85685 If the total maximum value of the function \(f(x)\)
\(=\left(\frac{\sqrt{3 \mathrm{e}}}{2 \sin \mathrm{x}}\right)^{\sin ^{2} \mathrm{x}}, \mathrm{x} \in\left(0, \frac{\pi}{2}\right)\), is \(\frac{\mathrm{k}}{\mathrm{e}}, \quad\) then
\(\left(\frac{\mathbf{k}}{\mathbf{e}}\right)^{8}+\frac{\mathbf{k}^{8}}{\mathbf{e}^{5}}+\mathbf{k}^{8}\) is equal to

85686 A wire of length \(22 \mathrm{~m}\) is to be cut into two pieces. One of the pieces is to be made into a square and the other into an equilateral triangle. Then, the length of the side of the equilateral triangle, so that the combined area of the square and the equilateral triangle is minimum, is :

85687 The function attains local maximum at

85688 If \(f(x)=a \ln |x|+b x^{2}+x\) has its extreme values at \(x=-1\) and \(x=2\), then what is the value of ' \(a\) '

85685 If the total maximum value of the function \(f(x)\)
\(=\left(\frac{\sqrt{3 \mathrm{e}}}{2 \sin \mathrm{x}}\right)^{\sin ^{2} \mathrm{x}}, \mathrm{x} \in\left(0, \frac{\pi}{2}\right)\), is \(\frac{\mathrm{k}}{\mathrm{e}}, \quad\) then
\(\left(\frac{\mathbf{k}}{\mathbf{e}}\right)^{8}+\frac{\mathbf{k}^{8}}{\mathbf{e}^{5}}+\mathbf{k}^{8}\) is equal to

85686 A wire of length \(22 \mathrm{~m}\) is to be cut into two pieces. One of the pieces is to be made into a square and the other into an equilateral triangle. Then, the length of the side of the equilateral triangle, so that the combined area of the square and the equilateral triangle is minimum, is :

85687 The function attains local maximum at

85688 If \(f(x)=a \ln |x|+b x^{2}+x\) has its extreme values at \(x=-1\) and \(x=2\), then what is the value of ' \(a\) '

85685 If the total maximum value of the function \(f(x)\)
\(=\left(\frac{\sqrt{3 \mathrm{e}}}{2 \sin \mathrm{x}}\right)^{\sin ^{2} \mathrm{x}}, \mathrm{x} \in\left(0, \frac{\pi}{2}\right)\), is \(\frac{\mathrm{k}}{\mathrm{e}}, \quad\) then
\(\left(\frac{\mathbf{k}}{\mathbf{e}}\right)^{8}+\frac{\mathbf{k}^{8}}{\mathbf{e}^{5}}+\mathbf{k}^{8}\) is equal to

85686 A wire of length \(22 \mathrm{~m}\) is to be cut into two pieces. One of the pieces is to be made into a square and the other into an equilateral triangle. Then, the length of the side of the equilateral triangle, so that the combined area of the square and the equilateral triangle is minimum, is :

85687 The function attains local maximum at

85688 If \(f(x)=a \ln |x|+b x^{2}+x\) has its extreme values at \(x=-1\) and \(x=2\), then what is the value of ' \(a\) '

85685 If the total maximum value of the function \(f(x)\)
\(=\left(\frac{\sqrt{3 \mathrm{e}}}{2 \sin \mathrm{x}}\right)^{\sin ^{2} \mathrm{x}}, \mathrm{x} \in\left(0, \frac{\pi}{2}\right)\), is \(\frac{\mathrm{k}}{\mathrm{e}}, \quad\) then
\(\left(\frac{\mathbf{k}}{\mathbf{e}}\right)^{8}+\frac{\mathbf{k}^{8}}{\mathbf{e}^{5}}+\mathbf{k}^{8}\) is equal to

85686 A wire of length \(22 \mathrm{~m}\) is to be cut into two pieces. One of the pieces is to be made into a square and the other into an equilateral triangle. Then, the length of the side of the equilateral triangle, so that the combined area of the square and the equilateral triangle is minimum, is :

85687 The function attains local maximum at

85688 If \(f(x)=a \ln |x|+b x^{2}+x\) has its extreme values at \(x=-1\) and \(x=2\), then what is the value of ' \(a\) '