Let m and M be respectively the minimum and maximum values of $\left| {\begin{array}{*{20}{c}} {{{\cos }^2}x}&{1 + {{\sin }^2}x}&{\sin 2x}\\ {1 + {{\cos }^2}x}&{{{\sin }^2}x}&{\sin 2x}\\ {{{\cos }^2}x}&{{{\sin }^2}x}&{1 + \sin 2x} \end{array}} \right|.$ Then, the ordered pair $(m,M)$ is equal to

JEE MATHEMATICS MCQ: MATRICES

1 Easy

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Analyzing +4 | -1

Let m and M be respectively the minimum and maximum values of

\left| {\begin{array}{cccccccccccccccccccc} {{{\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{array}} \right|.

Then, the ordered pair

(m,M)

is equal to

View answer and explanation

Correct option: B

( - 3, - 1)

Option B ((-3, -1)) is correct because the minimum and maximum values of the determinant are found by simplifying the determinant and analyzing the range of the sine function.

More Questions from MATRICES

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\left|\begin{array}{ccc}a & b-c & b+c \\ c+a & b & c-a \\ a-b & a+b & c\end{array}\right|=0

and

a, b, c

are real numbers then the line

a x+b y+c=0

passes through the fixed point is The number of solutions of the system of equations

{x_2} - {x_3} = 1,\; - {x_1} + 2{x_3} = - 2,\;{x_1} - 2,\;{x_1} - 2{x_2} = 3

is If the equations

2x + 3y + 1 = 0,3x + y - 2 = 0

and

ax + 2y - b = 0

are consistent, then The value of the determinant

\left|\begin{array}{ccc}1 & \left(\alpha^{2 x}-\alpha^{-2 x}\right)^2 & \left(\alpha^{2 x}+\alpha^{-2 x}\right)^2 \\ 1 & \left(\beta^{2 x}-\beta^{-2 x}\right)^2 & \left(\beta^{2 x}+\beta^{-2 x}\right)^2 \\ 1 & \left(\gamma^{2 x}-\gamma^{-2 x}\right)^2 & \left(\gamma^{2 x}+\gamma^{-2 x}\right)^2\end{array}\right|

, is If

\omega

is the cube root of unity, then

\left| {\begin{array}{cccccccccccccccccccc} 1&\omega &{{\omega ^2}}\\ \omega &{{\omega ^2}}&1\\ {{\omega ^2}}&1&\omega \end{array}} \right|

is equal to For any matrix

A

of order

2 \times 2

, if

A(\operatorname{adj} A)=\left[\begin{array}{cc}10 & 0 \\ 0 & 10\end{array}\right]

, then

|A|

is equal to