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

$A$ convex lens has its radii of curvature equal. The focal length of the lens is $f$. If it is divided vertically into two identical plano-convex lenses by cutting it,then the focal length of the plano-convex lens is ($\mu$ = the refractive index of the material of the lens).

Match the following columns:

Column-$I$	Column-$II$
$A$. Halophiles	$i$. Gram-negative bacteria
$B$. Thermoacidophiles	$ii$. Inhabit extremely salty areas
$C$. Spirochetes	$iii$. Responsible for methane production
$D$. Firmicutes	$iv$. Survive in acidic and high-temperature conditions
	$v$. Gram-positive bacteria

Three rods of same dimensions have thermal conductivities $3K$,$2K$,and $K$. They are arranged as shown in the figure. In the steady state,the temperature of the junction $P$ is

Sunlight of intensity $1.3 ~kW ~m^{-2}$ is incident normally on a thin convex lens of focal length $20 ~cm$. Ignore the energy loss of light due to the lens and assume that the lens aperture size is much smaller than its focal length. The average intensity of light,in $kW m^{-2}$,at a distance $22 ~cm$ from the lens on the other side is.

The figure shows the vertical section of a frictionless surface. $A$ block of mass $2 \, kg$ is released from position $A$. Its kinetic energy $(KE)$ as it reaches position $C$ is ............ $J$.