03%20-%20Mathematics%20-%20March%202007

03%20-%20Mathematics%20-%20March%202007 - Time 3 hours 03...

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Unformatted text preview: Time : 3 hours 03 - Mathematics - March 2007 Marks : 100 Pg - 1 Instructions : 1. Answer all questions. 2. Write your answers according to the instructions given below with the questions. 3. Begin each section on a new page. S E CT I O N - A • Given below are 1 to 15 multiple choice questions. Each carries one mark. Write the serial number ( a or b or c or d ) in your answer book of the alternative which you feel is the correct answer of the question. 15 1. For Δ ABC, A is ( 1, 2 ), B is ( 3, 4 ) and C is on X - axis. If the centroid of Δ ABC is on Y - axis, then find the coordinates of C. ( a ) ( - 4, 0 ) ( b ) ( 2, 0 ) ( c ) ( 0, - 4 ) ( d ) none of these 2. Find the equation of the perpendicular bisector of AB, where A is (2, 2 ) and B is (4, 2 ). ( a ) y - 3 = 0 ( b ) y + 3 = 0 ( c ) x - 3 = 0 ( d ) x - 2 = 0 3. Find the radius of a circle touching X - axis and having its centre at ( 4, - 3 ) ( a ) 4 ( b ) 3 ( c ) 5 ( d ) none of these. 4. There is a point on the parabola y 2 = 2x, whose x - coordinate is two times the y - coordinate. Find the point. ( a ) ( 4, 2 ) ( b ) ( 6, 3 ) ( c ) ( 4, 8 ) ( d ) ( 8, 4 ) 5. Find the measure of the angle between the asymptotes of x 2- y 2 = 16. ( a ) 2 π ( b ) 3 π ( c ) 4 π ( d ) none of these 6. If a = 5, b = 3 and b a- = 4, then find b . a . ( a ) - 9 ( b ) 0 ( c ) 9 ( d ) none of these 7. Force k j i + + is applied at B ( 1, 2, 3 ). Find the torque around A ( - 1, 2, 0 ) and its magnitude. ( a ) 14 ( b ) ( - 3, 1, 2 ) ( c ) ( 3, - 1, - 2 ) ( d ) none of these 8. Find the measure of the angle between the planes ax + by + d = 0 and z = 0, ( a 2 + b 2 ≠ 0 ). ( a ) 3 π ( b ) 2 2 1 b a d cos +- ( c ) 4 π ( d ) 2 π Time : 3 hours 03 - Mathematics - March 2007 Marks : 100 Pg - 2 9. Find x x sin lim x → . ( a ) - 1 ( b ) 1 ( c ) 0 ( d ) limit does not exist 10. Find 1 x , e dx d x 1 cos x 1 sin < ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ +-- ( a ) ( b ) ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + x 1 cos x 1 sin e-- 2 x 1 cos x 1 sin x 1 e--- ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + ( c ) 0 ( d ) none of these 11. Find dx. ) x tan 1 ( x sec e x + ∫ ( a ) ( b ) ( c ) ( d ) none of these c x tan e x...
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03%20-%20Mathematics%20-%20March%202007 - Time 3 hours 03...

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