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 the values of λ for which the shortest distance between the lines (x − 1)/2 = (y − 2)/3 = (z − 3)/4 and (x − λ)/3 = (y − 4)/4 = (z − 5)/5 is 1/√6 be λ₁ and λ₂. Then the radius of the circle passing through the points (0, 0), (λ₁, λ₂) and (λ₂, λ₁) is
Let f(x) = x − 1 and g(x) = eˣ for x ∈ ℝ. If dy/dx = (e^(−2√x)·g(f(f(x))) − y/√x), y(0) = 0, then y(1) is
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