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

If $C, R, L$ and $I$ denote capacity,resistance,inductance and electric current respectively,the quantities having the same dimensions of time are :
$(1)$ $C R$
$(2)$ $\frac{L}{R}$
$(3)$ $\sqrt{L C}$
$(4)$ $L I^2$

$A$ coil of wire of radius $r$ has $600$ turns and a self-inductance of $108 \ mH$. The self-inductance of a coil with the same radius and $500$ turns is (in $mH$)

$A$ mass of $0.5\, kg$ moving with a speed of $1.5\, m/s$ on a horizontal smooth surface,collides with a nearly weightless spring of force constant $k=50\, N/m$. The maximum compression of the spring would be ................. $m$.

$A$ wire of length $l$ is bent into a circular coil of one turn of radius $R_1$. Another wire of the same material,same area of cross-section,and same length is bent into a circular coil of two turns of radius $R_2$. When the same current flows through the two coils,the ratio of magnetic induction at the centres of the two coils is

The point $P$ is equidistant from $A(1, 3)$,$B(-3, 5)$,and $C(5, -1)$. Then $PA =$