CBSE Class 12th Maths Sample Paper 2025 by Experts: Practice for Last Minute Revision

CBSE Class 12th Maths Board Exam 2025: The CBSE Class 12 Maths exam is scheduled for March 8, 2025 (Saturday). As an important subject, it plays a major role in boosting overall board exam scores. To help students prepare effectively, we provide the CBSE Class 12 Maths Sample Paper with Solutions. Designed by experts, this resource is ideal for last-minute revision and practising important questions. The solutions offer clarity on correct answers. Download the CBSE Class 12 Maths Paper PDF from the links below to strengthen your preparation and score well in the exam.

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CBSE Class 12th Maths Sample Paper 2025

SECTION A

GENERAL INSTRUCTIONS: 

• This Question paper contains five sections A, B, C, D and E. Each section is compulsory. However, there are internal choices in some questions. 
• Section A has 18 MCQs and 02 Assertion-Reason based questions of 1 mark each. 
• Section B has 5 Very Short Answer (VSA)-type questions of 2 marks each. 
• Section C has 6 Short Answer (SA)-type questions of 3 marks each. 
• Section D has 4 Long Answer (LA)-type questions of 5 marks each. 
• Section E has 3 source based/case based/passage based/integrated units of assessment (4 marks each) with sub parts.

1. If A = 

(a) 5A

(b) 10A

(c) 16A

(d) 32A

2. If A is a square matrix of order 3 such that |A| = 3 then the value of |adj(adjA)| 

(a)9 

(b) 81 

(c) 6 

(d) 27

3. 

(a)0

(b) 5⁰

(c) 5⁹

(d) 5¹²

4. Find the value of a d/dx (cos²x- sin²x/ cos x + sin x)

(a) Sinx +cosx 

(b) - cosx – sinx 

(c) −sinx −cosx 

(d) sinx -cosx

5. If A2 -A+I =0, then the inverse of A is 

(a)A+I 

(b)I-A 

(c) A-I 

(d)I+A 

6. If f(x) = 

(a)m =1,n=0

(b) m =𝑛 𝜋/2 +1

(c) n= 𝑚 𝜋/2

(d) n =m =𝜋/2

7. If the area of a triangle is 35 sq. units with vertices (2,-6), (5,4) and (k,4) then k is 

(a) 12 

(b) -2 

(c) -12,-2 

(d) 12,-2 

8. The value of

(a) 𝜋/2

(b) - 𝜋/2

(c) 0

(d) 2𝜋

9. Determine the sum of order and degree of the differential equation: 

(a) 2 

(b) 1 

(c) 3 

(d) 4

10. Evaluate 

(a) tanx + cotx 

(b) tanx- cotx +c

(c) 1 

(d) -1

11.   Solve the differential equation cos(𝑑𝑦/𝑑𝑥) = a, a∈ 𝑅.

Answer: b

12. 𝑎⃗ and 𝑏⃗unit vectors and 𝜃 is the angle between them then 𝑎⃗ + 𝑏⃗ is a unit vector if 𝜃 is equal to

(a) −2𝜋/3

(b) −𝜋/3

(c) 2𝜋/3

(d) 𝜋/3

13. Find the area of a parallelogram whose one diagonal is 2i+j-2k and one side is 3i +j –k

(a) √21 

(b) √6 

(c) √21/2

(d) 3√2

14.  |𝑎⃗ x 𝑏⃗ | 2 + |𝑎⃗. 𝑏⃗ | 2 =400 , |𝑎⃗| = 5 then find the value of |𝑏⃗| 

(a) 5

(b) 4

(c) 5√2

(d) √2

15. If objective function Z =px +qy is maximum at (4,-2) and maximum value is 10 such that p = 3q then find p &q 

(a) P = 3, q=1 

(b) p = -3 q = -1 

(c) p=3 , q= -1 

(d) p =-3 , q= 1

16. The point which does not lie in the half-plane 2x + 3y -12 < 0 is: (a)(2,1) 

(b)(1,2) 

(c)(-2,3) 

(d)(2,3)

17. A line makes angle α, β, γ with x-axis, y-axis and z-axis respectively, then cos 2α + cos 2β + cos 2γ is equal to 

(a) -1 

(b) 1 

(c) 3 

(d) 2

18. An urn contains 10 black and 5 white balls. Two balls are drawn from the urn one after the other without replacement. What is the probability that both drawn balls are black? 

(a) 3/7 

(b) 7/3 

(c) 1/7 

(d) ⅓

ASSERTION-REASON BASED QUESTIONS In the following questions, a statement of assertion (A) is followed by a statement of Reason (R). Choose the correct answer out of the following choices.

(a) Both A and R are true and R is the correct explanation of A. 

(b) Both A and R are true but R is not the correct explanation of A. 

(c) A is true but R is false. 

(d) A is false but R is true. 

19. Assertion (A) Range of 𝑡𝑎𝑛⁻¹ x is (− 𝜋/2 , 𝜋/2 ) 

Reason (R) Domain of 𝑡𝑎𝑛⁻¹ x is R 

(b) Both A and R are true but R is not the correct explanation of A. 

20. Assertion (A) The position vector of a particle in a rectangular coordinate system is (3,2,5) then its position vector is 3𝑖̂+5𝑗̂+ 3 𝑘̂

Reason (R) the displacement vector of the particle that moves from (2,3,5) to the point (3,4,5) is 𝑖̂+𝑗̂

(d) A is false but R is true. 

SECTION B

This section comprises of very short answer type-questions (VSA) of 2 marks each. 

