# If P = 3 1 2 2 1 3 2 2 é ù ê ú ê ú ê ú ê ú – ë û , A = 1 1 0 1 é ù ê ú ë û and Q = PAPT, then P T Q2015 P is ;

Question:

If $\mathrm{P}=\left[\begin{array}{cc}\frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2}\end{array}\right], \mathrm{A}=\left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right]$ and $\mathrm{Q}=\mathrm{PAP}^{\mathrm{T}}$, then $\mathrm{P}^{\mathrm{T}} \mathrm{Q}^{2015} \mathrm{P}$ is ;

1. $\left[\begin{array}{cc}0 & 2015 \\ 0 & 0\end{array}\right]$

2. $\left[\begin{array}{cc}2015 & 0 \\ 1 & 2015\end{array}\right]$

3. $\left[\begin{array}{cc}1 & 2015 \\ 0 & 1\end{array}\right]$

4. $\left[\begin{array}{cc}2015 & 1 \\ 0 & 2015\end{array}\right]$

Correct Option: 3

JEE Main Previous Year 1 Question of JEE Main from Mathematics Inverse Trigonometric Functions chapter.
JEE Main Previous Year Online April 9, 2016

Solution:

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