सिद्ध कीजिए : ` r C(n,r)=n C (n-1,r-1)`.

Given that C(n, r) : C(n,r + 1) = 1 : 2 and C(n,r + 1) : C(n,r + 2) = 2 : 3 . What is P(n, r) : C(n, r) equal to ?

Prove that if 1 le r le n " then " n xx^((n-1))C_(r-1)= (n-r+1).^(n)C_(r-1)

Prove that C(n,r)+C(n-1,r)+C(n-2,r)+......+C(r,r)=C(n+1,r+1)

Verify that ""^(n)C_(r )=(n)/(r ) ""^(n-1)C_(r-1) where n=6 and r=3 .

If ^n+1C_(r+1) : ^n C_r : ^(n-1)C_(r-1)=11 :6:3, then n r =

The value of determinant |[ ^n C_(r-1), ^n C_r, (r+1)^(n+2)C_(r+1)],[ ^n C_r, ^n C_(r+1),(r+2)^(n+2)C_(r+2)],[ ^n C_(r+1), ^n C_(r+2), (r+3)^(n+2)C_(r+3)]| is n^2+n-2 b. 0 c. ^n+3C_(r+3) d. ^n C_(r-1)+^n C_r+^n C_(r+1)

The value of determinant |[ ^n C_(r-1), ^n C_r, (r+1)^(n+2)C_(r+1)],[ ^n C_r, ^n C_(r+1),(r+2)^(n+2)C_(r+2)],[ ^n C_(r+1), ^n C_(r+2), (r+3)^(n+2)C_(r+3)]| is n^2+n-2 b. 0 c. ^n+3C_(r+3) d. ^n C_(r-1)+^n C_r+^n C_(r+1)

The value of determinant |[ ^n C_(r-1), ^n C_r, (r+1)^(n+2)C_(r+1)],[ ^n C_r, ^n C_(r+1),(r+2)^(n+2)C_(r+2)],[ ^n C_(r+1), ^n C_(r+2), (r+3)^(n+2)C_(r+3)]| is n^2+n-2 b. 0 c. ^n+3C_(r+3) d. ^n C_(r-1)+^n C_r+^n C_(r+1)

If ^n P_r=^n P_(r+1)a n d^n C_r=^n C_(r-1,) then the value of n+r is.

If ^n P_r=^n P_(r+1)a n d^n C_r=^n C_(r-1,) then the value of n+r is.