JAC Class 12 Math Question Paper 2020 with Solution

About this paper

This is the Jharkhand Academic Council (JAC) Class 12 Mathematics paper from the 2020 board examination, with a worked solution under every question. It carries 100 marks (pass marks 33) and runs for three hours. There are 29 questions in three sections: Section A has ten one-mark questions, Section B twelve four-mark questions and Section C seven six-mark questions. Calculators are not permitted, though log and statistical tables may be requested. Most longer questions offer an alternative, and both are solved. Some questions repeat earlier JAC papers: Q2, evaluating sin(π/3 − sin⁻¹(−1/2)), appeared in 2014, and the alternative in Q26, x log x dy/dx + y = (2/x) log x, appeared in 2019.

Exam

JAC Class 12

Subject

Math

Year

2020

Maximum marks

100

Time allowed

3 hours

Questions

29

Pages

12

Answers included

Yes

Paper pattern

• Section A

  10 marks

  Questions 1–10, 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. Find the slope of the tangent to the curve x² + y² = 25 at the point (−3, 4).
2. For what value of p are the vectors 3i + 2j + 9k and i + pj + 3k parallel?
3. Find the relationship between a and b so that the function f defined by f(x) = ax + 1 if x ≤ 3 and f(x) = bx + 3 if x > 3 is continuous at x = 3.
4. An edge of a variable cube is increasing at the rate of 3 cm/s. How fast is the volume of the cube increasing when the edge is 10 cm long?
5. Find the local maximum and local minimum values of the function f(x) = 3x⁴ + 4x³ − 12x² + 12.
6. Bag A contains 2 red and 3 black balls while Bag B contains 3 red and 4 black balls. One ball is drawn at random from one of the bags and it is found to be red. Find the probability that it was drawn from Bag B.