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 = [[α, −1], [6, β]], α > 0, such that det(A) = 0 and α + β = 1. If I denotes the 2 × 2 identity matrix, then the matrix (I + A)⁸ is:
Let the vertices Q and R of the triangle PQR lie on the line (x + 3)/5 = (y − 1)/2 = (z + 4)/3, QR = 5, and the coordinates of the point P be (0, 2, 3). If the area of the triangle PQR is m/n, then:
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