The equation of the plane passing through the line $\frac{x - 1}{5} = \frac{y + 2}{6} = \frac{z - 3}{4}$ and the point $(4, 3, 7)$ is

If $A$ and $B$ are square matrices of order $3$,$A$ is non-singular,and $AB = O$,then $B$ is a:

If $\alpha + \beta = \frac{\pi}{2}$ and $\beta + \gamma = \alpha$,then $\tan \alpha$ equals

The locus of a point such that the sum of its distances from the points $(0, 2)$ and $(0, -2)$ is $6$,is

Two bodies have their moments of inertia $I$ and $2I$ respectively about their axes of rotation. If their kinetic energies of rotation are equal,their angular momenta will be in the ratio:

$A$ car $P$ approaching a crossing at a speed of $10\, m/s$ sounds a horn of frequency $700\, Hz$ when $40\, m$ in front of the crossing. The speed of sound in air is $340\, m/s$. Another car $Q$ is at rest on a road which is perpendicular to the road on which car $P$ is reaching the crossing (see figure). The driver of car $Q$ hears the sound of the horn of car $P$ when he is $30\, m$ in front of the crossing. The apparent frequency heard by the driver of car $Q$ is .... $Hz$.