The currents $i_1$ and $i_2$ through the resistors $R_1 = 10\,\Omega$ and $R_2 = 30\,\Omega$ in the circuit diagram with $E_1 = 3\,V$,$E_2 = 3\,V$,and $E_3 = 2\,V$ are respectively:

The value of $k$ for which the function $f(x) = \begin{cases} (\frac{4}{5})^{\frac{\tan 4x}{\tan 5x}}, & 0 < x < \frac{\pi}{2} \\ k + \frac{2}{5}, & x = \frac{\pi}{2} \end{cases}$ is continuous at $x = \frac{\pi}{2}$ is

$A$ block rests on a rough inclined plane making an angle of $30^o$ with the horizontal. The coefficient of static friction between the block and the plane is $0.8$. If the frictional force on the block is $10 \, N$,the mass of the block (in $kg$) is (take $g = 10 \, m/s^2$)

According to molecular orbital theory,the total number of bonding electron pairs in $O_2$ is

Lenz's law is a consequence of the law of conservation of:

$A$ candidate takes three tests in succession and the probability of passing the first test is $p$. The probability of passing each succeeding test is $p$ if he passes the preceding one,or $\frac{p}{2}$ if he fails the preceding one. The candidate is selected if he passes at least two tests. The probability that the candidate is selected is: