JEE PYQ: Application Of Derivatives Question 72
Question 72 - 2019 (10 Jan Shift 1)
Let $d \in \mathbb{R}$, and $A = \begin{bmatrix} -2 & 4+d & (\sin\theta)-2 \ 1 & (\sin\theta)+2 & d \ 5 & (2\sin\theta)-d & (-\sin\theta)+2+2d \end{bmatrix}$, $\theta \in [0, 2\pi]$. If the minimum value of $\det(A)$ is 8, then a value of $d$ is:
(1) $-5$
(2) $-7$
(3) $2(\sqrt{2}+1)$
(4) $2(\sqrt{2}+2)$
Show Answer
Answer: (1)
Solution
After row operations: $\det(A) = (d+2)^2 - \sin^2\theta$. Min when $\sin^2\theta = 1$: $(d+2)^2 - 1 = 8 \Rightarrow (d+2)^2 = 9 \Rightarrow d = 1$ or $d = -5$.
BETA
