CBSE Class 10th Maths Answer Key 2025, Download PDF - All SETs

CBSE Class 10 Maths Answer Key 2025: The CBSE Class 10 Maths Exam 2025 took place on 10 March 2025. According to initial student reactions, the paper was moderately difficult. To help the students assess their performance, we have provided the CBSE Class 10 Maths Answer Key 2025 in this article. Subject experts prepared the answer key, which serves as an essential resource for students to verify their answers and estimate their scores. By using the answer key, students can learn from their mistakes and enhance their preparation for future exams.

This answer key is also helpful for the students who will be appearing for the compartment exam tomorrow. 

• CBSE Class 10 Maths Paper Analysis - Exam Review & Difficulty Level 
• CBSE Class 10 Maths Question Paper 2025 FREE (PDF)

CBSE Class 10 Maths Exam 2025: Highlights

The CBSE Class 10 Maths question paper had 38 questions for 80 marks. The time allowed to write the paper was 3 hours. All questions were compulsory with some questions having internal choices.

The Central Board of Secondary Education is conducting the Maths Compartment board exam tomorrow. This exam is an amazing oppurtunity for the students to score well in the exam and get promoted to the 11th class. Students can check these MCQ's to prepare for tomorrow's exam. 

To pass the compartment exam, students must score at least 33% in the subject. For subjects with practical components, students need to score 33% separately in theory, practical, and overall combined.

CBSE Class 10th Maths Exam 2025: High Weightage Topics

Check below some of the high-weightage topics for the Maths exam 2025: 

• Algebra (Quadratic Equations

• Arithmetic Progressions

• Pair of Linear Equations in Two Variables, Polynomials, and Geometry (Circles, Triangles, Introduction to Trigonometry, Some Applications of Trigonometry).

• Other important topics include Probability, Surface Areas and Volumes.

• Practising NCERT textbook questions and past year papers is highly recommended.

Features Of CBSE Class 10th Maths Answer Key?

1. Self-Evaluation:

Students can compare their answers with the official solutions to understand their performance.

2. Score Estimation:

By checking the answer key, students can predict their approximate marks before the official results are announced.

3. Identify Mistakes:

Analysing incorrect answers helps students understand their weak areas for improvement in future exams.

CBSE Class 10 Mathematics Marking Scheme 2024-2025

Check the CBSE 10th Maths Marking Scheme 2025 in the table below. 

CBSE Class 10 Maths Answer Key 2025

Set-1 Answer Key (Maths- STANDARD)

1. √0.4 is a/an
(A) natural number
(B) integer
(C) rational number
(D) irrational number
Answer: (D) irrational number

2. Which of the following cannot be the unit digit of 8ⁿ, where n is a natural number?
(A) 4
(B) 2
(C) 0
(D) 6
Answer: (C) 0

3. Which of the following quadratic equations has real and equal roots?
(A) (x+1)²=2x+1
(B) x²+x=0
(C) x²−4=0
(D) x²+x+1=0
Answer: (B) x²+x=0

4. If the zeroes of the polynomial ax²+bx+2a/b are reciprocal of each other, then the value of b is 

(A) 2
(B) 1/2
(C) -2
(D) −1/2

Answer: (A) 2

5. The distance of the point A(-3, -4) from the x-axis is
(A) 3
(B) 4
(C) 5
(D) 7
Answer: (B) 4

6. In the adjoining figure, PQ || XY || BC, AP = 2 cm, PX = 1.5 cm, and BX = 4 cm. If QY = 0.75 cm, then AQ + CY =

(A) 6 cm
(B) 4.5 cm
(C) 3 cm
(D) 5.25 cm
Answer: (B) 4.5 cm

7.Given △ABC ~ △PQR, ∠A = 30° and ∠Q = 90°. The value of (∠R + ∠B) is:
(A) 90°
(B) 120°
(C) 150°
(D) 180°

Answer: (C) 150°

8. Two coins are tossed simultaneously. The probability of getting at least one head is:

(A) 1/4

(B) 1/2

(C) 3/4

(D) 1

Answer: (C) 3/4

9. In the adjoining figure, PA and PB are tangents to a circle with center O such that ∠P = 90°. If AB = 3√2 cm, then the diameter of the circle is:

(A) 3√2 cm

(B) 6√2 cm

(C) 3 cm

(D) 6 cm

Answer: (D) 6 cm

10. For a circle with center O and radius 5 cm, which of the following statements is true?

P: Distance between every pair of parallel tangents is 5 cm.
Q: Distance between every pair of parallel tangents is 10 cm.
R: Distance between every pair of parallel tangents must be between 5 cm and 10 cm.
S: There does not exist a point outside the circle from where the length of the tangent is 5 cm.

