CBSE 2013 Mathematics Question Paper for Class 12

About this paper

This is the CBSE Class 12 Mathematics question paper code 65/2/1 (Series SMA/2) from the 2013 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 have internal choices, and calculators are not permitted. Section C includes the cone of maximum volume inscribed in a sphere, a plane through two points perpendicular to a given plane, a linear programming problem on chemical mix packets for a soft-drink company and a Bayes' theorem question on students' heights. Questions only, no answers.

Exam

CBSE Class 12

Subject

Mathematics

Year

2013

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

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

Questions from this paper

1. If the binary operation * on the set Z of integers is defined by a * b = a + b − 5, write the identity element for the operation * in Z.
2. Write the direction cosines of a line parallel to the z-axis.
3. Write the value of the area of the parallelogram determined by the vectors 2î and 3ĵ.
4. 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 and hence find its mean.
5. Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius R is 4R/3.
6. In a certain college, 4% of boys and 1% of girls are taller than 1.75 metres, and 60% of the students are girls. A student selected at random is found to be taller than 1.75 metres. Find the probability that the selected student is a girl.