Physics-
General
Easy
Question
A point
moves in counter-clockwise direction on a circular path as shown in the figure. The movement of
is such that it sweeps out a length
, where
is in metres and
is in seconds. The radius of the path is
. The acceleration of
when
is nearly
![](data:image/png;base64,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)
The correct answer is: ![14 blank m divided by s to the power of 2 end exponent](data:image/png;base64,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)
As ![S equals t to the power of 3 end exponent plus 5](data:image/png;base64,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)
![fraction numerator d s over denominator d t end fraction equals 3 t to the power of 2 end exponent equals v](data:image/png;base64,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)
![therefore a subscript t end subscript equals fraction numerator d v over denominator d t end fraction equals 6 t](data:image/png;base64,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)
at ![t equals 2 blank s e c](data:image/png;base64,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)
![open vertical bar stack a with rightwards arrow on top close vertical bar equals square root of a subscript c end subscript superscript 2 end superscript plus a subscript t end subscript superscript 2 end superscript end root](data:image/png;base64,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)
![equals square root of open parentheses fraction numerator v to the power of 2 end exponent over denominator R end fraction close parentheses to the power of 2 end exponent plus a subscript t end subscript superscript 2 end superscript end root equals square root of open parentheses fraction numerator 4 t to the power of 4 end exponent over denominator R end fraction close parentheses to the power of 2 end exponent plus open parentheses fraction numerator d v over denominator d t end fraction close parentheses to the power of 2 end exponent end root](data:image/png;base64,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)
![equals square root of open parentheses 7.2 close parentheses to the power of 2 end exponent plus 144 end root](data:image/png;base64,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)
![open vertical bar stack a with rightwards arrow on top close vertical bar equals 14 m divided by s to the power of 2 end exponent](data:image/png;base64,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)
Related Questions to study
physics-
In a two dimensional motion of a particle, the particle moves from point
, position vector
. If the magnitudes of these vectors are respectively,
=3 and
and the angles they make with the
-axis are
and 15
, respectively, then find the magnitude of the displacement vector
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486202/1/923334/Picture13.png)
In a two dimensional motion of a particle, the particle moves from point
, position vector
. If the magnitudes of these vectors are respectively,
=3 and
and the angles they make with the
-axis are
and 15
, respectively, then find the magnitude of the displacement vector
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486202/1/923334/Picture13.png)
physics-General
physics-
A block(B) is attached to two unstretched springs
with springs constants
representively (see Fig. I) The other ends are attached to identical supports
and
not attached to the walls. The springs and supports have negligible mass. There is no friction anywhere. The block
is displaced towards wall I by small distance
and released. The block returns and moves a maximum distance y towards wall 2.Displacements
are measured with respect to the equilibrium position of the block
The ratio
is
![](data:image/png;base64,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)
A block(B) is attached to two unstretched springs
with springs constants
representively (see Fig. I) The other ends are attached to identical supports
and
not attached to the walls. The springs and supports have negligible mass. There is no friction anywhere. The block
is displaced towards wall I by small distance
