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The value of ((30), (0))((30), (10))-((3...

The value of `((30), (0))((30), (10))-((30), (1))((30),( 11)) +(30 2)(30 12)++(30 20)(30 30)=` a. `^60 C 20` b. `^30 C 10` c. `^60 C 30` d. `^40 C 30`

A

`""^(30)C_(11)`

B

`""^(60)C_(10)`

C

`""^(30)C_(10)`

D

`""^(65)C_(55)`

Text Solution

Verified by Experts

The correct Answer is:
c
We have,
`""^(30)C_(0)xx""^(30)C_(10)- ""^(30)C_(1)xx""^(30)C_(11)+...+ ""^(30)C_(10)xx""^(30)C_(0)`
= Coefficient of `x^(20)` in `{(1 + x )^(30) (1 - x)^(30)}`
= Coefficient of `x^(20)` in ` (1 - x^(2))^(30)`
` = ""^(30)C_(10) (-1)^(10) = ""^(30)C_(10)`
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