The number of common tangents to the circles $x^2 + y^2 = 4$ and $x^2 + y^2 - 6x - 8y = 24$ is:

The coefficient of static friction,$\mu_s$ between block $A$ of mass $2\,kg$ and the table as shown in the figure is $0.2$. What would be the maximum mass value of block $B$ so that the two blocks do not move (in $,kg$)? The string and the pulley are assumed to be smooth and massless. $(g = 10\,m/s^2)$

The family in which many plants are $C_4$ type is:

The velocity of a particle at time $t$ is given by the relation $v = 6t - \frac{t^2}{6}$. The distance traveled in $3$ seconds is,if $s = 0$ at $t = 0$.

$A$ narrow tube is bent in the form of a circle of radius $R,$ as shown in the figure. Two small holes $S$ and $D$ are made in the tube at positions right-angled to each other. $A$ source placed at $S$ generates a wave of intensity $I_0$ which is equally divided into two parts: one part travels along the longer path,while the other travels along the shorter path. Both the waves meet at the point $D$ where a detector is placed. The maximum value of $\lambda$ to produce a maxima at $D$ is given by

$A$ common emitter transistor amplifier has a current gain of $50$. If the load resistance is $4 \ k\Omega$ and input resistance is $500 \ \Omega$,the voltage gain of the amplifier is