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

MEDIUM

JEE Main

IMPORTANT

Earn 100

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:

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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 - 2nd April 2017>Q 130

If

A = [\begin{matrix} 2 & - 3 \\ - 4 & 1 \end{matrix}]

, then

Adj (3 A^{2} + 12 A)

is equal to:

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 8th April 2017>Q 131

The number of real values of $λ$ for which the system of linear equations, $2 x + 4 y - λ z = 0$ , $4 x + λ y + 2 z = 0$ and $λ x + 2 y + 2 z = 0$ , has infinitely many solutions, is:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 8th April 2017>Q 132

Let

A

be any

3 \times 3

invertible matrix. Then which one of the following is not always true?

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 8th April 2017>Q 133

If

S = \{x \in [0, 2 π] : |\begin{matrix} 0 & \cos x & - \sin x \\ \sin x & 0 & \cos x \\ \cos x & \sin x & 0 \end{matrix}| = 0\},

then

\sum_{x \in S} \tan (\frac{π}{3} + x)

is equal to:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 9th April 2017>Q 134

For two

3 \times 3

matrices

A

and

B

, let

A + B = 2 B^{'}

and

3 A + 2 B = I_{3},

where

B^{'}

is the transpose of

B

and

I_{3}

is

3 \times 3

identity matrix. Then :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 9th April 2017>Q 135

If

x = a, y = b, z = c

is a solution of the system of linear equations

x + 8 y + 7 z = 0

9 x + 2 y + 3 z = 0

x + y + z = 0

Such that the point

(a, b, c)

lies on the plane

x + 2 y + z = 6

, then

2 a + b + c

equals:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 9th April 2016>Q 136

The number of distinct real roots of the equation,

|\begin{matrix} \cos x & \sin x & \sin x \\ \sin x & \cos x & \sin x \\ \sin x & \sin x & \cos x \end{matrix}| = 0

in the interval

[- \frac{π}{4}, \frac{π}{4}]

is :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 9th April 2016>Q 137

If

P = [\begin{matrix} \frac{\sqrt{3}}{2} & \frac{1}{2} \\ - \frac{1}{2} & \frac{\sqrt{3}}{2} \end{matrix}], A = [\begin{matrix} 1 & 1 \\ 0 & 1 \end{matrix}]

and

Q = P A P^{T},

then

P^{T} Q^{2015} P

is :