Differential (calculus) Question no. 1 If f(x)= tanx + e -2x -7x 3 , then what is the value of f'(0)? looks_one -2 looks_two -1 looks_3 0 looks_4 3 Answer Option looks_two -1 Solution Solution : f(x)= tanx + e -2x -7x 3 f'(x) = sec 2 x - 2e -2x - 21x 2 f'(0) = 1 - 2 = -1 Question no. 2 looks_one ( 3 x+y - 3 x ) / 3 y looks_two (3 x-y )( 3 y - 1 ) / ( 1 - 3 x ) looks_3 ( 3 x + 3 y ) /(3 x - 3 y ) looks_4 ( 3 x + 3 y ) /( 1 + 3 x+y ) Answer option looks_two (3 x-y )( 3 y - 1 ) / ( 1 - 3 x ) Solution Solution : 3 x + 3 y = 3 x+y diferentiate with respect to x 3 x log3 + 3 y log3(dy/dx) = 3 x+y log3( 1 + dy/dx) 3 x + 3 y (dy/dx) = 3 x+y ( 1 + dy/dx) dy/dx = (3 x+y - 3 x )/(3 y - 3 x+y ) dy/dx = (3 x )( 3 y - 1 ) /((3 y )) ( 1 - 3 x ) dy/dx = (3 x-y )( 3 y - 1 ) / ( 1 - 3 x ) Question no. 3 If f(x)= sin 2 x 2 , then what is f(x) equal to ? lo...

Straight lines Question no. 31 The point whose abscissa is equal to its ordinate and which is equidistant from the points (1,0) and (0,3) is looks_one (1,1) looks_two (2,2) looks_3 (3,3) looks_4 (4,4) Answer Option looks_two (2,2) Solution Solution : point of abscissa (x) = point on ordinate (y) = a PA = PB [(a-1) 2 + a 2 ] 1/2 = [a 2 + (a-3) 2 ] 1/2 (a-1) 2 + a 2 = a 2 + (a-3) 2 a 2 + 1 - 2a + a 2 = a 2 + a 2 + 9 - 6a 4a = 8 a = 2 point is (2,2) Question no. 32 Equation of a line passing through (1,-2) and perpendicular to the line 3x-5y +7 =0 is looks_one 5x + 3y +1=0 looks_two 3x + 5y +1=0 looks_3 5x - 3y - 1=0 looks_4 3x - 5y + 1=0 Answer Option looks_one 5x + 3y +1=0 Solution Solution : Slope of line : 3x-5y +7 =0 y = (3/5)x + (7/5) m 1 = 3/5 m 1 .m 2 = -1 m 2 = -5/3 y = mx + c point (1 , -2) satisfy the equation -2 = (-5/3)(1) + c c = -1/3 y = (-5/3)x - 1/3 3y = ...

General Instruction 1. All the questions are compulsory 2. The question paper consists of 40 question and it is divided into four sections A,B , C and D. SECTION A Comprises of 20 questions carrying 1 mark each. Section B comprises of 6 questions carrying 2 marks each, Second C comprises of 8 questions carrying 3 marks each. Section D comprises of 6 questions carrying 4 marks each. 3. There is no overall choice 4. Use of calculator is not permitted. Section A 1. What is the mean of first 12 prime number? 2. If the zeros of the quadratic polynomial x 2 + (a+1)x + b are 2 and -3 , then a) a=-7 ,b=-1 b) a=5 , b=-1 c) a=2 ,b=-6 d) a=0, b=-6 3. If the probability of an event is 'p' the probability of its complementary event will be a) p-1 b) p c ) 1-p d) 1-1/p 4. The decimal expansion of the rational number 237/(2 3 ✕5) will terminate after a) one decimal place b) two decimal place c) three decimal place d) more than three decimal place ...