While a collector to emitter voltage is constant in a transistor,the collector current changes by $8.2 ~mA$ when the emitter current changes by $8.3 ~mA$. The value of forward current ratio is

Due to the Doppler effect,the shift in wavelength observed is $0.1 \ \mathring{A}$ for a star producing a wavelength of $6000 \ \mathring{A}$. The velocity of recession of the star will be ...... $km/s$.

$A$ vehicle sounding a whistle of frequency $256 ~Hz$ is moving on a straight road towards a hill with a velocity of $10 ~ms^{-1}$. The number of beats per second observed by a person travelling in the vehicle is (velocity of sound $= 330 ~ms^{-1}$).

Which of the following reactions occurs at the cathode during the charging of a lead storage battery?

Given that,$a \alpha^2+2 b \alpha+c \neq 0$ and that the system of equations
$\begin{aligned} & (a \alpha+b) x+a y+b z=0 \\ & (b \alpha+c) x+b y+c z=0 \\ & (a \alpha+b) y+(b \alpha+c) z=0\end{aligned}$
has a non-trivial solution,then $a, b$ and $c$ lie in

$A$ lead shot of $1\, mm$ diameter falls through a long column of glycerine. The variation of its velocity $v$ with distance covered is represented by