Physics-
General
Easy
Question
A disc is rolling (without slipping) on a horizontal surface
is its centre and
and
are two points equidistant from
. Let
,
and
be the magnitude of velocities of pints
and
respectively, then
![](data:image/png;base64,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)
,
The correct answer is: ![v subscript Q end subscript greater than v subscript C end subscript greater than v subscript P end subscript](data:image/png;base64,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)
In case of pure rolling bottommost point is the instantaneous centre of zero velocity.
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/generalfeedback/904720/1/919100/Picture106.png)
Velocity of any point on the disc,
,
where
is distance of point from
.
![r subscript Q end subscript greater than r subscript C end subscript greater than r subscript P end subscript](data:image/png;base64,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)
![therefore v subscript Q end subscript greater than v subscript C end subscript greater than v subscript P end subscript](data:image/png;base64,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)
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with respect to the initial position. The object is
![](data:image/png;base64,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)
A small object of uniform density roll up a curved surface with an initial velocity
. If reaches up to a maximum height of
with respect to the initial position. The object is
![](data:image/png;base64,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)
physics-General
physics-
A uniform rod
of length
and mass
is free to rotate about point
. The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about
is
, the initial angular acceleration of the rod will be
![](data:image/png;base64,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)
A uniform rod
of length
and mass
is free to rotate about point
. The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about
is
, the initial angular acceleration of the rod will be
![](data:image/png;base64,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)
physics-General
physics-
A particle of mass
moves in the
plane with a velocity
along the straight line
. If the angular momentum of the particle with respect to origin
is
when it is at
and
when it is at
, then
![](data:image/png;base64,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)
A particle of mass
moves in the
plane with a velocity
along the straight line
. If the angular momentum of the particle with respect to origin
is
when it is at
and
when it is at
, then
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANoAAADACAYAAABiUH0mAAAZg0lEQVR4nO3da2xT5/3A8a8vuTiJkzhO4sSJEyckDpAbAUIboKylBXqBlXZdxZg2bZq6qeuratLWTpq0F5v6rptWqeo0qVWlTdtKq2pqGTDoCoUECISQhJDUcYITYifO/eZbfPu/qPB/FGghCSeB/j7vsIP9OPI35/g5x89RxWKxGEKIu0q93AMQ4ptAQhNCARKaEAqQ0IRQgIQmhAIkNCEUIKEJoQAJTQgFSGhCKEBCE0IBEpoQCpDQhFDAsoUWiUSW66mFUNyyhBYKhXC73YRCoeV4eiEUp3ho0WiUvr4+vve973HixAlmZmaUHoIQilM8tLm5Oex2O2fOnKGpqYmxsTGlhyCE4hQPbXJyksuXLxOLxTh37hyjo6NKD0GsILFYjNHRURwOB+Pj48s9nLtGq/QTjo+P09bWhkqloqOjg4mJCaWHIJZZNBrF6/UyNjbG8PAw/f39xGIx1q1bh9FoXO7h3RWLCi0UCuHz+fD7/QAkJyeTmppKOBzG5/MRDodJSEggIyMDjUYDwMjICC0tLUQiEVwuF9PT00Qikfj94v4VCoUIBoNMT0/jcDg4fvw4R44cISMjg3379pGenr7cQ7xrFhXaxYsXeeedd/jnP/+JRqNh9+7dvPzyy3R3d/PWW29ht9upq6vjzTffpLCwkHA4zNTUFFevXgVAp9PhdDpxuVwUFRUtyQsSK1MkEqGrq4uDBw9y/PhxQqEQ27Zt44033sBqtZKWlkZCQsJyD/OuWVRoFRUV7Nmzh/n5eYLBID/72c8oLS3FaDQSjUZpbW3lmWeeITs7G/hia+ZyueJbr2AwSHd3N4ODgxLafSgYDNLf38+pU6f473//SywWo6KighdeeAGr1UpOTg65ubkkJyejUqmWe7h31aJCS09Pp7a2lvHxcQ4ePEhxcTGpqakMDQ2Rn59PTU0NZWVlaLVfPI3L5cJut8ePn4VCITo7O+nv72fz5s2LfzVi2UWjUQYHB7l48SIdHR1MTk6i1+t54IEHyM/Pp7S0lOLiYgwGA2r1N+fEpEVPhmRlZVFcXExbWxtTU1NEo1EmJibIzMxkzZo11/1sf38/ly9fjocWi8VwOp243W6i0eg36hd/P4lGo0xOTnLlyhUcDgdut5uZmRnm5+fJy8ujqqqK9evXYzQav7GfxRcdWnJyMhkZGfj9fpxOJzqdjuzsbIqLi6/7uVgsxtWrV+np6SEajcZvn52dZWxsjNnZWTIyMhY7HKGQWCyG3+/H4/Hg8XgYGBjAbrfjcDhIS0ujoaGBhoYGioqK4ns032RL8hvIzMzkiSeeoKOjgw0bNpCTk0NaWtp1P+P3+xkbG7thOl+j0TA6OsqVK1dYt27dUgxH3EXhcJhAIIDP58PpdHL06FFOnToFwEMPPcTLL7/M2rVr7+uJjYVYktCSk5Ox2Wz09vby2GOPxSc//ldXVxdut5uEhITrznEMBoP09PRw+fJlCW2FC4fD2O12Dh8+zKFDh5ienmbnzp288sorrFmzBr1eT2Ji4jd29/CrLElos7OzNDY2sn//fiwWy00/a3V3d9Pb20s0GkWv1zM7O4tOpyMUCtHb20tHR8dSDEUssUgkwtDQEJ988glNTU3Mzc1RWlrKCy+8QElJCbm5uRiNRlJSUuQz9ldYdGjz8/N4PB7OnTvHb37zm1t+zrLb7UxNTVFXV8eaNWt4++232b9/f3zf3u12Ew6HZX9+hfB4PLS1tXH+/HlGR0fJyMigsrKSvLw8SkpKsFqtGI1Gies2LfpdPT4+Tk9PD2azGYPBcMt986KiIvbs2cPq1avJzMzknXfeYefOnahUKtrb28nJyVnsUMQixGIx5ubmcDgc9Pb24na7mZqawu/3k5OTw7p166iqqiI/P18+fy3AokLr6enh+PHjNDY2YrVacblcGAyGGyZCAHbt2kVycjLZ2dlcunQJAIPBwObNm3nssccIBoOyNVsG1845HBkZYXBwkM8//xy73U5iYiIbNmzg4YcfprS0VD53LdKi3tkHDhzgzTffBL6YPSwoKCArKwubzXbDzxYWFt7ycQwGw2KGIe5QJBLB7/cTCARwOBycPHmS06dPMzw8zI4dO/jpT39KVVXVTf9gioVRLeb6aH6/n2AwGP93YmIiSUlJX/vX79KlS9TU1HDkyBE2b95MamrqQocg7lA4HGZoaIiPP/6Yjz76CJ/PR319PY8++iibNm1Cp9ORkJCARqO570+LUtKitmg6nQ6dTrdUYxF3UX9/P01NTZw+fRqn08natWv5/ve/z6pVq8jLy8NgMJCeni5x3SXyoegeNDs7S3t7O83NzUxMTGCxWNi1axdmszk+URGNRpmbm4vPHHo8HhITEyktLWXz5s1Yrdb4zKFMbtx9Eto9qLGxkffff59Tp04xNTWF2WxmZGSE559/HpPJxMDAAH19ffT29uLz+fD5fGRlZbF69WoqKyspKSmRaXmFSWj3GK/Xy0cffcSHH34YP53N4/EwOjqKVqvFZrPR19eH0+lkYmKCTZs28cQTT2Cz2dDr9cs8+m8uCe0e43a76evru+Gc0cHBQd566y1sNht1dXXs3buXRx55RKblVwgJ7R6Tm5tLSkrKTe/78Y9/zA9+8APMZjNarVYiW0EktHtENBrF5/Px2WefMTExQWJiIvPz8/H7d+7cydatW7FYLDK5sQJJaCvc5OQkdrudlpYWurq60Ov1PP744zQ0NDAwMIDf7yc7O5unn36a2tpaiWyFktBWmFgsRjAYxOl0xtdTmZqaIhgMkpmZSWVlJXV1dWi1WjweD36/Pz6jKMc0Vy4JbYUIBAJMTEwwPDyMy+Wir6+Pzz//nHA4TFlZGY888gj19fUkJCTEDyqvWrVqmUctbpeEtoyi0Sh+vx+fz8fVq1e5cOECJ0+epLOzky1btvDss8+yfv16srKylnuoYpEktGUSiUSYmZnh6NGjHDhwAJfLhc1mY/fu3bz++uvodDr5tvJ9REJT2OTkJO3t7XzyySdcvHgRq9UaP6Ccn59PVlYWGRkZcubGfUZCu8tisRjz8/N0dHTQ0tLClStXiEQi5Obm8p3vfAer1UppaSm5ubkkJSXd8eN7vV5OnDiBy+WKT/cnJiZiMpnYuHEjOTk5MhO5Akhod4nP58PlctHd3c2VK1eYm5vD7/eTmpqKxWJh3bp1VFRULHqV3mg0yszMDIcOHcJgMGCxWFCpVFy6dInGxkZefPFFioqKZAu5zCS0JRKLxYhEIoyOjjI8PIzb7Y4vKOrxeKitrWXHjh1UVlYu6RVTkpOT2bhxI++++y4bN25kx44dBAIBDh48yOuvv86jjz6KyWSSqf9lJqEtUjQaJRgMMjs7y9TUFKdPn+b48eO4XC5KSkrYs2cP27ZtIy0t7a5sVbRaLcXFxfEl/2pra5mfn2d+fp633nqLqakpAoGAhLbMJLRFmp6epqmpiffee4/Tp0+zadMmnnrqKR588EHMZjMajeaufls5HA7T399PSkpKfF3F3t5ePv74Y6qrq6mqqiIzM/OuPLe4fRLaAoTDYZqamvjss8+4fPkyKSkpbNmyhRdeeAGTyYTRaESv1ysyCeH3+zl79iytra34fD4++OADAOrq6ti/fz9Wq1W+Nb0CSGi3yev10tvby/nz52lvbycxMZGsrCx27NhBcXExpaWl8W84K/nG9vl8HDt2jO3bt1NaWsrIyAh2u52enh727dtHcnKyYmMRtyahfYVIJBKf0HA6nYyPjxMMBklJScFms1FZWUlZWdmyreJ17cKOnZ2d/Pa3v2XNmjUMDw9z6NAhjh49it1up7q6+pZfqxHKkdC+JBQKMTk5yfDwMENDQzgcDq5cucL09DRms5mHHnqI+vp60tPTl33K/NrVXDIyMrDZbJSUlFBQUMDVq1f585//TGdnJ2VlZRLaCiCh8cXU/LUrpHg8Htrb2zlx4gStra3U1dXx6KOP0tDQQEFBwXIP9TpTU1MMDAywe/duMjIy4q/D6/WiUqnQ6XTL/sdAfEFC44ut2NmzZ/nXv/7FuXPnyM7OZs+ePbz66qvxMytW4jmHQ0NDNDU18dJLL6HX65mfn+fs2bP8+9//Jikpifr6elkzc4W470ILh8NMT09z8eJF1Go1ZWVl5Ofn37DcuNfrpauri08//ZTGxsb4ZYKfeuqp+KVfMzIyVuTpS2NjYxw5coS//e1vdHZ2otFoSE5O5vLlyzgcDsxmM6+99hoFBQUrcvzfRPdVaH6/n9bWVt5++216e3sBKCkpYffu3Tz11FOo1Wp6enpobW2ls7MTn89HTk4Ou3fvxmKxYLVaKSgoWPFLYScmJsbXcty6dSv5+fkA5OXlsXPnTioqKti4ceM34iLs94r7KjSn08nHH3/MP/7xD3w+H7FYjJaWFmZmZpiensbv98e/rZycnIzVaqWqqoq1a9eSkZFxz7wpU1JSqK6uvukXP/V6Penp6cswKvFV7qvQ+vr6OH36NF6vN37b7OwsZ8+eZW5ujtzcXIqLi6mvr6e+vj6+JbjXaLVaDAaDXBzkHnJfhRYMBq+L7H+Vl5fz61//GpPJJDNxQnH3VWgJCQk3PROivLycHTt2kJeXd8/sHor7yz0dWjQaZWpqis8++4xjx47hdDpRq9WUlJTQ399PNBqltraWZ555hm9961sSmVg292Roo6OjdHZ20traSldXF0ajkbKyMrZt20ZmZiZ+vx+Xy4VarcZisVBZWXnLa2sLoYR7IrRrywF0d3fT3d2Ny+Vibm6OSCRCcXExa9asoaqqCovFgk6nIxaL4fV60Wg0ssCNWBFWdGiBQIDx8XHcbjeDg4P09vbS19eHRqNh9erVbNq0iQ0bNtwwuaFSqVb8sTDxzbLiQru2xvzc3ByDg4O0tbXR2NhIV1cX27dvZ//+/VRXVy9oVzAWi8nnNLEsVlRo0WiU2dlZjhw5wnvvvcfAwADl5eU8/fTTvP7666SkpKDVahc0PR+JRAgGg+h0OolNKG5FhDYyMsKFCxf49NNPaWlpwWaz8eSTT7JmzZrrrq+8mONfDoeDv//97/zqV7+S9TOE4pY1tGtrHXo8HhISEsjLy+MnP/lJ/LzDnJycBa11+GVut5uWlhYGBweJRCJLMHIh7oyioV1b67CxsZFYLEZbWxtms5n8/HysViuVlZXYbDa0Wu2S7d55vV7sdjttbW1L8nhCLMRdDy0SiTAyMoLb7cblcjEwMEBraysAaWlpPPnkk9TW1t61E2EHBwdxu92oVCrF1/MQ4pq7ElokEiEQCDAzM8PU1BTNzc2cOnUKt9uNxWKhoqIClUrF3r17Wb9+/V37cuLc3BxOp5PExEQeeOABzp07J6GJZXFXQpucnKSpqYn333+fEydO0NDQwJ49e9iyZQuFhYVcvnyZV1555W489XWOHj1KcXExFouFS5cuUV5eLgevxbJYstCi0SiNjY0cO3aM7u5uUlNT2bp1Kz//+c/Jzc3FYDCQlpa24On5OxEKhejr62N0dJTk5GQCgUD8m8dCLIdFheb1eunr66O5uZkLFy6g0+nIzc1lz549FBUVUVxcTH5+vqKfjaLRKJOTkxw4cAC3243dbmdycpJQKERlZaXsOoplccehRaNRent7sdvtOJ1OJiYmCIfDGI1GysvLqayspLS0dNmWoZ6ZmaG7u5uioiKsVitqtZq2tjaGh4fJycmR76KJZXFboc3PzzM5OYnb7Y5fJWVgYIC5uTlMJhNbt25d9rUOfT4fw8PDOBwOhoaGePbZZ0lNTSUQCBCNRpmYmCAUChEIBEhJSZHghKJuGdq1NQLn5ubweDzx6221tLRQV1fHww8/zIMPPojFYlFyvLfkdDo5dOgQXV1dbN26laSkJNRqNU6nk+7ubvr7++no6KCwsJDCwsIlORAuxO26ZWiRSITm5mYOHjzI6dOn0ev1PPPMM7z66qtkZ2cv6UHlpdDc3MzFixfRarXMzc3Fbz9x4gRdXV2kpaVx7tw56urqMJlMEppQlCoWi8W+fGM4HGZ4eJg//OEPmEwm6urqWLVqFZmZmaSnpy/6MkSXLl2ipqaGI0eOsHnz5iU5jjYxMcHc3Fx8hV6j0YhKpWJ8fJzZ2VkA1Go1RqNRVvAVirvpFk2tVmMwGHj++efJzMwkPz9/xS9hlpWVRVZW1g23G43GJb3CphALccvQUlNTeeCBB5QejxD3Jdl/EkIBEpoQCpDQhFCAhCaEAiQ0IRQgoQmhAAlNCAVIaEIoQEITQgESmhAKkNCEUICEJoQCJDQhFCChCaEACU0IBUhoQihAQhNCARKaEAqQ0IRQgIQmhAIkNCEUIKEJoQAJTQgFSGhCKEBCE0IBEpoQCpDQhFCAhCaEAiQ0IRQgoQmhAAlNCAVIaEIoQEITQgESmhAKkNCEUICEJoQCJDQhFCChCaEACU0IBUhoQihAQhNCARKaEAqQ0IRQgIQmhAIkNCEUIKEJoQAJTQgFSGhCKEBCE0IBEpoQCpDQhFCAhCaEAiQ0IRQgoQmhAAlNCAVIaEIoQEITQgESmhAKkNCEUICEJoQCJDQhFCChCaEACU0IBUhoQihAQhNCARKaEAqQ0IRQgIQmhAIkNCEUIKEJoQAJTQgFSGhCKEBCE0IBEpoQCpDQhFCAhCaEAiQ0IRQgoQmhAAlNCAVIaEIoQLvcAxBipYvFYoTDYWKxGLFYDI1Gg0ajQaVSEQqF4rer1Wo0Gg1q9Y3bLwlNiK8RCAQ4duwYU1NTRCIRrFYr69atQ6fT0dTUxNDQEPPz85jNZqqrq8nPz7/hMZYkNL/fz+eff47b7SYcDmM2myktLSUrK2spHl6IBYnFYoRCIf70pz+hUqlYu3Yt1dXVFBYW3tHjhMNhBgYGOHDgAIWFhezdu5doNEokEsHlcvHuu++Sm5vLt7/9bbTamye1qNDC4TBdXV385z//YWRkBLPZTDQa5eTJk6SmpvL444/z4IMPLuYphFgUjUbD8PAw58+f59ixY1gsFgwGAwUFBdhsNqxWK2azmfT09Fs+RlJSEg0NDZw/f57MzEwyMzNJTk4mEAgwNDTEtm3bsNls1NbWotfrb/oYiwqtq6uLw4cP09HRQU1NDRUVFfH91vb2dt59913S09MpKysjMTFxMU8lxB1TqVRoNBoaGho4c+YMx48fJxaLAWCxWKisrKSsrIzCwkJyc3PJzc0lPz+fvLw80tPTSUhIACAxMZH169fz9NNP43Q6UavVRCIRHA4HxcXF1NfXU1BQ8JXv8QWHNjs7y8GDB2lubua5555j//798fu2b9/Ohx9+yO9//3vS0tL4xS9+gclkQqVSXfdL6O7uJiEhAZ1Ot9BhCPG19Ho9er2eaDTK/Pw8AA6HA6fTGY9Jr9dTWVnJhg0bqKqqori4mMLCQvLz80lNTQVg/fr1XLp0iba2NkwmE8PDw+zatQu9Xn/TCZD/teDQ2tvbaW5uJjExkV27dl13X0JCAlVVVWzfvp0//vGP7Nu3D6PRGH9RGo0Gg8HA7373u68doBBLwev1EolErrstHA4TDoeBL+YZxsbGOHPmDKFQiKysLJ577jlefPFFqqqqACgqKmJwcJCuri5MJhN79+5Fp9NdtwG5lUWFNjMzQ21tLQaD4Yb7c3JyqKurIxaLMTg4SFlZGRkZGfEBv/fee7S2tuL3+xc6BCFu2+HDh2ltbcXn8930fq1Wi06nw+v1YrVa2bJlC4899hgWi+W6nysqKkKn01FRUXHbkcEiQpueniYlJQWTyXTTrZJGo4nvs0Yikfi+MYBOp2PTpk1UVFTc8FdGiKV29epVzp07RzQaBb742KLT6QgEAmRnZ7N69WpqampYu3Ytq1atIi0tDYPBQG5uLmlpafHHOX/+PKFQiOTkZMbHx287MlhEaFqtllAoRCAQuOP/q1arSUtLu+5FCLHUYrEYkUiEv/71rzgcDpKSkigqKqK8vBybzYbZbMZoNJKXl4fZbMZkMt0wlwAQCoXo6enB6/VSU1OD0+mkp6eHnTt33vZYFhzatWMRQ0NDBAIBkpOTr7t/fn6emZkZ4IsPmtc+nwmhpFgsRjAYpKGhgfT0dCwWCzabjVWrVmG1Wm94336Z3+9ncHCQK1euUFpaSnl5OSMjI1y4cIFwOHzL42ZftuDQqqqqyM3NZWhoiJ6eHqqrq+P3RSIR3G43HR0d8enTr3tBQiw1lUpFQkICP/zhD+PHvzQazW3936mpKcbHx3G5XPT29lJUVITZbEar1TI+Pk5bWxvd3d2YTCYMBsPXBrfgKb+ysjJqamqYm5vjwIEDzMzMEAgECAQCeDwejh8/zuHDh/nlL3+J2Wy+7RcoxFJbtWoVRqPxjt6DFy5c4I033uC1117jzJkzlJaWotPpcDgcXL16lbGxMf7yl79w8uTJ+J7bV1nwFi0pKYnvfve7pKSk8MEHH/CjH/2I7du3o1arOXr0KB6Ph5deeol9+/bJ1kzck0pKSrBYLKSlpV0X6aZNmygpKSE1NfW2jqEBqGL/Ox14h0KhEGNjY/T29mK32wkEAmi1WlJSUjCbzaxevRqz2bzQhxdi2UxOTuL1eoH/P+6blJSE1+vF6/USCoVQqVSkpKSg1+u/dtdxUaFdEwqF8Hg8TE9Po1arMRgM8YEJIZYoNCHEV5Pzn4RQgIQmhAIkNCEUIKEJoQAJTQgFSGhCKEBCE0IBEpoQCpDQhFCAhCaEAiQ0IRTwfytgitdyVE6RAAAAAElFTkSuQmCC)
physics-General
maths-
Assertion (A): If the system of equations
have non zero solution then ![lambda equals 5](data:image/png;base64,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)
Reason (R): If the system of equations
has a non zero solution then
is singular
Assertion (A): If the system of equations
have non zero solution then ![lambda equals 5](data:image/png;base64,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)
Reason (R): If the system of equations
has a non zero solution then
is singular
maths-General
physics-
Consider a body, shown in figure, consisting of two identical balls, each of mass
connected by a light rigid rod. If an impulse
is impared to the body at one of its ends, what would be its angular velocity?
![](data:image/png;base64,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)
Consider a body, shown in figure, consisting of two identical balls, each of mass
connected by a light rigid rod. If an impulse
is impared to the body at one of its ends, what would be its angular velocity?
![](data:image/png;base64,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)
physics-General
physics-
A binary star consists of two stars
(mass 2.2
) and B (mass 11
), where
is the mass of the sun. They are separated by distance
and are rotating about their centre of mass, which is stationary. The ratio of the total angular momentum of the binary star to the angular momentum of star
about the centre of mass is
A binary star consists of two stars
(mass 2.2
) and B (mass 11
), where
is the mass of the sun. They are separated by distance
and are rotating about their centre of mass, which is stationary. The ratio of the total angular momentum of the binary star to the angular momentum of star
about the centre of mass is
physics-General
physics-
A force of- F
acts on
, the origin of the coordinate system. The torque about the point 1, -(a) is
![](data:image/png;base64,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)
A force of- F
acts on
, the origin of the coordinate system. The torque about the point 1, -(a) is
![](data:image/png;base64,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)
physics-General
Maths-
The area of the region bounded by y=|x-1| and y=1 in sq. units is
![](data:image/png;base64,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)
For such questions, we should know area of different shapes.
