86852 The area defined by \(1 \leq|x-2|+|y+1| \leq 2\) is

86853 Let the ellipse \(E: x^{2}+9 y^{2}=9\) intersect the positive \(x\) - axes and \(y\)-axes at the points \(A\) and \(B\) respectively. Let the major axis of \(E\) be a diameter of the circle \(C\). Let the line passing through \(A\) and \(B\) meet the circle \(C\) at the point \(P\). If the area of the triangle which vertices \(A, P\) and the origin \(O\) is \(\frac{m}{n}\), where \(m\) and \(n\) are coprime, then \(m-n\) is equal to

86854 The area of the region given by
\(A=\left\{(x, y): x^{2} \leq y \leq \min \{x+2,4-3 x\}\right.\) is :

86855 The area enclosed by the curve \(y=\log _{e}\left(x+e^{2}\right)\), \(x=\log _{e}\left(\frac{2}{y}\right)\) and \(x=\log _{e} 2\), above the line \(y=1\) is

86852 The area defined by \(1 \leq|x-2|+|y+1| \leq 2\) is

86853 Let the ellipse \(E: x^{2}+9 y^{2}=9\) intersect the positive \(x\) - axes and \(y\)-axes at the points \(A\) and \(B\) respectively. Let the major axis of \(E\) be a diameter of the circle \(C\). Let the line passing through \(A\) and \(B\) meet the circle \(C\) at the point \(P\). If the area of the triangle which vertices \(A, P\) and the origin \(O\) is \(\frac{m}{n}\), where \(m\) and \(n\) are coprime, then \(m-n\) is equal to

86854 The area of the region given by
\(A=\left\{(x, y): x^{2} \leq y \leq \min \{x+2,4-3 x\}\right.\) is :

86855 The area enclosed by the curve \(y=\log _{e}\left(x+e^{2}\right)\), \(x=\log _{e}\left(\frac{2}{y}\right)\) and \(x=\log _{e} 2\), above the line \(y=1\) is

86852 The area defined by \(1 \leq|x-2|+|y+1| \leq 2\) is

86853 Let the ellipse \(E: x^{2}+9 y^{2}=9\) intersect the positive \(x\) - axes and \(y\)-axes at the points \(A\) and \(B\) respectively. Let the major axis of \(E\) be a diameter of the circle \(C\). Let the line passing through \(A\) and \(B\) meet the circle \(C\) at the point \(P\). If the area of the triangle which vertices \(A, P\) and the origin \(O\) is \(\frac{m}{n}\), where \(m\) and \(n\) are coprime, then \(m-n\) is equal to

86854 The area of the region given by
\(A=\left\{(x, y): x^{2} \leq y \leq \min \{x+2,4-3 x\}\right.\) is :

86855 The area enclosed by the curve \(y=\log _{e}\left(x+e^{2}\right)\), \(x=\log _{e}\left(\frac{2}{y}\right)\) and \(x=\log _{e} 2\), above the line \(y=1\) is

86852 The area defined by \(1 \leq|x-2|+|y+1| \leq 2\) is

86853 Let the ellipse \(E: x^{2}+9 y^{2}=9\) intersect the positive \(x\) - axes and \(y\)-axes at the points \(A\) and \(B\) respectively. Let the major axis of \(E\) be a diameter of the circle \(C\). Let the line passing through \(A\) and \(B\) meet the circle \(C\) at the point \(P\). If the area of the triangle which vertices \(A, P\) and the origin \(O\) is \(\frac{m}{n}\), where \(m\) and \(n\) are coprime, then \(m-n\) is equal to

86854 The area of the region given by
\(A=\left\{(x, y): x^{2} \leq y \leq \min \{x+2,4-3 x\}\right.\) is :

86855 The area enclosed by the curve \(y=\log _{e}\left(x+e^{2}\right)\), \(x=\log _{e}\left(\frac{2}{y}\right)\) and \(x=\log _{e} 2\), above the line \(y=1\) is