and released. The block returns and moves a maximum distance y towards wall 2.Displacements
are measured with respect to the equilibrium position of the block
The ratio
is
![](data:image/png;base64,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)
physics-General
physics-
A small roller coaster starts at point A with a speed
on a curved track as shown in the figure.
The friction between the roller coaster and the track is negligible and it always remains in contact with the track. The speed of roller coaster at point
on the track will be
![](data:image/png;base64,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)
A small roller coaster starts at point A with a speed
on a curved track as shown in the figure.
The friction between the roller coaster and the track is negligible and it always remains in contact with the track. The speed of roller coaster at point
on the track will be
![](data:image/png;base64,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)
physics-General
Physics-
A body of mass
is moving with a uniform speed
along a circle of radius
, what is the average acceleration in going from
to
?![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/904297/1/923294/Picture8.png)
A body of mass
is moving with a uniform speed
along a circle of radius
, what is the average acceleration in going from
to
?![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/904297/1/923294/Picture8.png)
Physics-General
physics-
A body of mass
is moving with a uniform speed of
on friction less surface under the influence of two forces
and
. The net power of the system is
![](data:image/png;base64,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)
A body of mass
is moving with a uniform speed of
on friction less surface under the influence of two forces
and
. The net power of the system is
![](data:image/png;base64,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)
physics-General
physics-
From an inclined plane two particles are projected with same speed at same angle
, one up and other down the plane as shown in figure, which of the following statements is/are correct?
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMsAAACeCAMAAACrZg5FAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAMAUExURf////39/eLi4vr6+vPz897e3rKysnNzcy8vLxcXF6ysrNnZ2bOzs4aGhk1NTRMTEwAAAAQEBLS0tPHx8bm5uYODg1ZWVikpKW1tbeHh4ZOTk1RUVC0tLREREYqKir29vbW1tba2tru7u6mpqcrKyomJiQICAiAgIB0dHQkJCQwMDB4eHh8fHygoKBQUFAMDAzU1Nf7+/uXl5Z2dnXBwcEZGRhgYGAUFBY2NjcTExL6+vr+/vwYGBpqamsHBwcDAwMnJyXl5eQoKCu/v787Oznh4eD4+PgEBAV9fXwcHB62trRkZGTQ0NDIyMt/f36qqqmlpaRsbG6enp/n5+VpaWuPj45CQkEpKSvX19SoqKtPT05ubm2RkZIKCgu7u7vv7+2pqavj4+GhoaPb29kxMTH9/f7Gxsfz8/BoaGmBgYHx8fBAQEMfHx9HR0UVFRezs7E9PTzg4ODo6Ol1dXdzc3D09PQsLC6GhoQgICCUlJdTU1IuLi8vLy6+vrxYWFq6urhUVFcLCwl5eXs3NzUFBQWxsbLe3t8/Pz9bW1ltbW5ycnEBAQJmZmXd3d2VlZbi4uKampg8PDzk5OdXV1W9vbxwcHFVVVefn5+Dg4JSUlKKioqCgoPLy8p+fn+3t7SEhIdLS0oCAgDs7O2NjY3p6eurq6lNTU4GBgaOjo46OjtjY2C4uLg0NDUlJSYyMjLq6uiMjI3V1devr64+Pjz8/P56ensbGxjMzM9fX14WFhVdXV3R0dGdnZ/T09GJiYlBQUENDQ7y8vCIiIubm5oiIiHZ2dqurqw4ODuTk5GFhYTY2NhISEiYmJsjIyFJSUmZmZjc3N5KSktvb29ra2lhYWIeHh5aWlsXFxbCwsFFRUenp6X5+foSEhDAwME5OTqSkpEdHRzExMZGRkTw8PGtra/f39/Dw8EtLS5iYmN3d3VxcXKioqJWVlUJCQqWlpW5ubnJycisrK5eXl9DQ0Ojo6CQkJHFxcczMzMPDw0hISH19fSwsLCcnJ1lZWURERAAAAP//vj4AAAEAdFJOU////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////wBT9wclAAAACXBIWXMAABcRAAAXEQHKJvM/AAAHJElEQVR4Xu2dT5KrIBDGPQIXYMOFuAEn0q1XcU+59xycwB31WkVtEzTS/gFezS/JPJPUm5qer7s/QMMUf/zxhXH/5o6RlebSPckYI1rLGSDcC5miIA49xAFU7rUsMWXduDgGWiHFcN97eF6aH7J33zIarQvCoTXncJ++fD7gbfjqfQv+H2vct4yGKqupUCbavhdwG7983vqKlf3OW/Be/FgABQ2scfF07jUvhrXu6AvJ6yaFWAaUkt0Yz2FPrvmO/7TMFrV2T5LAlJ09LGCx0+cqVheFTSqW33Re3boxNdPSZRdoEC6G5jvLVD2plYkuAgppSj7DrRoPFiCUqSNkokvTiKadYpBDaSBMM6ddHrpI+HGrObla1qD+0OtlBJeHLi0X8JgjkHwdTAu9vFzYVPzlkBJiMd3yQxvL3BPB9doKstDFQHXLsindUyj3ivEOUqtkDWoEWdRLxxmMHzfDG1NxbsHscU/LQ5eOl2ao/w0l/+hoefSxoV7EWuQTLeu2TpNPH6u2XWo2e0QeuvS1LOwmoSCUtRU4MvH9uu45nrqsZo/Iw1+KEqbBaEzZN77lmkzGlspqJIvgn31gJBNdih61LDB7Xyi51AtGssY/Uc4kxxDl1uwR2ekyzuz95KZLdbDolJcuHrNH5NLHRpTdX+sDcsox0xyfnMlIF++4BZNPveyYPSKbHNsze0QuuuyaPSITXfbNHpGHLgdmj8ihj6kjs0dkkGPHZo9