Q59 / 160 · TS EAMCET 2024 (11 May Shift 1) · Mathematics
The coefficient of $x y^2 z^3$ in the expansion of $(x-2 y+3 z)^6$ is
- Correct answerA$6480$
- B$3240$
- C$1620$
- D$810$
Solution
General term $=\frac{6!}{a!b!c!} x^a(-2 y)^b \cdot(3 z)^c$
For $x y^2 z^3 ; a=1, b=2, c=3$ Coefficient of $x y^2 z^3=\frac{6!}{1!\times 2!\times 3!} \times(-2)^2 \times 3^3=6480$
For $x y^2 z^3 ; a=1, b=2, c=3$ Coefficient of $x y^2 z^3=\frac{6!}{1!\times 2!\times 3!} \times(-2)^2 \times 3^3=6480$
Hence, the correct answer is option: 'A'.