ISC Maths Specimen Paper 2023 Sec A Solved for ISC Class-12. Step by step solutions as council prescribe guideline of model sample question paper.

During solutions of Maths specimen paper we explain with figure , graph, table whenever necessary so that student can achieve their goal in next upcoming exam of council. Visit official website CISCE for detail information about ISC Board Class-12.

## ISC Maths Specimen Paper 2023 Sec A Solved

Board | ISC |

Class | 12th (xii) |

Subject | Maths |

Topic | Specimen Paper Solved |

Syllabus | Revised Syllabus |

Session | 2022-23 |

Question Type | Sec-A MCQs and Subjective questions |

Section | A (65 Marks) |

Max mark | 80 |

### ISC Maths Specimen Paper 2023 Sec-A Solved Class-12

**Warning :-** before viewing solution view Question Paper

### ISC SPECIMEN QUESTION PAPER 2023

MATHEMATICS

Maximum Marks: 80

Time Allowed: Three hours

(Candidates are allowed additional 15 minutes for only reading the paper. They must NOT start writing during this time).

- This Question Paper consists of three sections A, B and C.
- Candidates are required to attempt all questions from Section A and all questions EITHER from Section B OR Section C.
**Section A:**Internal choice has been provided in two questions of two marks each, two questions of four marks each and two questions of six marks each.**Section B:**Internal choice has been provided in one question of two marks and one question of four marks.**Section C:**Internal choice has been provided in one question of two marks and one question of four marks.- All working, including rough work, should be done on the same sheet as, and adjacent to the rest of the answer.
- The intended marks for questions or parts of questions are given in brackets [ ].
**Mathematical tables and graph papers are provided.**

### SECTION A – 65 MARKS

### ISC Maths Specimen Paper 2023 Solved Class-12

**Question 1: In subparts (i) to (x) choose the correct options and in subparts (xi) to (xv), answer the questions as instructed.**

**(i) Which of the following is NOT an equivalence relation on Z?**

(a) 𝑎𝑅𝑏 ⇔ 𝑎 + 𝑏 𝑖𝑠 𝑎𝑛 𝑒𝑣𝑒𝑛 𝑖𝑛𝑡𝑒𝑔𝑒𝑟

(b) 𝑎𝑅𝑏 ⇔ 𝑎 − 𝑏 𝑖𝑠 𝑎𝑛 𝑒𝑣𝑒𝑛 𝑖𝑛𝑡𝑒𝑔𝑒𝑟

(c) 𝑎𝑅𝑏 ⇔ 𝑎 < 𝑏

(d) 𝑎𝑅𝑏 ⇔ 𝑎 = b

**(ii) Let A be the set of all 50 cards numbered from 1 to 50. Let 𝑓: 𝐴 → 𝑁 be a function defined by 𝑓(𝑥) = card number of the card ‘𝑥’. Then the function ‘𝑓’ is:**

(a) one to one but not onto.

(b) onto but not one to one.

(c) neither one to one nor onto.

(d) one to one and onto.

……………..

………………

(xi) Write the smallest equivalence relation on the set 𝐴 = {𝑎, 𝑏, 𝑐}

#### (xiii) If ∫ log 2𝑥 𝑑𝑥 = 𝑥log2𝑥 − 𝑘 + 𝑐 where 𝑘 is a function of 𝑥, then find 𝑘.

(xiv) 50 tickets in a box are numbered 00, 01, 02 , .. .. , 49. One ticket is drawn randomly from the box. Find the probability of the ticket having the product of its digits 7, given that the sum of the digits is 8?

(xv) A speaks truth in 60% of cases and B speaks truth in 90% of the cases. In what percentage of cases are they likely to contradict each other in stating the same fact?

**Question 2:** If 𝑦 = √sin 𝑥 + 𝑦 , then find 𝑑𝑦/𝑑𝑥.

**Question 3:** Let 𝑓: 𝑅 → 𝑅 defined as 𝑓(𝑥) = 2𝑥 − 3. Find

……………

**Question 4: **The function 𝑓 is defined for all x ∈ R . The line with equation 𝑦 = 6𝑥 − 1 is the tangent to the graph of 𝑓 at 𝑥 = 4.

(i) Write down the value of 𝑓′(4).

(ii) Find 𝑓(4)

**Question 5: **(i) Evaluate: ∫[sin(log 𝑥) + cos(log 𝑥)] 𝑑𝑥

……….

**Question 6:**Solve the differential equation: (1 + 𝑦²)(1 + log 𝑥)𝑑𝑥 + 𝑥𝑑𝑦 = 0…………

**Question 10: **(i) A student answers a multiple choice question with 5 alternatives, of which exactly

one is correct. The probability that he knows the correct answer is 1/5. If he does not know the correct answer, he randomly ticks one answer. Given that he has answered the question correctly, find the probability that he did not tick the answer randomly.

OR

(ii) A candidate takes three tests in succession and the probability of passing the first test is 1/2. The probability of passing each succeeding test is 1/2 or 1/4 depending on whether he passes or fails in the preceding one. The candidate is selected, if he passes at least two tests. Find the probability that the candidate is selected.

…………..

……………

**Question 14: **A biased four-sided die with ……………… Ajay wins the game.

** ISC Maths Specimen Paper Sec A 2023 Class-12 PDF Solution**

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