JEE MATHEMATICS MCQ: MATRICES

1 Medium

1 of 1

Analyzing +4 | -1

If maximum and minimum values of the determinant

\left|\begin{array}{lll}1+\operatorname{Sin}^2 x & \operatorname{Cos}^2 x & \operatorname{Sin} 2 x \\ \operatorname{Sin}^2 x & 1+\operatorname{Cos}^2 x & \operatorname{Sin} 2 x \\ \operatorname{Sin}^2 x & \operatorname{Cos}^2 x & 1+\operatorname{Sin} 2 x\end{array}\right|

are

\alpha

and

\beta

respectively, then which of the statements are FALSE ?

View answer and explanation

Correct option: D

A triangle can be constructed having it's sides as

\alpha, \beta

and

\alpha-\beta

Option D (A triangle can be constructed having it's sides as

\alpha, \beta

and

\alpha-\beta

) is false because the triangle inequality is not satisfied with the given values of

\alpha

and

\beta

More Questions from MATRICES

Practice All Chapter MCQs →

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

a, b, c

a x+b y+c=0

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

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

ax + 2y - b = 0

\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|

\omega

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

A

2 \times 2

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

|A|