JEE Mains · Maths · STD 11 - 7. binomial theoram
If the number of integral terms in the expansion of \(\left(3^{\frac{1}{2}}+5^{\frac{1}{8}}\right)^{\text {n }}\) is exactly \(33,\) then the least value of \(n\) is
- A \(264\)
- B \(256\)
- C \(128\)
- D \(248\)
Answer & Solution
Correct Answer
(B) \(256\)
Step-by-step Solution
Detailed explanation
\(T _{ r +1}={ }^{ n } C _{ r }(3)^{\frac{ n - r }{2}}(5)^{\frac{ r }{8}} \quad( n \geq r )\) Clearly r should be a multiple of 8 . \(\because\) there are exactly 33 integral terms Possible values of \(r\) can be \(0,8,16, \ldots \ldots \ldots, 32 \times 8\) \(\therefore\) least…
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