CBSE 2016 Mathematics Question Paper for Class 12 (Set 1)

About this paper

This is CBSE Class 12 Mathematics Set 1, question paper code 65/1/C (Series ONS), from the 2016 board examination. 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. One four-mark question is value-based: a trust's investment in two bonds, found by the matrix method, with the interest going to HelpAge India. Section C includes a fertiliser linear programming problem, the distribution of bad oranges drawn with replacement, and proving that two parabolas divide a square into three equal areas. Questions only, no answers.

Exam

CBSE Class 12

Subject

Mathematics

Year

2016

Paper code

65/1/C

Maximum marks

100

Time allowed

3 hours

Questions

26

Pages

11

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

• Matrices and determinants
• Vectors
• Three-dimensional geometry
• Probability and expected value
• Binomial distribution
• Continuity and differentiability
• Tangents and maxima–minima
• Integrals
• Differential equations
• Inverse trigonometric functions
• Binary operations
• Linear programming and area under curves

Questions from this paper

1. Write the number of all possible matrices of order 2 × 2 with each entry 1, 2 or 3.
2. Find the coordinates of the point where the line through the points A(3, 4, 1) and B(5, 1, 6) crosses the XZ-plane. Also find the angle which this line makes with the XZ-plane.
3. In a game, a man wins ₹5 for getting a number greater than 4 and loses ₹1 otherwise when a fair die is thrown. He decides to throw the die thrice but to quit as soon as he gets a number greater than 4. Find the expected value of the amount he wins or loses.
4. Differentiate x^(sin x) + (sin x)^(cos x) with respect to x.
5. Five bad oranges are accidentally mixed with 20 good ones. If four oranges are drawn one by one successively with replacement, find the probability distribution of the number of bad oranges drawn, and hence its mean and variance.
6. Prove that the least perimeter of an isosceles triangle in which a circle of radius r can be inscribed is 6√3 r.