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Class 12 ISC Mathematics Answer Key 2025 (Available): Unofficial key PDF download

Prasanthi Boodati

Updated On: March 26, 2025 05:02 PM

For the exam held on March 3, Class 12 ISC Mathematics Answer Key 2025 will be provided here. The answer key is unofficial and given for all set codes.

Class 12 ISC Mathematics Answer Key 2025Class 12 ISC Mathematics Answer Key 2025

Class 12 ISC Mathematics Answer Key 2025: Candidates who appeared for the Class 12 ISC Mathematics 2025 examination can access unofficial answer keys for objective-type questions. As the exam has ended on March 3, 2025 , at 5 PM, our subject experts have provided answers for Section A, i.e., from sub sections (i) to (x) which consist of objective questions. However, the answers for Sections B and C will not be provided, as these sections depend on individual student calculations.

The question paper of the Class 12 ISC Mathematics exam was worth 80 marks and divided into three sections with a total of 22 questions. Section A contained 14 questions, of which question 1 included sub-sections of 11 multiple-choice and 4 short answer questions, each carrying one mark. The remaining 2 to 6, 7 to 10, and 11 to 17 questions carried 2, 4 and 6 marks respectively. Sections B and C will contain solution-based questions, with internal choices available in Sections C and D, totaling 15 marks. Section A was compulsory and they had to attempt either Section B or C.

Also Read | Class 12 ISC Result Expected Release Date 2025

Class 12 ISC Mathematics Answer Key 2025

Obtain unofficial answer key solutions for Section A Questions 1 here and anticipate your marks.

Check the expert's answers for Question 1 comprising (i) to (xv) multiple-choice questions in the tabular format below.

Question

ISC Mathematics Answer Key 2025

(i) If A = then A 16 is:
(a) Unit matrix
(b) Null matrix
(c) Diagonal matrix
(d) Skew matrix

(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 + 2xy dy = 0
(d) dy² dx + (x² - xy - y²) dy = 0

(d) dy² dx + (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 (2).
Statement 2: The function f(x) is strictly increasing in (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.

(c) Both the statements are true.

(iv) is equal to:
(a) 2/3
(b) 1/3
(c) -2/3
(d) 0

(c) -2/3

(v) Assertion: Consider the two events A and B such that n(A) = n(B), P(A/B) = P(B/A)
Reason: The events A and B are mutually exclusive.
(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.

(c) Assertion is true and Reason is false.

(vi) The existence of unique solution of the system of equations x + y = λ, 5x + ky = 2 depends on:
(a) λ only
(b) λ/k = 1
(c) both k and λ
(d) k only

(b) λ/k = 1

(vii) A cylindrical popcorn tub of radius 10 cm is being filled with popcorns at the of 314 cm³ per minute. The level of the popcorn in the tub is increasing at the of:
(a) 1 em/minute
(b) 0-1 cm/minute
(c) 1-1 cm/minute
(d) 0-5 cm/minute

(b) 0-1 cm/minute

(viii)
then the number of point (s) of discontinuity of f (x), is / are:
(a) 1
(b) 3
(c) 2
(d) 0

(a) 1

(ix) Assertion: If Set A has m elements, Set B has n elements and of one-one function(s) from AB is zero. then the number of one-one function(s) from A →B is zero.
Reason: A function f = A→B is defined only if all elements in Set A have an image 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 the Assertion
(c) Assertion is true and Reason is false
(d) Assertion is false and Reason is true

(b) Both Assertion and Reason are true but Reason is not the correct explanation for the Assertion

(x) Let X be a discrete random variable. The probability distribution of X is given below:

X 30 10 -10
P(X) 1/5 3/10 1/2

Then E(X) will be:
(a) 1
(b) 4
(c) 2
(d) 30

(d) 30

(xi) Statement 1: If A is an invertible matrix, then (A 2 ) -1 = (A -1 ) 2
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.

(c) Both the statements are true.

Class 12 ISC Mathematics Exam Analysis 2025 Link

Learners can click on the link to view the analysis of the Class 12 ISC Mathematics exam for 2025 and evaluate their exam results.

