Statement 1: `^m C_r+^m C_(r-1)^n C_1+^mC_(r-2)^n C_2++^n C_r=0,ifm+n

Statement 1: ^m C_r+^m C_(r-1)(^nC_1)+^mC_(r-2)(^n C_2)+....+^n C_r=0 , if m+n lt r Statement 2: ^n C_r=0 , if n lt r

Statement 1: ""^m C_r+ ""^m C_(r-1)(""^nC_1)+ ""^mC_(r-2)(""^n C_2)+....+ ""^n C_r=0 , if m+n lt r Statement 2: ""^n C_r=0 , if n lt r (a) Statement 1 and Statement 2, both are correct. Statement 2 is the correct explanation for Statement 1. (b) Statement 1 and Statement 2, both are correct. Statement 2 is not the correct explanation for Statement 1. (c) Statement 1 is true but Statement 2 is false. (d) Statement 2 is true but Statement 1 is false.

Statement 1:^mC_(r)+mC_(r-1)^(n)C_(1)+mC_(r-2)^(n)C_(2)+...+^(n)C_(r)=0, if m+n

If n is a positive integer such that (1+x)^n=^nC_0+^nC_1+^nC_2x^2+…….+^nC_nx^n , for epsilonR . Also .^nC_r=C_r On the basis of the above information answer the following questions the value of .^mC_r.^nC_0+^mC_(r-1).^nC_1+^mC_(r-2).^nC_2+….+^mC_1.^nC_(r-1)+^nC_0^nC_r where m,n, r are positive interges and rltm,rltn= (A) .^(mn)C_r (B) .^(m+n)C_r (C) 0 (D) 1

If n is a positive integer such that (1+x)^n=^nC_0+^nC_1+^nC_2x^2+…….+^nC_nx^n, for epsilonR . Also ^nC_r=C_r On the basis o the above information answer the following questions the value of ^mC_r.^nC_0+^mC_(r-1).^nC_1+^mC_(r-2).^nC_2+….+^mC_1.^nC_(r-1)+^nC_0^nC_r where m,n, r are positive interges and rltm,rltn= (A) ^(mn)C_r (B) ^(m+n)C_r (C) 0 (D) 1

mC_(r)+mC_(r-1)nC_(1)+mC_(r-2)nC_(2)+.........+nC_(r)=(m+n)C_(r)

Prove that (r+1)^n C_r-r^n C_r+(r-1)^n C_2-^n C_3++(-1)^r^n C_r = (-1)^r^(n-2)C_rdot

If m,n,r are positive integers such that rltm,n, then: ""^(m)C_(r)+""^(m)C_(r-1)""^(n)C_(1)+""^(m)C_(r-2)""^(n)C_(2)+ . . ..+""^(m)C_(1)""^(n)C_(r-1)+""^(n)C_(r) equals:

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)