CBSE 2016 Mathematics Question Paper for Class 12 (Set 2)

About this paper

This is CBSE Class 12 Mathematics Set 2, question paper code 65/2/C (Series ONS), from the 2016 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 questions in Section A, thirteen four-mark questions in Section B and seven six-mark questions in Section C, several with an internal choice. It uses the same questions as Sets 1 and 3 of this series in a different order. Highlights include a value-based bond-investment question solved by matrices, a shopkeeper's pen prices found by the matrix method, a fertiliser linear programming problem and the image of a point in a plane. Questions only, no answers.

Exam

CBSE Class 12

Subject

Mathematics

Year

2016

Paper code

65/2/C

Maximum marks

100

Time allowed

3 hours

Questions

26

Pages

12

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 binomial distribution
• Continuity and differentiability
• Tangents and maxima–minima
• Integrals
• Differential equations
• Inverse trigonometric functions
• Binary operations
• Linear programming
• Area under curves

Questions from this paper

1. Find the vector equation of the plane with intercepts 3, −4 and 2 on the x, y and z-axes respectively.
2. The equation of the tangent at (2, 3) on the curve y² = ax³ + b is y = 4x − 5. Find the values of a and b.
3. Form the differential equation of the family of circles in the second quadrant touching the coordinate axes.
4. Solve for x: sin⁻¹x + sin⁻¹(1 − x) = cos⁻¹x.
5. A shopkeeper has three varieties of pens, A, B and C. Meenu bought one pen of each for ₹21, Jeevan bought 4 of A, 3 of B and 2 of C for ₹60, and Shikha bought 6 of A, 2 of B and 3 of C for ₹70. Using the matrix method, find the cost of each variety of pen.
6. Prove that the curves y² = 4x and x² = 4y divide the area of the square bounded by x = 0, x = 4, y = 4 and y = 0 into three equal parts.