(A) P
(B) Q
(C) R
(D) S

Answer: (B) Q

11. In the adjoining figure, TS is a tangent to a circle with center O. The value of 2x° is:

(A) 22.5
(B) 45
(C) 67.5
(D) 90

Answer: (B) 45°

12.If y= (2 tan 30°/ 1- tan²30°) then x : y = ?

Options:
(A) 1: 1
(B) 1: 2
(C) 2: 1
(D) 4: 1

Answer: (C) 2: 1

13. A  peacock sitting on the top of 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°

Answer: (C) 30°

14. If a cone of greatest possible volume is hollowed out from a solid wooden cylinder, then the ratio of the volume of remaining wood to the volume of the cone hollowed out is:

(A) 1: 1
(B) 1 : 3
(C) 2: 1
(D) 3: 1

Answer: (D) 2: 1

15.If the mode of some observations is 10 and the sum of mean and median is 25, then the mean and median respectively are:

(A) 12 and 13
(B) 13 and 12
(C) 10 and 15
(D) 15 and 10

Answer: (B) 13 and 12

16. If the maximum number of students has obtained 52 marks out of 80, then:

(A) 52 is the mean of the data.
(B) 52 is the median of the data.
(C) 52 is the mode of the data.
(D) 52 is the range of the data.

Answer: (C) 52 is the mode of the data.

17. The system of equations 2x+1=0 and 3y−5=0 has:

(A) Unique solution
(B) Two solutions
(C) No solution
(D) Infinite number of solutions

Answer: (A) Unique solution

18. In a right triangle ABC, right-angled at A, if sinB=1/4, then the value of sec B is:

(A) 4
(B) √15/4
(C) √15
(D) 4/√15

Answer: (D) 4/√15

(Assertion-Reason Type)

19. Assertion (A): For any two prime numbers p and q, their HCF is 1 and LCM is p+qp + qp+q.

Reason (R): For any two natural numbers, HCF × LCM = product of numbers.

Answer: (D) A is false, but R is true.

20. In an experiment of throwing a die,

Assertion (A): Event E₁ (getting a number less than 3) and Event E₂ (getting a number greater than 3) are complementary events.

Reason (R): If two events E and F are complementary, then:

P(E)+P(F)=1

Answer: (D) A is false, but R is true.

Set-2 Answer Key (Maths- STANDARD)

1. The system of equations x+5=0 and 2x−1=0 has
(A) No solution
(B) Unique solution
(C) Two solutions
(D) Infinite solutions
Answer: (B) Unique solution

2. In a right triangle ABC, right-angled at A, if sin⁡B=1/4, then the value of sec⁡B is
(A) 4
(B) √15/4
(C) √15
(D) 4/√15

Answer: (D) 4/√15

3. √0.4 is a/an
(A) natural number
(B) integer
(C) rational number
(D) irrational number
Answer: (D) irrational number

4. Which of the following cannot be the unit digit of 8ⁿ, where n is a natural number?
(A) 4
(B) 2
(C) 0
(D) 6
Answer: (C) 0

5. Which of the following quadratic equations has real and distinct roots?
(A) x²+2x=0
(B) x²+x+1=0
(C) (x−1)²=1−2x
(D) 2x²+x+1=0
Answer: (A)  x²+2x=0

