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 in a triangle ABC, the length of the side AC be 6, the vertex B be (1, 2, 3) and the vertices A, C lie on the line (x − 6)/3 = (y − 7)/2 = (z − 7)/(−2). Then the area (in sq. units) of triangle ABC is:
Let the product of the focal distances of the point (√3, 1/2) on the ellipse x²/a² + y²/b² = 1, (a > b), be 7/4. Then the absolute difference of the eccentricities of two such ellipses is
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