Two identical $5\,kg$ blocks are moving with the same speed of $2\,m/s$ towards each other along a frictionless horizontal surface. The two blocks collide,stick together,and come to rest. Considering the two blocks as a system,the work done on the system by the external forces will be .............. $Joule$.

If $A$ and $B$ are two independent events such that $P(B)=\frac{2}{7}$ and $P(A \cup B^c)=0.8$, then $P(A)$ is equal to:

The oxidation states of $S$ atoms in Caro's and Marshall's acids are

$A$ cylinder of radius $R$ made of a material of thermal conductivity $K_1$ is surrounded by a cylindrical shell of inner radius $R$ and outer radius $2R$ made of material of thermal conductivity $K_2$. The two ends of the combined system are maintained at two different temperatures. There is no loss of heat across the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system is

The number of non-trivial solutions of the system $x-y+z=0, x+2y-z=0, 2x+y+3z=0$ is

In a rectangle $ABCD$ where $BC = 2AB$,the moment of inertia will be minimum about which axis?