The coefficient of ${\lambda ^n}{{\rm{\mu }}^n}$ in the expansion of ${\left[ {\left( {1 + \lambda } \right)\left( {1 + {\rm{\mu }}} \right)\left( {\lambda + {\rm{\mu }}} \right)} \right]^n}$ is

$\mathop \sum \limits_{r = 0}^n C_r^3$

$\mathop \sum \limits_{r = 0}^n C_r^2$

$\mathop \sum \limits_{r = 0}^n C_{r + 2}^2$

$\mathop \sum \limits_{r = 0}^n C_{r + 3}^2$

JEE MATHEMATICS MCQ: BINOMIAL THEOREM

1 Easy

1 of 1

Analyzing +4 | -1

The coefficient of

{\lambda ^n}{\mathrm{\mu }^n}

in the expansion of

{\left[ {\left( {1 + \lambda } \right)\left( {1 + \mathrm{\mu }} \right)\left( {\lambda + \mathrm{\mu }} \right)} \right]^n}

View answer and explanation

Correct option: D

\sum \limits_{r = 0}^n C_r^3

Option D (

\sum \limits_{r = 0}^n C_r^3

) is correct because it represents the coefficient of

\lambda ^n \mu^n

in the expansion of the given expression, which simplifies to the sum of cubes of binomial coefficients.