28 verified questions · ~42 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).
If the domain of the function f(x) = (√(x²−25))/(4−x²) + log₁₀(x²+2x−15) is (−∞, α) ∪ [β, ∞), then α² + β³ is equal to:
Consider a triangle ABC where A(1, 3, 2), B(−2, 8, 0) and C(3, 6, 7). If the angle bisector of ∠BAC meets the line BC at D, then the length of the projection of the vector AD⃗ on the vector AC⃗ is:
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