In the given circuit,the readings of voltmeters $V_1$ and $V_2$ are $300 \, V$ each. The readings of voltmeter $V_3$ and ammeter $A$ are respectively:

If $a$ and $b$ are unit vectors such that $(a + 2b)$ and $(5a - 4b)$ are perpendicular to each other,then the angle between $a$ and $b$ is ................... $^o$.

The shortest distance between the line $y-x=1$ and the curve $x=y^2$ is

The plates of a parallel plate capacitor are charged up to $100\;V$. $A$ $2\;mm$ thick plate is inserted between the plates. Then,to maintain the same potential difference,the distance between the plates is increased by $1.6\;mm$. The dielectric constant of the plate is:

For a binomial variate $X$ with $n=6$,if $P(X=2)=9 P(X=4)$,then its variance is

In which of the following reactions is an aromatic aldehyde treated with an acid anhydride in the presence of the corresponding salt of the acid to give an unsaturated aromatic acid?