The value of the determinant of `n^(t h)` order, being given by `|x1 11x11 1x |` is `(x-1)^(n-1)(x+n-1)` b. `(x-1)^n(x+n-1)` c. `(1-x)^(-1)(x+n-1)` d. none of these

The value of the determinant of n^(t h) order, being given by |[x, 1, 1...], [1, x, 1...], [1, 1, x...],[... , ... , ...]| is a. (x-1)^(n-1)(x+n-1) b. (x-1)^n(x+n-1) c. (1-x)^(-1)(x+n-1) d. none of these

The value of the determinant of n^(t h) order, being given by |[x, 1, 1...], [1, x, 1...], [1, 1, x...],[... , ... , ...]| is a. (x-1)^(n-1)(x+n-1) b. (x-1)^n(x+n-1) c. (1-x)^(-1)(x+n-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 (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 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 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 sum of 1+n(1-1/x)+(n(n+1))/(2!)(1-1/x)^2+oo will be a. x^n b. x^(-n) c. (1-1/x)^n 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-1)!(2n+1)!)/((2n-1)!(2n+1)!) d.none of these

The derivative of y=(1-x)(2-x)....(n-x) at x=1 is (a) 0 (b) (-1)(n-1)! (c) n !-1 (d) (-1)^(n-1)(n-1)!