87055 The area bounded by the curve \(4 y^{2}=x^{2}(4-x)\) \((x-2)\) is equal to

87056 The area (in sq. units) of the region, given by the set \(\left\{(x, y) \in R \times R|x| \geq 0,2 x^{2}+\leq y \leq 4-2 x\right\}\) is

87057 if the area of the bounded region \(R=\{(x, y)\) : \(\left.\max \left\{0, \log _{e} x\right\} \leq y \leq 2^{x,} \frac{1}{2}, \leq x \leq 2\right\}\) is \(\alpha\left(\log _{e} 2\right)^{-1}\) \(+\beta\left(\log _{\mathrm{e}} 2\right)+\gamma\), then the value of \((\alpha+\beta-2 \gamma)^{2}\) is equal

87058 If the straight line \(x=b\) divides the area enclosed by \(y=(1-x)^{2}, y=0\) and \(x=0\) in two parts \(R_{1}(0 \leq x \leq b)\), and \(R_{2}(b \leq x \leq 1)\) such that \(R_{1}-R_{2}=\frac{1}{4}\). Then \(b\) equals

87055 The area bounded by the curve \(4 y^{2}=x^{2}(4-x)\) \((x-2)\) is equal to

87056 The area (in sq. units) of the region, given by the set \(\left\{(x, y) \in R \times R|x| \geq 0,2 x^{2}+\leq y \leq 4-2 x\right\}\) is

87057 if the area of the bounded region \(R=\{(x, y)\) : \(\left.\max \left\{0, \log _{e} x\right\} \leq y \leq 2^{x,} \frac{1}{2}, \leq x \leq 2\right\}\) is \(\alpha\left(\log _{e} 2\right)^{-1}\) \(+\beta\left(\log _{\mathrm{e}} 2\right)+\gamma\), then the value of \((\alpha+\beta-2 \gamma)^{2}\) is equal

87058 If the straight line \(x=b\) divides the area enclosed by \(y=(1-x)^{2}, y=0\) and \(x=0\) in two parts \(R_{1}(0 \leq x \leq b)\), and \(R_{2}(b \leq x \leq 1)\) such that \(R_{1}-R_{2}=\frac{1}{4}\). Then \(b\) equals

87055 The area bounded by the curve \(4 y^{2}=x^{2}(4-x)\) \((x-2)\) is equal to

87056 The area (in sq. units) of the region, given by the set \(\left\{(x, y) \in R \times R|x| \geq 0,2 x^{2}+\leq y \leq 4-2 x\right\}\) is

87057 if the area of the bounded region \(R=\{(x, y)\) : \(\left.\max \left\{0, \log _{e} x\right\} \leq y \leq 2^{x,} \frac{1}{2}, \leq x \leq 2\right\}\) is \(\alpha\left(\log _{e} 2\right)^{-1}\) \(+\beta\left(\log _{\mathrm{e}} 2\right)+\gamma\), then the value of \((\alpha+\beta-2 \gamma)^{2}\) is equal

87058 If the straight line \(x=b\) divides the area enclosed by \(y=(1-x)^{2}, y=0\) and \(x=0\) in two parts \(R_{1}(0 \leq x \leq b)\), and \(R_{2}(b \leq x \leq 1)\) such that \(R_{1}-R_{2}=\frac{1}{4}\). Then \(b\) equals

87055 The area bounded by the curve \(4 y^{2}=x^{2}(4-x)\) \((x-2)\) is equal to

87056 The area (in sq. units) of the region, given by the set \(\left\{(x, y) \in R \times R|x| \geq 0,2 x^{2}+\leq y \leq 4-2 x\right\}\) is

87057 if the area of the bounded region \(R=\{(x, y)\) : \(\left.\max \left\{0, \log _{e} x\right\} \leq y \leq 2^{x,} \frac{1}{2}, \leq x \leq 2\right\}\) is \(\alpha\left(\log _{e} 2\right)^{-1}\) \(+\beta\left(\log _{\mathrm{e}} 2\right)+\gamma\), then the value of \((\alpha+\beta-2 \gamma)^{2}\) is equal

87058 If the straight line \(x=b\) divides the area enclosed by \(y=(1-x)^{2}, y=0\) and \(x=0\) in two parts \(R_{1}(0 \leq x \leq b)\), and \(R_{2}(b \leq x \leq 1)\) such that \(R_{1}-R_{2}=\frac{1}{4}\). Then \(b\) equals