JEE Mains · Maths · STD 11 - 7. binomial theoram
The sum of coefficients of integral power of \(x\) in the binomial expansion \({\left( {1 - 2\sqrt x } \right)^{50}}\) is :
- A \(\frac{1}{2}\left( {{2^{50}} + 1} \right)\)
- B \(\;\frac{1}{2}\left( {{3^{50}} + 1} \right)\)
- C \(\;\frac{1}{2}\left( {{3^{50}}} \right)\)
- D \(\;\frac{1}{2}\left( {{3^{50}} - 1} \right)\)
Answer & Solution
Correct Answer
(B) \(\;\frac{1}{2}\left( {{3^{50}} + 1} \right)\)
Step-by-step Solution
Detailed explanation
\({\left( {1 - 2\sqrt x } \right)^{50}} = {^{50}}{c_0} - {^{50}}{c_1}{\left( {2\sqrt x } \right)^1}\)\({\left( {1 - 2\sqrt x } \right)^{50}} = {^{50}}{c_0} - {^{50}}{c_1}{\left( {2\sqrt x } \right)^1}\)\( + {^{50}}{c_4}\left( {2\sqrt x } \right)4.....\)…
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