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).
Suppose f(x) = ((2ˣ + 2⁻ˣ) · tan x · √(tan⁻¹(x² − x + 1))) / (7x² + 3x + 1)³. Then the value of f′(0) is equal to
Let a⃗, b⃗ and c⃗ be three non-zero vectors such that b⃗ and c⃗ are non-collinear. If a⃗ + 5b⃗ is collinear with c⃗, b⃗ + 6c⃗ is collinear with a⃗, and a⃗ + αb⃗ + βc⃗ = 0⃗, then α + β is equal to
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