01%20-%20Mathematics%20-%20March%202006

01%20-%20Mathematics%20-%20March%202006 - Time : 3 hours 01...

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Unformatted text preview: Time : 3 hours 01 - Mathematics - March 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. If the co-ordinates of a point ( 6, -1 ) changes to ( 8, - 4 ), then write the co-ordinates of the point where the origin is shifted. ( a ) ( 2, - 3 ) ( b ) ( -3, 2 ) ( c ) ( 3, - 2 ) ( d ) ( - 2, 3 ) 2. Write the measure of the angle between the lines x + y = 0 and y = [ ] ( a ) 4 ( b ) 3 ( c ) 2 ( d ) 0 3. How many tangents to the circle x 2 + y 2 = 29 pass through the point ( 5, 2 ) ? ( a ) 0 ( b ) 1 ( c ) 2 ( d ) none of these 4. The standard equation of the parabola having vertex at the origin, passing through ( -1, 1 ) and symmetric about y - axis is ( a ) y 2 = - x ( b ) x 2 = y ( c ) y 2 = x ( d ) x 2 = - y 5. Write the equation of the auxiliary circle of 1 9 y 4 x 2 2- = . ( a ) x 2 + y 2 = - 5 ( b ) x 2 + y 2 = 5 ( c ) x 2 + y 2 = 4 ( d ) x 2 + y 2 = 9 6. Obtain l cos cos , cos sin , sin l ( a ) - 1 ( b ) 0 ( c ) 1 ( d ) none of these 7. Find the resultant force of ( 1, 2, - 1 ) and ( 1, - 2, 1 ) ( a ) ( 2, 0, 0 ) ( b ) ( - 1, 4, 2 ) ( c ) ( 2, 4, 2 ) ( d ) ( - 2, 0, 0 ) 8. Find the centre of the sphere x 2 + y 2 + z 2- 2x - 4y - 6z - 11 = 0. ( a ) ( - 1, - 2, - 3 ) ( b ) ( 3, 2, 1 ) ( c ) ( 1, 2, 3 ) ( d ) ( 1, 2, - 3 ) Time : 3 hours 01 - Mathematics - March 2006 Marks : 100 Pg - 2 9. Find x 1 e lim- 3x x ( a ) 3 ( b ) 3 1 ( c ) log e e ( d ) log e 3 10. Find dx d (sin 2 x) ( a ) - sin 2x ( b ) cos 2 x ( c ) cos 2x ( d ) sin 2x 11. Find c, of Mean - value theorem for f(x) = log x, x [ 1, e ] ( a ) e - 1 ( b ) 1...
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01%20-%20Mathematics%20-%20March%202006 - Time : 3 hours 01...

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