If second term of expansion {left[ {{a^{frac{1}{{13}}}},, + ,,frac{a}{{√ {{a^{ - 1}}} }}} right]^n

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7.Binomial Theorem

normal

If the second term of the expansion ${\left[ {{a^{\frac{1}{{13}}}}\,\, + \,\,\frac{a}{{\sqrt {{a^{ - 1}}} }}} \right]^n}$ is $14a^{5/2}$ then the value of $\frac{{^n{C_3}}}{{^n{C_2}}}$ is :

A

$4$

B

$3$

C

$12$

D

$6$

Solution

$T_{2}={ }^{n} C_{1}\left(a^{1 / 13}\right)^{n-1} \cdot a \sqrt{a}=14 a^{5 / 2}$

$\Rightarrow n-1$

$\frac{n-1}{13}=14 a$

$\Rightarrow \frac{n-1}{13}=14$

$\Rightarrow \frac{n-14}{13}=0$

$\Rightarrow n=14$

$\frac{14}{14} C_{2}=\frac{14 !}{3 ! 1 !} \frac{2 ! 2 !}{14 !}=\frac{12}{3}=4$

Standard 11

Mathematics

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