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)!`

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 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

(d^(n))/(dx^(n))(log x)=(a)((n-1)!)/(x^(n))(b)(n!)/(x^(n))(c)((n-2)!)/(x^(n))(d)(-1)^(n-1)((n-1)!)/(x^(n))

The nth derivative of the function f(x)=(1)/(1-x^(2))[ where in(-1,1) at the point x=0 where n is even is (a) 0 (b) n! (c) n^(n)C_(2)(d)2^(n)C_(2)

If y=x^(2)e^(x) ,show that y_(n)=(1)/(2)n(n-1)y_(2)-n(n-2)y_(1)+(1)/(2)(n-1)(n-2)}

If the middle term of (1+x)^(2n) is the greatest term,then x lies between (A)n-1

If f(x)=(x+1)(x+2)(x+3)...(x+n) then f'(0) is n!(b)(n(n+1))/(2)(n!)(ln n!)(d)n!(1+(1)/(2)+(1)/(3)+(1)/(4)+...+(1)/(n))

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