Let A = {1, 2, 3, 4, . . . , 10} and B = { m/n : m, n∈ A, m< n and gcd (m, n) = 1}
Question 17: Let A = {1, 2, 3, 4, . . . , 10} and B = { m/n : m, n∈ A, m< n and gcd (m, n) = 1}. Then n(B) is equal to : (i) 31 (ii) 36 (iii) 37 … Read more
Team Gmath
Let f(x) be a real differentiable function such that f(0) = 1
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
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
A circle C of radius 2 lies in the second quadrant and touches bothe the coordinate axes
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
Let the parabola y = x³ + px – 3 meet the coordinate axes
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
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
From all the English alphabets five letters are chosen
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
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
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)
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