If the vectors $a \hat{i}+\hat{j}+\hat{k}, \hat{i}+b \hat{j}+\hat{k}, \hat{i}+\hat{j}+c \hat{k}$ $(a \neq b, c \neq 1)$ are coplanar, then $\frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}$ has the value __________.

The sides of a triangle are $\sin \theta, \cos \theta$ and $\sqrt{1+\sin \theta \cos \theta}$ for some $0<\theta<\frac{\pi}{2}$, then the greatest angle of a triangle is

If $\lim\limits_{x \rightarrow \infty}\left(\frac{x^2+x+1}{x+1}-a x-b\right)=4$ then

If $y=y(x)$ is the solution of the differential equation $x \frac{\mathrm{dy}}{\mathrm{d} x}+2 y=x^2$ satisfying $y(1)=1$, then the value of $y\left(\frac{1}{2}\right)$ is