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Number of Terms in Binomial Expansion

The number of...

Question

The number of distinct terms in the expansion of $(x + y^{2})^{13} + (x^{2} + y)^{14}$ is

A

27

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B

29

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C

28

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D

25

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Solution

The correct option is C 28
To get common terms in both the expansions
$x^{r_{1}} {(y^{2})}^{13 - r_{1}} = (x^{2})^{r_{2}} (y)^{14 - r_{2}}$
$r_{1} = 2 r_{2}$ & $26 - 2 r_{1} = 14 - r_{2}$
$r_{1} = 8; r_{2} = 4$
$∴$ Only one term is common.

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