Given below are two statements. STATEMENT - 1: If n ∈ N and 'n' is not a multiple of 3…
Mathematics · JEE Main · NTA Exams — Binomial Theorem And Its Simple Applications
STATEMENT - 1: If n ∈ N and 'n' is not a multiple of 3 and \(\left(1+x+x^{2}\right)^{n}=\sum_{\mathrm{r}=0}^{2 \pi} a_{\mathrm{r}} x^{\mathrm{r}},\) then the value of \(\sum_{r=0}^{n}(-1) a_{r}^{n} c_{r}\) is zero.
STATEMENT - 2: The coefficient of \(\mathbf{x}^{\Pi}\) in the expansion of \(\left(1-x^{3}\right)^{n}\) is zero, if \(n=3 \mathbf{k}+1 \text { or } n=3 \mathbf{k}+2\).
In the light of the above statements, choose the correct answer from the options given below:
- Both the Statements are true and Statement - 2 is the correct explanation of
- Both the Statements are true and Statement - 2 is not the correct explanation of Statement - 1
- Statement - 1 is true and Statement - 2 is false
- Statement - 1 is false and Statement - 2 is true
Answer
(C) Statement - 1 is true and Statement - 2 is false
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