Gmath

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

Let a1 a2 a3 . . . be a G.P. of increasing positive terms Question 7:-  Let be a G.P. of increasing positive terms. If and , the is equal to (i) 628               (ii) 526 (iii) 784              (iv) 812          … Read more

Question 6:- A coin is tossed three times. Let X denote the number of times a tail follows a head. If μ and σ² denote the mean and variance of X, then the value of 64(μ + σ²) is : (i)  51                 (ii)  48 (iii) 32          … Read more

Question 5:- Using the principal values of the inverse trigonometric functions the sum of the maximum and the minimum values of  is : (1) 24 π²             (2) 18 π² (3) 31 π²             (4) 22 π²                    [JEE … Read more

Let Z1 Z2 and Z_3 be three complex numbers on the circle Question 4:- Let and be three complex numbers on the circle |Z| = 1 with and . If , then the value of α² + β² is : (1) 24                (2) 41 (3) 31      … Read more