If `f(x)=|[a,-1, 0],[a x, a,-1],[a x^2,a x, a]|,t h e nf(2x)-f(x)` is divisible by (a) `a` (b) `b` (c) `c ,d ,e` (d) none of these

If f(x)="cos"((log)_e x),t h e nf(x)f(y)-1/2[f(x/y)+f(x y)] has value (a) -1 (b) 1/2 (c) -2 (d) none of these

If a (A) x=0 (B) x=1 (C) x=2 (D) None of these.

f(x)=(1n(x^2+e^x))/(1n(x^4+e^(2x)))dotT h e n lim_(x->oo)f(x) is equal to (a) 1 (b) 1/2 (c) 2 (d) none of these

Let f(x)=a+b|x|+c|x|^(4), where a,b and c are real constants.Then,f(x) is differentiable at x=0, if a=0 (b) b=0( c) c=0(d) none of these

Let f(x)=a+b|x|+c|x|^(4), where a,b, and c are real constants.Then,f(x) is differentiable at x=0, if a=0( b) b=0 (c) c=0( d) none of these

If f(x)=|x-3| and g(x)= fof (x), then for x>10,g'(x) is equal to (a)1(b)-1(c)0 (d) none of these

Instead of the usual definition of derivative Df(x), if we define a new kind of derivative D^*F(x) by the formula D*f(x)=lim_(h->0)(f^2(x+h)-f^2(x))/h ,w h e r ef^2(x) mean [f(x)]^2 and if f(x)=xlogx ,then D^*f(x)|_(x=e) has the value (A)e (B) 2e (c) 4e (d) none of these

If f(x)=|0x-a x-b x+a0x-c x+b x+c0|,t h e n f(x)=0 (b) f(b)=0 (c) f(0)=0 f(1)=0

If intf(x)*cosxdx=1/2{f(x)}^2+c , then f(0)= (A) 1 (B) 0 (C) -1 (D) none of these

If f(x)= e^(coscos^-1x^2+tancot^-1 x^2), then minimum value of f(x) is (A) e (B) e^2 (C) e^(2/3 (D) none of these