24 verified questions · ~36 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 S = ℕ ∪ {0}. Define a relation R from S to ℝ by: R = {(x, y) : log_e y = x log_e(2/5), x ∈ S, y ∈ ℝ}. Then the sum of all the elements in the range of R is equal to:
Let A = [a_(ij)] be a 2 × 2 matrix such that a_(ij) ∈ {0, 1} for all i and j. Let the random variable X denote the possible values of the determinant of the matrix A. Then the variance of X is:
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