EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 17 - Matrices and Determinants>KEAM 2019>Q 6

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IMPORTANT

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A determinant of second order is made up of elements $0$ and $1 .$ The number of determinants with non-negative values is

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Important Questions on Matrices and Determinants

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KEAM

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 17 - Matrices and Determinants>KEAM 2018>Q 7

If

|\begin{matrix} x & 2 & x \\ x^{2} & x & 6 \\ x & x & 6 \end{matrix}| = a x^{4} + b x^{3} + c x^{2} + d x + e

,

then

5 a + 4 b + 3 c + 2 d + e

is equal to

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 17 - Matrices and Determinants>KEAM 2020>Q 8

The value of the determinant

|\begin{matrix} bc & ca & ab \\ a^{3} & b^{3} & c^{3} \\ \frac{1}{a} & \frac{1}{b} & \frac{1}{c} \end{matrix}|

is

EASY

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 17 - Matrices and Determinants>KEAM 2020>Q 9

If the matrix

[\begin{matrix} 1 & 2 & - 1 \\ - 3 & 4 & k \\ - 4 & 2 & 6 \end{matrix}]

is singular, then the value of

k

is equal to

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 17 - Matrices and Determinants>KEAM 2019>Q 10

The points

(k, 2 - 2 k), (- k + 1, 2 k)

and

(- 4 - k, 6 - 2 k)

are collinear for

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 17 - Matrices and Determinants>KEAM 2019>Q 11

If

α, β

and

γ

are the roots of the equation

x^{3} + p x + q = 0,

then the value of the determinant

|\begin{array}{l} α & β & γ \\ β & γ & α \\ γ & α & β \end{array}|

is

EASY

KEAM

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 17 - Matrices and Determinants>KEAM 2019>Q 12

If

A

is an invertible matrix of order

n

and

k

is any positive real number, then the value of

[det (k A)]^{- 1} det (A)

is

EASY

KEAM

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 17 - Matrices and Determinants>KEAM 2018>Q 13

Let

f (x) = |\begin{matrix} x & 3 & 7 \\ 2 & x & 2 \\ 7 & 6 & x \end{matrix}|

.

If

x = - 9

is a root of

f (x) = 0

,

then the other roots are

EASY

KEAM

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 17 - Matrices and Determinants>KEAM 2018>Q 14

|\begin{matrix} 1 & a & b + c \\ 1 & b & c + a \\ 1 & c & a + b \end{matrix}| =