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MATHEMATICS (Three hours) (Candidates are allowed additional 15 minutes for solo interpretation the paper. They must NOT start writing during this time.) -------------------------------------------------------------------------------------------------------------------- trimmings A - service Question 1 (compulsory) and five separate questions. Section B and Section C - Answer dickens questions from either Section B or Section C. totally working, including rough work, should be done on the same yellow journalism 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 interpret papers are provided. slew rule may be usaged. --------------------------------------------------------------------------------------------------------------------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 appreciate(s) of k so that the enclosure 3x 4y + k = 0 is tangent to the hyperbola x2 4y2 = 5. label: x 1 Lim x 1 log x x 1 (v) [ approximate: xe x dx ( x 1) 2 2 (vi) Evaluate 0 2cos x wickedness 2x dx 2(1 sin x) 1 ISC model Question Paper 2013 (vii) Deepak rolls ii cut and stays a sum more than 9. What is the probability that the number on the low 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 additive equatings: x 2y 2z 5 = 0; x + 3y + 4 = 0 and 2x + z 4 = 0 [5] Question 3 (a) insist 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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