CBSE 2018 Mathematics Question Paper for Class 12

About this paper

This is the CBSE Class 12 Mathematics question paper from the 2018 board examination, Series SGN, Set 2, code 65/2. It carries 100 marks over three hours, with 15 minutes of reading time, and has 29 questions in four sections: four one-mark questions in Section A, eight two-mark questions in Section B, eleven four-mark questions in Section C and six six-mark questions in Section D. Three questions in Section C and three in Section D offer an internal choice. One Section C question on the cheapest open water tank also asks what value is hidden in it. Section D includes a graphical LPP on manufacturing two types of screws and a definite integral to be evaluated as the limit of a sum. This copy has the questions only, without answers.

Exam

CBSE Class 12

Subject

Mathematics

Year

2018

Paper code

65/2

Maximum marks

100

Time allowed

3 hours

Questions

29

Pages

11

Answers included

No, questions only

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. If a * b denotes the larger of a and b and if a ∘ b = (a * b) + 3, write the value of (5) ∘ (10), where * and ∘ are binary operations.
2. If θ is the angle between the vectors î − 2ĵ + 3k̂ and 3î − 2ĵ + k̂, find sin θ.
3. Suppose a girl throws a die. If she gets 1 or 2, she tosses a coin three times and notes the number of tails; if she gets 3, 4, 5 or 6, she tosses a coin once. If she obtained exactly one tail, what is the probability that she threw 3, 4, 5 or 6 with the die?
4. An open tank with a square base and vertical sides is to be made from a metal sheet to hold a given quantity of water. Show that the cost of material will be least when the depth of the tank is half of its width.
5. Let A = {x ∈ Z : 0 ≤ x ≤ 12}. Show that R = {(a, b) : a, b ∈ A, |a − b| is divisible by 4} is an equivalence relation, and find the set of all elements related to 1.
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.