JEE MATHEMATICS MCQ: BINOMIAL THEOREM

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Analyzing +4 | -1

For

r=0,1, \ldots, 10

, let

A_r, B_r

and

C_r

denote, respectively the coefficient of

x^r

in the expansions of

(1+x)^{10},(1+x)^{20}

and

\left(1+x^{30}\right)

Then,

\sum\limits_{{r=1}}^{10} A_r\left(B_{10} B_r-C_{10} A_r\right)

is equal to

View answer and explanation

Correct option: D

C_{10}=B_{10}

Option D (

C_{10}=B_{10}

) is correct because simplifying the summation using properties of binomial coefficients leads to the conclusion that

C_{10} - B_{10} = 0

, thus

C_{10} = B_{10}

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