Previous Year NEET Question- Binomial Theorem

• 2017:

The answer is (C)

The sum of the coefficients in the expansion of $(x+y)^n$ is given by the formula $^nC_0 + ^nC_1 + ^nC_2 + … + ^nC_n$

This is equal to $2^n$

So, the greatest coefficient in the expansion is $\binom{n}{\lfloor n/2 \rfloor}$

Since the sum of the coefficients is 4096, we have $2^{n} = 4096$

Taking the log base 2 of both sides, we get $\log_2(n-1) = 12$

Adding 1 to both sides, we get $n = 13$

So, the greatest coefficient in the expansion is $2^{12} = 4096$

• 2018:

The answer is (C)

The number of terms in the expansion of $(x+y)^n$ is given by the formula $n+1$

Since the number of terms is 25, we have $n=25$