The number of subsets of $\{1, 2, 3, \ldots, 9\}$ containing at least one odd number is

An object $1\;cm$ tall is placed $4\;cm$ in front of a mirror. In order to produce an upright image of $3\;cm$ height,one needs a:

The flux linked with a coil at any instant $t$ is given by $\phi = 10t^2 - 50t + 250$. The induced emf at $t = 3 \ s$ is ....... $V$.

When compound $X$ is oxidised by acidified potassium dichromate,compound $Y$ is formed. Compound $Y$ on reduction with $LiAlH_4$ gives $X$. $X$ and $Y$ respectively are :

$A$ metal wire $PQ$ slides on parallel metallic rails having a separation of $0.25\ m$,each having negligible resistance. There is a $2\,\Omega$ resistor and a $10\ V$ battery as shown in the figure. $A$ uniform magnetic field of magnitude $0.5\ T$ is directed into the plane of the paper. $A$ force of $0.5\ N$ to the left is required to keep the wire $PQ$ moving with a constant speed to the right. With what speed is the wire $PQ$ moving? (Neglect self-inductance of the loop)

See the diagram. The area of each plate is $2.0\ m^2$ and $d = 2 \times 10^{-3}\ m$. $A$ charge of $8.85 \times 10^{-8}\ C$ is given to plate $Q$. Then the potential of $Q$ becomes......$V$.