CBSE 2017 Mathematics Question Paper for Class 12

About this paper

This is the CBSE Class 12 Mathematics question paper from the 2017 board examination, Series GBM, Set 1, code 65/1. It carries 100 marks over three hours, with 15 minutes of reading time before writing begins, and has 29 compulsory questions in four sections rising from one-mark answers in Section A to six-mark long answers in Section D. Internal choices are given in three four-mark and three six-mark questions, and calculators are not allowed. One four-mark probability question on school attendance and A grades also asks whether regularity is required only in school. The paper covers calculus, vectors and 3D geometry, matrices, linear programming and probability. This copy has the questions only, without answers.

Exam

CBSE Class 12

Subject

Mathematics

Year

2017

Paper code

65/1

Maximum marks

100

Time allowed

3 hours

Questions

29

Pages

12

Answers included

No, questions only

Paper pattern

• Section A

  4 marks

  Questions 1–4, one mark each

• Section B

  16 marks

  Questions 5–12, two marks each

• Section C

  44 marks

  Questions 13–23, four marks each, including a value-based probability question; internal choice in three

• Section D

  36 marks

  Questions 24–29, six marks each; internal choice in three

Topics covered

• Relations, functions and binary operations
• Inverse trigonometric functions
• Matrices and determinants
• Continuity and differentiability
• Applications of derivatives
• Integrals
• Applications of integrals
• Differential equations
• Vectors
• Three-dimensional geometry
• Linear programming
• Probability

Questions from this paper

1. If A is a skew-symmetric matrix of order 3, prove that det A = 0.
2. A die whose faces are marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be the event "number obtained is even" and B the event "number obtained is red". Find whether A and B are independent events.
3. There are 4 cards numbered 1, 3, 5 and 7. Two cards are drawn at random without replacement, and X denotes the sum of the numbers on them. Find the mean and variance of X.
4. Of the students in a school, 30% have 100% attendance and 70% are irregular. 70% of students with full attendance and 10% of irregular students attain an A grade. A student chosen at random has an A grade. What is the probability that the student has 100% attendance?
5. Solve the differential equation (tan⁻¹x − y) dx = (1 + x²) dy.
6. Find the coordinates of the point where the line through (3, −4, −5) and (2, −3, 1) crosses the plane determined by the points (1, 2, 3), (4, 2, −3) and (0, 4, 3).