Mathematics

General Instructions:

(i) All questions are compulsory.

(ii) The question paper consists of 29 questions divided into three Sections A, B and C. Section A comprises of 10 questions of one marks each, Section B comprises of 12 questions of four marks each and Section C comprises of 7 questions of six marks each.

(iii) All questions in Section A are to be answered in one word, one sentence or as per the exact requirement of the question.

(iv) There is no overall choice. However, internal choice has been provided in 4 questions of four marks each and 2 questions of six marks each. You have to attempt only one of the alternatives in all such questions.

(v) Use of calculators is not permitted.

SECTION –A

Question number 1 to 10 carry one mark each.

4. If matrix A = (1 2 3), write AA’, where A’ is the transpose of matrix A.

6. Using principal value, evaluate the following: sin-1(sin 3π/5)

7. Evaluate : ∫ [sec2x/(3 + tanx) ]dx

9. If the binary operation * on the set of integers Z, is defined by a * b = a + 3b2, then find the value of 2 * 4.

10. If A is an invertible matrix of order 3 and |A| = 5, then find |adj A|.

SECTION – B

12. Prove that sin-1(4/5) + sin-1(5/13) + sin-1(16/65) = π/2

                                               OR

Solve for x : tan-13x + tan-12x = π/4

13. Find the value of λ so that the lines (1 – x)/3 = (7y – 14)/2λ = (5z – 10)/11 and (7 – 7x)/3λ = (y – 5)/1 = (6 – z)/5 are perpendicular to each other.

14. Solve the following differential equation:              dy/dx + y = cos x – sin x.

15. Find the particular solution, satisfying the given condition, for the following differential equation:

                                        dy/dx – y/x + coses (y/x) = 0; y = 0 when x = 1.

17. A die is thrown again and again until three sixes are obtained. Find the probability of obtaining the third six in the sixth throw of the die.

18. Differentiate the following function w.r.t. x: xsin x + (sin x)cos x .

19. Evaluate : ∫...