CBSE Maths 2025

CBSE Class 10 Maths 2025 — all 38 questions from the paper

The complete question list from the CBSE 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.√0.4 is a/an:A) Natural numberB) IntegerC) Rational numberD) Irrational number
2. Q2.Which of the following cannot be the unit digit of 8ⁿ, where n is a natural number?A) 4B) 2C) 0D) 6
3. Q3.Which of the following quadratic equations has real and equal roots?A) (x+1)² = 2x + 1B) x² + x = 0C) x² − 4 = 0D) x² + x + 1 = 0
4. Q4.If the zeroes of the quadratic polynomial ax² + bx + (2a/b) are reciprocal of each other, then the value of b is:A) 2B) 1/2C) −2D) −1/2
5. Q5.The distance of the point A(−3, −4) from the x-axis is:A) 3B) 4C) 5D) 7
6. Q6.In a triangle ABC, PQ ∥ XY ∥ BC where P and X are points on AB, and Q and Y are on AC. If AP = 2 cm, PX = 1.5 cm, BX = 4 cm and QY = 0.75 cm, then AQ + CY equals:A) 6 cmB) 4.5 cmC) 3 cmD) 5.25 cm
7. Q7.If ΔABC ~ ΔPQR, ∠A = 30° and ∠Q = 90°, then the value of (∠R + ∠B) is:A) 90°B) 120°C) 150°D) 180°
8. Q8.Two coins are tossed simultaneously. The probability of getting at least one head is:A) 1/4B) 1/2C) 3/4D) 1
9. Q9.PA and PB are tangents drawn to a circle with centre O. If ∠APB = 90° and AB = 3√2 cm, then the diameter of the circle is:A) 3√2 cmB) 6√2 cmC) 3 cmD) 6 cm
10. Q10.A circle has centre O and radius 5 cm. Which of the following statements is true?
    P: Distance between two parallel tangents is 5 cm
    Q: Distance between two parallel tangents is 10 cm
    R: Distance between two parallel tangents is between 5 and 10 cm
    S: No point outside the circle has tangent length exactly 5 cmA) Statement PB) Statement QC) Statement RD) Statement S
11. Q11.TS is a tangent to a circle with centre O at point T on the circle. OT is a radius. If ∠OTS = 90° and ∠TOS = 2x°, then the value of 2x° is:A) 22.5B) 45C) 67.5D) 90
12. Q12.If x = 2tan30°/(1 + tan²30°) and y = 2tan30°/(1 − tan²30°), then x : y equals:A) 1 : 1B) 1 : 2C) 2 : 1D) 4 : 1
13. Q13.A peacock sitting on a tree of height 10 m observes a snake moving on the ground. If the snake is 10√3 m away from the base of the tree, then the angle of depression of the snake from the eye of the peacock is:A) 30°B) 45°C) 60°D) 90°
14. Q14.A cone of the greatest volume is hollowed out from a solid wooden cylinder. The ratio of the volume of the remaining wood to the volume of the cone is:A) 1 : 1B) 1 : 3C) 2 : 1D) 3 : 1
15. Q15.If the mode of a distribution is 10 and the sum of mean and median is 25, then the mean and median of the data are respectively:A) 12 and 13B) 13 and 12C) 10 and 15D) 15 and 10
16. Q16.In a class test, maximum number of students obtained 52 marks out of 80. Then 52 is the:A) MeanB) MedianC) ModeD) Range
17. Q17.The system of equations 2x + 1 = 0 and 3y − 5 = 0 has:A) A unique solutionB) Two solutionsC) No solutionD) Infinite solutions
18. Q18.In a right triangle ABC, right-angled at A, if sinB = 1/4, then the value of secB is:A) 4B) √15/4C) √15D) 4/√15
19. Q19.Assertion (A): For two prime numbers p and q, their HCF is 1 and LCM is p + q.
    Reason (R): For two natural numbers, HCF × LCM = Product of the numbers.
    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.A die is thrown once. Event E₁ is 'getting a number less than 3' and E₂ is 'getting a number greater than 3'.
    Assertion (A): E₁ and E₂ are complementary events.
    Reason (R): If E and F are complementary events, then P(E) + P(F) = 1.
