1^(100)C_(7)+6.^(300)C_(8)+4^(100)C_(9)+^(100)C_(10)" has the value equal to "^(2)C_(v)

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_(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

If ""^(100)C_(r)=""^(100)C_(3r) then r is:

Let S_(n)=1+q+q^(2)+?+q^(n) and T_(n)=1+((q+1)/(2))+((q+1)/(2))^(2)+?+((q+1)/(2)) If alpha T_(100)=^(101)C_(1)+^(101)C_(2)xS_(1)+^(101)C_(101)xS_(100), then the value of alpha is equal to (A) 2^(99)(B)2^(101)(C)2^(100) (D) -2^(100)

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)

If K=.^(11)C_(2)+2[.^(10)C_(2)+.^(9)C_(2)+.^(8)C_(2)+.^(2)C_(2)] then the value of (K)/(100) is equal to

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

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

Prove that ^100C_(2)^(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)]