If `x+y=2a` then the value of `a/(x-a)+a/(y-a)` is (a) 2 (b) 0 (c) `-1` (d) 1

Let y=y(x) be the solution of the differential equation, (x^(2)+1)^(2)dy/dx+2x(x^(2)+1)y=1 such that y(0) =0. If sqrta y(1)=pi/32 ,then tha value of 'a' is (a) 1/4 (b) 1/2 (c) 1 (d) 1/16

If y+1/z=1 and x+1/y=1 , then what is the value of x y z ? -1 (b) 0 (c) 1/2 (d) 1

If y is a function of x and ln(x+y)-2x y=0, then the value of y^(prime)(0) is equal to 1 (b) -1 (c) 2 (d) 0

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

The Tangent to the curve y=x+(1)/(x) at (a,b) is parallel to X - axis , then the value of : (a,b)= (a) (0,+-1) (b) (+-2,+-3) (c) (+-1,0) (d) (+-1,+-2)

If the operation ^^ is defined by the equation x^^y=2x+y , what is the value of a in 2^^a=a^^3? (a) 0 (b) -1 (c) 1 (d) 4

If y is a function of xand log(x+y)-2xy=0, then the value of y'(0) is (a) 1 (b) -1(c)2(d)0

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

If (x+1)/(x-1)=(a)/(b) and (1-y)/(1+y)=(b)/(a), then the value of (x-y)/(1+xy) is (2ab)/(a^(2)-b^(2)) (b) (a^(2)-b^(2))/(2ab) (c) (a^(2)+b^(2))/(2ab) (d) (a^(2)-b^(2)backslash)/(ab)

If x y z=0, then find the value of (a^x)^(y z)+(a^y)^(z x)+(a^z)^(x y)= (a)3 (b) 2 (c)1 (d) 0