    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.Find the values of a and b so that x⁴ + x³ + 8x² + ax + b is divisible by x² + 1.A) a = 1, b = 8B) a = 1, b = 7C) a = 8, b = 1D) a = 7, b = 1
22. Q22.How many two-digit numbers are divisible by 6?A) 15B) 14C) 16D) 13
23. Q23.PA and PB are tangents drawn from an external point P to a circle with centre O. If ∠APB = 80°, what is ∠APO?A) 80°B) 50°C) 40°D) 60°
24. Q24.The point P(x, 2) divides the line segment joining A(12, 5) and B(4, −3) in a certain ratio. What is this ratio?A) 3 : 5B) 5 : 3C) 2 : 3D) 3 : 2
25. Q25.12 defective pens are mixed with 132 good pens. One pen is taken out at random from the lot. What is the probability that the pen taken out is not defective?A) 11/12B) 1/12C) 11/13D) 1/11
26. Q26.If x = √3 + √2 and y = √3 − √2, what is the value of x² + y²?A) 8B) 10C) 12D) 6
27. Q27.Two students A and B solved a pair of linear equations. A correctly solved the second equation but made a mistake in the first, getting the solution (1, 2). B correctly solved the first equation but made a mistake in the second, getting (−1, 3). What is the correct solution of the pair of equations?A) (1, 3)B) (−1, 2)C) (2, 1)D) (−1, −2)
28. Q28.What are the zeroes of the polynomial 3x² − x − 4?A) 4/3 and −1B) −4/3 and 1C) 4/3 and 1D) −4/3 and −1
29. Q29.If sinA = 3/5, what is the value of (cotA + cosecA)(cotA − cosecA)?A) -1B) 1C) 7/9D) -7/9
30. Q30.A tree breaks due to a storm and the broken part bends so that the top of the tree touches the ground making an angle of 30° with it. The distance between the foot of the tree and the point where the top touches the ground is 30 m. What is the height of the tree?A) 30√3 mB) 20√3 mC) 10√3 mD) 15√3 m
31. Q31.Find the mean of the following frequency distribution:
    Class: 0–10 (f = 8), 10–20 (f = 16), 20–30 (f = 36), 30–40 (f = 34), 40–50 (f = 6).
    What is the mean?A) 24.4B) 25.4C) 26.4D) 27.4
32. Q32.Two water taps together can fill a tank in 6 hours. The tap with the larger diameter takes 9 hours less than the smaller one to fill the tank separately. How many hours does the smaller tap take to fill the tank alone?A) 18 hoursB) 9 hoursC) 12 hoursD) 15 hours
33. Q33.A 4 m wide path surrounds a circular pond. If the area of the path is 11/25 of the area of the pond, what is the radius of the pond?A) 40 mB) 20 mC) 36 mD) 50 m
34. Q34.PQ and RS are two parallel tangents to a circle with centre O, touching the circle at T and U respectively. If ∠QPT = 50° and ∠RUS = 60°, what is the value of ∠TOU?A) 110°B) 125°C) 100°D) 120°
35. Q35.A triangle has vertices A(4, −6), B(3, −2), and C(5, 2). What is the length of the median from vertex A to the midpoint of BC?A) 5B) 6C) √34D) √13
36. Q36.An electrician has to repair an electrical fault on a pole at a height of 5 m. She needs to reach a point 1.3 m below the top of the pole to undertake the repair work. She uses a ladder inclined at 60° to the horizontal. What is the length of the ladder that she should use?A) (7.4√3)/3 mB) (7.4)/√3 mC) 3.7√3 mD) 7.4/3 m
37. Q37.ABCD is a trapezium with AB ∥ DC. Diagonals AC and BD intersect at point P. If PA = PC/3 and AB = 3 cm, DC = 5 cm, what is the ratio AB : DC?A) 3 : 5B) 5 : 3C) 1 : 3D) 9 : 25
38. Q38.A bag contains balls numbered 1 to 50. A ball is drawn at random from the bag. What is the probability that the number on the drawn ball is a perfect square?A) 7/50B) 1/10C) 3/25D) 1/5

Worked solutions from the CBSE 2025 paper

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