JEE Mains · Maths · STD 11 - 7. binomial theoram
If \(C_{x} \equiv^{25} C_{x}\) and \(\mathrm{C}_{0}+5 \cdot \mathrm{C}_{1}+9 \cdot \mathrm{C}_{2}+\ldots .+(101) \cdot \mathrm{C}_{25}=2^{25} \cdot \mathrm{k}\) then \(\mathrm{k}\) is equal to
- A \(42\)
- B \(45\)
- C \(51\)
- D \(48\)
Answer & Solution
Correct Answer
(C) \(51\)
Step-by-step Solution
Detailed explanation
\(\mathrm{S}=1 .^{25} \mathrm{C}_{0}+5.2^{25} \mathrm{C}_{1}+9.2^{25} \mathrm{C}_{2}+\ldots .+(101)^{25} \mathrm{C}_{25}\) \(\mathrm{S}=101^{25} \mathrm{C}_{25}+97^{25} \mathrm{C}_{1}+\ldots \ldots \ldots .+1^{25} \mathrm{C}_{25}\) \(2 \mathrm{S}=(102)\left(2^{25}\right)\)…
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