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 C₁ be the circle in the third quadrant of radius 3, that touches both coordinate axes. Let C₂ be the circle with centre (1, 3) that touches C₁ externally at the point (α, β). If (β − α)² = m/n, gcd(m, n) = 1, then m + n is equal to
Let P be the parabola, whose focus is (−2, 1) and directrix is 2x + y + 2 = 0. Then the sum of the ordinates of the points on P, whose abscissa is −2, is
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