#Mathematics

PHYSICS

Which function represents SHM? ( omega is a positive constant)

SHM requires a = -omega² x : (a) 5 cos (3omega t + π/6) : a = -5 (3omega)² cos (3omega t + π/6) = -omega² x, SHM. (b) sin omega t + cos 2omega t : Not SHM (mixed frequencies). e^{-omega t : Not periodic. (d) sin² omega t : Periodic, not SHM.

Ref: NCERT Physics Textbook - Latest Edition for Academic Session 2026-27 (Rationalized Textbook for Class XI and XII, continuing as per NCERT advisory for 2026-27),Topic: Fundamental laws, definitions and applications as per latest NCERT. The section explains governing laws, formulas like μ₀ = 4π.

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BOTANY

Which statement about differentiation is correct?

Differentiation results in specialized lls with specific functions. Dedifferentiation allows some lls to regain division capacity, but xylem vessels cannot dedifferentiate.

Ref: NCERT Biology Textbook for Class XI and XII (Botany section), Chapter: Cell Structure and Function, Cell Cycle and Biomolecules, Topic: Cell organelles and biomolecular structure.

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PHYSICS

Which of the following equations is dimensionally inconsistent?

(a) [s] = [L], [u t] = [L T^{-1] [T] = [L], consistent. (b) [v] = [L T^{-1], [a t] = [L T^{-2] [T] = [L T^{-1], consistent. (c) [F] = [M L T^{-2], [m v / t] = [M L T^{-1] / [T] = [M L T^{-2], consistent. (d) [E] = [M L² T^{-2], [m v t] = [M L T^{-1] [T] = [M L T⁰], inconsistent.

Ref: NCERT Physics Textbook for Class XI and XII, Chapter: Units and Measurements and Physical World, Topic: Dimensional analysis and fundamental principles.

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PHYSICS

According to dimensional analysis, what must be true for two physical quantities to be added or subtracted?

From Section 1.6.1: Physical quantities can only be added or subtracted if they have the same dimensions (principle of homogeneity). This follows from NCERT principle where relation explains outcome clearly for students.

Ref: NCERT Physics Textbook for Class XI and XII, Chapter: Units and Measurements, Topic: Dimensional analysis, requirement for addition/subtraction, same dimensions. The section explains definitions, governing laws, formulas like μ₀ = 4π × 10⁻⁷ T·m/A, units and illustrative examples.

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PHYSICS

In dimensional analysis, what is true about the arguments of functions like sine or logarithm?

From Section 1.6.1: Arguments of trigonometric, logarithmic, and exponential functions must be dimensionless (e.g., angle as [L]/[L] ). This follows from NCERT principle where the relation explains the outcome clearly for students in simple steps.

Ref: NCERT Physics Textbook for Class XI and XII, Chapter: Units and Measurements and Physical World, Topic: Dimensional analysis and fundamental principles.

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