ICSE Maths 2025

ICSE Class 10 Maths 2025 — all 35 questions from the paper

The complete question list from the ICSE Class 10 Mathematics 2025 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 2025 paper

1. Q1.The quadratic equation √3x² + √7x + 2√3 = 0 has:A) Two equal real rootsB) Two distinct real rootsC) More than two real rootsD) No real roots
2. Q2.Mr. Anuj deposits ₹500 per month for 18 months in a recurring deposit account. If he earns ₹570 as interest at maturity, his matured amount is:A) ₹(500 × 18 + 570)B) ₹(500 × 19 + 570)C) ₹(500 × 18 × 19 + 570)D) ₹(500 × 9 × 19 + 570)
3. Q3.Which of the following cannot be the probability of any event?A) 5/4B) 0.25C) 1/33D) 67%
4. Q4.The equation of the line passing through origin and parallel to 3x + 4y + 7 = 0 is:A) 3x + 4y + 5 = 0B) 4x − 3y − 5 = 0C) 4x − 3y = 0D) 3x + 4y = 0
5. Q5.If A = [[0, 1], [1, 0]], then A² is equal to:A) [[1, 1], [0, 0]]B) [[0, 0], [1, 1]]C) [[1, 0], [0, 1]]D) [[0, 1], [1, 0]]
6. Q6.In a circle, chords AC and BC are equal. If the exterior angle ∠ACD = 120°, then the angle ∠AEC (where E is a point on the major arc) is:A) 30°B) 60°C) 90°D) 120°
7. Q7.The factor common to (x² − 4) and (x³ − x² − 4x + 4) is:A) (x + 1)B) (x − 1)C) (x − 2)D) (x − 4)
8. Q8.A man invested in ₹100 shares of a company paying 12% dividend. If his percentage return on investment is 10%, then the shares are:A) At parB) Below parC) Above parD) Cannot be determined
9. Q9.Statement 1: The point equidistant from three non-collinear points D, E, F is the circumcentre of △DEF.
   Statement 2: The incentre of a triangle is the point where all the angle bisectors intersect.
   
   Which is correct?A) Both statements are trueB) Both statements are falseC) Statement 1 is true, Statement 2 is falseD) Statement 1 is false, Statement 2 is true
10. Q10.Assertion (A): If sin²A + sinA = 1, then cos⁴A + cos²A = 1.
    Reason (R): 1 − sin²A = cos²A.
    
    Choose the correct option:A) A is true, R is falseB) A is false, R is trueC) Both A and R are true, and R is the correct explanation of AD) Both A and R are true, but R is not the correct explanation of A
11. Q11.△ABC ~ △EFG with ∠ABC = ∠EFG = 60°. If AB = 10 cm, BC = 20 cm, and EF = 7.5 cm, then FG is:A) 15 cmB) 20 cmC) 25 cmD) 30 cm
12. Q12.If the ratio of the volumes of two spheres is 27:64, then the ratio of their radii is:A) 3:4B) 4:3C) 9:16D) 16:9
13. Q13.The marked price of an article is ₹1,375. If CGST is 4%, the price of the article including GST is:A) ₹55B) ₹110C) ₹1,430D) ₹1,485
14. Q14.The solution set for 0 < −x/3 < 2, where x ∈ Z (integers), is:A) {−5, −4, −3, −2, −1}B) {−6, −5, −4, −3, −2, −1}C) {−5, −4, −3, −2, −1, 0}D) {−6, −5, −4, −3, −2, −1, 0}
15. Q15.Assertion (A): The mean of the first 9 natural numbers is 4.5.
    Reason (R): Mean = Sum of observations / Number of observations.
    
