If the sum of binomial coefficients in the expansion of \( (x + y)^n \) is 256, then the greatest binomial coefficient occurs in which one of the following terms?
Fifth
The sum of binomial coefficients in \( (x + y)^n \) is \( 2^n \). Given \( 2^n = 256 \Rightarrow n = 8 \).
The binomial coefficients in \( (x + y)^8 \) are symmetric. The greatest coefficient is the middle one(s), which is at term \( \left( \lfloor \frac{n}{2} \rfloor + 1 \right) \).
So, the term is \( \frac{8}{2} + 1 = 5^{th} \) term.
Answer: (c) Fifth
Similar Questions
What is the coefficient of the middle term in the binomial expansion of (2 + 3x) 4?
How many terms are there in the expansion of (3x - y)4(x + 3y)4 ?
What is T1 + 2T2 + 3T3 + ... + nTn equal to ?
What is 1 - T1 + 2T2 - 3T3 + ... + (-1)nnTn equal to ?
What is the greatest integer among the following by which the number 5 5+ 7 5is divisible?
How many terms are there in the expansion of (1 + 2x + x 2) 5+ (1 + 4y + 4y 2) 5?
Let the coefficient of the middle term of the binomial expansion of (1 + x) 2n be α and those of two middle terms of the binomial expansion of (1 + x) 2n - 1 be β and γ. Which one of the following relations is correct?
What is the number of non-zero terms in the expansion of (1 + 2√3x) 11 + (1 – 2√3x) 11 (after simplification)?
In the expansion of (1 + x) 43 , if the coefficients of (2r + 1) th and (r + 2) th terms are equal, then what is the value of r (r ≠ 1)?
If the coefficients of a mand a nin the expansion of (1 + a) m + n are α and β, then which one of the following is correct?
Important Questions from Binomial Theorem
Find the sum of the coefficients in the expansion of $(x - 2y + 3z)^4 \cdot (x^2 + y - z^3)^3$.
What is the coefficient of the middle term in the binomial expansion of (2 + 3x) 4?
If (1 + 2x + x2)n = \(\displaystyle\sum_{r = 0}^{2n} a_r x^r\) then ar =
How many terms are there in the expansion of (3x - y)4(x + 3y)4 ?
The statement (52n – 1) is always divisible by
