For the natural numbers $m,\,\,n,\,\,{\rm{if}}\,\,{\left( {1 - y} \right)^m}{(1 + y)^n} = 1 + {a_1}y + {a_2}{y^2} + ...... + {a_{m + n}}{y^{m + n}}{\rm{)}}$ and ${a_1} = {a_2} = 10$, then the value of $(m + n)$ is equal to

JEE MATHEMATICS MCQ: BINOMIAL THEOREM

1 Medium

1 of 1

Application +4 | -1

For the natural numbers

m,\,\,n,\,\,\mathrm{if}\,\,{\left( {1 - y} \right)^m}{(1 + y)^n} = 1 + {a_1}y + {a_2}{y^2} + ...... + {a_{m + n}}{y^{m + n}}\mathrm{)}

and

{a_1} = {a_2} = 10

, then the value of

(m + n)

is equal to

View answer and explanation

Correct option: D

Option D (80) is correct because by expanding the given expression and equating coefficients, we can solve for m and n, and find m + n = 80.

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