If f is even function and g is an odd function, then $f _og$ is ............function.

If $f\left( x \right) = \dfrac{{x + 1}}{{x - 1}},$ then $f\left( x \right) + f\left( {\dfrac{1}{x}} \right) = 0$

The identity function on real numbers given by $f(x)=x$ is continuous at every real numbers.

The minimum value of $f\left( x \right) ={ x }^{ 2 }+2x+3 ,x\in R$ is equal to 

Supposen(A) $= 3$ and $n ( B ) = 5 .$ find the number of elements in $A \times B$

If $f:\,\left( {3,6} \right) \to \left( {1,3} \right)$ is a function defined by $f\left( x \right) = x - \left[ {\frac{x}{3}} \right],\,then\,{f^{ - 1}}\left( x \right) = $

The tangents to the graph of the function  $y=f(x)$ at the point with abscissa $x=1$ forms an angle of $\pi/6$ and the point $x=2$ an angle of $\pi/3$ and at the point $x=3$ an angle of $\pi/4$. The value of 
$\displaystyle \int _{1}^{2}{f'(x)f''(x)dx}+\displaystyle \int _{2}^{3}{f''(x)dx}$

The graph of the function $\cos x\cos x(x+2)-\cos^{2}(x+1)$ is  

If $f(x)=\left | \sin x \right |$, then domain of $f$ for the existence of inverse is  

If $|z-1|+ |z+3| \le 8$, then the range of values of $|z-4|$ is

If all the roots of $z^3 +az^2 +bz+c=0$ are of unit modulus, then

The solution set of the equation $(x+1)^2+[x-1]^2=(x-1)^2+[x+1]^2$ where $[x]$ and $(x)$ are the greatest integer and nearest integer to $x$, is 

Two lines $L _{1} :2x+3y-5=0$ and $L _{2} :3x-4y+1=0$ intersect a point $P$ and make an angle $\theta$ with each other. Equation of a line which passes through $P$ and makes an angle $(\pi/2-\theta)$ with the line $L _{1}$ is

If the line $3x+4y=\sqrt{7}$ touches the ellipse $3x^{2}+4y^{2}=1$, then the point of contact is 

A graph with all vertices having equal degree is known as a .....

The column sum in an incidence matrix for a simple graph is ________________.

Which of the following ways can be used to represent a graph?