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# ISC Class XII Prelims 2019 : Mathematics (Madhusthali Vidyapeeth, Deoghar)

5 pages, 55 questions, 45 questions with responses, 65 total responses,    2    0
 Soumya Roy Sikkim Manipal University (SMU), Gangtok Master of Computer Application Computer Application
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F.M 100 Tim e 3 Hrs HALF-YEARLY EXAMINATION 2018-2019 SUBJECT: MATHEMATICS CLASS- XII (Candidates are allowed additional 15 minutes for only reading the paper. They must NOT start writing during this time.) The Question Paper consists of three sections A, B and C. Candidates are required to attempt all question from Section A and all question EITHER from Section B OR Section C Section A: Internal choice has been provided in three questions of 4 marks each and two questions of 6 marks each. Section B: Internal choice has been provided in two questions of 4 marks each. Section C: Internal choice has been provided in two questions of 4 marks each. All working, including rough work, should be done on the same sheet as, and adjacent to the rest of the answer. The intended marks for questions or parts of questions are given in brackets [ ]. Mathematical tables and graph papers are provided. SECTION A(80 Marks) Question 1 (i) The binary operation *: R X R R is defined as a * b = 2a + b. Find ( 2 * 3 ) * 4. 5 a (ii) If A = and A is symmetric matrix, show that a = b. b 0 (iii) Solve 3 tan 1 x + cot 1 x = (iv) Without expanding at any stage, find the value of: 2 x y+z 2 y z+ x 2 z x+ y (v) Find the value of k so that f(x) defined as: [10 2] [ ] | | { (vi) (vii) (viii) (ix) x 2 2 x 3 f(x) = is continuous at x = -1 , x 1 x+1 k , x= 1 Find the approximate change in the volume V of a cube of side x metres caused by decreasing the side by 1%. 1 1 1 If A and B are events such that P(A) = , P(B) = and P(A B) = , then find: 2 3 4 P(A|B) and P(B|A) 1 1 In a race, the probabilities of A and B winning a race are 3 respectively. Find the 6 probability of neither of them winning the race. Using L Hospital s Rule, evaluate: 1

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