The value of $m$,such that the line $\frac{x-4}{1}=\frac{y-2}{1}=\frac{z-m}{2}$ lies in the plane $2x-4y+z=7$,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.......$mm/s$.

Assertion : Replication and transcription occur in the nucleus but translation takes place in the cytoplasm.
Reason : $mRNA$ is transferred from the nucleus into the cytoplasm where ribosomes and amino acids are available for protein synthesis.

Three point charges $+q, -2q$ and $+q$ are placed at points $(x = 0, y = a, z = 0)$,$(x = 0, y = 0, z = 0)$ and $(x = a, y = 0, z = 0)$ respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are

If the circle $x^2+y^2+2x+3y+1=0$ cuts another circle $x^2+y^2+4x+3y+2=0$ at points $A$ and $B$,then the equation of the circle with $AB$ as a diameter is

If $(x, y, z)$ is an arbitrary point lying on a plane $P$ which passes through the points $(42, 0, 0)$,$(0, 42, 0)$,and $(0, 0, 42)$,then the value of the expression $3 + \frac{x-11}{(y-19)^2(z-12)^2} + \frac{y-19}{(x-11)^2(z-12)^2} + \frac{z-12}{(x-11)^2(y-19)^2} - \frac{x+y+z}{14(x-11)(y-19)(z-12)}$ is: