ISC 2014 Mathematics Question Paper for Class 12

About this paper

This is the ISC Class 12 Mathematics paper, code 860, set by CISCE for the 2014 board examination. The time allowed is three hours, with an extra fifteen minutes for reading. Candidates answer Question 1, which is compulsory, and five other questions from Section A, then two questions from either Section B or Section C. There are fifteen questions in all. Mathematical tables and graph paper are provided, and a slide rule may be used. Section B covers vectors, three-dimensional lines and planes, and probability; Section C covers commercial arithmetic, linear programming and statistics. All working, including rough work, is to be shown beside the answer. This copy has the questions only.

Exam

ISC Class 12

Subject

Mathematics

Year

2014

Paper code

860

Time allowed

3 hours + 15 min reading

Questions

15

Pages

6

Answers included

No, questions only

Paper pattern

• Section A

  Question 1, ten compulsory parts, and any five of Questions 2–9; each of Questions 2–9 is in two parts

• Section B

  Questions 10–12 on vectors, three-dimensional geometry and probability; answer any two questions from either this section or Section C

• Section C

  Questions 13–15 on commercial mathematics, linear programming and statistics; the alternative to Section B

Topics covered

• Matrices and determinants
• Inverse trigonometric functions
• Limits and L'Hospital's rule
• Indefinite and definite integrals
• Differential equations
• Conic sections
• Complex numbers
• Boolean algebra and switching circuits
• Probability
• Correlation and regression
• Vectors and three-dimensional geometry
• Linear programming and index numbers

Questions from this paper

1. If A = [[3, 1], [7, 5]], find the values of x and y such that A² + x I₂ = y A.
2. Find the eccentricity and the coordinates of the foci of the hyperbola 25x² − 9y² = 225.
3. Using L'Hospital's rule, evaluate lim (x → 0) of (1 + sin x)^(cot x).
4. Using properties of definite integrals, evaluate ∫ from 0 to π/2 of √(sin x) / (√(sin x) + √(cos x)) dx.
5. Using De Moivre's theorem, find the least positive integer n such that ((2i)/(1 + i))^n is a positive integer.
6. A company makes two types of toys. Type A needs 5 minutes of cutting and 10 minutes of assembling; type B needs 8 minutes of each. With 3 hours for cutting and 4 hours for assembling, and profits of ₹50 and ₹60, how many of each toy maximise the profit? Use linear programming.