JAC Class 12 Math Question Paper 2013 with Solution

About this paper

This is the Jharkhand Academic Council (JAC) Class 12 Mathematics paper from the 2013 board examination, with a worked answer under every question. Questions are printed in both English and Hindi. The 29 questions are split into Section A (ten one-mark questions), Section B (twelve four-mark questions) and Section C (seven six-mark questions), for 100 marks in total. Two integration questions ask you to evaluate any one of two integrals, and other questions offer an internal choice. Calculators are not allowed. Two questions repeat from the 2012 paper: the probability of exactly five heads when ten coins are tossed, and the differential equation x dx + y dy = x dy − y dx.

Exam

JAC Class 12

Subject

Math

Year

2013

Maximum marks

100

Questions

29

Pages

9

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; choice of one integral in two questions

• Section C

  42 marks

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

Topics covered

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

Questions from this paper

1. Prove that 2 tan⁻¹(1/5) + tan⁻¹(1/4) = tan⁻¹(32/43).
2. Test the continuity of the function f(x) = sin x / x for x ≠ 0, f(0) = 2, at x = 0.
3. Find the equation of the plane perpendicular to the line joining the points (2, −1, 2) and (3, 2, −1) and passing through the point (4, −3, 1).
4. Find the maximum and minimum values of the function f(x) = 2x³ − 15x² + 36x + 11.
5. Find the area of the region bounded by the parabola y² = 4ax, its axis and the two ordinates x = 4 and x = 9.
6. Solve the following L.P.P. graphically: maximise Z = 5x + 3y subject to 3x + 5y ≤ 15, 5x + 2y ≤ 10 and x, y ≥ 0.