Property:- (i) `nC_r=nC_(n-r)` (ii) `(nC_r)/(r+1)=((n+1)C_(r+1))/(n+1)`

Property :-( iii) nC_(r)+nC_(r-1)=(n+1)C_(i)

Show that nC_(r)=(n-r+1)/(r)*(nC_(r-1))

Prove that ^nC_(r)+^(n-1)C_(r)+...+^(r)C_(r)=^(n+1)C_(r+1)

^nC_r+^nC_(r+1)+^nC_(r+2) is equal to (2lerlen) (A) 2^nC_(r+2) (B) 2^(n+1)C_(r+1) (C) 2^(n+2)C_(r+2) (D) none of these

Prove that nC_(r)+n-1C_(r)+n-2C_(r)+.......+rC_(r)=n+1C_(1)

Prove that "^nC_r + 2. ^nC_(r-1) + ^nC_(r-2) = ^(n+2)C_r

If sum_(r=0)^(n-1)((^nC_(r))/(nC_(r)+^(n)C_(r+1)))^(3)=(4)/(5) then n=

Property (iv) If ^nC_x=^nC_y ; then either x=yx=y or x+y=nx+y=n (v) r.nC_r=n. (n-1)C_(r-1)r.nC_r=n. (n-1)C_(r-1)

Prove that (3!)/(2(n+3))=sum_(r=0)^(n)(-1)^(r)((^nC_(r))/(r+3C_(r)))

Assertion: If n is an even positive integer n then sum_(r=0)^n ^nC_r/(r+1) = (2^(n+1)-1)/(n+1) , Reason : sum_(r=0)^n ^nC_r/(r+1) x^r = ((1+x)^(n+1)-1)/(n+1) (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.