Bismuth has a half-life period of $5 \text{ days}$. $A$ sample originally has a mass of $1000 \text{ mg}$. What is the mass of Bismuth remaining after $30 \text{ days}$ (in $.625$)?

$A$ bag contains $4$ red and $3$ black balls. One ball is drawn and then replaced in the bag and the process is repeated. Let $X$ denote the number of times a black ball is drawn in $3$ draws. Assuming that at each draw each ball is equally likely to be selected,the probability distribution of $X$ is given by:

In a box containing $100$ bulbs,$10$ are defective. The probability that out of a sample of $5$ bulbs,none is defective is

If the mean and standard deviation of a binomial distribution are $20$ and $4$,respectively,then the number of trials is $.......$

$A$ fair coin is tossed a fixed number of times. If the probability of getting $5$ heads is equal to the probability of getting $4$ heads, then the probability of getting $6$ heads is

If $\mu$ and $\sigma^{2}$ are the mean and variance of a random variable $X$ whose probability mass function is given by $P(X=x) = \binom{6}{x} \left(\frac{1}{3}\right)^{x} \left(\frac{2}{3}\right)^{6-x}$ for $x = 0, 1, 2, \ldots, 6$,then the value of $2\mu + 12\sigma^{2}$ is: