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 A = [[1/√2, −2], [0, 1]] and P = [[cos θ, −sin θ], [sin θ, cos θ]], θ > 0. If B = PAPᵀ, C = PᵀB¹⁰P and the sum of the diagonal elements of C is m/n, where gcd(m, n) = 1, then m + n is :
If the components of a⃗ = αî + βĵ + γk̂ along and perpendicular to b⃗ = 3î + ĵ − k̂ respectively, are (16/11)(3î + ĵ − k̂) and (1/11)(−4î − 5ĵ − 17k̂), then α² + β² + γ² is equal to :
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