Class 12 ISC Subject-Wise Answer Key 2025 |

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Commerce Class 12 ISC Commerce Answer Key 2025
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Physical Education Class 12 ISC Physical Education Answer Key 2025

Class 12 ISC Mathematics Answer Key 2025 Live Updates

  • 11 00 PM IST - 03 Mar'25

    ISC Class 12 Mathematics Answer Key 2025: Section A Question 1 (xi) Answer

    Ques: (xi) Statement 1: If A is an invertible matrix, then (A2)-1 = (A-1)2
    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.

    Ans: Option C

  • 10 40 PM IST - 03 Mar'25

    ISC Class 12 Mathematics Answer Key 2025: Section A Question 1 (x) Answer

    Ques: Let X be a discrete random variable. The probability distribution of X is given below:

    X3010-10
    P(X)1/53/101/2

    Then E(X) will be:
    (a) 1
    (b) 4
    (c) 2
    (d) 30

    Ans: Option D

  • 10 20 PM IST - 03 Mar'25

    ISC Class 12 Mathematics Answer Key 2025: Section A Question 1 (ix) Answer

    Ques: (ix) Assertion: If Set A has m elements, Set B has n elements and of one-one function(s) from AB is zero. then the number of one-one function(s) from A →B is zero. 
    Reason: A function f = A→B is defined only if all elements in Set A have an image 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 the Assertion
    (c) Assertion is true and Reason is false
    (d) Assertion is false and Reason is true

    Ans: Option B

  • 10 00 PM IST - 03 Mar'25

    ISC Class 12 Mathematics Answer Key 2025: Section A Question 1 (viii) Answer

    Ques: (viii) 
    then the number of point (s) of discontinuity of f (x), is / are: 
    (a) 1
    (b) 3
    (c) 2
    (d) 0

    Ans: (a) 1

  • 09 40 PM IST - 03 Mar'25

    ISC Class 12 Mathematics Answer Key 2025: Section A Question 1 (vii) Answer

    Ques: (vii) A cylindrical popcorn tub of radius 10 cm is being filled with popcorns at the of 314 cm³ per minute. The level of the popcorn in the tub is increasing at the of:
    (a) 1 em/minute
    (b) 0-1 cm/minute
    (c) 1-1 cm/minute
    (d) 0-5 cm/minute

    Ans: Option B

  • 09 20 PM IST - 03 Mar'25

    ISC Class 12 Mathematics Answer Key 2025: Section A Question 1 (vi) Answer

    Ques: (vi) The existence of unique solution of the system of equations x + y = λ, 5x + ky = 2 depends on:
    (a) λ only
    (b) λ/k = 1
    (c) both k and λ
    (d) k only

    Ans: Option B

  • 09 00 PM IST - 03 Mar'25

    ISC Class 12 Mathematics Answer Key 2025: Section A Question 1 (v) Answer

    Ques: (v) Assertion: Consider the two events A and B such that n(A) = n(B), P(A/B) = P(B/A)
    Reason: The events A and B are mutually exclusive.
    (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.

    Ans: Option C

  • 08 40 PM IST - 03 Mar'25

    ISC Class 12 Mathematics Answer Key 2025: Section A Question 1 (iv) Answer

    Ques: (iv) is equal to:
    (a) 2/3
    (b) 1/3
    (c) -2/3
    (d) 0

    Ans: Option C

  • 08 20 PM IST - 03 Mar'25

    ISC Class 12 Mathematics Answer Key 2025: Section A Question 1 (iii) Answer

    Ques: (iii) Consider the graph of the function f(x) shown below: 
    Statement 1: The function f(x) is increasing in (2).
    Statement 2: The function f(x) is strictly increasing in (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.

