25 verified questions · ~38 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).
If I = ∫₀^(π/2) sin^(3/2)x / (sin^(3/2)x + cos^(3/2)x) dx, then ∫₀^(2I) (x sin x cos x)/(sin⁴x + cos⁴x) dx equals :
The number of complex numbers z, satisfying |z| = 1 and |z/z̄ + z̄/z| = 1, is :
Answers are revealed after you attempt — that's what makes the diagnosis honest.