NCERT Exemplar Mathematics - Class 12>Chapter 4 - Determinants>EXERCISE>Q 38

EASY

12th CBSE

IMPORTANT

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If $A$ is a matrix of order $3 \times 3$ , then $| 3 A | =$ $| A |$

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Important Questions on Determinants

EASY

12th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 12>Chapter 4 - Determinants>EXERCISE>Q 39

If

A

is invertible matrix of order

3 \times 3

, then

| A | |A^{- 1}|

is _____.

EASY

12th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 12>Chapter 4 - Determinants>EXERCISE>Q 40

If

x, y, z \in R

, then the value of determinant

|\begin{array}{l} {(2^{x} + 2^{- x})}^{2} & {(2^{x} - 2^{- x})}^{2} & 1 \\ {(3^{x} + 3^{- x})}^{2} & {(3^{x} - 3^{- x})}^{2} & 1 \\ {(4^{x} + 4^{- x})}^{2} & {(4^{x} - 4^{- x})}^{2} & 1 \end{array}|

is equal to _____.

MEDIUM

12th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 12>Chapter 4 - Determinants>EXERCISE>Q 41

If

\cos 2 θ = 0

and

{|\begin{matrix} 0 & \cos θ & \sin θ \\ \cos θ & \sin θ & 0 \\ \sin θ & 0 & \cos θ \end{matrix}|}^{2} = \frac{k}{2}

, then the value of

k =

_____.

MEDIUM

12th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 12>Chapter 4 - Determinants>EXERCISE>Q 42

If

A

is a matrix of order

3 \times 3

, then

{(A^{2})}^{- 1} = {(A^{- 1})}^{k}

,

k =

_____.

EASY

12th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 12>Chapter 4 - Determinants>EXERCISE>Q 43

If

A

is a matrix of order

3 \times 3

, then number of minors in determinant of

A

are _____.

EASY

12th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 12>Chapter 4 - Determinants>EXERCISE>Q 44

The sum of the products of elements of any row with the corresponding co-factors is equal to the value of _____.

MEDIUM

12th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 12>Chapter 4 - Determinants>EXERCISE>Q 45

If

x = - 9

is a root of

|\begin{array}{l} x & 3 & 7 \\ 2 & x & 2 \\ 7 & 6 & x \end{array}| = 0

, then other two roots are _____.

MEDIUM

12th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 12>Chapter 4 - Determinants>EXERCISE>Q 46

|\begin{matrix} 0 & x y z & x - z \\ y - x & 0 & y - z \\ z - x & z - y & 0 \end{matrix}| =

_____