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7.Binomial Theorem
easy
${\left( {\frac{{{x^2}}}{2} - \frac{2}{x}} \right)^8}$ के प्रसार में ${x^7}$ का गुणांक होगा
A
$-56$
B
$56$
C
$-14$
D
$14$
Solution
$(8 – r)(2) + r( – 1) = 7 \Rightarrow 16 – 2r – r = 7 \Rightarrow r = 3$
अत: $x^7$ का गुणांक
$ = {\,^8}{C_3}{\left( {\frac{1}{2}} \right)^5}{( – 2)^3} = – \frac{{8 \times 7 \times 6}}{{3 \times 2 \times 1}} \times \frac{1}{4} = – 14$.
Standard 11
Mathematics
