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 a curve y = f(x) pass through the points (0, 5) and (logₑ2, k). If the curve satisfies the differential equation 2(3 + y)e^(2x) dx − (7 + e^(2x)) dy = 0, then k is equal to
Let P be the foot of the perpendicular from the point Q(10, −3, −1) on the line (x − 3)/7 = (y − 2)/(−1) = (z + 1)/(−2). Then the area of the right angled triangle PQR, where R is the point (3, −2, 1), is
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