A rectangle `A B C D ,` where `A-=(0,0),B-=(4,0),C-=(4,2)D-=(0,2)` , undergoes the following transformations successively: `f_1(x ,y)vec(y ,x)` `f_2(x , y)vec(x+3y ,y)` `f_3(x , y)vec((x-y)//2),(x+y)//2)` The final figure will be

If f (x,y) =e ^(2x+3y) find 3f_(x) (0,0) - 2f_(y) (0,0):

If a function satisfies (x-y)f(x+y)-(x+y)f(x-y)=2(x^2 y-y^3) AA x, y in R and f(1)=2 , then

The equation of the incircle of equilateral triangle A B C where B-=(2,0),C-=(4,0), and A lies in the fourth quadrant is: (a) x^2+y^2-6x+(2y)/(sqrt(3))+9=0 (b) x^2+y^2-6x-(2y)/(sqrt(3))+9=0 (c) x^2+y^2+6x+(2y)/(sqrt(3))+9=0 (d) none of these

Which one of the following function(s) is/are homogeneous? (a) f(x,y)= (x-y)/(x^2 + y^2) (b) f(x,y)= x^(1/3)y^(-2/3)tan^-1(x/y) (c)f(x,y)=x(lnsqrt(x^2+y^2)-lny)+ye^(x/y) (d) none of these

Which of the following line can be normal to parabola y^2=12 x ? (a) x+y-9=0 (b) 2x-y-32=0 (c) 2x+y-36=0 (d) 3x-y-72=0

If f (x/y)= f(x)/f(y) , AA y, f (y)!=0 and f' (1) = 2 , find f(x) .

If f(x,y) = 2x^(2) - 3xy + 5y^(2) +7 , then f(0,0) and f(1,1) is

If f(2x+3y, 2x-7y)=20x, then f(x,y) equals :

Let f(x,y) = (y^(2) -xy)/(sqrt(x)-sqrt(y)) for (x,y) ne (0,0) . Show that lim_((x,y) to (0,0)) f(x,y) =0

Given the function f(x)=(a^x+a^(-x))/2(w h e r ea >2)dotT h e nf(x+y)+f(x-y)= (A) 2f(x).f(y) (B) f(x).f(y) (C) f(x)/f(y) (D) none of these