CBSE Class 10 Mathematics 2022 — Set 2

Questions in this 2022 Mathematics paper (Set 2)

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.
   Solve the quadratic equation x^2 + 2*sqrt(2)*x - 6 = 0 for x.
2. 2.
   Which term of the A.P. -11/2, -3, -1/2, ... is 49/2?
3. 3.
   A solid piece of metal in the form of a cuboid of dimensions 11 cm x 7 cm x 7 cm is melted to form 'n' number of solid spheres of radii 7/2 cm each. Find the value of n.
4. 4.
   AB is the diameter of a circle centered at O. BC is tangent to the circle at B. If OP bisects the chord AD and angle AOP = 60 degrees, find the measure of angle C.
5. 5.
   If the mode of the following frequency distribution is 55, find the value of x. Class: 0-15, 15-30, 30-45, 45-60, 60-75, 75-90 Frequency: 10, 7, x, 15, 10, 12
6. 6.
   Find the sum of the first 20 terms of an A.P. whose nth term is given as a_n = 5 - 2n.
7. 7.
   Draw two concentric circles of radii 2 cm and 5 cm. From a point on the outer circle, construct a pair of tangents to the inner circle.
8. 8.
   AB is a tower of height 50 m. A man standing on its top observes two cars on the opposite sides of the tower with angles of depression 30 degrees and 45 degrees respectively. Find the distance between the two cars.
9. 9.
   The mean of the following frequency distribution is 25. Find the value of f. Class: 0-10, 10-20, 20-30, 30-40, 40-50 Frequency: 5, 18, 15, f, 6
10. 10.
    Heights of 50 students of class X of a school are recorded and the following data is obtained. Height (in cm): 130-135, 135-140, 140-145, 145-150, 150-155, 155-160 Number of students: 4, 11, 12, 7, 10, 6 Find the median height of the students.
11. 11.
    PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q meet at a point T. Find the length of TP.
12. 12.
    A 2-digit number is such that the product of its digits is 24. If 18 is subtracted from the number, the digits interchange their places. Find the number.
13. 13 (a).
    Case Study - Kite Festival: A man at point C is flying two kites A and B. The angles of elevation of kites A and B from C are 30 degrees and 60 degrees respectively. If AD = 50 m and BE = 60 m (where D and E are the feet of perpendiculars from A and B to the ground), find the lengths of strings used for kites A and B (assume strings are taut/straight).
14. 13 (b).
    Case Study - Kite Festival: A man at point C is flying two kites A and B. The angles of elevation of kites A and B from C are 30 degrees and 60 degrees respectively. AD = 50 m and BE = 60 m (heights of kites from ground). D and E are points on the ground on opposite sides of C. Find the distance 'd' between the two kites A and B.
15. 14 (a).
    Case Study - Circus Tent: A tent is in the shape of a cylinder surmounted by a conical top. The height and diameter of the cylindrical part are 9 m and 30 m respectively, and the height of the conical part is 8 m with the same diameter as the cylindrical part. Find the area of the canvas used in making the tent.
16. 14 (b).
    Case Study - Circus Tent: A tent is in the shape of a cylinder surmounted by a conical top. The canvas area of the tent is 1650 sq m. Find the cost of the canvas bought at the rate of Rs 200 per sq m, if 30 sq m of canvas was wasted during stitching.

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