The differential equation of all circles which pass through the origin and whose centre lies on the $y$-axis is

The probability that a student is not a swimmer is $1/5$. What is the probability that $4$ out of $5$ students are swimmers?

Two slabs $A$ and $B$ of different materials but of the same thickness are joined end to end to form a composite slab. The thermal conductivities of $A$ and $B$ are $k_1$ and $k_2$ respectively. $A$ steady temperature difference of $12^{\circ} C$ is maintained across the composite slab. If $k_1 = \frac{k_2}{2}$,the temperature difference across slab $A$ is (in $^{\circ} C$)

The plates of a parallel plate capacitor are charged up to $100\, V$. $A$ $2\, mm$ thick plate is inserted between the plates. To maintain the same potential difference,the distance between the capacitor plates is increased by $1.6\, mm$. The dielectric constant of the plate is:

Which of the following is the most stable conformer of butane?

If $S_n = 1^3 + 2^3 + \ldots + n^3$ and $T_n = 1 + 2 + \ldots + n$,then