JAC Class 12 Math Question Paper 2012 with Solution

About this paper

This is the Jharkhand Academic Council (JAC) Class 12 Mathematics paper from the 2012 board examination, with a worked answer under every question. The questions are printed in both English and Hindi. There are 29 questions in three sections: Section A has ten one-mark multiple-choice questions, Section B has twelve four-mark questions and Section C has seven six-mark questions, giving 100 marks in all. Several questions in Sections B and C offer an internal choice. Calculators are not allowed, but log and statistical tables may be asked for. The paper ends with a linear programming problem solved graphically.

Exam

JAC Class 12

Subject

Math

Year

2012

Maximum marks

100

Questions

29

Pages

9

Answers included

Yes

Paper pattern

• Section A

  10 marks

  Questions 1–10, multiple-choice, 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

• 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. If a line makes angles α, β, γ, δ with the four diagonals of a cube, prove that sin²α + sin²β + sin²γ + sin²δ = 8/3.
2. Find the area of the triangle ABC whose vertices are A(1, 1, 2), B(2, 3, 5) and C(1, 5, 5).
3. Find the acute angle between the planes 2x − y + z + 8 = 0 and x + y + 2z − 14 = 0.
4. Solve the following equations by the matrix method: 5x + 3y + z = 16, 2x + y + 3z = 19, x + 2y + 4z = 25.
5. Find the image of the point (1, 2, −1) in the plane 2x + y − z = 2.
6. A card is drawn from an ordinary pack and a gambler bets that it is a spade or an ace. What are the odds against his winning the bet?