CBSE Class 10 Mathematics 2023 — Set 6

Questions in this 2023 Mathematics paper (Set 6)

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 p^2 = 32/50, then p is a/an:

   • (a) whole number
   • (b) integer
   • (c) rational number
   • (d) irrational number
2. 2.
   The distance of the point (-6, 8) from the x-axis is:

   • (a) 6 units
   • (b) -6 units
   • (c) 8 units
   • (d) 10 units
3. 3.
   The number of quadratic polynomials having zeroes -5 and -3 is:

   • (a) 1
   • (b) 2
   • (c) 3
   • (d) more than 3
4. 4.
   The point of intersection of the line represented by 3x - y = 3 and the y-axis is given by:

   • (a) (0, -3)
   • (b) (0, 3)
   • (c) (2, 0)
   • (d) (-2, 0)
5. 5.
   The circumferences of two circles are in the ratio 4 : 5. What is the ratio of their radii?

   • (a) 16 : 25
   • (b) 25 : 16
   • (c) 2 : sqrt(5)
   • (d) 4 : 5
6. 6.
   If alpha and beta are the zeroes of the polynomial x^2 - 1, then the value of (alpha + beta) is:

   • (a) 2
   • (b) 1
   • (c) -1
   • (d) 0
7. 7.
   (cos^2(theta)/sin^2(theta)) - (1/sin^2(theta)) in simplified form is:

   • (a) tan^2(theta)
   • (b) sec^2(theta)
   • (c) 1
   • (d) -1
8. 8.
   If triangle PQR ~ triangle ABC, PQ = 6 cm, AB = 8 cm and the perimeter of triangle ABC is 36 cm, then the perimeter of triangle PQR is:

   • (a) 20.25 cm
   • (b) 27 cm
   • (c) 48 cm
   • (d) 64 cm
9. 9.
   If the quadratic equation ax^2 + bx + c = 0 has two real and equal roots, then 'c' is equal to:

   • (a) -b/(2a)
   • (b) b/(2a)
   • (c) -b^2/(4a)
   • (d) b^2/(4a)
10. 10.
    In the given figure, DE||BC. If AD = 3 cm, AB = 7 cm and EC = 3 cm, then the length of AE is:

    • (a) 2 cm
    • (b) 2.25 cm
    • (c) 3.5 cm
    • (d) 4 cm
11. 11.
    A bag contains 5 pink, 8 blue and 7 yellow balls. One ball is drawn at random from the bag. What is the probability of getting neither a blue nor a pink ball?

    • (a) 1/4
    • (b) 2/5
    • (c) 7/20
    • (d) 13/20
12. 12.
    The volume of a right circular cone whose area of the base is 156 cm^2 and the vertical height is 8 cm, is:

    • (a) 2496 cm^3
    • (b) 1248 cm^3
    • (c) 1664 cm^3
    • (d) 416 cm^3
13. 13.
    3 chairs and 1 table cost Rs 900; whereas 5 chairs and 3 tables cost Rs 2100. If the cost of 1 chair is Rs x and the cost of 1 table is Rs y, then the situation can be represented algebraically as:

    • (a) 3x + y = 900, 3x + 5y = 2100
    • (b) x + 3y = 900, 3x + 5y = 2100
    • (c) 3x + y = 900, 5x + 3y = 2100
    • (d) x + 3y = 900, 5x + 3y = 2100
14. 14.
    In the given figure, PA and PB are tangents from the external point P to a circle with centre C and Q is any point on the circle. Then the measure of angle AQB is:

    • (a) 62.5 degrees
    • (b) 125 degrees
    • (c) 55 degrees
    • (d) 90 degrees
15. 15.
    A card is drawn at random from a well shuffled deck of 52 playing cards. The probability of getting a face card is:

    • (a) 1/2
    • (b) 3/13
    • (c) 4/13
    • (d) 1/13
16. 16.
    If theta is an acute angle of a right angled triangle, then which of the following equation is not true?

    • (a) sin(theta) * cot(theta) = cos(theta)
    • (b) cos(theta) * tan(theta) = sin(theta)
    • (c) cosec^2(theta) - cot^2(theta) = 1
    • (d) tan^2(theta) - sec^2(theta) = 1
17. 17.
    If the zeroes of the quadratic polynomial x^2 + (a + 1)x + b are 2 and -3, then:

    • (a) a = -7, b = -1
    • (b) a = 5, b = -1
    • (c) a = 2, b = -6
    • (d) a = 0, b = -6
18. 18.
    If the sum of the first n terms of an A.P. is 3n^2 + n and its common difference is 6, then its first term is:

    • (a) 2
    • (b) 3
    • (c) 1
    • (d) 4
19. 19.
    Assertion (A): If 5 + sqrt(7) is a root of a quadratic equation with rational coefficients, then its other root is 5 - sqrt(7). Reason (R): Surd roots of a quadratic equation with rational coefficients occur in conjugate pairs.

    • (a) Both Assertion (A) and Reason (R) are true; and Reason (R) is the correct explanation of Assertion (A).
    • (b) Both Assertion (A) and Reason (R) are true; but Reason (R)…
20. 20.
    Assertion (A): For 0 < theta <= 90 degrees, cosec(theta) - cot(theta) and cosec(theta) + cot(theta) are reciprocal of each other. Reason (R): cosec^2(theta) - cot^2(theta) = 1.

