JAC Class 12 Math Question Paper 2014 with Solution

About this paper

This is the Jharkhand Academic Council (JAC) Class 12 Mathematics paper from the 2014 board examination, with a worked solution under every question. The general instructions, printed in Hindi, describe 29 questions in three sections: ten one-mark objective questions in Section A, twelve four-mark questions in Section B and seven six-mark questions in Section C, for 100 marks. Calculators are not allowed. Several questions offer an internal choice. Section C includes finding a matrix inverse by elementary row transformations, the area of a triangle using integration, a Bayes' theorem problem on three machine operators, and a graphical linear programming problem.

Exam

JAC Class 12

Subject

Math

Year

2014

Maximum marks

100

Questions

29

Pages

10

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

• Binary operations
• Inverse trigonometric functions
• Matrices and determinants
• Continuity and differentiability
• Application of derivatives
• Integrals
• Application of integrals
• Differential equations
• Vector algebra
• Three-dimensional geometry
• Probability and Bayes' theorem
• Linear programming

Questions from this paper

1. A binary composition * is defined on R × R by (a, b) * (c, d) = (ac, bc + d), where a, b, c, d ∈ R. Find (2, 3) * (1, −2).
2. If x = a sin 2t (1 + cos 2t) and y = b cos 2t (1 − cos 2t), prove that dy/dx = b/a at t = π/4.
3. A stone is dropped into a quiet lake and the waves move in circles. If the radius of a circular wave increases at the rate of 5 cm/s, find the rate of increase in its area at the instant when its radius is 8 cm.
4. If A and B are two independent events such that P(A) = 0.35 and P(A ∪ B) = 0.6, find P(B).
5. Using integration, find the area of the triangle whose vertices are (1, 3), (2, 5) and (3, 4).
6. Solve graphically: minimise Z = 5x + 10y subject to x + y ≥ 60, x + 2y ≤ 120, x − 2y ≥ 0 and x, y ≥ 0.