Prove that `^100 C_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)]dot`

Prove that 100C_(0),100C_(2)+100C_(2),100C_(4)+100C_(4)+100C_(6)+....+100C_(98),100C_(100)=(1)/(2)[200C_(98)-100C_(49)

Evaluate: (i) ^(10)C_3 (ii) ^(100)C_(98) (iii) ^(60)C_(60)

Prove:- (100-100)/(100-100) =2

Sum of the series (100C_(1))^(2)+2.(100C_(2))^(2)+3.(100C_(3))^(2)+....+100(100C_(100))^(2) equals

The coefficient of x^(53) in the expansion sum_(m=0)^(100)^(100)C_m(x-3)^(100-m)2^m is ^100 C_(47) b. ^100 C_(53) c. -^(100)C_(53) d. none of these

Evaluate: ^100C_97

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 :

the value of lambda if sum^(100)C_(m)*^(m)C_(97)=2^(lambda)*^(100)C_(97)

Consider a sequence of 101 term as (.^(100)C_(0))/(1.2.3.4),(.^(100)C_(1))/(2.3.4.5),(.^(100)C_(2))/(3.4.5.6),.....(.^(100)C_(100))/(101.102.103.104) If n^(th) ​ term is greatest term of sequence, then n is equal to :- A)48 B)49 C)50 D)51