Which of the following statements are correct? (a) Singlet carbene is paramagnetic. (b) In the two species \(\mathrm{CN}^{-}\) and \(\mathrm{CO}\), the common feature is that bond order is three and they are isoelectronic. (c) Between \(\mathrm{CH}_{3} \mathrm{Cl}\) and \(\mathrm{CH}_{2} \mathrm{Cl}_{2}\), the former has a higher dipole moment. (d) In the species \(\mathrm{CH}_{3}-\mathrm{C}^{2} \mathrm{H}+\mathrm{HCN} \stackrel{\mathrm{H}_{3}}{\longrightarrow}\) the order of acidity with respect to the positions indicated is \((2)>(1)>(3)\)

Let's analyze the first statement: "Singlet carbene is paramagnetic." To understand this, we need to know that singlet carbene is a specific type of carbene with paired electrons in its vacant p-orbital. Paramagnetism refers to the tendency of a molecule to have an induced magnetic moment in a magnetic field, which is determined by unpaired electrons. In singlet carbene, since the electrons are paired, the molecule has no unpaired electrons. This means it is not paramagnetic. Therefore, statement (a) is incorrect.

Moving on to the statement (b), "In the two species \(\mathrm{CN}^{-}\) and \(\mathrm{CO}\), the common feature is that bond order is three and they are isoelectronic." Let's break down this statement. Isoelectronic specifies that the two species have the same number of electrons. \(\mathrm{CN}^{-}\) has 14 electrons (7 from carbon, 7 from nitrogen, and 1 from the extra negative charge), while \(\mathrm{CO}\) has 14 electrons (6 from carbon and 8 from oxygen). Therefore, these species are indeed isoelectronic. Now, let's analyze the bond order. Bond order is a measure of the bond strength between two atoms. It is half the difference between the number of bonding electrons and the number of antibonding electrons. For \(\mathrm{CN}^{-}\), we have a triple bond (σ and 2π) between C and N, so the bond order is 3. For \(\mathrm{CO}\), the electronic configuration of C and O shows a triple bond (σ and 2π) between them, so the bond order is also 3. So, the statement (b) is correct.

Next, let's analyze statement (c): "Between \(\mathrm{CH}_{3} \mathrm{Cl}\) and \(\mathrm{CH}_{2} \mathrm{Cl}_{2}\), the former has a higher dipole moment." To address this, we need to understand the concept of dipole moment. It is the measure of the polarity of a bond or a molecule and depends on the electronegativity difference between the atoms and the symmetry of the molecule. In \(\mathrm{CH}_{3} \mathrm{Cl}\), the electronegative chlorine atom pulls electron density away from the carbon and hydrogen atoms, resulting in a net dipole moment towards the chlorine atom. In \(\mathrm{CH}_{2} \mathrm{Cl}_{2}\), there are two chlorine atoms, positioned symmetrically around the carbon atom. These two dipoles caused by the chlorine atoms cancel each other out, resulting in a reduced net dipole moment. Thus, statement (c) is correct, as \(\mathrm{CH}_{3} \mathrm{Cl}\) has a higher dipole moment.

Finally, let's examine statement (d): "In the species \(\mathrm{CH}_{3}-\mathrm{C}^{2} \mathrm{H}+\mathrm{HCN} \stackrel{\mathrm{H}_{3}}{\longrightarrow}\) the order of acidity with respect to the positions indicated is \((2)>(1)>(3)\)". To discuss this statement, we need to understand acidity. The acidity of a hydrogen atom in a molecule is determined by the stability of the conjugate base after the hydrogen atom is lost as a proton. In other words, the more stable the resulting anion, the more acidic the hydrogen. 1. In \(\mathrm{CH}_{3} - \mathrm{C}^{2} \mathrm{H}\), the acidic hydrogen atom is at position 2, so the resulting anion is \(\mathrm{CH}_{2}^- \mathrm{CH}\). 2. In \(\mathrm{CH}_{3} - \mathrm{C}^{1} \mathrm{H}+\mathrm{HCN}\), the acidic hydrogen atom is at position 1, so the resulting anion is \(\mathrm{CH}^- \mathrm{CH}_{2}+\mathrm{HCN}\). 3. In \(\mathrm{CH}_{3} - \mathrm{C}^{3} \mathrm{H}\), the acidic hydrogen atom is at position 3, so the resulting anion is \(\mathrm{CH}_{2} - \mathrm{C}^{1} \mathrm{H}+\mathrm{HC}^-\). Now let's compare the stability of these anions. The order of stability is given as: \(\mathrm{CH}_{2}^- \mathrm{CH} > \mathrm{CH}^- \mathrm{CH}_{2}+\mathrm{HCN} > \mathrm{CH}_{2} - \mathrm{C}^{1} \mathrm{H}+\mathrm{HC}^-\). This implies that the order of acidity is indeed \((2) > (1) > (3)\). So, statement (d) is correct.