List of top Mathematics Questions on binomial distribution asked in Telangana State Engineering Agriculture & Medical CET

If the coefficient of $x^r$ in the expansion of $(1 + x + x^2)^{100}$ is $a_r$ , and $S = \sum\limits_{r=0}^{300} a_r$ , then

$\sum\limits_{r=0}^{300} r a_r =$

Given below are two statements, one is labelled as Assertion (A) and the other one labelled as Reason (R).
Assertion (A): $1 + \frac{2.1}{3.2} + \frac{2.5.1}{3.6.4} + \frac{2.5.8.1}{3.6.9.8} + \dots \infty = \sqrt{4}$ Reason (R): $|x| <1, \quad (1 - x)^{-1} = 1 + nx + \frac{n(n+1)}{1.2} x^2 + \frac{n(n+1)(n+2)}{1.2.3} x^3 + \dots$

If

\frac{1}{x^4 + x^2 + 1} = \frac{Ax + B}{x^2 + ax + 1} + \frac{Cx + D}{x^2 - ax + 1}

then $A + B - C + D = ?$

If the probability that a randomly selected student from a college is good at mathematics is 0.6, then the probability of having exactly two students who are good at mathematics in a group of 8 students standing in front of the college is:

If on average 4 customers visit a shop in an hour, then the probability that more than 2 customers visit the shop in a specific hour is:

The mean of a binomial variate $X \sim B(n, p)$ is 1. If $n>2$ and $P(X = 2) = \frac{27}{128}$ , then the variance of the distribution is:}