JAC Class 12 Math Question Paper 2016 with Solution

About this paper

This is the Jharkhand Academic Council (JAC) Class 12 Mathematics paper from the 2016 board examination, with a worked solution under every question. According to its Hindi general instructions, the paper has 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, totalling 100 marks. Calculators are not allowed. Several questions carry an internal choice. Questions include a sliding-ladder rate problem, a definite integral evaluated as the limit of a sum, verifying matrix properties for given matrices, absolute maxima and minima on an interval, and a graphical linear programming problem.

Exam

JAC Class 12

Subject

Math

Year

2016

Maximum marks

100

Questions

29

Pages

8

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
• Linear programming

Questions from this paper

1. Find the length of the projection of the vector i + 3j + 7k on the vector 7i − j + 8k.
2. A ladder 5 m long is leaning against a wall. The bottom of the ladder is pulled along the ground, away from the wall, at the rate of 2 cm/s. How fast is its height on the wall decreasing when the foot of the ladder is 4 m away from the wall?
3. Evaluate ∫ e^x dx from −1 to 1 as a limit of a sum.
4. A family has two children. What is the probability that both the children are boys, given that at least one of them is a boy?
5. Find the absolute maximum and absolute minimum values of f(x) = 2x³ − 15x² + 36x + 1 on the interval [1, 5].
6. Find the area of the region bounded by the curve y = x² and the line y = 4.