In $YDSE$, the separation between the slits is halved and the distance between the slit and the screen is doubled. The fringe width is

Consider the following reaction equilibrium:
$N_{2(g)} + 3H_{2(g)} \rightleftharpoons 2NH_{3(g)}$
Initially,$1 \text{ mole}$ of $N_2$ and $3 \text{ moles}$ of $H_2$ are taken in a $2 \text{ L}$ flask. At equilibrium state,if the number of moles of $N_2$ is $0.6$,what is the total number of moles of all gases present in the flask?

If $f:[2, \infty) \rightarrow B$ defined by $f(x)=x^2-4x+5$ is a bijection,then $B$ is equal to

If $\alpha$ is a non-real root of the equation $x^6-1=0$,then $\frac{\alpha^2+\alpha^3+\alpha^4+\alpha^5}{\alpha+1}$ is equal to

If a line $l$ passes through $(k, 2k), (3k, 3k)$ and $(3, 1)$ where $k \neq 0$,then the distance from the origin to the line $l$ is

The thickness of a uniform rectangular metal plate is $5 ~mm$ and the area of each surface is $5 ~cm^2$. In steady state, the temperature difference between the two surfaces of the plate is $14^{\circ} C$. If the heat flowing through the plate in one second from one surface to the other surface is $42 ~J$, then the thermal conductivity of the metal is: