CBSE Class 12 Maths Question Paper 2020 with Solution

About this paper

This is the CBSE Class 12 Mathematics question paper from the 2020 board examination, Series HMJ/3, Set 1, code 65/3/1. It carries 80 marks over three hours and has 36 compulsory questions in four sections. Section A has 20 one-mark questions: ten multiple-choice, five fill-in-the-blanks and five very short answers. Sections B, C and D carry two, four and six marks per question. Internal choices are given in three one-mark, two two-mark, two four-mark and two six-mark questions, and calculators are not allowed. The paper ranges from relations and inverse trigonometry to a graphical LPP, Bayes' theorem with a biased coin and intersecting lines in 3D. This copy has questions only, with no solutions, and its last seven images belong to a Physical Education paper.

Exam

CBSE Class 12

Subject

Mathematics

Year

2020

Paper code

65/3/1

Maximum marks

80

Time allowed

3 hours

Questions

36

Pages

15

Answers included

No, questions only

Paper pattern

• Section A

  20 marks

  Questions 1–20, one mark each: 10 multiple-choice, 5 fill-in-the-blanks and 5 very short answers; internal choice in three

• Section B

  12 marks

  Questions 21–26, two marks each; internal choice in two

• Section C

  24 marks

  Questions 27–32, four marks each; internal choice in two

• Section D

  24 marks

  Questions 33–36, six marks each; internal choice in two

Topics covered

• Relations and functions
• Inverse trigonometric functions
• Matrices and determinants
• Continuity and differentiability
• Applications of derivatives
• Integrals
• Applications of integrals
• Differential equations
• Vectors
• Three-dimensional geometry
• Linear programming
• Probability

Questions from this paper

1. An unbiased coin is tossed 4 times. Find the probability of getting at least one head.
2. Find the coordinates of the point where the line through (−1, 1, −8) and (5, −2, 10) crosses the ZX-plane.
3. Show that the relation R in the set A = {1, 2, 3, 4, 5, 6} given by R = {(a, b) : |a − b| is divisible by 2} is an equivalence relation.
4. Solve the following LPP graphically: minimise z = 5x + 7y subject to 2x + y ≥ 8, x + 2y ≥ 10, x, y ≥ 0.
5. A bag contains two coins, one biased and the other unbiased. When tossed, the biased coin has a 60% chance of showing heads. One of the coins is selected at random and on tossing it shows tails. What is the probability that it was the unbiased coin?
6. Using integration, find the area of a triangle whose vertices are (1, 0), (2, 2) and (3, 1).