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In the expansion of (sqrt((q)/(p) )+ ro...

In the expansion of `(sqrt((q)/(p) )+ root(10) ((p^(7))/(q^(3))))^(n)` , there is a term
similar to pq , then that term is equl to

A

45pq

B

120 pq

C

210 pq

D

252 pq

Text Solution

Verified by Experts

The correct Answer is:
d
We have ,
`T_(r+1) = ""^(n)C_(r) (sqrt((q)/(p)))^(n-r)(root(10)((p^(7))/(q^(3))))^(r) = ""^(n)C_(r) (q)^( (n-r)/(2)- (3r)/(10))xx(p)^( (n-r)/(2)- (7r)/(10))`
` = ""^(n)C_(r) *q ^((5n-8r)/(10) )*P^((12n-5r)/(10) )`
For coefficient of pq , we get
`(5n-8r)/(10) = 1 (12n-5r)/(10) = 1`
` rArr 5n- 8r -10 = 0, 12r - 5n- 10 = 0 `
` rArr r = 5, n=10`
` therefore t_(6) = ""^(10)C_(5) pq = 252 pq`
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