New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Matrices and Determinants question

2019 · 10 Apr · Shift 1 · Q24

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Matrices and Determinants
2019 · 10 Apr · Shift 1 · Q24

Matrices and Determinants question

2019 · 10 Apr · Shift 1 · Q24

JEE MainMathematicsMatrices and DeterminantsMCQ+4 / −1

If

{\Delta _1} = \left| {\begin{matrix} x & {\sin \theta } & {\cos \theta } \\ { - \sin \theta } & { - x} & 1 \\ {\cos \theta } & 1 & x \\ \end{matrix} } \right|

and

{\Delta _2} = \left| {\begin{matrix} x & {\sin 2\theta } & {\cos 2\theta } \\ { - \sin 2\theta } & { - x} & 1 \\ {\cos 2\theta } & 1 & x \\ \end{matrix} } \right|

,

x e 0

; then for all

\theta \in \left( {0,{\pi \over 2}} \right)

:

A
${\Delta _1} - {\Delta _2}$ = x (cos 2 $\theta$ – cos 4 $\theta$ )
B
${\Delta _1} + {\Delta _2}$ = - 2x3
C
${\Delta _1} + {\Delta _2}$ = – 2(x3 + x –1)
D
${\Delta _1} - {\Delta _2}$ = - 2x3

More from Matrices and Determinants

If the system of linear equations x + y + z = 5 x + 2y + 2z = 6 x + 3y + $λ$ z = $μ$ , ( $λ$ , $μ \in$ R), has infinitely many solutions, then the value of $λ$ + $μ$ is :2019 · MCQ
The sum of the real roots of the equation $x 2 - 3 - 6 - 3 x 2 x - 1 x - 3 x + 2 = 0$ , is equal to :2019 · MCQ
Let $λ$ be a real number for which the system of linear equations x + y + z = 6, 4x + $λ$ y – $λ$ z = $λ$ – 2, 3x + 2y – 4z = – 5 has infinitely many solutions. Then $λ$ is a root of the quadratic equation:2019 · MCQ
If the system of equations x + y + z = 5 x + 2y + 3z = 9 x + 3y + az = $β$ has infinitely many solutions, then $β - α$ equals -2019 · MCQ
Let d $\in$ R, and $A = - 2 15 4 + d (sin θ) + 2 (2 sin θ) - d (sin θ) - 2 d (- sin θ) + 2 + 2 d, θ \in [0, 2 π]$ …2019 · MCQ
The number of values of $θ \in$ (0, $π$ ) for which the system of linear equations x + 3y + 7z = 0 $-$ x + 4y + 7z = 0 (sin3 $θ$ )x + (cos2 $θ$ )y + 2z = 0. has a non-trival solution, is -2019 · MCQ
Let A = $2 b 1 b b^{2} + 1 b 1 b 2$ where b > 0. Then the minimum value of $\frac{d e t ( A )}{b}$ is -2019 · MCQ
Let A = $0 p p 2 q q - q r - r r .$ If AAT = I3, then $∣ p ∣$ is :2019 · MCQ