    • (a) Both Assertion (A) and Reason (R) are true; and Reason (R) is the correct explanation of Assertion (A).
    • (b) Both Assertion (A) and Reason (R) are true; but Reason (R) is not the correct explanation of Assertion (A)…
21. 21.
    Show that 6^n can not end with digit 0 for any natural number 'n'.
22. 22.
    A line intersects y-axis and x-axis at point P and Q, respectively. If R(2, 5) is the mid-point of line segment PQ, then find the coordinates of P and Q.
23. 23.
    Find the length of the shadow on the ground of a pole of height 18 m when the angle of elevation theta of the sun is such that tan(theta) = 6/7.
24. 24.
    In the given figure, PA is a tangent to the circle drawn from the external point P and PBC is the secant to the circle with BC as diameter. If angle AOC = 130 degrees, then find the measure of angle APB, where O is the centre of the circle.
25. 25.
    In the given figure, ABC is a triangle in which DE||BC. If AD = x, DB = x - 2, AE = x + 2 and EC = x - 1, then find the value of x.
26. 26.
    Find the ratio in which the line segment joining the points A(6, 3) and B(-2, -5) is divided by the x-axis.
27. 27.
    Find the HCF and LCM of 26, 65 and 117, using prime factorisation.
28. 28.
    In the given figure, E is a point on the side CB produced of an isosceles triangle ABC with AB = AC. If AD ⊥ BC and EF ⊥ AC, then prove that triangle ABD ~ triangle ECF.
29. 29.
    The sum of two numbers is 15. If the sum of their reciprocals is 3/10, find the two numbers.
30. 30.
    Prove that (1 + sec A)/sec A = sin^2(A)/(1 - cos A).
31. 31.
    In a circle of radius 21 cm, an arc subtends an angle of 60 degrees at the centre. Find the area of the sector formed by the arc. Also, find the length of the arc.
32. 32.
    Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that angle PTQ = 2 * angle OPQ.
33. 33.
    A solid is in the shape of a right-circular cone surmounted on a hemisphere, the radius of each of them being 7 cm and the height of the cone is equal to its diameter. Find the volume of the solid.
34. 34.
    The ratio of the 11th term to the 18th term of an A.P. is 2 : 3. Find the ratio of the 5th term to the 21st term. Also, find the ratio of the sum of first 5 terms to the sum of first 21 terms.
35. 35.
    250 apples of a box were weighed and the distribution of masses is given in the following table: Mass (in grams): 80-100 | 100-120 | 120-140 | 140-160 | 160-180 Number of apples: 20 | 60 | 70 | x | 60

    • (i) Find the value of x and the mean mass of the apples.
    • (ii) Find the modal mass of the apples.
36. 36 (a).
    Case Study: A coaching institute of Mathematics conducts classes in two batches I and II and fees for rich and poor children are different. In batch I, there are 20 poor and 5 rich children, whereas in batch II, there are 5 poor and 25 rich children. The total monthly collection of fees from batch I is Rs 9000 and from batch II is Rs 26,000. Assume that each poor child pays Rs x per month and…
37. 36 (b).
    Case Study: A coaching institute has two batches. Batch I: 20 poor + 5 rich children, total fees Rs 9000. Batch II: 5 poor + 25 rich children, total fees Rs 26,000. Each poor child pays Rs x and each rich child pays Rs y per month. The equations are 20x + 5y = 9000 and 5x + 25y = 26000. (ii) Find the monthly fee paid by a poor child.
38. 36 (c).
    Case Study: A coaching institute has two batches. Each poor child pays Rs 200 and each rich child pays Rs 1000 per month. (iii) If there are 10 poor and 20 rich children in batch II, what is the total monthly collection of fees from batch II?
39. 37 (a).
    Case Study: A radio station tower was built in two Sections A and B. Tower is supported by wires from a point O. Distance between the base of the tower and point O is 36 cm. From point O, the angle of elevation of the top of Section B is 30 degrees and the angle of elevation of the top of Section A is 45 degrees. (i) Find the length of the wire from the point O to the top of Section B.
40. 37 (b).
    Case Study: A radio station tower was built in two Sections A and B. Tower is supported by wires from a point O. Distance between the base of the tower and point O is 36 cm. From point O, the angle of elevation of the top of Section B is 30 degrees and the angle of elevation of the top of Section A is 45 degrees. (ii) Find the distance AB.
41. 37 (c).
    Case Study: A radio station tower was built in two Sections A and B. Base P, point O is 36 cm from P. Angle of elevation of top of A from O is 45 degrees. (iii) Find the height of Section A from the base of the tower.
42. 38 (a).
    Case Study: 'Eight Ball' is a game played on a pool table with 15 balls numbered 1 to 15 and a 'cue ball' that is solid and white. Of the 15 numbered balls, eight are solid (non-white) coloured and numbered 1 to 8, and seven are striped balls numbered 9 to 15. The 15 numbered pool balls (no cue ball) are placed in a large bowl and mixed, then one ball is drawn out at random. (i) What is the…
43. 38 (b).
    Case Study: 'Eight Ball' is a game with 15 balls numbered 1 to 15. Eight solid balls numbered 1-8, seven striped balls numbered 9-15. One ball drawn at random. (ii) What is the probability that the drawn ball bears an even number?
44. 38 (c).
    Case Study: 'Eight Ball' game with 15 balls. Solid balls numbered 1-8, striped balls numbered 9-15. One ball drawn at random. (iii) What is the probability that the drawn ball is a solid coloured and bears an even number?

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