The energy of an electromagnetic radiation is $19.875 \times 10^{-13} \ erg$. What is its wave number in $cm^{-1}$? $(h = 6.625 \times 10^{-27} \ erg \ sec, c = 3 \times 10^{10} \ cm \ sec^{-1})$

Consider the set of all triangles $OPQ$ where '$O$' is the origin and $P$,$Q$ are distinct points in the plane with non-negative integral coordinates $(x, y)$ such that $5x + y = 99$. The number of such distinct triangles whose area is a positive integer is:

An image formed by a concave mirror of focal length $6 \ cm$ is $3$ times the size of the object. What is the distance of the object from the mirror in $cm$?

Arrange the following compounds in the decreasing order of their reactivity towards $HBr$:
$(a)$ $(CH_3)_2C=CH_2$
$(b)$ $CH_3O-C(CH_3)=CH_2$
$(c)$ $CH_3OCH_2-C(CH_3)=CH_2$

The maximum tension a rope can withstand is $60 ~kg-wt$. The ratio of maximum acceleration with which two boys of masses $20 ~kg$ and $30 ~kg$ can climb up the rope at the same time is

When a resistor of $11 \Omega$ is connected in series with an electric cell,the current flowing in it is $0.5 \ A$. Instead,when a resistor of $5 \Omega$ is connected to the same electric cell in series,the current increases by $0.4 \ A$. The internal resistance of the cell is (in $\Omega$)