In a classroom there are certain number of benches. If 6 students are made to sit on a bench, then to accommodate all of them, one more bench is needed. However, if 7 students are made to sit on a bench then, after accomodating all of them, space for 5 students is left. What is the total number of students in the class ?

Find the value/values of x for the given equation. 

$2^{\left(2x+3\right)}-17=9\left(2^x-2\right)$

The population of Patna city is $96000$, the decreasing rate of population is $800$ per year. Population of Patliputra is $68000$, the increasing rate of population is $1200$ per year. In how many years will the population of both places be equal?

For what value of $p,$ the following pair of linear equations in two variables will have infinitely many solutions?

$$\begin{gathered} p x+3 y-(p-3)=0 \\ 12 x+p y-p=0 \end{gathered}$$