The coefficient of ${x^6}$ in $\left\{ {{{\left( {1 + x} \right)}^6} + {{\left( {1 + x} \right)}^7} + \ldots + {{\left( {1 + x} \right)}^{15}}} \right\}$ is

JEE MATHEMATICS MCQ: BINOMIAL THEOREM

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The coefficient of

{x^6}

\left\{ {{{\left( {1 + x} \right)}^6} + {{\left( {1 + x} \right)}^7} + \ldots + {{\left( {1 + x} \right)}^{15}}} \right\}

View answer and explanation

Correct option: A

{\;^{16}}{C_9}

Option A (^{16}C_9) is correct because the coefficient of x⁶ in the given sum of binomial expansions is found by using the formula for the sum of a geometric series and then finding the coefficient of x⁷ in the resulting expression.

More Questions from BINOMIAL THEOREM

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\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

equals If

a

and

d

are two complex numbers, then the sum to

\left( {n + 1} \right)

terms of the following series

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

is The number of different terms in the expansion of

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

is The sum of the coefficient of the binomial expansion of

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

is equal to 6561 . The constant term in the expansion is The coefficient of

{x^5}

in the expansion of

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

is If

\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

, then

n

equals