IX5dlGf8nydcLOOTXIsUOqecYhHL6QozEdTnhkCtp6xIUStq6nDF7RMp97JTZIxLOsXNmj0hXFzD7IFXSrZfTZo9INMfOmz0iTV0CzB6RpC6/Fil2SFEXfM4+hAT72O9Fih3Sy7FAs0ckp0uo2SNSqxcwe2ooqeVY8LgFk5QuFLNHpKQLyewRCeliLMXsEen0sZCZvZ9kcoxq9ohUdCGbPSKReqGbPSKNHAOzvx5KGrq0F8wekYIuJ5fxfxJfl4tmj4jex66aPSJ2jtFm9n4i60Kc2fuJWy+95hfHLZioOXaH2SNi6nKL2SMi6lLeHMpVXYwkGzaYvTu6i4t9rGXUX+1dZo+4lmM9J8Zyn9kjrulSMVosN5o94lK99IwWy+WZvZ9LOWZpscC45T6zR1zRRUIoe591PgDM/k6HXLmgixq2QwiPJeycfQgXdBk3ROCh/nK32SPofUyNmweE6vJgKBdyDPpxuC43zez9kHUBmxxjCfotX1rG/wm1XsDtgmNR3QNmj6Dm2PCB+sBYnjF7BFWXljWjMvp0+j9k9giqLqpXgrU1Qx/TPubORYodLvhLyYzafoDzgF7rG2f2fi6Mk61WhTqZYkI/ZfYIur+YgKb0pEOu0HUR5/P/9pm9H3q9dKfb8aNmj6DnmMbbMxwRfoEeEbIuZ8sFzP72RYodyLqU5+aGj5s9gqyL5e7gkOfNHkHtY+rUxmVPzez90MeWJ1Ln3mX8n1B1ad22U0f0j83s/VDrpdY/++w7Zo8g5pjhPxvtS2aPIOoiftb0W2aPIOqylEu/U9wRQiHqorS7wBM6lU+gp2f2fmh9TM3jksZaz8zyTbNH0HJs3nNK8l7qL2FeNXsETZd5+89KK/gOH4XxrtkjaPWi3W9gcBlrp+OZl80eQcqxnrvK7rQquu3spH9jZu+HpEs1dWRVaVZ3dtOx5PlVptsh6dKxUQpjOdcNx0by+rgFQ9HF6HlVbKiXDrXfGA65Qulj6wrMUC927b9xQyHl2HqBAuhiFuOPY/YIii52abrCGjk/iWT2CEK9GMbmTdqU7WarjGX2CEKO9azq5uuJoStPYUUzewRBl44rmGi5ViabMYR4Zo8g6DIOYMTcssaV/ohmjwjXxUzj/RJVusA7/8YjvI8Ne7MO1EtnlvSP3t1KeI7ZaQAztIDxX7AbK+MXCxCuSzOP8d0G4GD28Nj0YyOipFxwvcjlx+7Ho3EZX1nckcFqooxlgnOsXBcsB4Wc2asGVX/LeJQOHaqLqtcrYGA0tph9v14dorQVzUunjzaE6qLQgmXJ0Dn7dsmyYR2witHZQnXBZ1wFQ6mk5jWA8USmQTOB1wjtY2h9/8PslxNlw6TmxHrz/QTmGNSCOwKz306HlZttyoZXbYfke41AXZYFS8/MvpouCa0ZtLEofyYssF6WTfI9WwZMfgOdDtoz6tzvEZhj84LlYPafzC1uqJczp81uJ1AX16z85+ztJFULU5ohntcJ08WMC5Z7ixTV5P0KxgP1t2zPE6bLuGC5mv0H5ZSAqrbCouHZa4T1sWHBUu3O7KVrXkJ//U2jVwjKsWHB0qx/0+cT6QpeVTyCuwTqAiMtc/DBArm8pT6s5x2C6gXm+B9mv6F1DTsWQTlW88NC6M5eUfYQIboMC5bjX2PcuTd288Kbt+HeN2GxpE1ALEpKWR7c0GGcW4Rx0x9//DcUxT+0JUewGLKWQwAAAABJRU5ErkJggg==)
From an inclined plane two particles are projected with same speed at same angle
, one up and other down the plane as shown in figure, which of the following statements is/are correct?
![](data:image/png;base64,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)
physics-General
physics-
A particle of a mass
is subjected to a force which varies with distance as shown in fig. If it starts its journey from rest at
, its velocity at
is
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)
A particle of a mass
is subjected to a force which varies with distance as shown in fig. If it starts its journey from rest at
, its velocity at
is
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)
physics-General
maths-
P is a point on the ellipse
, S and
are the focii of the ellipse then ![S P plus S to the power of l end exponent P equals](data:image/png;base64,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)
P is a point on the ellipse
, S and
are the focii of the ellipse then ![S P plus S to the power of l end exponent P equals](data:image/png;base64,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)
maths-General
physics-
As per given future to complete the circular loop what should be the radius if initial height is ![5 blank m](data:image/png;base64,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)
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486200/1/923095/Picture4.png)
As per given future to complete the circular loop what should be the radius if initial height is ![5 blank m](data:image/png;base64,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)
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486200/1/923095/Picture4.png)
physics-General
physics-
Figure shows four paths for a kicked football. Ignoring the effects of air on the flight, rank the paths according to initial horizontal velocity component, highest first
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486199/1/923080/Picture1.png)
Figure shows four paths for a kicked football. Ignoring the effects of air on the flight, rank the paths according to initial horizontal velocity component, highest first
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486199/1/923080/Picture1.png)
physics-General
maths-
The area of the region bounded by
and y=1 in sq. units is
![](data:image/png;base64,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)
The area of the region bounded by
