79076 The value of \(\left|\begin{array}{ll}\log _{5} 729 & \log _{3} 5 \\ \log _{5} 9 & \log _{9} 25\end{array}\right|\)
\(x\left|\begin{array}{cc} \log _{3} 5 & \log _{27} 5 \\ \log _{5} 9 & \log _{5} 9 \end{array}\right| \text { is }\)

79077 If \(\theta \in\left(0, \frac{\pi}{2}\right)\), then
\(\left|\begin{array}{llc} (\sin \theta+\operatorname{cosec} \theta)^{2} & (\sin \theta-\operatorname{cosec} \theta)^{2} & 2020 \\ (\cos \theta+\sec \theta)^{2} & (\cos \theta-\sec \theta)^{2} & 2020\\ (\tan \theta+\cot \theta)^{2} & (\tan \theta-\cot \theta)^{2} & 2020\end{array}\right|=\)

79078 The values of \(x\) for which the given matrix \(\left[\begin{array}{ccc}-x & x & 2 \\ 2 & x & -x \\ x & -2 & -x\end{array}\right]\) will be non-singular, are

79079 If \(\alpha, \beta\) and \(\gamma\) are the roots of the equation \(x^{3}+\) \(\mathbf{p x}+\mathbf{q}=\mathbf{0}\), then value of the determinant \(\left|\begin{array}{lll}\boldsymbol{\alpha} & \boldsymbol{\beta} & \gamma \\ \boldsymbol{\beta} & \boldsymbol{\gamma} & \boldsymbol{\alpha} \\ \boldsymbol{\gamma} & \boldsymbol{\alpha} & \boldsymbol{\beta}\end{array}\right|\) is

79076 The value of \(\left|\begin{array}{ll}\log _{5} 729 & \log _{3} 5 \\ \log _{5} 9 & \log _{9} 25\end{array}\right|\)
\(x\left|\begin{array}{cc} \log _{3} 5 & \log _{27} 5 \\ \log _{5} 9 & \log _{5} 9 \end{array}\right| \text { is }\)

79077 If \(\theta \in\left(0, \frac{\pi}{2}\right)\), then
\(\left|\begin{array}{llc} (\sin \theta+\operatorname{cosec} \theta)^{2} & (\sin \theta-\operatorname{cosec} \theta)^{2} & 2020 \\ (\cos \theta+\sec \theta)^{2} & (\cos \theta-\sec \theta)^{2} & 2020\\ (\tan \theta+\cot \theta)^{2} & (\tan \theta-\cot \theta)^{2} & 2020\end{array}\right|=\)

79078 The values of \(x\) for which the given matrix \(\left[\begin{array}{ccc}-x & x & 2 \\ 2 & x & -x \\ x & -2 & -x\end{array}\right]\) will be non-singular, are

79079 If \(\alpha, \beta\) and \(\gamma\) are the roots of the equation \(x^{3}+\) \(\mathbf{p x}+\mathbf{q}=\mathbf{0}\), then value of the determinant \(\left|\begin{array}{lll}\boldsymbol{\alpha} & \boldsymbol{\beta} & \gamma \\ \boldsymbol{\beta} & \boldsymbol{\gamma} & \boldsymbol{\alpha} \\ \boldsymbol{\gamma} & \boldsymbol{\alpha} & \boldsymbol{\beta}\end{array}\right|\) is

79076 The value of \(\left|\begin{array}{ll}\log _{5} 729 & \log _{3} 5 \\ \log _{5} 9 & \log _{9} 25\end{array}\right|\)
\(x\left|\begin{array}{cc} \log _{3} 5 & \log _{27} 5 \\ \log _{5} 9 & \log _{5} 9 \end{array}\right| \text { is }\)

79077 If \(\theta \in\left(0, \frac{\pi}{2}\right)\), then
\(\left|\begin{array}{llc} (\sin \theta+\operatorname{cosec} \theta)^{2} & (\sin \theta-\operatorname{cosec} \theta)^{2} & 2020 \\ (\cos \theta+\sec \theta)^{2} & (\cos \theta-\sec \theta)^{2} & 2020\\ (\tan \theta+\cot \theta)^{2} & (\tan \theta-\cot \theta)^{2} & 2020\end{array}\right|=\)

79078 The values of \(x\) for which the given matrix \(\left[\begin{array}{ccc}-x & x & 2 \\ 2 & x & -x \\ x & -2 & -x\end{array}\right]\) will be non-singular, are

79079 If \(\alpha, \beta\) and \(\gamma\) are the roots of the equation \(x^{3}+\) \(\mathbf{p x}+\mathbf{q}=\mathbf{0}\), then value of the determinant \(\left|\begin{array}{lll}\boldsymbol{\alpha} & \boldsymbol{\beta} & \gamma \\ \boldsymbol{\beta} & \boldsymbol{\gamma} & \boldsymbol{\alpha} \\ \boldsymbol{\gamma} & \boldsymbol{\alpha} & \boldsymbol{\beta}\end{array}\right|\) is

79076 The value of \(\left|\begin{array}{ll}\log _{5} 729 & \log _{3} 5 \\ \log _{5} 9 & \log _{9} 25\end{array}\right|\)
\(x\left|\begin{array}{cc} \log _{3} 5 & \log _{27} 5 \\ \log _{5} 9 & \log _{5} 9 \end{array}\right| \text { is }\)

79077 If \(\theta \in\left(0, \frac{\pi}{2}\right)\), then
\(\left|\begin{array}{llc} (\sin \theta+\operatorname{cosec} \theta)^{2} & (\sin \theta-\operatorname{cosec} \theta)^{2} & 2020 \\ (\cos \theta+\sec \theta)^{2} & (\cos \theta-\sec \theta)^{2} & 2020\\ (\tan \theta+\cot \theta)^{2} & (\tan \theta-\cot \theta)^{2} & 2020\end{array}\right|=\)

79078 The values of \(x\) for which the given matrix \(\left[\begin{array}{ccc}-x & x & 2 \\ 2 & x & -x \\ x & -2 & -x\end{array}\right]\) will be non-singular, are

79079 If \(\alpha, \beta\) and \(\gamma\) are the roots of the equation \(x^{3}+\) \(\mathbf{p x}+\mathbf{q}=\mathbf{0}\), then value of the determinant \(\left|\begin{array}{lll}\boldsymbol{\alpha} & \boldsymbol{\beta} & \gamma \\ \boldsymbol{\beta} & \boldsymbol{\gamma} & \boldsymbol{\alpha} \\ \boldsymbol{\gamma} & \boldsymbol{\alpha} & \boldsymbol{\beta}\end{array}\right|\) is