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 the line x + y = 1 meet the circle x² + y² = 4 at the points A and B. If the line perpendicular to AB and passing through the mid-point of the chord AB intersects the circle at C and D, then the area of the quadrilateral ADBC is equal to :
Let M and m respectively be the maximum and the minimum values of f(x) = det [[1 + sin²x, cos²x, 4 sin 4x], [sin²x, 1 + cos²x, 4 sin 4x], [sin²x, cos²x, 1 + 4 sin 4x]], x ∈ ℝ. Then M⁴ − m⁴ is equal to :
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