The value of $k$, if the slope of one of the lines given by $4 x^2+k x y+y^2=0$ is four times that of the other, is given by

The differential equation of $y=\mathrm{e}^x\left(\mathrm{a}+\mathrm{bx}+x^2\right)$ is

The mean of the numbers $a, b, 8,5,10$ is 6 and the variance is $6.8$ . Then which of the following gives possible values of $a$ and $b$ ?

Let $\overline{\mathrm{u}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}, \overline{\mathrm{v}}=\hat{\mathrm{i}}-\hat{\mathrm{j}}$ and $\overline{\mathrm{w}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}$. If $\hat{\mathrm{n}}$ is a unit vector such that $\overline{\mathbf{u}} \cdot \hat{\mathrm{n}}=0$ and $\overline{\mathrm{v}} \cdot \hat{\mathrm{n}}=0$, then $|\overline{\mathrm{w}} \cdot \hat{\mathrm{n}}|$ is equal to