Gmath

Question 16:  Let f(x) be a real differentiable function such that f(0) = 1 and f(x + y) = f(x).f'(y) + f'(x).f(y) for all x, y ∈ R. Then is equal to : (i) 2384                   (ii) 2525 (iii) 5220                 (iv) … Read more

Let for (x) = 7 tan^8 x + 7 tan^6 – 3 tan^4 x – 3 tan^2 Question 15 : Let for , and . Then is equal to (i) 2π            (ii) π (iii) 1             (iv) 2 Answer : (iii) 1  Explanation :  Let for … Read more

Question 14: A circle C of radius 2 lies in the second quadrant and touches bothe the coordinate axes. Let r be the radius of a circle that has centre at the point (2, 5) and intersects the circle C at exactly two points. If the set of all possible values of r is the … Read more

Question 13: Let the parabola y = x³ + px – 3 meet the coordinate axes at the points P, Q and R. If the circle C with centre at (-1, -1) passes through the points P, Q and R, then the area of ΔPQR is : (i)  4                … Read more

Let x = x(y) be the solution of the differential equation y² dx + (x – 1/y) dy = 0 Question 12 : Let x = x(y) be the solution of the differential equation . x(1) = 1 then x(1/2) is : (i) 1/2 + e         (ii) 3/2 + e (iii) 3 … Read more

Question 11: From all the English alphabets five letters are chosen and are arranged in alphabetical order. The total number of ways, in which the middle letter is ‘M’, is : (1) 14950              (2) 6084 (3) 4356                (4) 5148        … Read more

If ∑Tr = (2n-1)(2n+1)(2n+3)(2n+5)/64 then  Question 10:-  If , then is equal to (i) 1                     (ii) 0 (iii) 2/3                (iv) 1/3                                      … Read more

The product of all solutions of the equation e^{5(log_e x)^2 + 3} = x^8, x > 0 Question 9:- The product of all solutions of the equation is : (i)                  (ii) (iii)                   (iv)           … Read more

Let L1: (x – 1)/(2)=(y-2)/(3)=(z-3)/(4) and L2 : (x – 2)/(3)=(y-4)/(4)=(z-5)/(5) Question 8:-  Let and be two lines. Then which of the following points lies on the line of the shortest distance between and ? (i) (-5/3, -7, 1)            (ii) (2, 3, 1/3) (iii) (8/3, -1, 1/3)        … Read more