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Let (x+10)^(50)+(x-10)^(50)=a(0)+a(1)x+a...

Let `(x+10)^(50)+(x-10)^(50)=a_(0)+a_(1)x+a_(2)x^(2)+...+a_(50)x^(50)` for all `x in R`, then `(a_(2))/(a_(0))` is equal to

A

`12.00`

B

`12.25`

C

`12.75`

D

`12.50`

Text Solution

Verified by Experts

The correct Answer is:
B
`(x+10) ^(50) = ""^(50) C_(0) x ^(50) + ""^(50) C _(1) x ^(49) . 10 + ""^(50) C _(2) x ^(48) . 10^(2) ……" "…(i)`
`(x-10) ^(50) = ""^(50) C _(0) x ^(50)- ""^(50) C _(1) x ^(49), 10 + ""^(50) C _(2)x ^(48) . 10 ^(2) ….." "…(ii)`
Adding (i) and (ii)
`(x +10)^(50) + (x-10)^(50)=2 [""^(50)C_(0)x ^(50) +""^(50) C _(2) x ^(48) . 10 ^(2) +...+ ""^(50) C_(48) x ^(2). 10 ^(48) + ""^(50) C _(50) 10^(50)]`
`therefore a _(0) =10 ^(50) , a _(2) = ""^(50) C _(48) 10 ^(48), (a_(2))/(a _(0))= (""^(50)C _(48).10 ^(48))/(10^(50))= (""^(50) C _(2))/(10 ^(2))=(50 xx 49)/(2xx100) = (49)/(4).`
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