CBSE Maths 2024

CBSE Class 10 Maths 2024 — all 38 questions from the paper

The complete question list from the CBSE Class 10 Mathematics 2024 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 2024 paper

1. Q1.The LCM of 12, 15 and 21 is:A) 60B) 180C) 420D) 840
2. Q2.The HCF of two numbers is 18 and their product is 12960. Their LCM is:A) 420B) 600C) 720D) 800
3. Q3.If α and β are the zeroes of x² − 5x + 6, then the value of α³ + β³ is:A) 35B) 45C) 55D) 65
4. Q4.If one zero of the polynomial 2x² + 3x + k is 1/2, then the value of k is:A) -2B) 2C) -1D) 1
5. Q5.The pair of equations 3x + 4y = 18 and 4x + (16/3)y = 24 has:A) Unique solutionB) Infinitely many solutionsC) No solutionD) Exactly two solutions
6. Q6.The roots of the quadratic equation x² − 0.04 = 0 are:A) ±0.2B) ±0.02C) 0.4D) 0.2
7. Q7.If the discriminant of a quadratic equation is equal to zero, then its roots are:A) Real and distinctB) Real and equalC) Not realD) Real and irrational
8. Q8.The 10th term of the AP: 2, 7, 12, ... is:A) 47B) 42C) 52D) 57
9. Q9.In ΔABC, DE ∥ BC, AD = 2 cm, DB = 3 cm. If AE = 1.6 cm, then EC is:A) 2.4 cmB) 3.6 cmC) 3.2 cmD) 1.8 cm
10. Q10.If ΔABC ~ ΔDEF and AB = 4 cm, DE = 6 cm, EF = 9 cm, then BC is:A) 6 cmB) 4 cmC) 9 cmD) 13.5 cm
11. Q11.The distance between the points (3, 4) and (8, −3) is:A) √74B) √24C) √34D) √58
12. Q12.If sin A = 3/4, then the value of cos A is:A) √7/4B) √5/4C) 5/4D) 7/4
13. Q13.The value of sin²60° + cos²60° is:A) 0B) 1/2C) 1D) 2
14. Q14.From an external point Q, the length of the tangent to a circle is 12 cm and the distance of Q from the centre is 13 cm. The radius of the circle is:A) 5 cmB) 7 cmC) 25 cmD) √313 cm
15. Q15.If the perimeter and area of a circle are numerically equal, then the radius of the circle is:A) 2 unitsB) π unitsC) 4 unitsD) 7 units
16. Q16.A solid hemisphere has radius 7 cm. Its total surface area is:A) 462 cm²B) 294 cm²C) 588 cm²D) 308 cm²
17. Q17.The median class of the following distribution is:
    Class: 0–10 (f=5), 10–20 (f=8), 20–30 (f=12), 30–40 (f=10), 40–50 (f=5)A) 10–20B) 20–30C) 30–40D) 0–10
18. Q18.A card is drawn at random from a well-shuffled deck of 52 cards. The probability of getting a red face card is:A) 3/13B) 3/26C) 6/13D) 1/2
19. Q19.Assertion (A): The sum of the first n terms of an AP with first term a and common difference d is n/2 [2a + (n−1)d].
    Reason (R): The nth term of an AP is a + (n−1)d.
    Choose the correct option:A) Both A and R are true, and R is the correct explanation of AB) Both A and R are true, but R is not the correct explanation of AC) A is true but R is falseD) A is false but R is true
20. Q20.Assertion (A): If the midpoint of AB where A(2, 5) and B(−2, k) is (0, 4), then k = 3.
    Reason (R): The midpoint of (x₁,y₁) and (x₂,y₂) is ((x₁+x₂)/2, (y₁+y₂)/2).
    Choose the correct option:A) Both A and R are true, and R is the correct explanation of AB) Both A and R are true, but R is not the correct explanation of AC) A is true but R is falseD) A is false but R is true
21. Q21.If the sum of the zeroes of the polynomial p(x) = (k² − 14)x² − 2x − 12 is 1, then the value of k is:A) ±4B) ±3C) ±2D) ±5