    Choose the correct option:A) A is true, R is falseB) A is false, R is trueC) Both A and R are true, and R is the correct explanation of AD) Both A and R are true, but R is not the correct explanation of A
16. Q16.Solve 2x² − 7x + 3 = 0 using the quadratic formula. The roots are:A) x = 3 and x = 1/2B) x = 3 and x = −1/2C) x = −3 and x = 1/2D) x = 7 and x = 3
17. Q17.Find the sum of the first 20 terms of the AP: 3, 7, 11, 15, ...A) 820B) 760C) 840D) 800
18. Q18.If A = [[2, 0], [0, 3]] and B = [[1, 4], [2, 5]], find the product AB.A) [[2, 8], [6, 15]]B) [[2, 0], [6, 15]]C) [[2, 8], [0, 15]]D) [[3, 4], [2, 8]]
19. Q19.Find the equation of the line passing through (2, 3) and parallel to 3x − 4y + 5 = 0.A) 3x − 4y + 6 = 0B) 3x − 4y − 6 = 0C) 4x − 3y + 6 = 0D) 3x + 4y − 6 = 0
20. Q20.Find the mean proportional between 4 and 25.A) 10B) 14.5C) 12D) 20
21. Q21.Solve: (x + 1)/(x − 1) + (x − 2)/(x + 2) = 3. The values of x are:A) x = 2 and x = −5B) x = 4 and x = −1C) x = −4 and x = 1D) x = 5 and x = −2
22. Q22.The observations 15, 17, x + 2, x + 4, 35, 38 are arranged in ascending order. If the median is 25, find x.A) 22B) 23C) 24D) 20
23. Q23.A cylindrical container of radius 6 cm and height 15 cm is full of ice cream. The ice cream is filled into cones of height 12 cm and radius 3 cm, each having a hemispherical top. How many such cones can be filled?A) 10B) 12C) 15D) 8
24. Q24.From a point on the ground 60 m away from the foot of a tower, the angle of elevation of the top is 30°. Find the height of the tower.A) 20√3 mB) 60√3 mC) 30√3 mD) 60/√3 m
25. Q25.Cards numbered 11 to 60 are placed in a bag. One card is drawn at random. Find the probability that the card drawn is a multiple of 7.A) 7/50B) 1/10C) 3/25D) 2/25
26. Q26.Which of the following is equal to (sinA − cosA + 1)/(sinA + cosA − 1)?A) 1/(secA − tanA)B) secA + tanAC) 1/(secA + tanA)D) secA − tanA
27. Q27.Points A(−1, y) and B(5, 7) have their midpoint at (2, 3). Find the value of y.A) −1B) 1C) −3D) 3
28. Q28.Mr. Kumar deposited ₹600 per month for 2 years in a recurring deposit account at 10% p.a. Find the maturity value.A) ₹15,900B) ₹16,500C) ₹15,600D) ₹16,100
29. Q29.If x, 5, y are in GP and x, −5/2, y are in AP, find the values of x and y.A) x = 1, y = 25B) x = −1, y = −25C) x = 5, y = 5D) x = 25, y = 1
30. Q30.Solve graphically: x + y = 3 and 3x − 2y = 4. The point of intersection is:A) (2, 1)B) (1, 2)C) (3, 0)D) (0, 3)
31. Q31.A triangle has sides 6 cm, 7 cm, and 8 cm. The incircle of this triangle is constructed. Using the formula r = Area/s, where s is the semi-perimeter, find the approximate inradius.A) 1.94 cmB) 2.00 cmC) 2.45 cmD) 1.63 cm
32. Q32.A shopkeeper buys an article for ₹500 and marks it up by 80%. He then offers a 25% discount. If GST is 18%, find the selling price (including GST) paid by the buyer.A) ₹796.50B) ₹826C) ₹750D) ₹810
33. Q33.Find the equation of a circle with centre (3, −2) and radius 5.A) x² + y² − 6x + 4y − 12 = 0B) x² + y² − 6x − 4y − 12 = 0C) x² + y² + 6x − 4y − 12 = 0D) x² + y² − 6x + 4y + 12 = 0
34. Q34.A hemispherical tank of radius 1.75 m is full of water. It is connected with a pipe of internal diameter 7 cm and water flows at 7 m/s. How long will it take to empty the tank (approximately)?A) 26.7 minutesB) 6.9 minutesC) 46.7 minutesD) 16.7 minutes
35. Q35.If two triangles are similar with sides in the ratio 3:5, what is the ratio of their areas?A) 9:25B) 3:5C) 6:10D) 27:125

Worked solutions from the ICSE 2025 paper

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