    Ans: Option C

  • 08 00 PM IST - 03 Mar'25

    ISC Class 12 Mathematics Answer Key 2025: Section A Question 1 (ii) Answer

    Ques: (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 + 2xy dy = 0
    (d) dy² dx + (x² - xy - y²) dy = 0

    Ans: Option D

  • 07 40 PM IST - 03 Mar'25

    ISC Class 12 Mathematics Answer Key 2025: Section A Question 1 (i) Answer

    Ques: (i) If A = then A16 is:
    (a) Unit matrix
    (b) Null matrix
    (c) Diagonal matrix
    (d) Skew matrix

    Ans: Option B

  • 07 20 PM IST - 03 Mar'25

    ISC Class 12 Mathematics Answer Key 2025: Which was the lengthiest section?

    In the overall paper, Section C was the lengthiest section among all.

  • 07 00 PM IST - 03 Mar'25

    Class 12 ISC Mathematics Answer Key 2025: Student Reactions

    Students opined that the paper was overall moderate. Calculus was a little time-consuming but easy. Most questions came from last year's paper.

  • 06 45 PM IST - 03 Mar'25

    Class 12 ISC Mathematics Answer Key 2025: Which was the most time-consuming section?

    As per the student reviews, the overall paper was not time-consuming. However, the Calculus questions required a lot of logical reasoning, and thoughtful answers. 

  • 06 30 PM IST - 03 Mar'25

    Class 12 ISC Mathematics Answer Key 2025: Difficulty Level of Section C

    Based on the initial feedback, the overall difficulty level of Section C is Moderate.

  • 06 15 PM IST - 03 Mar'25

    Class 12 ISC Mathematics Answer Key 2025: Difficulty Level of Section B

    Based on the initial feedback, the overall difficulty level of Section B is Moderate.

  • 06 00 PM IST - 03 Mar'25

    Class 12 ISC Mathematics Answer Key 2025: Difficulty Level of Section A

    Based on the initial feedback, the overall difficulty level of Section A is Easy to Moderate.

  • 05 45 PM IST - 03 Mar'25

    Class 12 ISC Mathematics Answer Key 2025: Overall Difficulty Level of the Paper

    Based on the initial feedback, the overall difficulty level of the paper is Moderate.

  • 05 30 PM IST - 03 Mar'25

    Class 12 ISC Mathematics Answer Key 2025: Score-Revalution

    If students are not satisfied with their score, they must apply for the score-revaluation, in accordance with CISCE’s rules and regulations.


     

  • 05 15 PM IST - 03 Mar'25

    Class 12 ISC Mathematics Answer Key 2025: Answer Keys Soon

    Our subject-experts will be providing the solutions for the Class 12 ISC Mathematics Answer Key 2025 shortly.  Be sure to keep refreshing the page for updates.


     

  • 05 00 PM IST - 03 Mar'25

    Class 12 ISC Mathematics Answer Key 2025: Exam Over


    CISCE has announced that the Class 12 ISC Mathematics exam concluded at 5 PM. Students can access the Mathematics answer key on the official CISCE website or through other reliable sources.

  • 04 40 PM IST - 03 Mar'25

    Class 12 ISC Mathematics Answer Key 2025: 20 Minutes for the conclusion of exam

    For Class 12 ISC Mathematics exam, only 20 minutes are left for the exam to conclude, stay tuned on this page for the official answer key. 


     

  • 04 20 PM IST - 03 Mar'25

    Class 12 ISC Mathematics Answer Key 2025: Importance of Answer Keys

    With the help of answer keys of Class 12 ISC Mathematics 2025, students can evaluate their performance, improvement of areas, and expect their scores.


     

  • 04 00 PM IST - 03 Mar'25

    Class 12 ISC Mathematics Answer Key 2025: Remaining one hour

    Students should begin to revise their answers with only one hour remaining for the Class 12 ISC Mathematics 2025. This final hour is crucial for reviewing that all answers are to be accurate.


     

  • 03 40 PM IST - 03 Mar'25

    Class 12 ISC Mathematics Answer Key 2025: Passing Marks

    Students are required to attain at least 40% of the total marks in both the theory and practical exams to achieve grades in the Class 12 ISC examination 2025.


     

  • 03 20 PM IST - 03 Mar'25

    Class 12 ISC Mathematics Answer Key 2025: Are all the Questions compulsory?

