Time : 3 hours 04 - Mathematics - July 2007 Marks : 100 Pg - 1Instructions : 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. 151. Find the angle between the lines x = 3 and y = 5. ( a ) 2π( b ) 3π( c ) 6π( d ) 4π2. If the lines 5x -Ky -7 = 0 and 2x + 3y + 5 = 0 are mutually perpendicular, then the value of K = ? 10-1015-153. How many tangents can be drawn from the origin ( 0, 0 ) to the curve x2+ y2= 25 ? 4. If x2= -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 ) 31,32,32( b ) -2, 2, 1 ( c ) 31,31,31( d ) 1, 1, 1 6. Find the eccentricity of hyperbola 3x2-12y2= 36. 3325- 57. Find the projection of vector ( 1, 1 ) on the direction ( 3, 4 ). 7( 1, 1 ) 7( 3, 4 ) 78. Find the rate of change of volume of a sphere having radius r with respect to its surface area. rr
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