and y=1 in sq. units is
![](data:image/png;base64,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)
maths-General
maths-
Area of the region bounded by
and y=2 is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAREAAADLCAYAAABJRqdzAAAgAElEQVR4nO2d53Jb2ZWFP+ScASIDBAMYJXWwPeVy1TzDvMC8i19nnmKmpmpq2nYHtSRmBIIACCIHIoeL+dFzj6V2d1sSxSDyfFWqarsk4hLAXfecffZeS7NcLpdIJBLJR6K97wuQSCSfN1JEJBLJjZAiIpFIboQUEYlEciOkiEgkkhshRUQikdwIKSISieRGSBGRSCQ3QoqIRCK5EVJEJBLJjZAiIpFIboQUEYlEciOkiEgkkhshRUQikdwIKSISieRGSBGRSCQ3QoqIRCK5EVJEJBLJjZAiIpFIboT+vi9Acv8sFgvm8zmKoqDVajEajWg0mvu+LMlnghSRJ46iKAwGA7rdLuPxGKvVis/nw2w23/elST4TpIg8ccbjMdVqlXw+T7PZZGVlhd3dXVZWVtBoNGi1cscr+W2kiDxhlssl/X6fi4sLvv32Wy4uLlhbW8Pr9eJyuTAYDGg0Grm1kfwmUkSeMJPJhFqtRjab5fXr12SzWTqdDtFoFIfDQSAQwOl03vdlSh44UkSeMJ1Oh/PzczKZDOVymaurK+bzOX/7299wOBw8f/4cm82GXi+/JpJf51F/O6bTKaPRiPl8jtFoxGg0otfr0el0931p94YaeDibzahUKpyenpLNZmk0GgwGA2azGa9evSIUChEKhfD5fNhstidTG1kulyiKwnw+Z7FYsFwu0Wq1GAwGKaa/wqN9VxRFod/vUywW6fV6OBwOfD4fTqfzST9dFUVhMpnQbre5uLigUChQqVTo9XpMJhPm8zmNRoPLy0uurq4IBALodDosFsuTqI0sFguur6/F+wFgNpvxeDw4HI57vrqHyaO9k5bLJcPhkHK5TKVSwel0MhgMCIfD6PX6Jysis9mMdrtNoVDg4uKCZrPJcDhkNpuxXC7FKq3X63F5eYnX68VkMolV3GNnOp3SaDSoVCqMRiMMBgMejweLxSJF5Fd4tN+K5XLJYrFgPB7TaDSo1+v0ej2m0yk2mw2bzXbfl3gvTCYTKpUKh4eHlEoltFotLpeLXq/HfD7H7/eTSCTQ6/UUCgUMBgNWqxWPx/PoRWS5XDIYDCgUCpyenqIoCn6/H6PRyGKxuO/Le7A86m+FVqvFZDIxm824vLykWq2iKArhcJhgMHjfl3fnLJdLxuMxpVKJ169f0+v18Pl8aLVasXRfXV3liy++YDqdUi6Xmc1mBAIB1tbWsFgs9/wb3B6KorBYLOh2u5ydnfHy5UtsNhsGg4FwOPwktnIfy6MVEa1Wi81mIxqNUq1WqVar1Ot1Li4uyOfz+Hw+3G43BoPhvi/1Tlkul8xmM2azGU6nk83NTXq9Hp1Oh8lkQiwW48WLFzSbTZrNJuPxmMlkgqIo933pt4paJyoUChQKBVqtFhaLBZvNhsvletQCelMerYhoNBrsdjurq6uMx2M6nQ7z+Zxer8fh4SFGo5GdnR1CodCTOXkAMBqN+P1+NjY2cDqdrK2tUalUODk5oVar4XQ6icfj+P1+ut0uWq0Wj8fzqE+05vM57Xab09NTjo6OuL6+xu/3s7q6yurqKqFQ6Mluf9+HRy0i6rFuKpWi1WoxnU6pVqvkcjmWy6V40thsNnQ63ZNYsppMJsLhMLPZDLfbjd/vZzKZYLVa0ev1GI1G3G434XCY0WjEcrkkGAxiNBrv+9JvBUVRuL6+FnUitRayvr5OOp0mFos9ehG9KY9WRN7G5XKRSqUYjUbMZjMymQy5XI6VlRXcbjfBYBCn0/notzYajQaDwYDP50Ov12O324XQvi2ger1erFYURcHtdj/aoupwOOTq6opCoUA+n6derxOLxVhfX2d1dfVJbnk/lMf5zfgZJpOJWCzGZDKh1WqJL0smk8Hr9Yrxd51O9+i3Nnq9HpfLJYqGi8Xind9ZURQ0Gg1Wq5VYLMZyuXy0R+KLxYJWqyX6ZarVqjihWl1dJRKJPKlGu4/l8X0zfgGNRoPD4SASiZBMJrm8vOT09JRMJoNOp0On0+F0OrFarfd9qbeOKpjq9kRdgSyXy3f+qELymJnP55RKJd68eUMul0NRFJLJJOl0mnA4jNPplNuY9+BJiIiK0+lkdXWV0WjEaDTib3/7G/1+H4/HQywWw+12P/obR/J3+v0+uVyO169f0+l0SCaT/P73v2dvbw+XyyUF5D15UiJiNBoJBAIsl0va7TbZbJZ2u02pVCKbzWK1WkkkEk9qD6zO0jwl5vM5nU6Hk5MTstks3W4Xk8nE2toa+/v7xOPxR1tIvg2elIioS3S/38/m5iZfffUVmUyG4XDIyckJRqMRm81GKBS670uV3CLqMf/f/vY3KpUKXq+XSCTCxsYGgUBAurp9IE9ORIxGo+iFePHiBRqNhkqlwuXlJVarlZWVFWw2GxaL5VEWE58y8/lcnMYcHR1xdHTEdDoVdZBkMonL5XoSR/2fkid3l6jHnF6vl62tLWazGdPplMvLS1FwtVgsRCIRXC6XrMw/EtS5mKurKzKZDJlMhmazSSAQIJlMsr6+/qj7YW6TJyciKlarlWg0ymQyoV6v02w2abfbHB0dYTQaMRgMmM1mTCaTFJJHwHw+p9vtUigUODs74/LyUgzYJZNJEokEHo9HrkI+gicrIlqtFrPZTCQSYX19nV6vx8nJCW/evGEwGGC323G73WKIT/J5M5lMaDQanJ6ecnx8zHg8JpFIsLW1RSwWw+v1yu3rR/Lk3zWbzcba2hqj0Yh6vc7BwQGDwUDMTGi1WnQ6nfyCfcYoikK326VSqXB+fs7V1RV+v58XL16wt7eHz+eT25gb8OTvDIPBIDoUS6USmUyGVqtFNpslEAig1+uftBPaY6DT6ZDP5ykUCnS7XcxmM6urq+zs7JBMJsXslOTjkHcGP/WPeL1eNjc3ub6+5ujoSNRHnE4nPp9P1kY+UxaLBaVSiePjY4rFIgaDgbW1Nba3t4lEIjgcDvR6vayF3AApIvw0T+JwOEgkEsznc2azGcfHx1xdXVEqlQgGg5jNZnla8xmhRoOqjvb5fJ52u43L5WJ9fZ21tTXxcJDcDCki/HTsazabhSlxv98XpjzlcllMu5rNZmlO85kwm83odDrkcjlOT0+pVCpoNBpWVlbY3NwkHo9jtVrlCuQTIEXk/9HpdNjtdsxmM/1+n1qt9k57tNlsxufzEY1GAcSQmuThoSgKo9GIYrEoQrnG4zErKyvEYjFWV1fx+/2yzvWJkO/iW6gTrmo3q6IonJyccHFxgdFoJBgMChMj+QV8uCwWC/r9PmdnZ3z77bc0m03i8TjpdJpUKiUK5pJPg3wnfwGn08nW1haTyYROp0Or1aJYLPLjjz+i1+tJpVLC2OehooYwLRYL4RGi2h485hWU2lR2dXVFNpulUCjgcrlIp9M8f/6cWCwmZ2M+MQ/3LrhHNBoNHo+HeDxOIpGg1WpRqVT44YcfUBQFo9GI1Wp9sIY1i8WC0WjE9fU1l5eXNBoNjEYjsVhMGO08Vvr9PoVCgZOTEyqVClqtllAoxOrqKvF4/ElEX9w18t38DdxuN6lUiuFwSK/XI5PJsFwuiUajwhHtIRbn5vM5/X6fSqXCd999x+vXr7Hb7fzpT38SCYCPkdlsRr1e5+zsjOPjYwaDgehKDYfDuFwu2VR2C0gR+Q3UyAm1SHd2dka1WqVQKLCysoLBYBBzNg+J5XLJfD5nNBpxeXnJ4eEhDoeD9fV1kS/z2FgsFnQ6HcrlMhcXF1QqFfR6Pevr62xtbREIBLBarbKp7BaQIvIbqPEKs9mMdDpNpVIR2TUOh0NktD40EVEDqC0Wi0hvG4/HzGazR5sfMxgMKJVK5PN5Li8vxSpkb2+PdDotDZdvESkiv4FqYhQIBNjd3WUymfDq1Sva7TZnZ2d4vV5CodCDC7tWndz9fj/hcBi/3y8GDh/jk3i5XIrhulwux2AwEJk66XSaSCSCVqt9UJ/RY0KKyD9Bo9Fgs9lYXV1Fr9czn8/57rvvaDQa5PN5sRLx+/0P5gbVarVYLBa8Xi8+nw+n08l8PsdgMDyYa/yUTCYTSqUSR0dHlEol7HY78Xicra0tgsGgXIHcMlJE3gM19Fqv19Nut6nX65TLZSqVCq9fv34n9OkhPO1U31Q11Hw6nTKZTBgOhwyHQxaLxaMQE7XuU6/XxTZmPp8TCoXY29tjbW1NHufeAVJE3gP1GNfpdJJIJNjc3GQ2m9FoNMhkMlgsFjFObjQa732gS+3YbLfbtFotOp0O0+mURqNBo9EgEAjgcrkAHoTofQyLxYLBYEClUhHbmPl8jtfrJRaLkUgk8Pv98jTmDpAi8oH4/X7S6TTD4VB4VJhMJkKhEFarFY/Hg91uv9cnvXqDqY5t4/GY6XRKt9ul0WjQ6/Xu/RpvwnK5FI2AmUyG77//nnK5LOogyWSSlZUVzGbzZyuSnxNSRD4Qu91OLBaj0+lweXlJrVbj6uqKw8NDLBYL6XQai8Vyrzeo2q2qKAo2m01MJ6uNVoqiiC2PRqP57G40tQ+mVquRz+fJ5XIsFgvS6TSbm5tEo1EZPHWHSBH5QNRu1kQiQaPRoN/vc3p6yl//+leWyyUej+fel9E6nU5EX/zud78jkUigKAo+n4+VlRWcTqcQDrUVXj290Gg0D7IL922m06mYsC6Xy3Q6HcLhMBsbG2xvb+P3+2Ut5A6RIvIRqIHXW1tbLBYLYat4dHTE9va2aES7r1MB1R/FbrcTiUT+YdXx9upjPB4zmUyYz+di9bJYLO7lut+H5XJJt9ulWCySy+Xo9XrCI2R9fZ1IJCI9Qu4YKSIfidVqJRwOM51OKRQKNBoNxuMxuVxOtJVHIpF7W1K/zzZlOp2KzJ1er8dkMmE8HtPr9ZhOp2i12gc1Z6LGPpTLZc7Ozsjn8ywWCzY2Ntjb2yMQCEgBuQcezjfkM0Nt6AqFQjx79ozJZCKya3Q6HSaTCbvd/mDd0BaLBa1Wi9PTU9HOPxgMaLVaFAoFQqEQLpcLm832IGom6olTpVIhn89TLBbpdrsEg0F2dnZIp9PYbDYURXmQ7/djRorIR6K6obndbtbX15nNZgDUajXK5TJutxuPxyPqEw+lyKfaBg4GAy4uLjg+PiaTyVCr1cTQ3sHBAT6fj83NzXsvEsPfZ4GazSaZTIZ8Ps9gMMBqtRKJREgmk8LC8iEI3lNDisgN0Gg0Ii3PaDTS7/dpt9u0223Oz8/FfE00GsVqtd735Yqbsd/vU61WyWQynJyccH5+TqvVYjgcUi6X+fHHHwkEAni9Xtxu971e+9vDhOVymaOjIy4uLtDpdEQiEVKpFNFoVNgySBG5e6SI3BCdTofD4cBqtYpVSD6fp1QqMZ/PReSE0WhEq9Xe61JbURSGw6FoET8+PqbdbotCqmroo/4O8Xgcu91OMBi8NyFRr7lWq5HL5UQxNZVKsbm5yfr6Ol6v995XS08ZKSKfCJ1ORyKRYHt7m+FwyKtXrygUCmg0GmKxmFiV3KeIzGYzut0uh4eH/Nd//Rftdhun08nq6qrIJNbr9Wi1WprNJicnJ+L4N5FI3MtTfjab0Ww2yeVyZDIZGo0GVquVWCzG1tYWiURCmmffM1JEPiEej4fNzU16vR75fJ5yuUwmk+H09FQ80dV287tmOp1Sr9c5Pz/n5OSEXC73Tj1HdUJTrQStVisXFxcsl0vMZjMOh0PEit4ViqLQ6/W4uLjgzZs3lMtlbDYbqVSK9fV14vH4vb2fkr+j+/Of//zn+76Ix4I6M6Pu4afTqSi4qgN6drv9zlcjai/L6ekph4eHFItFFEVhZ2eHvb09jEYj1WqVTqfD2toaf/rTn7DZbFxeXtLtdtHr9cIO0mAw3Mn1K4rC9fU1pVKJg4MDXr16xXA4ZGNjgy+//JL19XVpuPxAkJ/AJ8ZutxONRnn+/DlarZbj42MuLi5wOp2srKzgcDhwuVx3todXb8ZiscjJyQmZTIb5fM7W1hZ/+MMfiMVinJ+fY7VasVgsRKNR9vf3ubq64scffxQ+pRaLBbPZLGInb3trM5lMqFarnJ+fUywWabVaeDwe0uk0Ozs7994VLPk7UkQ+MSaTCa/Xy9ramrDsU+36zs/PsVgsaLVa3G73nVzPz5uz1CnedDrN9vY2NpuNWq2GXq9Hr9fjdDrx+/0MBgNxIjIcDtHr9bhcLhwOh+jGvc0VSbfbpVAokM/n6XQ62O12EokEiURCWB3KfpCHgRSRT4xqYhSNRtFoNNRqNdrtNr1ej1wuh06nw2KxYLfbb30priiKcGE7OjqiWCwynU5xu91sb2+La1SvQ6PRYDAYMJlM6PV6JpMJtVqNarXKYrEgGAwSjUZxOBxia3MbK5L5fE6j0SCbzYoR/2Qyyf7+vnCrl6cxDwcpIreAOrsSDofZ2dkRAlIul5nNZtjtdjweDz6f79amaNXR/1wux5s3bzg4OKDRaGCz2TCZTGJUXmW5XL7zZ7FYiMa0xWLB9fU1FxcXIg0wHo/fympqPB7TarVEV2qn0yEUCon6jeqyL3k4SBG5RWw2G5ubm8zncyaTCcfHx5yfn4stg9o6/6kH9dTuznw+z8HBAWdnZxQKBXq9Hh6Ph9Fo9JvCpYqIVqvF4XCIsHPVY1btfXE4HJ90RaAoCp1Oh+PjY05OTmi321gsFsLhMGtra0SjUdmV+gCRInKLaLVa/H4/m5ubVKtVqtWqaJpyOBwi0uBTOaGpoVXqVuDw8JBsNstkMhGDaePxmNFo9E+jIxRFQafT4fP5WF9fJ51O0+12KZVK2Gw2wuEwdrsdr9f7SbZl6mxMuVzm1atXZLNZdDod0WhUTOc+hK5fyT8iReQWUYXB5XKRTCapVqvCmfzHH3/EarXidrsxGo2YTKYbC8loNOLi4kKEN2UyGRRFEW35Go2GyWQiRv5/DdXUSO3GVQOgrq6u6HQ6NJtNstksBoOBjY0N4Sb/sahdqc1mk4uLC7LZLO12m42NDTY2NlhdXZX9IA8YKSJ3gMlkIhKJsLW19U7Tl8/nI5lMCjG56Rh7v98nm83y8uVLzs7OaDQarK6usrGxQTAYZDAYcHV1Jeoev8VyuRSRGcFgkLW1NVwuF9VqlW63Sz6fB8BsNoseEvg4z9bpdEq73aZUKnF+fk6tVkOr1YrXjUQisiv1ASNF5A7Q6XR4PB6SyaQ4clUnZs/OzsRpiLpa+Fh6vR6FQoHT01OazSYWi4XV1VXS6bSIl2w2m+8lIipqo5nf78fj8QgDplqtJorEbrebSCTy0ZEUw+GQy8tLTk5OKJVK6PV6IpEI8XhcWBLI05iHixSRO8JqtRIKhRiNRtRqNUajEd1ul6OjI0wmEy6XC6fT+dFF1uVySafToVQqUS6XMRqNrK2t8dVXX7GxscFyuXznaPR9RQR+qu3YbDZcLhfj8Zhms0mxWKTZbGI2m/H7/cKk+kNv9sViQa/Xo1gs8ubNG6rVKisrKzx//pzV1VWZXPcZIEXkjtBoNMKu8Pnz5yyXS3744QcuLy+x2+0EAgHsdjsrKysfdCMul0shTEdHR5yfn9Pr9VhbW2Nvb49nz57h8XgoFosf9TRX6yc6nQ6r1crq6iper1cUQSeTCWazGZPJxM7OzgetppbLpdjGlMtl6vU6er2ezc1Nnj17RiQSkV6pnwFSRO4QrVaL0+lkY2MDgHa7zdHREbVa7Z1tTSAQeK+fpygK4/GYcrnMy5cv+ctf/sL5+Tmz2QyXy0U8HheipNFoPmgb83NUYTAajeh0OtGI1mw2RQKgak+oduX+M4bDIefn52Kbpa7WNjc3xeSznI15+MhP6I4xGo14vV5Rq2i323Q6HbLZLIDov1CLrL/2VF8ulwyHQ1qtFrlcjtevX3N0dES9XhfFzp9vLz5WQH4JRVGYTqfM53ORQBeLxdDr9QSDQVFo/bV/u1gshHhmMhnG4zHhcJitrS1xGnPfIWCS90OKyB2jdqiqQUvtdpvj42MajQaLxULk56qO8b/2JJ5MJjSbTQqFArlcjmq1ynA4ZDabieDu2ypGLpdLMZSnpv/1+32Oj4/R6XQYjcZfDQ9XFIXJZCLsEnK5HPV6HbfbTTweZ3NzUzTiSQH5PJAick+YTCYSiQTX19c0m01h8pzJZAiHwxgMBhE29XPm8zm9Xo/Ly0vRjao2lKnzLLcZSrVcLkUPSTweZ3V1lfl8TiaTESstp9OJ0+n8h3+rFlILhYI4jRmNRkSjURKJBMlkEofDIQXkM0KKyD2h0+lwu92iCU21VlSzfdWW+F/qj1CPiU9PT3n9+jXX19cEg0Hxd4fDoWhdvw3UQqvH42FnZ4fd3V3y+Tynp6dks1n8fj8Wi+UXA7XVbcxf//pXvvvuO0ajEcFgkHg8TjQa/VXhlDxc5Kd1j6ht8RsbG/T7fQAODg4YDod4vV5SqdQ/PM1ns5moJbx584Y3b97g8/n405/+hMFgENk38GlrICpqcVan0+FyuVhbW2N3d5fBYMDLly85Pz8X80Aul4toNPrOv1ULwd988w0HBwek02nRmbqysiIF5DNEfmL3jMViIRaLMZvNmM1mnJ+fU6/XyWaz5PN5sWJRDXjUEOsffviB169fUygUcDqdhMNhHA4Hfr+fcrkM3I6IqD9Xo9EItzav14vZbOb6+pper8d8Pkej0RAIBHC73SIP5vr6mkqlQqlUolarodFoiEajbG9vk0wmf3H7I3n4SBG5ZzQaDQ6Hg0gkwvX1NXt7e5yentJqtXj9+jXz+ZyNjQ28Xi/z+ZxCoSCmXIvFIr1eTxQ67yMyQVEUYQfZ6XRoNBoAOJ1OYrEYLpdLZAFXKhVOTk6oVCp4vV7i8Tj7+/vE43E8Ho9sKvtMkSLyADAajXg8HuLxOM+fPwd+CsFSJ1lNJpMwUj4+PqZUKtHtdplMJiwWC7EyuEkfyMegDuqpVgfq9SiKwmAwIJfLYbFYmM1mmEwmzs/POT09pdFoEAqF2NjYYGtrC7/f/2CS9iQfjhSRB4BGo8FkMuH3+9nZ2WG5XPLdd9/RaDQ4Pz/HZDJRqVSoVCoUCgWGwyEulwu32814PBbicZsnMr+FGjCl0+nECsPj8Yj2/tFohM/no1gscnFxwWw2I51O8+zZM+LxuHQq+8yRIvJAUI9MTSYTWq2WSqVCrVajVqsBPxVhi8Uig8GAQCBANBoVcZjAb4723zZq85h6LL25uYndbieXy1EqlZhOp0QiEVqtFu12G4/HI5rtvF6v3MZ85kgReUCoZsmxWIzt7W0xV3J2dsZgMOD6+ppQKEQikcDpdKLVaqlWq8D9ioj6+gaDgUAgwObmJk6nUzi2q7YEanbx5uYmGxsbMvLhkSA/wQeI2WwmlUrRbDbFfE29XsfhcIhagsvlotfrYbVaRW3iPlGPfdWQrmAwyHQ6pVQqcXp6SqfTIZVKsbOzw7Nnz4hGo1JAHgnyU3yAqC3lqh1gv9+n0+kIzxGXy4XH48HhcDyY7JW3j31tNhtOp1PES6jt+GpXrdPplCZDjwhpm/0AmU6ntFotGo0G4/EYk8kkBtr6/T79fp/RaMRsNrv3FcjbqCui6XTKcDik0+kwGAxETIYaYVGtVrm+vr7vy5V8IuRK5AGhend0Oh3K5TJXV1ci78VisTCZTESkAvzkZDadTrFarfd+PKoeMatmS1qtVpzOuN1uLBYLJpOJVqvFxcUF0WgUl8sl3Nvv+/olH48UkQfCcrkUwdrqXEypVEKn07G9vY2iKJRKJebzucjILZfLDAaDOw/a/iW0Wi3z+Vy4q6lCuFgsSCaT+Hw+RqMRrVaLk5MTAoEAPp8Pn88nfFQknyfyk3sgLBYL+v0+V1dXnJ6ekslk6HQ6JBIJ9vf3sVgsHB0dcXFxIfxNz8/P6Xa7RKPRexURjUaDVqtlNpuJuAqn00mr1cJms4m0vUKhwMHBAaVSSQgJIE9pPnPkJ/dAmE6nVKtVvv32W7777jtqtRo+n49UKsX29jYulwuXy4XRaCSbzZLJZERCHHAvLe9vo9VqmUwmdLtd9Ho9oVBIhHd98cUXInFPTdI7OjpCr9cLtzdZaP18kSLyABiPxzQaDfL5PN9++y0nJyeEw2H29vbY3t4mEongdDpxuVwoikKr1WI4HNLr9RiPx8DHRTV8CtRViF6vF0N29Xodr9fL/v4+X3/9NTs7O8LeQLUReP36NT/88AN+v59IJCJsFSWfH1JE7hk1hyaXy5HP52k0Guj1euLxOOl0mkQiIQqTNpuN1dVVEokEoVCIVqvFdDoVHaN3fVKjFkT1ej0mkwmr1cpwOBTJeKlUinQ6TSgUEn9XnaspFot0u10RVqXVaqUx82eKFJF7RFEUcSOdnp5SLpdF9uzu7i7xeByv1/tOOp7X6xWxnKrH6XK5ZDAYiC3FXYmJOny3WCyEZYHJZBKBWaurq/j9fsxmM8vlEqfTiaIorK+vc3V1RTabFdm7Wq0Ws9lMKBS69yKx5MOQInJPLBYLrq+vuby8pFAoUCqVGAwGBINB0uk06XRaxEi8PZzmcDhYXV2l3W7T6/XEcWqz2aTf79PtdpnNZsDtbXHU49zZbEa326XdbjOdTrHZbHi9XjY2Ntjc3CQajYr2fEC4wCeTSbrdLoqiUK/XKRaLmM1mXC4XVqv1nX8jefhIEbknFosF1WqV09NTcrkc7XYbk8nE1tYWX3/9tTAZ+vl0q9FoJBQKsbW1RavVol6vMxwOyefzzGYzLi8vGY1GwO2KyGKxYDAYcHl5icfjodVqibjQdDrN5uYmgUDgnevXaDSYzWaCwSDPnz9Hp9PxzTffUKlUhB2k6or2W27xkoeFFJE7RvX7UGMi1NwZvV5PNBpld3eXdDqNwWD4xafx2yFYm5ubtFot8vk8l5eXVKtVEUMJ3MrTXK1tLBYLut0uuVwOnU5Ht9vF6XSSSCRYW1sjFotht9t/8WfYbDaSySRarZbLy0sajQaNRoPj42PMZjMWi4V4PJWPdUsAABj8SURBVC6PfT8T5Kd0x4zHY7rdLtlsllevXpHL5UQdQbUJ/GfB3hqNBrfbzfr6OoqiYDKZePnyJZVKhXa7jdvtRqPR3IpHh3oas1gs6HQ6nJyciK5a1WRI3cb82kpILcaqW7dms0k+n+f4+JjJZCJOotTwKtnN+rCRInKHzOdz2u02mUyGH3/8kWw2y3Q6JR6Ps7W1xdbWFm63+71+lnoTmkwmlsulCOxWhWOxWDCfzz/576CKiGq6PB6P8fv9bG9vs7e3x8bGxntn8hoMBtbW1ri+vmY4HIqA82g0it/vJxaLSff3zwD56dwRiqLQ7/ep1WqcnJxwcnLCcDgkGAySSqWIx+P4/f5/ugpR0Wg0WCwWdDodyWSSzc1N8vk8g8GA5XLJZDIRDvLw923Up3yqqysKh8NBOBwmmUwSDAaxWq3vJSJ6vR6fz0cymaRWq1GpVMT2zO/3i8G9X9sWSR4GUkTuAPWp3Ww2KZfL5HI5rq6u8Hq97OzssLW1JW6+D0XNwd3Z2eHq6koI1WQyodFoMBgM3luY3ofZbMZ8Pker1Yp+kLW1NVKpFCsrK6Iw+j6oQhgMBllfXxcperVajTdv3uByuUSGjbRPfLhIEbkDFosFrVaLQqEgIiE0Gg2RSIStrS2SySRut/ujlu1qoTWVSlGv16nX6+I1i8Ui+XyeaDQq/D4+5uerPw9+CiHv9/vodDp8Ph/r6+vs7++L/Ny3e1reB71eL0K8FosFk8mEly9fUi6XKRQKhEIhYWQtheRhIkXkDlgsFpRKJVEHmc1mrK6usr+/TyqVIhAI3MhcyGg0irpEs9lkuVzSbrc5PDzE4/GIJ7k6q/IhvF1Ivb6+Jp/Pi8yYcDjMixcv+N3vfkc8Hv9oSwK1ycxkMjEcDkWkaD6fFy7wVqv1o1ZqkttHisgtM5vNuLq6IpPJcHZ2RrvdJhKJ8OWXX7K3tyc6Um+CRqPBYDAQCoXY29tjsVjw+vVrzs/POTg4IJFIMBqNmEwm7x0poTrIq12pg8GAdrvN69evqdVqOJ1OIpEI+/v7bGxs3KivQ6PRYLPZMBqNohtX7eY9OjrCaDTi8/lIJBKyCe0BIkXkFplOpxSLRV69esXp6Snj8Vi4oe/u7hKNRj/prIjD4SCRSIhp2lqtJvw7hsMh1WqV8XgsVhf/DEVRmM1mDIdD6vU6V1