Equations of the latus rectum of the ellipse $9x^2 + 4y^2 - 18x - 8y - 23 = 0$ are:

Two tangent galvanometers $A$ and $B$ have coils of radii $8 \, cm$ and $16 \, cm$ respectively and resistance $8 \, \Omega$ each. They are connected in parallel with a cell of emf $4 \, V$ and negligible internal resistance. The deflections produced in the tangent galvanometers $A$ and $B$ are $30°$ and $60°$ respectively. If $A$ has $2$ turns, then $B$ must have: (in $turns$)

$A$ particle of mass $4 m$ explodes into three pieces of masses $m, m$ and $2 m$. The equal masses move along $X$-axis and $Y$-axis with velocities $4 ms^{-1}$ and $6 ms^{-1}$ respectively. The magnitude of the velocity of the heavier mass is

If $ax^2-34xy-5y^2+2x+26y-5=0$ represents a pair of straight lines,then the value of $a$ is

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

The resultant gate and its Boolean expression in the given circuit is