New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Matrices and Determinants question

2021 · 31 Aug · Shift 1 · Q36

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

PYQ Library
JEE Main
Mathematics
Matrices and Determinants
2021 · 31 Aug · Shift 1 · Q36

Matrices and Determinants question

2021 · 31 Aug · Shift 1 · Q36

JEE MainMathematicsMatrices and DeterminantsMCQ+4 / −1

If

{a_r} = \cos {{2r\pi } \over 9} + i\sin {{2r\pi } \over 9}

, r = 1, 2, 3, ....., i =

\sqrt { - 1}

, then the determinant

\left| {\begin{matrix} {{a_1}} & {{a_2}} & {{a_3}} \\ {{a_4}} & {{a_5}} & {{a_6}} \\ {{a_7}} & {{a_8}} & {{a_9}} \\ \end{matrix} } \right|

is equal to :

A
a2a6 $-$ a4a8
B
a9
C
a1a9 $-$ a3a7
D
a5

More from Matrices and Determinants

If $α$ + $β$ + $γ$ = 2 $π$ , then the system of equations x + (cos $γ$ )y + (cos $β$ )z = 0 (cos $γ$ )x + y + (cos $α$ )z = 0 (cos $β$ )x + (cos $α$ )y + z = 0 has :2021 · MCQ
The number of elements in the set ${A = (a 0 b d) : a, b, d \in {- 1, 0, 1} an d (I - A)^{3} = I - A^{3}}$ , where I is 2 $\times$ 2 identity matrix, is :2021 · Numerical
Let S be the set of all $λ \in$ R for which the system of linear equations 2x – y + 2z = 2 x – 2y + $λ$ z = –4 x + $λ$ y + z = 4 has no solution. Then the set S :2020 · MCQ
Let A be a 2 $\times$ 2 real matrix with entries from {0, 1} and |A| $e$ 0. Consider the following two statements : (P) If A $e$ I2 , then |A| = –1 (Q) If |A| = 1, then tr(A) = 2, where I2 denotes 2 $\times$ 2 identity matrix and tr(A)…2020 · MCQ
Let a, b, c $\in$ R be all non-zero and satisfy a3 + b3 + c3 = 2. If the matrix A = $a b c b c a c a b$ satisfies ATA = I, then a value of abc can…2020 · MCQ
Let A = {X = (x, y, z)T: PX = 0 and x2 + y2 + z2 = 1} where $P = 1 - 2 1 239 1 - 4 - 1$ , then the set A :2020 · MCQ
If $Δ$ = $x - 2 2 x - 3 3 x - 5 2 x - 3 3 x - 4 5 x - 8 3 x - 4 4 x - 5 10 x - 17$ = Ax3 + Bx2 + Cx + D, then B + C is equal to :2020 · MCQ
Let A = $[x 1 10]$ , x $\in$ R and A4 = [aij]. If a11 = 109, then a22 is equal to .2020 · Numerical