    Yes, all the questions are compulsory to be answered in Section A. While, students must choose and attempt either Section B or C.


     

  • 03 00 PM IST - 03 Mar'25

    Class 12 ISC Mathematics Answer Key 2025: Section-Wise Weightage

    • Section A: 65 Marks
    • Section B: 15 Marks
    • Section C: 15 Marks

  • 02 20 PM IST - 03 Mar'25

    Class 12 ISC Mathematics Answer Key 2025: Marking scheme of Section B

    In this section, there will be 4 questions (15 to 18). ie, 

    • Question 15: 5 Marks
    • Question 16: 2 Marks
    • Questions (17 to 18): 4 Marks  

  • 02 00 PM IST - 03 Mar'25

    Class 12 ISC Mathematics Answer Key 2025: Exam Commences

    Class 12 ISC Mathematics paper exam began at 2 PM, after all the students had entered the examination. 


     

  • 01 40 PM IST - 03 Mar'25

    Class 12 ISC Mathematics Answer Key 2025: Most Important Chapters for Section B

    • Vectors
    • Three-Dimensions Geometry
    • Applications of Integrals

     

  • 01 20 PM IST - 03 Mar'25

    Class 12 ISC Mathematics Answer Key 2025: Most Important Chapters for Section A

    • Relations and Functions
    • Algebra
    • Calculs
    • Probability

  • 01 00 PM IST - 03 Mar'25

    Class 12 ISC Mathematics Answer Key 2025: Internal choice for Section A

    Yes, there will be an internal choice available for Class 12 ISC Mathematics Answers, with 2 questions each for 2, 4 and 6 mark questions in Section A.  


     

  • 12 45 PM IST - 03 Mar'25

    Class 12 ISC Mathematics Answer Key 2025: Marking scheme of Section A

    • Question 1 subparts (i) to (xv): 1 Mark
    • Questions (2 to 6): 2 Marks
    • Questions (7 to 10): 4 Marks
    • Questions (11 to 14): 6 Marks

  • 12 30 PM IST - 03 Mar'25

    Class 12 ISC Mathematics Answer Key 2025: Total number of questions in Section A

    Section A of Class 12 ISC Mathematics exam paper consists of a total of 11 questions and worth 65 marks.

  • 12 15 PM IST - 03 Mar'25

    Class 12 ISC Mathematics Answer Key 2025: Total of number of Sections

    According to the exam pattern, Class 12 ISC Mathematics 2025 exam paper contains 3 sections namely, sections A, B and C.


     

  • 12 00 PM IST - 03 Mar'25

    Class 12 ISC Mathematics Answer Key 2025: Total number of questions

    According to the exam pattern, Class 12 ISC Mathematics consists of a total of 22 questions and worth 80 marks.


     

  • 11 45 AM IST - 03 Mar'25

    Class 12 ISC Mathematics Answer Key 2025: Type of the Questions

    • Multiple-Choice questions
    • Very short answer questions
    • Short answer questions
    • Long answer type questions

  • 11 30 AM IST - 03 Mar'25

    Class 12 ISC Mathematics Answer Key 2025: Total Marks

    According to the exam pattern, candidates will have 80 marks for the theory section and 20 marks for the practical section.


     

  • 11 15 AM IST - 03 Mar'25

    Class 12 ISC Mathematics Answer Key 2025: Time for reading question paper?

    According to the official notice, additional “Fifteen” minutes have been allotted for the students to read the Class 12 ISC Mathematics Question Paper 2025.


     

  • 11 00 AM IST - 03 Mar'25

    Class 12 ISC Mathematics Answer Key 2025: When will the exam start?

    As per the exam time slot, the ISC Class 12 Mathematics exam will start at 2 PM. The time duration of the exam will be 3 hours.


     

  • 02 40 PM IST - 03 Feb'25

    Class 12 ISC Mathematics Answer Key 2025: Marking scheme of Section C

     In this section also, there will be 4 questions (19 to 22). ie, 

    • Question 19: 5 Marks
    • Question 20: 2 Marks
    • Questions (21 to 22): 4 Marks  

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