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7.Binomial Theorem
easy
${\left( {\frac{1}{2}{x^{1/3}} + {x^{ - 1/5}}} \right)^8}$ ના વિસ્તરણમાં અચળપદ મેળવો.
A
$5$
B
$6$
C
$7$
D
$8$
Solution
(c) $\frac{1}{3}(8 – r) + r\left( { – \frac{1}{5}} \right) = 0 \Rightarrow \frac{8}{3} – \frac{r}{3} – \frac{r}{5} = 0 \Rightarrow r = 5$
Thus term independent of $x = {\,^8}{C_5} \times {\left( {\frac{1}{2}} \right)^3}{(1)^5}$
$ = \frac{{8 \times 7 \times 6}}{{3 \times 2 \times 1}} \times \frac{1}{8} = 7$
Standard 11
Mathematics
