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Jee Main 2025 — Hard JEE math MCQ

Let \( A = [a_{ij}] \) be a \( 2 \times 2 \) matrix such that \( a_{ij} \in \{0, 1\} \) 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
  1. A. \( \frac{3}{8} \)
  2. B. \( \frac{5}{8} \)
  3. C. \( \frac{3}{8} \)
  4. D. \( \frac{1}{4} \)

Solution

The correct option is **C**. (C. \( \frac{3}{8} \))

MATH

hard • PYQ Reworded
Question
Read carefully, then pick the best option.
Let A=[aij] A = [a_{ij}] be a 2×2 2 \times 2 matrix such that aij∈{0,1} a_{ij} \in \{0, 1\} for all i i and j j . Let the random variable X X denote the possible values of the determinant of the matrix A A . Then, the variance of X X is
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Jee Main 2025 — Hard JEE Mathematics MCQ | MyGoalPrep