Consider a binary operation choose the correct answer:

If $$\frac{d}{dx}(f(x)) = 4x^{3} - \frac{3}{x^{4}}$$​ and $$f(2) = 0,$$  then  $$f(x)$$ is:

​$$\frac{d}{dx}\left[\log_{2}\sqrt{x^{2}+1}\right]$$ equals to :​

The function f(x) = |x| + |x − 1| is:

If $$f(x)=|x|–\lfloor x \rfloor$$ where $$\lfloor x \rfloor$$ is the greatest integer not exceeding x, then the value of $$f(–3.5)$$ is​

If $$f(x)=kx(1-x),0<x<1$$

=0        otherwise

is the probability density function of certain distribution, then value of k is

The function $$f(x) = 2x + |x - 1| \quad \text{at } x = 1 \text{ is}$$​​

Let $$N^+$$ be the set of positive integers and $$f:N^+\rightarrow N^+$$ be a mapping defined by $$f(x)=2x, x\in N^+$$. Then mapping $$f$$ is​

A relation $$\rho$$ is defined on the set of integers $$Z$$ so that $$\varrho = \{(a,b) \in {Z} \times {Z} \mid |a - b| \leq 5\}.$$ The the relation is​

If the function

$$f(x)=\left\{\begin{array}{l}\frac{\sin x}{x}+\sec x, x\space\# \space0 \\a\space\ x\ =\ 0\end{array}\right.$$​ is continuous at x = 0, what is the value of a?