QJEEM23Mae1b3: JEE Main 2023 Mathematics - Class 11 JEEM23Mae1b3 Solution: Let the sum of the coefficients of the first three terms in the …

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QJEEM23Mae1b3: JEE Main 2023 Mathematics - Class 11 JEEM23Mae1b3 Solution: Let the sum of the coefficients of the first three terms in the …

Let the sum of the coefficients of the first three terms in the expansion of ${(x - \frac{3}{x^{2}})}^{n}, x \neq 0. n \in N$ , be 376. Then the coefficient of $x^{4}$ is __________.

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Accepted Answer

S=1-3 n+\frac{9 n(n-1)}{2}=376

\begin{aligned} 3 n^{2} - 5 n - 250 = 0 \\ n = 10, \frac{- 25}{3} (Rejected) \\ T_{r + 1} =^{n} C_{r} \cdot x^{n - r} {(\frac{- 3}{x^{2}})}^{r} \\ =^{n} C_{r} x x^{n - 3 r} (- 3)^{r} \\ =^{10} C_{r} x^{10 - 3 r} (- 3)^{r} \end{aligned}

Here

r=2

\begin{aligned} Required coefficient & =^{10} C_{2} (- 3)^{2} \\ = 45 \times 9 \\ = 405 \end{aligned}

QJEEM23Mae1b3: JEE Main 2023 Mathematics - Class 11 JEEM23Mae1b3 Solution: Let the sum of the coefficients of the first three terms in the …

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