The length of the transverse common tangent of the circles $x^2+y^2-2x+4y+4=0$ and $x^2+y^2+4x-2y+1=0$ is

Plants which are attached to the rocks are called

In the random experiment of tossing two unbiased dice,let $E$ be the event of getting the sum $8$ and $F$ be the event of getting even numbers on both the dice. Then:
$I. P(E) = \frac{7}{36}$
$II. P(F) = \frac{1}{3}$
Which of the following is a correct statement?

$A$ conducting rod $AC$ of length $4l$ is rotated about a point $O$ in a uniform magnetic field $\vec{B}$ directed into the paper. $AO = l$ and $OC = 3l$. Then:

Two bodies $A$ and $B$ of equal surface area have thermal emissivities of $0.01$ and $0.81$ respectively. The two bodies are radiating energy at the same rate. Maximum energy is radiated from the two bodies $A$ and $B$ at wavelengths $\lambda_A$ and $\lambda_B$ respectively. The difference in these two wavelengths is $1 \mu m$. If the temperature of the body $A$ is $5802 \ K$,then the value of $\lambda_B$ is:

In a transistor circuit,when the base current is increased by $50 \mu A$ keeping the collector voltage fixed at $2 \ V$,the collector current increases by $1 \ mA$. The current gain of the transistor is