$A$ person walks along a straight road from his house to a market $2.5 \ km$ away with a speed of $5 \ km/h$ and instantly turns back and reaches his house with a speed of $7.5 \ km/h$. The average speed of the person during the time interval $0$ to $50 \ min$ is (in $m/s$):

The same current is flowing in two alternating circuits. The first circuit contains only an inductor and the second contains only a capacitor. If the frequency of the $e.m.f.$ of the $ac$ source is increased,what will be the effect on the value of the current in these circuits?

The increasing order of the atomic radius of $Si, S, Na, Mg, Al$ is

If $y=\sin (\log _e x)$,then $x^2 \frac{d^2 y}{d x^2}+x \frac{d y}{d x}$ is equal to

Condenser $A$ has a capacity of $15 \mu F$ when it is filled with a medium of dielectric constant $15$. Another condenser $B$ has a capacity of $1 \mu F$ with air between the plates. Both are charged separately by a battery of $100 V$. After charging,both are connected in parallel without the battery and the dielectric material being removed from condenser $A$. The common potential now is.......$V$

Which of the following orders is incorrect?