If `.^(2n)C_(3):^(n)C_(3)=11:1`, find the value of n.

If .^(2n)C_(3):.^(n)C_(3)=12:1 , find n.

If .^(2n)C_(4): .^(n)C_(3)=21:1 , then find the value of n.

If .^(n+1)C_(3)=2(.^(n)C_(2)) , find the value of n.

If .^(n+1)C_(r+1):^(n)C_(r):^(n-1)C_(r-1)=11:6:3 , find the values of n and r.

If .^(n)C_(r-1): .^(n)C_(r): .^(n)C_(r+1)=3:4:5 , find the values of n and r.

If .^(n)C_(r-1)=.^(n)C_(3r) , find r.

If ^(n+1)C_(r+1): ^nC_r: ^(n-1)C_(r-1)=11:6:2 find the values of n and r.

(i) If ""^(2n)C_(3) : ""^(n)C_(3)= 11 : 1 , find n. (ii) If ""^(2n)C_(3) : ""^(n)C_(2) = 12 : 1 , find n.

If .^(2n)C_(3):^(n)C_(2)=44:3 , for which of the following value of r , the value of .^(n)C_(r) will be 15.