JEE MATHEMATICS MCQ: BINOMIAL THEOREM

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Application +4 | -1

\left(\begin{array}{c} 20 \\ 0 \end{array}\right)-\left(\begin{array}{c} 20 \\ 1 \end{array}\right)+\left(\begin{array}{c} 20 \\ 2 \end{array}\right)-\left(\begin{array}{c} 20 \\ 3 \end{array}\right)+\ldots+\left(\begin{array}{l} 20 \\ 10 \end{array}\right)=

View answer and explanation

Correct option: B

\frac{1}{2}\left(\begin{array}{l}20 \\ 10\end{array}\right)

Option B is correct because by substituting x = -1 into the binomial expansion and using the property that C(n,r) = C(n, n-r), the given sum simplifies to half of C(20, 10).

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