JEE Mains · Maths · STD 11 - 7. binomial theoram
The coefficient of \(x^{1012}\) in the expansion of \({\left( {1 + {x^n} + {x^{253}}} \right)^{10}}\) , (where \(n \leq 22\) is any positive integer), is
- A \(1\)
- B \(^{10}{C_4}\)
- C \(4n\)
- D \(^{253}{C_4}\)
Answer & Solution
Correct Answer
(B) \(^{10}{C_4}\)
Step-by-step Solution
Detailed explanation
Given expansion \(\left(1+x^{n}+x^{253}\right)^{10}\) Let \(x^{1012}=(1)^{a}\left(x^{n}\right)^{b} \cdot\left(x^{253}\right)^{c}\) Here \(a, b, c, n\) are all \(+ve\) integers and \(a\) \(\leq 10, b \leq 10, c \leq 4, n \leq 22, a+b+c=10\) Now \(b n+253 c=1012\)…
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