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Question

The total number of terms in the expansion of (x+y)50+(xy)50 is

A
51
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B
26
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C
102
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D
25
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Solution

Consider given the expression,

(x+y)50+(xy)50

We know that,

(x+y)n=nC0xn+nC1xn1y+nC2xn2y2+......nCrxnryr.....nCnyn

Now,

(x+y)50+(xy)50

=50C0x50+50C1x49y+50C2x48y2+.....50C50y50+50C0x5050C1x49y+50C2x48y2+.....+50C50y50

=2[50C0x50+50C2x502y+50C4x504y4+......50Crx50ryr.....50C50y50]

Here, 50C0,50C1,50C2,...50C49,50C50 contain 51 terms.

In 26-coefficients , r is even.

In 25-coefficients, r is odd.

Therefore, there are 26 terms

Hence, Option B is correct.


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