ISC 2026 Mathematics Question Paper for Class 12

About this paper

This is the ISC Class 12 Mathematics paper, code 860, from the 2026 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 and has fourteen questions, opening with multiple-choice and very short items. Internal choices are given in two questions of two marks, two of four marks and two of six marks. Candidates then answer either Section B or Section C, four questions worth 15 marks. Distinctive items include a red-and-green die, a van whose path on a hill locates two ATMs, a gardener using a rain forecast, and three drone cameras in a straight line. Tables and graph paper are provided. This copy has the questions only.

Exam

ISC Class 12

Subject

Mathematics

Year

2026

Paper code

860

Maximum marks

80

Time allowed

3 hours + 15 min reading

Questions

22

Pages

11

Answers included

No, questions only

Paper pattern

• Section A

  65 marks

  Questions 1–14, compulsory, including multiple-choice 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 is vectors, lines, planes and area; Section C is cost, regression and linear programming. Internal choice in one two-mark and one four-mark question

Topics covered

• Determinants and matrices
• Functions and inverse trigonometric functions
• Continuity and probability of events
• Rates of change and normals
• Differential equations
• Definite integrals
• Conditional probability
• Applications of derivatives
• Vectors and three-dimensional geometry
• Area under curves
• Cost, revenue and regression
• Linear programming

Questions from this paper

1. A die is marked 1, 2, 3 in red and 4, 5, 6 in green. Let A be the event that the number is odd and B the event that it is green. Prove that A and B are not independent.
2. Find the equation of the normal at (1, 2) to the curve x² = 4y.
3. A gardener plants saplings only when rain is not predicted. The probability of rain today is 0.4. If it rains today, the probability of rain tomorrow is 0.8; otherwise it is 0.7. Find the probability that he does not plant tomorrow.
4. Drone cameras at A(1, 4, 6), B(3, 4, 5) and C(5, 4, 4) record a match. Using vectors, show that A, B and C lie on a straight line.
5. If a and b are perpendicular, |a + b| = 13 and |a| = 5, find |b|.
6. The means of x and y are 25 and 30. The regression coefficient of x on y is 0.4 and of y on x is 1.6. Find both lines of best fit, estimate y when x = 60, and find the correlation coefficient.