STATEMENT - 1 :
If `.^(2n+1)C_(1)` + `.^(2n+1)C_(2)+………+ .^(2n+1)C_(n)= 4095`, then `n = 7`
STATEMENT - 2 :
`.^(n)C_(r )= .^(n)C_(n-r)` where `n epsilon N, r epsilon W and n ge r`

Options

A. STATEMENT - 1 is True, STATEMENT- 2 is True , STATEMENT - 2 is a correct explanation for STATEMENT - 1
B. STATEMENT - 1 is True, STATEMENT - 2 is True , STATEMENT - 2 is NOT a correct explanation for STATEMENT - 1
C. STATEMENT -1 is True, STATEMENT - 2 is False
D. STATEMENT -1 is False, STATEMENT - 2 is True

Answer

D

Explanation

Statement -1 : If `.^(2n+1)C_(1)+……..`
Statement -1 :
`.^(2n-1)C_(1)+^(2n+1)C_(2)+…..+.^(2n+1)C_(n)= (1)/(2) (.^(2n+1)C_(1)+^(2n+1)C_(2)+…..+ .^(2n+1)C_(n)+^(2n-1)C_(n-1)+…….+ .^(2n+1)C_(2n)) = (1)/(2)`
`(2^(2n-1)-2) = 2^(2n) -1 = 4095`
`:. 4^(n) = 4096 :. n = 6`
`:.` statement is false
Statement - 2 is true