If $f(x) = \begin{cases} x-5, & \text{for } x \leq 1 \\ 4x^2-9, & \text{for } 1 < x < 2 \\ 3x+4, & \text{for } x \geq 2 \end{cases}$,then $f^{\prime}(2^{+})$ is equal to

Solid targets of different elements are bombarded by highly energetic electron beams. The frequency $(f)$ of the characteristic $X-$rays emitted from different targets varies with atomic number $(Z)$ as

$A$ particle of mass $2\, kg$ is initially at rest. $A$ force acts on it whose magnitude changes with time. The force-time graph is shown below. The velocity of the particle after $10\, s$ is ......... $ms^{-1}$.

Water is pumped from a depth of $10\, m$ and delivered through a pipe of cross section $10^{-2}\, m^2$. If it is needed to deliver a volume of $10^{-1}\, m^3$ per second,the power required will be: ............ $kW$

Which of the following ray diagrams shows physically possible refraction?