Magnetic induction at the centre of a circular loop of area $\pi \ m^2$ is $0.1 \ T$. The magnetic moment of the loop is ( $\mu_0 = \text{permeability of air}$ ).

Cerium $(Z = 58)$ is an important member of the lanthanoids. Which of the following statements is $NOT$ correct for Cerium?

The adjoining diagram shows the spectral energy density distribution $E_{\lambda}$ of a black body at two different temperatures. If the areas under the curves are in the ratio $16 : 1$,the value of temperature $T$ is ........ $K$. (in $,000$)

$A$ transistor is used as a common emitter amplifier with a load resistance of $2 \ k\Omega$. The input resistance is $150 \ \Omega$. Base current is changed by $20 \ \mu A$,which results in a change in collector current by $1.5 \ mA$. The voltage gain of the amplifier is

If $X = \{ 4^n - 3n - 1 : n \in N \}$ and $Y = \{ 9(n - 1) : n \in N \}$,then $X \cup Y$ is equal to

If the work done in blowing a bubble of volume $V$ is $W$,then the work done in blowing the bubble of volume $2V$ from the same soap solution will be