CBSE Class 10 Mathematics 2020 — Set 1

Questions in this 2020 Mathematics paper (Set 1)

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.
   If one of the zeroes of the quadratic polynomial x² + 3x + k is 2, then the value of k is

   • (a) 10
   • (b) –10
   • (c) –7
   • (d) –2
2. 2.
   The total number of factors of a prime number is

   • (a) 1
   • (b) 0
   • (c) 2
   • (d) 3
3. 3.
   The quadratic polynomial, the sum of whose zeroes is –5 and their product is 6, is

   • (a) x² + 5x + 6
   • (b) x² − 5x + 6
   • (c) x² − 5x − 6
   • (d) −x² + 5x + 6
4. 4.
   The value of k for which the system of equations x + y − 4 = 0 and 2x + ky = 3, has no solution, is

   • (a) –2
   • (b) ≠2
   • (c) 3
   • (d) 2
5. 5.
   The HCF and the LCM of 12, 21, 15 respectively are

   • (a) 3, 140
   • (b) 12, 420
   • (c) 3, 420
   • (d) 420, 3
6. 6.
   The value of x for which 2x, (x + 10) and (3x + 2) are the three consecutive terms of an AP, is

   • (a) 6
   • (b) –6
   • (c) 18
   • (d) –18
7. 7.
   The first term of an AP is p and the common difference is q, then its 10th term is

   • (a) q + 9p
   • (b) p − 9q
   • (c) p + 9q
   • (d) 2p + 9q
8. 8.
   The distance between the points (a cos θ + b sin θ, 0) and (0, a sin θ − b cos θ), is

   • (a) a² + b²
   • (b) a² − b²
   • (c) √(a² + b²)
   • (d) √(a² − b²)
9. 9.
   If the point P(k, 0) divides the line segment joining the points A(2, −2) and B(−7, 4) in the ratio 1 : 2, then the value of k is

   • (a) 1
   • (b) 2
   • (c) –2
   • (d) –1
10. 10.
    The value of p, for which the points A(3, 1), B(5, p) and C(7, −5) are collinear, is

    • (a) –2
    • (b) 2
    • (c) –1
    • (d) 1
11. 11.
    In Fig. 1, a triangle ABC is circumscribing a circle, the length of BC is ______ cm. (Given: A triangle ABC with a circle inscribed touching AB at a point with segment 4 cm from A, touching AC at a point with segment 11 cm from A, and touching BC at Q with segment 3 cm from B on the AB side.)
12. 12.
    Given ΔABC ~ ΔPQR, if AB/PQ = 1/3, then ar(ΔABC)/ar(ΔPQR) = ______
13. 13.
    ABC is an equilateral triangle of side 2a, then length of one of its altitudes is ______
14. 14.
    (cos 80°)/(sin 10°) + cos 59° cosec 31° = ______
15. 15.
    The value of (sin²θ + 1/(1 + tan²θ)) = ______
16. 16.
    The ratio of the length of a vertical rod and the length of its shadow is 1 : √3. Find the angle of elevation of the sun at that moment.
17. 17.
    Two 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.
    A letter of English alphabet is chosen at random. What is the probability that the chosen letter is a consonant?
19. 19.
    A die is thrown once. What is the probability of getting a number less than 3?
20. 20.
    If the mean of the first n natural numbers is 15, then find n.
21. 21.
    Show that (a − b)², (a² + b²), and (a + b)² are in AP.
22. 22.
    In Fig. 2, DE ∥ AC and DC ∥ AP. Prove that BE/EC = BC/CP.
23. 23.
    The rod AC of a TV disc antenna is fixed at right angles to the wall AB and a rod CD is supporting the disc as shown in Fig. 4. If AC = 1.5 m long and CD = 3 m, find

    • (i) tan θ
    • (ii) sec θ + cosec θ.
24. 24.
    A piece of wire 22 cm long is bent into the form of an arc of a circle subtending an angle of 60° at its centre. Find the radius of the circle. [Use π = 22/7]
25. 25.
    If a number x is chosen at random from the numbers −3, −2, −1, 0, 1, 2, 3, what is the probability that x² ≤ 4?
26. 26.
    Find the mean of the following distribution: Class: 3-5, 5-7, 7-9, 9-11, 11-13 Frequency: 5, 10, 10, 7, 8
27. 27.
    Find a quadratic polynomial whose zeroes are reciprocals of the zeroes of the polynomial f(x) = ax² + bx + c, a ≠ 0, c ≠ 0.
28. 28.
    Determine graphically the coordinates of the vertices of a triangle, the equations of whose sides are given by 2y − x = 8, 5y − x = 14 and y − 2x = 1.
29. 29.
    In a flight of 600 km, an aircraft was slowed due to bad weather. Its average speed for the trip was reduced by 200 km/hr and time of flight increased by 30 minutes. Find the original duration of flight.
30. 30.
    Find the area of triangle PQR formed by the points P(−5, 7), Q(−4, −5) and R(4, 5).
31. 31.
    In Fig. 5, ∠D = ∠E and AD/DB = AE/EC, prove that BAC is an isosceles triangle.
32. 32.
    In a triangle, if the square of one side is equal to the sum of the squares of the other two sides, then prove that the angle opposite to the first side is a right angle.
33. 33.
    If sin θ + cos θ = √3, then prove that tan θ + cot θ = 1.
34. 34.
    A cone of base radius 4 cm is divided into two parts by drawing a plane through the mid-point of its height and parallel to its base. Compare the volumes of the two parts.
35. 35.
    Show that the square of any positive integer cannot be of the form (5q + 2) or (5q + 3) for any integer q.
36. 36.
    The sum of four consecutive numbers in AP is 32 and the ratio of the product of the first and last terms to the product of two middle terms is 7:15. Find the numbers.
37. 37.
    Draw a line segment AB of length 7 cm. Taking A as centre, draw a circle of radius 3 cm and taking B as centre, draw another circle of radius 2 cm. Construct tangents to each circle from the centre of the other circle.
38. 38.
    A vertical tower stands on a horizontal plane and is surmounted by a vertical flag-staff of height 6 m. At a point on the plane, the angle of elevation of the bottom and top of the flag-staff are 30° and 45° respectively. Find the height of the tower. (Take √3 = 1.73)
39. 39.
    A bucket in the form of a frustum of a cone of height 30 cm with radii of its lower and upper ends as 10 cm and 20 cm, respectively. Find the capacity of the bucket. Also find the cost of milk which can completely fill the bucket at the rate of Rs. 40 per litre. [Use π = 22/7]
40. 40.
    The following table gives production yield per hectare (in quintals) of wheat of 100 farms of a village: Production yield (quintals/hectare): 40-45, 45-50, 50-55, 55-60, 60-65, 65-70 Number of farms: 4, 6, 16, 20, 30, 24 Change the distribution to a 'more than' type distribution and draw its ogive.

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