For natural numbers $m,n$ if ${\left( {1 - y} \right)^m}{\left( {1 + y} \right)^n} = 1 + {a_1}{y^2} + $….and ${a_1} = {a_2} = 10,\;$ then $\left( {m,n} \right)$ is

JEE MATHEMATICS MCQ: BINOMIAL THEOREM

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Application +4 | -1

For natural numbers

m,n

{\left( {1 - y} \right)^m}{\left( {1 + y} \right)^n} = 1 + {a_1}{y^2} +

….and

{a_1} = {a_2} = 10,\;

then

\left( {m,n} \right)

View answer and explanation

Correct option: C

\left( {35,45} \right)

Option C ((35,45)) is correct because these values satisfy the equations derived from the given conditions on the binomial expansion.

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