JEE PYQ: Binomial Theorem Question 4
Question 4 - 2021 (17 Mar Shift 1)
If the fourth term in the expansion of $(x + x^{\log_2 x})^7$ is 4480, then the value of $x$ where $x \in N$ is equal to:
(1) 2 (2) 4 (3) 3 (4) 1
Show Answer
Answer: (1)
Solution
$T_4 = 35 x^{4+3\log_2 x} = 4480$, so $x^{4+3\log_2 x} = 128$. Taking $\log_2$: $(4+3t)t = 7$ where $t = \log_2 x$. Solving: $t = 1$, $x = 2$.