6. If the zeroes of the polynomial ax²+bx+2a/b are reciprocal of each other, then the value of b is 

(A) 2
(B) 1/2
(C) -2
(D) −1/2

Answer: (A) 2

7. The distance of point (a, -b) from the x-axis is
(A) a
(B) -a
(C) b
(D) -b

Answer: (C) b

8. In the adjoining figure, PQ || XY || BC, AP = 2 cm, PX = 1.5 cm, and BX = 4 cm. If QY = 0.75 cm, then AQ + CY =

(A) 6 cm
(B) 4.5 cm
(C) 3 cm
(D) 5.25 cm
Answer: (B) 4.5 cm

9. Given ΔABC ~ ΔPQR, ∠A = 30° and ∠Q = 90°. The value of (∠R + ∠B) is
(A) 90°
(B) 120°
(C) 150°
(D) 180°

Answer: (C) 150°

10. Two coins are tossed simultaneously. The probability of getting at least one head is
(A) 1/4
(B) 1/2
(C) 3/4
(D) 1

Answer: (C) 3/4

11. In the adjoining figure, PA and PB are tangents to a circle with center O such that ∠P = 90°. If AB = 3√2 cm, then the diameter of the circle is:

(A) 3√2 cm

(B) 6√2 cm

(C) 3 cm

(D) 6 cm

Answer: (D) 6 cm

12.  If x = cos 30° - sin 30° and y = tan 60° - cot 60°, then

(A) x=y (B) x>у (C) x<у (D) x> 1, y <1

Answer: (C) x<y

13. For a circle with center O and radius 5 cm, which of the following statements is true?

P: Distance between every pair of parallel tangents is 5 cm.
Q: Distance between every pair of parallel tangents is 10 cm.
R: Distance between every pair of parallel tangents must be between 5 cm and 10 cm.
S: There does not exist a point outside the circle from where the length of the tangent is 5 cm.

(A) P
(B) Q
(C) R
(D) S

Answer: (B) Q

14. In the adjoining figure, TS is a tangent to a circle with center O. The value of 2x° is:

(A) 22.5
(B) 45
(C) 67.5
(D) 90

Answer: (B) 45°

15. A peacock sitting on the top of 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°

Answer: (A) 30°

16. If a cone of greatest possible volume is hollowed out from a solid wooden cylinder, then the ratio of the volume of remaining wood to the volume of the cone hollowed out is

(A) 1:1 (B) 1:3 (C) 2:1 (D) 3:1

Answer: (C) 2:1

17.  If the mode of some observations is 10 and the sum of the mean and the median is 25, then the mean and the median respectively are

(A) 12 and 13 (C) 10 and 15 (B) 13 and 12 (D) 15 and 1

Answer: (B) 13 and 12

 18. If the maximum number of students has obtained 52 marks out of 80, then,

(A) 52 is the mean of the data.

(B) 52 is the median of the data.

(C) 52 is the mode of the data.

(D) 52 is the range of the data.

Answer: (C) 52 is the mode of the data.

Directions: In Question Numbers 19 and 20, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option from the following:

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true, but Reason (R) is false.

(D) Assertion (A) is false, but Reason (R) is true.

19. Assertion (A): For two prime numbers x and y (x < y), HCF(x, y) = x and LCM(x, y) =y.

Reason (R): HCF(x, y) ≤ LCM(x, y), where x, y are any two natural numbers.

Answer: (A) is incorrect, but (R) is correct.

 20. In an experiment of throwing a die,

Assertion (A): Event E₁: getting a number less than 3 and Event E₂: getting a number greater than 3 are complementary events.

Reason (R): If two events E and F are complementary events, then P(E) +P(F) = 1.

Answer: (A) is incorrect, but (R) is correct

Set-3 Answer Key (Maths- STANDARD)

1. For a circle with centre O and radius 5 cm, which of the following statements is true?

P: Distance between every pair of parallel tangents is 5 cm.
Q: Distance between every pair of parallel tangents is 10 cm.
R: Distance between every pair of parallel tangents must be between 5 cm and 10 cm.
S: There does not exist a point outside the circle from which the length of the tangent is 5 cm.

(A) P
(B) Q
(C) R
(D) S

Answer: (B) Q

2. In the adjoining figure, AP and AQ are tangents to the circle with centre O. If reflex ∠POQ = 210°, the value of 2x is

(A) 30°
(B) 60°
(C) 120°
(D) 300°

Answer: (C) 120°

3. If x=2  sin⁡60^∘ cos⁡60^∘and y = sin²30° - cos²30° and x²= ky² , the value of k is

(A) √3
(B) √−3
(C) 3
(D) -3

Answer: (C) 3

4. A peacock sitting on the top of 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°

Answer: (A) 30°

5. If a cone of greatest possible volume is hollowed out from a solid wooden cylinder, then the ratio of the volume of remaining wood to the volume of the cone hollowed out is

(A) 1:1 (B) 1:3 (C) 2:1 (D) 3:1

Answer: (C) 2:1

6. If the mode of some observations is 10 and the sum of the mean and the median is 25, then the mean and the median respectively are

(A) 12 and 13 (C) 10 and 15 (B) 13 and 12 (D) 15 and 1

Answer: (B) 13 and 12

7. If the maximum number of students has obtained 52 marks out of 80, then,

(A) 52 is the mean of the data.

(B) 52 is the median of the data.

(C) 52 is the mode of the data.

(D) 52 is the range of the data.

Answer: (C) 52 is the mode of the data.

8. The system of equations y+a=0 and 2x=b has

(A) No solution
(B) (−a,b/2) as its solution
(C) (b/2,−a) as its solution
(D) Infinite solutions

Answer: (C) (b/2,−a)

9. In a right triangle ABC, right-angled at A, if sin 𝐵 =1/4,  then the value of sec 𝐵 is

(A) 4
(B) √15/4
(C) √15
(D) 4/√15

Answer: (D) 4/√15

10. √0.4 is a/an
(A) natural number
(B) integer
(C) rational number
(D) irrational number
Answer: (D) irrational number

11. Which of the following cannot be the unit digit of 8ⁿ, where n is a natural number?
(A) 4
(B) 2
(C) 0
(D) 6
Answer: (C) 0

12. Which of the following equations does not have a real root?

(A) x²=0
(B) 2x-1 =3 
(C) x² + 1 = 0
(D) x³ + x²= 0

Answer: (C) x² + 1 = 0

13. If the zeroes of the polynomial ax²+bx+2a/b are reciprocal of each other, then the value of b is 

(A) 2
(B) 1/2
(C) -2
(D) −1/2

Answer: 2

14. The distance of the point P(3a, 4a) from the y-axis is
(A) 3a
(B) -3a
(C) 4a
(D) -4a
Answer: (A) 3a 

15. In the adjoining figure, PQ || XY || BC, AP = 2 cm, PX = 1.5 cm, and BX = 4 cm. If QY = 0.75 cm, then AQ + CY =

(A) 6 cm
(B) 4.5 cm
(C) 3 cm
(D) 5.25 cm
Answer: (B) 4.5 cm

16. .Given △ABC ~ △PQR, ∠A = 30° and ∠Q = 90°. The value of (∠R + ∠B) is:
(A) 90°
(B) 120°
(C) 150°
(D) 180°

Answer: (C) 150°

17. Two coins are tossed simultaneously. The probability of getting at least one head is:

(A) 1/4

(B) 1/2

(C) 3/4

(D) 1

Answer: (C) 3/4

18. In the adjoining figure, PA and PB are tangents to a circle with center O such that ∠P = 90°. If AB = 3√2 cm, then the diameter of the circle is:

(A) 3√2 cm

(B) 6√2 cm

(C) 3 cm

(D) 6 cm

Answer: (D) 6 cm

In Question Numbers 19 and 20, a statement of Assertion (A) is followed by a statement of Reason (R).
Choose the correct option from the following:

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
(C) Assertion (A) is true, but Reason (R) is false.
(D) Assertion (A) is false, but Reason (R) is true.

19. Assertion (A): Event E₁: Getting a number less than 3 and Event E₂: Getting a number greater than 3 are complementary events.

Reason (R): If two events E and F are complementary events, then P(E) + P(F) = 1.

Answer: (D) Assertion (A) is false, but Reason (R) is true.

20. Assertion (A): For two odd prime numbers x and y, (x≠y): LCM(2x,4y)=4xy

Reason (R): LCM(x,y) is a multiple of HCF(x,y).

Answer: (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).

