A) (20, 45)
B) (35, 20)
C) (45, 35)
D) (35, 45)
Correct Answer: D
Solution :
[d] \[{{(1-y)}^{m}}{{(1+y)}^{n}}\] |
\[=[1-{{\,}^{m}}{{C}_{1}}y+{{\,}^{m}}{{C}_{2}}{{y}^{2}}-....][1+{{\,}^{n}}{{C}_{1}}y+{{\,}^{n}}{{C}_{2}}{{y}^{2}}+....]\] |
\[=1+(n-m)y+\left\{ \frac{m(m-1)}{2}+\frac{n(n-1)}{2}-mn \right\}{{y}^{2}}+....\] |
\[=1+(n-m)y+\left\{ \frac{m(m-1)}{2}+\frac{n(n-1)}{2}-mn \right\}{{y}^{2}}+....\]By comparing coefficients with the given expression, we get |
\[\therefore {{a}_{1}}=n-m=10\] and |
\[{{a}_{2}}=\frac{{{m}^{2}}+{{n}^{2}}-m-n-2mn}{2}=10\] |
So, \[n-m=10\] and \[{{(m-n)}^{2}}-(m+n)=20\] |
\[\Rightarrow \,\,m+n=80\therefore \,\,m=35,n=45\] |
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