Let [t] denotes greatest integer ≤ t . If constant term in expansion of left(3 x^2-frac{1}{2 x^5}r

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7.Binomial Theorem

hard

Let $[t]$ denotes the greatest integer $\leq t$. If the constant term in the expansion of $\left(3 x^2-\frac{1}{2 x^5}\right)^7$ is $\alpha$, then $[\alpha]$ is equal to $............$.

A

$1274$

B

$1275$

C

$1273$

D

$1272$

(JEE MAIN-2023)

Solution

$\left(3 x ^2-\frac{1}{2 x ^5}\right)^7$

$T _{ r +1}={ }^7 C _{ r }\left(3 x ^2\right)^{7- r }\left(-\frac{1}{2 x ^5}\right)^{ r }$

$14-2 r -5 r =14-7 r =0$

$\therefore r =2$

$\therefore T _3={ }^7 C _2 \cdot 3^5\left(-\frac{1}{2}\right)^2=\frac{21 \times 243}{4}=1275.75$

$\therefore[\alpha]=1275$

Standard 11

Mathematics

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