If `f(x)=cos^2x+s e c^2x ,t h e n` `f(x)<1` (b) `f(x)=1` (c) `2ltf(x)<1` (d) `""""f(x)ge2`

If intsinx d(secx)=f(x)-g(x)+c ,t h e n f(x)=secx (b) f(x)=tanx g(x)=2x (d) g(x)=x

A function f: R->R satisfies sinxcosy(f(2x+2y)-f(2x-2y)=cosxsiny(f(2x+2y)+f(2x-2y))dot If f^(prime)(0)=1/2,t h e n (a) f''(x)=f(x)=0 (b) 4f''(x)+f(x)=0 (c) f''(x)+f(x)=0 (d) 4f''(x)-f(x)=0

If f(x)=int_0^x("cos"(sint)+"cos"(cost)dt ,t h e nf(x+pi)i s f(x)+f(pi) (b) f(x)+2(pi) f(x)+f(pi/2) (d) f(x)+2f(pi/2)

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

If f(x)=log((1+x)/(1-x)),t h e n (a) f(x_1)f(x)=f(x_1+x_2) (b) f(x+2)-2f(x+1)+f(x)=0 (c) f(x)+f(x+1)=f(x^2+x) (d) f(x_1)+f(x_2)=f((x_1+x_2)/(1+x_1x_2))

If f^(prime)(x)=sqrt(2x^2-1)a n dy=f(x^2),t h e n(dy)/(dx)a tx=1 is 2 (b) 1 (c) -2 (d) none of these

If f(x)={x^2, for xgeq1x ,for x<0 ,t h e n fof(x) is given by

If f (x) = cos ( log _e x ) then f(x) . f(y) - (1)/(2) [f(y/x ) + f (xy)] has the value

If f(x)=x^3-x^2+100x+2002 ,t h e n f(1000)>f(1001) f(1/(2000))>f(1/(2001)) f(x-1)>f(x-2) f(2x-3)>f(2x)

If f(x)=lim_(n->oo)n(x^(1/n)-1),t h e nforx >0,y >0,f(x y) is equal to : (a) f(x)f(y) (b) f(x)+f(y) (c) f(x)-f(y) (d) none of these