Set-1 Answer Key (Maths- BASIC)

1. In the given figure, the graph of polynomial p(x) is shown. Number of zeroes of p(x) is

(A) 3
(B) 2
(C) 1
(D) 4
Answer: (A) 3

2. 22nd term of the A.P: 3, 1/2, −1/2, −3....... is
(A) 45/2
(B) -9
(C) −39/2
(D) -21
Answer: (C) −39/2

3. The line $2x-3y=6$ intersects x-axis at

(A) (0, -2)
(B) (0, 3)
(C) (-2, 0)
(D) (3, 0)
Answer: (D) (3,0)

4. Two identical cones are joined as shown in the figure. If the radius of the base is 4 cm and the slant height of the cone is 6 cm, then the height of the solid is

(A) 8 cm
(B) 4√5 cm
(C) 2√5 cm
(D) 12 cm
Answer: (B) 4√5 cm

5. The value of k for which the system of equations 3x−7y=1 and kx+14y=6 is inconsistent, is

(A) -6
(B) 2/3
(C) 6
(D) −3/2
Answer: (D) −3/2

6. Two dice are rolled together. The probability of getting a sum more than 9 is

(A) 5/6
(B) 5/18
(C) 1/6
(D) 1/2
Answer: (B) 5/18

7. ABCD is a rectangle with its vertices at (2, -2), (8, 4), (4, 8), and (-2, 2) taken in order. Length of its diagonal is

(A) 4√2
(B) 6√2
(C) 4√26
(D) 2√26
Answer: (B) 6√2

8. In the given figure, PA is tangent to a circle with center O. If ∠APO = 30° and OA = 2.5 cm, then OP is equal to

(A) 2.5 cm
(B) 5 cm
(C) 5√3
(D) 2 cm

Answer: (C) 5√3

9. If the probability of happening of an event is 57%, then the probability of non-happening of the event is:

(A) 0.43
(B) 0.57
(C) 53%
(D) 1/57

Answer: (A) 0.43

10. OAB is a sector of a circle with centre O and radius 7 cm. If length of arc AB = 22/3 cm, then ∠AOB is equal to
(A) (120/7)°
(B) 45°
(C) 60°
(D) 30°

Answer: (C) 60°

11. In △ABC, DE || BC. If AE = (2x + 1) cm, EC = 4 cm, AD = (x + 1) cm, and DB = 3 cm, then value of x is

(A) 1
(B) 1/2
(C) -1
(D) 1/3

Answer: (B) 1/2

12. Three coins are tossed together. The probability that exactly one coin shows a head, is
(A) 1/8
(B) 1/4
(C) 1
(D) 3/8

Correct Answer: (D) 3/8

13. In two concentric circles centred at O, a chord AB of the larger circle touches the smaller circle at C. If OA = 3.5 cm, OC = 2.1 cm, then AB is equal to

(A) 5.6 cm
(B) 2.8 cm
(C) 3.5 cm
(D) 4.2 cm

Answer: (D) 4.2 cm

14. If √3sin⁡θ=cos⁡θ, then value of θ is
(A) √3
(B) 60°
(C) 1/√3
(D) 30°

Correct Answer: (D) 30°

15. To 

Answer: (B) 

16. If the sum of first $n$ terms of an A.P. is given by S_n=n/2(3n+1), then the first term of the A.P. is
(A) 2
(B) 3/2
(C) 4
(D) 5/2

Answer: (A) 2

17. In △ABC, ∠B=90°, If AB/AC=1/2, then, $\cos C$ is equal to
(A) 3/2
(B) 1/2
(C) √3/2
(D) 1/√3

Answer: (D) 1/√3

18. The volume of air in a hollow cylinder is 450 cm³. A cone of the same height and radius as that of the cylinder is kept inside it. The volume of empty space in the cylinder is

(A) 225 cm³
(B) 150 cm³
(C) 250 cm³
(D) 300 cm³

Answer: (A) 225 cm³

(Assertion – Reason based questions)

Directions: In question numbers 19 and 20, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option:

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation for Assertion (A).
(C) Assertion (A) is true, but Reason (R) is false.
(D) Assertion (A) is false, but Reason (R) is true.

19. Assertion (A): (a+√b)⋅(a−√b) is a rational number, where a and b are positive integers.
Reason (R): Product of two irrationals is always rational.

Correct Answer: (C) Assertion (A) is true, but Reason (R) is false.

20. Assertion (A): △ABC∼△PQR  such that ∠A=65∘,∠C=60∘. Hence ∠Q=55∘.
Reason (R): Sum of all angles of a triangle is 180°.

Answer: (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

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