CBSE Class 10 Mathematics 2023 — Set 5

Questions in this 2023 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 number of polynomials having zeroes -3 and 5 is:

   • (a) only one
   • (b) infinite
   • (c) exactly two
   • (d) at most two
2. 2.
   The pair of equations ax + 2y = 9 and 3x + by = 18 represent parallel lines, where a, b are integers, if:

   • (a) a = b
   • (b) 3a = 2b
   • (c) 2a = 3b
   • (d) ab = 6
3. 3.
   The common difference of the A.P. whose n-th term is given by a_n = 3n + 7, is:

   • (a) 7
   • (b) 3
   • (c) 3n
   • (d) 1
4. 4.
   In a triangle where DE || BC, AD = 2 cm, DB = 3 cm, and DE = 4 cm. The value of BC (x cm) is:

   • (a) 6
   • (b) 12.5
   • (c) 8
   • (d) 10
5. 5.
   A quadratic equation whose roots are (2 + sqrt(3)) and (2 - sqrt(3)) is:

   • (a) x^2 - 4x + 1 = 0
   • (b) x^2 + 4x + 1 = 0
   • (c) 4x^2 - 3 = 0
   • (d) x^2 - 1 = 0
6. 6.
   If tan(theta) = 5/12, then the value of (sin(theta) + cos(theta))/(sin(theta) - cos(theta)) is:

   • (a) -17/7
   • (b) 17/7
   • (c) 17/13
   • (d) -7/13
7. 7.
   The distance between the points P(-11/3, 5) and Q(-2/3, 5) is:

   • (a) 6 units
   • (b) 4 units
   • (c) 2 units
   • (d) 3 units
8. 8.
   In a triangle with AB = BC = 10 cm and AC = 7 cm, a circle is inscribed touching AB at P, BC at Q, and AC at R. The length of BP is:

   • (a) 3.5 cm
   • (b) 7 cm
   • (c) 6.5 cm
   • (d) 5 cm
9. 9.
   Water in a river which is 3 m deep and 40 m wide is flowing at the rate of 2 km/h. How much water will fall into the sea in 2 minutes?

   • (a) 800 m^3
   • (b) 4000 m^3
   • (c) 8000 m^3
   • (d) 2000 m^3
10. 10.
    If the mean and the median of a data are 12 and 15 respectively, then its mode is:

    • (a) 13.5
    • (b) 21
    • (c) 6
    • (d) 14
11. 11.
    AB is a tangent to a circle centered at O. If OA = 6 cm and angle OAB = 30 degrees, then the radius of the circle is:

    • (a) 3 cm
    • (b) 3*sqrt(3) cm
    • (c) 2 cm
    • (d) sqrt(3) cm
12. 12.
    The value of (2*tan(30))/(1 + tan^2(30)) is equal to:

    • (a) sin 60
    • (b) cos 60
    • (c) tan 60
    • (d) sin 30
13. 13.
    In triangles ABC and DEF, AB/DE = BC/FD. Which of the following makes the two triangles similar?

    • (a) angle A = angle D
    • (b) angle B = angle D
    • (c) angle B = angle E
    • (d) angle A = angle F
14. 14.
    The 11th term from the end of the A.P.: 10, 7, 4, ......, -62 is:

    • (a) 25
    • (b) 16
    • (c) -32
    • (d) 0
15. 15.
    Two coins are tossed together. The probability of getting at least one tail is:

    • (a) 1/4
    • (b) 1/2
    • (c) 3/4
    • (d) 1
16. 16.
    AC and AB are tangents to a circle centered at O. If angle COD = 120 degrees, then angle BAO is equal to:

    • (a) 30
    • (b) 60
    • (c) 45
    • (d) 90
17. 17.
    Which of the following numbers cannot be the probability of happening of an event?

    • (a) 0
    • (b) 7/0.01
    • (c) 0.07
    • (d) 0.07/3
18. 18.
    If every term of the statistical data consisting of n terms is decreased by 2, then the mean of the data:

    • (a) decreases by 2
    • (b) remains unchanged
    • (c) decreases by 2n
    • (d) decreases by 1
19. 19.
    Assertion (A): If the points A(4, 3) and B(x, 5) lie on a circle with centre O(2, 3), then the value of x is 2. Reason (R): Centre of a circle is the mid-point of each chord of the 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…
20. 20.
    Assertion (A): The number 5^n cannot end with the digit 0, where n is a natural number. Reason (R): Prime factorisation of 5 has only two factors, 1 and 5.

