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).
Let f : ℝ → ℝ be a polynomial function of degree four having extreme values at x = 4 and x = 5. If lim_(x→0) f(x)/x² = 5, then f(2) is equal to :
Let y = y(x) be the solution of the differential equation (x² + 1)y′ − 2xy = (x⁴ + 2x² + 1)cos x, y(0) = 1. Then ∫_(−3)^(3) y(x) dx is :
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