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

Solve the following system of equations: 1/(2x)+1/(3y)=2,\ \ \ 1/(3x)+1/(2y)=(13)/6

Let y(x) be the solution of the differential equation (dy)/(dx)+(3y)/(cos^2x)=1/(cos^2x) and y(pi/4)=4/3 then vaue of y(-pi/4) is equal to (a) -4/3 (b) 1/3 (c) e^6+1/3 (d) 3

The number of solutions of te equation |2x^2-5x+3|+x-1=0 is (A) 1 (B) 2 (C) 0 (D) infinite

For 0

Let Y = y(x) be the solution of the differential equation ( dy ) /( dx) + 2y = f(x) , where f(x) = { {:(1, x in [0,1]),( 0, " Otherwise "):} IF y(0) =0 then y ((3)/(2)) is :

If x=1\ a n d\ y=6 is a solution of the equation 8x-a y+a^2=0 , find the value of a

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)(3-x)+c(3-x)^2=0 are (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

The roots of the equation det [(1-x, 2, 3),(0,2-x,0),(0,2,3-x)]=0 are (A) 1 and 2 (B) 1 and 3 (C) 2 and 3 (D) 1,2, and 3

The number of values of a for which the lines 2x+y-1=0 , a x+3y-3=0, and 3x+2y-2=0 are concurrent is (a).0 (b) 1 (c) 2 (d) infinite

If y=3^(x-1)+3^(-x-1) , then the least value of y is (a) 2 (b) 6 (c) 2//3 (d) 3//2