(A) The general term in the expansion of $(x-2y+3z)^6$ is given by the multinomial theorem as $\frac{6!}{a!b!c!} x^a (-2y)^b (3z)^c$,where $a+b+c=6$.F

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(A) The general term in the expansion of $(x-2y+3z)^6$ is given by the multinomial theorem as $\frac{6!}{a!b!c!} x^a (-2y)^b (3z)^c$,where $a+b+c=6$.For the term $xy^2z^3$,we have $a=1, b=2, c=3$.Substituting these values,the coefficient is $\frac{6!}{1! \times 2! \times 3!} \times (-2)^2 \times (3)^3$.Calculating the values: $\frac{720}{1 \times 2 \times 6} \times 4 \times 27 = 60 \times 4 \times 27 = 240 \times 27 = 6480$.

Class 11 Mathematics Binomial Theorem Multinomial theorem, Terms free from radical sign in the expansion of (a1/p + b1/q), Problems regarding to three/four consecutive terms or coefficients

Medium

The coefficient of $xy^2z^3$ in the expansion of $(x-2y+3z)^6$ is

TS EAMCET 2024 All TS EAMCET

A
$6480$
B
$3240$
C
$1620$
D
$810$

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Binomial Theorem

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Multinomial theorem, Terms free from radical sign in the expansion of (a1/p + b1/q), Problems regarding to three/four consecutive terms or coefficients

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