Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 51

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Let $Δ = |\begin{array}{l} b + c & q + r & y + z \\ c + a & r + p & z + x \\ a + b & p + q & x + y \end{array}|$ and $Δ_{1} = |\begin{array}{l} x & a & p \\ y & b & q \\ z & c & r \end{array}| .$ If $Δ = λ Δ_{1},$ then the value of $λ$ is

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Important Questions on Matrices and Determinants

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 52

If

y = \sin m x,

then the value of the determinant

|\begin{matrix} y & y_{1} & y_{2} \\ y_{3} & y_{4} & y_{5} \\ y_{6} & y_{7} & y_{8} \end{matrix}|

, where

y_{n} = \frac{d^{n} y}{d x^{n}},

is

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Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 53

If

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

then

k

equals to

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Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 54

Which one of the following factors does the expansion of the determinant $|\begin{matrix} x & y & 3 \\ x^{2} & 5 y^{3} & 9 \\ x^{3} & 10 y^{5} & 27 \end{matrix}|$ contain?

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Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 55

If

n \neq 3 k

and

1, ω, ω^{2}

are the cube roots of unity, then

Δ = |\begin{matrix} 1 & ω^{n} & ω^{2 n} \\ ω^{2 n} & 1 & ω^{n} \\ ω^{n} & ω^{2 n} & 1 \end{matrix}|

has the value, where

k \in I

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Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 56

If

x, y

and

z

are all distinct and

|\begin{array}{l} x & x^{2} & 1 + x^{3} \\ y & y^{2} & 1 + y^{3} \\ z & z^{2} & 1 + z^{3} \end{array}| = 0

, then the value of

x y z

is

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Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 57

If

x_{1}, x_{2}, x_{3}, \dots, x_{13}

are in

AP

, then the value of

|\begin{array}{l} e^{x_{1}} & e^{x_{4}} & e^{x_{7}} \\ e^{x_{4}} & e^{x_{7}} & e^{x_{10}} \\ e^{x_{7}} & e^{x_{10}} & e^{x_{13}} \end{array}|

is

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Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 58

Let

| A | = {|a_{i j}|}_{3 \times 3} \neq 0

. Each element

a_{i j}

is multiplied by

k^{i - j}

. Let

| B |

be the resulting determinant, where

k_{1} | A | + k_{2} | B | = 0

, then

k_{1} + k_{2} = ?

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Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 59

If

a, b

and

c

are in arithmetic progression, then the value of the determinant

|\begin{matrix} x + 2 & x + 3 & x + 2 a \\ x + 3 & x + 4 & x + 2 b \\ x + 4 & x + 5 & x + 2 c \end{matrix}|

is -