CBSE 2011 Mathematics Question Paper for Class 12

About this paper

This is the CBSE Class 12 Mathematics question paper code 65/2/1 (Series SOS/2) from the 2011 board examination. It carries 100 marks, allows three hours plus 15 minutes of reading time, and has 29 compulsory questions: ten one-mark questions in Section A, twelve four-mark questions in Section B and seven six-mark questions in Section C. Four four-mark and two six-mark questions offer an internal choice, and calculators are not allowed. Section C has a window-design maximisation problem, the area bounded by three lines, a linear programming problem on a cottage industry making pedestal lamps and wooden shades, and a Bayes' theorem question on defective items from two machines. In this copy the cover page appears as the last image. Questions only, no answers.

Exam

CBSE Class 12

Subject

Mathematics

Year

2011

Paper code

65/2/1

Maximum marks

100

Time allowed

3 hours

Questions

29

Pages

11

Answers included

No, questions only

Paper pattern

• Section A

  10 marks

  Questions 1–10, one mark each, answered in a word, a sentence or as the question requires

• Section B

  48 marks

  Questions 11–22, four marks each; internal choice in four

• Section C

  42 marks

  Questions 23–29, six marks each; internal choice in two

Topics covered

• Functions and invertibility
• Inverse trigonometric functions
• Matrices and determinants
• Continuity and differentiability
• Increasing and decreasing functions
• Maxima and minima
• Integrals and definite integral as a limit of sums
• Area under curves
• Differential equations
• Vectors and three-dimensional geometry
• Linear programming
• Probability and Bayes' theorem

Questions from this paper

1. If f: R → R is defined by f(x) = 3x + 2, define f(f(x)).
2. What are the direction cosines of a line which makes equal angles with the coordinate axes?
3. Find the intervals in which the function f given by f(x) = sin x + cos x, 0 ≤ x ≤ 2π, is strictly increasing or strictly decreasing.
4. Find the mean number of heads in three tosses of a fair coin.
5. A window is in the form of a rectangle surmounted by a semicircular opening. The total perimeter of the window is 10 metres. Find the dimensions of the rectangle so as to admit maximum light through the whole opening.
6. A factory has two machines A and B. Machine A produced 60% of the output and machine B 40%; 2% of the items from A and 1% from B were defective. An item chosen at random from the combined stockpile is defective. What is the probability that it was produced by machine B?