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 y = y(x) be the solution curve of the differential equation sec y (dy/dx) + 2x sin y = x³ cos y, y(1) = 0. Then y(√3) is equal to :
If the shortest distance between the lines (x − λ)/2 = (y − 4)/3 = (z − 3)/4 and (x − 2)/4 = (y − 4)/6 = (z − 7)/8 is 13/√29, then a value of λ is :
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