Find the value of `^4n C_0+^(4n)C_4+^(4n)C_8++""^(4n)C_(4n)` .

Find the sum ^(n)C_(0)+^(n)C_(4)+^(n)C_(8)+...

Find n if ""^(n)C_(4)=""^(n)C_(6)

The value of |1 1 1\ ^n C_1\ ^(n+2)C_1\ ^(n+4)C_1\ ^n C_2\ ^(n+2)C_2\ ^(n+4)C_2| is (a) 2 (b) 4 (c) 8 (d) n^2

If ""^(n)C_(7)=""^(n)C_(5) , find ""^(n)C_(4) .

The value of |111^(n)C_(1)^(n+2)C_(1)^(n+4)C_(1)^(n)C_(2)^(n+2)C_(2)^(n+4)C_(2)| is

(i) If .^(n)C_(18)=.^(n)C_(12) then find the value of .^(32)C_(n) . (ii) If .^(10)C_(r)=.^(10)C_(r+4) then find the value of .^(5)C_(r) .

Find .^(n)C_(3) , if .^(n)C_(7)=.^(n)C_(4) .

Find the sum sum_(j=0)^n(^(4n+1)C_j+^(4n+1)C_(2n-j)) .