If $X \sim B(n, p)$ with $n = 10, p = 0.4$,then $E(X^2) =$

In an examination,there are $10$ true-false type questions. Out of $10$,a student can guess the answer of $4$ questions correctly with probability $\frac{3}{4}$ and the remaining $6$ questions correctly with probability $\frac{1}{4}$. If the probability that the student guesses the answers of exactly $8$ questions correctly out of $10$ is $\frac{27 k}{4^{10}}$,then $k$ is equal to

Five cards are drawn successively with replacement from a well-shuffled deck of $52$ cards. What is the probability that all the five cards are spades?

The mean and standard deviation of a binomial variate $X$ are $4$ and $\sqrt{3}$ respectively. Then $P(X \geq 1)$ is equal to

The variance of the following probability distribution of $X$ is given by:
$X: 0, 1, 2, 3$
$P(X): q^3, 3pq^2, 3p^2q, p^3$
where $0 < p < 1$ and $q = 1 - p$.

For an initial screening of an admission test,a candidate is given $50$ problems to solve. If the probability that the candidate can solve any problem is $\frac{4}{5}$,then the probability that he is unable to solve less than two problems is