 30
   • (b) 22
   • (c) 4
   • (d) 40
9. 9.
   The value of k for which the points A(0, 1), B(2, k) and C(4, −5) are collinear is

   • (a) 2
   • (b) −2
   • (c) 0
   • (d) 4
10. 10.
    If ΔABC ~ ΔDEF such that AB = 1.2 cm and DE = 1.4 cm, the ratio of the areas of ΔABC and ΔDEF is

    • (a) 49 : 36
    • (b) 6 : 7
    • (c) 7 : 6
    • (d) 36 : 49
11. 11.
    √2 times the distance between (0, 5) and (−5, 0) is ________.
12. 12.
    The distance between two parallel tangents of a circle of radius 4 cm is ________.
13. 13.
    In the figure, PA and PB are tangents to the circle with centre O such that ∠APB = 50°. The measure of ∠OAB is ________.
14. 14.
    (3 cot 40°)/(tan 50°) − (1/2)(cos 35°/sin 55°) = ________.
15. 15.
    If cot θ = 7/8, then the value of ((1 + sin θ)(1 − sin θ)) / ((1 + cos θ)(1 − cos θ)) is ________.
16. 16.
    What is the value of (1/(1 + cot²θ) + 1/(1 + tan²θ))?
17. 17.
    Two right circular cones have their heights in the ratio 1 : 3 and radii in the ratio 3 : 1. What is the ratio of their volumes?
18. 18.
    Using the empirical formula, find the mode of a distribution whose mean is 8.32 and the median is 8.05.
19. 19.
    The probability that it will rain tomorrow is 0.85. What is the probability that it will not rain tomorrow?
20. 20.
    What is the arithmetic mean of first n natural numbers?
21. 21.
    Find the 11th term from the last term (towards the first term) of the AP 12, 8, 4, ..., −84.
22. 22.
    In the figure, AB is a chord of a circle with centre O, AOC is a diameter and AT is tangent at A. Prove that ∠BAT = ∠ACB.
23. 23.
    If tan θ = 3/4, find the value of (1 − cos²θ)/(1 + cos²θ).
24. 24.
    Students of Class XII presented a gift to their school in the form of an electric lamp — a glass hemispherical base surmounted by a metallic cylindrical top of same radius 21 cm and height 3.5 cm. The top was silver coated and the glass surface was painted red.

    • (i) What is the cost of silver coating the top at the rate of ₹5 per 100 cm²?
    • (ii) What is the surface area of the glass part to be…
25. 25.
    A leap year is randomly chosen. Find the probability that it will contain 53 Sundays and 53 Mondays.
26. 26.
    Find the value of p if the mean of the following distribution is 7.5. Classes: 2–4, 4–6, 6–8, 8–10, 10–12, 12–14 Frequency: 6, 8, 15, p, 8, 4
27. 27.
    Find a, b and c if it is given that the numbers a, 7, b, 23, c are in AP.
28. 28.
    Find the values of k for which the quadratic equation (k + 4)x² + (k + 1)x + 1 = 0 has equal roots.
29. 29.
    On dividing x³ − 3x² + x + 2 by a polynomial g(x), the quotient and remainder were x − 2 and −2x + 4 respectively. Find g(x).
30. 30.
    In what ratio does the point P(−4, y) divide the line segment joining the points A(−6, 10) and B(3, −8)? If it lies on AB, hence find the value of y.
31. 31.
    Prove that a tangent to a circle is perpendicular to the radius through the point of contact.
32. 32.
    In a right triangle, prove that the square of the hypotenuse is equal to the sum of squares of the other two sides (Pythagoras Theorem).
33. 33.
    If sin θ + cos θ = p and sec θ + cosec θ = q, show that q(p² − 1) = 2p.
34. 34.
    500 persons are taking dip into a cuboidal pond which is 80 m long and 50 m broad. What is the rise of water level in the pond, if the average displacement of water by a person is 0.04 m³?
35. 35.
    Show that (12)^n cannot end with digit 0 or 5 for any natural number n.
36. 36.
    A train covered a certain distance at a uniform speed. If the train would have been 6 km/hr faster, it would have taken 4 hours less than the scheduled time and if the train were slower by 6 km/hr, it would have taken 6 hrs more than the scheduled time. Find the length of the journey.
37. 37.
    In an equilateral triangle ABC, D is a point on the side BC such that BD = (1/3)BC. Prove that 9 AD² = 7 AB².
38. 38.
    If the angle of elevation of a cloud from a point 10 metres above a lake is 30° and the angle of depression of its reflection in the lake is 60°, find the height of the cloud from the surface of the lake.
39. 39.
    A solid iron cuboidal block of dimensions 4.4 m × 2.6 m × 1 m is cast into a hollow cylindrical pipe of internal radius 30 cm and thickness 5 cm. Find the length of the pipe.
40. 40.
    For the following frequency distribution, draw a cumulative frequency curve of 'more than' type and hence obtain the median value. Classes: 0–10, 10–20, 20–30, 30–40, 40–50, 50–60, 60–70 Frequency: 5, 15, 20, 23, 17, 11, 9

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