EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main 17 March 2021 Shift 2>Q 39

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IMPORTANT

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If $x, y, z$ are in arithmetic progression with common difference $d, x \neq 3 d,$ and the determinant of the matrix $[\begin{matrix} 3 & 4 \sqrt{2} & x \\ 4 & 5 \sqrt{2} & y \\ 5 & k & z \end{matrix}]$ is zero, then the value of $k^{2}$ is

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Important Questions on Matrices and Determinants

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main 17 March 2021 Shift 2>Q 40

Let

A = [\begin{array}{l} a & b \\ c & d \end{array}]

and

B = [\begin{array}{l} α \\ β \end{array}] \neq [\begin{array}{l} 0 \\ 0 \end{array}]

such that

A B = B

and

a + d =2021,

then the value of

a d - b c

is equal to ______ .

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main 18 March 2021 Shift 1>Q 41

The solutions of the equation

|\begin{matrix} 1 + \sin^{2} x & \sin^{2} x & \sin^{2} x \\ \cos^{2} x & 1 + \cos^{2} x & \cos^{2} x \\ 4 \sin 2 x & 4 \sin 2 x & 1 + 4 \sin 2 x \end{matrix}| = 0, (0 < x < π),

are

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main 18 March 2021 Shift 1>Q 42

Let

α, β, γ

be the real roots of the equation,

x^{3} + a x^{2} + b x + c = 0,

(

a, b, c \in R

and

a, b \neq 0

). If the system of equations (in,

u, v, w

) given by

α u + β v + γ w = 0, β u + γ v + α w = 0, γ u + α v + β w = 0

has non-trivial solution, then the value of

\frac{a^{2}}{b}

is

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main 18 March 2021 Shift 1>Q 43

Let

A + 2 B = [\begin{matrix} 1 & 2 & 0 \\ 6 & - 3 & 3 \\ - 5 & 3 & 1 \end{matrix}]

and

2 A - B = [\begin{matrix} 2 & - 1 & 5 \\ 2 & - 1 & 6 \\ 0 & 1 & 2 \end{matrix}] .

If

T r (A)

denotes the sum of all diagonal elements of the matrix

A,

then

Tr (A) - Tr (B)

has value equal to

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main 18 March 2021 Shift 2>Q 44

Let the system of linear equations

4 x + λ y + 2 z = 0

2 x - y + z = 0

μ x + 2 y + 3 z = 0, λ, μ \in R

has a non-trivial solution. Then which of the following is true?

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main 18 March 2021 Shift 2>Q 45

Let

I

be an identity matrix of order

2 \times 2

and

P = [\begin{matrix} 2 & - 1 \\ 5 & - 3 \end{matrix}]

. Then the value of

n \in N

for which

P^{n} = 5 I - 8 P

is equal to ___ .

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 24 Feb 2021 Shift 1>Q 46

The system of linear equations

$3 x - 2 y - k z = 10$

$2 x - 4 y - 2 z = 6$

$x + 2 y - z = 5 m$
is inconsistent if :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 24 Feb 2021 Shift 1>Q 47

Let

P = [\begin{array}{r} 3 & - 1 & - 2 \\ 2 & 0 & α \\ 3 & - 5 & 0 \end{array}],

where

α \in R .

Suppose

Q = [q_{i j}]

is a matrix satisfying

P Q = k I_{3}

for
some non-zero

k \in R .

If

q_{23} = - \frac{k}{8}

and

|Q| = \frac{k^{2}}{2}

, then

α^{2} + k^{2}

is equal to_________.