Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>Assignment>Q 25

EASY

JEE Main/Advance

IMPORTANT

Earn 100

If $a, b, c$ are positive and not equal then value of $|\begin{array}{l} a & b & c \\ b & c & a \\ c & a & b \end{array}|$ may be

50% studentsanswered this correctly

Important Questions on Determinants

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>Assignment>Q 26

The greatest value of

x

satisfying the equation

|\begin{matrix} 2^{11} - x & - 2^{12} & 2^{11} \\ - 2^{12} & 2^{11} - x & 2^{11} \\ 2^{11} & 2^{11} & - 2^{12} - x \end{matrix}| = 0

is

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>Assignment>Q 27

The largest value of a third order determinant whose elements are equal to

1

or

0

is

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>Assignment>Q 28

If

|\begin{matrix} x^{k} & x^{k + 2} & x^{k + 3} \\ y^{k} & y^{k + 2} & y^{k + 3} \\ z^{k} & z^{k + 2} & z^{k + 3} \end{matrix}| = (x - y) (y - z) (z - x) (\frac{1}{x} + \frac{1}{y} + \frac{1}{z})

then

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>Assignment>Q 29

If all elements of a third order determinant are equal to

1

or

- 1

, then determinant itself is

EASY

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>Assignment>Q 30

If

A

is a

3 \times 3

matrix and

det (3 A) = k {det (A)}

, then

k

is

EASY

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>Assignment>Q 31

If

A

is any of square matrix of order

n

, then

A (adj A)

is equal to

EASY

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>Assignment>Q 32

If

A

is a square matrix of order

3, | A | = 3

, then

| adj adj A |

is equal to

EASY

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>Assignment>Q 33

If

A = [\begin{matrix} 11 & 7 \\ - 13 & 17 \end{matrix}]

, then

adj (adj A)

is