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If .^(m+n)P(2)=90 and .^(m-n)P(2)=30, fi...

If `.^(m+n)P_(2)=90 and .^(m-n)P_(2)=30`, find the value of m and .

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`because.^(m+n)P_(2)=90=10xx9=.^(10)P_(2)`
`thereforem+n=10` . . . (i)
and `.^(m-n)P_(2)=30=6xx5=.^(6)P_(2)`
`thereforem-n=6` . . . (ii)
From eqs. (i) and (ii), we get
`m=8 and n=2`.
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ARIHANT MATHS-PERMUTATIONS AND COMBINATIONS -Exercise (Questions Asked In Previous 13 Years Exam)
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  18. Let a(n) denote the number of all n-digit numbers formed by the digits...

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