EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 10th January 2019 Shift 2>Q 113

MEDIUM

JEE Main

IMPORTANT

Earn 100

The number of values of $θ \in (0, π)$ for which the system of linear equations
$x + 3 y + 7 z = 0$
$- x + 4 y + 7 z = 0$
$(\sin 3 θ) x + (\cos 2 θ) y + 2 z = 0$
has a non-trivial solution, is:

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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 - 10th January 2019 Shift 2>Q 114

Let

a_{1}, a_{2}, a_{3} \dots, a_{10}

be in

G . P .

with

a_{i} > 0

for

i = 1, 2, \dots, 10

and

S

be the set of pairs

(r, k), r, k \in N

(the set of natural numbers) for which

|\begin{matrix} \log_{e} a_{1}^{r} a_{2}^{k} & \log_{e} a_{2}^{r} a_{3}^{k} & \log_{e} a_{3}^{r} a_{4}^{k} \\ \log_{e} a_{4}^{r} a_{5}^{k} & \log_{e} a_{5}^{r} a_{6}^{k} & \log_{e} a_{6}^{r} a_{7}^{k} \\ \log_{e} a_{7}^{r} a_{8}^{k} & \log_{e} a_{8}^{r} a_{9}^{k} & \log_{e} a_{9}^{r} a_{10}^{k} \end{matrix}| = 0

Then the number of elements in

S,

is:

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 12th April 2019 Shift 1>Q 115

If

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

is the inverse of a

3 \times 3

matix

A,

then the sum of all values of

α

for which

d e t (A) + 1 = 0,

is:

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 12th April 2019 Shift 1>Q 116

If

A

is a symmetric matrix and

B

is skew- symmetric matrix such that

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

, then

A B

is equal to:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 12th April 2019 Shift 2>Q 117

A value of

θ \in (0, \frac{π}{3}),

for which

|\begin{matrix} 1 + {c o s}^{2} θ & {s i n}^{2} θ & 4 c o s 6 θ \\ {c o s}^{2} θ & 1 + {s i n}^{2} θ & 4 c o s 6 θ \\ {c o s}^{2} θ & {s i n}^{2} θ & 1 + 4 c o s 6 θ \end{matrix}| = 0,

is

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 12th January 2019 Shift 1>Q 118

Let

P = [\begin{matrix} 1 & 0 & 0 \\ 3 & 1 & 0 \\ 9 & 3 & 1 \end{matrix}]

and

Q = [q_{i j}]

be two

3 \times 3

matrices such that

Q - P^{5} = I_{3}

. Then

\frac{q_{21} + q_{31}}{q_{32}}

is equal to :

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 12th January 2019 Shift 1>Q 119

An ordered pair $(α, β)$ for which the system of linear equations
$(1 + α) x + β y + z = 2$
$α x + (1 + β) y + z = 3$
$α x + β y + 2 z = 2$

has a unique solution, is :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 12th January 2019 Shift 2>Q 120

If

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

, then for all

θ \in (\frac{3 π}{4}, \frac{5 π}{4})

,

\det (A)

lies in the interval :

MEDIUM

JEE Main

IMPORTANT

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

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 :