If $\bar{a}, \bar{b}, \bar{c}, \bar{d}$ are unit vectors such that $\overline{\mathrm{a}} \cdot \overline{\mathrm{b}}=\frac{1}{2}, \overline{\mathrm{c}} \cdot \overline{\mathrm{d}}=\frac{1}{2}$ and the angle between $\overline{\mathrm{a}} \times \overline{\mathrm{b}}$ and $\overline{\mathrm{c}} \times \overline{\mathrm{d}}$ is $\frac{\pi}{6}$, then the value of $|[\overline{\mathrm{a}} \overline{\mathrm{b}} \overline{\mathrm{d}}] \overline{\mathrm{c}}-[\overline{\mathrm{a}} \overline{\mathrm{b}} \overline{\mathrm{c}}] \overline{\mathrm{d}}|=$

If $\bar{a}=4 \hat{i}+3 \hat{j}+\hat{k}, \bar{b}=\hat{i}-2 \hat{j}+2 \hat{k}$ then $\overline{\mathrm{a}} \times(\overline{\mathrm{a}} \times(\overline{\mathrm{a}} \times(\overline{\mathrm{a}} \times \overline{\mathrm{b}})))=$

If X is a binomial variable with range $\{0,1,2,3,4\}$ and $\mathrm{P}(\mathrm{X}=3)=3 \mathrm{P}(\mathrm{X}=4)$ then the parameter ' $p$ ' of the binomial distribution is

If a statement $q$ has truth value False and $(\mathrm{p} \wedge \mathrm{q}) \leftrightarrow \mathrm{r}$ has truth value True then which of the following has truth value true?