The mid-point of a chord of the ellipse $x^2+4y^2-2x+20y=0$ is $(2, -4)$. The equation of the chord is

$A$ 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 (see figure). 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 .... $Hz$.

$A$ circular disc of radius $R$ is removed from a bigger circular disc of radius $2R$ such that the circumferences of the discs touch. The centre of mass of the new disc is at a distance $\alpha R$ from the centre of the bigger disc. The value of $\alpha$ is

$A$ semiconductor $X$ is made by doping a germanium crystal with arsenic $(Z=33)$. $A$ second semiconductor $Y$ is made by doping germanium with indium $(Z=49)$. The two are joined end to end and connected to a battery as shown. Which of the following statements is correct?

Two parallel metal plates having charges $+Q$ and $-Q$ face each other at a certain distance between them. If the plates are now dipped in a kerosene oil tank,the electric field between the plates will

$A$ rotating body has angular momentum $L$. If its frequency of rotation is halved and its rotational kinetic energy is doubled,what will be its new angular momentum?