21. Find the value of 𝑠𝑖𝑛−1 (cos 3𝜋 /5 )

OR

Prove that the f 𝑅 → 𝑅 𝑑𝑒𝑓𝑖𝑛𝑒𝑑 𝑏𝑦 f ( x) = 𝑥³ + 4 is one one and onto

Answer: −𝜋/10 OR Proof

22. If 𝑎⃗ = 𝑖̂+ 𝑗̂− 5𝑘̂ and𝑏⃗=𝑖̂-4 𝑗̂+3 𝑘̂ find a unit vector parallel to 𝑎⃗+𝑏⃗

OR

Find the direction cosines of a line passing through the origin and lying in the first quadrant, making equal angles with the three coordinate axis

Answer: 

23. Solve x log x 𝑑𝑦/𝑑𝑥 + y = 2/𝑥 log x

Answer: Y log x = −2/𝑥 (1+logx) +c

24. If |𝑎⃗| = 4 ,|𝑏⃗| = 3 and 𝑎⃗. 𝑏⃗ =6√3 find |𝑎⃗ x 𝑏⃗ | 

Answer: 6

25. Water is leaking from a conical funnel at the rate of 5 cubic centimeters per second. if the radius of the base of the funnel is 10 cm and the altitude is 20 cm , find the rate at which the water level is dropping when it is 5cm from the top

Answer: 4/45𝜋 

SECTION C

(This section comprises of short answer type questions (SA) of 3 marks each)

26. Evaluate

Answer: 

27. Bag A contains 4 black and 6 red balls and Bag B contains 7 black and 3 red balls. A die is thrown if 1 or 2 appears, bag A is chosen, otherwise bag B. If two balls are drawn at random without replacement from the selected bag, find the probability of getting one red and one black.

OR

In a game, a man wins Rs 5 for 6 and loses rupees one for any other number, when a fair die is thrown. The man decided to throw a die thrice but quits as and when he gets a six. Find the expected value of the amount he wins/loses.

Answer: P(E1) = 2/6 , P(E2) = 4/6 , P(A/E1) = 24/45 P(A/E2) = 21/45 ,P(A) = 22/45

OR

X = 4,3,-3 P(x=5) =1/6 , P(x=4) = 5/36 , P(x=3) = 25/216 , P(x=-3) =125/216 ,E(x)=0

28. 𝐸𝑣𝑎𝑙𝑢𝑎𝑡𝑒 ∫ 𝑡𝑎𝑛⁻¹ x dx

Answer: 

29. Evaluate

Answer: 

30. Maximise Z = 80x +120y subject to constraints 9x +12y ≤ 180 , 3𝑥 + 4𝑦 ≤ 60, 𝑥 + 3𝑦 ≤ 30, 𝑥 ≥ 0 𝑦 ≥ 0.

Answer: Max Z= 1680 and max point is (12,6)

31. Solve

Answer:

SECTION D

(This section comprises of long answer-type questions (LA) of 5 marks each)

32. If A= 

Answer: X= 2, y= -1, z= 4

33. Find the area of the region { (x,y) : 𝑥² + 𝑦 ² ≤ 4 , x + y ≥ 2 } using integration. 

Answer: 

34. Let N be the set of all natural numbers and R be a relation defined by (𝑎, 𝑏) 𝑅 (𝑐, 𝑑)) If bc(a+d) = ad(b+c). show that R is an equivalence relation. 

Answer: Proof

35. Find the points on the line 𝑥+2 3 = 𝑦+1 2 = 𝑧−3 2 at a distance of 5 units from the point ( 1,3,3 )

OR

Find the foot of the perpendicular from ( 0,2,3 ) on the line 𝑟⃗ = -3𝑖̂ + 𝑗̂-4𝑘̂ +k(5𝑖̂ + 2 𝑗̂+3𝑘̂ ) 

Answer: Points are (-2,-1,3) and (4,3,7)

OR

K =1, Point is (2,3,-1)

SECTION E 

36. A telephone company in a town has 500 subscribers on its list and collects fixed charges of 300 per subscriber per year. The company proposes to increase the annual subscription and it is believed that for every increase of 1 one subscriber, one will discontinue the service.

(i) If x be the annual subscription, then the total revenue of the company after increment will be

(ii) How much fee the company should increase to have maximum profit.

Correct Answer:

(i) R(x)= (500-x)(300+x) = –x 2+200x+150000

(ii) 100

37. One day, a sangeet mahotsav is to be organised in an open area of Rajasthan. In recent years, it has rained only 6 days each year. Also, it is given that when it actually rains, the weatherman correctly forecasts rain 80% of the time. When it doesn’t rain, he incorrectly forecasts rain 20% of the time. If leap year is considered, then answer the following questions.

(i) The probability that it rains on a chosen day is

(ii) The probability that it does not rain on the chosen day is

(iii) The probability that the weatherman predicts correctly is

(iv) The probability that it will rain on the chosen day, if the weatherman predicts rain for that day, is

Correct Answer:

(i) 1/61

(ii) 60/61

(iii) 4/5

(iv) 0.94

38. The Relation between the height of the plant (y in cm) with respect to exposure to sunlight is governed by the following equation y = 4x-1/2 x² where x is the number of days exposed to sunlight.

(i) The rate of growth of the plant with respect to sunlight is

(ii) What is the number of days it will take for the plant to grow to the maximum height?

(iii) What is the maximum height of the plant?

(iv) If the height of the plant is 7/2 cm, the number of days it has been exposed to the sunlight is

Correct Answer:

(i) 4 – x

(ii) 4

(iii) 8cm

(iv) 1

 Other Related Links

• NCERT Books for Class 12 (Revised Edition)

• NCERT Solutions for Class 12 (Updated)

• CBSE Class 12 Syllabus (All Subjects) 2024-25

• CBSE Class 12 Sample Papers (All Subjects) 2024-25