JAC Class 12 Math Question Paper 2015 with Solution

About this paper

This is the Jharkhand Academic Council (JAC) Class 12 Mathematics paper from the 2015 board examination, with a worked solution under each question. The Hindi general instructions describe 29 questions in three sections: Section A has ten one-mark objective questions, Section B twelve four-mark questions and Section C seven six-mark questions, totalling 100 marks. Calculators are not permitted. Several questions give an internal choice, such as a related-rates balloon problem or verifying Rolle's theorem. This copy is incomplete: it runs from Q1 to Q23, then jumps to the end of Q28's solution and the graphical linear programming question, Q29.

Exam

JAC Class 12

Subject

Math

Year

2015

Maximum marks

100

Questions

29

Pages

7

Answers included

Yes

Paper pattern

• Section A

  10 marks

  Questions 1–10, short objective questions, one mark each

• Section B

  48 marks

  Questions 11–22, four marks each; internal choice in some

• Section C

  42 marks

  Questions 23–29, six marks each; internal choice in some

Topics covered

• Relations and functions
• Inverse trigonometric functions
• Matrices
• Determinants
• Continuity and differentiability
• Application of derivatives
• Integrals
• Vector algebra
• Three-dimensional geometry
• Probability
• Linear programming

Questions from this paper

1. Evaluate cos⁻¹(cos 13π/6).
2. Write the Cartesian equation of the straight line passing through the point (−1, 2, 0) whose direction ratios are 2, 4, −3.
3. A balloon which always remains spherical is being inflated by pumping in 900 cubic centimetres of gas per second. Find the rate at which the radius of the balloon is increasing when the radius is 15 cm.
4. Verify Rolle's theorem for the function f(x) = x² − 4x + 3 in the interval [1, 3].
5. Let A and B be two events such that 2P(A) = P(B) = 5/13 and P(A|B) = 2/5. Find P(A ∪ B).
6. Using elementary row transformations, find the inverse of the matrix A = [1 2 3; 2 5 7; −2 −4 −5].