CBSE Class 10 Mathematics 2024 — Set 5

Questions in this 2024 Mathematics paper (Set 5)

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 next (4th) term of the A.P. √18, √50, √98, … is:

   • (a) √128
   • (b) √140
   • (c) √162
   • (d) √200
2. 2.
   If x/3 = 2 sin A, y/3 = 2 cos A, then the value of x² + y² is:

   • (a) 36
   • (b) 9
   • (c) 6
   • (d) 18
3. 3.
   If 4 sec θ − 5 = 0, then the value of cot θ is:

   • (a) 3/4
   • (b) 4/5
   • (c) 5/3
   • (d) 4/3
4. 4.
   Which out of the following type of straight lines will be represented by the system of equations 3x + 4y = 5 and 6x + 8y = 7?

   • (a) Parallel
   • (b) Intersecting
   • (c) Coincident
   • (d) Perpendicular to each other
5. 5.
   The ratio of the sum and product of the roots of the quadratic equation 5x² − 6x + 21 = 0 is:

   • (a) 5:21
   • (b) 2:7
   • (c) 21:5
   • (d) 7:2
6. 6.
   For the data 2, 9, x + 6, 2x + 3, 5, 10, 5; if the mean is 7, then the value of x is:

   • (a) 9
   • (b) 6
   • (c) 5
   • (d) 3
7. 7.
   One ticket is drawn at random from a bag containing tickets numbered 1 to 40. The probability that the selected ticket has a number which is a multiple of 7 is:

   • (a) 1/7
   • (b) 1/8
   • (c) 1/5
   • (d) 7/40
8. 8.
   The perimeter of the sector of a circle of radius 21 cm which subtends an angle of 60° at the centre of circle, is:

   • (a) 22 cm
   • (b) 43 cm
   • (c) 64 cm
   • (d) 462 cm
9. 9.
   The length of an arc of a circle with radius 12 cm is 10π cm. The angle subtended by the arc at the centre of the circle is:

   • (a) 120°
   • (b) 6°
   • (c) 75°
   • (d) 150°
10. 10.
    The greatest number which divides 281 and 1249, leaving remainder 5 and 7 respectively, is:

    • (a) 23
    • (b) 276
    • (c) 138
    • (d) 69
11. 11.
    The number of terms in the A.P. 3, 6, 9, 12, …, 111 is:

    • (a) 36
    • (b) 40
    • (c) 37
    • (d) 30
12. 12.
    A chord of a circle of radius 10 cm subtends a right angle at its centre. The length of the chord (in cm) is:

    • (a) 5√2
    • (b) 10√2
    • (c) 5/√2
    • (d) 5
13. 13.
    The LCM of three numbers 28, 44, 132 is:

    • (a) 258
    • (b) 231
    • (c) 462
    • (d) 924
14. 14.
    If the product of two co-prime numbers is 553, then their HCF is:

    • (a) 1
    • (b) 553
    • (c) 7
    • (d) 79
15. 15.
    If α and β are the zeroes of the polynomial p(x) = kx² − 30x + 45k and α + β = αβ, then the value of k is:

    • (a) -2/3
    • (b) 3/2
    • (c) 3/2
    • (d) 2/3
16. 16.
    In the given figure, RJ and RL are two tangents to the circle. If ∠RJL = 42°, then the measure of ∠JOL is:

    • (a) 42°
    • (b) 84°
    • (c) 96°
    • (d) 138°
17. 17.
    In the given figure, in △ABC, DE ∥ BC. If AD = 2.4 cm, DB = 4 cm and AE = 2 cm, then the length of AC is:

    • (a) 10/3 cm
    • (b) 3/10 cm
    • (c) 16/3 cm
    • (d) 1.2 cm
18. 18.
    If a vertical pole of length 7.5 m casts a shadow 5 m long on the ground and at the same time, a tower casts a shadow 24 m long, then the height of the tower is:

    • (a) 20 m
    • (b) 40 m
    • (c) 60 m
    • (d) 36 m
19. 19.
    Assertion (A): ABCD is a trapezium with DC ∥ AB. E and F are points on AD and BC respectively, such that EF ∥ AB. Then AE/ED = BF/FC. Reason (R): Any line parallel to parallel sides of a trapezium divides the non-parallel sides proportionally.

