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).
Let the circle C₁ : x² + y² − 2(x + y) + 1 = 0 and C₂ be a circle having centre at (−1, 0) and radius 2. If the line of the common chord of C₁ and C₂ intersects the y-axis at the point P, then the square of the distance of P from the centre of C₁ is:
Let f, g : R → R be defined as f(x) = |x − 1| and g(x) = { eˣ, x ≥ 0 ; x + 1, x ≤ 0 }. Then the function f(g(x)) is
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