EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 20 July 2021 Shift 1>Q 15

HARD

JEE Main

IMPORTANT

Earn 100

Let $A = [\begin{array}{l} 2 & 3 \\ a & 0 \end{array}], a \in R$ be written as $P + Q$ where $P$ is a symmetric matrix and $Q$ is skew symmetric matrix. If $det (Q) = 9$ , then the modulus of the sum of all possible values of determinant of $P$ is equal to:

62.9% studentsanswered this correctly

Important Questions on Matrices and Determinants

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 20 July 2021 Shift 1>Q 16

Let

A = [\begin{matrix} \begin{matrix} 1 & - 1 & 0 \\ 0 & 1 & - 1 \\ 0 & 0 & 1 \end{matrix} \end{matrix}]

and

B = 7 A^{20} - 20 A^{7} + 2 I

,
where

I

is an identity matrix of order

3 \times 3 .

If

B = [b_{i j}]

, then

b_{13}

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 20 July 2021 Shift 1>Q 17

Let

a, b, c, d

be in arithmetic progression with common difference

λ

. If

|\begin{array}{l} x + a - c & x + b & x + a \\ x - 1 & x + c & x + b \\ x - b + d & x + d & x + c \end{array}| = 2

, then value of

λ^{2}

is equal to________.

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 20 July 2021 Shift 2>Q 18

The value of $k \in R,$ for which the following system of linear equations

$3 x - y + 4 z = 3$

$x + 2 y - 3 z = - 2$

$6 x + 5 y + k z = - 3$

has infinitely many solutions, is:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 20 July 2021 Shift 2>Q 19

Let

A = \{a_{i j}\}

be a

3 \times 3

matrix, where

a_{i j} = \{\begin{matrix} {(- 1)}^{j - i} if i < j \\ 2 if i = j \\ {(- 1)}^{i + j} if i > j \end{matrix}

then

\det (3 Adj (2 A^{- 1}))

is equal to ________.

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 22 July 2021 Shift 1>Q 20

The values of

λ

and

μ

such that the system of equations

x + y + z = 6, 3 x + 5 y + 5 z = 26

and

x + 2 y + λ z = μ

has no solution, are:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 22 July 2021 Shift 1>Q 21

Let

A = [a_{i j}]

be a real matrix of order

3 \times 3,

such that

a_{i 1} + a_{i 2} + a_{i 3} = 1,

for

i = 1, 2, 3 .

Then, the sum of all the entries of the matrix

A^{3}

is equal to:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 25 July 2021 Shift 1>Q 22

The values of $a$ and $b$ , for which the system of equations

$2 x + 3 y + 6 z = 8$

$x + 2 y + a z = 5$

$3 x + 5 y + 9 z = b$

has no solution, are :

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 25 July 2021 Shift 1>Q 23

Let

M = \{A = [\begin{matrix} a & b \\ c & d \end{matrix}] : a, b, c, d \in (\pm 3, \pm 2, \pm 1, 0)\}

. Define

f : M \to Z,

as

f (A) = det (A),

for all

A \in M

where

Z

is set of all integers. Then the number of

A \in M

such that

f (A) = 15

is equal to .