CBSE Class 10 Mathematics 2020 — Set 4

Questions in this 2020 Mathematics paper (Set 4)

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 number of zeroes for a polynomial p(x) where graph of y = p(x) is given in Figure-1, is:

   • (a) 3
   • (b) 4
   • (c) 0
   • (d) 5
2. 2.
   The first term of an A.P. is 5 and the last term is 45. If the sum of all the terms is 400, the number of terms is:

   • (a) 20
   • (b) 8
   • (c) 10
   • (d) 16
3. 3.
   It is being given that the points A(1, 2), B(0, 0) and C(a, b) are collinear. Which of the following relations between a and b is true?

   • (a) a = 2b
   • (b) 2a = b
   • (c) a + b = 0
   • (d) a − b = 0
4. 4.
   In Figure-2, TP and TQ are tangents drawn to the circle with centre O. If ∠POQ = 115°, then ∠PTQ is:

   • (a) 115°
   • (b) 57.5°
   • (c) 55°
   • (d) 65°
5. 5.
   The value of θ for which cos(10° + θ) = sin 30°, is:

   • (a) 50°
   • (b) 40°
   • (c) 80°
   • (d) 20°
6. 6.
   A bag contains 3 red, 5 black and 7 white balls. A ball is drawn from the bag at random. The probability that the ball drawn is not black, is:

   • (a) 1/3
   • (b) 9/15
   • (c) 5/10
   • (d) 2/3
7. 7.
   The pair of linear equations y = 0 and y = −6 has:

   • (a) a unique solution
   • (b) no solution
   • (c) infinitely many solutions
   • (d) only solution (0, 0)
8. 8.
   The mean and median of a distribution are 14 and 15 respectively. The value of mode is:

   • (a) 16
   • (b) 17
   • (c) 18
   • (d) 13
9. 9.
   The quadratic equation x² − 4x + k = 0 has distinct real roots if:

   • (a) k = 4
   • (b) k > 4
   • (c) k = 16
   • (d) k < 4
10. 10.
    Point P(a/8, 4) is the mid-point of the line segment joining the points A(−5, 2) and B(4, 6). The value of 'a' is:

    • (a) −4
    • (b) 4
    • (c) −8
    • (d) −2
11. 11.
    ((2 + √5) / 3) is a(n) __________ number.
12. 12.
    Let △ABC ~ △DEF and their areas be respectively 81 cm² and 144 cm². If EF = 24 cm, then length of side BC is __________ cm.
13. 13.
    The distance between the points (a, b) and (−a, −b) is __________.
14. 14.
    If tan A = 1, then 2 sin A cos A = __________.
15. 15.
    A spherical metal ball of radius 8 cm is melted to make 8 smaller identical balls. The radius of each new ball is __________ cm.
16. 16.
    Given that HCF(135, 225) = 45, find the LCM(135, 225).
17. 17.
    In Figure-3, a tightly stretched rope of length 20 m is tied from the top of a vertical pole to the ground. Find the height of the pole if the angle made by the rope with the ground is 30°.
18. 18.
    Two dice are thrown simultaneously. What is the probability that the sum of the two numbers appearing on the top is 13?
19. 19.
    After how many decimal places will the decimal representation of the rational number 229 / (2² × 5⁷) terminate?
20. 20.
    In Figure-4, AB and CD are common tangents to circles which touch each other at D. If AB = 8 cm, then find the length of CD.
21. 21.
    Solve for x: 6x² + 11x + 3 = 0
22. 22.
    The perimeters of two similar triangles are 30 cm and 20 cm respectively. If one side of the first triangle is 9 cm long, find the length of the corresponding side of the second triangle.
23. 23.
    Evaluate: (sin 47° / cos 43°)² + (cos 30° / cot 30°)² − (sin 60°)²
24. 24.
    Find the mode of the following distribution: Class: 0–20, 20–40, 40–60, 60–80, 80–100 Frequency: 10, 8, 12, 16, 4
25. 25.
    In Figure-6, a tent is in the shape of a cylinder surmounted by a conical top. The cylindrical part is 2.1 m high and conical part has slant height 2.8 m. Both the parts have same radius 2 m. Find the area of the canvas used to make the tent. (Use π = 22/7)
26. 26.
    Tree Plantation Drive: A Group Housing Society has 600 members, who have their houses in the campus and decided to hold a Tree Plantation Drive on the occasion of New Year. Each household was given the choice of planting a sapling of its choice. The number of different types of saplings planted were:

    • (i) Neem – 125
    • (ii) Peepal – 165
    • (iii) Creepers – 50
    • (iv) Fruit plants – 150
    • (v) Flowering…
27. 27.
    Prove that √5 is an irrational number.
28. 28.
    The sum of the first 30 terms of an A.P. is 1920. If the fourth term is 18, find its 11th term.
29. 29.
    Find the co-ordinates of the points of trisection of the line segment joining the points (3, −1) and (6, 8).
30. 30.
    In Figure-7, XY and MN are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and MN at B. Prove that ∠AOB = 90°.
31. 31.
    Solve the pair of equations: 2/x + 3/y = 11 5/x − 4/y = −7 Hence, find the value of 5x − 3y.
32. 32.
    Prove that: (sin θ − cos θ + 1) / (cos θ + sin θ − 1) = 1 / (sec θ − tan θ)
33. 33.
    In Figure-8, find the area of the shaded region where a circular arc of radius 7 cm has been drawn with vertex O of an equilateral triangle OAB of side 14 cm as centre. (Use π = 22/7 and √3 = 1.73)
34. 34.
    Construct a triangle with sides 5 cm, 6 cm and 7 cm. Now construct another triangle whose sides are 2/3 times the corresponding sides of the first triangle.
35. 35.
    In a flight of 600 km, the speed of the aircraft was slowed down due to bad weather. The average speed of the trip was decreased by 200 km/hr and the time of the flight increased by 30 minutes. Find the average speed of the aircraft originally.
36. 36.
    Draw a 'more than' cumulative frequency curve for the following distribution. Also, find the median from the graph. Weight (in kg): 40–44, 44–48, 48–52, 52–56, 56–60, 60–64, 64–68 Number of students: 7, 12, 33, 47, 20, 11, 5
37. 37.
    If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then prove that the other two sides are divided in the same ratio.
38. 38.
    A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. After covering a distance of 50 m, the angle of depression of the car becomes 60°. Find the height of the tower. (Use √3 = 1.73)
39. 39.
    A bucket open at the top has top and bottom radii of circular ends as 40 cm and 20 cm respectively. Find the volume of the bucket if its depth is 21 cm. Also find the area of the tin sheet required for making the bucket. (Use π = 22/7)
40. 40.
    Obtain other zeroes of the polynomial f(x) = 2x⁴ + 3x³ − 5x² − 9x − 3, if two of its zeroes are √3 and −√3.

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