Which of the following contains $p\pi - d\pi$ bonding?

If $f(x) = \begin{cases} \frac{1-\sqrt{2} \sin x}{\pi-4x} & \text{if } x \neq \frac{\pi}{4} \\ a & \text{if } x = \frac{\pi}{4} \end{cases}$ is continuous at $x = \frac{\pi}{4}$, then $a$ is equal to

$A$ conducting rod of length $L$ rotates with angular speed $\omega$ in a uniform magnetic field of induction $B$ which is perpendicular to its motion. The induced emf developed between the two ends of the rod is

The kinetic energy $K$ of a particle moving along the $x$-axis varies with its position $x$ as shown in the figure. The magnitude of the force acting on the particle at $x = 9 \, m$ is ............ $N$.

The ratio of momenta of an electron and an $\alpha$-particle which are accelerated from rest by a potential difference of $100\, V$ is

In the process of transcription in eukaryotes, the $\text{RNA}$ polymerase $\text{II}$ transcribes