    • (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…
21. 21.
    The line segment joining the points A(4, -5) and B(4, 5) is divided by the point P such that AP:AB = 2:5. Find the coordinates of P.
22. 22.
    In the given figure, PT is a tangent to the circle centered at O. OC is perpendicular to chord AB. Prove that PA · PB = PC² − AC².
23. 23.
    Using prime factorisation, find the HCF and LCM of 96 and 120.
24. 24.
    Find the ratio in which the y-axis divides the line segment joining the points (5, -6) and (-1, -4).
25. 25.
    If a cos θ + b sin θ = m and a sin θ − b cos θ = n, then prove that a² + b² = m² + n².
26. 26.
    Prove that √3 is an irrational number.
27. 27.
    If pᵗʰ term of an A.P. is q and qᵗʰ term is p, then prove that its nᵗʰ term is (p + q − n).
28. 28.
    In the given figure, CD is the perpendicular bisector of AB. EF is perpendicular to CD. AE intersects CD at G. Prove that CF/CD = FG/DG.
29. 29.
    Two people are 16 km apart on a straight road. They start walking at the same time. If they walk towards each other with different speeds, they will meet in 2 hours. Had they walked in the same direction with same speeds as before, they would have met in 8 hours. Find their walking speeds.
30. 30.
    Prove that: tan θ/(1 − cot θ) + cot θ/(1 − tan θ) = 1 + sec θ cosec θ.
31. 31.
    Find the mean of the following frequency distribution: Classes: 25-30, 30-35, 35-40, 40-45, 45-50, 50-55, 55-60 Frequency: 14, 22, 16, 6, 5, 3, 4
32. 32.
    One observer estimates the angle of elevation to the basket of a hot air balloon to be 60 degrees, while another observer 100 m away estimates the angle of elevation to be 30 degrees. Find:

    • (a) The height of the basket from the ground.
    • (b) The distance of the basket from the first observer's eye.
    • (c) The horizontal distance of the second observer from the balloon.
33. 33.
    A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC are of lengths 10 cm and 8 cm respectively. Find the lengths of the sides AB and AC, if it is given that area of triangle ABC = 90 cm^2.
34. 34.
    A train travels at a certain average speed for a distance of 54 km and then travels a distance of 63 km at an average speed of 6 km/h more than the first speed. If it takes 3 hours to complete the journey, what was its first average speed?
35. 35.
    A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 5 m long rope. Find the area of that part of the field in which the horse can graze. Also, find the increase in the grazing area if the length of the rope is increased to 10 m. (Use pi = 3.14)
36. 36 (a).
    Case Study: A golf ball is spherical with about 300-500 dimples that help increase its velocity while in play. A golf ball has diameter 4.2 cm and the surface has 315 dimples (hemi-spherical) of radius 2 mm. (i) Find the surface area of one such dimple.
37. 36 (b).
    Case Study: A golf ball is spherical with diameter 4.2 cm and has 315 hemi-spherical dimples of radius 2 mm. (ii) Find the volume of the material dug out to make one dimple.
38. 36 (c).
    Case Study: A golf ball is spherical with diameter 4.2 cm and has 315 hemi-spherical dimples of radius 2 mm. (iii)(a) Find the total surface area exposed to the surroundings.
39. 37 (a).
    Case Study: A middle school decided to run a spinner game as a fund-raiser on Christmas Carnival. Spinner I has 4 equal sectors: Red (R), Green (G), Yellow (Y), and one more. Spinner II has 3 equal sectors: Red (R), Green (G), and Blue (B). Making Purple means spinning Red on one and Blue on the other, written as 'RB'. (i) List all possible outcomes of the game.
40. 37 (b).
    Case Study: Spinner game at Christmas Carnival. Spinner I has sectors R, G, Y. Spinner II has sectors R, G, B. Making Purple = spinning Red on one and Blue on other. (ii) Find the probability of 'Making Purple'.
41. 37 (c).
    Case Study: Spinner game. For each win, a participant gets Rs 10, but if he/she loses, he/she has to pay Rs 5 to the school. If 99 participants played, calculate how much fund could the school have collected. If 99 participants played, calculate how much fund the school collected.
42. 38 (a).
    Case Study: In a pool at an aquarium, a dolphin jumps out of the water travelling at 20 cm per second. Its height above water level after t seconds is given by h = 20t - 16t^2. (i) Find zeroes of the polynomial p(t) = 20t - 16t^2.
43. 38 (b).
    Case Study: A dolphin's height above water is given by h = 20t - 16t^2. (ii) Which of the following types of graph represents p(t)? (a) A parabola opening downward, crossing x-axis at 0 and 5/4 (b) A parabola opening upward, crossing x-axis at 0 and 5/4 (c) A wave/sinusoidal curve (d) A parabola opening upward with vertex above x-axis
44. 38 (c).
    Case Study: A dolphin's height above water is h = 20t - 16t^2. (iii)(a) What would be the value of h at t = 3/2? Interpret the result.

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