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

If for a continuous function f,f(0)=f(1)=0,f^(prime)(1)=2a n dy(x)=f(e^x)e^(f(x)) , then y^(prime)(0) is equal to a. 1 b. 2 c. 0 d. none of these

If for a continuous function f,f(0)=f(1)=0,f^(prime)(1)=2 and y(x)=f(e^x)e^(f(x)) , then y^(prime)(0) is equal to a. 1 b. 2 c. 0 d. none of these

If f(x)=(sin^(-1)x)/(sqrt(1-x^2)),t h e n(1-x^2)f^(x)-xy(x)= 1 (b) -1 (c) 0 (d) none of these

If f(x)=(sin^(-1)x)/(sqrt(1-x^2)),t h e n(1-x^2)f^(x)-xf(x)= (a)1 (b) -1 (c) 0 (d) none of these

Suppose that F(n+1)= (2F(n)+1)/2 'for n=1,2,3 a n dF(1)=2. T h e ndotF(101) equals a. 50 b. 52 c. 54 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 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

Let f(x) be a polynomial of degree 3 such that f(3)=1,f^(prime)(3)=-1,f^(3)=0,a n df^(3)=12. Then the value of f^(prime)(1) is 12 (b) 23 (c) -13 (d) none of these

If f^(prime)(a)=1/4, t h e n(lim)_(hvec0)(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