CBSE 2015 Mathematics Question Paper for Class 12

About this paper

This is CBSE Class 12 Mathematics Set 3, question paper code 65/3/P (Series SSO), from the 2015 board examination, printed in Hindi and English. It carries 100 marks, allows three hours plus 15 minutes of reading time, and has 26 compulsory questions: six one-mark very short answers in Section A, thirteen four-mark long-answer I questions in Section B and seven six-mark long-answer II questions in Section C, several with an internal choice. A value-based question asks students to use matrices to total the money three schools raised for an orphanage by selling recycled-paper products, and Section C includes a postmaster's linear programming problem on hiring extra helpers for Deepawali. This copy has the questions only, without answers.

Exam

CBSE Class 12

Subject

Mathematics

Year

2015

Paper code

65/3/P

Maximum marks

100

Time allowed

3 hours

Questions

26

Pages

13

Answers included

No, questions only

Paper pattern

• Section A

  6 marks

  Questions 1–6, very short answers, one mark each

• Section B

  52 marks

  Questions 7–19, long answer I, four marks each, including a value-based question; internal choice in some

• Section C

  42 marks

  Questions 20–26, long answer II, six marks each; internal choice in some

Topics covered

• Differential equations
• Matrices and determinants
• Vectors
• Three-dimensional geometry
• Probability and Bayes' theorem
• Continuity and differentiability
• Integrals
• Inverse trigonometric functions
• Functions and binary operations
• Maxima and minima
• Linear programming
• Area under curves

Questions from this paper

1. Write the integrating factor of the differential equation (1 + y²) dx − (tan⁻¹ y − x) dy = 0.
2. Show that the four points A, B, C and D with position vectors 4î + 5ĵ + k̂, −ĵ − k̂, 3î + 9ĵ + 4k̂ and 4(−î + ĵ + k̂) respectively are coplanar.
3. A and B throw a die alternately till one of them gets a number greater than four and wins the game. If A starts the game, what is the probability of B winning?
4. If A = [2 0 1; 2 1 3; 1 −1 0], find A² − 5A + 16I.
5. Find the differential equation for all the straight lines which are at a unit distance from the origin.
6. Using integration, find the area of the region bounded by the lines y = 2 + x, y = 2 − x and x = 2.