The magnifying power of a telescope is $9$. When it is adjusted for parallel rays,the distance between the objective and the eye-piece is found to be $20\, cm$. The focal lengths of the two lenses are

The given graph represents $V-I$ characteristic for a semiconductor device. Which of the following statements is correct?

$A$ car $P$ approaching a crossing at a speed of $10 \, m/s$ sounds a horn of frequency $700 \, Hz$ when $40 \, m$ in front of the crossing. The speed of sound in air is $340 \, m/s$. Another car $Q$ is at rest on a road which is perpendicular to the road on which car $P$ is reaching the crossing. The driver of car $Q$ hears the sound of the horn of car $P$ when he is $30 \, m$ in front of the crossing. The apparent frequency heard by the driver of car $Q$ is ...... $Hz$.

Which concentrations can be calculated if the mole fraction and density of an aqueous solution of $HCl$ are known?
$1.$ Molality $\ \ 2.$ Molarity $\ \ 3.$ $\%(w/w)$

The number of ways that $8$ beads of different colours can be strung as a necklace is

The spring balance $A$ reads $2 \ kg$ with a block $m$ suspended from it. $A$ balance $B$ reads $5 \ kg$ when a beaker with liquid is placed on the pan of the balance. The two balances are now arranged such that the hanging mass is inside the liquid in the beaker as shown in the figure. In this situation: