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7.Binomial Theorem
easy
${\left( {x - \frac{1}{x}} \right)^6}$ ના વિસ્તરણમાં અચળ પદમેળવો.
A
$-20$
B
$20$
C
$30$
D
$-30$
Solution
(a) In the expansion of ${\left( {x – \frac{1}{x}} \right)^6}$,
the general term is $^6{C_r}{x^{6 – r}}{\left( { – \frac{1}{x}} \right)^r}{ = ^6}{C_r}{( – 1)^r}{x^{6 – 2r}}$
For term independent of $x,\,\,6 – 2r = 0 $
$\Rightarrow r = 3$
Thus the required coefficient $ = {( – 1)^3}{.^6}{C_3} = – 20$.
Standard 11
Mathematics