The area of the region bounded by y=|x-1| and y=1 in sq. units is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAR4AAADtCAYAAABpuBrVAAAgAElEQVR4nO2dV5fbVpa2XxAEQIAECYI5FItVSmP3dE/PxVzP/5wfNe4LTytYgSzmHEES+bvQd06zJEu2ElPtZy2utluWBBbBF/vs8G4hDMMQBEEQByRy7AsgCOLhQcJDEMTBIeEhCOLgkPAQBHFwSHgIgjg4JDwEQRwcEh6CIA4OCQ9BEAeHhIcgiINDwkMQxMEh4SEI4uCQ8BAEcXBIeAiCODgkPARBHBwSHoIgDg4JD0EQB4eEhyCIg0PCQxDEwSHhIQji4JDwEARxcEh4CII4OCQ8BEEcHBIegiAODgkPQRAHJ3rsCzg3wjBEEAQIggAAIAgCIpEIBEHg/04QP5IgCPDhHs79++8c7kESni/E8zxYloXNZoMgCCDLMlRVhSRJiEajiEQiiEQokCR+DL7vw7ZtOI7DBSgSiUAURUSjUUiSBFEUT/4eJOH5Qmzbxng8xmAwgOM4SCaTME0Tuq4jFotBkiTIsnwWTx3ivAjDEI7jYLVaYblcwrZtAIAkSVAUBaqqIh6PIxaLkfBcGrZtYzKZ4N27d9hut8hms3BdF77vQ9d1aJqGaDQKURSPfanEhREEAWzbxmw2w3A4hGVZiEQiiMViSCQSMAwD0WgUsiwf+1L/EBKeL8TzPGw2G8xmM6xWK/i+DwBwHAfZbBaCIEBV1SNfJXGJsHtvMpmg3W5jtVpBURQYhgFRFKFpGnzf/yj/c4qQ8Hwh+8llFv1sNhtMp1PsdjvEYjEYhnHsyyQuCHbP2baN5XKJfr+Pd+/eYbFYIJ1OIxqNwjRNAOdT3CDh+UIikQhkWUY8HsdqtYJlWTzn4/s+MpkM8vn8WYS7xOkThiE8z4PjOFiv15jNZuj3+zziAYBSqQRRFHmB4xzEh4TnCxFFEaqqIpVKYbVaYb1eYzKZIAgCaJqG6XSK1WoFWZZ5hevUE33EaRGGIRcP3/ex2+2wWq0wGo0wHA4xHo+xWCyw3W7heR4ikQgURYEsyxBFkYTnEpFlGel0Gq7rIggCWJYFz/OwWq0wHo/5zRGJRKBp2llUGIjThEU7q9UKvV4PrVYL7XYbi8UCkUgEyWQShmEglUohkUjwto5zuN9IeL4QWZZhmiZUVYUoilgsFvy8vV6vMRgMoOs6fN9HLpdDJpOBJEnHvmzizAiCAL7vY7vdYjabodls4vXr1xiNRtjtdjAMA+l0GldXVygUCkilUiQ8l4wkSdB1HfF4HEEQoNvtwjAMzOdzeJ6H8XgMSZIQBAFEUUQikeBRz34I/b0IggCe5/FOalEUz6KBjPg0LNKxbRur1QqTyQTdbpfndWKxGLLZLCqVCqrVKrLZLL/P6Kh1oeznbHRdRyaTQaVSgW3b2O12mE6nsCwLtm1D0zRkMhkkEokfIjz7DWWbzQYAEI/HkUgkoCjKWdyAxMewCtZ8PsdoNMJgMMBoNMJyuYTv+9A0DcViEdVqFYVCAclkEoqiIBo9n6/z+VzpCSLLMjKZDG5ubiAIAjqdDjqdDlarFW8urFarSKfT94TnewlCGIbYbrcYDoeYTCYAgFwuB1EUqXv6jPF9H5ZlYTgcotPpoNfr8YhaURT+sLu6uuLRzrk1rJLwfAMswXd9fQ1RFGHbNprNJkajEQBgOBxiOp0inU4jDEM+R/O9CIIA2+0Wg8EAzWaT/3/JZBK6rtNx68wIwxBhGMK2bSwWC142Hw6HsG0biqIgnU6jUCigVCqhUCggkUjwCuo5QcLzDYiiiHg8jnw+D9/3MRqNkEgkEI1G4bouFosFBoMB4vE4stksUqkUJEn67hHPYDDA27dvAbw/alWr1bPoXiX+BWtKZf06k8kEvV4P3W4Xi8UCoigilUqhWCyiVCohk8lA1/WzPVKT8HwDkUiEVxI8z+NPosViAQCwLOteJMJmar4XTHj6/T7evHkD4P1Ra7vdkvCcGWEYwnVdWJaF+XyOwWCAdruNdrsNAMjn87i+vkatVkO1WkUymTzr4zQJzzcgCALvFk2lUvzmcF0Xy+USruui3W7D930oigLTNHnU8z0IwxC73Q7j8ZjfoGx0gzgfwjCE7/t89GY4HKLf72M4HGI+n0PXdaTTadzc3KBeryObzULTtLMVHYCE55sQBIHnbFRVhWmauLq6gu/76Pf7mM/nmE6nCMMQpmmiXC4jlUohHo9zD5VvuXk+fEoC76Ms13Up4jkDWLGBHbGWyyWGwyG63S7G4zF2ux1vychmsygUCsjlctB1/WxGIz4FCc93QpIkpFIpXF1dIRqNIhqNYrfbYTAYwPM8/gSLx+MIwxCxWAyKonxzspk9LV3XhSAIZzOdTLyHDYCyyLXRaKDZbPJ+sFKphHK5jGKxiFQqBU3TzvqIxSDh+U5EIhHous7tCTzPQ6/Xg+/7WCwWGI/H6Pf7iMViEAQBpml+9yoXcV6wKhaLWofDIZrNJprNJjzPg2maKBQKvDs5Ho9/1+LEMSHh+U4IggBFUbgD4Xw+h2maiMfj8H0f6/UavV6PdxZLkgRN075Lvof1Bp2L3y7xHhbpsO7k0WiEyWSCxWIBTdOQTqdRq9V4v46qqmdXNv8UJDzfEZbzURQFqVSKP60GgwHCMESv14PjOBBFkVumsgjoR4xTEKcNa7lgjYLT6RSu60KWZaRSKeRyORSLReRyOV7FIuEhPglLCJZKJViWhWg0im63i06ng/F4jGg0ikqlAsdxjn2pxBFxHAfT6RR3d3dot9uYTCYIwxC6rnPRYcLDLHUv5eFEwvODiMViyOVy8DwPvu9jPp+j3W5juVxiMBhgMplguVxCVVX+JKN8z+XDksms5WI4HKLdbqPb7cKyLG7YXiqVkM/nYZomEokEJEm6qKIBCc8PQBAEyLKMZDLJ8zv9fh/dbher1YpXMDqdDgDAMAzE43ESnguHDfVuNhus12t0u110u130ej3MZjNEo1EYhoF8Po9KpcLtV1ge8FKiHYCE54chyzKfl7IsC8ViEf1+H6Io8j4f1vEMvI+QiMuGzWGxJsG7uzs0Gg10Oh1st1vep3Nzc4NKpQLDMC7WQpeE5wfAkszsXJ7NZlEsFlGpVCAIAr/5fN/nZfh0Og1N04596cQPhA31jsdjtFotNJtN9Pt9LBYLCILAfXaY3UUsFjsrq4sv4TLf1QmwX+FKJpPI5/Oo1WqIRCIYDAbYbDawbZvfbNlsli9mo3zP5cB6dVi0s1qtMBwO0Wq10Ov1YFkWFEVBPB5HLpdDNptFOp3mVheXUsX6EBKeHwxbuJbP5xEEARRFge/7aDQamM/nkCQJ+Xwe2WyWTyAzx8JLOtM/ZJiN6W63w3w+R6/XQ6PRwGQygSzLPJFcr9d5i8Uliw5AwnMQVFVFPp+HpmlQFAXT6RTv3r3DbDYDAPR6PeRyOd6AyEYuSHguAzaLxfyTe70ems0mNpsNarUaKpUK6vU6rq+vYZrmdxmlOXVIeA4Ay/fIsgzHcfign6IocF0Xs9kM3W4XsixDURT+Is4fdsRiNqbD4RCLxQK73Y4byZVKpY/GIi4dEp4Dwo5dmUwGV1dXcF0X6/UalmXh7u4OAPjOrnO0syQ+xvd9LJdLtFotvp7GcRwYhgFN01Aul5HP57k3N8vxXTokPAeG+TTX63UAwN3dHUajEWazGWzb5vM5dMy6DARBwHK5xLt37/Dq1SuMRiO+cTaXy/EKlmma0DTtbLZEfCskPAdEEARuGlapVHhzIfNmliQJo9EIi8WCD5hSkvk8CYIAYRjCsixMp1N0u13c3d1hu93CNE1eNi+VSjBNk3vsPBQezjs9EaLRKOLxOEzT5P08g8EA6/UaQRBgsVjwfA8Lv2kb6XnB3AQ3mw0mkwn6/T5fe8Qql/s7sdhyyIcECc+BEUURsVgMhmFwoWFuc0EQYD6f4+3bt3BdF7Zto1KpXNRU8kOAeTCxqfNWq4X5fA7XdaGqKrLZLGq1Gmq1GtLpNBRFeXDuBCQ8B0QQBEQiEb58LRKJYLFYoFAoYLFYYLFYYLVaod1uw/M8yLIMwzCQTCYfVBh+7jC7i3a7jWaziV6vh/V6jTAMuUVuuVxGqVR6UHmdfehuPjDMrCsSiUDTNH4TbjYbiKLIDaE8z0MymUQul+ObKZhYPbSb9BxgOZ0gCLBerzEajbib4HK5hKIoUFUVlUoFuVyOdyfLsszXTz8kSHiOCOvjqFar/N8ty8JgMIDrunxSmfk0x+PxB9Fcdo4w32vmsdPv99FoNNBut6EoCiqVCvL5PKrVKorF4kdugg/tYULCc0REUeQT7JIkYbfbodlswrIsLJdL6LrON1NIksRfJDynBxuJYCtq+v0+7u7u0Ov1UC6Xkclk8OTJE1xdXd0rnQMPT3QAEp6jwhoKWf5mNBohnU5DVVWs12us12sMBgMekquqilgs9iA6W88J1p3Mjsl3d3f3bEzZkblSqfBoZ39TBAkPcVDYDSeKIvfZLZVKmE6n3AZzOBxyc/hkMolUKnXkqyYYrBLleR4vCrx69Yonk5l96c3NDUqlEtLpNOLxOM/VPWRIeE6EaDSKZDKJq6srOI4DTdPQ6/UwGo2w3W6hqipKpRJKpdKxL5X4/wRBAEEQuI1ps9nEP/7xD0wmE2QyGZ7Xubq6QrlcvmfY/hCjnH1IeE4A1tGcSCRQLBbhui7v8WGjFGysYrVaQVEUxGIxXkkhDg/bh8Xm7ZirYLfbxXq9RiaTQaFQQL1eR6VS4c2gl7IX61sh4TkR9gdIPc/jYjOZTPjupcFgAMMw4Ps+8vk8fN8/9mU/WNje+ul0itFohE6ng+VyCQB8J1ahUODl80QiQVYne5DwnAjMID6RSPAKCZvhms1mcF0X3W4X0WgUrutCUZSL9eM9B1i/TrvdRqPRwGAwgOM4vDjA1g4zCxSKdO5DwnMiRCIRbgAmiiJ2ux0KhQJvJvR9H8PhEGEYIhKJIJPJwDAMeJ5Hx60DwhLKtm1jsVig0+ng3bt3mM/nEAQBhmEgk8mgWCxyG1P2gCDh+RckPCcEq3Qwn+ZCoYD5fI4wDDEajTCfz7HdbhGNRlEsFhGJRLDb7XhOiPp7fixsHxabxRqPx3wswnVdFAoFFItFPg7BbGyJjyHhOUHYxoFcLsdXHtu2zaecZVlGpVKBJElYLpfY7XZ8YwXx42BT55Zl8URyt9vFYDCALMu4ubnB9fU1rq+vkc/nSXQ+AwnPiSJJEkzThCAICIIAg8GAT69rmobBYABVVTGbzbDZbOB5HjUW/mA8z4NlWTyZ3O/3MZlMsFqtYBgGEokEqtUq6vU699cmfh8SnhOF+fYAwGaz4Tmd5XIJ3/e5cdhkMsFiseCWC2wIlfj+uK6L+XyOVqvFE8q+7/Nd52xNkWmaiEajlHv7DCQ8JwjbySUIAlRV5Td2rVZDEAS8omLbNsbjMS+567p+7Eu/OFgyeX8L6Js3b/D27Vtst1vE43FkMhlUq1VUKpV7FSwSnk9DwnPisA0V+Xwejx49QjQaxWQy4dYLrORu2/axL/UiYULPupNHoxEajQaazSY0TUO9Xke9XsfV1RX31yH+GBKeE4Udl6LRKHet2+123MvHsiysVissFgtsNhv4vs+fsHTc+n54nofNZsMbOJnQW5aFRCKBbDbLhSedTiMWiz3o4c8/CwnPGaBpGjKZDB8W9TwPs9kM/X6fm0+xI8F+PxDx7bB8WqfTQbPZxGg0QhAE0HUd2WwW5XKZz2LFYjGqZP1JHszd+eF5+5zO377v81mudDrNKyjMQnXfOtP3fTiOA9u2qaryDbBq4nK5RLvdxosXL7h3ciQSgWmayOVyfAcas7nwPO8i2xq+dxR38cITBAE8z4PneXyojzWB7UcKpwy7xiAIsNlsYNv2vffBRJQNLDKTcTZISnw5kUgEvu9jMBjgzZs3ePnyJbrdLjzPA/B+PxpLOC+Xy3vJ5FO/n74E1inPrFtlWf4uFrwXLzye52G9XmM+n2M+n3NT9fV6zb+455ATYU/RzWaDbreLt2/fotvtYjab8QbCzWaDu7s7/O///i8mkwlkWebCdA4CeyoIgsCPtKyK9ebNG0wmEwDv827L5ZKL/2AwgKZpF+UWwN5HGIa8mbVarSKfz/Mp+0gk8tXR3UULTxiGcByH76rqdDpot9vodDrc54YJzynDhFEQBDiOg+VyyYdHLcuCbdt8OeDbt29h2zb+7//+D9FolE+wX8oX4kfw4efPcmX7C/kmkwksy+KtDoqi8JEJXdfvmbZf0s86DEPouo7Hjx/DcRzIsszXLFPE8xl834dt21itVphMJuj1emg2m+h2u7Asi98spy4+DHZ0dF0XYRhCFEWIogjP87Db7dDr9bBYLPj0uiiKZMfwBzChYBGL7/t8MJcdydl9wgSJPdDYdpBLy+vsiyebObu+vsZut+Nd8t8isBcvPJFIBLIsIx6PwzAM5HI57HY7RKNRbDYb7iJ3TPb//v1/3g93PyQSicDzPMznc/T7fYxGIz4wutvtIIoiEokETNPke7ku6Un8PdkXG/aQYiVzANxylm11/ZTh/iX9fPffi67rKBQKSCaTPNr5Vi5aeJjHTTKZRKlU4kZbtVoN6/UajuMc/WbZP0Z9mGva39W0D9tKsd1u0Wq18Msvv/AnkaIo0DQNuVwO9Xod//Zv/4ZKpQJVVY/+Xk8NlhAOggC2bcO2bcznc3S7Xbx8+RK9Xg+CIKBWq+H29pbbl7IcB/D+M9pP8F/iz1hRFOTzeVxfX8MwjHsLKb+WixYe4P2wpa7rUBQFmUwGtm3DcRweSh8blvhlIrOfCGbJuw8/YGaVul6v8c9//hOTyQTNZhOr1QqqqsIwDJRKJTx69Ah///vf8eTJE2iaxr17LvHL8TUw4WHGa9vtFpPJBMlkErvdjld06vU6fv75Z9zc3NyLfNgxdz/fcezo+UfAclrxeByqqvKREMrxfAZ21GJPqP0v3rErPftP2u12C9u2+Q511rej6/q9HUwMQRCw2Wwwm8343i0mSMyTmeV4gH/tfXIc5ywS6odk/3NwHAeCIPAZLFEUYZom79UJw5C7AcTjcWiaxh9s+0Zul8anovKv5eKFBzjdEQLWl8NMpabTKZ+70jQNtVoNNzc3SCaTv3szx2Kxj8JeJqxsoLHRaPDq3XQ6xWKx4F+uh8j+w2b/vmAJZFaMCIKAuwfKsoz1eo1Wq3Wvb4fNz11fX8M0TUiSdG9fFvFpHoTwnCr7DX+tVou/LMtCKpWCbdswDAPpdPqTycz9Ixrwr1Kw53l8Nxf7M9mcEZv5oi/Ie/aPtYqiQNd1mKaJTCbDm+bW6zXG4zFGoxFarRZc10WtVuN5NTaiwra9Ep+HhOeIsCes4zjYbDY8sTmdTvmWAhbWf+r374uOKIo8x6PrOoIgQK/Xg+M4fL0uazbct954aDDBZrvO95tI2TYITdNQKpW4+f52u4VlWXxFMdt1xlYObTYbKIoC3/dJeP4EJDxHZP8Jy5KWkiTxL4XneX9q5IEJD3MtrNfrSKfTmM1maDab3C61UCjwLQisv2dffB6KCLGcDttbxuxjHceBqqpIJpO8ipNKpeC6LjabDTdas20blmUhl8txG4z9ERzijyHhOSJsl1YqlUIul8N4POYrbgH86QoU++8URUE2m8WjR49gmiYajQZ+++03zGYzXl7/61//imKxyI8EH1YoLt3AShAE+L6P1WqFXq+HVquFXq+H6XSK5XIJSZL41Hm9XodpmtzyNJVK8arOarVCKpVCKpWCKIo0E/eFkPAcESY8yWQStm0jnU7fm4P5s3kYdtNLkoR0Os1narbbLTRNu+fpU6vVUKvVeGfzfoR16U/sSCQCURQRhiFWqxWi0Shvq5AkiU/8V6tVlMtlFAoFmKbJiwCxWIx3Li8WC2iaBsMwuBg91KPr10DCc0RY+VtVVSQSCW4Q/qU3MBMLlptgHdrT6RSVSgWbzQapVAq+72M2m0GWZaiqyo8J6/Uai8UClmVdbKmdNZOyZPFut0O/38d4PIZlWZAkCYVCAdlsFtVqFcViEbqu88bLaDTKLWfj8Tgcx0E8Hoeu6zAMA8lkkgsT8ceQ8BwRVknRNA2u6/LGNFYe/1QD4ef+vFgsxqsyxWIRNzc3vHHQsiy8fv0ag8EAiUQCiUQCjuOg2+2i0WhgNBrBtu1vHgA8RZiFLDPNj0QimM/nGI/HcF0XuVwOxWIRjx49QqVSQbFYhKZp/CjKvI0WiwVvY9A0DaZpIp/PI5VKkQHbF0A/pSPzYav9/ojE/rDin2l2ZO6DTHzy+Txub28RhiHm8zl2ux0ajQYkSYJhGEilUnAcB81mE69evUKv1+NzXpfCfjSoqioymQy3KN3tdtjtdnz+Kp/Po16vo1QqIZlM8kFI1uPDGjw3mw2vagG4179zaYL9oyDhOSJMWFirPltVY1kWRFGEZVn8xRLBn4tG9vtRZFmGYRi4vr6GIAhot9totVpYLpdcxGRZ5hFXLpeDJElwXfeijgsf9jiJosjN1NjPwDAMvpomnU5D13VuYbrb7bBYLDCfzzEcDnF3d4c3b95gvV5ju93yaiTzrfm9LnPiY0h4jojneVitVuj3+7i7u8Nvv/2GRqOBfr8PRVH4FoliscinzffHIH4P9kWLRqNIpVKo1WrQNA2RSIR7EHmex0vBhmGgXC7jL3/5ywHf+WHYjyJd1+W+TMPhkEcs2WwWlUoFtVoN2Wz23vGKJaFfvXqF58+f482bN+j1emi323BdF+VymY+71Go15PN5fkQjPg8JzxEJggCWZXFDqU6nww2n2K8tl0ssFouPPJY/BTsaiKLIzcd1Xcd6vcbz58+59QMTJ5aIZrkPZp9xCdUt9j5834dlWeh0Ovjll1/4TjJN01AsFlGv11GpVGCaJu9xYliWhXa7jX/84x/49ddfMRqNMB6PEYlEeG8PKwiwQWTijyHhOQHY0YjZd7AO5EKhwPt6vjR3wI4VbDNFJpPhx4nVagXgfTVruVxy4alUKhd3TGDWtyxBLMsyYrEY4vE4TNNEqVRCpVJBPp/ny/j2j5rs6CpJEm8uZNXIbDZ7Lwql/M6fh4TniLDjEztKGYaBSqWC1WoFSZJQLBZxfX2NXC6HeDz+0ZfiS9A0DdVqFT///DMGgwFs20aj0cBsNkMkEuEreC/tmLBardBut9FsNtFut3m0wkZSisUi8vk878f58OebSCRwe3uLIAhQr9e51WwkEoFhGMjn88jn81y8ZVk+0js9L0h4jgizvpBlGaZpcmtJluCNxWL3SuzfYr4Uj8dRq9UgCAJisRhevHiBt2/f8h3tT58+heu63/kdHp/NZoN2u43nz5+j0+lguVzy/BfLyRQKBaRSKZ5sZ7DZrUePHqFQKHCzNdbrJEkSP84qisIjKuKPIeE5ImxWi81r/UhUVUU+n4coirBtG61WC47jYLVaYTgcot/vo9PpYLvdci/nc69ubbdbPjbCRkdYoyCLdrLZLFKp1CcjPfb5UO7m+0LC8wBgT+dEIgEA/ElfLpcxm83gOA7evXuH3W4HRVH4+MS5wnIttm1jMBjwVUAA+CjE1dUV706mpr/DQz/xBwJroBNFEYVCAdVqFaPRiC+pe/nyJV68eMEnrz/cx37KVS5W+maCw3qdmFvgYrGA53nI5/NQVRXlchm3t7colUrQdZ2SwkeAhOeBwMrwLJ9ULBZRq9UQBAE/ajGHws1mw4WHNSWeOh92fu/bVEQiESQSCb4poVAooFQqIZvN8p4d4rCQ8DwgWEt/PB7nyVK2qpcNSzJPGlZFYzmOUy+zsx1YbN/VfD7nHeCpVArlchk3NzeoVqvIZrPcJ/nSbUBOFRKeBwjznGEzRtvtFt1ul0/Jsy9nJpNBKpXiIwSn+iUNw5AvNFwul2g0Gnj9+jW63S4kSUK1WsXTp0/x+PFjPHnyBIZh3DP/Jw4PCc8DRJZlLiqSJGE4HHJx0TQNV1dXuL29xdXVFQqFAnK5HBKJxMkKz/622OFwyG0rXNeFoih49OgR/vrXv+LRo0eoVqv3tnIQx4GE5wHCOqVZvieXy6FQKGC5XPJOZ1ZSZ93U8Xj82Jf9Sdj0PduewXqTMpkMdF1HrVbD9fU1KpUKstnsR2MRxOEh4XngiKKIdDrN7TMWiwVWqxXevHkD13X5IOUpC89yuUS73cbr169xd3eHXq+HIAiQyWSQz+d5IpntAKdd8seHhOeBw0Y16vU6BEHAu3fv0Gq1uH8Ps0tlDnun0t/D8jqu62IymeDu7g7Pnz/ne8SY1QezMTVNkyeUL9Ho7Nwg4XngSJKEZDKJcrnMrT37/T622y2m0ykGgwE6nQ6CIIAsyx/tmz90zocJBrO68DwPo9EIr1+/xrt379Dr9bjpfblc5nkq1p18Dq0BDwESngcOswRl2xSm0ym63S5msxmCIMBgMMCvv/6KRqPBTc+ZleqxYSV0tjGi2+1it9shkUggm83i+voatVoNmUyG/JBPDBKeBw6bF2P9PGyUghnAj0YjzOdz+L6PzWbDvWyCIDjqcWXfkpT17wRBgEQiwRPi19fXqFar3Nzrz9jHEoeBhOeBw+w/WV8LS8Yul0u+laLX6/FtmbZtw3Vd3tF86OoQ60j2PA+O43CLClVVYZom4vE4stksn0czTfOLVgURh4GEh+BfSkVRkE6nUalU+Grf9XoNy7KwXq+5j42iKIjFYlyw9mejftT1fbh2eLlcYjwec6sKVVVRrVbx+PFj3N7eolAo0ADoCUOfCsFhM03lchmRSITnfPr9PjzP455B+XyeV4lUVeXl6R8pPEEQ8B3zlmWh1+vh9evXeP36NVzXRb1ex3/8x3/gp59+wu3tLXK5HInOCUOfDMERBOHexonVaoVGowFN0xCGITKZDK6urnjuJJvNwjCMH25+xdYOW5aF6XSK6XTKu5PZfNn19TWePXuGn376CaVSCYlEgoTnhKFPhuAw3x4WvWSzWeAGpzcAAA75SURBVG6YNZ/PEYvFuHl6NBpFOp3mHtGHYDweY7FYYLfbwXEcxGIxFItFRCIR1Ot17rFjmib3myZOExIegsOSr8w+g/X3zOdz7tM8Ho8RBAHvaC4UCgf5gnueh8Vigbu7O7x48QKj0QgAUCwWYRgGbm5u7pmvUzL5tCHhIX6XfSP67XYLURTRarV4eV2WZT6GkEqleB7me8OqWMw7+bfffsM///lPbLdblMtlVKtV/jIMg7cGACDhOWFIeIiPYKtxWGmaVZImkwl6vR7m8zlUVYVhGPB9H7qu8z6g75lgZrmdIAiw2+3QbDbRarUwHo+5oyKzMc3n80gkEjR1fiaQ8BC/C2ssTKfT3EK03W4DeD+U+fbtW9i2jbdv30JRFADvoxPg+4xRsKMScxH0PI+X0G3bRiKRuLcpgpX5Ka9zHpDwEJ9k3yB+uVzyEvpwOMRwOMRkMuEL7wB8NHz5oRfy5/hQrNi/s85ktvlUVVVeeWO7wAzDoDmsM4OEh/hd2HGLiUk6nebL66bTKVarFcbjMTabDd/Vpaoq36r5tZs1WVey7/twXRe73Y6vdE6n03zBYbVaRaFQgGEY/IhFIxHnAwkP8VlYiV3XdZTLZTx79oxPhm+3W6zXa8RiMWSzWRSLRaRSqXsC9KV/F/tzt9stF7d2u839kwuFAp4+fYqnT5+iUqnwtcPs9xPnAQkP8afQNA3lchlhGHJ7jM1mgyAIkEql8OTJEzx79gyFQgHpdPreyuU/k/NhorHb7TCbzTCbzTAcDtFsNhEEAcbjMXK5HG5vb/GXv/wFjx8/RjqdRiwW+9FvnfgBkPAQfwib48pkMnw8Yjqd8p4eNg1erVZRq9VQKpVgmia3GP0j4WFHpDAMucVFu92GIAjY7XZYLBZQFIV3TbNtEYqiUHfymUKfGvGnEEWRdy5ns1lUKhW+l4sldS3Lwna7hSAI0HUdqVTqi/4ONgTKpuInkwl830cul0Mmk+G+yZlMBvF4nCpYZwwJD/GHsNI2Ozbpuo5CoYB6vQ4AfAlgp9PhHs6lUumL/x7m+TMcDvHq1Su0Wi2oqsqrVyyaYsc44nwh4SG+CFEU+bjE1dUVwjBEq9VCv99Hv9+HIAjIZDLI5XIQRRHRaBRhGPLXPux45bour2Dd3d3hzZs3ePHiBQaDAWq1Gp4+fYonT56gWq0ik8n88KFU4sdDwkN8EayxMJVKoVQq8a5iFvXMZjN0Oh0kEglMp1MAgOM4H3k1A/9KKDPvZNu20e/38fLlSzSbTazXaz5pXiwWUSwWKdq5EEh4iC+Cldf38zfr9RrD4RCz2Qyr1QrNZhO73Q6SJGG73WKxWPBenP1eG5YbYiZfbBC00+mg0WhAFEVu8mWaJtLpNN8BT5w3JDzEF8OsRlnOZz6fI5vNYjKZ8DL4dDqF4zhYrVaYz+e89L4vPPvdyezF+nh2ux3S6TQ0TUMikYCu69wXiPp1zh8SHuKLYZEK27VumiYKhQJmsxnfc2VZFjabDa9SsQ2lLFphRyt2DGNezqx6VqlUUKlUcH19DdM0oWka/72nsOGC+DZIeIivhvX3GIaBarUK27bh+z7m8zlWqxUcx0E6nebmXKqqQlVVBEEAy7Iwn8/5azqdYrlcIhaL8X1YNzc3ePbsGUqlEh9EZX8vcd6Q8BDfRDQaRTKZRKVSQRiG2G63aDab8DwPAJDJZPDTTz/h0aNHME0TqVQKQRBgOp2i0+mg0+lgMBig1+thNBohkUjg559/xn/+53/iyZMn3N+ZKlmXBQkP8U1EIhFomgbg/fFpMpkgm80imUzC8zzoug7DMJDL5VAqlZDL5SAIAgaDARzHubeni3n8PHv2DP/+7/+O29tb3ihICeXLgoTnjNmfHmccet/V702wX19fY71eY71eQ5ZlLBYLdLtdnr+RZRmWZWE8HqPf78OyLG46VigUcHNzg1wuh2QySZHOhULCc8ZIksQTtuzLz5K4h5xh2p/lqlQqmM/nCIIAo9GIdyKzPh5VVaHrOiaTCVqtFhqNBqLRKB49eoTHjx+jXq+jUqkgn8+T6Fwwn707t9vtvVInVRNOg/1JblZBYts9LcvCZDLBcDjkCdkf/bmx67Ftm/szq6rK+3iWyyUmkwmCIIAkSUgmk2i1Wmg2m2i324jH46hWq5AkCYqiwPd9LBYLOI7zp6fbiR8Hi6Kj0SiPpr91O+tnhee3337jniubzYYnDKmqcHxEUcRut8ObN2/Qbre5IVer1cIvv/yC5XIJWZYP8qVl9wNrAByNRhgMBhiPxxiNRlgul4hEInBdl9uWDodDtFotTCYTbLdb3N3dQVVVrFYraJoGTdP4tggSnuPAeqai0Sji8TgMw0AymUQikYCmaYjFYl/dRS6En/lU/+d//gfj8RidTgej0Qjb7fb9byLhOSrsCeS6Lu/0HY1GEAQBuVwO5XIZqVTqYH0v7H7wfR+2bfNtn+x/HceBIAj85mU5ntFohNVqhWg0imw2y61V94+QJDzHgwmPqqoolUp4/PgxdwjI5XJ8V/3X8NmIp9FooNPp4PXr19wFDgB5254IzASdNd8BQK/Xw3Q65eHwoa+HjT+w7RDsBYBvAmUbKVzX5b/Oup2ZhzPtxTou7LNkD4zb21uey9M0DfF4HKlU6qs7yT8rPKlUCrvdDqvVivdohGFIwnMCsN3m2+2Wz0jt++Ac0/ycicaH4rE/of7hrzPB+r0pduLw7H8GmqZxZ8lEIoFYLMYN4b6WzwrPf/3Xf2G9XnNzb/ZUpSfRcWFHLdu20W638csvv+DVq1cQBAHPnj3D3/72N1xdXfHz9zG+yF97j5DonA7ss5BlmbdK5HI5GIYBXdd5Du5r+Kzw/P3vf+chMQudiePDIoXtdotff/0Vy+USvV4PgiDgyZMn+O///m/87W9/O1hV68Nr+x6QAB2X/dwaq2jJsgxZlhGNRr/ZJeCzwmOa5lf/wcRhWC6XSKfT/OljmiZqtRqePHly7EsjiE9CyZozZj+By/gwoUsQpwgJzxnDnPv2k7LMUIvl4wjiFKGRiSPyYfnZ8zy+RRMA9yxm5+lzKzMzEWTvab9Euz/aQVXShwcJzxEJgoAvxmP+NJPJBKvVCgCg6zqy2SxSqRQSicRXb+g8BmEYci/m+XwOy7J4v1E0GkUqlUIul0M6nb7ntUM8DEh4jkgQBNhut5hOpxgMBmg2m3j58iW63S4AoFKp4NmzZ7i+vkahUOAL9c5FeDabDfr9PhqNBgaDAVarFTabDWKxGK6urvDzzz9D0zQSngcICc8RYRsa5vM5ut0u3r17h+fPn+Pu7g6CIGC1WvESpqIoiMfj3Pvm1GFra5bLJQaDARqNBqbTKebzOVRVhe/7KJVKlIt6oJDwHBG2wG4ymWAwGGA2m3FDLEEQ+EbNfr8PXdeRTqe/eDvnMWEDhiyXw96v67pYr9dwHIeqbw8UEp4jEYYhfN/nNhbj8Ri+76NcLuP6+hoA+KK78XgM0zRRLpfP5ou678dcLpd56Z9ZrbCW+3NJlBPfFxKeI+L7Pp+1mk6nCIIAhUIBxWIRwPuBz8FggOl0itlsxr+05wDbv6XrOnK5HBzHwXK5xHA4xG63+2jFDfGwIOE5ImEYwnEc7HY7bLdbSJIETdOQyWQAvN9JzkZWdrsdXNc9qy8qszrVdR3JZBLxeByyLHObDOLhQsJzAnw4kf17E93nJDgMFvUoisJNo5jHDvGwIeE5Msx/hpXImZkW8N7Rb9+8/dwa7di173vsACArXYKE55iwDl5WMmfVnvF4DOD9TvIwDPmvn1u0wBokmX0uezF3QtZQ6Pv+R9syiMuGhOdIsGhAlmXenzOfz9Hv9zGZTACA50KY49u3+J8cA8dxsFgs0Ov1cHd3h1arhU6ng81mA8MwsFwuYVkWdrsdt1s4p/dHfD0kPEckEolAVVWkUikYhoHVaoV+v8/dBBOJBIrFItLpNJLJJGKx2Nl8MVnifD6fo9frodVqodvtYjQa8cZCFv3Yts2jv3N5f8S3cV5JgwuDCU86nUYul+MG7a7rwnEcSJLEt3AahoFYLHYW4xIA7k3K27YNx3EAvN8FxmbOBEHg/w3lfB4WFPEcEVEUEY/Hkcvl4LouIpEIJElCPp9HJBJBJpPB9fU1qtUqstksNE07G+FhFS22IZQJaTKZRBiGuLq6QqlUQiKRgCRJZ5c4J74NEp4jIooiNE1DLpdDLBZDJpNBrVbjO7I0TYNhGEilUtB1ne8RPwcEQUAsFkMul+Ni+ujRI744wDAMFItFmKbJIzk6Zj0cSHiOyP7GTV3Xkc/neZWHJZ/ZnBN7nUtkwEYm0uk0dF3n78vzPIRhyPt7WFKZ/R7iYUDCc0RYQlUUxYu0hrjk90Z8G+fx+CQI4qIg4SEI4uCQ8BAEcXBIeAiCODgkPARBHBwSHoIgDg4JD0EQB4eEhyCIg0PCQxDEwSHhIQji4JDwEARxcEh4CII4OCQ8BEEcHBIegiAODgkPQRAHh4SHIIiDQ8JDEMTBIeEhCOLgkPAQBHFwSHgIgjg4JDwEQRwcEh6CIA4OCQ9BEAeHhIcgiINDwkMQxMEh4SEI4uCQ8BAEcXBIeAiCODgkPARBHJzosS+A+D6EYXjsSyCIPw1FPBcAiQ5xblDEc+ZEIhHIsoxYLAZBECBJEiKRCARBOPalEcQnIeE5YwRBgCzLSKVSyOfzEAQByWQSsiyT8BAnDQnPGSMIAmKxGLLZLGq1GgRBQCaTQSwWO/alEcRnIeE5Y5jw5HI51Go1AEA2m+XHLoI4VUh4zphIJAJN01AqleB5HgCgWCxC0zQSHuKkIeE5YwRBgKZpKJfLUFUVAJBOp0l4iJNHCKkWe7aEYQjP8+A4DhzHAQBIkgRFURCNRkl8iJOFhIcgiINDDYQEQRwcEh6CIA4OCQ9BEAeHhIcgiINDwkMQxMEh4SEI4uCQ8BAEcXBIeAiCODgkPARBHBwSHoIgDg4JD0EQB4eEhyCIg0PCQxDEwSHhIQji4JDwEARxcEh4CII4OCQ8BEEcHBIegiAODgkPQRAHh4SHIIiDQ8JDEMTBIeEhCOLgkPAQBHFwSHgIgjg4JDwEQRwcEh6CIA4OCQ9BEAfn/wE1iaxKChz8SgAAAABJRU5ErkJggg==)
Maths-General
For such questions, we should know area of different shapes.
Maths-
The area of the elliptic quadratic with the semi major axis and semi minor axis as 6 and 4 respectively
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)
For such questions, we should know the formula of area of different shapes.
