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

If the graph of the function f(x)=(a^x-1)/(x^n(a^x+1)) is symmetrical about the y-a xi s ,then n equals 2 (b) 2/3 (c) 1/4 (d) 1/3

A relation 'f' is defined by f(x)=x^(2)-2 where xin{-2, -1, 0, 3} Is f a function?

The first derivative of the function [cos^(-1)(sinsqrt((1+x)/2))+x^x] with respect to x at x=1 is (a) 3//4 (b) 0 (c) 1//2 (d) -1//2

Consider the function f(x)={xsin(pi/x) , for x >0 ,0 for x=0 The, the number of point in (0,1) where the derivative f^(prime)(x) vanishes is 0 (b) 1 (c) 2 (d) infinite

The integral value of m for which the root of the equation m x^2+(2m-1)x+(m-2)=0 are rational are given by the expression [where n is integer] (A) n^2 (B) n(n+2) (C) n(n+1) (D) none of these

If sinthetaa n d-costheta are the roots of the equation a x^2-b x-c=0 , where a , ba n dc are the sides of a triangle ABC, then cosB is equal to 1-c/(2a) (b) 1-c/a 1+c/(c a) (d) 1+c/(3a)

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

Let f(x) = (x^2 - 1)^(n+1) + (x^2 + x + 1) . Then f(x) has local extremum at x = 1 , when n is (A) n = 2 (C) n = 4 (B) n = 3 (D) n = 5

If (1-x^2)^n=sum_(r=0)^n a_r x^r(1-x)^(2n-r),t h e na_r is equal to a.) ^n C_r b.) ^nC_r3^r c.) ^2n C_r d.) ^nC_r2^r