04%20-%20Mathematics%20-%20July%202007

04%20-%20Mathematics%20-%20July%202007 - Time : 3 hours 04...

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Time : 3 hours 04 - Mathematics - July 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. Find the angle between the lines x = 3 and y = 5. ( a ) 2 π ( b ) 3 π ( c ) 6 π ( d ) 4 π 2. If the lines 5x - Ky - 7 = 0 and 2x + 3y + 5 = 0 are mutually perpendicular, then the value of K = ? ( a ) 3 10 - ( b ) 3 10 ( c ) 2 15 - ( d ) 2 15 3. How many tangents can be drawn from the origin ( 0, 0 ) to the curve x 2 + y 2 = 25 ? ( a ) 1 ( b ) 0 ( c ) 2 ( d ) 1 or 2 4. If x 2 = - 16y, then find the equation of the tangent which is perpendicular to Y - axis. ( a ) x = 0 ( b ) y = 0 ( c ) x = 4 ( d ) x = - 4 5. Find the direction cosines of the vector 2i + 2j + k. ( a ) 3 1 , 3 2 , 3 2 ( b ) - 2, 2, 1 ( c ) 3 1 , 3 1 , 3 1 ( d ) 1, 1, 1 6. Find the eccentricity of hyperbola 3x 2 - 12y 2 = 36. ( a ) 4 3 ( b ) - 4 3 ( c ) 2 5 - ( d ) 2 5 7. Find the projection of vector ( 1, 1 ) on the direction ( 3, 4 ). ( a ) 5 7 ( 1, 1 ) ( b ) 5 7 ( 3, 4 ) ( c ) 25 7 ( d ) none of these 8. Find the rate of change of volume of a sphere having radius r with respect to its surface area. ( a ) r ( b ) 4r ( c ) 2 r ( d ) 3 r
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Time : 3 hours 04 - Mathematics - July 2007 Marks : 100 Pg - 2 9. Find the centre of the sphere l r 2 l - r . (2, 1, 3 ) - 2 = 0. ( a ) ( - 4, - 2, - 6 ) ( b ) 2 3 , 2 1 1, ( c ) ( 2, 1, 3 ) ( d ) ( 0, 0, 0 ) 10. ? 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.

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04%20-%20Mathematics%20-%20July%202007 - Time : 3 hours 04...

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