EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 9th January 2019 Shift 1>Q 99

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JEE Main

IMPORTANT

Earn 100

The system of linear equations
$x + y + z = 2$
$2 x + 3 y + 2 z = 5$
$2 x + 3 y + (a^{2} - 1) z = a + 1$

57.69% studentsanswered this correctly

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 - 9th January 2019 Shift 2>Q 100

If

A = [\begin{matrix} e^{t} & e^{- t} c o s t & e^{- t} \sin t \\ e^{t} & - e^{- t} \cos t - e^{- t} \sin t & - e^{- t} \sin t + e^{- t} \cos t \\ e^{t} & {2 e}^{- t} \sin t & - 2 e^{- t} \cos t \end{matrix}],

then

A

is:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 9th January 2019 Shift 2>Q 101

If the system of linear equations

x - 4 y + 7 z = g

;

3 y - 5 z = h

;

- 2 x + 5 y - 9 z = k

is consistent, then:

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 8th April 2019 Shift 1>Q 102

Let

A = [\begin{matrix} \cos α & - \sin α \\ \sin α & \cos α \end{matrix}], (a \in R)

such that

A^{32} = [\begin{matrix} 0 & - 1 \\ 1 & 0 \end{matrix}] .

Then, a value of

α

is:

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 8th April 2019 Shift 1>Q 103

The greatest value of

c \in R

for which the system of linear equations

x - c y - c z = 0

,

c x - y + c z = 0

,

c x + c y - z = 0

has a non-trivial solution, is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 8th April 2019 Shift 2>Q 104

Let the numbers

2, b, c

be in an A.P. and

A = [\begin{matrix} 1 & 1 & 1 \\ 2 & b & c \\ 4 & b^{2} & c^{2} \end{matrix}]

. If

d e t (A) \in [2,16],

then

c

lies in the interval:

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 8th April 2019 Shift 2>Q 105

If the system of linear equations

x - 2 y + k z = 1

2 x + y + z = 2

3 x - y - k z = 3

has a solution

(x, y, z), z \neq 0,

then

(x, y)

lies on the straight line whose equation is:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 10th April 2019 Shift 1>Q 106

If the system of linear equations

x + y + z = 5

,

x + 2 y + 2 z = 6

,

x + 3 y + λ z = µ, (λ, µ \in R)

, has infinitely many solutions, then the value of

λ + µ

is:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 10th April 2019 Shift 1>Q 107

If

Δ_{1} = |\begin{matrix} x & s i n θ & c o s θ \\ - s i n θ & - x & 1 \\ c o s θ & 1 & x \end{matrix}|

and

Δ_{2} = |\begin{matrix} x & s i n 2 θ & c o s 2 θ \\ - s i n 2 θ & - x & 1 \\ c o s 2 θ & 1 & x \end{matrix}|,

x \neq 0;

then for all

θ \in (0, \frac{π}{2})

: