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 = ? 10 - 10 15 - 15 3. How many tangents can be drawn from the origin ( 0, 0 ) to the curve x 2 + y 2 = 25 ? 4. If x 2 = - 16y, then find the equation of the tangent which is perpendicular to Y - axis. 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. 3 3 2 5 - 5 7. Find the projection of vector ( 1, 1 ) on the direction ( 3, 4 ). 7 ( 1, 1 ) 7 ( 3, 4 ) 7 8. Find the rate of change of volume of a sphere having radius r with respect to its surface area. r r
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