If $X$ is a binomial variate with the range $\{0, 1, 2, 3, 4, 5, 6\}$ and $P(X=2) = 4 P(X=4)$,then the parameter $p$ of $X$ is

In a binomial distribution $B(n, p = \frac{1}{4})$,if the probability of at least one success is greater than or equal to $\frac{9}{10}$,then $n$ is greater than:

The probability of getting $4$ heads in $8$ throws of a coin is:

$A$ random variable $X$ follows a binomial distribution in which the difference between its mean and variance is $1$. If $2 P(X=2)=3 P(X=1)$,then $n^2 P(X>1)=$

An ordinary dice is rolled for a certain number of times. If the probability of getting an odd number $2$ times is equal to the probability of getting an even number $3$ times,then the probability of getting an odd number for an odd number of times is

An objective type test paper has $5$ questions. Out of these $5$ questions, $3$ questions have four options each $(a, b, c, d)$ with one option being the correct answer. The other $2$ questions have two options each, namely true and false. $A$ candidate randomly ticks the options. Then, the probability that he/she will tick the correct option in at least four questions, is