For `""^(n) C_(r) ` + 2`""^(n) C_(r-1) ` + `""^(n) C_(r-2) ` =

""^(n-2)C_(r)+2""^(n-2)C_(r-1)+""^(n-2)C_(r-2) equals :

If ""^(n)C_r : ""^(n)C_(r+1) =1 : 2 and^(n)C_(r+1): ""^(n)C_(r+2) = 2 : 3 determine the values of n and r.

If ""^(n)C_(r -1) = 36, ""^(n)C_(r) = 84 " and " ""^(n)C_(r +1) = 126 , then find the value of ""^(r)C_(2) .

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

If ([""^(n)C_(r) + 4*""^(n)C_(r+1) + 6*""^(n)C_(r+2)+ 4*""^(n)C_(r+3) + ""^(n)C_(r+4)])/([""^(n)C_(r) + 3. ""^(n)C_(r+1)+ 3*""^(n)C_(r+2) + ""^(n)C_(r +3)])=(n + lambda)/(r+lambda) the value of lambda is

If ""^(n)C _r denots the numbers of combinations of n things taken r at a time, then the expression ""^(n) C_(r+1) +""^(n)C_(r-1) +2 xx ""^(n)C_r equals ""^(n+2) C_(r+1)

If ""^(n)C _r denots the numbers of combinations of n things taken r at a time, then the expression ""^(n) C_(r+1) +""^(n)C_(r-1) +2 xx ""^(n)C_r equals ""^(n+2) C _(r+1)

If ""^(n)C _4 denots the numbers of combinations of n things taken r at a time, then the expression ""^(n) C_(r+1) +""^(n)C_(r-1) +2 xx ""^(n)C_r equals ""^(n+2)C_(r+1)

""^(n)C_(r)+2""^(n)C_(r-1)+^(n)C_(r-2) is equal to

If ""^(n)C _r denotes the numbers of combinations of n things taken r at a time, then the expression ""^(n) C_(r+1) +""^(n)C_(r-1) +2 xx ""^(n)C_r equals