    • (a) Both A and R are true and R is the correct explanation of A.
    • (b) Both A and R are true, but R is not the correct explanation of A.
    • (c) A is true, but…
20. 20.
    Assertion (A): Degree of a zero polynomial is not defined. Reason (R): Degree of a non-zero constant polynomial is 0.

    • (a) Both A and R are true and R is the correct explanation of A.
    • (b) Both A and R are true, but R is not the correct explanation of A.
    • (c) A is true, but R is false.
    • (d) A is false, but R is true.
21. 21.
    If two tangents inclined at an angle of 60° are drawn to a circle of radius 3 cm, then find the length of each tangent.
22. 22.
    Evaluate: (2 tan 30° · sec 60° · tan 45°) / (1 − sin² 60°)
23. 23.
    If α, β are zeroes of the polynomial p(x) = 5x² − 6x + 1, then find the value of α + β + αβ.
24. 24.
    Find the ratio in which the point P(−4, 6) divides the line segment joining the points A(−6, 10) and B(3, −8).
25. 25.
    A carton consists of 60 shirts of which 48 are good, 8 have major defects and 4 have minor defects. Nigam accepts only good shirts; Anmol rejects only shirts with major defects. One shirt is drawn at random. Find the probability that it is acceptable to Anmol.
26. 26.
    Prove that √3 is an irrational number.
27. 27.
    If the sum of the first 14 terms of an A.P. is 1050 and the first term is 10, then find the 20th term and the nth term.
28. 28.
    Prove that the parallelogram circumscribing a circle is a rhombus.
29. 29.
    Prove that: tanA/(1 − cotA) + cotA/(1 − tanA) = 1 + secA·cosecA.
30. 30.
    Three unbiased coins are tossed simultaneously. Find the probability of getting:

    • (i) at least one head,
    • (ii) exactly one tail,
    • (iii) two heads and one tail.
31. 31.
    An arc of a circle of radius 10 cm subtends a right angle at the centre of the circle. Find the area of the corresponding major sector. (Use π = 3.14)
32. 32.
    Find the value of k for which the quadratic equation (k+1)x² − 6(k+1)x + 3(k+9) = 0, k ≠ −1 has real and equal roots.
33. 33.
    From a point on a bridge across the river, the angles of depressions of the banks on opposite sides of the river are 30° and 60° respectively. If the bridge is at a height of 4 m from the banks, find the width of the river.
34. 34.
    In the given figure, ΔFEC ≅ ΔGDB and ∠1 = ∠2. Prove that ΔADE ~ ΔABC.
35. 35.
    A wooden article was made by scooping out a hemisphere from each end of a solid cylinder. If the height of the cylinder is 5.8 cm and its base is of radius 2.1 cm, find the total surface area of the article.
36. 36 (i).
    Case Study 1 (Essel World): Ticket charges are ₹150 per child and ₹250 per adult. On a day, 300 tickets were sold and ₹55,000 was collected. If the number of children is x and adults is y, write the given situation algebraically.
37. 36 (ii).
    Case Study 1 (Essel World): How many children visited the amusement park that day? OR How many adults visited the amusement park that day?
38. 36 (iii).
    Case Study 1 (Essel World): How much amount will be collected if 250 children and 100 adults visit the amusement park?
39. 37 (i).
    Case Study 2 (Garden): A garden is in the shape of a square. A triangular region PQR inside is used for rose plants. A chart is made on a coordinate system with A as origin. If A is taken as origin, what are the coordinates of the vertices of △PQR?
40. 37 (ii).
    Case Study 2 (Garden): Find distances PQ and QR. OR Find the coordinates of the point which divides the line segment joining points P and R in the ratio 2:1 internally.
41. 37 (iii).
    Case Study 2 (Garden): Find out if △PQR is an isosceles triangle.
42. 38 (i).
    Case Study 3 (Running): Time taken by students to run 100 m — 0–20s: 8, 20–40s: 10, 40–60s: 13, 60–80s: 6, 80–100s: 3 students. What is the median class?
43. 38 (ii).
    Case Study 3 (Running): Find the mean time taken by students to finish the race. OR Find the mode of the above given data. (Data: 0–20:8, 20–40:10, 40–60:13, 60–80:6, 80–100:3)
44. 38 (iii).
    Case Study 3 (Running): How many students took time less than 60 seconds?

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