CBSE Class 10 Mathematics 2024 — Set 3

Questions in this 2024 Mathematics paper (Set 3)

All 38 questions from this set, exactly as asked. Try each one, then open the question-paper PDF above for the complete paper.

1. 1.
   The pair of linear equations x + 2y + 5 = 0 and -3x = 6y - 1 has

   • (a) unique solution
   • (b) exactly two solutions
   • (c) infinitely many solutions
   • (d) no solution
2. 2.
   The common difference of the A.P. 1/(2x), (1-4x)/(2x), (1-8x)/(2x), ... is

   • (a) -2x
   • (b) -2
   • (c) 2
   • (d) 2x
3. 3.
   Two dice are thrown together. The probability that they show different numbers is

   • (a) 1/6
   • (b) 5/6
   • (c) 1/3
   • (d) 2/3
4. 4.
   The probability of guessing the correct answer to a certain test question is x/6. If the probability of not guessing the correct answer to this question is 2/3, then the value of x is

   • (a) 2
   • (b) 3
   • (c) 4
   • (d) 6
5. 5.
   If a = 2² × 3^x, b = 2² × 3 × 5, c = 2² × 3 × 7 and LCM(a, b, c) = 3780, then x is equal to

   • (a) 1
   • (b) 2
   • (c) 3
   • (d) 0
6. 6.
   The zeroes of the quadratic polynomial 2x² - 3x - 9 are

   • (a) 3, -3/2
   • (b) -3, -3/2
   • (c) -3, 3/2
   • (d) 3, 3/2
7. 7.
   From a point on the ground, which is 30 m away from the foot of a vertical tower, the angle of elevation of the top of the tower is found to be 60°. The height (in metres) of the tower is

   • (a) 10√3
   • (b) 30√3
   • (c) 60
   • (d) 30
8. 8.
   If cos θ = √3/2 and sin φ = 1/2, then tan(θ + φ) is

   • (a) √3
   • (b) 1/√3
   • (c) 1
   • (d) not defined
9. 9.
   Maximum number of common tangents that can be drawn to two circles intersecting at two distinct points is

   • (a) 4
   • (b) 3
   • (c) 2
   • (d) 1
10. 10.
    In the given figure, if PT is a tangent to a circle with centre O and ∠TPO = 35°, then the measure of ∠x is

    • (a) 110°
    • (b) 115°
    • (c) 120°
    • (d) 125°
11. 11.
    If the diagonals of a quadrilateral divide each other proportionally, then it is a

    • (a) parallelogram
    • (b) rectangle
    • (c) square
    • (d) trapezium
12. 12.
    In △ABC, DE || BC (as shown in the figure). If AD = 2 cm, BD = 3 cm, BC = 7.5 cm, then the length of DE (in cm) is

    • (a) 2.5
    • (b) 3
    • (c) 5
    • (d) 6
13. 13.
    Given HCF(2520, 6600) = 40, LCM(2520, 6600) = 252 × k, then the value of k is

    • (a) 1650
    • (b) 1600
    • (c) 165
    • (d) 1625
14. 14.
    A pair of irrational numbers whose product is a rational number is

    • (a) (√16, √4)
    • (b) (√5, √2)
    • (c) (√3, √27)
    • (d) (√36, √2)
15. 15.
    If a digit is chosen at random from the digits 1, 2, 3, 4, 5, 6, 7, 8, 9; then the probability that this digit is an odd prime number is

    • (a) 1/3
    • (b) 2/3
    • (c) 4/9
    • (d) 5/9
16. 16.
    The mean of five observations is 15. If the mean of first three observations is 14 and that of the last three observations is 17, then the third observation is

    • (a) 20
    • (b) 19
    • (c) 18
    • (d) 17
17. 17.
    Perimeter of a sector of a circle whose central angle is 90° and radius 7 cm is

    • (a) 35 cm
    • (b) 11 cm
    • (c) 22 cm
    • (d) 25 cm
18. 18.
    In the given figure, O is the centre of the circle. MN is the chord and the tangent ML at point M makes an angle of 70° with MN. The measure of ∠MON is

    • (a) 120°
    • (b) 140°
    • (c) 70°
    • (d) 90°
19. 19.
    Assertion (A): The point which divides the line segment joining the points A(1, 2) and B(-1, 1) internally in the ratio 1:2 is (-1/3, 5/3). Reason (R): The coordinates of the point which divides the line segment joining the points A(x₁, y₁) and B(x₂, y₂) in the ratio m₁:m₂ are ((m₁x₂ + m₂x₁)/(m₁ + m₂), (m₁y₂ + m₂y₁)/(m₁ + m₂)). (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the…
20. 20.
    Assertion (A): In a cricket match, a batsman hits a boundary 9 times out of 45 balls he plays. The probability that in a given ball, he does not hit the boundary is 4/5. Reason (R): P(E) + P(not E) = 1.

