Binomial Theorem · Mathematics · NDA

What is the coefficient of $x^{10}$ in the expansion of $(1-x^2)^{20}\left(2-x^2-\frac{1}{x^2}\right)^{-5}$?

If the 4th term in the expansion of $\left(mx + \frac{1}{x}\right)^n$ is $\frac{5}{2}$, then what is the value of $mn$?

In a binomial expansion of $(x+y)^{2 n+1}(x-y)^{2 n+1}$, the sum of middle terms is zero. What is the value of $\left(\frac{x^2}{y^2}\right)$ ?

What is the number of real roots of the equation?

What is the sum of all the roots of the equation?

What is T1 + 2T2 + 3T3 + ... + nTn equal to ?...

What is 1 - T1 + 2T2 - 3T3 + ... + (-1)nnTn equal to ? ...

What is T1 + T2 + T3 + ... + Tn equal to ?...

What is the mean of the numbers 1, 2, 3, ... 10 with frequencies 9C0, 9C1, 9C2 ..., 9C9, respectively?...

In a Binomial distribution B(n, p), n = 6 and 9P(X = 4) = P(X = 2). What is p equal to ?

If the sixth term in the binomial expansion of $\left(x^{-\frac{8}{3}}+x^2 \log _{10} x\right)^8$ is 5600, then what is the value of x ?&nbs...

How many terms are there in the expansion of (3x - y)4(x + 3y)4 ?  

Consider the following statements for a fixed natural number n: 1. C(n, r) is greatest if n = 2r 2. C(n, r) is greatest if n = 2r - 1 and n = 2...