If `""^(100)C_(6)+4." "^(100)C_(7)+6." "^(100)C_(8)+4." "^(100)C_(9)+""^(100)C_(10)` has the value equal to `" "^(x)C_(y)` , then the possible value (s) of `x+y` can be :

If ^100 C_5+5^(100)C_6+10^(100)C_7+10^(100)C_8+5^(100)C_9+^(100)C_(10) has the value equal to ^n C_r , then least value of (n+r) is equal to 200 (2) 195 (3) 115 (4) 105

""^(15)C_(9)-_""^(15)C_(6)+""^(15)C_(7)-^(15)C_(8) equals to

""^(15)C_(8) + ""^(15)C_(9) - ""^(15)C_(6) - ""^(15)C_(7) is equal to ………. .

The value of sum_(r=0)^50 (.^(100)C_r.^(200)C_(150+r)) is equal to

The coefficient of x^(50) in the expansion sum_(k=0)^(100)""^(100)C_(k)( x-2)^(100-k)3^(k) is also equal to :

If |{:(.^(9)C_(4),.^(9)C_(5),.^(10)C_(r)),(.^(10)C_(6 ),.^(10)C_(7),.^(11)C_(r+2)),(.^(11)C_(8),.^(11)C_(9),.^(12)C_(r+4)):}|=0 , then the value of r is equal to

Prove that ^100 C_0^(100)C_2+^(100)C_2^(100)C_4+^(100)C_4^(100)C_6++^(100)C_(98)^(100)C_(100)=1/2[^(200)C_(98)-^(100)C_(49)]dot

Let t_(100)=sum_(r=0)^(100)(1)/(("^(100)C_(r ))^(5)) and S_(100)=sum_(r=0)^(100)(r )/(("^(100)C_(r ))^(5)) , then the value of (100t_(100))/(S_(100)) is (a) 1 (b) 2 (c) 3 (d) 4

Prove the following identieties using the theory of permutation where C_(0),C_(1),C_(2),……C_(n) are the combinatorial coefficents in the expansion of (1+x)^n,n in N: ""^(100)C_(10)+5.""^(100)C_(11)+10 .""^(100)C_(12)+ 10.""^(100)C_(13)+ 10.""^(100)C_(14)+ 10.""^(100)C_(15)=""^(105)C_(90)

Evaluate the following: \ ^(100)C_(98)