$A$ black body at a high temperature $T \ K$ radiates energy at the rate $E \ W/m^2$. When the temperature falls to $(T/2) \ K$,the radiated energy will be:

If $y=a \cos (\log x)+b \sin (\log x)$,where $a, b$ are parameters,then $x^2 y^{\prime \prime}+x y^{\prime}$ is equal to

If the pair of straight lines $xy-x-y+1=0$ and the line $ax+2y-3a=0$ are concurrent,then $a$ is equal to

$A$ body of weight $64\, N$ is pushed with just enough force to start it moving across a horizontal floor and the same force continues to act afterwards. If the coefficients of static and dynamic friction are $0.6$ and $0.4$ respectively,the acceleration of the body will be (Acceleration due to gravity $= g$)

The substance used in the thermite process of reducing metal ores is

$A$ ball rises to the surface at a constant velocity in a liquid whose density is $4$ times greater than that of the material of the ball. The ratio of the force of friction acting on the rising ball and its weight is