Let $X=\left[\begin{array}{l}\mathrm{a} \\ \mathrm{b} \\ \mathrm{c}\end{array}\right], \mathrm{A}=\left[\begin{array}{ccc}1 & -1 & 2 \\ 2 & 0 & 1 \\ 3 & 2 & 1\end{array}\right]$ and $\mathrm{B}=\left[\begin{array}{l}3 \\ 1 \\ 4\end{array}\right]$. If $A X=B$, then the value of $2 a-3 b+4 c$ will be

Let in a Binomial distribution, consisting of 5 independent trials, probabilities of exactly 1 and 2 successes be 0.4096 and 0.2048 respectively. Then the probability of getting exactly 3 successes is equal to

The unit vector which is orthogonal to the vector $5 \hat{i}+2 \hat{j}+6 \hat{k}$ and is coplanar with the vectors $2 \hat{i}+\hat{j}+\hat{k}$ and $\hat{i}-\hat{j}+\hat{k}$ is

The probability distribution of a random variable X is given by

Then the variance of X is