20 verified questions · ~22 minutes · answer key checked against the official NTA final key across multiple sources. Text-only questions (diagram-based excluded until they can be shown properly).
The centre of mass of a thin rectangular plate with sides of length a and b — placed with one corner at the origin, the side of length a along the x-axis and the side of length b along the y-axis — whose mass per unit area σ varies as σ = σ₀x/(ab) (where σ₀ is a constant), would be:
A proton of mass mₚ has the same energy E as that of a photon of wavelength λ. If the proton is moving at non-relativistic speed, then the ratio of its de Broglie wavelength to the wavelength of the photon is:
Answers are revealed after you attempt — that's what makes the diagnosis honest.