79032 Let \(d \in R\), and
\(A=\left[\begin{array}{ccc} -2 & 4+d & \sin \theta-2 \\ 1 & \sin \theta+2 & d \\ 5 & 2 \sin \theta-d & -\sin \theta+2+2 d \end{array}\right]\)
\(\theta \in[0,2 \pi]\). If minimum value of \(\operatorname{det}(A)=8\), then the value of \(d\) is

79033 Let the matrix \(A=\left[\begin{array}{lll}0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0\end{array}\right]\) and the matrix
\(B_{0}=A^{49}+2 A^{98}\). If \(B_{n}=A d j\left(B_{n-1}\right)\) for all \(n \geq 1\), then \(\operatorname{det}\left(B_{4}\right)\) is equal to :

79034 Let \(A\) be a \(3 \times 3\) matrix such that \(\mid \mathbf{a d j}(\mathrm{adj}\) \((\operatorname{adj} A)) \mid=12^{4}\) Then \(\mid A^{-1}\) adj \(A \mid\) is equal to

79035 Which let \(f(x)=\left|\begin{array}{ccc}\mathbf{a} & -1 & 0 \\ \mathbf{a x} & \mathbf{a} & -1 \\ \mathrm{ax}^{2} & \mathbf{a x} & \mathbf{a}\end{array}\right|, \mathbf{a} \in \mathbf{R}\). Then the sum of which the squares of all the values of a for \(2 f^{\prime}(\mathbf{1 0})-f^{\prime}(\mathbf{5})+\mathbf{1 0 0}=\mathbf{0}\) is :

79036 Let \(S=\{\sqrt{n}: 1 \leq n \leq 50\) and \(n\) is odd \(\}\) Let \(a \in S\)
and \(A=\left[\begin{array}{ccc}1 & 0 & a \\ -1 & 1 & 0 \\ -a & 0 & 1\end{array}\right]\)
If \(\sum_{\mathrm{a} \in \mathrm{S}} \operatorname{det}(\operatorname{adj} \mathrm{A})=100 \lambda\), then \(\boldsymbol{\lambda}\) is equal to

79032 Let \(d \in R\), and
\(A=\left[\begin{array}{ccc} -2 & 4+d & \sin \theta-2 \\ 1 & \sin \theta+2 & d \\ 5 & 2 \sin \theta-d & -\sin \theta+2+2 d \end{array}\right]\)
\(\theta \in[0,2 \pi]\). If minimum value of \(\operatorname{det}(A)=8\), then the value of \(d\) is

79033 Let the matrix \(A=\left[\begin{array}{lll}0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0\end{array}\right]\) and the matrix
\(B_{0}=A^{49}+2 A^{98}\). If \(B_{n}=A d j\left(B_{n-1}\right)\) for all \(n \geq 1\), then \(\operatorname{det}\left(B_{4}\right)\) is equal to :

79034 Let \(A\) be a \(3 \times 3\) matrix such that \(\mid \mathbf{a d j}(\mathrm{adj}\) \((\operatorname{adj} A)) \mid=12^{4}\) Then \(\mid A^{-1}\) adj \(A \mid\) is equal to

79035 Which let \(f(x)=\left|\begin{array}{ccc}\mathbf{a} & -1 & 0 \\ \mathbf{a x} & \mathbf{a} & -1 \\ \mathrm{ax}^{2} & \mathbf{a x} & \mathbf{a}\end{array}\right|, \mathbf{a} \in \mathbf{R}\). Then the sum of which the squares of all the values of a for \(2 f^{\prime}(\mathbf{1 0})-f^{\prime}(\mathbf{5})+\mathbf{1 0 0}=\mathbf{0}\) is :

79036 Let \(S=\{\sqrt{n}: 1 \leq n \leq 50\) and \(n\) is odd \(\}\) Let \(a \in S\)
and \(A=\left[\begin{array}{ccc}1 & 0 & a \\ -1 & 1 & 0 \\ -a & 0 & 1\end{array}\right]\)
If \(\sum_{\mathrm{a} \in \mathrm{S}} \operatorname{det}(\operatorname{adj} \mathrm{A})=100 \lambda\), then \(\boldsymbol{\lambda}\) is equal to

79032 Let \(d \in R\), and
\(A=\left[\begin{array}{ccc} -2 & 4+d & \sin \theta-2 \\ 1 & \sin \theta+2 & d \\ 5 & 2 \sin \theta-d & -\sin \theta+2+2 d \end{array}\right]\)
\(\theta \in[0,2 \pi]\). If minimum value of \(\operatorname{det}(A)=8\), then the value of \(d\) is

79033 Let the matrix \(A=\left[\begin{array}{lll}0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0\end{array}\right]\) and the matrix
\(B_{0}=A^{49}+2 A^{98}\). If \(B_{n}=A d j\left(B_{n-1}\right)\) for all \(n \geq 1\), then \(\operatorname{det}\left(B_{4}\right)\) is equal to :

79034 Let \(A\) be a \(3 \times 3\) matrix such that \(\mid \mathbf{a d j}(\mathrm{adj}\) \((\operatorname{adj} A)) \mid=12^{4}\) Then \(\mid A^{-1}\) adj \(A \mid\) is equal to

79035 Which let \(f(x)=\left|\begin{array}{ccc}\mathbf{a} & -1 & 0 \\ \mathbf{a x} & \mathbf{a} & -1 \\ \mathrm{ax}^{2} & \mathbf{a x} & \mathbf{a}\end{array}\right|, \mathbf{a} \in \mathbf{R}\). Then the sum of which the squares of all the values of a for \(2 f^{\prime}(\mathbf{1 0})-f^{\prime}(\mathbf{5})+\mathbf{1 0 0}=\mathbf{0}\) is :

79036 Let \(S=\{\sqrt{n}: 1 \leq n \leq 50\) and \(n\) is odd \(\}\) Let \(a \in S\)
and \(A=\left[\begin{array}{ccc}1 & 0 & a \\ -1 & 1 & 0 \\ -a & 0 & 1\end{array}\right]\)
If \(\sum_{\mathrm{a} \in \mathrm{S}} \operatorname{det}(\operatorname{adj} \mathrm{A})=100 \lambda\), then \(\boldsymbol{\lambda}\) is equal to

79032 Let \(d \in R\), and
\(A=\left[\begin{array}{ccc} -2 & 4+d & \sin \theta-2 \\ 1 & \sin \theta+2 & d \\ 5 & 2 \sin \theta-d & -\sin \theta+2+2 d \end{array}\right]\)
\(\theta \in[0,2 \pi]\). If minimum value of \(\operatorname{det}(A)=8\), then the value of \(d\) is

79033 Let the matrix \(A=\left[\begin{array}{lll}0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0\end{array}\right]\) and the matrix
\(B_{0}=A^{49}+2 A^{98}\). If \(B_{n}=A d j\left(B_{n-1}\right)\) for all \(n \geq 1\), then \(\operatorname{det}\left(B_{4}\right)\) is equal to :

79034 Let \(A\) be a \(3 \times 3\) matrix such that \(\mid \mathbf{a d j}(\mathrm{adj}\) \((\operatorname{adj} A)) \mid=12^{4}\) Then \(\mid A^{-1}\) adj \(A \mid\) is equal to

79035 Which let \(f(x)=\left|\begin{array}{ccc}\mathbf{a} & -1 & 0 \\ \mathbf{a x} & \mathbf{a} & -1 \\ \mathrm{ax}^{2} & \mathbf{a x} & \mathbf{a}\end{array}\right|, \mathbf{a} \in \mathbf{R}\). Then the sum of which the squares of all the values of a for \(2 f^{\prime}(\mathbf{1 0})-f^{\prime}(\mathbf{5})+\mathbf{1 0 0}=\mathbf{0}\) is :

79036 Let \(S=\{\sqrt{n}: 1 \leq n \leq 50\) and \(n\) is odd \(\}\) Let \(a \in S\)
and \(A=\left[\begin{array}{ccc}1 & 0 & a \\ -1 & 1 & 0 \\ -a & 0 & 1\end{array}\right]\)
If \(\sum_{\mathrm{a} \in \mathrm{S}} \operatorname{det}(\operatorname{adj} \mathrm{A})=100 \lambda\), then \(\boldsymbol{\lambda}\) is equal to

79032 Let \(d \in R\), and
\(A=\left[\begin{array}{ccc} -2 & 4+d & \sin \theta-2 \\ 1 & \sin \theta+2 & d \\ 5 & 2 \sin \theta-d & -\sin \theta+2+2 d \end{array}\right]\)
\(\theta \in[0,2 \pi]\). If minimum value of \(\operatorname{det}(A)=8\), then the value of \(d\) is

79033 Let the matrix \(A=\left[\begin{array}{lll}0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0\end{array}\right]\) and the matrix
\(B_{0}=A^{49}+2 A^{98}\). If \(B_{n}=A d j\left(B_{n-1}\right)\) for all \(n \geq 1\), then \(\operatorname{det}\left(B_{4}\right)\) is equal to :

79034 Let \(A\) be a \(3 \times 3\) matrix such that \(\mid \mathbf{a d j}(\mathrm{adj}\) \((\operatorname{adj} A)) \mid=12^{4}\) Then \(\mid A^{-1}\) adj \(A \mid\) is equal to

79035 Which let \(f(x)=\left|\begin{array}{ccc}\mathbf{a} & -1 & 0 \\ \mathbf{a x} & \mathbf{a} & -1 \\ \mathrm{ax}^{2} & \mathbf{a x} & \mathbf{a}\end{array}\right|, \mathbf{a} \in \mathbf{R}\). Then the sum of which the squares of all the values of a for \(2 f^{\prime}(\mathbf{1 0})-f^{\prime}(\mathbf{5})+\mathbf{1 0 0}=\mathbf{0}\) is :

79036 Let \(S=\{\sqrt{n}: 1 \leq n \leq 50\) and \(n\) is odd \(\}\) Let \(a \in S\)
and \(A=\left[\begin{array}{ccc}1 & 0 & a \\ -1 & 1 & 0 \\ -a & 0 & 1\end{array}\right]\)
If \(\sum_{\mathrm{a} \in \mathrm{S}} \operatorname{det}(\operatorname{adj} \mathrm{A})=100 \lambda\), then \(\boldsymbol{\lambda}\) is equal to