dXHB4eMhwOxYlSMpn8ZI1hBoOBSCTC119/DfwUKdpoNMjlcgQCAUwmEx6PR87XPDCkiNwCaph2q9Xi8PCQb7/9lnq9jtvtJh6Ps729TSwW++SBTVqtVoRgtdttOp2OaGqr1WoUi0Umk8l7iYjRaBTBU51Oh0KhQKFQoFariR4VNXhKUZRPskJYLpc4HA42NzeZTqd0u13Ozs64urri1atX6HQ6UYTW6XSyf+SBIEXkFlBXAsVikUwmw+XlJXq9nnA4zPr6OvF4HJfLdSuFQpPJJI5N+/0+mUyGUqlEoVCg2WxiMBh+9eZTty9arRaXy0UwGGSxWNDr9cSEsclkIhwOk0gkhEXBp9piqA1yagRnMpmk0+lQq9U4Pj5+pzZis9l+83eR3B1SRD4xqkNZuVzm7OyMi4sLRqMRsViM1dVV1tbWWFlZubXAJvVGi8ViwrJQFZDr6+t/Gpq9WCzQaDQiyU6N7xyNRuJEaWNjg2g0itfrvTW3eY/Hw9raGr1eT3TGTiYTQqGQmMmR3awPA1ml+oQsl8t3LA6Pj4+5vr5mZWWFjY0NUqkUkUjk1pun9Hq9SJlTT3+sVqt4cr+dU/PzJjT1KNjpdBIIBHA6nYzHY9rtNmazWXTWqj/ztm5ii8VCLBZjY2ODUCiETqejWq2SyWQ4Pz+n3W7fSkeu5MORK5FPiGowlM1mxXGu1+vl66+/Zn9/n3g8/pszJZ8SdVsQj8fZ39+nVquhKAqTyYT5fM50OgXeTc5Tr0vNjzGbzWKlodVqCYVC4jTGbrffaju6muubTCZpNBq0Wi3Oz8/JZrPY7XasVit+v//B5O48ZaSIfCKWyyWNRoOzszOOj49FBm08HufLL79kfX39XlzNfT4fz58/5/r6msViQblcZjKZUCqVSKVS4u+pAqKeyFxfX9PpdBiPx9hsNtxuN+l0mtXVVXw+351cu3q0u729Lf53Lpfj7OyMUCjEysoKsVjsk3bkSj4cKSI3RF3+DwYDCoUCh4eHXFxcoNPpWF9fJ51Os7Kycm/+GDabjXA4zNbWFp1OB51Ox2w24+DgAK/XSzgcfmdrMx6P6XQ6jEYjYZTk9/tFfq7D4bjT67darYRCIeCnnB3VV/bi4gKXywVAPB6XK5J7RIrIDZnP54zHYyqVCplMhkKhwGAwYGVlhb29PdLp9L0a7Oh0Olwul3ATWy6XIiTc6XQKa8XZbCacyi4uLuj3+9TrdRRFIRQKsb29fS83q7ot0+l0pNNpMT7QaDQ4PDwUZkaBQOBJhWCpU9rT6ZTZbMZyucRgMIjV7l2OCEgRuQGLxUKETR0dHZHP55lOp7hcLlZXV0mn0w/CfNhkMuH3+1lfX2exWDAcDsnlcuRyOZxOJ71e751x/OPjY1F89Xg8RKNRotEobrf7zudX1PqMTqcjkUjQ7XZZLBZUKhWKxSIWi0V0/b5dPH7MvL1ibDab1Ot1JpMJHo+HSCSCx+PBZrPd2WclReQGqE/u09NTvv32W66urnC5XCQSCdLpNKlU6qMH6z41DoeDZDKJRqOhXq9TKBREO36/36fRaIhMGJvNht/vFx2wsVgMr9d7rwNwOp2OQCDA/v4+0+mUTqdDsVgkm83i8Xiw2+2EQiGxannMLJdLMWOUzWY5PDzk+vqaZDLJF198wXK5RKfTidOz27CBeJv7/3Z/piwWC9rttmgoK5VKmM1mNjY2hMWhupd/CKhu7DqdjlarRavVolwuUywWqdVqXF5e0u/3GY/HXF1dEQgEWF9fZ3d3l9XV1X/aX3IXWCwWkskko9GIer0uir+vXr1Cr9ej1+vv9Al8X2i1WgwGA3q9XgiKmoqo1+u5vr4mEong9/tF3Mht9SUB6P785z//+dZ++iOm1+uRyWQ4PDwkm80yn89ZW1vjq6++Ynt7m3A4/CCX1SaTCaPRiMlkYjAYkM1mOT09FXM1JpOJQCDA7u6uCJ5Sc2MeCiaTSdQE1FrUeDwmFAoJ/5HHjvoZqjUQNTjs6uqKUqlEtVrl+vpaRHGonr238Tne+krk9evXt/0St87bb7xOp0NRFMrlMq9eveLo6IhqtYrFYhGB1RcXFzQajXcauO4b9VpmsxmTyYTRaES/36dUKlEsFun3++j1ehaLBePxmF6vR61Ww26302g0gPv/PdTfYTgc0mg0GI/HtFotjo6O6PV6BINB5vM5Pp9PCIk6jfyYULco8/lcCIVOp6PdbovWArUud3V1xe7uLslkkpWVFRwOxydfldy6iPzHf/zHbb/EnfG2t4b6galuYhaLRcRhut1uDAbDg/wCK4qCoiiMRiOy2SzVapXRaCRS9MbjMfV6nTdv3jAcDnn16tWD+V3evnl6vR6NRoNCoUCn02G5XPI///M/FItF7HY7RqMRrVZ756mAd4UqqJPJhF6vx9XVFcVikUajwXQ6pdFo0O12qdfrVKtVXrx4wbNnz26l4fHWReSbb7657Ze4E9TTitlsJrw55vM5iqKg0WiYTCZUq1V6vd6vnhC8/f+9fUPex82p5sbo9XpcLhej0Yj5fC7qCWoyndFovLUV1W99kX/Jie3thrj5fC4+A7fbjaIonJ2dUSgUMBqN6PV6zGbzO0ZM9y2Cn5K3oztUP91Op8P19bWwb1BXlMvlUkyQB4PBT34tty4ib3dFfq68/fS+vLyk3W6jKAqBQIBQKPRO1OXPn9hvt5K/3cfwtunPfaHVaoVpkjqkt7Kywvb2Nl6vF0VRbv3Ge3ufrr4nv/T+qf/98/cQftqiqcVhtTPXZrPhcDiED8ld/C53jSoi6mmVumJUzboNBgMOhwOPx4PL5RKh6p+aWxeRf//3f7/tl7h11Kdes9nk22+/FUv/vb09vvzyS9HJqU7N/tI8ys//G+53v66O3asuaP/5n//J2dkZe3t7/Nu//RuxWOxOQsJ/biPwa+/J2+LxtpgYDAbRgfu///u/lEolDAYDgUCAZ8+esbu7KzKAH9PW5u0o0+vra4rFIm/evOHo6IhGo8FisSAQCLC3t8fvf/97dnd3CYfDWCyWT15cvXUR+dd//dfbfolbR/VIPTo6eqdpKxwO43a78Xq9RCIRvF7vOycD6v5dtRbsdrvCFMjhcLCysnJncyi/hVarFS7rsViMf/mXfyGRSNz66yqKwuXlJZ1OB6PRiMvlEqHg8Pf37+1u2mazyWQywWKx4HQ6hUt+OBzGaDRyeHhIv9/HZrMRj8f54osvHtRR+6dE7e8plUp0u10CgQDT6VQ45sViMZ4/f87+/j6hUEhYUH5qZJ/Ie9Dr9Tg+Pua///u/qVar+Hw+dDod19fXfP/995TLZdLpNDs7O0QiERwOB4qiMBgMxLHb0dERx8fHwkg5kUjwxz/+kd/97nf3nqvy86f8XfmYdrtdvvnmG46OjnA4HKTTaZ49e0YkEkGn0zEYDOj1egwGAwaDAWdnZ7x69YpmsymsDr766iv29/eJxWK8ePGC+XzOwcGByPdR3eJvywTqvhgOh5TLZTKZDAcHB5TLZRRFIZFI4PP5iEQihMNh8XCzWq231vQoReQ3mE6nNJtNzs/P+eGHH/jxxx+x2Wxsb29jNpspFAqUy2XR6GOxWMT+ezKZ0G63xVFppVKhUChQLBbpdDpcXFzg8XhYX1+/VxFRj3zVbZg6C3SbqNsVNdD85cuXuFwulsslXq9XZNfU63UajQb9fp/RaESlUhEubSaTiXq9LnxHgsEgiUSCVqtFpVKhWq1ydnaGwWBgOp2ytbXFysrKoxjUU42vut0u7XabVqvFaDQiEAgI35pEIvFOre42HwxSRH6F2WxGs9kkl8txcnLC1dUVJpOJeDxOKpXCarWKPeloNGKxWDCbzUShS+2mnE6n2O12NjY2RCPX6empqJ88NdSah9osphY/zWYzOp1OiJl63KweP5vNZtbW1kQ8RrPZRKvVMplMRCaO3W4nHA6ztrbGcDgkn8/z5s0bkdJntVpxOp0PYgzhJmg0GsxmM36/X3SpDgYDPB4PiUSClZUV/H7/nUVsfN7v5i2hKr2aDXt2dsZgMBDTrKlUCqPRKJ7ijUZDNKGpx8CDwUCEPHm9XkKhELFYjEgkgsFgoNlsPtlkN0VRmE6naDQaEQWhpuGpJ1aqKM9mM+