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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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This note was uploaded on 11/28/2011 for the course MATH 300 taught by Professor Jones during the Spring '06 term at ITT Tech Flint.
 Spring '06
 Jones
 Math

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