In an astronomical telescope in normal adjustment,a straight black line of length $L$ is drawn on the inside part of the objective lens. The eyepiece forms a real image of this line. The length of this image is $I$. The magnification of the telescope is

The locus of the poles of focal chords of the parabola $y^2 = 4ax$ is

Two plane mirrors $A$ and $B$ are placed parallel to each other as shown in the figure. $A$ light ray is incident at an angle of $30^{\circ}$ at a point on mirror $A$. The plane of incidence coincides with the plane of the figure. What is the maximum number of reflections (including the first one) the ray will undergo before it emerges?

The number of arrangements of the letters of the word $PALANHAR$ in which no two vowels are together and exactly two vowels are at odd places,is

Let $S$ be the sample space of the random experiment of throwing simultaneously two unbiased dice with six faces (numbered $1$ to $6$) and let $E_k = \{(a, b) \in S : ab = k\}$ for $k \geq 1$. If $p_k = P(E_k)$ for $k \geq 1$, then which of the following is correct?

$A$ cylindrical vessel open at the top is $20 \ cm$ high and $10 \ cm$ in diameter. $A$ circular hole whose cross-sectional area is $1 \ cm^2$ is cut at the centre of the bottom of the vessel. Water flows from a tube above it into the vessel at the rate of $100 \ cm^3 s^{-1}$. The height of water in the vessel under steady state is ....... $cm$ (Take $g = 1000 \ cm s^{-2}$)