Let `x ,\ y` be two variables and `x >0,\ \ x y=1` , then minimum value of `x+y` is (a) 1 (b) 2 (c) `2 1/2` (d) `3 1/3`

Let x and y be two real variable such that x >0 and x y=1 . Find the minimum value of x+y .

If x ,y in R and x^2+y^2+x y=1, then find the minimum value of x^3y+x y^3+4.

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

Let A B C be a triangle. Let A be the point (1,2),y=x be the perpendicular bisector of A B , and x-2y+1=0 be the angle bisector of /_C . If the equation of B C is given by a x+b y-5=0 , then the value of a+b is (a) 1 (b) 2 (c) 3 (d) 4

If two lines represented by x^4+x^3y+c x^2y^2-x y^3+y^4=0 bisect the angle between the other two, then the value of c is (a) 0 (b) -1 (c) 1 (d) -6

If [2x+y,4x,5x-7 4x]=[7 7y-13 y x+6] , then the value of x+y is x=3 , y=1 (b) x=2 , y=3 (c) x=2 , y=4 (d) x=3 , y=3

Consider the points O(0,0), A(0,1) , and B(1,1) in the x-y plane. Suppose that points C(x,1) and D(1,y) are chosen such that 0ltxlt1 . And such that O,C, and D are collinear. Let the sum of the area of triangles OAC and BCD be denoted by S. Then which of the following is/are correct?. (a) Minimum value of S is irrational lying in ( 1 / 3 , 1 / 2 ) (b) Minimum value of S is irrational in ( 2 / 3 , 1 ) . (c) The value of x for the minimum value of S lies in ( 2 / 3 , 1 ) . (d) The value of x for the minimum values of S lies in ( 1 / 3 , 1 / 2 ) .

If two lines represented by x^4+x^3y+c x^2y^2-x y^3+y^4=0 bisector of the angle between the other two, then the value of c is (a) 0 (b) -1 (c) 1 (d) -6

If y=int1/(1+x^2)^(3/2)dx and y=0 when x=0 , then value of y when x=1 is

Find the value of x and y (1)/(2x)+(1)/(3y)=2 (1)/(3x)+(1)/(2y)=(13)/(6)