If ${\left( \frac{2}{3} \right)^{x + 2}} = {\left( \frac{3}{2} \right)^{2 - 2x}}$,then $x =$

$A$ cylindrical conductor of radius $R$ carries a current $i$. The value of the magnetic field at a point which is $R/4$ distance inside from the surface is $10 \ T$. Find the value of the magnetic field at a point which is $4R$ distance outside from the surface.

The normal at a point on the parabola $y^2=4x$ passes through $(5,0)$. If two more normals to this parabola also pass through $(5,0)$,then the centroid of the triangle formed by the feet of these three normals is

A small block of mass $m$ slides down from the top of a frictionless inclined surface, while the inclined plane is moving towards left with constant acceleration $a_{0}$. The angle between the inclined plane and ground is $ heta$ and its base length is $L$. Assuming that initially the small block is at the top of the inclined plane, the time it takes to reach the lowest point of the inclined plane is . . . . . . . .

Three samples of the same gas $A, B$ and $C$ $(\gamma = 3/2)$ initially have equal volume. Now the volume of each sample is doubled. The process is adiabatic for $A$,isobaric for $B$ and isothermal for $C$. If the final pressures are equal for all three samples,the ratio of their initial pressures is:

Which of the following is the correct order of reducing power for $Al, Ga, In,$ and $Tl$?