ISC 2025 Mathematics Question Paper for Class 12

About this paper

This is the ISC Class 12 Mathematics paper, code 860, from the 2025 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, has fourteen compulsory questions, beginning 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 attempt all four questions of either Section B or Section C, each section worth 15 marks. Longer items include three shopkeepers' carry bags, paintings by Pia, Sia and Dia, and stacking books. For a multiple-choice question, only one option is to be written. Tables and graph paper are provided. This copy has the questions only.

Exam

ISC Class 12

Subject

Mathematics

Year

2025

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, planes and area; Section C is revenue, regression and linear programming. Internal choice in one two-mark and one four-mark question

Topics covered

• Matrices and determinants
• Differential equations
• Inverse trigonometric functions
• Continuity, derivatives and turning points
• Indefinite and definite integrals
• Probability
• Vectors and three-dimensional geometry
• Area under curves
• Revenue, cost and profit
• Correlation and regression
• Linear programming

Questions from this paper

1. Find the point on the curve y = 2x² − 6x − 4 at which the tangent is parallel to the x-axis.
2. Gaurav, Rizwan and Jacob use (20, 30, 40), (30, 40, 20) and (40, 20, 30) polythene, handmade-paper and newspaper bags, costing ₹1, ₹5 and ₹2. Use matrices to find what each shopkeeper spends.
3. Pia, Sia and Dia display 15, 5 and 10 paintings. A buyer takes three. Find the probability of one painting from each artist, and of all three from the same artist.
4. Find the equation of the plane through the points (2, 2, −1), (3, 4, 2) and (7, 0, 6).
5. The curve y = 4 − x² meets the x-axis. Find the area enclosed by the curve, the x-axis and the lines x = 0 and x = 2.
6. One kind of book weighs 1 kg and is 6 cm thick; another weighs 1.5 kg and is 4 cm thick. A shelf is 96 cm long and holds at most 21 kg. How should the books be stacked to maximise the number? Formulate the linear programming problem and solve it graphically.