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7.Binomial Theorem
hard
$\left(2 \mathrm{x}+\frac{1}{\mathrm{x}^7}+3 \mathrm{x}^2\right)^5$ के प्रसार में अचर पद है______.
A
$1089$
B
$1080$
C
$1050$
D
$1562$
(JEE MAIN-2023)
Solution
General term is $\sum \frac{5 !(2 x)^{n_1}\left(x^{-7}\right)^{n_2}\left(3 x^2\right)^{n_3}}{n_{1} ! n_{2} ! n_{3} !}$
For constant term,
$n _1+2 n _3=7 n _2$
$n _1+ n _2+ n _3=5$
Only possibility $n _1=1, n _2=1, n _3=3$
$\Rightarrow$ constant term $=1080$
Standard 11
Mathematics
