The equations of motion of a projectile are given by $x = 36 t$ metre and $2 y = 96 t - 9.8 t^2$ metre. The angle of projection is:

If the pair of straight lines $xy-x-y+1=0$ and the line $ax+2y-3a=0$ are concurrent,then $a$ is equal to

Two strings $A$ and $B$ of lengths $L_A = 80 \ cm$ and $L_B = x \ cm$ respectively are used separately in a sonometer. The ratio of their densities $(d_A / d_B)$ is $0.81$. The diameter of $B$ is one-half that of $A$. If the strings have the same tension and fundamental frequency,the value of $x$ is:

Two identical condensers $M$ and $N$ are connected in series with a battery. The space between the plates of $M$ is completely filled with a dielectric medium of dielectric constant $8$,and a copper plate of thickness $d/2$ is introduced between the plates of $N$ ($d$ is the distance between the plates). Then the potential differences across $M$ and $N$ are,respectively,in the ratio:

The angle between the line joining the points $(1, -2)$ and $(3, 2)$ and the line $x + 2y - 7 = 0$ is

If the lines $4x + 3y - 1 = 0$,$x - y + 5 = 0$ and $kx + 5y - 3 = 0$ are concurrent,then $k$ is equal to: