Physics-
General
Easy
Question
A particle
is sliding down a frictionless hemispherical bowl. It passes the point
at
. At this instant of time, the horizontal component of its velocity
. A bead
of the same mass as
is ejected from
to
along the horizontal string
(see figure) with the speed
. Friction between the bead and the string may be neglected. Let
and
be the respective time taken by
and
to reach the point
. Then![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/904324/1/923382/Picture15.png)
- All of these
The correct answer is: ![t subscript p end subscript less than t subscript Q end subscript](data:image/png;base64,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)
For particle
, motion between
and
will be an accelerated one while between
and
a retarded one. But in any case horizontal component of it’s velocity will be greater than or equal to
on the other hand in case of particle
, it is always equal to
. Horizontal displacement of both the particles are equal, so ![t subscript P end subscript less than t subscript Q end subscript](data:image/png;base64,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)
Related Questions to study
Maths-
If the chords of contact of
and
w.r.t the ellipse
are at right angle then ![fraction numerator x subscript 1 end subscript x subscript 2 end subscript over denominator y subscript 1 end subscript y subscript 2 end subscript end fraction equals](data:image/png;base64,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)
If the chords of contact of
and
w.r.t the ellipse
are at right angle then ![fraction numerator x subscript 1 end subscript x subscript 2 end subscript over denominator y subscript 1 end subscript y subscript 2 end subscript end fraction equals](data:image/png;base64,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)
Maths-General
Maths-
The area of an ellipse is 8π sq. units dist. between the foci is
then e=
The area of an ellipse is 8π sq. units dist. between the foci is
then e=
Maths-General
Physics-
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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)
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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)
Physics-General
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