What is the value of $m^{3} - 3 m^{2} n + 3 m n^{2} - n^{3}$ ?
I.m = n
II. m =3
III. m is odd

Both II and III

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Both I and III

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None of the three statements can be dispensed with

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The question cannot be answered even using all the three statements

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Solution

The correct option is A Both II and III
$T o s o l v e a n e q u a t i o n w i t h 2 v a r i a b l e s, w e w i l l n e e d b o t h t h e v a l u e s . F o r t h e e q u a t i o n m^{3} - {3 m}^{2} n + 3 m n^{2} - n^{3}, g i v e n, m = n, l e t k = m = n, t h e e q u a t i o n b e c o m e s k^{3} - 3 k^{2} k + 3 k k^{2} - k^{3}, k^{3} - 3 k^{3} + 3 k^{3} - k^{3} = 0 T h e e q u a t i o n c a n b e s o l v e s j u s t u s i n g s t a t e m e n t I$

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