Time complexity to check if an edge exists between two vertices would be __________.

If $p = q$ then $px =$ ________

Which of the following functions are identity functions?

If ${ (x, 2), (4, y) }$ represents an identity function, then $( x, y)$ is :

Which of the following functions is/are constant ?

An identity function is a?

State whether the following statement is True or False.
The inverse of an identity function is the identity function itself.

Let $f:\mathbb{R}\rightarrow \mathbb{R}$ be a function such that for any irrational number $r,$ and any real number $x$ we have $f(x)=f(x+r)$. Then, $f$ is

The graph of an Identity function is?

Let $f$ be a linear function for which $f (6)  - f (2) = 12$. The value of $f (12) - f(2)$ is equal the 

The set values of $x$ for which function $f(x)=x\ln {x}-x+1$

Let $f$ be an injective map with domain {x, y, z} and range {1, 2, 3} such that exactly one of the following statements is correct and the remaining are false :
$f (x) = 1, f (y) \sqrt 1, f (z) \sqrt 2$. The value of $f^{-1} (1)$ is

$c \to c\,\,is\,defined\,as\,f\left( x \right) = \frac{{ax + b}}{{cx + d}}\,\,bd \ne 0$.then f is a constant function when

$f:c \to c$ is defined as $f(x) = \dfrac{{ax + b}}{{cx + d}},bd \ne 0$ then $f$ is a constant function when,

If $f(n+1)=f(n)$ for all $n\in N, f(7)=5$  then  $f(35)=$

Let $f(x)$ is a cubic polynomial with real coefficients, $x\ \in R$ such that $f"(3)=0,\ f'(5)=0$  
If $f(3)=1$ and $f(5)=-3$, then $f(1)$ is equal to

The complete set of values of $x$ for which the function $f(x)=2\tan^{-1}x+\sin^{-1} \dfrac{2x}{1+x^{2}}$ behaves like a constant function with positive output is equal to

Let f be a polynomial function such that $f(3x)=f'(x).f"(x)$, for all $x\epsilon R$. Then :

If  $f \left( \dfrac { x + y } { 2 } \right) = \dfrac { f ( x ) + f ( y ) } { 2 }$  for all  $x , y \in R$  and  $f ^ { \prime } ( o ) = - 1 , f ( o ) = 1$  then  $f(2)=$

let $f(x)$ be a polynomial of degree $4$ having extreme values at $x=2$.if $\underset { x\rightarrow 0 }{ lim } \left( \frac { f\left( x \right)  }{ { x }^{ 2 } } +1 \right) =3$ then $f(1)$

If $\alpha$ and $\beta$ are the polynomial  $f(x)=x^2-5x+k$ such that $\alpha-\beta=1$, then value of k is 

If $y^2 = ax^2 +bx+c$, then $y^2 \dfrac{d^2y}{dx^2}$ is

If $fxln\left(1+\dfrac{1}{x}\right)dx=p(x)ln\left(1+\dfrac{1}{x}\right)+\dfrac{1}{2}x-\dfrac{1}{2}ln(1+x)+c$, being arbitary costant, then

Let $f(x)$ is cubic polynomial with real coefficient such that $f''(3) = 0, f'(5) = 0$. If $f(3) = 1$ and $f(5) = -3$, then $f(1)$ is equal to

$f (x) = x^4 - 10x^3 + 35x^2 - 50x + c$ is a constant. the number of real roots of . f (x) = 0 and 
f'' (x) = 0 are respectively 

Let $\displaystyle f(x)=ax^{2}+bx+c,$ where $a,b,c$ are rational, and $f: Z\rightarrow Z,$ where $Z$ is the set of integers. Then $a+b$ is

The positive integers $x$ for which $f(x)=x^{3}-8x^{2}+20x-13$ is a prime is

If $f\quad \left( x \right) ={ x }^{ 2 }+2bx+{ 2c }^{ 2 }\quad and\quad g\quad (x)\quad ={ -x }^{ 2 }\quad -2cx+{ b }^{ 2 }\quad are\quad such\quad that\quad min\quad f\quad (x)\quad >\quad max\quad g\quad (x),\quad then$ relation between b and c, is

If $f(x)$ is a polynomial function satisfying $f(x)f\left(\dfrac{1}{x}\right)=f(x)+\left(\dfrac{1}{x}\right)$ and $f(3)=28$, then $f(4)=$

If $f\left(x\right)$ is a polynomial such that $ f\left(a\right) f\left(b\right)<0$, then number of zeros lieing between $a$ and $b$ is 

If $ P ( X ) = x ^ { 3 } - 3 x ^ { 2 } + 2 x + 5 $ and P ( a ) = P ( b ) = P ( c ) = 0 then the value of ( 2 - a ) ( 2 - b ) ( 2 - c ) is

If f : R $\rightarrow$ R, g : R $\rightarrow$ R and h : R $\rightarrow$ R is such that $f(x) = x^2, g(x) = tan  x$ and $h(x) = log  x$, then the value of [ho(gof)], if $x = \displaystyle \dfrac{\pi}{2}$ will be

If f is a constant function and f(100)=100  then f(2007)=_____

The number of elements of an identity function defined on a set containing four elements is______

On differentiating an identity function, we get?

If $f,g,h$ are three functions from a set of positive real numbers into itself satisfying the condition,
$f(x) \cdot g(x)=h \sqrt{x^2 + y^2}$ such that $x,y \epsilon (0,\infty)$.then, $\dfrac{f(x)}{g(x)}$ is a?

A constant function is a periodic function.

Let $f(-2, 2)\rightarrow(-2, 2)$ be a continuous function given $f(x)=f{(x}^{2})$. Given $f(0)=\dfrac{1}{2}$ then the $4f(\dfrac{1}{2})$

If $f\left( x \right)$ is a function satisfying  $f\left( x \right).f\left( {\frac{1}{x}} \right) = f\left( x \right) + f\left( {\frac{1}{x}} \right)$ and $f\left( 4 \right) = 65$ then find $f\left( 6 \right)$

Let $f\left( x \right) = p{x^2} + qx - \left( {{a^2} + {b^2} + {c^2} - ab - bc - ca} \right),\,\left( {p,q,a,b,c \in R} \right)(a,b,c$ are distinct). If both roots of $f(x)=0$ are non-real, then 

If $f(x)$ is a polynomial function satisfying the condition $f(x) \times f\left(\dfrac{1}{x}\right)=f(x)+f\left(\dfrac{1}{x}\right)$ and $f(2)=9$ then

If $\displaystyle f(x)=27x^{3}+\frac{1}{x^{3}}$ and $\alpha,\beta$ are the roots of $\displaystyle 3x+\frac{1}{x}=2$ is

If a function satisfies $(x-y)f(x+y)-(x+y)f(x-y)=2(x^{2}y-y^{3}),\forall x,y\in R$ and $ f(1)=2,$ then

If $g(x)$ is a polynomial satisfying $g(x) g(y) = g(x) + g(y) + g(xy) - 2$ for all real $x$ and $y$ and $g(2) = 5$ then $g(3)$ is equal  to -

Write a rational function $f$ that has vertical asymptote at $x=4$, a horizontal asymptote at $y=5$ and a zero at $x=-7$.

A large mixing tank currently contains $200$ gallons of water into which $10$ pounds of sugar have been mixed. A tap will open pouring $20$ gallons per minute of water into the tank at the same time sugar is poured into the tank at a rate of $2$ pound per minute. Find the concentration (pounds per gallon) of sugar in the tank after $14$ minutes. Then