ISC 2016 Mathematics Question Paper for Class 12

About this paper

This is the ISC Class 12 Mathematics paper, code 860, from the 2016 CISCE board examination. It carries 100 marks and runs for three hours, with fifteen minutes extra for reading only. Question 1 is compulsory, with ten parts of three marks each, and candidates add any five of Questions 2 to 9. They then answer two questions from either Section B or Section C. Section B covers vectors, the image of a point in a line, planes, and probability including a binomial distribution. Section C covers a semi-annual loan, a nickel-and-chromium linear programming problem, demand and revenue, a discounted bill, an aggregate index number and five-yearly moving averages. Tables and graph paper are provided, and a slide rule may be used. This copy has the questions only.

Exam

ISC Class 12

Subject

Mathematics

Year

2016

Paper code

860

Maximum marks

100

Time allowed

3 hours + 15 min reading

Questions

15

Pages

5

Answers included

No, questions only

Paper pattern

• Section A

  80 marks

  80 marks. Question 1, compulsory, ten parts of three marks each, and any five of Questions 2–9, ten marks each

• Section B or Section C

  20 marks

  20 marks. Any two questions from either Section B (Questions 10–12) or Section C (Questions 13–15), ten marks each

Topics covered

• Matrices and determinants
• Inverse trigonometric functions
• Conic sections
• Limits and L'Hospital's rule
• Definite integrals and area
• Differential equations and complex numbers
• Rolle's theorem and maxima
• Boolean algebra and switching circuits
• Correlation and regression
• Probability and binomial distribution
• Vectors and three-dimensional geometry
• Linear programming, index numbers and bills of exchange

Questions from this paper

1. Prove that the line 2x − 3y = 9 touches the conic y² = −8x, and find the point of contact.
2. The lines of regression are x + 2y − 5 = 0 and 2x + 3y − 8 = 0, and the variance of x is 12. Find the variance of y and the coefficient of correlation.
3. A pair of dice is thrown. What is the probability of getting an even number on the first die or a total of 8?
4. Verify Rolle's theorem for f(x) = log(x² + 2) − log 3 on [−1, 1], and find a point where the tangent is parallel to the x-axis.
5. A committee of 4 is chosen from 8 boys and 6 girls and must include at least one girl. Find the probability that it has more girls than boys.
6. A bill of ₹1,800 drawn on 10 September 2010 at 6 months was discounted for ₹1,782 at 5% per annum. On what date was the bill discounted?