H5GovFiMfjrKyscHJywvX19TsrCzUNcH19nclkwtXVFblcDrPZTCqVEnaOn9og+65R3ys1cTAYDDKbzTCbzbhcLqxW6516rEgR+QXG4zHlcpmTkxMymYzIWdnZ2eGLL74gGo2KmsdgMBDLRZ1OJxqc1BvAbDbj8/lwuVyMx2PMZjPz+ZxGo0Eikbj3Cd/7RHUnU7dTNpvtnTF29TTFbDbj9Xrxer2Mx2MURRFP32g0+k4x2+FwEI/Hmc/nov271WqRyWSw2WyYTKZ7tWb4FKinUgaDQUSZqgbb9+GCL0XkF+h0OpyennJwcEClUkFRFOLxOH/4wx9YX1/HbDbT6/XE+Lk6y6Hu9dUlu/rEUJeVaq0hHA4TDAYJh8NPTkTUo2WTyYTdbsdkMolVnMrbjWbq7IfNZmOxWNBsNhmNRqysrGCxWP5h2a66oSmKwv7+Pr1eT8SJqo116vbpsXDf2zMpIv+PWt8YDodkMhlevXrF+fk5FouFeDzO7u6u8BYFGI1GYpT+/Pwc+HscpNPpfGdv3+v1aDabnJycUKvVmE6neL1ekUOr1+ufhA+GikajEROo1WqVo6MjMe+hvidWq1XUjNTsm3q9zsuXL6nX68LnRKvVvnMsrPqPeL1e9vb2WC6XaLVaKpUK5+fnBINB/H4/kUhExnJ+IqSI/D/T6ZRWq0WpVOL169fk83nm87k4Otzc3Hxn2TwYDIQZUSaTwWw24/F4SKVSYqoSfpptUI8bv/nmG/L5vBjVVo1kLBYLWq323p8od814POby8pLj42PG47GYwPV6vQQCARRFQafTib93dnbGX//6V3K5nBD34XBIIBD4hy2KwWAgHA4DP/VTqEOH+Xwei8UijkMf04rkvnha39pfYT6fi6yYN2/ecHp6ymg0EiFQm5ubhMNhsVdXl9s6nU4U6qxW6zvB2RaLhcViIY585/O5+DOdTplMJuI05zF1Un4I6qrBarWi0+lEW7b6/qqzL2qhej6fi6PK6XQq5kN+6f3T6XTY7Xbi8TjNZpNGo8HFxYVwvVe3U2qGjcz4/XievIiopi5q5qvaqOT1etna2hK5LT/3qHC5XKTTaYxGIzs7OxiNRpEKp/Y8qMeJ6kmDVqtlc3OT0WiE2+1ma2sLj8fzzpDbU8Jut7O7u4vRaGQ+n4vOU/U9fLu1W80QNplMbG1todFoxGfwS/4h6vupdm6m02nm8znZbJZ8Po/VasXn84nipNlsfpKfwafgyYuI2hRWLpfJ5/MUCgUURSGZTLK3t/eLo9MajQa3283Ozg7JZJLpdIpWqxWrEdWvQZ3wVRRFmCWrfQ3ql9fhcIix9aeG3W5nf3+ftbU1sXUxm81iBfL21O5isXjn+BYQ7+E/a9ZTm7AGgwHFYlEYGYVCISwWC9FoVDiFST6cJ/+uDQYD0ZRUKpXQaDQkk0l2d3fZ3NzE7/f/4pm76irl9Xrf63VsNtuDmJN5SKh9He/Lx8ZVqPnB3W6XUqnE9fU1tVqN7777Dq1Wi8ViufUwrsfMk37XFEXh6uqK4+Njjo6OmEwmpFIpvvjiC9LptNjGyGXu54+6Vdrf30dRFP7yl79wdHQktjter1cWWT+SJysiajzC4eEh5+fn9Pt9/H4/e3t7vHjxgkgkIk5NJJ8/Op0Oj8fDxsYGi8WCy8tLDg4OuLq6IpvNYrPZMBgMIhBL8v48SRGZz+dUq1W+//57Xr16JQRkY2NDZMVYrVYpII8I9bRHbbPf398Xc0/n5+cYDAZRj5GxnB/GkxKR5XIphuMuLi44PDykUCjgcrmIRCKsra2JQqoUkMeHmpYXDAbZ3t5mPB6Ty+VotVrk83ncbjdut5tAIPCOraLkt3lSIrJYLOh0OlxeXnJ6ekoul2MwGJBMJllfXxdDWvLL83jR6XQ4HA5SqZQwPTo9PaVWq5HNZoXviMfjkSuS9+TJiMhyuRSTucfHx5ydndHtdnG5XESjUdbX1x9E5KXk9lEtGYxGI51Oh1qtRq1WI5/Pi8E21ez5KU5ZfyhPRkRGoxHVapWTkxO+//57SqUSPp+Pvb09tre3hSOZPIl5Guj1enw+H2tra9TrdWazGefn53Q6HWHfYDKZhM+J5Nd5EiIynU65urri7OyM09NT8vk8Op2Ovb09/vjHPxKPx6WAPFGCwSA7OzuMx2MKhYKokSUSCWH4/Ln7j9w2T0JEut0uuVyOw8NDKpUKOp2OeDwu2trdbvejsM2TfDgOh4NoNEq73SaRSNDv96lWqxwcHIitjclkutUs28+dRysiqgXfdDoVE6Dn5+fM53NWV1fZ399ndXX1SbedS37a1jidTuLxOC9evECj0YiQdrvdLkKxpYj8Oo9aRNRIyEKhQKVSEYNvGxsbbG9vi9kJKSBPF41Gg9VqJRAIsLW1xWw2o9friQjKdrvNYDCQfUO/waMVEUVR6HQ6HB0dcXh4SLfbxe12k0ql2NnZIZVKyX4QCYBwPFtdXUVRFKrVKplMRmTdtNtt7Hb7Z2+reFs8WhFRVyK1Wo1OpyP2vpubm7IfRPIPqHWPxWLB9vY2gLAHGI/HTKdTKSK/wqMVEXU0PxaLYTAYsNlshEIhQqEQPp9PCojkH1CtFre3t3E6ncBPvjGqbaPkl3m074xWq8Xr9fLFF18wHo+FObDJZJJfCMmvotfriUajeL3ed1zV5endr/No7ybVBctkMgkX9rejIiWSX0Kn02Gz2f5h6yK/M7/OoxURkKIh+Tjk9+XDkIUBiURyI6SISCSSGyFFRCKR3AgpIhKJ5EZIEZEAf88PVk+yJJL3RYqIRCK5EVJEJCISVKvVyk5eyQcjvzES9Ho9VqsVh8Mh8oQlkvdFisgT5+0ohUgkgtfrld4Zkg/iUXesSv45ajB2KpXCZDKRTCalWbXkg5Ai8sTRarV4PB7S6TTBYFDGSUo+GM1Snuk9adRAr9FoxGw2w2g0YrPZ5KSz5L2RIiIB/t4notFo5ACa5IOQIiKRSG6EPJ2RSCQ3QoqIRCK5EVJEJBLJjZAiIpFIboQUEYlEciOkiEgkkhshRUQikdwIKSISieRGSBGRSCQ3QoqIRCK5EVJEJBLJjZAiIpFIboQUEYlEciOkiEgkkhshRUQikdwIKSISieRGSBGRSCQ3QoqIRCK5EVJEJBLJjZAiIpFIboQUEYlEciOkiEgkkhshRUQikdwIKSISieRGSBGRSCQ3QoqIRCK5Ef8H2hoV5muxt9EAAAAASUVORK5CYII=)
Area of the region bounded by
and y=2 is
![](data:image/png;base64,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)
maths-General
maths-
The area bounded by
and y=0 in the second quadrant is
![](data:image/png;base64,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)
The area bounded by
and y=0 in the second quadrant is
![](data:image/png;base64,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)
maths-General
maths-
The area bounded by the two curves
is
![](data:image/png;base64,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)
The area bounded by the two curves
is
![](data:image/png;base64,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)
maths-General
maths-
The area bounded by y =
in [0,2
]
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)
The area bounded by y =
in [0,2
]
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)
maths-General