CBSE Class 10 Mathematics 2022 — Set 4

Questions in this 2022 Mathematics paper (Set 4)

All 14 questions from this set, exactly as asked. Try each one, then open the question-paper PDF above for the complete paper.

1. 1.
   The mode of a grouped frequency distribution is 75 and the modal class is 65-80. The frequency of the class preceding the modal class is 6 and the frequency of the class succeeding the modal class is 8. Find the frequency of the modal class.
2. 2.
   How many natural numbers are there between 1 and 1000 which are divisible by 5 but not by 2?
3. 3.
   If the sum of the roots of the quadratic equation kx^2 - 11x + (k - 23) = 0 is 13/21 more than the product of the roots, then find the value of k.
4. 4.
   Find the mean of the following frequency distribution: Class: 1-5, 5-9, 9-13, 13-17 Frequency: 4, 8, 7, 6
5. 5.
   In Fig. 1, there are two concentric circles with centre O. If ARC and AQB are tangents to the smaller circle from the point A lying on the larger circle, find the length of AC, if AQ = 5 cm.
6. 6 (a).
   The curved surface area of a right circular cylinder is 176 sq cm and its volume is 1232 cu cm. What is the height of the cylinder?
7. 6 (b).
   The largest sphere is carved out of a solid cube of side 21 cm. Find the volume of the sphere.
8. 7.
   Construct a pair of tangents to a circle of radius 4 cm which are inclined to each other at an angle of 60°.
9. 8 (a).
   Find the value of 'p' for which the quadratic equation p(x - 4)(x - 2) + (x - 1)^2 = 0 has real and equal roots.
10. 8 (b).
    Had Aarush scored 8 more marks in a Mathematics test, out of 35 marks, 7 times these marks would have been 4 less than the square of his actual marks. How many marks did he get in the test?
11. 9.
    An aeroplane when flying at a height of 3125 m from the ground passes vertically below another plane at an instant when the angles of elevation of the two planes from the same point on the ground are 30 degrees and 60 degrees respectively. Find the distance between the two planes at that instant.
12. 10.
    If the last term of an A.P. of 30 terms is 119 and the 8th term from the end (towards the first term) is 91, then find the common difference of the A.P. Hence, find the sum of all the terms of the A.P.
13. 11 (a).
    In Fig. 2, if a circle touches the side QR of triangle PQR at S and extended sides PQ and PR at M and N respectively, then prove that PM = (1/2)(PQ + QR + PR).
14. 11 (b).
    In Fig. 3, a triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 6 cm and 8 cm respectively. If the area of triangle ABC is 84 sq cm, find the lengths of sides AB and AC.
15. 12.
    From the top of an 8 m high building, the angle of elevation of the top of a cable tower is 60 degrees and the angle of depression of its foot is 45 degrees. Determine the height of the tower. (Take sqrt(3) = 1.732)
16. 13 (a).
    (Case Study - Yoga Camp) Green Park society in Pune organised a 7-day Yoga camp. The number of people of different age groups who enrolled for the camp is as follows: Age Group: 15-25, 25-35, 35-45, 45-55, 55-65, 65-75, 75-85 Number of People: 8, 10, 15, 25, 40, 24, 18 Find the median age of people enrolled for the camp.
17. 13 (b).
    (Case Study - Yoga Camp) Green Park society in Pune organised a 7-day Yoga camp. The number of people of different age groups who enrolled for the camp is as follows: Age Group: 15-25, 25-35, 35-45, 45-55, 55-65, 65-75, 75-85 Number of People: 8, 10, 15, 25, 40, 24, 18 If x more people of age group 65-75 had enrolled for the camp, the mean age would have been 58. Find the value of x.
18. 14 (a).
    (Case Study - Khurja Pottery) The internal radius of a hemispherical bowl (filled completely with water) in shape I is 9 cm and the radius and height of a cylindrical jar in shape II is 1.5 cm and 4 cm respectively. If the hemispherical bowl is to be emptied into cylindrical jars, then how many cylindrical jars are required?
19. 14 (b).
    (Case Study - Khurja Pottery) If in a cylindrical jar (radius 1.5 cm, height 4 cm) full of water, a conical funnel of same height and same diameter is immersed, then how much water will flow out of the jar?

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 2022 paper — FAQ