એક બહુવિકલ્પ પરીક્ષામાં \(5\) પ્રશ્નો છે.દરેક પ્રશ્નોનોનાં ત્રણ જવાબો છે,જેમાંથી ફક્ત એક જવાબ સાચો છે.કેાઇ વિર્ધાથી માત્ર અટકળ દ્વારા ચાર અથવા ચારથી વધારે સાચા જવાબો મેળવે તેની સંભાવના . .. . . . હોય.

A \(\frac{{17}}{{{3^5}}}\)
B \(\;\frac{{13}}{{{3^5}}}\)
C \(\;\frac{{11}}{{{3^5}}}\)
D \(\;\frac{{10}}{{{3^5}}}\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(\;\frac{{11}}{{{3^5}}}\)

Step-by-step Solution

Detailed explanation

\(p=\frac{1}{3}, q=\frac{2}{3}\) \(^{5} \mathrm{C}_{4}\left(\frac{1}{3}\right)^{4} \cdot \frac{2}{3}+^{5} \mathrm{C}_{5}\left(\frac{1}{3}\right)^{5}\) \(=5 \cdot \frac{2}{3^{5}}+\frac{1}{3^{5}}=\frac{11}{3^{5}}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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