The coefficient of x^3y^4 in (2x + 3y^2)^5 is: - Vidyadip

MCQ

The coefficient of $x^3y^4$ in $(2x + 3y^2)^5$ is:

A
360
✓
720
C
240
D
1080

✓

Answer

Correct option: B.

720

720

Solution:
Given: $\left(2 x+3 y^2\right)^5$
Therefore, the general form for the expression $\left(2 x+3 y^2\right)^5$ is $T_{r+1}={ }^5 C_{r \times}(2 x)^r \times\left(3 y^2\right)^{5-r}$
Hence, $T_{3+1}={ }^5 C_3(2 x)^3 \times\left(3 y^2\right)^{5-3}$
$T_4={ }^5 C_3(2 x)^3 \times\left(3 y^2\right)^2$
$T 4={ }^5 C_3 \times 8 x^3 \times 9 y^4$
On simplification, we get
$T_4=720 x^3 y^4$
Therefore, the coefficient of $x^3 y^4$ in $\left(2 x+3 y^2\right)^2$ is 720 .

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