If `f(1)=3,f^(prime)(1)=2,f^(1)=4,t h e n(f^(-1))^(' ')(3)=` a. 1 b. `-1/2` c. -2 d. none of these

If f(1)=3,f'(1)=2,f''(1)=4, then (f^(-))''(3)= (where f^(-1)= inverse of y=f(x))

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

Suppose that F(n+1)=(2(F(n+1))/2forn=1,2,3 a n dF(1)=2. T h e ndotF(101) equals 50 b. 52 c. 54 d. none of these

The equation of the curve is y=f(x)dot The tangents at [1,f(1),[2,f(2)],a n d[3,f(3)] make angles pi/6,pi/3,a n dpi/4, respectively, with the positive direction of x-axis. Then the value of int_2^3f^(prime)(x)f^(x)dx+int_1^3f^(x)dx is equal to (a)-1/(sqrt(3)) (b) 1/(sqrt(3)) (c) 0 (d) none of these

If f'(a)=(1)/(4), then lim_(h rarr0)(f(a+2h^(2))-f(a-2h^(2)))/(f(a+h^(3)-h^(2))-f(a-h^(3)+h^(2)))=0 b.1 c.-2 d.none of these

Let f(x) be a polynomial of degree 3 such that f(3)=1,f'(3)=-1,f''(3)=0, and f'''(3)=12 Then the value of f'(1) is (a)12(b)23(c)-13 (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

The function f(x)=e^(x)+x, being differentiable and one-to-one,has a differentiable inverse f^(-1)(x) .The value of (d)/(dx)(f^(-1)) at the point f(log2) is (a) (1)/(1n2) (b) (1)/(3)( c) (1)/(4) (d) none of these

If f(x)=int_0^1(dt)/(1+|x-t|) ,then f^(prime)(1/2) is equal to (a)0 (b) 1/2 (c) 1 (d) none of these

If 2f(x)-3f((1)/(x))=x^(2)(x!=0), then f(2) is equal to (a)-(7)/(4)(b)(5)/(2)(c)-1 (d) none of these