$A$ smooth cylinder of mass $m$ and radius $R$ is resting on two corner edges $A$ and $B$ as shown in the figure. The relation between the normal reactions at the edges $A$ and $B$ is

The input resistance of a common emitter transistor amplifier,if the output resistance is $500 \, k\Omega$,the current gain $\alpha = 0.98$ and power gain is $6.0625 \times 10^6$,is....$\Omega$

Let $A$ and $B$ be two sets. Then $(A \cup B)' \cup (A' \cap B)$ is equal to:

$A$ number $n$ is chosen at random from $S=\{1, 2, 3, \ldots, 50\}$. Let $A=\{n \in S: n+\frac{50}{n} > 27\}$,$B=\{n \in S: n \text{ is a prime}\}$ and $C=\{n \in S: n \text{ is a square}\}$. Then,the correct order of their probabilities is

If a slab of insulating material $4 \times 10^{-3} \ m$ thick is introduced between the plates of a parallel plate capacitor,the separation between plates has to be increased by $3.5 \times 10^{-3} \ m$ to restore the capacity to its original value. The dielectric constant of the material will be

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