Which of the following is/are CORRECT? 

Let f(0) = 0 and  $\underset{0}{\overset{2}{\int }}f\text{'}\left(2t\right)e^{f\left(2t\right)}dt=5$, then the value of f(4) equals ln (11).

The minimum value of the function  $f\left(x\right)=x^{\frac{3}{2}}+x^{\frac{-3}{2}}-4(x+\frac{1}{x})$ for all permissible real x, is –10.

Let f(x) be a differentiable function such that  $f\left(x\right)+f\text{'}\left(x\right)\le 1\forall x\in R$ and f(0) = 0, then the greatest value of f(1) is  $1-\frac{1}{e}$.

If $x_1,x_1,x_2,x_3,\mathrm{........}{x}_{n-1}$  be n zero’s of the polynomial  $P\left(x\right)=x^n+\alpha x+\beta$ , where  $x_i\ne x_j\forall i,j$ then  $(x_1-x_2)(x_1-x_3)(x_1-x_4)\mathrm{......}(x_1-x_{n-1}),$ equals  $n(n-1)x_1^{n-2}$.