CBSE 2012 Mathematics Question Paper for Class 12

About this paper

This is the CBSE Class 12 Mathematics question paper code 65/1 (Series SMA) from the 2012 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. Internal choice is given in four of the four-mark and two of the six-mark questions, and calculators are not allowed. Notable questions include a ladder sliding down a wall (rate of change), the family of circles touching the coordinate axes, a die-and-coin Bayes' theorem problem and a dietician's linear programming problem on mixing two foods for vitamins A and C. Questions only, no answers.

Exam

CBSE Class 12

Subject

Mathematics

Year

2012

Paper code

65/1

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 and functions
• Inverse trigonometric functions
• Matrices and determinants
• Continuity and differentiability
• Rate of change and maxima–minima
• Integrals
• Area of a region
• Differential equations
• Vectors
• Three-dimensional geometry
• Probability distributions and Bayes' theorem
• Linear programming

Questions from this paper

1. The binary operation * : R × R → R is defined as a * b = 2a + b. Find (2 * 3) * 4.
2. Let A be a square matrix of order 3 × 3. Write the value of |2A|, where |A| = 4.
3. Find the distance of the plane 3x − 4y + 12z = 3 from the origin.
4. A ladder 5 m long is leaning against a wall. The bottom of the ladder is pulled along the ground, away from the wall, at the rate of 2 cm/s. How fast is its height on the wall decreasing when the foot of the ladder is 4 m away from the wall?
5. Two cards are drawn simultaneously (without replacement) from a well-shuffled pack of 52 cards. Find the mean and variance of the number of red cards.
6. Prove that the radius of the right circular cylinder of greatest curved surface area which can be inscribed in a given cone is half of that of the cone.