CBSE 2017 Mathematics Solved Paper for Class 12

About this paper

This is the CBSE Class 12 Mathematics paper from the 2017 board examination, Series GBM, Set 1, code 65/1, printed with a worked solution under each question. It carries 100 marks over three hours and has 29 compulsory questions in four sections, 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. The worked solutions cover integration by partial fractions, Rolle's theorem, a graphical linear programming problem, Bayes' theorem on school attendance and A grades, and the area of a triangle found by integration. Some pages of this copy are out of order and one page is missing.

Exam

CBSE Class 12

Subject

Mathematics

Year

2017

Paper code

65/1

Maximum marks

100

Time allowed

3 hours

Questions

29

Pages

18

Answers included

Yes

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; 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. Find the distance between the planes 2x − y + 2z = 5 and 5x − 2.5y + 5z = 20.
2. Find the value of c in Rolle's theorem for the function f(x) = x³ − 3x in [−√3, 0].
3. The volume of a cube is increasing at the rate of 9 cm³/s. How fast is its surface area increasing when the length of an edge is 10 cm?
4. Two tailors, A and B, earn ₹300 and ₹400 per day respectively. A can stitch 6 shirts and 4 pairs of trousers while B can stitch 10 shirts and 4 pairs of trousers per day. If at least 60 shirts and 32 pairs of trousers are to be produced at minimum labour cost, formulate this as an LPP.
5. Show that the surface area of a closed cuboid with a square base and given volume is minimum when it is a cube.
6. Using the method of integration, find the area of the triangle ABC whose vertices are A(4, 1), B(6, 6) and C(8, 4).