If $N$ denotes the set of all positive integers and if $f: N \rightarrow N$ is defined by $f(n) =$ the sum of positive divisors of $n$,then $f(2^k \cdot 3)$,where $k$ is a positive integer,is

$A$ positively charged $(+q)$ particle of mass $m$ has kinetic energy $K$ and enters a region with a horizontal magnetic field $\overrightarrow{B}$ in a vertically downward direction. The acceleration of the particle is:

In the Young's double slit experiment using a monochromatic light of wavelength $\lambda$,the path difference (in terms of an integer $n$) corresponding to any point having half the peak intensity is :-

The coefficients of apparent expansion of a liquid when determined using two different vessels $A$ and $B$ are $\gamma_1$ and $\gamma_2$,respectively. If the coefficient of linear expansion of the vessel $A$ is $\alpha$,the coefficient of linear expansion of the vessel $B$ is

The number of radial nodes of $3s$ and $2p$ orbitals respectively are

If the decimal $0.d25d25d25\ldots$ is expressible in the form $n/27$,then $d+n$ must be