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Jee Main 2025 — Hard JEE math MCQ

Let \( A = [a_{ij}] = \begin{bmatrix} \log_5 128 \log_4 5 \\ \log_5 8 \log_4 25 \end{bmatrix} \). If \( A_{ij} \) is the cofactor of \( a_{ij} \), \( C_{ij} = \sum_{k=1}^{2} a_{ik}A_{jk}, 1 \leq i, j \leq 2 \), and \( C = [C_{ij}] \), then \( 8|C| \) is equal to:
  1. A. \quad 288 \\
  2. B. \quad 222 \\
  3. C. \quad 242 \\
  4. D. \quad 262 \\

Solution

The correct option is **C**. (C. \quad 242 \\)

MATH

hard • PYQ Reworded
Question
Read carefully, then pick the best option.
Let A=[aij]=[log⁡5128log⁡45log⁡58log⁡425] A = [a_{ij}] = \begin{bmatrix} \log_5 128 \log_4 5 \\ \log_5 8 \log_4 25 \end{bmatrix} . If Aij A_{ij} is the cofactor of aij a_{ij} , Cij=∑k=12aikAjk,1≤i,j≤2 C_{ij} = \sum_{k=1}^{2} a_{ik}A_{jk}, 1 \leq i, j \leq 2 , and C=[Cij] C = [C_{ij}] , then 8∣C∣ 8|C| is equal to:
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Jee Main 2025 — Hard JEE Mathematics MCQ | MyGoalPrep