[" (19) "m_(c_(1))=n_(c_(2))" twn."],[[" (9) "2m=n," (b) "2m=n(n+1)],[" (c) "2m=n(n-1)," (d) "2n=m(m-1)]]

If ^(m)C_(1)=^(n)C_(2) then 2m=nb2m=n(n+1) c.2m=(n-1)d2n=m(m-1)

If \ ^m C_1=\ \ ^n C_2 then which is correct a. 2m=n b. 2m=n(n+1) c. 2m=(n-1) d. 2n=m(m-1)

""^(2n)C_(n+1)+2. ""^(2n)C_(n) + ""^(2n) C_(n-1) =

The value of ^n C_1+^(n+1)C_2+^(n+2)C_3++^(n+m-1)C_m is equal to (a) ^m+n C_(n-1) (b) ^m+n C_(n-1) (c) ^mC_(1)+^(m+1)C_2+^(m+2)C_3++^(m+n-1) (d) ^m+1C_(m-1)

If m=""^(n)C_(2) , then ""^(m)C_(2) is equal to a) 3""^(n)C_(4) b) ""^(n+1)C_(4) c) 3""^(n+1)C_(4) d) 3""^(n+1)C_(3)

If .^(m)C_(1)=.^(n)C_(2) prove that m=(1)/(2)n(n-1) .

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + …+ C_(n) x^(n) , prove that C_(0) *""^(2n)C_(n) - C_(1) *""^(2n-2)C_(n) + C_(2) *""^(2n-4) C_(n) -…= 2^(n)

Let m, in N and C_(r) = ""^(n)C_(r) , for 0 le r len Statement-1: (1)/(m!)C_(0) + (n)/((m +1)!) C_(1) + (n(n-1))/((m +2)!) C_(2) +… + (n(n-1)(n-2)….2.1)/((m+n)!) C_(n) = ((m + n + 1 )(m+n +2)…(m +2n))/((m +n)!) Statement-2: For r le 0 ""^(m)C_(r)""^(n)C_(0)+""^(m)C_(r-1)""^(n)C_(1) + ""^(m)C_(r-2) ""^(n)C_(2) +...+ ""^(m)C_(0)""^(n)C_(r) = ""^(m+n)C_(r) .