ISC 2024 Mathematics Question Paper for Class 12

About this paper

This is the ISC Class 12 Mathematics paper, code 860, from the 2024 CISCE board examination. It carries 80 marks and runs for three hours, with fifteen minutes extra for reading only, and it has 22 questions. Section A, worth 65 marks, is compulsory. It opens with one-mark multiple-choice and very short items, and there is an internal choice in two questions of two marks, two of four marks and two of six marks. Candidates then attempt either Section B or Section C, each worth 15 marks, with an internal choice in one two-mark and one four-mark question. Section B includes vectors and a mobile tower standing on a hillside. Section C includes cost, regression and linear programming. Tables and graph paper are provided. This copy has the questions only.

Exam

ISC Class 12

Subject

Mathematics

Year

2024

Paper code

860

Maximum marks

80

Time allowed

3 hours + 15 min reading

Questions

22

Pages

12

Answers included

No, questions only

Paper pattern

• Section A

  65 marks

  Questions 1–14, compulsory. Question 1 is one-mark multiple-choice and very short items; internal choice in two questions of two marks, two of four marks and two of six marks

• Section B or Section C

  15 marks

  Four questions in the section attempted. Section B (Questions 15–18) is vectors, three-dimensional geometry and area; Section C (Questions 19–22) is cost, correlation, regression and linear programming. Internal choice in one two-mark and one four-mark question

Topics covered

• Relations and functions
• Inverse trigonometric functions
• Determinants and matrices
• Continuity and differentiability
• Applications of derivatives
• Indefinite integrals
• Differential equations
• Probability and probability distributions
• Vectors and three-dimensional geometry
• Area under curves
• Cost, correlation and regression
• Linear programming

Questions from this paper

1. If y = 3 cos(log x) + 4 sin(log x), show that x² d²y/dx² + x dy/dx + y = 0.
2. Find k so that f(x) = ((x + 3)² − 36)/(x − 3) for x ≠ 3, and f(3) = k, is continuous at x = 3.
3. A window is a rectangle surmounted by an equilateral triangle, and its perimeter is 12 m. Find the dimensions that let in the most sunlight.
4. A factory has 29 tonnes of teak, 13 tonnes of rosewood and 16 tonnes of satinwood. A table, a chair and a cot need (2, 1, 3), (3, 1, 2) and (4, 2, 1) tonnes of those woods. How many of each can be made?
5. A tower stands at P(2, 3, 1) on the plane through A(1, 0, 2), B(3, −1, 1) and C(1, 2, 1). Find the equation of the plane and the height of the tower.
6. Using integration, find the area bounded by the curve y² = 4ax and the line x = a.