30 verified questions · ~45 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).
Considering only the principal values of inverse trigonometric functions, the number of positive real values of x satisfying tan⁻¹(x) + tan⁻¹(2x) = π/4 is :
Consider the function f : (0, 2) → ℝ defined by f(x) = (x/2) + (2/x), and the function g defined by g(x) = min{f(t) : 0 < t ≤ x}, for 0 < x ≤ 1 g(x) = (3/2) + x, for 1 < x < 2 Then :
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