If one of the lines of the pair $ax^2 + 2hxy + by^2 = 0$ bisects the angle between the positive directions of the axes,then $a, b, h$ satisfy the relation:

$A$ student connects a long air-cored coil of manganin wire to a $100\, V$ $D.C.$ supply and records a current of $25\, A$. When the same coil is connected across a $100\, V$,$50\, Hz$ $A.C.$ supply,the current reduces to $20\, A$. The reactance of the coil is ...... $\Omega$.

The Nobel Prize was awarded to Paul Muller for the discovery of which of the following pesticides?

For $0 < x \leq \pi$,$\sinh ^{-1}(\cot x)$ is equal to

Observe the following reaction: $2 A + B \longrightarrow C$. The rate of formation of $C$ is $2.2 \times 10^{-3} \ mol \ L^{-1} \ min^{-1}$. What is the value of $-\frac{d[A]}{dt}$ (in $mol \ L^{-1} \ min^{-1}$)?

$A$ capacitor of capacity $4 \mu F$ is charged to $80 \ V$ and another capacitor of capacity $6 \mu F$ is charged to $30 \ V$. When they are connected,the energy lost by the $4 \mu F$ capacitor is: (in $mJ$)