$\left( {\begin{array}{*{20}{c}} {30}\\ 0 \end{array}} \right)\left( {\begin{array}{*{20}{c}} {30}\\ {10} \end{array}} \right) - \left( {\begin{array}{*{20}{c}} {30}\\ 1 \end{array}} \right)\left( {\begin{array}{*{20}{c}} {30}\\ {11} \end{array}} \right) + ... + \left( {\begin{array}{*{20}{c}} {30}\\ {20} \end{array}} \right)\left( {\begin{array}{*{20}{c}} {30}\\ {30} \end{array}} \right)$ is equal to

JEE MATHEMATICS MCQ: BINOMIAL THEOREM

1 Hard

1 of 1

Analyzing +4 | -1

\left( {\begin{array}{cccccccccccccccccccc} {30}\\ 0 \end{array}} \right)\left( {\begin{array}{cccccccccccccccccccc} {30}\\ {10} \end{array}} \right) - \left( {\begin{array}{cccccccccccccccccccc} {30}\\ 1 \end{array}} \right)\left( {\begin{array}{cccccccccccccccccccc} {30}\\ {11} \end{array}} \right) + ... + \left( {\begin{array}{cccccccccccccccccccc} {30}\\ {20} \end{array}} \right)\left( {\begin{array}{cccccccccccccccccccc} {30}\\ {30} \end{array}} \right)

is equal to

View answer and explanation

Correct option: C

{\;^{30}}{C_{10}}

Option C is correct because the given expression is the coefficient of x²⁰ in (1-x²)³⁰, which simplifies to ^{30}C_{10}.