If $P=\begin{bmatrix}1&0\\ \frac{1}{2}&1\end{bmatrix}$, then $P^{50}$ is :

Option 3: $\begin{bmatrix}1&0\\25&1\end{bmatrix}$

$\begin{bmatrix}1&0\\50&1\end{bmatrix}$

$\begin{bmatrix}1&25\\0&1\end{bmatrix}$

$\begin{bmatrix}1&0\\25&1\end{bmatrix}$

$\begin{bmatrix}1&50\\0&1\end{bmatrix}$

JEE Main 2021 · MathsMultiple choiceSingle correctEasyApplication

JEE Main 25 July 2021, Shift 2, Maths Q75

Question 75 of 90 in this shift, Maths question 15 of 30, Section A.

P=\begin{bmatrix}1&0\\ \frac{1}{2}&1\end{bmatrix}

, then

P^{50}

is :

(1) $\begin{bmatrix}1&0\\50&1\end{bmatrix}$
(2) $\begin{bmatrix}1&25\\0&1\end{bmatrix}$
(3) $\begin{bmatrix}1&0\\25&1\end{bmatrix}$ Official answer
(4) $\begin{bmatrix}1&50\\0&1\end{bmatrix}$

Official answer

Option 3

NTA final key.

Chapter: Matrices
Topic: Matrix Multiplication
Idea tested: Powers of Square Matrices

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Asked 21× in all

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Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.