Ans: Electric flux = \(\Phi_E = \int \mathbf{E} \cdot d\mathbf{A}\). Gauss theorem states that the net electric flux through a closed surface is equal to the net charge enclosed inside divided by ε₀.

Ans: \(C = \dfrac{ε₀ A}{d}\) where A = area of plates, d = separation. Derivation involves definition C = Q/V and E-field between plates.

Ans: Based on electromagnetic induction: when a conductor coil rotates in magnetic field, flux changes → induced emf; output alternating current with frequency depending on rotation speed.

Ans: Emission of electrons from metal surface when lit by light of threshold frequency. \( K_{\text{max}} = hν – φ \), where φ = work function.

Ans: Inside shell (in hollow region) field = 0; outside equivalent to point charge +q at center (Gauss law application).

Ans: Vapour pressure of solution = mole fraction of solvent × vapour pressure of pure solvent. Used to determine molecular masses, colligative properties.

Ans: SN1 → first order, involves carbocation intermediate; SN2 → second order, direct nucleophilic attack, backside attack. Example: t-Butyl chloride (SN1), Methyl bromide (SN2).

Ans: Buffer resists pH changes; use Henderson–Hasselbalch equation: \( pH = pK_a + \log(\tfrac{[A^-]}{[HA]}) \).

Ans: Complex compounds having central metal ion + ligands. [Fe(CN)₆]^4– → low spin, diamagnetic, pale; [Fe(H₂O)₆]^3+ → high spin, paramagnetic.

Ans: \([ \frac{x^3}{3} + x ]_0^2 = \frac{8}{3} + 2 = \frac{14}{3}\)

Ans: Corner points: (0,0),(4,0),(0,4),(2,2). Evaluate Z → maximum at (4,0) gives Z = 12.

Ans: f′(x) = 2x ln x + x.

Ans: Lac operon in E. coli regulates lactose metabolism — consists of promoter, operator, structural genes; explains induction when lactose present, repression when absent.

Ans: Hormonal stimulation → egg retrieval → fertilization in lab → embryo transfer in uterus; advantages & ethical considerations discussed.

Ans: Isolation of DNA → restriction enzyme digestion → vector insertion → transformation → screening; used in recombinant DNA technology.

Ans: Sample answer structure: Introduction – Pros & Cons – Personal Opinion – Conclusion. Emphasize time-management, mental health, misuse of information, alternate healthy activities.

Ans: Summary: Emotional bond, fear of losing loved ones, importance of time; central theme: age, mortality, love and time’s passage.

Ans: Structure: Sender’s address/date → Subject → Salutation → Body (reason, request, promise) → Regards → Signature.

Ans: [Provide sample journal entries — Goodwill A/c Dr, Partner’s capital A/c Cr … etc.]

Ans: Principle of Division of Work, Authority & Responsibility, Discipline, Unity of Command, Unity of Direction, Subordination of Individual Interest, Remuneration.

Ans: Demand inversely proportional to price (ceteris paribus); demand curve slopes downward from left to right — diagram + explanation.