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).
If the domain of the function f(x) = sin⁻¹((x − 1)/(2x + 3)) is R − (α, β), then 12αβ is equal to :
Let three vectors a⃗ = αî + 4ĵ + 2k̂, b⃗ = 5î + 3ĵ + 4k̂, c⃗ = xî + yĵ + zk̂ form a triangle such that c⃗ = a⃗ − b⃗ and the area of the triangle is 5√6. If α is a positive real number, then |c⃗|² is equal to :
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