If coefficient of $a^2 b^3 c^4$ in $(a+b+c)^m$, (where $\left.m \in N\right)$ is $L(L \neq 0)$ then in same expansion coefficient of $a^4 b^4 c^1$ will be

JEE MATHEMATICS MCQ: BINOMIAL THEOREM

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Application +4 | -1

If coefficient of

a^2 b^3 c^4

(a+b+c)^m

, (where

\left.m \in N\right)

L(L \neq 0)

then in same expansion coefficient of

a^4 b^4 c^1

will be

View answer and explanation

Correct option: D

\frac{\mathrm{L}}{2}

Option D (

\frac{\mathrm{L}}{2}

) is correct because the ratio of the coefficients is determined by the multinomial theorem and the given condition that

L \ne 0

Practice All Chapter MCQs →

\left({ }^{10} C_0\right)^2-\left({ }^{10} C_1\right)^2+\ldots-\left({ }^{10} C_9\right)^2+\left({ }^{10} C_{10}\right)^2

a

d

\left( {n + 1} \right)

a{C_0} - \left( {a + d} \right){C_1} + \left( {a + 2d} \right){C_2} - ... + ...

(1-x)^{201}\left(1+x+x^2\right)^{200}

\left(\frac{1}{x}+2 x\right)^n

{x^5}

\frac{{1 + {x^2}}}{{1 + x}},\left| x \right| < 1,

\left(\begin{array}{c}2 n+1 \\ 0\end{array}\right)+\left(\begin{array}{c}2 n+1 \\ 3\end{array}\right)+\left(\begin{array}{c}2 n+1 \\ 6\end{array}\right)+\ldots=170

n