Question

The value of `(.^(21)C_(1) - .^(10)C_(1)) + (.^(21)C_(2) - .^(10)C_(2)) + (.^(21)C_(3) - .^(10)C_(3)) + (.^(21)C_(4) - .^(10)C_(4)) + … + (.^(21)C_(10) - .^(10)C_(10))` is
A. `2^(20) - 2^(10)`
B. `2^(21) - 2^(11)`
C. `2^(21) - 2^(10)`
D. `2^(20) - 2^(9)`

Answer 1

Correct Answer - A
We have
`(.^(21)C_(1)+.^(21)C_(2)"....."+.^(21)C_(10))-(.^(10)C_(1)+.^(10)C_(2)"....".^(10)C_(10))`
`= 1/2[.^(21)C_(0)+.^(21)C_(1)+.^(21)C_(2)+"..."+.^(21)C_(21)]-2^(10)`
`= 2^(20) - 2^(10)`