Exponential Function (a^x)

Q. The graph of $f\left(x\right)=e^{x^2}$, where $e>1$

1. 
2. 
3. 
4. 

Q. Number of solutions of the equation
$|x^2-2|x||=2^x$ is

1. $1$
2. $2$
3. $3$
4. $4$

Q.

Number of solutions of the equation $[y+\left[y\right]]=2$ = 2 cosx is not equal to, where $y=\frac{1}{3}[sinx+[sinx+\left[sinx\right]\left]\right]$ and [.] denotes the greatest integer function

1. 1

2. 0

3. 2

4. 3

Q. Number of solutions of the equation
$2^x+x=2^{\sin x}+\sin x$ in $[0,10\pi ]$ is

1. $5$
2. $1$
3. $6$
4. $11$

Q. The number of real solutions of $x-\frac{1}{x^2-4}=2-\frac{1}{x^2-4}$ is

1. 2
2. infinite
3. 1
4. 0

Q. Number of solutions of the equation
$|x^2-2|x||=2^x$ is

1. $1$
2. $2$
3. $3$
4. $4$

Q. The number of solution(s) of the equation $3^{|x|}(|2-|x||)=1$ is

1. $0$
2. $1$
3. $2$
4. $4$

Q. If $f:[0,\infty )\to [0,\infty )$ is a function with $f\left(0\right)=0$ and $f^{\prime }\left(x\right)>1\forall x\in (0,\infty ),$ then the number of solution(s) of the equation $f\left(x\right)=f^{-1}\left(x\right)$ is

1. $0$
2. $1$
3. $2$
4. infinite

Q. The graph of $x^2+y=10$ and the graph of $x+y=10$ intersect in two points, what is the distance between the points?

1. $\sqrt{1}$
2. 1
3. $\sqrt{2}$
4. 2

Q. The number of solutions for the equation $x^2-5\left|x\right|+6=0$ is:

1. $4$
2. $3$
3. $2$
4. $1$

Q.

Which of the following represents the graph of $y=-x^2+6x+1$

1. 

2. 

3. 

4. 

Q. Solve the trignometric equation and find ALL solutions in the interval $[0,2\pi )$
${\sin }^{2}x+\sin x=6$

1. 1
2. $2,-3$
3. no solutions
4. $2$
5. $0$

Q.

$If{e}^{sinx}-e^{-sinx}-4=0,then,x=$

1. 1

2. none of these

3. $si{n}^{-1}\left\{lo{g}_e\right(2-\sqrt{5}\left)\right\}$

4. 0

Q. The graph of $f\left(x\right)=e^{x^2}$, where $e>1$

1. 
2. 
3. 
4. 

Q. The function $f:(-\infty ,-1)\to (0,e^5)$ defined by $f\left(x\right)=e^{x^3-3x+2}$ is

1. one-one and into
2. one-one and onto
3. many-one and onto
4. many-one and into

Q. Number of solutions of the equation
$2^x+x=2^{\sin x}+\sin x$ in $[0,10\pi ]$ is

1. $5$
2. $6$
3. $11$
4. $1$

Q. The graph of $f\left(x\right)=e^x$, where $e>1$

1. 
2. 
3. 
4. 

Q. The number of real solution(s) of $1+|e^x-1|=e^x(e^x-2)$ is

1. $0$
2. $1$
3. $2$
4. $4$

Q. The number of real solutions of the equation $|x{|}^2-3|x|+2=0$ is:

1. $4$
2. $1$
3. $3$
4. $2$

Q. The graph of the function $f\left(x\right)=2x^3-7$ goes :

1. up to the right and down to the left
2. down to the right and up to the left
3. up to the right and up to the left
4. down to the right and down to the left
5. none of these ways.

Q. The graph of $f\left(x\right)=e^x$, where $e>1$

1. 
2. 
3. 
4. 

Q. The graph of the function$f\left(x\right)=x^3+1$ after translation $4$ units to the right and $2$ units up, resulted in a new graph $l\left(x\right)$. What is the value of $l\left(3.7\right)$?

1. $0.973$
2. $1.784$
3. $1.973$
4. $2.027$
5. $2.973$

Q. The number of solutions of the equations $\sin x=x^2+x+1$ is:

1. $0$
2. $1$
3. $2$
4. None of these

Q. Find the number of solutions of equation $2^x+3^x+4^x-5^x=0$ .

Q. The given figure represents the graph of?

1. $f\left(x\right)=x$
2. $f\left(x\right)=\frac{1}{x}$
3. $f\left(x\right)=\frac{1}{x-2}$
4. $f\left(x\right)=\frac{1}{x+2}$

Q. Number of solutions of the equation
$2^x+x=2^{\sin x}+\sin x$ in $[0,10\pi ]$ is

1. $5$
2. $6$
3. $11$
4. $1$

Q. Number of solutions of the equation
$|x^2-2|x||=2^x$ is

1. $1$
2. $2$
3. $3$
4. $4$

Q. Number of solutions of the equation
$|x^2-2|x||=2^x$ is

1. $1$
2. $2$
3. $4$
4. $3$