Let n ≥ 5 be an integer such..... | JEE Main 2022

JEE MAIN 2022

29-06-2022 S2

Question

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

Select the correct option:

$1+{ }^n C_2(8-5)+{ }^n C_3\left(8^2-5^2\right)+\ldots+{ }^n C_n\left(8^{n-1}-5^{n-1}\right)$

$1+{ }^n C_3(8-5)+{ }^n C_4\left(8^2-5^2\right)+\ldots+{ }^n C_n\left(8^{n-2}-5^{n-2}\right)$

${ }^n C_3(8-5)+{ }^n C_4\left(8^2-5^2\right)+\ldots+{ }^n C_n\left(8^{n-2}-5^{n-2}\right)$

${ }^n C_4(8-5)+{ }^n C_5\left(8^2-5^2\right)+\ldots+{ }^n C_n\left(8^{n-3}-5^{n-3}\right)$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

Question Tags

JEE Main

Mathematics

Medium

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