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  • Find the number of solutions of  <img alt="\left[\left(\frac{10 \times 2}{5}\right)(m+m+m+n+n+n)\right]=60" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cleft%5B%5Cleft%28%5Cfra

Find the number of solutions of  \left[\left(\frac{10 \times 2}{5}\right)(m+m+m+n+n+n)\right]=60 , such that m and n are odd numbers

Option: 1

6


Option: 2

2


Option: 3

1


Option: 4

10


Answers (1)

best_answer

Given,
\begin{aligned} & {\left[\left(\frac{10 \times 2}{5}\right)(m+m+m+n+n+n)\right]=60 \text { and }} \\ & m, n>0 \end{aligned}
Generalized formula to find the number of solutions of equations is
a_1+a_2+\ldots . .+a_r=(n+r-1) c_{r-1} Let, $m=m, n=n Then $m+n=5So the equation becomes
m + n = 5
Hence from above equation, n = 5 and r = 2
Hence the total number of solutions =(5+2-1) c_{2-1}=6 c_1=6

Posted by

HARSH KANKARIA

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