Which of the following ray diagrams shows physically possible refraction?

$A$ body is thrown vertically upwards and reaches its maximum height in $t$ seconds. The total time from the time of projection to reach a point at half of its maximum height while returning (in seconds) is:

Due to the Doppler effect,the shift in wavelength observed is $0.1 \ \mathring{A}$ for a star producing a wavelength of $6000 \ \mathring{A}$. The velocity of recession of the star will be ...... $km/s$.

Consider the set of all triangles $OPQ$ where '$O$' is the origin and $P$,$Q$ are distinct points in the plane with non-negative integral coordinates $(x, y)$ such that $5x + y = 99$. The number of such distinct triangles whose area is a positive integer is:

If for $x \in \left( 0, \frac{1}{4} \right)$,the derivative of $\tan^{-1} \left( \frac{6x\sqrt{x}}{1 - 9x^3} \right)$ is $\sqrt{x} \cdot g(x)$,then $g(x)$ equals:

If $A = \begin{bmatrix} \cos \alpha & \sin \alpha \\ -\sin \alpha & \cos \alpha \end{bmatrix}$,then verify that $A^{\prime} A = I$.