CBSE Class 10 Mathematics 2024 — Set 2

Questions in this 2024 Mathematics paper (Set 2)

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 value of k for which the system of equations 3x - y + 8 = 0 and 6x - ky + 16 = 0 has infinitely many solutions, is

   • (a) -2
   • (b) 2
   • (c) 1/2
   • (d) -1/2
2. 2.
   Point P divides the line segment joining the points A(4, -5) and B(1, 2) in the ratio 5:2. Co-ordinates of point P are

   • (a) (5/2, -3/2)
   • (b) (11/7, 0)
   • (c) (13/7, 0)
   • (d) (0, 13/7)
3. 3.
   The common difference of an A.P. in which a(15) - a(11) = 48, is

   • (a) 12
   • (b) 16
   • (c) -12
   • (d) -16
4. 4.
   The quadratic equation x^2 + x + 1 = 0 has _____ roots.

   • (a) real and equal
   • (b) irrational
   • (c) real and distinct
   • (d) not-real
5. 5.
   If the HCF(2520, 6600) = 40 and LCM(2520, 6600) = 252 * k, then the value of k is

   • (a) 1650
   • (b) 1600
   • (c) 165
   • (d) 1625
6. 6.
   In the given figure, triangle ABC is shown. DE is parallel to BC. If AD = 5 cm, DB = 2.5 cm and BC = 12 cm, then DE is equal to

   • (a) 10 cm
   • (b) 6 cm
   • (c) 8 cm
   • (d) 7.5 cm
7. 7.
   If sin theta = cos theta, (0 < theta < 90), then value of (sec theta . sin theta) is

   • (a) 1/sqrt(2)
   • (b) sqrt(2)
   • (c) 1
   • (d) 0
8. 8.
   Two dice are rolled together. The probability of getting the sum of the two numbers to be more than 10, is

   • (a) 1/9
   • (b) 1/6
   • (c) 7/12
   • (d) 1/12
9. 9.
   If alpha and beta are zeroes of the polynomial 5x^2 + 3x - 7, the value of 1/alpha + 1/beta is

   • (a) -3/7
   • (b) 3/5
   • (c) 3/7
   • (d) 5/7
10. 10.
    The perimeters of two similar triangles ABC and PQR are 56 cm and 48 cm respectively. PQ/AB is equal to

    • (a) 7/8
    • (b) 6/7
    • (c) 7/6
    • (d) 8/7
11. 11.
    AB and CD are two chords of a circle intersecting at P. Choose the correct statement from the following:

    • (a) triangle ADP ~ triangle CBA
    • (b) triangle ADP ~ triangle BPC
    • (c) triangle ADP ~ triangle BCP
    • (d) triangle ADP ~ triangle CBP
12. 12.
    If value of each observation in a data is increased by 2, then median of the new data

    • (a) increases by 2
    • (b) increases by 2n
    • (c) remains same
    • (d) decreases by 2
13. 13.
    A box contains cards numbered 6 to 55. A card is drawn at random from the box. The probability that the drawn card has a number which is a perfect square, is

    • (a) 7/50
    • (b) 7/55
    • (c) 1/10
    • (d) 5/49
14. 14.
    In the given figure, tangents PA and PB to the circle centred at O, from point P are perpendicular to each other. If PA = 5 cm, then length of AB is equal to

    • (a) 5 cm
    • (b) 5*sqrt(2) cm
    • (c) 2*sqrt(5) cm
    • (d) 10 cm
15. 15.
    XOYZ is a rectangle with vertices X(-3, 0), O(0, 0), Y(0, 4) and Z(x, y). The length of its each diagonal is

    • (a) 5 units
    • (b) sqrt(5) units
    • (c) x^2 + y^2 units
    • (d) 4 units
16. 16.
    Which term of the A.P. -29, -26, -23, ..., 61 is 16?

    • (a) 11th
    • (b) 16th
    • (c) 10th
    • (d) 31st
17. 17.
    In the given figure, AT is tangent to a circle centred at O. If angle CAT = 40, then angle CBA is equal to

    • (a) 70
    • (b) 50
    • (c) 65
    • (d) 40
18. 18.
    After an examination, a teacher wants to know the marks obtained by maximum number of students in her class. She requires to calculate _____ of marks.

    • (a) median
    • (b) mode
    • (c) mean
    • (d) range
19. 19.
    Assertion (A): If sin A = 1/3 (0 < A < 90), then the value of cos A is 2*sqrt(2)/3. Reason (R): For every angle theta, sin^2(theta) + cos^2(theta) = 1.

