If $(1, a)$ and $(b, 2)$ are conjugate points with respect to the circle $x^2+y^2=25$,then $4a+2b$ is equal to

If $P(A \cup B)=0.8$ and $P(A \cap B)=0.3$,then $P(\bar{A})+P(\bar{B})$ is equal to:

In a meter bridge,a $30 \Omega$ resistance is connected in the left gap and a pair of resistances $P$ and $Q$ in the right gap. Measured from the left,the balance point is $37.5 \text{ cm}$ when $P$ and $Q$ are in series,and $71.4 \text{ cm}$ when they are in parallel. The values of $P$ and $Q$ (in $\Omega$) are:

$A$ $4 \mu F$ capacitor is charged by a $200 \ V$ battery. It is then disconnected from the supply and connected to another uncharged $2 \mu F$ capacitor. During the process,the loss of energy (in $J$) is:

The moment of inertia of a body about a given axis is $1.2 ~kg \cdot m^2$. Initially,the body is at rest. In order to produce a rotational kinetic energy of $1500 ~J$,an angular acceleration of $25 ~rad/s^2$ must be applied about the axis for a time duration of: (in $~s$)

$\operatorname{sech}^{-1}(\sin \theta)$ is equal to