ICSE Maths 2024

ICSE Class 10 Maths 2024 — all 35 questions from the paper

The complete question list from the ICSE 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.If the quadratic equation 2x² − kx + 3 = 0 has equal roots, then the value of k is:A) ±2√6B) ±√6C) ±6D) ±3√2
2. Q2.Mrs. Sharma deposits ₹400 per month for 2 years in a recurring deposit account. If the rate of interest is 8% p.a., the interest earned is:A) ₹800B) ₹820C) ₹780D) ₹810
3. Q3.A bag contains 5 red, 3 blue and 2 green balls. One ball is drawn at random. The probability that it is NOT green is:A) 1/5B) 4/5C) 2/5D) 3/5
4. Q4.The slope of the line perpendicular to the line 3x − 2y + 8 = 0 is:A) 3/2B) −3/2C) 2/3D) −2/3
5. Q5.If A = [[2, 3], [4, 5]] and B = [[1, 0], [0, 1]], then A − B equals:A) [[1, 3], [4, 4]]B) [[1, 3], [4, 5]]C) [[3, 3], [4, 6]]D) [[2, 3], [4, 5]]
6. Q6.In a cyclic quadrilateral ABCD, if ∠A = 70°, then ∠C equals:A) 70°B) 110°C) 90°D) 180°
7. Q7.The HCF of the polynomials x³ − 1 and x² − 1 is:A) x − 1B) x + 1C) x² + x + 1D) x² − 1
8. Q8.A man buys 50 shares of face value ₹100 at a premium of ₹20. If the dividend is 15%, his annual income is:A) ₹750B) ₹900C) ₹600D) ₹1,000
9. Q9.If sin θ + cos θ = √2, then tan θ + cot θ equals:A) 1B) 2C) √2D) 1/√2
10. Q10.The total surface area of a solid hemisphere of radius 7 cm is:A) 462 cm²B) 308 cm²C) 154 cm²D) 616 cm²
11. Q11.If x, y, z are in continued proportion, then y² equals:A) xzB) x + zC) (x + z)/2D) x²z²
12. Q12.The solution set of −3 ≤ x/2 < 1, x ∈ R, when represented on the number line includes:A) −6 ≤ x < 2B) −6 < x ≤ 2C) −6 ≤ x ≤ 2D) −6 < x < 2
13. Q13.A dealer buys an article for ₹8,000 and sells it for ₹10,000. If the GST rate is 12%, the GST paid by the dealer to the government is:A) ₹240B) ₹1,200C) ₹960D) ₹200
14. Q14.The mean of 5 numbers is 18. If one number is excluded, the mean becomes 16. The excluded number is:A) 26B) 24C) 22D) 28
15. Q15.If the roots of 3x² + kx + 12 = 0 are real and equal, then k equals:A) ±12B) ±6C) ±6√2D) ±4√3
16. Q16.Solve the equation 3x² − 5x − 2 = 0 by factorization. The roots are:A) x = 2 and x = −1/3B) x = −2 and x = 1/3C) x = 3 and x = −2/3D) x = 1 and x = −2
17. Q17.Find the sum of the AP: 7 + 10.5 + 14 + ... + 84. The number of terms is:A) 22B) 23C) 24D) 25
18. Q18.If A = [[3, 1], [−1, 2]] and I is the 2×2 identity matrix, find A² − 5A + 7I. The result is:A) [[0, 0], [0, 0]]B) [[1, 0], [0, 1]]C) [[7, 0], [0, 7]]D) [[−1, 1], [1, −1]]
19. Q19.The line joining A(2, −3) and B(6, 5) is divided by the point (4, k) in a certain ratio. The value of k is:A) 1B) 0C) −1D) 2
20. Q20.If a/b = c/d, prove that (a + b)/(a − b) = (c + d)/(c − d). This is an application of:A) Componendo-DividendoB) AlternendoC) InvertendoD) Cross multiplication
21. Q21.A shopkeeper sells a TV for ₹24,000 (inclusive of GST) at 20% GST. The marked price of the TV before GST is:A) ₹20,000B) ₹19,200C) ₹21,000D) ₹22,000
22. Q22.Find the median of the following frequency distribution:
    
    Class: 0-10, 10-20, 20-30, 30-40, 40-50
    Frequency: 5, 8, 12, 7, 3
    
    The median is:A) 23.33B) 25.00C) 22.50D) 24.17
23. Q23.A cone of height 24 cm and radius of base 6 cm is made up of modelling clay. It is reshaped into a sphere. The radius of the sphere is:A) 6 cmB) 8 cmC) 4 cmD) 12 cm
24. Q24.Prove that (1 + tan²A)/(1 + cot²A) = tan²A. The expression (1 + tan²A) simplifies to:A) sec²AB) cosec²AC) sin²AD) cos²A
25. Q25.Two dice are thrown simultaneously. The probability of getting a sum of 9 is:A) 1/9B) 1/12C) 4/36D) 5/36
26. Q26.Simplify: (cosA/(1 − tanA)) + (sinA/(1 − cotA)). The result is:A) sinA + cosAB) sinA − cosAC) 1D) sinA cosA
27. Q27.Find the equation of the line passing through (1, 2) and (3, −4).A) 3x + y − 5 = 0B) 3x + y + 5 = 0C) x + 3y − 5 = 0D) x − 3y + 5 = 0
28. Q28.Mrs. Kapoor has ₹25,000 to invest. She invests some in 8% ₹100 shares at ₹120 and the rest in 10% ₹100 shares at ₹125. If her total annual income is ₹2,100, how much did she invest in 8% shares?A) ₹12,000B) ₹15,000C) ₹10,000D) ₹18,000
29. Q29.Mr. Gupta opens a recurring deposit account of ₹800 per month at 6% p.a. for 3 years. His maturity value is:A) ₹32,148B) ₹31,332C) ₹30,528D) ₹32,004
30. Q30.If 4x + 3y ≤ 12, x ≥ 0, y ≥ 0, the maximum value of y in the solution region is:A) 3B) 4C) 12D) 0
31. Q31.Construct a triangle ABC with BC = 6.5 cm, AB = 5.5 cm, and AC = 5 cm. The circumradius of this triangle (using construction) is approximately:A) 3.5 cmB) 4.0 cmC) 3.3 cmD) 4.5 cm
32. Q32.The angle of elevation of the top of a tower from a point 100 m away from its base is 45°. The height of the tower is:A) 100 mB) 50 mC) 100√2 mD) 50√2 m
33. Q33.A tangent is drawn from an external point P to a circle with centre O and radius 5 cm. If OP = 13 cm, the length of the tangent is:A) 12 cmB) 8 cmC) 10 cmD) √194 cm
34. Q34.A cylindrical container of diameter 12 cm and height 15 cm is filled with ice cream. This is distributed to 10 children in cones of diameter 6 cm and height 12 cm, topped with a hemispherical scoop. How many such cones can be filled?A) 10B) 12C) 15D) 8
35. Q35.If (x − 2) is a factor of x³ − 3x² + kx + 10, find the value of k.A) −3B) 3C) −1D) 1

Worked solutions from the ICSE 2024 paper

Start the test above to see visual step-by-step solutions for all 35 questions — free, with AI coaching when you get stuck.