    • (a) Both A and R are true. R is the correct explanation of A.
    • (b) Both A and R are true. R does not give correct explanation of A.
    • (c) A is true but R is not true.
    • (d) A is not true but R is true.
20. 20.
    Assertion (A): Two cubes each of edge length 10 cm are joined together. The total surface area of newly formed cuboid is 1200 cm^2. Reason (R): Area of each surface of a cube of side 10 cm is 100 cm^2.

    • (a) Both A and R are true. R is the correct explanation of A.
    • (b) Both A and R are true. R does not give correct explanation of A.
    • (c) A is true but R is not true.
    • (d) A is not true but R is true.
21. 21.
    Can the number (15)^n, n being a natural number, end with the digit 0? Give reasons.
22. 22.
    Find the type of triangle ABC formed whose vertices are A(1, 0), B(-5, 0) and C(-2, 5).
23. 23.
    Evaluate: 2 sin^2(30) sec(60) + tan^2(60).
24. 24.
    In the given figure, AB and CD are tangents to a circle centred at O. Is angle BAC = angle DCA? Justify your answer.
25. 25.
    In what ratio is the line segment joining the points (3, -5) and (-1, 6) divided by the line y = x?
26. 26.
    If the sum of first m terms of an A.P. is the same as the sum of its first n terms (m ≠ n), then show that the sum of its first (m + n) terms is zero.
27. 27.
    Prove that √5 is an irrational number.
28. 28.
    In the given figure, PQ is a tangent to a circle centred at O and ∠BAQ = 30°. Show that BP = BQ.
29. 29.
    Prove that (1 + sec θ − tan θ) / (1 + sec θ + tan θ) = (1 − sin θ) / cos θ.
30. 30.
    In a test, the marks obtained by 100 students (out of 50) are given below: Marks obtained: 0-10, 10-20, 20-30, 30-40, 40-50 Number of students: 12, 23, 34, 25, 6 Find the mean marks of the students.
31. 31.
    In a 2-digit number, the digit at the unit's place is 5 less than the digit at the ten's place. The product of the digits is 36. Find the number.
32. 32.
    Using graphical method, solve the following system of equations: 3x + y + 4 = 0 and 3x - y + 2 = 0.
33. 33.
    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. (Basic Proportionality Theorem)
34. 34.
    From the top of a 45 m high light house, the angles of depression of two ships, on the opposite side of it, are observed to be 30 and 60. If the line joining the ships passes through the foot of the light house, find the distance between the ships. (Use sqrt(3) = 1.73)
35. 35.
    The perimeter of a certain sector of a circle of radius 5.6 m is 20.0 m. Find the area of the sector.
36. 36 (i).
    A ball is thrown in the air so that t seconds after it is thrown, its height h metre above its starting point is given by the polynomial h = 25t - 5t^2. Write zeroes of the given polynomial.
37. 36 (ii).
    A ball is thrown in the air so that t seconds after it is thrown, its height h metre above its starting point is given by the polynomial h = 25t - 5t^2. Find the maximum height achieved by the ball.
38. 36 (iii)(a).
    A ball is thrown in the air so that t seconds after it is thrown, its height h metre above its starting point is given by the polynomial h = 25t - 5t^2. After throwing upward, how much time did the ball take to reach the height of 30 m?
39. 37 (i).
    A circus tent is cylindrical upto a height of 8 m and conical above it. The diameter of the base is 28 m and total height of the tent is 18.5 m. Find the slant height of the conical part.
40. 37 (ii).
    A circus tent is cylindrical upto a height of 8 m and conical above it. The diameter of the base is 28 m and total height of the tent is 18.5 m. Determine the floor area of the tent.
41. 37 (iii)(a).
    A circus tent is cylindrical upto a height of 8 m and conical above it. The diameter of the base is 28 m and total height of the tent is 18.5 m. Find the area of the cloth used for making the tent.
42. 38 (i).
    In a survey on holidays, 120 people were asked to state which type of transport they used. The pie chart shows sectors: Train, Bus, Car (177 degrees), Ship (33 degrees), Aeroplane. If one person is selected at random, find the probability that he/she travelled by bus or ship.
43. 38 (ii).
    In a survey on holidays, 120 people were asked to state which type of transport they used. The pie chart shows sectors for Train, Bus, Car (177 degrees), Ship (33 degrees), Aeroplane. Which is the most favourite mode of transport and how many people used it?
44. 38 (iii)(a).
    In a survey on holidays, 120 people were asked to state which type of transport they used. If the probability that a randomly selected person did not use train is 4/5, find the number of people who used train.

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