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AlgebraHard JEE math MCQ

Let $P=\left[\begin{array}{ccc}1 & 0 & 0 \\ 4 & 1 & 0 \\ 16 & 4 & 1\end{array}\right]$ and $I$ be the identity matrix of order 3. If $Q=\left[q_{i j}\right]$ is a matrix such that $P^{50}-Q=I$, then $\frac{q_{31}+q_{32}}{q_{21}}$ equals
  1. A. 52
  2. B. 103
  3. C. 201
  4. D. 205

Solution

The correct option is **B**.

MATH

hardPYQ Reworded
Question
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Let P=[1004101641]P=\left[\begin{array}{ccc}1 & 0 & 0 \\ 4 & 1 & 0 \\ 16 & 4 & 1\end{array}\right] and II be the identity matrix of order 3. If Q=[qij]Q=\left[q_{i j}\right] is a matrix such that P50Q=IP^{50}-Q=I, then q31+q32q21\frac{q_{31}+q_{32}}{q_{21}} equals
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Algebra — Hard JEE Mathematics MCQ | MyGoalPrep