If the lines $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$ and $\frac{x-3}{1}=\frac{y-k}{2}=\frac{z}{1}$ intersect,then the value of $k$ is:

The ratio of the centripetal accelerations of the electron in two successive orbits of hydrogen is $81: 16$. Due to a transition between these two states,the angular momentum of the electron changes by ($h$ - Planck's constant).

If $\sin \theta + \cos \theta = p$ and $\sin^3 \theta + \cos^3 \theta = q$,then $p(p^2 - 3)$ is equal to

Let $\overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c}$ be the position vectors of the vertices $A, B, C$ respectively of $\triangle ABC$. The vector area of $\triangle ABC$ is :

In Young's double-slit experiment,the intensity at a point is $(1/4)$ of the maximum intensity. The angular position of this point is:

$A$ point object on the principal axis at a distance $15\, cm$ in front of a concave mirror of radius of curvature $20\, cm$ has a velocity of $2\, mm/s$ perpendicular to the principal axis. The velocity of the image at that instant will be.......$mm/s$.