Let's examine each statement:
1. PEt$_3$ and AsPh$_3$ can form d$\pi$-d$\pi$ bonds: PEt$_3$ (triethylphosphine) and AsPh$_3$ (triphenylarsine) are ligands that can act as $\pi$-acceptors. The phosphorus or arsenic atom in these ligands has empty d orbitals that can accept electron density from the filled d orbitals of transition metals, forming d$\pi$-d$\pi$ backbonds. This is a correct statement.
2. N-N single bond strength: The N-N single bond is considerably weaker than the P-P single bond. This weakness is due to the lone pair repulsion between the nitrogen atoms. The lone pairs on the relatively small nitrogen atoms are close enough to experience significant repulsion, weakening the N-N single bond. Phosphorus atoms are larger, and their lone pairs are further apart, resulting in less repulsion and a stronger P-P bond. Therefore, statement (2) is incorrect.
3. Nitrogen's p$\pi$-p$\pi$ multiple bonds: Nitrogen readily forms p$\pi$-p$\pi$ multiple bonds with itself (N$_2$), carbon (C$\equiv$N, CN), and oxygen (N=O). This is a key aspect of nitrogen chemistry and is a correct statement.
4. Nitrogen's d$\pi$-p$\pi$ bonding: Nitrogen does not have accessible d orbitals in its valence shell. Therefore, it cannot form d$\pi$-p$\pi$ bonds, unlike heavier elements in its group (phosphorus, arsenic, etc.) which have d orbitals available. This is a correct statement.
A sphere of radius R is cut from a larger solid sphere of radius 2R as shown in the figure. The ratio of the moment of inertia of the smaller sphere to that of the rest part of the sphere about the Y-axis is :
Predict the major product $ P $ in the following sequence of reactions:
(i) HBr, benzoyl peroxide
(ii) KCN
(iii) Na(Hg), $C_{2}H_{5}OH$
AB is a part of an electrical circuit (see figure). The potential difference \(V_A - V_B\), at the instant when current \(i = 2\) A and is increasing at a rate of 1 amp/second is: