The middle term in the expansion of `((2x)/3-3/(2x^2))^(2n)` is a. `\ ^(2n)C_n` b. `(-1)^n\ ^(2n)C_(n\ )x^(-n)` c. `\ ^(2n)C_n x^(-n)` d. none of these

Show that the middle term in the expansion (x-1/x)^(2n)i s (1. 3. 5 (2n-1))/n(-2)^n .

Show that the middle term in the expansion (x-1/x)^(2n)i s (1. 3. 5 (2n-1))/n(-2)^n .

Show that the middle term in the expansion of (1+x)^(2n)" is "(1.3.5. ..(2n-1))/(n!)(2x)^(n).

If the middle term in the expansion of (1 + x)^(2n) is (1.3.5…(2n - 1))/(n!) k^(n).x^(n) , the value of k is

Show that the middle term in the expansion of (1+ x)^(2n) is (1.3.5…(2n-1) )/( n!). 2^(n) . x^(n) , where n in N .

The number of terms in the expansion of (x+1/x+1)^n is (A) 2n (B) 2n+1 (C) 2n-1 (D) none of these

The coefficient of 1//x in the expansion of (1+x)^n(1+1//x)^n is (n !)/((n-1)!(n+1)!) b. ((2n)!)/((n-1)!(n+1)!) c. ((2n)!)/((2n-1)!(2n+1)!) d. none of these

The coefficient of 1//x in the expansion of (1+x)^n(1+1//x)^n is (a). (n !)/((n-1)!(n+1)!) (b). ((2n)!)/((n-1)!(n+1)!) (c). ((2n)!)/((2n-1)!(2n+1)!) (d). none of these

The middle term in the expansion of (1-3x+3x^2-x^3)^(2n) is (a) ((6n)!x^(n))/((3n)!(3n)!) (b) ((6n)!x^(3n))/((3n)!) (c) ((6n)!)/((3n)!(3n)!)(-x)^(3n) (d) none of these

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 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