Let `f(x)` be differentiable function on` R` such that `f'(5-x)=f'(x)AA x in[0,5]` with `f(0)=-10&f(5)=50`,then the value of `(5int_0^5 f(x)dx )` is

Let f(x) is a differentiable function on x in R , such that f(x+y)=f(x)f(y) for all x, y in R where f(0) ne 0 . If f(5)=10, f'(0)=0 , then the value of f'(5) is equal to

Let f be a differentiable function defined on R such that f(0) = -3 . If f'(x) le 5 for all x then

Let f(x) be a real valued function such that f(x)=f((121)/(x)),AA x>0. If int_(1)^(11)(f(x))/(x)dx=5, then the value of int_(1)^(121)(f(x))/(x)dx is equal to

Let f(x) be a differentiable function satisfying f(y)f((x)/(y))=f(x)AA,x,y in R,y!=0 and f(1)!=0,f'(1)=3 then

Let f(x) be a continuous & differentiable function on R satisfying f(-x)=f(x)&f(3+x)=f(3-x)AA x in R . If f'(1)=-5 then f'(7) =

Let f(x) be a differentiable function on x in R such that f(x+y)=f(x). F(y)" for all, "x,y . If f(0) ne 0, f(5)=12 and f'(0)=16 , then f'(5) is equal to

If f is a differentiable function of x such that f(1)=0,f'(1)=(3)/(5)" and "y=e^(x)*f(e^(2x))," then the value of "(dy)/(dx)" at "x=0 is

Let f be a differentiable function satisfying f '(x) =2 f(x) +10 AA x in R and f (0) =0, then the number of real roots of the equation f (x)+ 5 sec ^(2) x=0 ln (0, 2pi) is: