05%20-%20Mathematics%20-%20March%202008

05%20-%20Mathematics%20-%20March%202008 - Time : 3 hours 05...

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Time : 3 hours 05 - Mathematics - March 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. Find the value of a, if P ( 2, 3 ) is circumcentre of the triangle with vertices A ( a, 6 ), B ( 5, 1 ) and C ( 4, 6 ). ( a ) - 4 ( b ) 1 ( c ) 4 ( d ) 0 2. Find α if a line x + y + 1 = 0 is converted in the form of a line x cos α + y sin α = p. ( a ) 4 π ( b ) 4 π 3 ( c ) 4 π 5 ( d ) 4 π 7 3. If the circle x 2 + y 2 + 4x + Ky - 4 = 0 touches both the axes, then find K. ( a ) ± 8 ( b ) ± 4 ( c ) ± 2 ( d ) ± 1 4. Obtain the equation of a parabola having focus ( 0, - 2 ) and the equation of directrix y = 2. The vertex of the parabola is ( 0, 0 ). ( a ) x 2 = - 8y ( b ) y 2 = 8x ( c ) x 2 = 8y ( d ) y 2 = - 8x 5. Find the radius of a director - circle of an ellipse 4x 2 + 9y 2 = 36. ( a ) 5 ( b ) 13 ( c ) 10 ( d ) 5 6. If a = 10, b = 2 and b . a = 12, then find b x a ( a ) 12 ( b ) 14 ( c ) 16 ( d ) 18 7. Find magnitude of projection of vector k j i + + on j. ( a ) - 1 ( b ) 0 ( c ) 1 ( d ) 2 8. Find the measure of the angle between planes r . ( 1, 2, 1 ) = 1 and 1 z 1 y 2 x - = = . ( a ) 6 π ( b ) 3 π ( c ) 4 π ( d ) none of them
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Time : 3 hours 05 - Mathematics - March 2008 Marks : 100 Pg - 2 9. Find x 1 ) x 1 ( lim 3 1 0 x - + ( a ) 0 ( b ) 1 ( c ) 3 1 ( d ) none of these 10. Find + 2 1 1 x cos 1 x cos 1 tan dx d - - : π < x < 2 π . ( a )
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05%20-%20Mathematics%20-%20March%202008 - Time : 3 hours 05...

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