EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 12th January 2019 Shift 2>Q 121

MEDIUM

JEE Main

IMPORTANT

Earn 100

The set of all values of $λ$ for which the system of linear equations
$x - 2 y - 2 z = λ x$
$x + 2 y + z = λ y$
$- x - y = λ z$
has a non-trivial solution :

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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 - 8th April 2018>Q 122

If the system of linear equations

$x + k y + 3 z = 0$
$3 x + k y - 2 z = 0$
$2 x + 4 y - 3 z = 0$

has a non-zero solution $(x, y, z),$ then $\frac{x z}{y^{2}}$ is equal to:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 8th April 2018>Q 123

If

|\begin{matrix} x - 4 & 2 x & 2 x \\ 2 x & x - 4 & 2 x \\ 2 x & 2 x & x - 4 \end{matrix}| = (A + B x) {(x - A)}^{2},

then the ordered pair

(A, B)

is equal to

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 15th April 2018>Q 124

If

f (x) = |\begin{matrix} \cos x & x & 1 \\ 2 \sin x & x^{2} & 2 x \\ \tan x & x & 1 \end{matrix}|

, then

\lim_{x \to 0} \frac{f^{'} (x)}{x}

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 15th April 2018>Q 125

Let

A

be a matrix such that

A \cdot [\begin{matrix} 1 & 2 \\ 0 & 3 \end{matrix}]

is a scalar matrix and

|3 A| = 108

. Then,

A^{2}

equals :

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 15th April 2018>Q 126

Let

S

be the set of all real values of

k

for which the system of linear equations

x + y + z = 2

2 x + y - z = 3

3 x + 2 y + k z = 4

has a unique solution. Then,

S

is :

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 16th April 2018>Q 127

Let

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

and

B = A^{20}

. Then the sum of the elements of the first column of

B

is

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 16th April 2018>Q 128

The number of values of

k

for which the system of linear equations

(k + 2) x + 10 y = k &

k x + (k + 3) y = k - 1

has no solution is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 2nd April 2017>Q 129

If

S

is the set of distinct values of

b

for which the following system of linear equations

x + y + z = 1

x + a y + z = 1

a x + b y + z = 0

has no solution, then

S

is: