79131 The constant term in the expansion of
\(\left|\begin{array}{ccc} 3 x+1 & 2 x-1 & x+2 \\ 5 x-1 & 3 x+2 & x+1 \\ 7 x-2 & 3 x+1 & 4 x-1 \end{array}\right| \text { is }\)

79132 If \(x, y, z \in R\), then the value of the determinant
\(A=\left[\begin{array}{lll}
\left(5^{x}+5^{-x}\right)^{2} & \left(5^{x}-5^{-x}\right)^{2} & 1 \\ \left(6^{x}+6^{-x}\right)^{2} & \left(6^{x}-6^{-x}\right)^{2} & 1 \\ \left(7^{x}+7^{-x}\right)^{2} & \left(7^{x}-7^{-x}\right)^{2} & 1 \end{array}\right] \text { is }\)

79134 If \(x y z\) are not equal and \(\neq 0, \neq 1\) the value of
\(\left|\begin{array}{ccc}\log x & \log y & \log z \\ \log 2 x & \log 2 y & \log 2 z \\ \log 3 x & \log 3 y & \log 3 z\end{array}\right|\) is equal to

79136 If \(a x^{4}+b x^{3}+c x^{2}+d x+e=\)
\(\left|\begin{array}{ccc}x^{3}+3 x & x-1 & x+3 \\ x+1 & -2 x & x-4 \\ x-3 & x+4 & 3 x\end{array}\right|\), then \(e=\)

79137 If \(\left|\begin{array}{lll}2 & 1 & 0 \\ 0 & 2 & 1 \\ 1 & 0 & 2\end{array}\right|\) then \(|\operatorname{adj} A|\)

79131 The constant term in the expansion of
\(\left|\begin{array}{ccc} 3 x+1 & 2 x-1 & x+2 \\ 5 x-1 & 3 x+2 & x+1 \\ 7 x-2 & 3 x+1 & 4 x-1 \end{array}\right| \text { is }\)

79132 If \(x, y, z \in R\), then the value of the determinant
\(A=\left[\begin{array}{lll}
\left(5^{x}+5^{-x}\right)^{2} & \left(5^{x}-5^{-x}\right)^{2} & 1 \\ \left(6^{x}+6^{-x}\right)^{2} & \left(6^{x}-6^{-x}\right)^{2} & 1 \\ \left(7^{x}+7^{-x}\right)^{2} & \left(7^{x}-7^{-x}\right)^{2} & 1 \end{array}\right] \text { is }\)

79134 If \(x y z\) are not equal and \(\neq 0, \neq 1\) the value of
\(\left|\begin{array}{ccc}\log x & \log y & \log z \\ \log 2 x & \log 2 y & \log 2 z \\ \log 3 x & \log 3 y & \log 3 z\end{array}\right|\) is equal to

79136 If \(a x^{4}+b x^{3}+c x^{2}+d x+e=\)
\(\left|\begin{array}{ccc}x^{3}+3 x & x-1 & x+3 \\ x+1 & -2 x & x-4 \\ x-3 & x+4 & 3 x\end{array}\right|\), then \(e=\)

79137 If \(\left|\begin{array}{lll}2 & 1 & 0 \\ 0 & 2 & 1 \\ 1 & 0 & 2\end{array}\right|\) then \(|\operatorname{adj} A|\)

79131 The constant term in the expansion of
\(\left|\begin{array}{ccc} 3 x+1 & 2 x-1 & x+2 \\ 5 x-1 & 3 x+2 & x+1 \\ 7 x-2 & 3 x+1 & 4 x-1 \end{array}\right| \text { is }\)

79132 If \(x, y, z \in R\), then the value of the determinant
\(A=\left[\begin{array}{lll}
\left(5^{x}+5^{-x}\right)^{2} & \left(5^{x}-5^{-x}\right)^{2} & 1 \\ \left(6^{x}+6^{-x}\right)^{2} & \left(6^{x}-6^{-x}\right)^{2} & 1 \\ \left(7^{x}+7^{-x}\right)^{2} & \left(7^{x}-7^{-x}\right)^{2} & 1 \end{array}\right] \text { is }\)

