CBSE Class 10 Mathematics 2023 — Set 4

Questions in this 2023 Mathematics paper (Set 4)

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 ratio of HCF to LCM of the least composite number and the least prime number is:

   • (a) 1:2
   • (b) 2:1
   • (c) 1:1
   • (d) 1:3
2. 2.
   The roots of the equation x² + 3x - 10 = 0 are:

   • (a) 2, -5
   • (b) -2, 5
   • (c) 2, 5
   • (d) -2, -5
3. 3.
   The next term of the A.P.: sqrt(6), sqrt(24), sqrt(54) is:

   • (a) sqrt(60)
   • (b) sqrt(96)
   • (c) sqrt(72)
   • (d) sqrt(216)
4. 4.
   The distance of the point (-1, 7) from x-axis is:

   • (a) -1
   • (b) 7
   • (c) 6
   • (d) sqrt(50)
5. 5.
   What is the area of a semi-circle of diameter 'd'?

   • (a) (1/16)*pi*d²
   • (b) (1/4)*pi*d²
   • (c) (1/8)*pi*d²
   • (d) (1/2)*pi*d²
6. 6.
   The empirical relation between the mode, median and mean of a distribution is:

   • (a) Mode = 3 Median - 2 Mean
   • (b) Mode = 3 Mean - 2 Median
   • (c) Mode = 2 Median - 3 Mean
   • (d) Mode = 2 Mean - 3 Median
7. 7.
   The pair of linear equations 2x = 5y + 6 and 15y = 6x - 18 represents two lines which are:

   • (a) intersecting
   • (b) parallel
   • (c) coincident
   • (d) either intersecting or parallel
8. 8.
   If alpha, beta are zeroes of the polynomial x² - 1, then the value of (alpha + beta) is:

   • (a) 2
   • (b) 1
   • (c) -1
   • (d) 0
9. 9.
   If a pole 6 m high casts a shadow 2*sqrt(3) m long on the ground, then the sun's elevation is:

   • (a) 60°
   • (b) 45°
   • (c) 30°
   • (d) 90°
10. 10.
    sec(theta) when expressed in terms of cot(theta), is equal to:

    • (a) (1 + cot²(theta)) / cot(theta)
    • (b) sqrt(1 + cot²(theta))
    • (c) sqrt(1 + cot²(theta)) / cot(theta)
    • (d) sqrt(1 - cot²(theta)) / cot(theta)
11. 11.
    Two dice are thrown together. The probability of getting the difference of numbers on their upper faces equals to 3 is:

    • (a) 1/9
    • (b) 2/9
    • (c) 1/6
    • (d) 1/12
12. 12.
    In the given figure, triangle ABC ~ triangle QPR. If AC = 6 cm, BC = 5 cm, QR = 3 cm and PR = x, then the value of x is:

    • (a) 3.6 cm
    • (b) 2.5 cm
    • (c) 10 cm
    • (d) 3.2 cm
13. 13.
    The distance of the point (-6, 8) from origin is:

    • (a) 6
    • (b) -6
    • (c) 8
    • (d) 10
14. 14.
    In the given figure, PQ is a tangent to the circle with centre O. If angle OPQ = x and angle POQ = y, then x + y is:

    • (a) 45°
    • (b) 90°
    • (c) 60°
    • (d) 180°
15. 15.
    In the given figure, TA is a tangent to the circle with centre O such that OT = 4 cm, angle OTA = 30°, then length of TA is:

    • (a) 2*sqrt(3) cm
    • (b) 2 cm
    • (c) 2*sqrt(2) cm
    • (d) sqrt(3) cm
16. 16.
    In triangle ABC, PQ || BC. If PB = 6 cm, AP = 4 cm and AQ = 8 cm, find the length of AC.

    • (a) 12 cm
    • (b) 20 cm
    • (c) 6 cm
    • (d) 14 cm
17. 17.
    If alpha, beta are the zeroes of the polynomial p(x) = 4x² - 3x - 7, then (1/alpha + 1/beta) is equal to:

    • (a) 7/3
    • (b) -7/3
    • (c) 3/7
    • (d) -3/7
18. 18.
    A card is drawn at random from a well-shuffled pack of 52 cards. The probability that the card drawn is not an ace is:

    • (a) 1/13
    • (b) 9/13
    • (c) 4/13
    • (d) 12/13
19. 19.
    Assertion (A): The probability that a leap year has 53 Sundays is 2/7. Reason (R): The probability that a non-leap year has 53 Sundays is 5/7. Select the correct option:

    • (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) (c)…
20. 20.
    Assertion (A): a, b, c are in A.P. if and only if 2b = a + c. Reason (R): The sum of first n odd natural numbers is n². Select the correct option:

