CBSE 2008 Mathematics Question Paper for Class 12

About this paper

This is the CBSE Class 12 Mathematics question paper code 65/1/1 (Series SSR/1) from the 2008 board examination. It carries 100 marks over three hours and has 29 compulsory questions in three sections: ten one-mark questions in Section A, twelve four-mark questions in Section B and seven six-mark questions in Section C. Internal choices are given in four of the four-mark and two of the six-mark questions, and calculators are not allowed. The paper ranges over binary operations, inverse trigonometry, matrices and determinants, calculus, differential equations, vectors and three-dimensional geometry, and ends with a linear programming problem on buying factory machines and a Bayes' theorem question on insured drivers. This copy has the questions only, without answers.

Exam

CBSE Class 12

Subject

Mathematics

Year

2008

Paper code

65/1/1

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

• Binary operations
• Inverse trigonometric functions
• Matrices and determinants
• Continuity and differentiability
• Tangents and maxima–minima
• Integrals
• Area under curves
• Differential equations
• Vectors
• Three-dimensional geometry
• Linear programming
• Probability and Bayes' theorem

Questions from this paper

1. Find a unit vector in the direction of a⃗ = 3î − 2ĵ + 6k̂.
2. For what value of λ are the vectors a⃗ = 2î + λĵ + k̂ and b⃗ = î − 2ĵ + 3k̂ perpendicular to each other?
3. A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability distribution of the number of successes.
4. Show that the rectangle of maximum area that can be inscribed in a circle is a square.
5. Using integration, find the area of the region bounded by the parabola y² = 4x and the circle 4x² + 4y² = 9.
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 persons meets with an accident. What is the probability that he is a scooter driver?