79134 If \(x y z\) are not equal and \(\neq 0, \neq 1\) the value of
\(\left|\begin{array}{ccc}\log x & \log y & \log z \\ \log 2 x & \log 2 y & \log 2 z \\ \log 3 x & \log 3 y & \log 3 z\end{array}\right|\) is equal to

79136 If \(a x^{4}+b x^{3}+c x^{2}+d x+e=\)
\(\left|\begin{array}{ccc}x^{3}+3 x & x-1 & x+3 \\ x+1 & -2 x & x-4 \\ x-3 & x+4 & 3 x\end{array}\right|\), then \(e=\)

79137 If \(\left|\begin{array}{lll}2 & 1 & 0 \\ 0 & 2 & 1 \\ 1 & 0 & 2\end{array}\right|\) then \(|\operatorname{adj} A|\)

79131 The constant term in the expansion of
\(\left|\begin{array}{ccc} 3 x+1 & 2 x-1 & x+2 \\ 5 x-1 & 3 x+2 & x+1 \\ 7 x-2 & 3 x+1 & 4 x-1 \end{array}\right| \text { is }\)

79132 If \(x, y, z \in R\), then the value of the determinant
\(A=\left[\begin{array}{lll}
\left(5^{x}+5^{-x}\right)^{2} & \left(5^{x}-5^{-x}\right)^{2} & 1 \\ \left(6^{x}+6^{-x}\right)^{2} & \left(6^{x}-6^{-x}\right)^{2} & 1 \\ \left(7^{x}+7^{-x}\right)^{2} & \left(7^{x}-7^{-x}\right)^{2} & 1 \end{array}\right] \text { is }\)

79134 If \(x y z\) are not equal and \(\neq 0, \neq 1\) the value of
\(\left|\begin{array}{ccc}\log x & \log y & \log z \\ \log 2 x & \log 2 y & \log 2 z \\ \log 3 x & \log 3 y & \log 3 z\end{array}\right|\) is equal to

79136 If \(a x^{4}+b x^{3}+c x^{2}+d x+e=\)
\(\left|\begin{array}{ccc}x^{3}+3 x & x-1 & x+3 \\ x+1 & -2 x & x-4 \\ x-3 & x+4 & 3 x\end{array}\right|\), then \(e=\)

79137 If \(\left|\begin{array}{lll}2 & 1 & 0 \\ 0 & 2 & 1 \\ 1 & 0 & 2\end{array}\right|\) then \(|\operatorname{adj} A|\)

79131 The constant term in the expansion of
\(\left|\begin{array}{ccc} 3 x+1 & 2 x-1 & x+2 \\ 5 x-1 & 3 x+2 & x+1 \\ 7 x-2 & 3 x+1 & 4 x-1 \end{array}\right| \text { is }\)

79132 If \(x, y, z \in R\), then the value of the determinant
\(A=\left[\begin{array}{lll}
\left(5^{x}+5^{-x}\right)^{2} & \left(5^{x}-5^{-x}\right)^{2} & 1 \\ \left(6^{x}+6^{-x}\right)^{2} & \left(6^{x}-6^{-x}\right)^{2} & 1 \\ \left(7^{x}+7^{-x}\right)^{2} & \left(7^{x}-7^{-x}\right)^{2} & 1 \end{array}\right] \text { is }\)

79134 If \(x y z\) are not equal and \(\neq 0, \neq 1\) the value of
\(\left|\begin{array}{ccc}\log x & \log y & \log z \\ \log 2 x & \log 2 y & \log 2 z \\ \log 3 x & \log 3 y & \log 3 z\end{array}\right|\) is equal to

79136 If \(a x^{4}+b x^{3}+c x^{2}+d x+e=\)
\(\left|\begin{array}{ccc}x^{3}+3 x & x-1 & x+3 \\ x+1 & -2 x & x-4 \\ x-3 & x+4 & 3 x\end{array}\right|\), then \(e=\)

79137 If \(\left|\begin{array}{lll}2 & 1 & 0 \\ 0 & 2 & 1 \\ 1 & 0 & 2\end{array}\right|\) then \(|\operatorname{adj} A|\)