JAC Class 12 Math Question Paper 2019 with Solution

About this paper

This is the Jharkhand Academic Council (JAC) Class 12 Mathematics paper from the 2019 board examination, with a worked solution under every 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, for 100 marks. Calculators are not allowed. Most longer questions offer an alternative, and both are solved. Several questions repeat earlier JAC papers, including the absolute maximum and minimum of 2x³ − 15x² + 36x + 1 on [1, 5] (2016) and the lost-card Bayes' theorem problem (2017).

Exam

JAC Class 12

Subject

Math

Year

2019

Maximum marks

100

Questions

29

Pages

13

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 many

• Section C

  42 marks

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

Topics covered

• Relations, functions and 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. Given |a| = 10, |b| = 2 and a · b = 12, find the value of |a × b|.
2. Find the intervals on which the function f(x) = 2x³ − 21x² + 36x − 40 is increasing or decreasing.
3. Find the angle between the planes r · (3i − 6j + 2k) = 7 and r · (2i + 2j − 2k) = 5.
4. Find the area of the region bounded by the parabola y² = 4x and the line x = 3.
5. A person buys 50 tickets of a lottery, in each of which his chance of winning a prize is 1/100. What is the probability that he will win a prize (a) at least once, (b) exactly once, (c) at least twice?
6. Solve the following LPP graphically: minimise Z = 20x + 50y subject to x + 2y ≥ 10, 3x + 4y ≤ 24, x ≥ 0, y ≥ 0.