CBSE Class 10 Mathematics 2024 — Set 4

Questions in this 2024 Mathematics paper (Set 4)

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.
   If ax + by = a^2 - b^2 and bx + ay = 0, then the value of x + y is

   • (a) a + b
   • (b) a - b
   • (c) a^2 - b^2
   • (d) a^2 + b^2
2. 2.
   The HCF of two numbers 65 and 104 is 13. If LCM of 65 and 104 is 40x, then the value of x is

   • (a) 5
   • (b) 13
   • (c) 40
   • (d) 8
3. 3.
   If a polynomial p(x) is given by p(x) = x^2 - 5x + 6, then the value of p(1) + p(4) is

   • (a) 0
   • (b) 4
   • (c) 2
   • (d) -4
4. 4.
   If the discriminant of the quadratic equation 3x^2 - 2x + c = 0 is 16, then the value of c is

   • (a) 1
   • (b) 0
   • (c) -1
   • (d) sqrt(2)
5. 5.
   If an arc subtends an angle of 90 degrees at the centre of a circle, then the ratio of its length to the circumference of the circle is

   • (a) 2 : 3
   • (b) 1 : 4
   • (c) 4 : 1
   • (d) 1 : 3
6. 6.
   The area of the sector of a circle of radius 12 cm is 60*pi cm^2. The central angle of this sector is

   • (a) 120 degrees
   • (b) 6 degrees
   • (c) 75 degrees
   • (d) 150 degrees
7. 7.
   If the difference of mode and median of a data is 24, then the difference of its median and mean is

   • (a) 12
   • (b) 24
   • (c) 8
   • (d) 36
8. 8.
   Two dice are tossed simultaneously. The probability of getting odd numbers on both the dice is

   • (a) 6/36
   • (b) 3/36
   • (c) 12/36
   • (d) 9/36
9. 9.
   The ratio of total surface area of a solid hemisphere to the square of its radius is

   • (a) 2*pi : 1
   • (b) 4*pi : 1
   • (c) 3*pi : 1
   • (d) 1 : 4*pi
10. 10.
    If sin(theta) = 1, then the value of (1/2) sin(theta/2) is

    • (a) 1/(2*sqrt(2))
    • (b) 1/sqrt(2)
    • (c) 1/2
    • (d) 0
11. 11.
    Two lines are given to be parallel. The equation of one of these lines is 5x - 3y = 2. The equation of the second line can be

    • (a) -15x - 9y = 5
    • (b) 15x + 9y = 5
    • (c) 9x - 15y = 6
    • (d) -15x + 9y = 5
12. 12.
    Three numbers in A.P. have the sum 30. What is its middle term?

    • (a) 4
    • (b) 10
    • (c) 16
    • (d) 8
13. 13.
    In triangle ABC, DE || BC (as shown in the figure). If AD = 4 cm, AB = 9 cm and AC = 13.5 cm, then the length of EC is

    • (a) 6 cm
    • (b) 7.5 cm
    • (c) 9 cm
    • (d) 5.7 cm
14. 14.
    At some time of the day, the length of the shadow of a tower is equal to its height. Then, the Sun's altitude at that time is

    • (a) 30 degrees
    • (b) 45 degrees
    • (c) 60 degrees
    • (d) 90 degrees
15. 15.
    In the given figure, AB and AC are tangents to the circle. If angle ABC = 42 degrees, then the measure of angle BAC is

    • (a) 96 degrees
    • (b) 42 degrees
    • (c) 106 degrees
    • (d) 86 degrees
16. 16.
    The fourth vertex D of a parallelogram ABCD whose three vertices are A(-2, 3), B(6, 7) and C(8, 3) is

    • (a) (0, 1)
    • (b) (0, -1)
    • (c) (-1, 0)
    • (d) (1, 0)
17. 17.
    For an event E, if P(E) + P(not E) = q, then the value of q^2 - 4 is

    • (a) -3
    • (b) 3
    • (c) 5
    • (d) -5
18. 18.
    In the given figure, QR is a common tangent to the two given circles touching externally at A. The tangent at A meets QR at P. If AP = 4.2 cm, then the length of QR is

    • (a) 4.2 cm
    • (b) 2.1 cm
    • (c) 8.4 cm
    • (d) 6.3 cm
19. 19.
    Assertion (A): Mid-point of a line segment divides the line segment in the ratio 1 : 1. Reason (R): The ratio in which the point (-3, k) divides the line segment joining the points (-5, 4) and (-2, 3) is 1 : 2.

