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ISC Class XII Board Exam 2019 : Mathematics

6 pages, 54 questions, 0 questions with responses, 0 total responses,    0    0
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MATHEMATICS (Maximum Marks: 100) (Time allowed: Three hours) (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 questions from Section A and all questions EITHER from Section B OR Section C Section A: Internal choice has been provided in three questions of four marks each and two questions of six marks each. Section B: Internal choice has been provided in two questions of four marks each. Section C: Internal choice has been provided in two questions of four 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) If f : R R, f(x)= x3 and g : R R, g(x) = 2x2+1, and R is the set of real numbers, then find fog (x) and gof (x). (ii) Solve: Sin (2 tan-1x) = 1 (iii) Using determinants, find the values of k, if the area of triangle with vertices ( 2, 0), (0, 4) and (0, k) is 4 square units. (iv) (v) (vi) [10 2] 2 4 Show that (A + A ) is symmetric matrix, if A = . 3 5 x2 9 is not defined at x = 3. What value should be assigned to f(3) for x 3 continuity of f(x) at x = 3? f x Prove that the function f(x) = x3 6x2 + 12x + 5 is increasing on R. --------------------------------------------------------------------------------------------------------------------This Paper consists of 6 printed pages. 1219-860 Turn over Copyright reserved.

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