The sum of the first four terms of an arithmetic progression is $56$ and the sum of its last four terms is $112$. If the first term is $11$,what is the number of terms in the progression?

The equation of a stationary wave along a stretched string is given by $y = 5 \sin \frac{\pi x}{3} \cos 40 \pi t$,where $x$ and $y$ are in $cm$ and $t$ is in $s$. The separation between two adjacent nodes is .... $cm$.

If $A$ and $B$ are any two sets,then $A \cup (A \cap B)$ is equal to

If the distance $s$ travelled by a particle in time $t$ is given by $s=t^2-2t+5$, then its acceleration is

When a ceiling fan is switched off,its angular velocity falls to half while it makes $36$ rotations. How many more rotations will it make before coming to rest? (Assume uniform angular retardation)

$75 \ mL$ of $0.2 \ M \ HCl$ is mixed with $25 \ mL$ of $1 \ M \ HCl$. To this solution,$300 \ mL$ of distilled water is added. What is the $pH$ of the resultant solution?