CBSE Class 10 Mathematics 2023 — Set 2

Questions in this 2023 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.
   Which of the following quadratic equations has sum of its roots as 4?

   • (a) 2x^2 - 4x + 8 = 0
   • (b) -x^2 + 4x + 4 = 0
   • (c) sqrt(2)*x^2 - 4/sqrt(2)*x + 1 = 0
   • (d) 4x^2 - 4x + 4 = 0
2. 2.
   What is the length of the arc of the sector of a circle with radius 14 cm and of central angle 90 degrees?

   • (a) 22 cm
   • (b) 44 cm
   • (c) 88 cm
   • (d) 11 cm
3. 3.
   If triangle ABC ~ triangle PQR with angle A = 32 degrees and angle R = 65 degrees, then the measure of angle B is:

   • (a) 32 degrees
   • (b) 65 degrees
   • (c) 83 degrees
   • (d) 97 degrees
4. 4.
   If 'p' and 'q' are natural numbers and 'p' is the multiple of 'q', then what is the HCF of 'p' and 'q'?

   • (a) pq
   • (b) p
   • (c) q
   • (d) p + q
5. 5.
   The coordinates of the vertex A of a rectangle ABCD whose three vertices are given as B(0, 0), C(3, 0) and D(0, 4) are:

   • (a) (4, 0)
   • (b) (0, 3)
   • (c) (3, 4)
   • (d) (4, 3)
6. 6.
   If the pair of equations 3x - y + 8 = 0 and 6x - ry + 16 = 0 represent coincident lines, then the value of 'r' is:

   • (a) -1/2
   • (b) 1/2
   • (c) -2
   • (d) 2
7. 7.
   A bag contains 100 cards numbered 1 to 100. A card is drawn at random from the bag. What is the probability that the number on the card is a perfect cube?

   • (a) 1/20
   • (b) 3/50
   • (c) 1/25
   • (d) 7/100
8. 8.
   The pair of equations x = a and y = b graphically represents lines which are:

   • (a) parallel
   • (b) intersecting at (b, a)
   • (c) coincident
   • (d) intersecting at (a, b)
9. 9.
   If one zero of the polynomial 6x^2 + 37x - (k - 2) is reciprocal of the other, then what is the value of k?

   • (a) -4
   • (b) -6
   • (c) 6
   • (d) 4
10. 10.
    What is the total surface area of a solid hemisphere of diameter 'd'?

    • (a) 3*pi*d^2
    • (b) 2*pi*d^2
    • (c) (1/2)*pi*d^2
    • (d) (3/4)*pi*d^2
11. 11.
    If three coins are tossed simultaneously, what is the probability of getting at most one tail?

    • (a) 3/8
    • (b) 4/8
    • (c) 5/8
    • (d) 7/8
12. 12.
    In a triangle, DE is parallel to BC. If AD = 2 units, DB = 3 units, AE = 3 units and EC = x units, then the value of x is:

    • (a) 2
    • (b) 3
    • (c) 5
    • (d) 9/2
13. 13.
    The hour-hand of a clock is 6 cm long. The angle swept by it between 7:20 a.m. and 7:55 a.m. is:

    • (a) (35/4) degrees
    • (b) (35/2) degrees
    • (c) 35 degrees
    • (d) 70 degrees
14. 14.
    The zeroes of the polynomial p(x) = x^2 + 4x + 3 are given by:

    • (a) 1, 3
    • (b) -1, 3
    • (c) 1, -3
    • (d) -1, -3
15. 15.
    In a figure, the quadrilateral PQRS circumscribes a circle. Here PA + CS is equal to:

    • (a) QR
    • (b) PR
    • (c) PS
    • (d) PQ
16. 16.
    If alpha and beta are the zeroes of the quadratic polynomial p(x) = x^2 - ax - b, then the value of alpha^2 + beta^2 is:

    • (a) a^2 - 2b
    • (b) a^2 + 2b
    • (c) b^2 - 2a
    • (d) b^2 + 2a
17. 17.
    The area of the triangle formed by the line x/a + y/b = 1 with the coordinate axes is:

    • (a) ab
    • (b) (1/2)*ab
    • (c) (1/4)*ab
    • (d) 2ab
18. 18.
    In the given figure, AB is parallel to PQ. If AB = 6 cm, PQ = 2 cm and OB = 3 cm, then the length of OP is:

    • (a) 9 cm
    • (b) 3 cm
    • (c) 4 cm
    • (d) 1 cm
19. 19.
    Assertion (A): A tangent to a circle is perpendicular to the radius through the point of contact. Reason (R): The lengths of tangents drawn from an external point to a circle are equal. Which of the following is correct?