    • (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
    • (b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct…
21. 21.
    One card is drawn at random from a well shuffled deck of 52 cards. Find the probability that the card drawn

    • (i) is queen of hearts;
    • (ii) is not a jack.
22. 22 (a).
    If 2x + y = 13 and 4x - y = 17, find the value of (x - y).
23. 23 (a).
    Find a relation between x and y such that the point P(x, y) is equidistant from the points A(7, 1) and B(3, 5).
24. 24.
    In the given figure, EA/EC = EB/ED. Prove that ΔEAB ~ ΔECD.
25. 25.
    Evaluate: (cos 45° + sin 60°) / (sec 30° + cosec 30°)
26. 26 (a).
    If the sum of first 7 terms of an A.P. is 49 and that of first 17 terms is 289, find the sum of first 20 terms.
27. 27.
    Find the zeroes of the quadratic polynomial x² − 15 and verify the relationship between the zeroes and the coefficients of the polynomial.
28. 28.
    Solve the following system of linear equations graphically: x - y + 1 = 0 and x + y = 5.
29. 29 (a).
    Find the ratio in which the line segment joining the points (5, 3) and (-1, 6) is divided by the Y-axis.
30. 30.
    Prove that (sin θ − 2 sin³θ) / (2 cos³θ − cos θ) = tan θ.
31. 31.
    Prove that the tangents drawn at the end points of a chord of a circle make equal angles with the chord.
32. 32 (a).
    In a flight of 2800 km, an aircraft was slowed down due to bad weather. Its average speed is reduced by 100 km/h and the time of flight is increased by 30 minutes. Find the original duration of the flight.
33. 33.
    State and prove the Basic Proportionality Theorem (Thales’ Theorem).
34. 34.
    From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are 45° and 60° respectively. Find the height of the tower.
35. 35 (a).
    A solid iron pole consists of a solid cylinder of height 200 cm and base diameter 28 cm, which is surmounted by another cylinder of height 50 cm and radius 7 cm. Find the mass of the pole, given that 1 cm³ of iron has approximately 8 g mass.
36. 36 (i).
    A stable owner has four horses. He ties each horse with a 7 m long rope to pegs at each corner of a square shaped grass field of 20 m length. Find the area of the square shaped grass field.
37. 36 (ii)(a).
    A stable owner has four horses tied with 7 m long ropes at each corner of a square shaped grass field of 20 m length. Find the area of the total field in which these horses can graze.
38. 36 (iii).
    In the stable owner scenario with four horses tied with 7 m ropes at corners of a 20 m square field, what is the area of the field that is left ungrazed?
39. 37 (i).
    A teacher made a frequency distribution table of students/adults undergoing vocational training from a training institute with the following data: Age (in years): 15-19, 20-24, 25-29, 30-34, 35-39, 40-44, 45-49, 50-54 Number of participants: 62, 132, 96, 37, 13, 11, 10, 4 What is the lower limit of the modal class of the above data?
40. 37 (ii)(a).
    Using the vocational training frequency distribution (Age groups 15-19:62, 20-24:132, 25-29:96, 30-34:37, 35-39:13, 40-44:11, 45-49:10, 50-54:4), find the median class of the above data.
41. 37 (iii).
    For the vocational training frequency distribution, give the empirical relationship between mean, median and mode.
42. 38 (i).
    Ms. Mukta planned a prime number game for class 5 students. She announces the number 2 in her class and asked the first student to multiply it by a prime number and then pass it to the second student. Second student also multiplied it by a prime number and passed it to third student. In this way by multiplying to a prime number, the last student got 173250. What is the least prime number used by…
43. 38 (ii)(a).
    Ms. Mukta's prime number game starts with 2 and each of 5 students multiplies by a prime, ending at 173250. How many students are in the class?
44. 38 (iii).
    In Ms. Mukta's prime number game where 173250 is the final product, which prime number has been used maximum times?

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 2024 paper — FAQ