If 0 < a < 1 and x > y > 0, then `a^x < a^y` (write true or false)

If 0 y > 0 then log_a^x < log_a^y (write true or false)

Solve: (x^2 + y^2).dx-2xydy = 0, given y = 0 when x = 1

(dy)/(dx) - (y)/(x) + cosec ((y)/(x)) = 0, y = 0 when x = 1.

Solve: (dy)/(dx)-y/x + cosec (y/x) =0, given y = 0 when x = 1

If three parabols touch all the lines x = 0, y = 0 and x +y =2 , then maximum area of the triangle formed by joining their foci is

Find the particular solution of the differential equation : dy/dx + y cot x = 4x cosec x, (x ≠ 0), given, that y = 0, when x = pi/2

If |(y,x,0),(0,y,x),(x,0,y)|=0 and x ne 0 , then which one of the following is correct ?

If x > 0, y >0, z > 0 and x +y + z = 1 , prove that (1+x)(1+y)(1+z)ge 8(1-x) (1-y) (1-z)

If F(x)=[("cos"x,-sin x,0),(sin x,cos x,0),(0,0,1)] and G(y)=[(cos y,0,sin y),(0,1,0),(-sin y,0,cos y)] , then [F(x) G(y)]^(-1) is equal to

A circle touches the lines x = 0 , y = 0 and x + y = 1. If the centre of the circle lies in first quadrant, show that there are two such circles and find their equations. Specify which of these is inscribed whithin the triangle formed by the given lines.