JEE MATHEMATICS MCQ: BINOMIAL THEOREM

1 Easy

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m

and

n

are positive integers, then value of

{ }^m C_0{ }^n C_k+{ }^m C_1{ }^n C_{k-1}+\ldots+{ }^m C_k{ }^n C_0

View answer and explanation

Correct option: A

{ }^{m+n} C_k

Option D (None of these) is correct because the value of

\arg(z) + \arg(\bar{z})

depends on whether z is a negative real number or not. If z is a negative real number, the sum is

2\pi

, otherwise it is 0.

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