$A$ car travels from point $A$ to point $B$ with a speed of $40 \ km/h$ and returns from $B$ to $A$ with a speed of $60 \ km/h$. What is the average speed of the car for the entire journey (in $km/h$)?

Let $R$ be a reflexive relation on a finite set $A$ having $n$ elements,and let there be $m$ ordered pairs in $R$. Then

If the function $f(x) = 2x^3 - 9ax^2 + 12a^2x + 1$,where $a > 0$,attains its maximum and minimum values at $p$ and $q$ respectively,such that $p^2 = q$,then what is the value of $a$?

The ratio of the centripetal accelerations of the electron in two successive orbits of hydrogen is $81: 16$. Due to a transition between these two states,the angular momentum of the electron changes by ($h$ - Planck's constant).

If $\cos ^{-1}\left(\frac{y}{b}\right)=2 \log \left(\frac{x}{2}\right)$,where $x>0$,then $x^2 \frac{d^2 y}{d x^2}+x \frac{d y}{d x}$ is equal to

If $N$ denotes the set of all positive integers and if $f: N \rightarrow N$ is defined by $f(n) =$ the sum of positive divisors of $n$,then $f(2^k \cdot 3)$,where $k$ is a positive integer,is