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 d be the distance of the point of intersection of the lines (x + 6)/3 = y/2 = (z + 1)/1 and (x − 7)/4 = (y − 9)/3 = (z − 4)/2 from the point (7, 8, 9). Then d² + 6 is equal to:
Let a rectangle ABCD of sides 2 and 4 be inscribed in another rectangle PQRS such that the vertices of the rectangle ABCD lie on the sides of the rectangle PQRS. Let a and b be the sides of the rectangle PQRS when its area is maximum. Then (a + b)² is equal to:
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