If `(1-x^2)^n=sum_(r=0)^n a_r x^r(1-x)^(2n-r),t h e na_r` is equal to `^n C_r` b. `^n C_r3^r` c. `^2n C_r` d. `^n C_r2^r`

If (1-x^2)^n=sum_(r=0)^na_rx^r(1-x)^(2n-r) , then a_r is equal to

If (1-x^2)^n=sum_(r=0)^n a_r x^r(1-x)^(2n-r),t h e na_r is equal to a.) ^n C_r b.) ^nC_r3^r c.) ^2n C_r d.) ^nC_r2^r

If (1-x^(2))^(n)=sum_(r=0)^(n)a_(r)x^(r)(1-x)^(2n-r), then a_(r) is equal to ^(n)C_(r) b.^(n)C_(r)3^(r) c.^(2n)C_(r) d.^(n)C_(r)2^(r)

If (1+2x+x^2)^n=sum_(r=0)^(2n)a_r x^r ,then a_r is a. (.^nC_2)^2 b. .^n C_r .^n C_(r+1) c. .^(2n) C_r d. .^(2n) C_(r+1)

If (1+2x+x^2)^n=sum_(r=0)^(2n)a_r x^r ,then a= (^n C_2)^2 b. ^n C_rdot^n C_(r+1) c. ^2n C_r d. ^2n C_(r+1)

If (1+2x+x^(2))^(n)=sum_(r=0)^(2n)a_(r)x^(r), then a=(^(n)C_(2))^(2) b.^(n)C_(r).^(n)C_(r+1) c.^(2n)C_(r) d.^(2n)C_(r+1)

If (1+x)^n=sum_(r=0)^n C_r x^r , then prove that C_1+2C_2+3C_3+....+n C_n=n2^(n-1)dot .

If (1+x)^n=sum_(r=0)^n C_r x^r , then prove that C_1+2C_2+3C_3+....+n C_n=n2^(n-1)dot .