CBSE 2007 Mathematics Question Paper for Class 12

About this paper

This is the CBSE Class 12 Mathematics question paper code 65/1/1 (Series SHC/1) from the 2007 board examination, printed in English and Hindi. It carries 100 marks over three hours and has 26 questions. Section A (Questions 1–18) is compulsory for everyone and covers matrices, determinants, probability, calculus, differential equations, and Boolean algebra and logic. Students then answer either Section B, on vectors, three-dimensional geometry, statics and dynamics, or Section C, on commercial mathematics such as bills of exchange, partnership, annuities, cost functions and linear programming. Some questions have internal choices. Calculators are not permitted, though logarithmic and statistical tables may be requested. This copy has the questions only, without answers.

Exam

CBSE Class 12

Subject

Mathematics

Year

2007

Paper code

65/1/1

Maximum marks

100

Time allowed

3 hours

Questions

26

Pages

15

Answers included

No, questions only

Paper pattern

• Section A

  70 marks

  Compulsory: Questions 1–8 of 3 marks, 9–15 of 4 marks and 16–18 of 6 marks

• Section B or Section C

  30 marks

  Attempt one: Questions 19–22 of 3 marks, 23–25 of 4 marks and 26 of 6 marks; Section B is vectors, 3D geometry and mechanics, Section C is commercial mathematics, probability and linear programming

Topics covered

• Matrices and determinants
• Probability and probability distributions
• Differential equations
• Indefinite and definite integrals
• Limits, continuity and differentiation
• Boolean algebra and mathematical logic
• Rolle's theorem and maxima–minima
• Area between curves
• Vectors and three-dimensional geometry
• Statics and dynamics
• Bills of exchange, partnership and annuities
• Cost functions and linear programming

Questions from this paper

1. If A = [2 −3; 3 4], show that A² − 6A + 17I = 0. Hence find A⁻¹.
2. An urn contains 7 red and 4 blue balls. Two balls are drawn at random with replacement. Find the probability of getting (a) 2 red balls, (b) 2 blue balls, (c) one red and one blue ball.
3. Verify Rolle's theorem for the function f(x) = x² − 5x + 4 on [1, 4].
4. Using integration, find the area of the region enclosed between the circles x² + y² = 1 and (x − 1)² + y² = 1.
5. A body of weight 70 N is suspended by two strings of lengths 27 cm and 36 cm, fastened to two points 45 cm apart in the same horizontal line. Find the tensions in the strings.
6. Find the face value of a bill discounted at 6% per annum 146 days before the legal due date, if the banker's gain is Rs. 36.