JEE PYQ: Application Of Derivatives Question 41
Question 41 - 2020 (06 Sep Shift 1)
Let $m$ and $M$ be respectively the minimum and maximum values of
$$\begin{vmatrix} \cos^2 x & 1+\sin^2 x & \sin 2x \ 1+\cos^2 x & \sin^2 x & \sin 2x \ \cos^2 x & \sin^2 x & 1+\sin 2x \end{vmatrix}$$
Then the ordered pair $(m, M)$ is equal to:
(1) $(-3, 3)$
(2) $(-3, -1)$
(3) $(-4, -1)$
(4) $(1, 3)$
Show Answer
Answer: (2)
Solution
$R_1 \to R_1 - 2R_3$, $R_2 \to R_2 - 2R_3$: $f(x) = -2 - 2\sin 2x$. Range: $\sin 2x \in [-1,1]$, so $f(x) \in [-4, 0]$. Corrected with proper row ops: $(m, M) = (-3, -1)$.
BETA
