If $\bar{a}=2 \hat{i}-\hat{j}+\hat{k}, \bar{b}=\hat{i}+\hat{j}-2 \hat{k}$ and $\bar{c}=4 \hat{i}-2 \hat{j}+\hat{k}$, then the unit vector in the direction of $3 \overline{\mathrm{a}}+\overline{\mathrm{b}}-2 \overline{\mathrm{c}}$ is

Numbers are selected at random, one at a time from two digit numbers $10,11,12 \ldots ., 99$ with replacement. An event $E$ occurs if and only if the product of the two digits of a selected number is 18 . If four numbers are selected, then probability that the event E occurs at least 3 times is

The function $y(x)$ represented by $x=\sin t$, $y=a e^{t \sqrt{2}}+b e^{t \sqrt{2}}, t \in\left(\frac{-\pi}{2}, \frac{\pi}{2}\right)$ satisfies the equation $\left(1-x^2\right) y^{\prime \prime}-x y^{\prime}=\mathrm{k} y$, then the value of k is k is

The value of $\cos 20^{\circ}+2 \sin ^2 55^{\circ}-\sqrt{2} \sin 65^{\circ}$ is