**ISC Board Class 12 Mathematics ****Sample paper: **This article provides insight into the sample exam and the answer key of Mathematics, published by ISC Board for class 12 students. Read the article for more details.

The **ISC Board** has released the latest model exams for the class 12 students on its official website. Model exams are an important resource provided by the ISC boards to the students to prepare for final exams. These model exams help them to practice and get better results in upcoming final exams. In this article, we have released the model exam for the **ISC Sample Examination Mathematics Class 12 2025**along with the answer key and a direct link to download the sample test for preparation and practice. Read the full article for comprehensive information.

**Exam: ISC Board Class 12 Sample Exam 2024-25**

**ISC Board Class 12 Mathematics ****Sample paper 2024-25: ****Instructions for candidates**

- You have an additional 15 minutes for reading the newspaper.
- You are NOT allowed to start writing during reading time.
- The questionnaire consists of 12 pre-printed pages.
- The questionnaire is divided into three sections and contains a total of 22 questions.
- Section A is compulsory and contains fourteen questions.
- You must answer all questions from either Section B or Section C.
- Section B and Section C each contain four questions.
- In Section A, internal choices were provided for two questions of 2 marks, two questions of 4 marks, and two questions of 6 marks.
- Internal choices are available for one 2-point question and one 4-point question in Section B and Section C.
- When answering the multiple-choice questions in sections A, B and C, you must provide only ONE option as your answer.
- The intended grades for questions or parts of questions are given in brackets ().
- The entire calculation, including rough drafts, should be on the same page and next to the rest of the answer.
- Mathematical tables and graph paper are provided.

**ISC Board Class 12 Mathematics ****Sample exam 2024-25**

### SECTION Aโ 65 POINTS

**Question 1**

**Select the correct options in subsections (i) to (xi) and answer the questions in subsections (xii) to (xv) as indicated.**

**(i) A matrix that is both symmetric and skew-symmetric is one:**

(a) Triangular matrix

b) Identity matrix

(c) Diagonal matrix

(d) Zero matrix

**Question 2: **

**Question 3: **

**Question 4: Statement: Degree of the differential equation: a(dy/dx)2 + b dy/dx = c, is 3**

**Reason: If every term containing derivatives of a differential equation is a polynomial (or can be expressed as a polynomial), then the highest exponent of the highest order derivative is called the degree of the differential equation. Which of the following statements is true?**

(a) Both the claim and the reason are true and the reason is the correct explanation for the claim.

(b) Both the claim and the reason are true, but the reason is not the correct explanation for the claim.

(c) The statement is true and the reason is false.

(d) The claim is false and the reason is true.

**Question 5: Five numbers x _{1}X_{2}X_{3}X_{4}X_{5} are randomly selected from the numbers 1, 2, 3, โฆโฆ., **

**18 and are arranged in ascending order so that x**

_{1}2 3 4 5. What is**the probability that x**

_{2}= 7 and x_{4}= 11?a) 26/51

b) 3/104

c) 1/68

d) 1/34

**Question 6:**

**Question 7: **

**Statement 1: The above graph is continuous at x = 0**

**Statement 2: The above graph is differentiable at x = 0.**

**Which of the following statements is correct?**

(a) Statement 1 is true and statement 2 is false.

(b) Statement 2 is true and statement 1 is false.

(c) Both statements are true.

(d) Both statements are false.

**Question 8: The value of ๐๐ฆ/๐๐ฅ when ๐ฆ = |๐ฅ โ 1| + |๐ฅ โ 4| at ๐ฅ = 3 is **

- โ2
- 0
- 2
- 4

**Question 9: Statement 1: The intersection of two equivalence relations is always an equivalence relation.**

**Statement 2: The union of two equivalence relations is always an equivalence relation.**

**Which of the following statements is correct?**

(a) Statement 1 implies statement 2.

(b) Statement 2 implies statement 1.

(c) Statement 1 is only true if statement 2 is true.

(d) Statements 1 and 2 are independent of each other

**Question 10. **

**Claim: Matrix โAโ is not invertible.**

**Reason: Determinant A = 0**

**Which of the following statements is correct?**

(a) Both the claim and the reason are true and the reason is the correct explanation for the claim.

(b) Both the claim and the reason are true, but the reason is not the correct explanation for the claim.

(c) The statement is true and the reason is false.

(d) The claim is false and the reason is true.

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To view and download all sections and answer key for ICS Class 12 Mathematics Sample Papers 2025, click on the link below to Download the complete sample test paper along with the answer key in the same PDF for the final exam 2025 via the direct link: