JAC Class 12 Math Question Paper 2018 with Solution

About this paper

This is the Jharkhand Academic Council (JAC) Class 12 Mathematics paper from the 2018 board examination, with a worked solution under every question. The Hindi general instructions describe 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. Many questions in Sections B and C offer an alternative question, and the solutions to both alternatives are given. Section C covers a matrix-method system of equations or an inverse by elementary operations, maxima and minima, area under y = sin x, differential equations, shortest distance between lines, a Bayes' theorem problem on insured drivers, and linear programming.

Exam

JAC Class 12

Subject

Math

Year

2018

Maximum marks

100

Questions

29

Pages

10

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. Find the projection of a = 2i + j + k on b = i + 2j + k.
2. A stone is dropped into a quiet lake and waves move in circles at a speed of 4 cm per second. At the instant when the radius of the circular wave is 10 cm, how fast is the enclosed area increasing?
3. If a = 2i + 2j + 3k, b = −i + 2j + k and c = 3i + j are such that a + λb is perpendicular to c, find the value of λ.
4. Two dice are thrown. Find the probability that the numbers that appear have a sum of 8, if it is known that the second die always shows 4.
5. Find the area bounded by the curve y = sin x between x = 0 and x = 2π.
6. An insurance company insured 2000 scooter drivers, 4000 car drivers and 6000 truck drivers. The probabilities of an accident involving a scooter, a car and a truck are 0.01, 0.03 and 0.15 respectively. One of the insured drivers meets with an accident. What is the probability that he is a scooter driver?