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how to solve such questions?

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is ans 15?
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10 will be the answer when u r taking x^2 as common inside it will be 1+x^2+x^4+x^6.... now it simple GP question

using simple formula$\binom{N+r-1}{r}$*x^2r which is $\binom{5}{2}$
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akshat sharma link for formula plZ

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see this formula is commonly used in generating function topic and chocolate problem type question in combinotrics right now i dont have any link u can refer those topic (this is just inverse of (1-x)^n
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here N=4,r=2
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Pull out first x^2 ,so it becomes 1+x^2+.....

The outside x^2 becomes x^8 because of power 4,subtract this from x^12,...

So we need to find coefficient of x^4 here

Since this series is has even numbers ,it clearly says it has x of the form x^2r.  ,And we are finding x^4 and thus r=2

Here n= 4,r=2 hence ,(4+2-1,2)=10

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For those who have dikkat in generating function can see it here  (download image and and then change its position ) open it in paint for clear view

by Boss (10.5k points)
edited
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