CBSE 2016 Mathematics Question Paper for Class 12 (Set 3)

About this paper

This is CBSE Class 12 Mathematics Set 3, question paper code 65/3/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 in three sections: six one-mark very short answers, thirteen four-mark long-answer I questions and seven six-mark long-answer II questions, several with an internal choice. The questions are those of Sets 1 and 2 of this series, rearranged. Section B includes a value-based question on a trust's bond investment for HelpAge India, and Section C covers a binary operation on R − {−1}, an isosceles-triangle determinant, a fertiliser linear programming problem and a binomial distribution of bad oranges. Questions only, no answers.

Exam

CBSE Class 12

Subject

Mathematics

Year

2016

Paper code

65/3/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

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

Questions from this paper

1. Write the position vector of the point which divides the join of the points with position vectors 3a⃗ − 2b⃗ and 2a⃗ + 3b⃗ in the ratio 2 : 1.
2. Write the number of vectors of unit length perpendicular to both the vectors a⃗ = 2î + ĵ + 2k̂ and b⃗ = ĵ + k̂.
3. Evaluate ∫₀^(π/2) sin²x / (sin x + cos x) dx.
4. A bag contains 4 balls. Two balls are drawn at random without replacement and are found to be white. What is the probability that all the balls in the bag are white?
5. Show that the binary operation * on A = R − {−1} defined as a * b = a + b + ab for all a, b ∈ A is commutative and associative on A. Also find the identity element of * in A and prove that every element of A is invertible.
6. Find the position vector of the foot of the perpendicular and the perpendicular distance from the point P with position vector 2î + 3ĵ + 4k̂ to the plane r⃗ · (2î + ĵ + 3k̂) − 26 = 0. Also find the image of P in the plane.