The correct answer is option 3 i.e. (ML²)/12.

To find the moment of inertia of a thin rod with mass M and length L about an axis perpendicular to the rod and passing through its center, we use the standard formula for the moment of inertia of a rod about its center.

The moment of inertia I of a thin rod of length L and mass M about an axis perpendicular to the rod and passing through its center is given by:

I = (ML²)/12

Therefore, the moment of inertia of the rod is:

I = (ML²)/12

The correct answer is option 4 i.e. Temperature.

Gravitational force does not depend on temperature. It is determined solely by the masses of the two interacting objects and the distance between them, as described by Newton's law of gravitation: F=G(m1m2/r). Here, F is the gravitational force,  G is the gravitational constant, m1 and m2 are the masses, and r is the distance between their centers. Temperature does not influence gravitational interactions.

The correct answer is option 2 i.e. 2.0 C.

The work done in moving a charge from one point to the other is 20 J.

The potential difference between the points is 10 V.

We know that:

Work done (W) = qV

⇒ 20 = 10q

⇒ q = 2.0 C

Hence, the charge =  2.0 C

The correct answer is option 3 i.e. Oxygen.

Oxygen is a part of the P block of the periodic table. The P block elements are found in groups 13 to 18 and include a variety of metals, nonmetals, and metalloids. Oxygen, a nonmetal, is located in Group 16 of the P block. In contrast, Rhodium and Silver are transition metals in the D block, and Hydrogen is a unique element not classified in the P block.

The correct answer is option 1 i.e. 11.

• Only 11 gases are under normal atmospheric conditions, out of the known elements in the periodic table.
• These gases include Hydrogen, Nitrogen, Oxygen, Fluorine, Chlorine, Argon, Neon, Helium, Krypton, Xenon and Radon.

The correct answer is option 4 i.e. Dodecane.

The straight-chain alkane containing 12 carbon atoms used as a major component in kerosene, some jet fuel research, and the rubber and paper processing industry is dodecane. Its chemical formula is C₁₂H₂₆. Dodecane is a saturated hydrocarbon with a long carbon chain, contributing to its utility in various industrial applications due to its stability and solubility properties. In addition to its use in fuels and industrial processes, dodecane also finds applications in solvents and detergents.

The correct answer is option 4 i.e. Dodecane.

The straight-chain alkane containing 12 carbon atoms used as a major component in kerosene, some jet fuel research, and the rubber and paper processing industry is dodecane. Its chemical formula is C₁₂H₂₆. Dodecane is a saturated hydrocarbon with a long carbon chain, contributing to its utility in various industrial applications due to its stability and solubility properties. In addition to its use in fuels and industrial processes, dodecane also finds applications in solvents and detergents.

The correct answer is option 3 i.e. Nitrogen trifluoride (NF₃).

• Covalent Bonds: In NF₃, nitrogen (N) and fluorine (F) atoms share electrons to form covalent bonds. Each fluorine atom shares one pair of electrons with the nitrogen atom, resulting in three covalent bonds.

• Molecular Structure: NF₃ consists of discrete molecules rather than a continuous network of ions or atoms. The compound exists as separate NF₃ molecules held together by intermolecular forces.

• Hence, NF₃ is classified as a molecular (covalent) compound due to its structure and the nature of its bonding.

The correct answer is Option 1 i.e. Zeeman effect.

In the presence of an external magnetic field, the degeneracy of energy levels in hydrogen-like atoms is lifted due to the Zeeman effect. This phenomenon results in the splitting of spectral lines into multiple components. The Zeeman effect occurs because the magnetic field interacts with the magnetic moment associated with the electron's orbital and spin angular momentum, causing them to align differently, thus altering the energy levels and breaking the degeneracy.

The correct answer is Option 1 i.e. M - Z.

Atomic number of nucleus = Number of protons = Z

Mass number of nucleus = Number of protons + Number of neutrons = M

Number of neutrons = M – Number of protons

Number of neutrons = M – Z