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

EASY

JEE Main

IMPORTANT

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If $f (x) = |\begin{matrix} \cos x & x & 1 \\ 2 \sin x & x^{2} & 2 x \\ \tan x & x & 1 \end{matrix}|$ , then $\lim_{x \to 0} \frac{f^{'} (x)}{x}$

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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 - 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:

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?