JEE Mains · Maths · STD 11 - 7. binomial theoram
The sum, of the coefficients of the first \(50\) terms in the binomial expansion of \((1-x)^{100}\), is equal to
- A \(-{ }^{101} C _{50}\)
- B \({ }^{99} C _{49}\)
- C \(-{ }^{99} C _{49}\)
- D \({ }^{101} C _{50}\)
Answer & Solution
Correct Answer
(C) \(-{ }^{99} C _{49}\)
Step-by-step Solution
Detailed explanation
\((1- x )^{100}= Co - C _1 x + C _2 x ^2-\) \(C _3 x ^3+\ldots C _{99 x }{ }^{99}+ C _{100 x } x ^{10}\) \(\Rightarrow Co ^{- C _1}+ C _2- C _3+\ldots \ldots- C _{99}+ C _{100}=0\) \(2\left( Co - C _1+ C _2+\ldots \ldots- C _9\right)+ C _{50}=0\)…
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