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  • Find the sixth term of the expansion (y^1/2 + x^1/3)^n if the binomial coefficient of the third term from the end is 45.

Find the sixth term of the expansion (y1/2 + x1/3)n, if the binomial coefficient of the third term from the end is 45.

 

Answers (1)

Given: (y1/2 + x1/3)n

From the end, binomial coefficient of 3rd term = 45

Thus, nCn-2 = 45 ,   nC2 = 45

i.e., n(n-1)(n-2)!/2!(n-2)! = 45

Now, n(n-1) = 90,

n2 – n – 90 = 0,

(n – 10)(n + 9) = 0

n = 10     …. (since n is not equal to -9)

Now, the 6th term,

=10C5 (y1/2)10-5 (x1/3)5

= 252y5/2.x5/3
 

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infoexpert22

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