The angle of elevation of an object from a point $P$ on the level ground is $\alpha$. Moving $d$ metres on the ground towards the object,the angle of elevation is found to be $\beta$. Then the height (in metres) of the object is

The internal energy of a monoatomic gas is $3 \ nRT$. $1$ mole of helium is kept in a cylinder having internal cross section area of $17 \ cm^2$ and fitted with a light movable frictionless piston. The gas is heated slowly by suppling $126 \ J$ heat. If the temperature rises by $4 \ ^\circ C$, then the piston will move $. . . . . . \ cm$.
(atmospheric pressure $= 10^5 \ Pa$)

Which of the following is the correct order of size of the given species?

Which of the following statements is incorrect?

What is the scientific name of modern man?

If $k > 1$ and the determinant of the matrix $A^2$,where $A = \begin{bmatrix} k & k\alpha & \alpha \\ 0 & \alpha & k\alpha \\ 0 & 0 & k \end{bmatrix}$,is $k^2$,then $|\alpha|$ is equal to