Binomial Theorem · Mathematics · NDA

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 ?

NDA Mathematics 16 April 2023

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

NDA Mathematics 16 April 2023

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 = 2r + 1

Which of the statements given above is/are correct ?

NDA Mathematics 16 April 2023

What is $\displaystyle\sum_{r=0}^n$2^rC(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 term has the highest value

2. The coefficient of the 3rd term is equal to coefficient of the 9th term

Which of the above statements is /are correct ?

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) ?