Question

Let 𝐾 be the sum of the coefficients of the odd powers of 𝑥 in the expansion of $(1+𝑥)^{99}$. Let 𝑎 be the middle term in the expansion of $(2+\frac{1}{\sqrt 2} )^{200}$. If $\frac{⁡^{200}𝐶_{99} 𝐾}{𝑎} =\frac{2^𝑙 𝑚}{𝑛}$, where 𝑚 and 𝑛 are odd numbers, then the ordered pair (𝑙, 𝑛) is equal to

• A. (50,51)
• B. (50,101)
• C. (51,99)
• D. (51,101)

Answer 1

Answer: (B)

(50,101)

Answer 2

The Correct Option is (B): (50,101)