Which one of the following is not true -

Important Questions on Determinants and Matrices

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Mathematics Crash Course MHT-CET>Chapter 10 - Determinants and Matrices>Exercise 1>Q 53

If $\alpha , \beta$ and $\gamma$ are the roots of $x^3+a{x}^2+b=0,$ then the value of $\left|\begin{array}{lll}\alpha & \beta & \gamma \\ \beta & \gamma & \alpha \\ \gamma & \alpha & \beta \end{array}\right|$ is

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IMPORTANT

Mathematics Crash Course MHT-CET>Chapter 10 - Determinants and Matrices>Exercise 1>Q 54

If $x, y$ and $z$ are all distinct and $\left|\begin{array}{lll}x& x^2& 1+x^3\\ y& y^2& 1+y^3\\ z& z^2& 1+z^3\end{array}\right|=0$, then the value of $xyz$ is

MEDIUM

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IMPORTANT

Mathematics Crash Course MHT-CET>Chapter 10 - Determinants and Matrices>Exercise 1>Q 55

If $A$ and $B$ are square matrices of order $3$ then

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IMPORTANT

Mathematics Crash Course MHT-CET>Chapter 10 - Determinants and Matrices>Exercise 1>Q 56

If $A$ and $B$ are matrices and $B=AB{A}^{-1}$, then the value of $\left(A+B\right)\left(A-B\right)$ is

HARD

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IMPORTANT

Mathematics Crash Course MHT-CET>Chapter 10 - Determinants and Matrices>Exercise 1>Q 57

If $A=\left[\begin{array}{ll}1& 0\\ 1& 1\end{array}\right]$, then $A^{-n}$ is equal to

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IMPORTANT

Mathematics Crash Course MHT-CET>Chapter 10 - Determinants and Matrices>Exercise 1>Q 58

If $a, b$ and $c$ are in $\mathrm{AP}$, then determinant $\left|\begin{array}{lll}x+2& x+3& x+2a\\ x+3& x+4& x+2b\\ x+4& x+5& x+2c\end{array}\right|$ is

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IMPORTANT

Mathematics Crash Course MHT-CET>Chapter 10 - Determinants and Matrices>Exercise 1>Q 59

If $A=\left[\begin{array}{lll}2& 0& 0\\ 2& 2& 0\\ 2& 2& 2\end{array}\right]$, then $\mathrm{adj}\left(\mathrm{adj}A\right)$ is equal to 

MEDIUM

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IMPORTANT

Mathematics Crash Course MHT-CET>Chapter 10 - Determinants and Matrices>Exercise 1>Q 60

If $∆\left(x\right)=\left|\begin{array}{ccc}1& \cos x& 1-\cos x\\ 1+\sin x& \cos x& 1+\sin x-\cos x\\ \sin x& \sin x& 1\end{array}\right|$, then ${\int }_0^{\pi /4}∆\left(x\right)dx$ is equal to