JEE Mains · Maths · STD 11 - 7. binomial theoram
\(25^{190}-19^{190}-8^{190}+2^{190}\) is divisible by
- A \(34\) but not by \(14\)
- B both \(14\) and \(34\)
- C neither \(14\) nor \(34\)
- D \(14\) but not by \(34\)
Answer & Solution
Correct Answer
(A) \(34\) but not by \(14\)
Step-by-step Solution
Detailed explanation
\(25^{190}-8^{190}\) is divisible by \(25-8=17\) \(19^{190}-2^{190}\) is divisible by \(19-2=17\) \(25^{190}-19^{190}\) is divisible by \(25-19=6\) \(8^{190}-2^{190}\) is divisible by \(8-2=6\) \(L.C.M.\) of \(1746=34\) \(\therefore\) divisible by \(34\) but not by \(14\)
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