The area of the elliptic quadratic with the semi major axis and semi minor axis as 6 and 4 respectively
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAARsAAADFCAYAAABkblbKAAAgAElEQVR4nO2d129iiZb1FxkOOQcbHCp2q1szUj+MNFf3df74udI83Hu7vgo4YDA558z30Fq7D5QrdHU1Nvb+SciAjQGbs87O27LZbDZQFEX5i7He9wtQFOVpoGKjKMpeULFRFGUvqNgoirIXVGwURdkLKjaKouwFFRtFUfaCio2iKHtBxUZRlL2gYqMoyl5QsVEUZS+o2CiKshdUbBRF2QsqNoqi7AUVG0VR9oKKjaIoe0HFRlGUvaBioyjKXlCxURRlL9jv+wUoD4/1ei0Xi8UCq9UKq9UKi8Vy3y9NOWBUbJQt1us1JpMJBoMBJpMJ7HY7AoEAvF4v7Hb9uCjfjn56lC1WqxUGgwEKhQJarRYMw0A2m4XT6VSxUf4U+ulRtqDYFItF3N7ewu/3w+fzIR6Pw+Px3PfLUw4YFRtli/V6LWLz4cMHRCIRHB8fY7lc3vdLUw4czUYpW6zXawyHQ5RKJeTzeVxfX6PdbmOxWNz3S1MOHLVslC1WqxXG4zHq9TqKxaJYOqvV6r5fmnLgqGWjbLHZbLBYLDAajdDr9TAYDDCbzbBer+/7pSkHjoqN8hGbzQbr9Rqr1Qrr9Rq6Dl75HqjYKB/BQj6bzabFfMp3Q8VGUZS9oGKjKMpeULFRFGUvqNgoirIXVGwURdkLKjaKouwFFRtFUfaCio2iKHtBxUZRlL2gYqMoyl5QsVEUZS+o2CiKshdUbBRF2QsqNoqi7AUVG0VR9oKKjaIoe0HFRtnCbrfL0Czgt0FaNptNd0YpfxoVG2WLzWYjl937FOXPoKere8Z8EHOouPmANx/onAd81/d2r+/+7i9dt1gssFgs6HQ6aLfbmE6nWK/XmM/n6PV6qNVqcDgcW8/zuXGhm81Gvs8xo3wOYr7O30tLihezhWW+fOn5lYeHis09wwNmtVphuVzKV1433zbfv1gs7vzZ9XotomQWp7uEynwfAFitVnS7Xbx9+xaNRgPz+Rz9fh/v379HMBhEKpXaEgVezIIAQF6D2QVzOBziotlsti0BWq/X8j5sNhv8fr/sF3c6nfIYu90Ou90Oq9Uqz6kcDio2DwQedLPZDNPpFPP5HNPpVG7zMpvN5D7z19lshvl8jvl8jsVigc1mI+KzK0Tm+zabDZbLpQjOaDRCq9XC7e0tJpMJ2u02/u///g/VahV+v18EggPRzRYIBYDiBwBOpxNutxsejwdutxsul0v2hvOxy+US4/EY0+kULpcL6XQa2WwW8XgcPp8PTqcTLpcLLpdry9pRDgsVm+/IXS4P77/LReIZfbVaibhMJpOPRGYymcj9d10mk4mIzXQ6xXK5/EhUdgXHfNssPLPZDOPxGIPBAMvlEtPpFPV6HZPJBC6Xa2vrgll4zKtf+LtsNhsMw4DP54PX64Xb7YbT6YTT6dxyq/ic0+kUhmGg3+9jtVphOp0iEAiI0LjdbhEscyDb/Fq+dAHU/bovVGy+EzyIF4sFlsulWBiLxeKz183WyK6rxOv8+d37aD04HA5YLBaxInbdpy+5UOYFdNPpFK1WS57D7XYjHo8jnU7D5/PJz1ksFhGp6XSKwWCA4XCI2WwGq9UKp9MJj8cDwzAQDAbh9Xphs9nk5/m+KZJ8z9PpVARlNBrB4/F85EaZrSKHwyHPRauJ9zkcjo+u83HK/lGx+U5YrVbZJknLgAfgXdcHgwFGoxFGoxHG4zGWy+XWwcQDynwG3z3QXC4XDMP4KJ7BmIj5bH7XmZ/uCB9jt9slRrNYLDCZTBAOh/Ef//Ef+OWXX5BMJrdiS7PZDKPRCM1mE1dXV7i8vMR8PofT6UQsFkMikUAikUAqlYLX68VsNkO320W32xUXrdVqYTabiau0Xq9Rq9VEdAB8ZJUBvweMXS4XAoEAotEowuEwgsEgfD4f/H4//H6/XPf5fPK3U+4HFZs/yG4KmNYBRabf76Pf76PX66HT6cjBddel3+9jNBphOBxivV7D7XbDMAwYhiExDo/Hs3WdomD+GV54dnc4HFsxFQrVbpzF/H1aRc1mEx6PB2/fvkWpVEIgEMCrV6/w97//HScnJyJC0+kU/X4frVYLxWJRYj2r1Qp+vx9HR0fIZrNIpVJIpVJwu93o9XrYbDYYjUYSnxoOhyK0dLFWqxW63S42mw3m8zkmkwnG47FcFosFgN8ExzAMxGIxZDIZpFIpRKNRBINBhEKhrct0OsVisYDP5xN3cNedusu9Mv+/1f36c6jYfAV0eWjym4OxdIHMsZXxeIzJZILRaLR1ez6fi7vj9/vhcDgQCATk/l1x+dRt8/0UGHM8wyw2dwVyPyU2VqsVDocDkUhEhM3pdCIUCiGVSiEWi2GxWKDf70sAejgcYjwew2q1IhaLwe/3IxKJ4OTkBOl0GoFAAIZhYLlciiVEsQkGgxJ/oVXC52U8azKZYDAYoNvtYrlcotvtYjAYwGq1wu12b7mCdMMAYD6fYzgcot1uizDzK90tWlP8yowZCxh5ApnNZrDb7QgEAvD5fHA4HPf5cTxYVGy+AM/A3W73I0ul1+uh3+9jMBiIK0TMBzPP2h6PRywMpoN5MbtPjC3w/t3bvDCrQ/eAP2cO3Jpdpt3r5vt4Bjfv974rwD0cDtFqtVCpVPDhwwfk83mJ8SSTSQQCAaRSKRGa+XyOwWCARqOBWq2GYrGIZrMJh8OBXC6HeDyOSCSCYDCIQCBwp9iwziefz+Pt27fy+EgkglgshnA4LGJls9lEEDudjrh8fE8UVp/Ph2AwKI8LhULw+/3weDzwer3yXiuVCjqdDgzDwPn5OXK5nIrNN/LkxeZThXA8uBaLBQaDAZrNJmq1Gur1Omq1GhqNBhqNBprNJjqdDkajETabjVgYPp8PPp8PgUAAfr8fhmFI/QjvN193uVxflU35I1kX4HfT/2vv23UvzEFlpqi73S5qtRpubm5weXmJfr+PWCyGeDyO09NTHB0dIRqNwmKxyN+t0WigXq+j2WxiOBwiHo/j+PgYP/74I7LZrPwt3G63ZLeYpWq32ygWi1itVuh0OlitVjAMA5lMBul0WgLQbrcb8/kc3W4Xo9FI3Nler4fRaITpdIrVagWHw4FwOCzxJMaWIpGIiBAAtNtt5PN5VKtVhMNhGIaBeDyOQCDwfT+ET4QnLzbMHJldI9atMP3c7/fFsun1ehJvYZWt3W6XbAtjLhSZUCiEQCAgZ+5gMLh1nQL0UNgNHi+XS4xGI3Q6HVitVhSLRVxfX6NYLEqMhgfh0dERjo6OEAqFAGBLpFutlqS2/X4/jo+PcX5+jmfPnuH4+Bherxcej0eEbrlcyt+Y/xebzYZwOAybzYZgMIhcLoejoyMRKZvNhvF4LC7hfD6XkwGroul+Wa1WSbOz1qfX64lLul6v0ev1cHNzg1arhdFoJO+P7hgD8crX8aTFhgcSBYRukVlcBoOBxFRohlssFgQCAYRCoa0UrDl2Yo6tmL/u3udyue77z3AnfL+TyQSNRgNXV1eo1+u4vLzE5eUlut0u1uu1WBY88L1eL0ajEdrtNqrVKmq1GsrlMkajEQzDQDabRSKRQCaTETfKMAw4nU55zul0il6vJ897fX2NarWK0WiEYDCIdDqNRCIhAWiPxwOn0wkAkkELh8Nwu92S9WKtDrNTkUgE0WgUfr8fwG9WTL1elxKExWIhltVyuYTH40Gj0UC5XJYYE0VO+TqehNh8qs9oOp2i0+mIa9RsNtFsNtFqtdBoNFCtVtHtdmGxWMRCCYVCCIfD8pXX6e8z8HhXUHY3Q8Tr5j6ihwJfD8Xm8vISDocDV1dXuLq6wmq1QiqVkrN9JpNBOBwGABGlm5sbsQadTidSqRRevnyJly9fIplMwuv1SksCADnAe70e6vU6SqUS3r59iw8fPqDb7cLn8+H4+BgnJyfIZDLIZrOIRqOSXVqv1xiPx2J5LBYL1Ot1+Hw+zOdzuFwuJBIJ+b/5fD5YLBYJQLfbbYnBzWYzKS/weDwYj8dotVool8tSL8TPEtPpu27pXW7tU+bJiA3dI1bnTiYTCXZSYOge9ft9OaMxoOj1ehEKhRCNRhGPxxGLxeTCAKfb7ZYg7qF/wPj6WUF8dXUFt9uNfr8Pq9UKr9eLeDwuWSqXyyW1Q+VyGdVqFZ1OB4vFAoZhIBwOI5PJ4OTkBGdnZ4hEIiK4tGYYDK7X67i9vcXt7S0qlQqGwyEAIBAIIJPJ4PT0VOI1fr8fFotF3OHRaCQp9clkAqvVikAgIFm1o6MjsXoASCq91+uh2WxiPB6LJWu327dqmYbDIW5vbyXo3W63EQgE4Ha7P+rbYgCfVdPKExIbmvatVksunU5HhGU+n0vzIAvCjo6OxLcPhUJb8RbGZFhEZhjGo8lSMGZDEajX63C5XIjFYiIy0WgUyWQS0WgUTqcTrVYL1WpVYiSMhTDjk06nkcvlkMlk5OAnPNhpTRYKBZRKJbRaLYzHY3F9Tk9PcXZ2huPjY3GB7Hb7VtaqXC7j4uIC19fXaDabmE6niMfj8Hg8SKfTEuNZLBYS2GcFNIsLE4mEZMZYgWy327FYLFAul6W2iEkAFg3yM+BwOODxeOTkRBF66jwqsblr/AJN62azidvbW5TLZTljdjodKa/3eDzw+XziHjEdyu5jwzC2+nJ209ZspHxsZjMzUP1+H+FwGMlkEs+ePUMymYTL5ZLA6s3NDT58+IBGo4HNZgOv1yvFdicnJzg6OkIsFkMoFILdbt9yZweDAarVKm5ubnBzc4NCoYBqtYrZbIZAICAFgrxEo1EYhgEAIhQMRBcKBbx79w4XFxeYzWaIx+NiBR0fHyMej8Nut6PdbqPX6201rrrdbsRiMQlau91uqV5mFq7X66HdbmO5XErNVCAQQCQSgd/vl88IXzdrlczZxqfKoxIbltCbM0rMJrHOg+nrXq+HyWQiJe8MGrLMPhqNSg2H1+sVYdmdy/JYG/woBna7HR6PR1oCmC4Oh8MS8+LfttvtSsaJblMul5MCP7/fL2LNmBktp3K5jEKhgNvbW0lvezwexGIxZLNZcZ3i8Ti8Xq9Yq/1+H81mE+VyGZVKRSwPtk2Ew2EcHR0hnU5LfIdFmCy6tFgsCAaDiEQiODo6wosXL3BycgKXyyVi1Ov1JOPVbrfFKlqtVmIx84TkdrsRiUSwXC6lL4tC9Bhc7G/l0YkNg32MxTQaDXQ6HfHh2RXt9XolSGgO+t6VmmYA8ilhdinPzs7w888/4/nz50gkEvD5fJjNZqhUKri4uECtVkOn04HNZpOalVwuh2w2i3Q6jWQyiVAoBLfbvZXa7vV6aLVauLm5QT6flyyXw+GQWh0GhBkbCgQCsFgsEtspl8solUq4vr5GuVzGdDqFw+EQcTk9PcXJyQkCgQDW6zUajQba7bY8rt/vw+l04vT0FNFoFJlMBmdnZ0ilUnA4HJKZGo/HSKVS6Ha7qNfruLm5we3trcT62u02AEj5QywWw3Q6lfQ4Xc7H4mp/C49CbOgyDYfDrQ/g7e0tSqWS9OQwsxAKhZBIJCTAG41GEQqFtnqLmFViR/VDzBj9VdD9NIvNL7/8gmw2K+Mwms0m8vk83r17h263K3NoOIsmm81KRTFjGfwbbjYbcZ1Yt3Nzc4N6vY7NZoNkMonXr1/L76B1aRgGLBYLJpOJNH9eXFygWCzi5uYGzWYThmHg+fPnkoqPx+MIhULS4FkoFFAul1Gv1zEYDGCz2ZBMJnF2doaTkxPE43Ep3GMlM6uZmVioVqtSizOfzzEejzEcDjGdTsUdm06nsNvtUtPDZANd8MdoDX+JgxYb/rP5D6/X6ygWiygWiyiXy2LVsIPY7XYjFApJoDCdTku5PIc07bpHu+X8Tw273Q6fzycVtK1WSwS9VqtJE6nP5xOrgPUv4XBYygBYEUwXhq0LtEhGo5EUR6bTabFIIpGI/F/MBYbFYhFXV1ciMuxfCgaDUp2cSCTgdDoxnU4xHA7FjW61WphMJvLzfL6zszOxdhljMVeSUyQMw9g6KXk8HqzXa2kipbvNsgGHwyH9daPRSOpzmL00d+o/Zg5abOi312o1VCoVVCoVlEol+fDabDbJRNAnD4fDYs2YRxJ8yVV67B+ET2FuUVitVri5ucHV1ZVUBDOAzorgXC6HRCIhbhNrUJbLpZQaNBoN3N7e4urqCsViEZPJBD6fD6enp0gkEjg/P0c6nZaTgMVikTk7lUoFt7e3IjZ0346PjxEMBpFIJOQkYrVapa2EVcRMo9OaTSQSOD4+lsAzTzp83RTKyWQiNVmlUkkqqOfzOcLhMLLZrGTYzL1ko9EI19fXksFiFo9d6szM3dWF/tg4aLFZLBbodru4vr7Ghw8fUCqVUK/X0Wq14HQ65UOUSqUQj8clLmOeGmfuklZ+h9bcbDZDp9PB7e0t7HY78vk8Pnz4gOl0ilgsJpmmk5MTsSbMcS66uPw9hUJB2h1ub29Rq9UkLf3y5UsJJtOSstvtYhGUy2X8v//3/3B5eSn9VqxifvnyJV68eIFIJCJWAnuq3r9/j2azidVqJb1PR0dH4mrxxMMCQ/NngQPR+v0+bm9vcXl5iUKhgGKxiEajAYvFgnQ6jefPn0umazqdSv8Y36PZLT05OcHPP/8sNTlsdXnsn8GDEBt+YDm4iZPrut0ubm5u5MNLc9qchXj+/Dmy2awEFzlEiTz1dOSn4Ad/NpvJWdnhcIhF43A4EI1GpUiPB625hoZxDrNgXV9fS+vDaDSSpki6YLlcTuIl5kFk9Xod19fXKBQKqFQqGI1G0jaSTCaRy+Vwfn4Ot9stNVTlclncvcFgAK/XC7/fv+U2pVKpO2fcMFvGERflclkGhFWrVQyHQ0l7n56e4ocffkA6nYbD4cBoNEK1WsVqtZKf5SgOp9OJ8XgsLtRyuRSx8/l8W8PgHxsHIzb09c2mOM9utVoNk8kEXq9XgpKs8WB9B4u0tJrz6zBbNsze0OV8+fIlQqEQstmsHLBmS2TXKmo0GuL+XF9fo1arYbVaIZlMIhgMIpPJSO0OD7jFYoHRaCT9SNVqFZVKBe12G1arVYr6otEoUqkUIpEINpsNWq2WxHJqtZo0V7IYkZZYJpNBLBYToeEJiLE5ZssoWKzRqtVqmM1mCIfDiEQiUnd0dHSESCQipQLL5RL1en0rOM56HQbXecI8PT2V8SQcQ/IYT4IHITbMBrA/JZ/P49dff0WhUMB4PMZ6vYbH40Emk8GLFy/EpGUHNl0mHQn5dZjPrKyDsdlsyGazOD8/F0uGsRmW7O+6o4vFAq1WCxcXF8jn81IHMxgMEI/Hkc1m8cMPP+Dk5ETiZywUpEX1/v17vHnzBqVSCePxWKqSabVmMhlxi1nh++9//xv/+te/0O/3xfJJpVI4OzvD6enp1lCv3c8FD/DNZoN+v4+Liwv8+uuvKBaLYp2wmvmnn36StLy5bcEwDKxWq61CP7ZlzGYz1Ot1TKdTVCoV1Go16dtiJ/ljtGqAAxAbWjU0pYvFIi4vL5HP51Eul2G1WqUuJpPJ4Pnz5/j5559lJonyfbBYLJIpev36tbg7LHbkQUpXl2dwVgaXSiV0u11xc2OxGE5PT/Hjjz/i+PhY4jtcimf+X19dXaHRaMjjWBWcy+WQTCaxXq+luO/6+hqlUgmVSgWr1UosH46zoEu9W+9Cy4NFfJ1OB6VSCYVCAYVCAY1GY2uSYS6Xw8uXL5HL5eD3+yVFzjGmk8kE6/UaDodD2iNcLhdms5kMrW+323A6nRKsdjgcIlKPcV7ygxUbmrM0p6vVKvL5vJSybzYbGUOZTCZxfHyM09NT6SZWvh0eeBQYDrl69eoVzs7OpA6F82fMQsPMVb1eF9ep3W5jvV5LFTItg+PjYznIGATudru4vb2VorlarQaLxYJoNIpIJILj42NkMhkZzsWuclYQ00VLpVIwDANnZ2c4Pz/HycmJFCTuCg3jgHTRq9WqjMdoNpsy8pTzjI+OjvDs2TNEo1FJe3OWdKfTkfIAjqxgYoLBZ05+HI/HMmQ+n89L0SlbHMzjKx6DS/VgxQb4vVt7OByiVCrh119/lfEGjM+kUilks1lkMhlEIpEHNYjqkGHqNhgM4tWrV/jb3/4msZpgMPhRjAP4fT7Q7e0t3r9/j2KxiF6vh/F4DJfLhWg0KvGSZDKJWCwmoyAGg4EEkd++fYt3796h0WjIa4jFYsjlclILs1qtMBqNpKYqn8/j9vYWAJBMJvHjjz8ilUpJRpJtDubiQgCyXZSFgvl8Hv/85z9xdXWF+XwOt9sNv98vbt/x8bEUGtKimUwmIjAcwcFMmd1uRzQalWroYDCIyWQihYXNZhP9fh9v375FvV7Her2WkSW0GB+LW/VgxYZFYIPBQOoraB77fD4kk0lks1mcnJyI3+zxeHQ163eCqVqO33z16hVevny5NaeHRW/MDppd3aurK5TLZaxWK8napFIpPH/+HCcnJzIvGPh9CydHjTK7OBgMJCbE+TWZTAZut1ssGtbcFItF1Ot1aTFhfIZlD8xwmbNNXMLHAWrsz3r//j0KhQKcTidyuRxCoRByuRyeP3+Os7MzsaooUkxzl0olGS7W7/fF6mb7xqtXrxCPx2UImM/nw2q1kibhbreLUCiEk5MTaVg1V7EfOg9WbBipp0ldrVZlPau5yY8l6WrR/DUw5hAKhaTTmjCexqwR3aZCoYB6vY75fA6fzydWAS2DRCIh82E6nQ6azaa0l5TLZXQ6HTgcDsRiMRlNkU6nYRiGjJKoVCq4vLzE7e0t+v0+PB6PtDecn5/LLGRau2bXiVsYOJGRLg9f/3Q6hcfjEbft/Pwc5+fnksFyOBzShMom0FKptFX74/f7RWT4WlKplASMOSS/VqtJLdFyuUSlUsHV1ZWkxWOx2FapxiHzIN8F56jUajV8+PABhUIBrVZLuo+z2ayMAWAn73q9VotmT5h3ZQ2HQzQaDbx//x7v3r1DqVTCcDjEZrORtDbrZ9hFb7VaJQ5XrVZRKpUkRjMcDuFyuZDL5aQLO5lMwjAMzGYzmZlTrVZxe3sr5f8vXryQrQ6JRELS6ubmT7726XSKdrst2TFaRu12G5vNRtL66XQa5+fnImI+n0+q1huNhhQmsuViOBzCbrcjkUhIEPv4+BipVArBYFBcuNlsJuuJmZb3+XzyuvL5vGyEcDqdMrzr0HlwYsNsBntZbm5uUCwWMZ/P5WxxcnIimQi/3/8k+kr2DWMxjBmYhZxxDg4k49n4/fv3qFarsNlsUqhm7pcyVwR3Oh1UKhVpwmQMg4V6rJHiNs3lcimFemwVaLVaErzN5XISpzEMA16vd6tQz5wt4sgRc7apVCrJ/GLW4+RyObGq/H6/ZKu63S7K5bLM3ikUCmg2m1iv1+I2sTyAA+BZOzMej2W0xXw+BwBZLcPZS7e3t1JtzEZS84qeQ+VBic1qtZKKTa7+4GR7j8cj/0T237CPRflrYaMgADkz9/t9aaZk1/VwOITNZkMoFJLsYC6XE/eBq1harZaU/t/c3KDdbmOxWEgJA5sw4/G47PxmfIZzoTebjdTm8OfZ38TOakKRMPc3MTZUqVTQ6/Vgs9kQiUREHM/OzmR+DssoOBif4sqUOAtKfT6fzN45OTlBMplEPB6H2+2WvxndNhYINptNbDYbRCIRuFwumfHD19loNOD3+7HZbLb2jh0iD0ps2IPCnhKOdeQKDxaVsUr4sfiyhwRjHdVqFR8+fMC7d+9kTrBhGNJkSGuGWSDWlXAaH+Mz9XodVqtVGiiTyaT0RtlsNrEieGCy8ZJ7n9jQyN1T5s594HcrjONHGBtiCQVbBygOdH0SiYRs6OScpFKpJE2YpVIJjUYD8/kcgUAA6XQaqVRKpgJyDbDL5cJqtUK/398afVIsFqWlgcFzivFgMJDtn+ZxFqx4PlQe1NFKsWFpeqfTwXq9hmEYMtiIA6t3P1TKXwNrbjgiYbfg7uLiQjZGcpYNXZB4PA6n04nNZiMuEB9Tr9dl/jOF49WrV8hkMuJSsO6lWCyiVqthPB7LVL3j42PJbLGJktlI81I9rvzlkC4GldmzxLUsz58/x/n5uQyzZ7c5CxRrtRqur6/l8Z1OB5PJRCzu169fizXGFgibzSb1Q3z81dWVPH+r1YLX60Uikdiad10ul+V5Of/Z4XDITJ9Djd88KLHZbDayAZFLxRggY1HXXVkR5fvB+AxNdY5aZcEdZ9Cww56d1IylMfPC0R7mHVA8yHq9nuz65vhVNnJy1xP3dnFmDgAZNM+xEBwV6vV6t8ZtMkZjdkdYyUyhACCfp9PTU6kuZqqd2TLGhpgVrVQq6Pf7EgiORqN49uyZdL0z82We3czUNoVqOBzC4XCIsLGZFYAUODLIztKPcDgsWx8OlQclNhaLRXzbwWAgVaeRSER8Z4/Hc98v81Gzuy+ctSj9fh/L5RIfPnzAv//9b4k1cAdTLpfDs2fPZH8US/NbrZaIU7vdRrfbBQBpYuTwMu7dYpaK2SHOCOZSObop5ol6n2IymaBSqSCfz4vb0u/35fmZis9kMlIUau7GHgwGW9ZQq9WS+E46nRaBMQ8LY6xoOp1K+wSfm0Ll8Xhk+Ho6nUYmk0EikcByuRRriGuK+bfnvONDtWqAL4gNhwCZF7Obl3N9L6jWnBnMObEAZNYHzWqOfuTrU74PbDvgGhautjGPmLDZbHjz5g3+9a9/YTQayc4s9iux6pWTE9vtNgqFAt6+fStDsgBIrRSzSH6/X0r4G40G8vk8rq6uZNwoZxiHQiF5TlYed7vdrSH05hGebHFhIyUDy5y3w/Q0e5G4U8xms2E0GuHm5gZv377F27dvUalUMJ/PsVqtxG1jjIbzjblTi71VbOLkkC+Op+UWUS7bY6KDYsLmUGb8ODu52WzKlL/7nh7Jvzd7uL4mI/xJsWHWgfNVmbIbjUaSsvteJh1/T6fTQT6fl50/3NXDcZKDwUDOmpKNpjAAABRMSURBVPf9x35sWCwWCci+f/9eMkTj8RilUglv3rzBZrPBu3fvUCgU5MDjwCmbzSYT9ywWC+bzuQyv4gyY5XIpoz+ZXbHZbHC73RgOh+j3+1LyXywWZWUvT3bA793Y5s+A+XPIk+N8Phfhev/+PWq1mowe5etkzQ+HrZnX8YzHYxSLRbx9+xYXFxdotVpb4yc49XG1WkmQm1AEuVamVCpJupsHJqcCcgMDxY7Fhc1mU0IJbrdbTvyNRuNeP/98TsaXaHGy5+xzs5Utm0+84vV6LbUQnOnBCsvBYPDJX/gtmLcvttttNJtNjEYj2efEugmfz