Greatest value of `f(x)=(x+1)^(1/3)-(x-1)^(1/3)` on [0,1] is 1 (b) 2 (c) 3 (d) `1/3`

f(x) = sin^(-1)x+x^(2)-3x + (x^(3))/(3),x in[0,1]

The greatest value of f(x)=cos(x e^([x])+7x^2-3x),x in [-1,oo], is (where [.] represents the greatest integer function). -1 (b) 1 (c) 0 (d) none of these

The maximum value of f(x)=x/(1+4x+x^2) is -1/4 (b) -1/3 (c) -1/6 (d) 1/6

The function f(x)=e^x+x , being differentiable and one-to-one, has a differentiable inverse f^(-1)(x)dot 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

Let (x_0, y_0) be the solution of the following equations: (2x)^(1n2)=(3y)^(1n3) 3^(1nx)=2^(1ny) The x_0 is 1/6 (b) 1/3 (c) 1/2 (d) 6

The range of the function f(x)=(x^2+x+2)/(x^2+x+1),x in R , is (1,oo) (b) (1,(11)/7) (c) (1,7/3) (d) (1,7/5)

The coefficient of the term independent of x in the exampansion of ((x+1)/(x^(2//3)-x^(1//3)+1)-(x-1)/(x-x^(1//2)))^(10) is 210 b. 105 c. 70 d. 112

Let f(x)=x^3-3(a-2)x^2+3ax+7 and f(x) is increasing in (0,1] and decreasing is [1,5) , then roots of the equation (f(x)-14)/((x-1)^2)=0 is (A) 1 (B) 3 (C) 7 (D) -2

Number of integers in the range of f(x)=1/pi(sin^(-1)x+tan^(-1)x)+(x+1)/(x^2+2x+5) is 0 b. 3 c. 2 d. 1

If 3tan^(-1)(1/(2+sqrt(3)))-tan^(-1)1/x=tan^(-1)1/3, then x is equal to 1 (b) 2 (c) 3 (d) sqrt(2)