The sum of `1+n(1-1/x)+(n(n+1))/(2!)(1-1/x)^2+oo` will be `x^n` b. `x^(-n)` c. `(1-1/x)^n` d. none of these

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

Find the sum (x+2)^(n-1)+(x+2)^(n-2)(x+1)^(+)(x+2)^(n-3)(x+1)^(2)++(x+1)^(n)(x+2)^(n-2)-(x+1)^(n) b.(x+2)^(n-2)-(x+1)^(n-1) c.(x+2)^(n)-(x+1)^(n) d.none of these

lim_(x rarr1)((1-x)(1-x^(2))...(1-x^(2n)))/({(1-x)(1-x^(2))...(1-x^(n))}^(2)),n in N, equals ^2nP_(n)(b)^(2n)C_(n)(c)(2n)!(d) none of these

lim_(x rarr oo){(1)/(1-n^(2))+(2)/(1-n^(2))+(n)/(1-n^(2))} is equal to 0 (b) -(1)/(2)(c)(1)/(2)(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

if int(dx)/(x^(2)(x^(n)+1)^(((n-1)/(n))))=-[f(x)]^((1)/(n))+c,thenf(x)is(a)(1+x^(n))(b)1+x^(-1)(c)x^(n)+x^(-n)(d) none of these

If |x|<1 then 1+n((2x)/(1+x))+(n(n+1))/(2!)((2x)/(1+x))^(2)+......oo

The value of ""(n)C_(1). X(1 - x )^(n-1) + 2 . ""^(n)C_(2) x^(2) (1 - x)^(n-2) + 3. ""^(n)C_(3) x^(3) (1 - x)^(n-3) + ….+ n ""^(n)C_(n) x^(n) , n in N is

If (x+1)+f(x-1)=2f(x)andf(0),=0 then f(n),n in N, is nf(1)(b){f(1)}^(n)(c)0 (d) none of these

" The coefficient of "x^(n)" in "(1-x/(1!)+(x^2)/(2!)+..+((-1)^n(x^n))/(n !))^2