$A$ body of $5\, kg$ weight kept on a rough inclined plane of angle $30^\circ$ starts sliding with a constant velocity. Then the coefficient of friction is:

If $A$ is a $3 \times 4$ matrix and $B$ is a matrix such that $A'B$ and $BA'$ are both defined,then $B$ is of the type:

Find the value of $k$,if the angle between the straight lines represented by $2x^2 + 5xy + 3y^2 + 6x + 7y + 4 = 0$ is $\tan^{-1}(k)$.

Two metal plates each of area $A$ form a parallel plate capacitor with air in between the plates. The distance between the plates is $d$. $A$ metal plate of thickness $d/2$ and of same area $A$ is inserted between the plates to form two capacitors of capacitances $C_1$ and $C_2$ as shown in the figure. If the effective capacitance of the two capacitors is $C^{\prime}$ and the capacitance of the capacitor initially is $C$,then $C^{\prime}/C$ is

To the free end of a spring hanging from a rigid support,a block of mass $m$ is hung and slowly allowed to come to its equilibrium position. Then the stretching in the spring is $d$. If the same block is attached to the same spring and allowed to fall suddenly,the amount of stretching is: (force constant,$k$)

The number of natural numbers less than $1000$,in which no two digits are repeated,is: