Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 2 - Determinant>Target Exercises>Q 52

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IMPORTANT

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If $a > b > c$ and the system of equations $a x + b y + c z = 0$ , $b x + c y + a z = 0$ and $c x + a y + b z = 0$ has a non-trivial solution, then both the roots of the quadratic equation $a t^{2} + b t + c = 0$ are

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Important Questions on Determinant

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 2 - Determinant>Target Exercises>Q 53

The multiplicative inverse of

A = [\begin{matrix} \cos θ & - \sin θ \\ \sin θ & \cos θ \end{matrix}]

is

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 2 - Determinant>Target Exercises>Q 54

If

a, b

and

c

are non-zero real numbers, then the inverse of the matrix

A = [\begin{array}{l} a & 0 & 0 \\ 0 & b & 0 \\ 0 & 0 & c \end{array}]

is

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JEE Advanced

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 2 - Determinant>Target Exercises>Q 55

The multiplicative inverse of the matrix

A = [\begin{array}{l} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array}]

is

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 2 - Determinant>Target Exercises>Q 56

The value of third order determinant is

11,

then the value of the square of the determinant formed by the cofactors will be

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 2 - Determinant>Target Exercises>Q 57

If a system of the equations

{(α + 1)}^{3} x + {(α + 2)}^{3} y - {(α + 3)}^{3} = 0, (α + 1) x + (α + 2) y - (α + 3) = 0

and

x + y - 1 = 0

is consistent. Then, what is the value of

α

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JEE Advanced

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 2 - Determinant>Target Exercises>Q 58

The rank of the matrix

[\begin{array}{l} 4 & 1 & 0 & 0 \\ 3 & 0 & 1 & 0 \\ 6 & 0 & 2 & 0 \end{array}]

is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 2 - Determinant>Target Exercises>Q 59

If

f (x) = |\begin{matrix} x & \sin x & \cos x \\ x^{2} & \tan x & - x^{3} \\ 2 x & \sin 2 x & 5 x \end{matrix}|,

then

\lim_{x \to 0} \frac{f^{'} (x)}{x}

equals

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IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 2 - Determinant>Entrances Gallery>Q 84

If

A = [\begin{matrix} 1 & 2 \\ - 4 & - 1 \end{matrix}],

then

A^{- 1}

is equal to