If the curves $x^2 - 6x + y^2 + 8 = 0$ and $x^2 - 8y + y^2 + 16 - k = 0$ $(k > 0)$ touch each other at a point,then the largest value of $k$ is

How many species are there in the genus $Homo$?

$A$ metal rod of length '$l$' rotates about one of its ends in a plane perpendicular to a magnetic field of induction '$B$'. If the e.m.f. induced between the ends of the rod is '$e$',then the number of revolutions made by the rod per second is

The de-Broglie wavelength of a particle moving with a velocity $2.25 \times 10^8 \ m/s$ is equal to the wavelength of a photon. The ratio of the kinetic energy of the particle to the energy of the photon is (velocity of light is $3 \times 10^8 \ m/s$). (in $/8$)

The position of a particle at time $t$ is given by the equation $x(t) = \frac{v_0}{A}(1 - e^{-At})$,where $v_0$ is a constant and $A > 0$. The dimensions of $v_0$ and $A$ respectively are:

For $k=1, 2, 3$,the box $B_k$ contains $k$ red balls and $(k+1)$ white balls. Let $P(B_1) = \frac{1}{2}$,$P(B_2) = \frac{1}{3}$,and $P(B_3) = \frac{1}{6}$. $A$ box is selected at random and a ball is drawn from it. If a red ball is drawn,then the probability that it has come from box $B_2$ is: