CBSE 2018 Mathematics Solved Paper for Class 12

About this paper

This is the CBSE Class 12 Mathematics paper from the 2018 board examination, Series SGN, Set 1, code 65/1, printed with a worked solution under each question. It carries 100 marks over three hours and has 29 compulsory questions in four sections, from one-mark answers in Section A to six-mark long answers in Section D. Internal choices are given in three four-mark and three six-mark questions, and calculators are not allowed. One four-mark question on the cheapest open water tank also asks what value is hidden in it. The solutions include an equivalence relation, a matrix inverse used to solve three equations, a definite integral as the limit of a sum, and a graphical LPP on manufacturing two types of screws. The page images are out of order.

Exam

CBSE Class 12

Subject

Mathematics

Year

2018

Paper code

65/1

Maximum marks

100

Time allowed

3 hours

Questions

29

Pages

20

Answers included

Yes

Paper pattern

• Section A

  4 marks

  Questions 1–4, one mark each

• Section B

  16 marks

  Questions 5–12, two marks each

• Section C

  44 marks

  Questions 13–23, four marks each, including a value-based question; internal choice in three

• Section D

  36 marks

  Questions 24–29, six marks each; internal choice in three

Topics covered

• Relations, functions and binary operations
• 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. The total cost C(x) of producing x units of an item is C(x) = 0.005x³ − 0.02x² + 30x + 5000. Find the marginal cost when 3 units are produced.
2. A black and a red die are rolled together. Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4.
3. Find the equations of the tangent and the normal to the curve 16x² + 9y² = 145 at the point (x₁, y₁), where x₁ = 2 and y₁ > 0.
4. Two numbers are selected at random (without replacement) from the first five positive integers. Let X denote the larger of the two numbers. Find the mean and variance of X.
5. Using integration, find the area of the region in the first quadrant enclosed by the x-axis, the line y = x and the circle x² + y² = 32.
6. Find the distance of the point (−1, −5, −10) from the point of intersection of the line r = 2î − ĵ + 2k̂ + λ(3î + 4ĵ + 2k̂) and the plane r · (î − ĵ + k̂) = 5.