One side and one diagonal of a parallelogram are represented by $3 \hat{i}+\hat{j}-\hat{k}$ and $2 \hat{i}+\hat{j}-2 \hat{k}$ respectively, then the area of parallelogram in square units is

If $\int \mathrm{e}^{x^2} \cdot x^3 \mathrm{dx}=\mathrm{e}^{x^2} \mathrm{f}(x)+\mathrm{c}$ and $\mathrm{f}(1)=0$ (where c is a constant of integration), then the value of $f(x)$ is

If $\cot ^{-1}(\sqrt{\cos \alpha})-\tan ^{-1}(\sqrt{\cos \alpha})=x$, then the value of $\sin x$ is

If $[x]^2-5[x]+6=0$, where $[\cdot]$ denotes the greatest integer function, then