JEE MATHEMATICS MCQ: BINOMIAL THEOREM

1 Easy

1 of 1

Application +4 | -1

If the coefficients of

{x^7}

and

{x^8}

{\left( {2 + x/3} \right)^n}

are equal, then

n

is equal to

View answer and explanation

Correct option: B

Option B (55) is correct because setting the coefficients of

{x^7}

and

{x^8}

equal leads to the equation

{\frac{{\;^n{C_7} \times {2^{n - 7}}}}{{{3^7}}} = {\frac{{\;^n{C_8} \times {2^{n - 8}}}}{{{3^8}}}}

which simplifies to

n = 55

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