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Jee Main 2025 — Hard JEE math MCQ

Let \( A = [a_{ij}] \) be a matrix of order \( 3 \times 3 \), with \( a_{ij} = (\sqrt{2})^{i+j} \). If the sum of all the elements in the third row of \( A^2 \) is \( \alpha + \beta\sqrt{2} \), \( \alpha, \beta \in \mathbb{Z} \), then \( \alpha + \beta \) is equal to
  1. A. 280
  2. B. 224
  3. C. 210
  4. D. 168

Solution

The correct option is **B**. (B. 224)

MATH

hard • PYQ Reworded
Question
Read carefully, then pick the best option.
Let A=[aij] A = [a_{ij}] be a matrix of order 3×3 3 \times 3 , with aij=(2)i+j a_{ij} = (\sqrt{2})^{i+j} . If the sum of all the elements in the third row of A2 A^2 is α+β2 \alpha + \beta\sqrt{2} , α,β∈Z \alpha, \beta \in \mathbb{Z} , then α+β \alpha + \beta is equal to
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