06%20-%20Mathematics%20-%20July%202008

# 06%20-%20Mathematics%20-%20July%202008 - Time 3 hours 06...

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Time : 3 hours 06 - Mathematics - July 2008 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. In Δ ABC, if A is ( 1, - 6 ), B is ( - 5, 2 ) and the centroid G is ( - 2, 1 ), then the coordinates of vertex C are ( a ) ( - 2, 1 ) ( b ) ( - 2, 6 ) ( c ) ( 3, 2 ) ( d ) ( - 2, 7 ) 2. d { ( a, 0 ), ( 0, b ) } = ? ( a ) a ( b ) b ( c ) l a - b l ( d ) 2 2 b a + 3. The t point of parabola y 2 = 20x is ….. ( t R ). ( a ) ( 5t, 4t 2 ) ( b ) ( 5t 2 , 4t ) ( c ) ( 5t 2 , 10t ) ( d ) ( t, 2t ) 4. If y = 2x + c touches a parabola y 2 = 16x, then the value of c is ….. ( a ) 2 ( b ) - 2 ( c ) 8 ( d ) 2 5. The equation of director circle of ellipse 1 16 y 9 x 2 2 = + is ….. ( a ) x 2 + y 2 = 9 ( b ) x 2 + y 2 = 16 ( c ) x 2 + y 2 = 25 ( d ) x 2 + y 2 = 7 6. The eccentricity of hyperbola x 2 - y 2 = 144 is ….. ( a ) 21 ( b ) 2 ( c ) 7 ( d ) 3 7. For distinct non - null vectors d , c , b , a R 3 , prove that ) d c ( . ) b a ( × × is ….. ( a ) d . b c . b d . a c . a ( b ) d . a c . a d . b c . b ( c ) c . b d . b c . a d . a ( d ) c . a d . a c . b d . b 8. The projection of a = ( 1, 1, 1 ) on b = ( 2, 2, 1 ) is ….. ( a ) 9 5 ( 2, 2, 1 ) ( b ) ( 1, 3, 2 ) ( c ) ( 0, 0, 1 ) ( d ) 9 1 ( 1, 3, 2 )

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Time : 3 hours 06 - Mathematics - July 2008 Marks : 100 Pg - 2 9. The direction of a line passing through points ( 3, 2, 1 ) and ( 5, 6, 7 ) is ….. ( a )
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06%20-%20Mathematics%20-%20July%202008 - Time 3 hours 06...

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