In the given circuit,with steady current,the potential drop across the capacitor must be

Considering ideal gas behavior, the expansion work done $(in kJ )$ when $144 g$ of water is electrolyzed completely under constant pressure at $300 K$ is $...$ .
Use: Universal gas constant $( R )=8.3 J K ^{-1} mol^{-1}$; Atomic mass $($in amu$)$: $H =1, O =16$

$A$ mass of $0.5\, kg$ moving with a speed of $1.5\, m/s$ on a horizontal smooth surface,collides with a nearly weightless spring of force constant $k=50\, N/m$. The maximum compression of the spring would be ................. $m$.

If an electron in a hydrogen atom jumps from the $3^{\text{rd}}$ orbit to the $2^{\text{nd}}$ orbit,it emits a photon of wavelength $\lambda$. When it jumps from the $4^{\text{th}}$ orbit to the $3^{\text{rd}}$ orbit,the corresponding wavelength of the photon will be

If $f(x) = \begin{cases} x \sin \frac{1}{x}, & x \ne 0 \\ k, & x = 0 \end{cases}$ is continuous at $x = 0$,then the value of $k$ is

The work done by a force $\vec F = (-6x^3 \hat i) \text{ N}$,in displacing a particle from $x = 4 \text{ m}$ to $x = -2 \text{ m}$ is .............. $J$.