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 A = [[2,a,0],[1,3,1],[0,5,b]]. If A³ = 4A² − A − 21I, where I is the identity matrix of order 3×3, then 2a + 3b is equal to
The value of k ∈ ℕ for which the integral Iₙ = ∫₀¹ (1 − x^k)^n dx, n ∈ ℕ, satisfies 147 I₂₀ = 148 I₂₁ is
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