Calculate molar mass of nonvolatile solute if a solution containing 0.35 g solute in 100 g water has boiling point elevation 0.01 K $\left[\mathrm{K}_{\mathrm{b}}=0.50 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right.$ ]

What is the number of Lewis structures for $\mathrm{NO}_2^{-}$?

Let two non-collinear unit vectors $\hat{\mathrm{a}}$ and $\hat{\mathrm{b}}$ form an acute angle. A point P moves, so that at any time $t$ the position vector $\overline{O P}$, where $O$ is the origin, is given by $\hat{a} \cos t+\hat{b} \sin t$. When $P$ is farthest from origin O , let M be the length of $\overline{\mathrm{OP}}$ and $\hat{\mathrm{u}}$ be the unit vector along $\overline{\mathrm{OP}}$, then

The vector equation of the plane passing through the point $\mathrm{A}(1,2,-1)$ and parallel to the vectors $2 \hat{i}+\hat{j}-\hat{k}$ and $\hat{i}-\hat{j}+3 \hat{k}$ is