CBSE Maths 2022

CBSE Class 10 Maths 2022 — all 20 questions from the paper

The complete question list from the CBSE Class 10 Mathematics 2022 board examination is below. Every question can be attempted in the timed interactive test above, with visual step-by-step solutions and AI coaching after each answer. Three fully worked solutions from this paper follow the question list.

Questions from the 2022 paper

1. Q1.Find the roots of the quadratic equation x² − 3x − 10 = 0.A) 5 and −2B) −5 and 2C) 5 and 2D) −5 and −2
2. Q2.Find the sum of the first 20 terms of the AP: −5, 0, 5, 10, ...A) 850B) 950C) 750D) 1050
3. Q3.Find the value of a₂₅ − a₁₅ for the AP: 6, 9, 12, 15, ...A) 30B) 20C) 15D) 10
4. Q4.PA and PB are tangents drawn from an external point P to a circle with centre O. If ∠OAB = 25°, then ∠APB is:A) 50°B) 25°C) 40°D) 130°
5. Q5.Find the number of natural numbers between 102 and 998 which are divisible by 2 and 5 both.A) 89B) 90C) 91D) 88
6. Q6.Find the ratio in which the y-axis divides the line segment joining the points (5, −6) and (−1, −4).A) 5 : 1B) 1 : 5C) 3 : 1D) 1 : 3
7. Q7.The angle of elevation of the top of a building from a point on the ground 50 m away from its foot is 60°. The height of the building is:A) 50√3 mB) 50/√3 mC) 100 mD) 25√3 m
8. Q8.A solid sphere of diameter 6 cm is dropped into a cylindrical vessel partly filled with water. The diameter of the vessel is 12 cm. If the sphere is completely submerged, what is the rise in the water level?A) 1 cmB) 2 cmC) 3 cmD) 0.5 cm
9. Q9.Find the mean of the following distribution by assumed mean method:
   Class: 10–20 (f=4), 20–30 (f=8), 30–40 (f=10), 40–50 (f=12), 50–60 (f=6). The mean is:A) 36.5B) 37.5C) 38.5D) 35.5
10. Q10.Two dice are thrown at the same time. Find the probability of getting the sum of the two numbers appearing on the top of the dice as 11.A) 1/36B) 2/36C) 1/18D) 1/12
11. Q11.In ΔABC, D and E are points on sides AB and AC respectively such that DE ∥ BC. If AD = 4 cm, DB = 5 cm and AE = 8 cm, find AC.A) 18 cmB) 16 cmC) 20 cmD) 12 cm
12. Q12.Solve for x: (2x)/(x − 3) + 1/(2x + 3) + (3x + 9)/[(x − 3)(2x + 3)] = 0. The roots are:A) -1 and -3B) 1 and 3C) -1 and 3D) 1 and -3
13. Q13.A metallic solid sphere of radius 3 cm is melted and recast into the form of a solid cylinder of radius 2 cm. The height of the cylinder is:A) 9 cmB) 8 cmC) 7 cmD) 12 cm
14. Q14.From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. The height of the cable tower is:A) 7(√3 + 1) mB) 14 mC) 7(√3 − 1) mD) 7√3 m
15. Q15.The mode of the following frequency distribution is 36. Find the missing frequency f.
    Class: 0–10 (f=8), 10–20 (f=10), 20–30 (f=f), 30–40 (f=16), 40–50 (f=12), 50–60 (f=6), 60–70 (f=7). The value of f is:A) 10B) 12C) 8D) 14
16. Q16.A jar contains 24 marbles: some are green and others are blue. If a marble is drawn at random from the jar, the probability that it is green is 2/3. The number of blue marbles is:A) 6B) 8C) 10D) 12
17. Q17.If ΔABC ~ ΔQRP, ar(ΔABC)/ar(ΔQRP) = 9/4, AB = 18 cm and BC = 15 cm, then PR is:A) 10 cmB) 12 cmC) 8 cmD) 9 cm
18. Q18.Find the coordinates of the point which divides the join of A(−1, 7) and B(4, −3) in the ratio 2 : 3.A) (1, 3)B) (2, 1)C) (1, 1)D) (3, 1)
19. Q19.Prove that 3 + 2√5 is irrational. What is the nature of this number?A) RationalB) IrrationalC) IntegerD) Natural
20. Q20.A circle with centre O has two tangents PA and PB drawn from external point P. If ∠APB = 70°, find ∠AOB.A) 110°B) 120°C) 70°D) 140°

Worked solutions from the CBSE 2022 paper

Start the test above to see visual step-by-step solutions for all 20 questions — free, with AI coaching when you get stuck.