JEE Main 2022 (29 Jun, Shift 2) Maths Q20: Binomial Theorem

Question

Let $n \geq 5$ be an integer. If $9^n - 8n - 1 = 64\alpha$ and $6^n - 5n - 1 = 25\beta$, then $\alpha - \beta$ is
equal to

Accepted Answer

Option 3: ${}^nC_3\,(8 - 5) + {}^nC_4\,(8^2 - 5^2) + \ldots + {}^nC_n\,(8^{n-2} - 5^{n-2})$

Answer

$1 + {}^nC_2\,(8 - 5) + {}^nC_3\,(8^2 - 5^2) + \ldots + {}^nC_n\,(8^{n-1} - 5^{n-1})$

Answer

$1 + {}^nC_3\,(8 - 5) + {}^nC_4\,(8^2 - 5^2) + \ldots + {}^nC_n\,(8^{n-2} - 5^{n-2})$

Answer

${}^nC_3\,(8 - 5) + {}^nC_4\,(8^2 - 5^2) + \ldots + {}^nC_n\,(8^{n-2} - 5^{n-2})$

Answer

${}^nC_4\,(8 - 5) + {}^nC_5\,(8^2 - 5^2) + \ldots + {}^nC_n\,(8^{n-3} - 5^{n-3})$

JEE Main 29 June 2022, Shift 2, Maths Q20