1.

Find the coefficient of 1/y^10 in the expansion of (y^3+a^7/y^5)^10

Answer»

SOLUTION :LET (R+1)th term contains `1/y^10`.
` THEREFORE (r+1)`term in the expansion of
`(y^3+a^7/y^5)^10` is `"^10C_r (y^3)^(10-r)(a^7/y^5)^r`
`"^10C_r y^(30-r) a^(7r) y^(-5R) = ^10C_r a^(7r) y^(30-8r)`
`therefore y^(30-8r) = 1/y^10 = y^-10` or , 30-8r = -10 or, 8r = 40 or, r = 5
The coefficient of `1/y^10` is `"^10C_5 a^(7xx5) = (10!)/(5!5!) a^35 = 252a^35`


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