JEE MATHEMATICS MCQ: BINOMIAL THEOREM

1 Medium

1 of 1

Application +4 | -1

Let

n \in N

. If

(1+x)^n=a_0+a_1 x+a_2 x^2+\ldots+a_n x^n

and

a_{n-3}, a_{n-2}, a_{n-1}

are in

\mathrm{AP}

, then

View answer and explanation

Correct option: A

a_1, a_2, a_3

are in

\mathrm{AP}

Option A (

a_1, a_2, a_3

are in AP) is correct because binomial coefficients equidistant from the beginning and the end are equal, implying

a_1, a_2, a_3

are in AP.

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