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...

What is $\displaystyle\sum_{r=0}^n$2r C(n, r) equal to ?...

What is the value of q if the coefficients of x3 and x6 are equal ? ...

What is the ratio of the coefficients of middle terms in the expansion (when expanded in ascending powers of x)?

Under what condition the coefficients of x2 and x4 are equal ? ...

How many terms are there in the expansion of $\left(1 + \frac{2}{x}\right)^9\left(1-\frac{2}{x}\right)^9 ? $

Consider the following statements in respect of the expansion of (x + y)10 1. Among all the coefficients of the terms, the coefficient of the 6th ter...

What is the value of C(51, 21) - C(51, 22) + C(51, 23) - C(51, 24) + C(51, 25) - C(51, 26) + C(51, 27) - C(51, 28) + C(51, 29) - C(51, 30) ? ...

In the expansion of $\left(x + \frac{1}{x}\right)^{2n} $, what is the (n + 1)th term from the end (when arranged in descending powers of x) ?...