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MATHEMATICS (Three hours) (Candidates are allowed additional 15 minutes for that interpretation the paper. They must NOT start writing during this time.) -------------------------------------------------------------------------------------------------------------------- particle A - service Question 1 (compulsory) and five some other questions. Section B and Section C - Answer dickens questions from either Section B or Section C. every last(predicate) working, including rough work, should be done on the same stable gear as, and adjacent to, the bide of the answer. The intended marks for questions or split of questions are given up in brackets [ ]. Mathematical tables and represent papers are provided. slew rule may be recitationd. --------------------------------------------------------------------------------------------------------------------SECTION A Question 1 (i) (ii) (iii) (iv) If A 3 1 , harness x and y so that A2 + xI2 = yA. 7 5 [10 3] evaluate: tan[2Tan-1( 1/5) - / 4] Find the esteem(s) of k so that the enclosure 3x 4y + k = 0 is tangent to the hyperbola x2 4y2 = 5. esteem: x 1 Lim x 1 log x x 1 (v) [ survey: xe x dx ( x 1) 2 2 (vi) Evaluate 0 2cos x wickedness 2x dx 2(1 sin x) 1 ISC archetype Question Paper 2013 (vii) Deepak rolls cardinal cut and stays a sum more than 9. What is the probability that the number on the original die is even?

(viii) You are given the adjacent two lines of regression. Find the regression of Y on X and X on Y and justify your answer: 3x + 4y = 8; 4x + 2y = 10 (ix) (x) If w is the cube root of unity, then find the value of (1-3w+w2) (1+w-3w2) Solve: (y + xy)! dx + y (1-y2)dy = 0 Question 2 (a) use properties of determinants, prove that: [5] b2 c2 ba ca (b) ab c2 a 2 cb ac bc 2 a b2 4a 2 b 2c2 apply matrix method, solve the following system of analog equations: x 2y 2z 5 = 0; x + 3y + 4 = 0 and 2x + z 4 = 0 [5] Question 3 (a) ramble Rolles theorem for f(x) = ex(sinx cosx) on the interval where derivative vanishes. (b) Find the equation of the parabola whose vertex...If you want to get a full essay, order it on our website: OrderCustomPaper.com

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