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# Class 12 ISC Pre board 2015 : Mathematics

3 pages, 38 questions, 28 questions with responses, 35 total responses,    0    0
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-4Question 9. (a) Find the particular solution of the differential equation: e given y (0) = 3. (b) If z = dy dx = x + 1, [5] 13 5i , using De Moivre s theorem prove that z 6 = 8i. [5] 4 9i SECTION B [Any TWO] Question 10. (a) In any triangle ABC, prove by vector method that [2x10=20] c = a cos B + b cos A. (b) Find vector equation of the line passing through the point (2,3, 2) and r r r r r r parallel to the line r = 2i + 3 j + (2i 3j + 6k). Also find the distance between them. Question 11. (a) Find the length and the foot of the perpendicular from the point (7,14,5) to the plane 2 x + 4 y z = 2. (b) Find the cartesian equation of the plane passing through the point (1, 1, 1) and perpendicular to the planes x + 2 y + 3 z 7 = 0 and 2x 3 y + 4z = 0 . Question 12. (a) The overall percentage of passes in a certain examination is 75. If five candidates from a certain town appear in the examination, what is the probability that at least four pass in the examination? (b) A consulting firm rents cars from three agencies such that 20% of the cars are rented from agency A, 30% from agency B and 50% from agency C. It is known that 70% of the cars from A, 80% of the cars from B and 90% of the cars from C are in good condition. If a car taken on rent is in good condition, what is the probability that it is from agency B? PRE BOARD EXAMINATION CLASS XII MATHEMATICS Marks: 100 Time: 3 Hours (Candidates are allowed additional 15 minutes for only reading the paper. They must NOT start writing during this time.) Section A - Answer Question 1 (compulsory) and any other five questions. Section B and Section C - Answer any two questions from either Section B or Section C. All working, including rough work, should be done on the same sheet as, and adjacent to, the rest of the answer. SECTION A Question 1. [10x3=30] 2 2 2 and A = kA, then find the value of k. 2 2 1. If A = 2. Using suitable substitution, express in the simplest form: 1 + x2 1 tan 1 . x 3. Find the value of k so that the line y = 2 x + k touches the ellipse 3 x 2 + 5 y 2 = 15. 4. Evaluate: 5. Evaluate: Lim ( 1 tan x ) sec 2 x x 4 log x ( 1 + log x ) 2 dx a 6. Using properties of definite integrals, evaluate: 0 x dx x + a x 7. A die is thrown three times. If the first outcome is a four, find the probability of getting 15 as a sum. 8. You are given the following two regression lines. Find the regression line of Y on X & that of X on Y. Justify your answer. 3 x + 4 y = 8; 4 x + 2 y = 10.

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