CBSE 2010 Mathematics Question Paper for Class 12

About this paper

This is the CBSE Class 12 Mathematics question paper code 65/1/1 (Series SMA/1) from the 2010 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 of the four-mark and two of the six-mark questions have an internal choice, and calculators are not permitted. Section C includes a linear programming problem on packages of nuts and bolts, a Bayes' theorem question on hostel students and day scholars, the area of a triangle bounded by three lines, and solving a system of equations using matrices. The paper has the questions only, without answers.

Exam

CBSE Class 12

Subject

Mathematics

Year

2010

Paper code

65/1/1

Maximum marks

100

Time allowed

3 hours

Questions

29

Pages

8

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

• Three-dimensional geometry
• Vectors
• Matrices and determinants
• Inverse trigonometric functions
• Functions and binary operations
• Continuity and differentiability
• Tangents, differentials and maxima–minima
• Integrals and definite integral as a limit of a sum
• Area under curves
• Differential equations
• Probability and Bayes' theorem
• Linear programming

Questions from this paper

1. If a line has direction ratios 2, −1, −2, what are its direction cosines?
2. Let * be a binary operation on N given by a * b = LCM(a, b) for all a, b ∈ N. Find 5 * 7.
3. How many times must a man toss a fair coin so that the probability of having at least one head is more than 80%?
4. Find the particular solution of the differential equation dy/dx = 1 + x + y + xy, given that y = 1 when x = 0.
5. Find the equation of the plane determined by the points A(3, −1, 2), B(5, 2, 4) and C(−1, −1, 6), and hence find the distance between the plane and the point P(6, 5, 9).
6. Show that the height of a closed right circular cylinder of given surface and maximum volume is equal to the diameter of its base.