Coefficient of x in the expansion of ( x 2 + a x ) 5 is

Question

Coefficient of $x$ in the expansion of ${(x^{2} + \frac{a}{x})}^{5}$ is

Smart Achievers · Accepted Answer

(2)

$Given, {(x^{2} + \frac{a}{x})}^{5}$

$= {}^{5}C_{0} {(x^{2})}^{5} + {}^{5}C_{1} {(x^{2})}^{4} (\frac{a}{x}) + {}^{5}C_{2} {(x^{2})}^{3} {(\frac{a}{x})}^{2}$ $+ {}^{5}C_{3} {(x^{2})}^{2} {(\frac{a}{x})}^{3} + {}^{5}C_{4} x^{2} {(\frac{a}{x})}^{4} + {}^{5}C_{5} {(\frac{a}{x})}^{5}$

$∴$ $Coefficient of x = {}^{5}C_{3} a^{3} = 10 a^{3}$

Solution

Q.
Coefficient of $x$ in the expansion of ${(x^{2} + \frac{a}{x})}^{5}$ is

1 $9 a^{2}$

2 $10 a^{3}$

3 $10 a^{2}$

4 $10 a$

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Solution

Q. Coefficient of x in the expansion of (x2+ax)5 is

1 9a2

2 10a3

3 10a2

4 10a