# Let dÎR, and A = 2 2 4 d (sin ) 1 (sin ) 2 d , 5 (2 sin ) d ( sin ) 2 2d – é ù -+ q ê ú q + q- – q+ + ë û q Î [0, 2p]. If the minimum value of det (A) is 8, then a value of d is:

Question:

Let $\mathrm{d} \in \mathbf{R}$, and

$$A=\left[\begin{array}{ccc} -2 & 4+d & (\sin \theta)^{-2} \\ 1 & (\sin \theta)+2 & d \\ 5 & (2 \sin \theta)-d & (-\sin \theta)+2+2 d \end{array}\right] \text {, }$$

$\theta \in[0,2 \pi]$. If the minimum value of $\operatorname{det}$ (A) is 8 , then a value of $d$ is:

1. $-5$

2. $-7$

3. $2(\sqrt{2}+1)$

4. $2(\sqrt{2}+2)$

Correct Option: 1

JEE Main Previous Year 1 Question of JEE Main from Mathematics Matrices and Determinants chapter.
JEE Main Previous Year Jan 10, $2019(I) Solution: ### Related Questions • Let$\theta=\frac{\pi}{5}$and$A=\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right]$. If$\mathrm{B}=\mathrm{A}+\mathrm{A}^{4}$, then det (B): View Solution • If$\Delta=\left|\begin{array}{ccc}x-2 & 2 x-3 & 3 x-4 \\ 2 x-3 & 3 x-4 & 4 x-5 \\ 3 x-5 & 5 x-8 & 10 x-17\end{array}\right|=A x^{3}+B x^{2}+C x+D$then$B+C$is equal to : View Solution • Let$a-2 b+c=1$. If$f(x)=\left|\begin{array}{lll}x+a & x+2 & x+1 \\ x+b & x+3 & x+2 \\ x+c & x+4 & x+3\end{array}\right|$then : View Solution • If$\Delta_{1}=\left|\begin{array}{ccc}x & \sin \theta & \cos \theta \\ -\sin \theta & -x & 1 \\ \cos \theta & 1 & x\end{array}\right|$and$\Delta_{2}=\left|\begin{array}{ccc}x & \sin 2 \theta & \cos 2 \theta \\ -\sin 2 \theta & -x & 1 \\ \cos 2 \theta & 1 & x\end{array}\right|, x \neq 0 ;$then for all$\theta \in\left(0, \frac{\pi}{2}\right)$: View Solution • The sum of the real roots of the equation$\left|\begin{array}{ccc}x & -6 & -1 \\ 2 & -3 x & x-3 \\ -3 & 2 x & x+2\end{array}\right|=0$, is equal to: View Solution • Let$\mathrm{A}=\left[\begin{array}{ccc}2 & \mathrm{~b} & 1 \\ \mathrm{~b} & \mathrm{~b}^{2}+1 & \mathrm{~b} \\ 1 & \mathrm{~b} & 2\end{array}\right]$where$\mathrm{b}>0$. Then the minimum value of$\frac{\operatorname{det}(\mathrm{A})}{\mathrm{b}}$is: View Solution • If$\left|\begin{array}{lll}x-4 & 2 x & 2 x \\ 2 x & x-4 & 2 x \\ 2 x & 2 x & x-4\end{array}\right|=(A+B x)(x-A)^{2}$, then the ordered pair$(A, B)$is equal to : View Solution • If$S=\left\{x \in[0,2 \pi]:\left|\begin{array}{ccc}0 & \cos x & -\sin x \\ \sin x & 0 & \cos x \\ \cos x & \sin x & 0\end{array}\right|=0\right\}$, then$\sum_{x \in S} \tan \left(\frac{\pi}{3}+x\right)$is equal to View Solution • If$\mathrm{A}=\left[\begin{array}{cc}-4 & -1 \\ 3 & 1\end{array}\right]$, then the determinant of the matrix$\left(A^{2016}-2 A^{2015}-A^{2014}\right)$is : View Solution •$\left|\begin{array}{ccc}x^{2}+x & x+1 & x-2 \\ 2 x^{2}+3 x-1 & 3 x & 3 x-3 \\ x^{2}+2 x+3 & 2 x-1 & 2 x-1\end{array}\right|=a x-12$, then ‘$a\$ ‘ is equal to :

View Solution

error: Content is protected !!