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7.Binomial Theorem
medium
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
$248$
(JEE MAIN-2020)
Solution
$T _{ r +1}={ }^{ n } C _{ r }(3)^{\frac{ n – r }{2}}(5)^{\frac{ r }{8}} \quad( n \geq r )$
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 value of $n =256$
Standard 11
Mathematics
