Let `(x_0, y_0)` be the solution of the following equations: `(2x)^(1n2)=(3y)^(1n3)` `3^(1nx)=2^(1ny)` The `x_0` is `1/6` (b) `1/3` (c) `1/2` (d) 6

The solution of the differential equation (d^2y)/(dx^2)=sin3x+e^x+x^2 when y_1(0)=1 and y(0)=0 is

The number of solutions of the equation tan^(-1)(1+x)+tan^(-1)(1-x)=pi/2 is 2 (b) 3 (c) 1 (d) 0

The number of solutions of the equation cos^(-1)((1+x^2)/(2x))-cos^(-1)x=pi/2+sin^(-1)x is 0 (b) 1 (c) 2 (d) 3

The sum of the solution of the equation 2sin^(-1)sqrt(x^2+x+1)+cos^(-1)sqrt(x^2+x)=(3pi)/2 is (a)0 (b) -1 (c) 1 (d) 2

The number of solution of equation sin^(-1)x+nsin^(-1)(1-x)=(mpi)/2,w h e r e n >0,m<=0, is 3 (b) 1 (c) 2 (d) None of these

Solve for x and y (2)/(x)+(2)/(3y)=(1)/(6),(3)/(x)+(2)/(y)=0

Coefficient of x^(6) in (1+x)(1+x^(2))^(2)(1+x^(3))^(3)…(1+x^(n))^(n) is

If the graph of the function f(x)=(a^x-1)/(x^n(a^x+1)) is symmetrical about the y-a xi s ,then n equals 2 (b) 2/3 (c) 1/4 (d) 1/3

The number of solutions of the matrix equation X^2=[1 1 2 3] is a. more than2 b. 2 c. 0 d. 1

If alphaa n dbeta are roots of the equation a x^2+b x+c=0, then the roots of the equation a(2x+1)^2-b(2x+1)(x-3)+c(x-3)^2=0 are a. (2alpha+1)/(alpha-3),(2beta+1)/(beta-3) b. (3alpha+1)/(alpha-2),(3beta+1)/(beta-2) c. (2alpha-1)/(alpha-2),(2beta+1)/(beta-2) d. none of these