The `n t h` derivative of `x e^x` vanishes when (a)`x=0` (b) `x=-1` (c)`x=-n` (d) `x=n`

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 nth derivative of the function f(x)=1/(1-x^2) [where x in(-1,1) at the point x=0 where n is even is (a) 0 (b) n! (c) n^nC_2 (d) 2^nC_2

The period of f(x)=[x]+[2x]+[3x]+[4x]+[n x]-(n(n+1))/2x , where n in N , is (where [dot] represents greatest integer function). (a) n (b) 1 (c) 1/n (d) none of these

If 1 is a twice repeated root of the equation a x^3+b x^2+b x+d=0,t h e n (a) a=b=d (b) a+b=0 (c) b+d=0 (d) a=d

If |[x^n, x^(n+2),x^(2n)],[1,x^a, a],[x^(n+5),x^(a+6),x^(2n+5)]|=0,AAx in R ,where n in N , then value of a is (a) n (b) n-1 (c) n+1 (d) none of these

Find the derivative of x^(n)+ax^(n-1)+a^(2)x^(n-1)+ . . .+a^(n-1)x+a^(n) for some fixed real number a.

The domain of f(x)i s(0,1)dot Then the domain of (f(e^x)+f(1n|x|) is (a) (-1, e) (b) (1, e) (c) (-e ,-1) (d) (-e ,1)

If x=(2sintheta)/(1+costheta+sintheta),t h e n(1-costheta+sintheta)/(1+sintheta) is equal to 1+x (b) 1-x (c) x (d) 1/x

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