Find the value of ` ^4nC_0+^(4n)C_4+^(4n)C_8++""^(4n)C_(4n)` .

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

Find the value of n such that "(i) "^(n)P_(5) =42 xx ""^(n)P_(3), n gt 4 " (ii) "(""^(n)P_(4))/(" "^(n-1)P_(4))=(5)/(3), n gt 4.

If ""^(n)C_4= ""^(n)C_6, find n.

Find the following sums : (i) .^(n)C_(0)-.^(n)C_(2)+.^(n)C_(4)-.^(n)C_(6)+"....." (ii) .^(n)C_(1)-.^(n)C_(3)+.^(n)C_(5)-.^(n)C_(7)+"...." (iii) .^(n)C_(0)+.^(n)C_(4)+.^(n)C_(8)+.^(n)C_(12)+"....." (iv) .^(n)C_(2) + .^(n)C_(6) + .^(n)C_(10)+.^(n)C_(14)+"......" (v) .^(n)C_(1) + .^(n)C_(5)+.^(n)C_(9)+.^(n)C_(13)+"...." (vi) .^(n)C_(3) + .^(n)C_(7) + .^(n)C_(11) + .^(n)C_(15) + "....."

Find the sum .^n C_0+^n C_4+^n C_8 + . . .

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

If .^nC_30=^nC_4 , find n

If ""^(n)C_(3) + ""^(n)C_4 gt ""^(n+1) C_3 , then.

""^(n-1)C_3+""^(n-1)C_4 gt ""^(n)C_3 if