$A$ Zener diode,having a breakdown voltage equal to $15\ V$,is used in a voltage regulator circuit as shown in the figure. The current through the Zener diode is $.....\ mA$.

If one of the lines of the pair of straight lines $ax^2 + 2hxy + by^2 = 0$ bisects the angle between the coordinate axes,then:

Which of the following compounds exhibits linkage isomerism?

The element having the greatest difference between its first and second ionization energies is

$A$ whistle $S$ of frequency $f$ revolves in a circle of radius $R$ at a constant speed $v$. What is the ratio of the largest and smallest frequency detected by a detector $D$ at rest at a distance $2R$ from the center of the circle as shown in the figure? (Take $c$ as the speed of sound.)

If $A=\begin{bmatrix} 1 & -2 \\ 4 & 5 \end{bmatrix}$ and $f(t)=t^2-3t+7$,then $f(A)+\begin{bmatrix} 3 & 6 \\ -12 & -9 \end{bmatrix}$ is equal to