    • (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…
20. 20.
    Assertion (A): The polynomial p(x) = x^2 + 3x + 3 has two real zeroes. Reason (R): A quadratic polynomial can have at most two real zeroes. Which of the following is correct?

    • (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.
    Prove that 2 + sqrt(3) is an irrational number, given that sqrt(3) is an irrational number.
22. 22.
    If 4*cot^2(45) - sec^2(60) + sin^2(60) + p = 3/4, then find the value of p.
23. 23.
    Show that the points (-2, 3), (8, 3) and (6, 7) are the vertices of a right-angled triangle.
24. 24.
    The length of the shadow of a tower on the plane ground is sqrt(3) times the height of the tower. Find the angle of elevation of the sun.
25. 25.
    In the given figure, O is the centre of the circle. AB and AC are tangents drawn to the circle from point A. If angle BAC = 65 degrees, then find the measure of angle BOC.
26. 26.
    Find by prime factorisation the LCM of the numbers 18180 and 7575. Also, find the HCF of the two numbers.
27. 27.
    Prove that: (1/cos(theta) - cos(theta)) * (1/sin(theta) - sin(theta)) = 1/(tan(theta) + cot(theta)).
28. 28.
    If Q(0, 1) is equidistant from P(5, -3) and R(x, 6), find the values of x.
29. 29.
    A car has two wipers which do not overlap. Each wiper has a blade of length 21 cm sweeping through an angle of 120 degrees. Find the total area cleaned at each sweep of the two blades.
30. 30.
    If the system of linear equations 2x + 3y = 7 and 2ax + (a + b)y = 28 have infinite number of solutions, then find the values of 'a' and 'b'.
31. 31.
    In the given figure, O is the centre of the circle and QPR is a tangent to it at P. A is a point on the circle such that AB is a chord. Prove that angle QAP + angle APR = 90 degrees.
32. 32.
    How many terms of the arithmetic progression 45, 39, 33, ... must be taken so that their sum is 180? Explain the double answer.
33. 33.
    As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are 30 degrees and 60 degrees. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships. (Use sqrt(3) = 1.73)
34. 34.
    A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised it in the table below. Find the mean and median of the following data. Number of cars: 0-10, 10-20, 20-30, 30-40, 40-50, 50-60, 60-70, 70-80 Frequency: 7, 14, 13, 12, 20, 11, 15, 8
35. 35.
    Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of triangle PQR. Show that triangle ABC ~ triangle PQR.
36. 36 (a).
    Case Study: In an annual day function of a school, the organizers wanted to give a cash prize along with a memento to their best students. Each memento is made as shown in the figure and its base ABCD is shown from the front side. The rate of silver plating is Rs. 20 per cm^2. A circle with centre O and radius 7 cm is inscribed, with DC = 7 cm (top chord), and the base AB is the diameter. (i)…
37. 36 (b).
    Case Study (continued): The circle has centre O and radius 7 cm. AB is the diameter at the base. (ii) Find the area of triangle AOB.
38. 36 (c).
    Case Study (continued): The memento has a circle with centre O, radius 7 cm, DC = 7 cm at the top, and AB is the diameter at the bottom. The shaded part ABCD needs silver plating at Rs. 20 per cm^2. (iii)(a) What is the total cost of silver plating the shaded part ABCD?
39. 37 (a).
    Case Study: In a coffee shop, coffee is served in two types of cups. One is cylindrical in shape with diameter 7 cm and height 14 cm, and the other is hemispherical with diameter 21 cm. (i) Find the area of the base of the cylindrical cup.
40. 37 (b).
    Case Study (continued): The hemispherical cup has diameter 21 cm. (ii)(a) What is the capacity of the hemispherical cup?
41. 37 (c).
    Case Study (continued): The cylindrical cup has diameter 7 cm and height 14 cm. (iii) What is the curved surface area of the cylindrical cup?
42. 38 (a).
    Case Study: Computer-based learning (CBL) refers to any teaching methodology that makes use of computers for information transmission. A survey was done on 1000 elementary and secondary schools of Assam and they were classified by the number of computers they had. Number of Computers: 1-10, 11-20, 21-50, 51-100, 101 and more Number of Schools: 250, 200, 290, 180, 80 (i) Find the probability that…
43. 38 (b).
    Case Study (continued): Number of Computers: 1-10, 11-20, 21-50, 51-100, 101 and more Number of Schools: 250, 200, 290, 180, 80 (ii)(a) Find the probability that the school chosen at random has 50 or fewer computers.
44. 38 (c).
    Case Study (continued): Number of Computers: 1-10, 11-20, 21-50, 51-100, 101 and more Number of Schools: 250, 200, 290, 180, 80 (iii) Find the probability that the school chosen at random has 10 or less than 10 computers.

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 2023 paper — FAQ