# If 1 sin 1 sin 1 sin 1 sin 1 é ù q ê ú =- q q – -q ë û A ; then for all 3 5 , 4 4 æ ö p p qÎç ÷ è ø , det (A) lies in the interval :

Question:

If $A=\left[\begin{array}{ccc}1 & \sin \theta & 1 \\ -\sin \theta & 1 & \sin \theta \\ -1 & -\sin \theta & 1\end{array}\right]$; then for all $\theta \in\left(\frac{3 \pi}{4}, \frac{5 \pi}{4}\right)$, $\operatorname{det}$ (A) lies in the interval :

1. $\left(1, \frac{5}{2}\right]$

2. $\left[\frac{5}{2}, 4\right)$

3. $\left(0, \frac{3}{2}\right]$

4. $\left(\frac{3}{2}, 3\right]$

Correct Option: 4

JEE Main Previous Year 1 Question of JEE Main from Mathematics Matrices and Determinants chapter.
JEE Main Previous Year Jan. 12, 2019 (II)

Solution:

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