    • (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)
    • (c) Assertion (A) is true but…
21. 21.
    Two numbers are in the ratio 2:3 and their LCM is 180. What is the HCF of these numbers?
22. 22.
    If one zero of the polynomial p(x) = 6x² + 37x - (k - 2) is reciprocal of the other, then find the value of k.
23. 23.
    Find the sum and product of the roots of the quadratic equation 2x² - 9x + 4 = 0.
24. 24.
    If a fair coin is tossed twice, find the probability of getting 'atmost one head'.
25. 25.
    Evaluate: (5*cos²(60°) + 4*sec²(30°) - tan²(45°)) / (sin²(30°) + cos²(30°))
26. 26.
    How many terms are there in an A.P. whose first and fifth terms are -14 and 2, respectively and the last term is 62.
27. 27.
    Prove that sqrt(5) is an irrational number.
28. 28.
    Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the centre.
29. 29.
    Prove that (sin A - 2*sin³A) / (2*cos³A - cos A) = tan A
30. 30.
    Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.
31. 31.
    Find the value of 'p' for which the quadratic equation px(x - 2) + 6 = 0 has two equal real roots.
32. 32.
    A straight highway leads to the foot of a tower. A man standing on the top of the 75 m high tower observes two cars at angles of depression of 30° and 60°, which are approaching the foot of the tower. If one car is exactly behind the other on the same side of the tower, find the distance between the two cars. (Use sqrt(3) = 1.73)
33. 33.
    D is a point on the side BC of a triangle ABC such that angle ADC = angle BAC. Prove that CA² = CB.CD.
34. 34.
    A student was asked to make a model shaped like a cylinder with two cones attached to its ends by using a thin aluminium sheet. The diameter of the model is 3 cm and its total length is 12 cm. If each cone has a height of 2 cm, find the volume of air contained in the model.
35. 35.
    The monthly expenditure on milk in 200 families of a Housing Society is given below: Monthly Expenditure (in Rs.): 1000-1500 | 1500-2000 | 2000-2500 | 2500-3000 | 3000-3500 | 3500-4000 | 4000-4500 | 4500-5000 Number of families: 24 | 40 | 33 | x | 30 | 22 | 16 | 7 Find the value of x and also, find the median and mean expenditure on milk.
36. 36 (a).
    Case Study: Two schools 'P' and 'Q' decided to award prizes to their students for two games of Hockey Rs. x per student and Cricket Rs. y per student. School 'P' decided to award a total of Rs. 9,500 for the two games to 5 and 4 students respectively; while school 'Q' decided to award Rs. 7,370 for the two games to 4 and 3 students respectively. (i) Represent the above information algebraically…
37. 36 (b).
    Case Study (continued): 5x + 4y = 9500 and 4x + 3y = 7370. (ii) (a) What is the prize amount for hockey?
38. 36 (c).
    Case Study (continued): Hockey prize = Rs. 980, Cricket prize = Rs. 1150. (iii) If there are 2 students each from two games, then what will be the total prize amount?
39. 37 (a).
    Case Study: Jagdish has a field which is in the shape of a right angled triangle AQC. He wants to leave a space in the form of a square PQRS inside the field for growing wheat and the remaining for growing vegetables. In the field, there is a pole marked as O. Taking O as origin, coordinates of P are (-200, 0) and of Q are (200, 0). PQRS being a square, what are the coordinates of R and S? (i)…
40. 37 (b).
    Case Study (continued): Square PQRS with P(-200, 0), Q(200, 0), R(200, 400), S(-200, 400). (ii) (a) What is the area of square PQRS?
41. 37 (c).
    Case Study (continued): Square PQRS with vertices P(-200,0), Q(200,0), R(200,400), S(-200,400). Point A is (200, 800). (iii) If S divides CA in the ratio K:1, what is the value of K, where point A is (200, 800)?
42. 38 (a).
    Case Study: Governing council of a local public development authority of Dehradun decided to build an adventurous playground on the top of a hill, which will have adequate space for parking. After survey, it was decided to build rectangular playground, with a semi-circular area allotted for parking at one end of the playground. The length and breadth of the rectangular playground are 14 units…
43. 38 (b).
    Case Study (continued): Rectangle 14 x 7, semi-circle parking (radius 3.5), two quadrants (radius 2). (ii) (a) What is the total area of parking and the two quadrants?
44. 38 (c).
    Case Study (continued): Rectangle 14 x 7, semi-circle parking area, two quadrants. (iii) Find the cost of fencing the playground and parking area at the rate of Rs. 2 per unit.

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