JEE MATHEMATICS MCQ: BINOMIAL THEOREM

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Application +4 | -1

(1+x)^n=C_0+C_1 x+C_2 x^2+\ldots+C_n x^n, n \in N

, then for

2 \leq m \leq n

C_0-C_1+C_2-C_3+\ldots+(-1)^{m-1} C_{m-1}

is equal to

View answer and explanation

Correct option: A

(-1)^{m-1} \cdot{ }^{n-1} C_{m-1}

Option A ((-1)^(m-1) * { }^{n-1} C_{m-1}) is correct because it is derived by equating coefficients of x^(m-1) in the expansion of (1-x)^n(1-x)^(-1).

More Questions from BINOMIAL THEOREM

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