Graph of a^x a>1

Q. Let $R$ be the set of Real numbers. Define the real function $f:R\to R$ by $f\left(x\right)=x+10$ and sketch the graph of this function.

Q. If $f:R^{+}\to R^{+}$ be defined as $f\left(x\right)=\{\begin{array}{c}{2}^x,x\in (0,1)\\ 3^x,x\in [1,\infty )\end{array},$
then which among the following options is correct?

1. $f\left(x\right)$ is many one function
2. $f\left(x\right)$ is one-one function
3. Range of $f\left(x\right)$ is $(0,\infty )$
4. Range of $f\left(x\right)$ is $(0,2)\cup (3,\infty )$

Q. The number of real solution(s) of the equation $e^x+x=0$ is

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

Q.

Solution set of the equation $\left|\frac{x}{x-1}\right|+|x|=\frac{x^2}{|x-1|}$ is :

1. 

2. ( 0 , )

3. ( 1 , )

4. {0} ( 1 , )

Q. The graph of $y=\frac{1}{x^2}$ is

1. 
2. 
3. 
4. None of these

Q. Let, $f\left(x\right)=\{\begin{array}{c}\left[x\right],-2\le x\le -1\\ |x|+1,-1<x\le 2\end{array}$ and $g\left(x\right)=\{\begin{array}{c}\left[x\right],-\pi \le x\le 0\\ \sin x,0<x\le \pi \end{array},$ then the number of integral points in the range of $g\left(f\right(x\left)\right)$ is

Q. The number of solutions of the equation $2^x=x{5}^x$ is

Q.

Which of these is the shape of graph of $y=x^2-2x+5$.

1. 

2. 

3. 

4. 

Q. The number of real solutions of the equation $e^x+x=0$ is

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

Q. If $a_i$ be the values of $a$ for which the equation $a{x}^2-8x+a=0$ has only one real solution, then the value of $\prod _{i=1}^n{a}_i$ (where $\prod$ stands for product) is

1. $16$
2. $-16$
3. $1$
4. $0$

Q. Which of the following is correct for the equation $x^2\cdot 2^{-x}=1$?

1. The equation doesn't have a solution.
2. The equation has all positive solutions.
3. The equation has $1$ positive and $2$ negative solutions.
4. The equation has $2$ positive and $1$ negative solutions.

Q.

Column 1

1.$Lo{g}_{a}x,a>1$

2.$Lo{g}_{a}x,0<a<1$

3.$a^x,a>1$

4.$a^x,0<a<1$

Column 2
Graph of P :

Graph of Q :

Graph of R :

Graph of S :

1. 1 - s 2 - r 3 - p 4 - q

2. 1 - p 2 - q 3 - r 4 - s

3. 1 - r 2 - s 3 - q 4 - p

4. 1 - p 2 - q 3 - s 4 - r

Q. Find all the real solutions to the logarithmic equation
$\ln \left(x\right)=2$

1. $2$
2. $2^e$
3. $1,0$
4. no real solutions
5. $e^2$

Q.

Which of the following statements is/are correct for the above given figure?

1.For all the function A, B and C, domain is R and Range is $(0,\infty )$.

2.Function B is a graph for $F\left(x\right)=a^x,a>1,xϵR$.

3.Function A is a graph for $F\left(x\right)=a^{x}0<a<1,xϵR$

4.Function C is a graph for $F\left(x\right)=a^x,a<0,xϵR$

5.If the graph of B is $5^x$, then the graph of A is $y=8^x$ and the graph of C is

$y=2^x$ (you have to choose graph from $2^x,8^{x}and{5}^x)$

6.If the graph of B is $5^x$, then the graph of A is $y=2^x$ and the graph of C is

$y=8^x$ (you have to choose graph from $2^x,8^{x}and{5}^x)$

1. Only 1, 3, 6

2. Only 1, 2, 5

3. Only 1, 4, 5

4. Only 3, 6

Q.

Column 1

1.$Lo{g}_{a}x,a>1$

2.$Lo{g}_{a}x,0<a<1$

3.$a^x,a>1$

4.$a^x,0<a<1$

Column 2
Graph of P :

Graph of Q :

Graph of R :

Graph of S :

1. 1 - s 2 - r 3 - p 4 - q

2. 1 - p 2 - q 3 - s 4 - r

3. 1 - p 2 - q 3 - r 4 - s

4. 1 - r 2 - s 3 - q 4 - p

Q. For what values of $a$ does the equation $2(lo{g}_{3}x{)}^2-|lo{g}_{3}x|+a=0$ possess four solutions?

Q. The number of real solution(s) of the equation $x^2=1-|x-5|$ is

1. $1$
2. $2$
3. $4$
4. no solution