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 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 0 (b) -1 (c) 1 (d) 2

Roots of this equation are, (x^3+1/x^3)+(x^2+1/x^2)-6(x+1/x)-7=0

let L be a straight line passing through the origin. Suppose that all the points on L are at a constant distance from the two planes P_1 : x + 2y-z +1 = 0 and P_2 : 2x-y + z-1 = 0 , Let M be the locus of the feet of the perpendiculars drawn from the points on L to the plane P_1 . Which of the following points lie(s) on M? (a) (0, - (5)/(6), - (2)/(3)) (b) (-(1)/(6), - (1)/(3), (1)/(6)) (c) (- (5)/(6), 0, (1)/(6)) (d) (-(1)/(3), 0, (2)/(3))

For what values of x and y are the following matrices equal ? A=[(2x+1,3y),(0,y^(2)-5y)], B=[(x+3,y^(2)+2),(0,-6)]

If alpha and beta 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

Let f(x)= x^3+3x^2+6x+2sinx , then the equation 1/(x-f(1))+2/(x-f(2))+3/(x-f(3))=0 ,has

For the primitive integral equation y dx+y^2dy=xdy ; x in R ,y >0,y(1)=1, then y(-3) is (a) 3 (b) 2 (c) 1 (d) 5

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