ISC Class 12th Maths Question Paper and Answer key 2025: The ISC Class 12 Maths Exam 2025 was conducted on March 3, 2025, with the help of the Council for the Indian School Certificate Examinations (CISCE). This exam plays an important role in the students' academic journey, testing their understanding of Mathematical concepts.
ISC Class 12 Maths 2025 Exam Overview
Exam Date: [3rd March, 2025]
Subject Code: [227]
Exam Duration: 3 Hours
Maximum Marks: 70
Also, check:
ISC Class 12th Maths Exam Pattern 2025
Here's a tabular format showing the types of questions for the ISC Class 12 Mathematics exam, along with their weightage in percentage:
| Question Type | Description | Weightage (%) |
| Very Short Answer (VSA) | Simple, direct questions that test basic understanding and recall of concepts. | 20% |
| Short Answer (SA) | Requires slightly detailed responses, often involving calculations or steps. | 30% |
| Long Answer (LA) | In-depth questions that test understanding, analytical skills, and application. | 30% |
| Application/Case-based | Real-life or case-based problems requiring application of mathematical concepts. | 20% |
| Total |
| 100% |
Also, check: CBSE Class 10th Maths Top 50 MCQ’s For Board Exam 2025
ISC Class 12 Maths Answer Key 2025
Students must be eagerly waiting to check their answers after giving the exam. Well, here, we are providing the answer key. Students can check their answers and can also calculate their estimated score.
SECTION A
Question 1
In subparts (i) to (xi) choose the correct options and in subparts (xii) to (xv), answer the questions as instructed.
(i)
(a) Unit matrix
(b) Null matrix
(c) Diagonal matrix
(d) Skew matrix
Answer: (b) Null matrix
(ii) Which of the following is a homogeneous differential equation?
(a) (4x2+6y+5)dy−(3y2+2x+4)dx=0
(b) (xy)dx−(x3+y3)dy=0
(c) (x3+2y2)dx+2xydy=0
(d) y2dx+(x2−xy−y2)dy=0
Answer: (d) y2dx+(x2−xy−y2)dy=0
(iii) Consider the graph of the function f(x) shown below:
Statement 1: The function f(x) is increasing in (1/2,2)
Statement 2: The function f(x) is strictly increasing in (1/2,1)
Which of the following is correct with respect to the above statements?
(a) Statement 1 is true and Statement 2 is false.
(b) Statement 2 is true and Statement 1 is false.
(c) Both the statements are true.
(d) Both the statements are false.
Answer: (c) Both the statements are true.
(iv)
is equal to:
(a) 2/3
(b) 1/3
(c) −2/3
(d) 0
Answer: (c) −2/3
(v) Assertion: Consider the two events A and B such that n(A)=n(B) and P(A/B) = P(B/A).
Reason: The events A and B are mutually exclusive.
Options:
(a) Both Assertion and Reason are true and Reason is the correct explanation for Assertion.
(b) Both Assertion and Reason are true but Reason is not the correct explanation for Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.
Answer: (d) Assertion is false and Reason is true.
(vi)
Answer: (d) 𝑘 only
(vii) A cylindrical popcorn tub of radius 10 cm is being filled with popcorn at the rate of 314 cm³ per minute. The level of the popcorn in the tub is increasing at the rate of:
(a) 1 cm/minute
(b) 0.1 cm/minute
(c) 1.1 cm/minute
(d) 0.5 cm/minute
Correct Answer: (a) 1 cm/minute
(viii)
Correct Answer: (c) 2
(ix) Assertion: If Set A has m elements, Set B has n elements and n<m, then the number of one-one function(s) from A to B is zero.
Reason: A function f: A→B is defined only if all elements in Set A have an image in Set B.
(a) Both Assertion and Reason are true and Reason is the correct explanation for Assertion.
(b) Both Assertion and Reason are true but Reason is not the correct explanation for Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.
Correct Answer: (b) Both Assertion and Reason are true but Reason is not the correct explanation for Assertion.
(x) Let XXX be a discrete random variable. The probability distribution of XXX is given below:
| X | 30 | 10 | -10 |
|---|---|---|---|
| P(X) | 1/5 | 1/3 | 1/2 |
Then E(X) will be:
(a) 1
(b) 4
(c) 30
(d) 0
Correct Answer: (b) 4
(xi) Statement 1: If ‘A’ is an invertible matrix, then (A3)−1=(A−1)3
Statement 2: If ‘A’ is an invertible matrix, then ∣A−1∣=∣A∣−1
(a) Statement 1 is true and Statement 2 is false.
(b) Statement 2 is true and Statement 1 is false.
(c) Both the statements are true.
(d) Both the statements are false.
Correct Answer: (c) Both the statements are true.
(xii) Write the smallest equivalence relation from the set A to A, where A = {1, 2, 3}.
Correct Answer: The smallest equivalence relation is the reflexive relation: R={(1,1),(2,2),(3,3)}
(xiii)
Correct Answer: For A to be skew symmetric, AT=−A. Solving, we get x=2
(xiv) Three critics review a book. Odds in favor of the book are 5:2, 4:3, and 3:4 respectively for the three critics. Find the probability that all critics are in favor of the book.
Correct Answer: The probability that all three critics favor the book is:
5/7x 4/7x3/7= 60/343
We are updating answers to the remaining questions. Keep visiting this page for the complete solution of the paper.
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