The number of dissimilar terms in the expansion of ${(a + b)^n}$ is $n + 1$ therefore no of dissimilar terms of the expansion ${\left( {a + b + c} \right)^{12}}$ is

JEE MATHEMATICS MCQ: BINOMIAL THEOREM

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The number of dissimilar terms in the expansion of

{(a + b)^n}

n + 1

therefore no of dissimilar terms of the expansion

{\left( {a + b + c} \right)^{12}}

View answer and explanation

Correct option: D

The correct answer is D (91) because the number of dissimilar terms in the expansion of

{(a + b + c)^{12}}

is calculated using the formula

{\;^{n + r - 1}}{C_{r - 1}}

, where n is the power and r is the number of variables.

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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

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