22. Q22.The sum of the first 20 terms of the AP: 3, 7, 11, 15, ... is:A) 820B) 840C) 860D) 800
23. Q23.Two concentric circles have radii 5 cm and 3 cm. The length of the chord of the larger circle which touches the smaller circle is:A) 6 cmB) 8 cmC) 10 cmD) 4 cm
24. Q24.The point which divides the line segment joining A(1, 2) and B(−1, −1) in the ratio 2 : 1 is:A) (−1/3, 0)B) (1/3, 0)C) (0, 1/3)D) (0, −1/3)
25. Q25.If tan(A + B) = √3 and tan(A − B) = 1/√3, where 0° < A + B ≤ 90°, then A and B are:A) A = 45°, B = 15°B) A = 30°, B = 30°C) A = 60°, B = 30°D) A = 50°, B = 10°
26. Q26.Prove that √5 is irrational. Using this, prove that 3 + 2√5 is irrational. What type of number is 3 + 2√5?A) RationalB) IrrationalC) IntegerD) Natural number
27. Q27.The sum of a two-digit number and the number obtained by reversing the order of its digits is 165. If the digits differ by 3, how many such two-digit numbers are possible?A) 2B) 1C) 3D) 4
28. Q28.If the sum of the first 7 terms of an AP is 49 and that of the first 17 terms is 289, find the sum of the first n terms.A) n²B) n² + 1C) 2n²D) n(n+1)
29. Q29.Prove that (sinθ − cosθ + 1)/(sinθ + cosθ − 1) = 1/(secθ − tanθ). The expression simplifies using which identity?A) sec²θ − tan²θ = 1B) sin²θ + cos²θ = 1C) 1 + cot²θ = cosec²θD) tan²θ + 1 = sec²θ
30. Q30.A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, surmounted by a cone of height 60 cm. The volume of the pole (in cm³) is: (Use π = 22/7)A) 102960B) 99456C) 105600D) 108240
31. Q31.The following distribution gives the daily income of 50 workers of a factory:
    Income (₹): 100–120 (f=12), 120–140 (f=14), 140–160 (f=8), 160–180 (f=6), 180–200 (f=10).
    The mean daily income is:A) ₹140B) ₹142C) ₹145.20D) ₹148
32. Q32.A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. What is the speed of the train?A) 40 km/hB) 45 km/hC) 36 km/hD) 48 km/h
33. Q33.A solid is in the shape of a cone mounted on a hemisphere. The diameter of the hemisphere is 14 cm and the total height of the solid is 18 cm. The total surface area of the solid is: (Use π = 22/7)A) 858 cm²B) 770 cm²C) 616 cm²D) 808 cm²
34. Q34.D is a point on the side BC of ΔABC such that ∠ADC = ∠BAC. If CA = 12 cm and BC = 18 cm, then CD is:A) 8 cmB) 6 cmC) 9 cmD) 10 cm
35. Q35.The following table gives the distribution of the lifetime (in hours) of 400 neon lamps:
    Lifetime: 1500–2000 (f=14), 2000–2500 (f=56), 2500–3000 (f=60), 3000–3500 (f=86), 3500–4000 (f=74), 4000–4500 (f=62), 4500–5000 (f=48).
    The median lifetime is:A) 3406.98 hrsB) 3500 hrsC) 3250 hrsD) 3100 hrs
36. Q36.A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60°. The length of the string is: (Assume no slack in the string)A) 40√3 mB) 60√3 mC) 30√3 mD) 20√3 m
37. Q37.In a cricket match, a batsman hits a boundary 8 times out of 40 balls. A ball is selected at random. What is the probability that the batsman does NOT hit a boundary?A) 4/5B) 1/5C) 3/5D) 2/5
38. Q38.The area of a sector of a circle of radius 14 cm with central angle 90° is: (Use π = 22/7)A) 154 cm²B) 308 cm²C) 616 cm²D) 77 cm²

Worked solutions from the CBSE 2024 paper

Start the test above to see visual step-by-step solutions for all 38 questions — free, with AI coaching when you get stuck.