JEE MATHEMATICS MCQ: BINOMIAL THEOREM

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Application +4 | -1

If the coefficient of

r

th,

(r+1)

th and

(r+2)

th terms in the expansion of

(1+x)^n

are in A.P., then

n

is a root of the equation

View answer and explanation

Correct option: D

x^2-x(4 r+1)-4 r^2-2=0

Option D (

x^2-x(4r+1)-4r^2-2=0

) is correct because the condition that the coefficients are in A.P. leads to a quadratic equation in n.

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