Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 12 - Determinants>Exercises>Q 12

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The determinant $|\begin{matrix} a & b & a α + b \\ b & c & b α + c \\ a α + b & b α + c & 0 \end{matrix}| = 0$ is equal to zero, if

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Important Questions on Determinants

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 12 - Determinants>Exercises>Q 13

If

|\begin{matrix} \sin x & \sin y & \sin z \\ \cos x & \cos y & \cos z \\ \cos^{3} x & \cos^{3} y & \cos^{3} z \end{matrix}| = 0

, then which of the following is / are possible?

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 12 - Determinants>Exercises>Q 14

If

|\begin{matrix} x^{2} + x & x + 1 & x - 2 \\ 2 x^{2} + 3 x - 1 & 3 x & 3 x - 3 \\ x^{2} + 2 x + 3 & 2 x - 1 & 2 x - 1 \end{matrix}| = x A + B

, then

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 12 - Determinants>Exercises>Q 15

If

|\begin{matrix} 1 & 1 & 1 \\ a & b & c \\ b c & c a & a b \end{matrix}| = |\begin{matrix} 1 & 1 & 1 \\ a & b & c \\ a^{3} & b^{3} & c^{3} \end{matrix}|,

where

a, b, c

are distinct positive real numbers, then possible values of

a b c

is / are

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 12 - Determinants>Exercises>Q 16

|\begin{matrix} {}^{x}C_{r} & {}^{x}C_{r + 1} & {}^{x}C_{r + 2} \\ {}^{y}C_{r} & {}^{y}C_{r + 1} & {}^{y}C_{r + 2} \\ {}^{z}C_{r} & {}^{z}C_{r + 1} & {}^{z}C_{r + 2} \end{matrix}|

is equal to

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 12 - Determinants>Exercises>Q 17

If

∆ = |\begin{matrix} \sin θ \cos ϕ & \sin θ \sin ϕ & \cos θ \\ \cos θ \cos ϕ & \cos θ \sin ϕ & - \sin θ \\ \sin θ \sin ϕ & - \sin θ \cos ϕ & 0 \end{matrix}|

, then

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 12 - Determinants>Exercises>Q 18

If $A, B$ and $C$ are angles of triangle, then the value of $|\begin{matrix} \sin^{2} A & \cot A & 1 \\ \sin^{2} B & \cot B & 1 \\ \sin^{2} C & \cot C & 1 \end{matrix}|$ is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 12 - Determinants>Exercises>Q 19

If determinant

|\begin{array}{ccc} \cos (θ + ϕ) & - \sin (θ + ϕ) & \cos 2 ϕ \\ \sin θ & \cos θ & \sin ϕ \\ - \cos θ & \sin θ & \cos ϕ \end{array}|

is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 12 - Determinants>Exercises>Q 20

If

g (x) = |\begin{matrix} a^{- x} & e^{x \log_{e} a} & x^{2} \\ a^{- 3 x} & e^{3 x \log_{e} a} & x^{4} \\ a^{- 5 x} & e^{5 x \log_{e} a} & 1 \end{matrix}|

, then