    • (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…
20. 20.
    Assertion (A): If the circumference of a circle is 176 cm, then its radius is 28 cm. Reason (R): Circumference = 2*pi*radius of a circle.

    • (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 explanation of the Assertion (A).
    • (c) Assertion (A) is true, but…
21. 21.
    Three bells toll at intervals of 9, 12 and 15 minutes respectively. If they start tolling together, after what time will they next toll together?
22. 22 (a).
    The minute hand of a clock is 14 cm long. Find the area of the face of the clock described by the minute hand in 5 minutes.
23. 22 (b).
    Find the length of the arc of a circle which subtends an angle of 60 degrees at the centre of the circle of radius 42 cm.
24. 23 (a).
    Evaluate: (5 cos^2 60 + 4 sec^2 30 - tan^2 45) / (sin^2 30 + sin^2 60)
25. 24.
    In the given figure, O is the centre of the circle. If angle AOB = 145 degrees, then find the value of x.
26. 25.
    In the given figure, triangle AHK ~ triangle ABC. If AK = 8 cm, BC = 3.2 cm and HK = 6.4 cm, then find the length of AC.
27. 26.
    Prove that (sinθ − cosθ + 1) / (sinθ + cosθ − 1) = 1 / (secθ − tanθ).
28. 27 (a).
    Three coins are tossed simultaneously. What is the probability of getting

    • (i) at least one head,
    • (ii) exactly two tails,
    • (iii) at most one tail?
29. 28.
    Rehana went to a bank to withdraw Rs 2,000. She asked the cashier to give her Rs 50 and Rs 100 notes only. Rehana got 25 notes in all. Find how many notes of Rs 50 and Rs 100 did she receive.
30. 29 (a).
    Find the zeroes of the polynomial 4x^2 + 4x - 3 and verify the relationship between zeroes and coefficients of the polynomial.
31. 30.
    Prove that (2 − √3) / 5 is an irrational number, given that √3 is an irrational number.
32. 31.
    Prove that the parallelogram circumscribing a circle is a rhombus.
33. 32.
    Two pillars of equal lengths stand on either side of a road which is 100 m wide, exactly opposite to each other. At a point on the road between the pillars, the angles of elevation of the tops of the pillars are 60 degrees and 30 degrees. Find the length of each pillar and distance of the point on the road from the pillars. (Use sqrt(3) = 1.732)
34. 33 (a).
    E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. Show that △ABE ~ △CFB.
35. 34 (a).
    A train travels a distance of 90 km at a constant speed. Had the speed been 15 km/h more, it would have taken 30 minutes less for the journey. Find the original speed of the train.
36. 35.
    The following table shows the ages of the patients admitted in a hospital during a year: Age (in years): 5-15, 15-25, 25-35, 35-45, 45-55, 55-65 Number of patients: 6, 11, 21, 23, 14, 5 Find the mode and mean of the data given above.
37. 36 (a).
    Ryan sketched a rocket design on a graph sheet. The coordinates of key points are: A(4, 4), B(4, 2), C(-1, -1.5), D(-2, -5), E(-5, 0), F(-3, 0), G(-2, 4). (i) Find the mid-point of the segment joining F and G.
38. 36 (b).
    (ii)(a) What is the distance between the points A and C?
39. 36 (c).
    What are the coordinates of the point D?
40. 37 (a).
    In a treasure hunt game, some clues (numbers) are hidden in various spots collectively forming an A.P. If the number on the nth spot is 20 + 4n, then answer the following: (i) Which number is on the first spot?
41. 37 (b).
    (ii)(a) Which spot is numbered as 112?
42. 37 (c).
    Which number is on the (n - 2)th spot?
43. 38 (a).
    Tamper-proof tetra-packed milk is packed in a cuboidal container of dimensions 15 cm x 8 cm x 5 cm. These milk packets are then packed in cuboidal cartons of dimensions 30 cm x 32 cm x 15 cm. (i) Find the volume of the cuboidal carton.
44. 38 (b).
    (ii)(a) Find the total surface area of a milk packet.
45. 38 (c).
    How much milk can the cup (as shown in the figure) hold? The cup is cylindrical with radius 7 cm and height 5 cm.

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