02%20-%20Mathematics%20-%20July%202006

02%20-%20Mathematics%20-%20July%202006 - Time : 3 hours 02...

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Time : 3 hours 02 - Mathematics - July 2006 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. 1. d [ ( l 7 l , - 8 ), ( l - 7 l , - 3 ) ] = ? ( a ) - 5 ( b ) 11 ( c ) 5 ( d ) - 11 2. The Cartesian equation of the line passing through ( 5, 6 ) and ( - 3, 6 ) is ( a ) y - 6 = 0 ( b ) y + 6 = 0 ( c ) x - 5 = 0 ( d ) x + 3 = 0 3. The equation of the circle touching the y - axis and having its centre at ( 3, - 4 ) is ( a ) x 2 + y 2 + 6x + 8y + 16 = 0 ( b ) x 2 + y 2 - 6x + 8y + 9 = 0 ( c ) x 2 + y 2 - 6x - 8y + 9 = 0 ( d ) x 2 + y 2 - 6x + 8y + 16 = 0 4. The end points of the latus - rectum for parabola x 2 = - 6y are ( a ) ± 2 3 3, - ( b ) 3 , 2 3 - ( c ) 3 , 2 3 - - ( d ) ± 2 3 3, 5. Measure of the angle between asymptotes of 4x 2 - y 2 = 9 is ( a ) 3 4 tan 1 - - ( b ) π 3 4 tan 1 - - ( c ) 3 π ( d ) 3 4 tan 1 - 6. Which is a unit vector ? ( a ) ( cos α , 2sin α ) ( b ) (sin α , cos α ) ( c ) ( 1, - 1 ) ( d ) (2cos α , sin α ) 7. x = ( 1, - 1 ) and y = ( 1, 0 ), then cos x ^ y = ( a ) 1 ( b ) 0 ( c ) 2 1 ( d ) y 8. Measure of the angle between x + 2y + z = 1 and r = ( 0, 0, 0 ) + k ( 2, 1, - 1 ), k R is ( a ) 6 π ( b ) 3 π ( c ) 2 π ( d ) 4 π
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Time : 3 hours 02 - Mathematics - July 2006 Marks : 100 Pg - 2 9. The plane r . ( 2, - 2, 1 ) = - 12 touches the sphere x 2 + y 2 + z 2 - 2x - 4y + 2z - 3 = 0, then the point of contact is ( a ) ( 1, - 4, 2 ) ( b ) ( - 1, 4, - 2 ) ( c ) ( - 1, 4, 2 ) ( d ) none of these 10. 4
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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.

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02%20-%20Mathematics%20-%20July%202006 - Time : 3 hours 02...

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