Home
Class 12
MATHS
If n is a positive integer such that (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

Promotional Banner

Similar Questions

Explore conceptually related problems

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 the series sum_(r=1)^n r^2.C_r= (A) 1 (B) (-1)^(n/2).n!/(n/2!)^2 (C) (n-1).^(2n)C_n+2(2n) (D) n(n+1)2^(n-2)

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 for any aepsilon R the value of the expression a-(a-1)C_1+(a-2)C-2-(a-3)C_3+.+(1)^n(a-n)C_n= (A) 0 (B) a^n.(-1)^n.^(2n)C_n (C) [2a-n(n+1)[.^(2n)C_n (D) none of these

If n is a positive integer,sum_(r=0)^(n)(^(^^)nC_(r))^(2)=

If n is a positive integer,then nC_(1)+nC_(2)+...+nC_(n)=2^(n)-1

If n is a positive integer, for (1+x)^(n) ,then sum_(r=0)^(n).^nC_(r)=

If n and r are integers such that 1

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

"^mC_1=^nC_2 , then -

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