7e10F3F5vvBOA2Dkvl8HvV6HQ6HQ1LA6/Ua1WpVengCgYBMQAwGg1LbAvw+BpTzbBin4ZZJNmWGw2E50Dgoi8OvuI7FvPWCg+nNqXhi3kVFN6jZbMpw88ViIeIWj8elx4muIx8LQGqBWBXM4DSbU9mXd1cGjEvz2NTJbne6ScFgEKlUColEYmtKH7Nm3Cw6mUywXC7hcDgknGBuu7hPsXE4HNKD9tNPPyGbzW7VvN2lDZ+0bMwBNja68cJKy+/tPzIYyXUr5mn0NptNTLZDDpI9ZPiBZ08arRdzbQsPGm6zWCwWaDQaW6tnAUg2iH1TfAyLBHu9Hmq1mpwNaZFwjS7dOGbB2MJg3t31KWgF8HeZXzMAuY9jK8wHh1mw+LeYzWbSBQ9A4lhsNbjr+ZnB4x4zc9W1uXjPfHDy+xxBwZ/lMryHMMKWYsxyAafTKScjwzA++7/5pNjwQ+FwOGTfcSAQQCgUAoC/RGwYHJ5OpwB+8+15xtwd5al8f6xWq2RCGL/gWZX7sXnQAL9P86Pbwv6ezWYjVinP/PtezmZ+jd/rcbuCBPxeMEhhoDhwKwU3pn6NQPBvyd4thi/W6zVsNpukvu+zvoxiYz42v+YEAHzBjRoOh1v7seniTCYT+UD9WcwvkJPZ3r17h/F4jHQ6jR9++AFHR0fwer1Pbn/TPuHJZTQa4fLyEv/4xz9QKBQQCoXwyy+/4KeffkI0Gt3aHGBOMXe7XXS7XQloWq1WGc/AIfO7B8ldH70vWSzf8r7+zO/73OPN7Q/9fl/cHuC3g5HD1Tnq9HPPz78r42TmLN5iscDR0RFevXola4Hv242y2+3SDX92doZYLLZl2fwhN4oBIE4mOzk5EZN4tVp9txdvflFc1j4cDtHtdvHs2TP87W9/w08//YRIJKIi8xfCD0iv18P//u//SnVvJBLBf/7nf+J//ud/kMlkPnoc58owttftdmXHEju+k8mk7H/6o68J+FgUvkUkdpsxv/T7vubxdIfYWsPd4RzNYZ6PbG6fuOv56XayLqlQKMhgrtlshtevX+Pvf/87fv75ZwnC33c2yuFwwO12y2zvL4U4PmuP2e12GeC8DzweD25ubpBMJmWodSqVks7fQ+0JOSSYMvb7/fK/T6VSePHiBWKx2J2P4SjLcDiMbrcrWSefz4dYLCbtJY8RZoji8biUDAAQsWG3+NfCauPZbCZpflo25+fneP369cGu8H1QRX0AJFMxnU63AolWq1VGUSp/HcvlcquWylxr9SmYoYnFYvB6vVIvQlfiUA+Or8Xj8SAcDstWBeC3Tu67XMfPwXYQ7g9fLBbweDySkbXb7eLCHiIPSmy4j5ujEwFIly2tGqvVKulV5fvDbAiLOM2Zlc/BdDSFijEgWsePOdbG7QkMEAP4w+99s9lImwZrbBaLBdxutyRo+Pc9VB6U2DCoGAgEMBqNAEBqJQzDQDAYPGhlf6zwBPAUTwJWqxVOp/O7jDrhDOdut4t+v4/VagWPxwOfzwe/33/wzccPSmxsNpuk2Jn26/V6sFgsMndYC/mUxwoLIdlDxoHrzGip2HxHuOArHA5jNBphNptJ4Ritnfl8LitEFOUxYM5EDQYDtNttOckahiHbFg5dbB5Ueod9Mxwn4fF4JGjGsRPsgDVXhCrKocI6pX6/j06nI42wHBrHtg4O4jpksXlwlg37RjjdjGNBOYHfMAwsFgvJfOi0PuWQYYd4o9GQLSKM13CwFrc6sGjuUHlQR6rdboff75dpa+12W7p1OZaRJfWM9muvlHKosL/MPPi90WhguVzC4/FInVk6nUYoFILb7Vax+V4wG2W327FcLmUS2ng8lt3RdJ1Yf8D+LRUd5VBg/xPHcHCKX7VaxWg0gtvtRiQSQSKRkPU3h27VAA9MbFgyz9UWyWQSp6enACCl8JxYRrHZbDYIBAK631s5GNji0ev1UCqVZLbxYDCAz+eTqvlsNisNsIc8oY88KLEx43Q6EY/Hpc9msVjIdP31ei0dsGwI5ZpSRXnoTKdTmXVD94l7yjnL+dmzZzg6OpIZMY+BBys2DBYDkHGVpVJJrJtarSZT+IHf/F/WIhzybh3l8cHUNufrcKUML51OB8vlUnrJuKo4Go0+mj3fwAMWG1orPp8PkUhEBkxzfepgMMD19bWMLe31ehLjiUQiKjbKg2I8Hstu8EqlgmKxKHvNLRYL0um0zGSOxWIIBAIfrQ4+dB6s2DB+w8bMo6MjKejjGYH/uGq1ikajgbOzM1gsFoTD4ft++YoiWCwWDIdDFAoFXFxciNvE2cVcjMcljKwxeyzuE3mwYkPMM2MBSFym1+thMBhITQK7bb1er0wU5NpY80Cfx3SmUB4e7JI3d8tz3s/V1RUuLi5QrVbRbre3FvS9ePFia8ndY6wfe/DviFP/Ocmds2W5tnQ4HMpMWQ7qns1miEajCAQC8Pv9Moib8RxF+Sswzy2eTCayMYJzvEulEnq9nqwb5jK/58+fy8pfrpl5jGGAgzjyOBuF1z0eD5LJJBqNBiqVCgqFAmq1GiqVClqtFt68eYNEIoHz83OcnZ1JUdT36MxVlE9htVqxWq1kQ0WxWMTV1RXK5TIGg4FsuYxGo7LgLpFIIBwOIxQKydrefc9r3hcHITZ0g+x2O9xuN8LhMI6Pj9Hv93F5eSlrOwaDgazd4LpSFvtx1ghN1Mf4z1T2j3lEKHucuG43n8/jzZs3KJfL2Gw2cDqdspzv5cuX+PHHHxGPx8XV/9z83sfAQYgN8PsMWLpBDocDTqdTMlMcNFSpVKTku9lsIp/Po9/vy5pXDt82DANut1tWZDy2YJzy17HZbGSbxHQ6xWQykZaaTqeDVquFer2OcrmM4XAomxGi0SjS6TSePXsmVo3b7b7vt7M3DkZs7oKWytnZGXw+H46OjlAqlVAul9Hr9bBYLHBxcYHr62v4/X5Ji3MIdzQalUXybH1QlC/BuTOcRlCv11Gv12UDiXkdkd/vl71KR0dH0lQZi8UerQXzKQ5abGw2myyk56J5BoSLxaKkF0ejkZiwrNkZj8eyfAyAmLnm/Tccbak8PczuEWF2aTKZoNPpoF6vo1qtolgsolQqoV6vo9PpYDKZwG63iyWTy+WQzWZxdnaGTCYjW0ueWrLioN8t10k4HA6xTFar1Ucd4Zz4D/w2vb7RaACATEWjheP1emXmq/miLtbTg9spp9OpZDuZZeLok0ajgWaziWaziV6vh+VyCZfLBbfbDa/Xi1QqJdXAmUxGCveemkVDDlpsdqH1YrVapZHz+fPnMtN1OBzKBMBKpYJ6vQ6Px4NgMCj7qkOh0NZuaQ4t4kJ45XHDRMJ8Ppd5wL1eb+trp9ORtpnZbAYAW9slAoGAfKaYaQoGgzAM48kKDfDIxMZut0v8JRqNylK9fr+Per2OSqUiy9QajYakIjlknfEcXrhz3DAMGWpt3s3MC12tp/xBOgR2N1Cat3uat0gsl8utTQfNZhP1eh3NZhONRgPdbhfj8Rir1UqWONI9z2QySCaTstqFljcvj3nLxJd4VGJD62M3wj8ajeQfbxYLh8Mhq4S5iXCz2WA2m0kanTEgXlgcuPuVbpvycLFYLDJLZrFYiHvEQrzZbCazk5hdYmFer9dDr9fDcDjEcrmUKQO0oI+Pj6XtIJlMIhgM6hSCHR6V2HwKVh9bLBaxeo6OjsQ0Hg6HYsVMJhNMJhNUKhWJ83AI+657xYvf79/ac6w8XLjOltmkXq+3JSacAzwYDLBaraQmi//bcDgsy/e4xzwcDiMajUoCwu/3q9DcwZMQG7pK0WhUUpHT6RSj0QjtdltMZX7Q+MFrtVoYDodwOByIRqOSOo9Go4jFYlv3UXC4mGzXtTIXa+32aalA/XHMGzv59XPX2T9Hoel2u2i1Wmg2m2i1WpK2ZuB3NBrB5XLJSSYcDkvPHd1tdmdz1zVrv2w225N2lz7FkxAb83AtwzAAQFwn7uQxDGOr0M9qtWKxWGw11TETAfw2qJoBxHq9Dq/XC4/HA5fLJf45hcdms8ltm80m95tv6wfzj8EeOfbJ8fqn7pvP55JdGo/H0sRLy2YwGMjWDovFIhmlYDAoJxbziYbjTMxNk3oC+TxPQmyA7Q8C4ShRxnnC4TBSqdSWWc0CLdZYMFPRaDRQr9dlUiAFzbybmRePxyNVy7zwtu7A+nYWiwXG4zEmk4nEWRhz2b3QPZ7NZrJemLDZl60E5tG0dJXZ1BsIBCTb9BT2mH9PnozYfAp22Ho8HsRisY8Ch7Rm6M93u12J9VCMWCBI0WIwmR9M84eUtxnr4ff+yES2bxGnfQvat+z0+trHcE0tg7e0THh99zYDvYzLMXZnFg5z2UMkEkEgEIBhGFJrRcuYF7pLytfzpMWGzZ0UCbOfT/eJqXPGdZrNpmS2rFar1GXw51erFWazmQQUaQnNZjOMRiP0+32xasxZLrpufByv/9H7diugze91937zfXws3wfh38JsCaxWq49iIp+LoZhv7/69zLc/df/ubbpDFBxaNbRsdq+brRlu4+CaZ8bd6B7RRTKvTtltkNTZSN/GkxYb4G73ygwtDvrxgUAAsVhMusxZKDiZTLBYLCS1ygAhDzia8q1WCwDE/aIJb7fb5Yxp/nrXfZ/6nt1u36oFukuQzPebf44B7bsOLPP3+drNw6F2RYGiu3ubKWde2Mxovs2vDObu/uxyudz6O5tF0Izb7ZaVKHwvjJ25XC4R+0AgAJ/P95HV6fV61UX6zjx5sfkS3GVl7tw1HzC8sJSdZ9UvXWjWT6dTzGYzETPGcTweD9xut3xl8Np8310/53a7xeripEJeeB+tOd7H7InT6fzoIDaLCgCx3CgwDMaaH2e+TdGhYPA9s1uaAVveZq0Lb/Nivr1cLkVYGR8zW4m7F5/PJ9f5d6I4m0V711VSvi8qNl8BD0oO8NqFBxOHr5uzHIzt9Ho9WQzPA5aNoPP5fMtK4NmbP+NyuTCZTCR2wP4tplx3+7mYejcLDr/SojHfR9fC5XKh3W6jUqlI8dp0OkW9Xsfl5aW8VrPYmEXG/B7M9/E90Trh+6LQmkWXgnTX93l7vV7L34KD1Zg5Ml/M8RhaLozDMN5Cy9NszekO+b8GFZuv5HOuFrMXvM4YkM/nQzgc3sqKmDMmzKJMp1OxHHZjBLvzk+ma0eXY/Zm7gpafi9UQis5wOMTl5SVqtRpmsxm63S5+/fVXWCwWxGIxEQ4zd8Vsdq8D+Cj+wvvW67X8zfh3M8eCzG6aeU+YOfN3V8bPnPWjZUgx/tz/VWMxfw2Wjcr4d2PXrWBs4VM1IOY4hTkLRgvAbAkwKGp+DC0E8+P5HHfFVD4VdDXHV+bzOQaDAdrtNkajkfT+mAOmnwpM33WhNWWuN6LbYs7y0I3h/fye2b3h/eZYFV2hu2qX7rpPq7zvD7VsviM8434tDJzyIGfMxxyn2LWCzHEMHshcgsavZreMl93YitndYaaGQsXYCe8bDodYrVZbCwDNsaDPXfjzPKexP80cbzHHpGih3PW93cLJ3cC18rBRy+aBQNeIcYnd+MVd3+N13jZbN2YrZjeusvs9s4vCbaP5fB7NZhOGYeD8/By5XA6hUOijVLk57vOp+BBvM6hrtl7MF97PAO7uV3NMSjk89L92z5gnwjH2w6DnrlCYrZDdzM9dbtJu3RCfZ/d5zfR6Pfzzn/+UeS6xWAz/9V//hf/+7/9GJpPZeq0AttyS3djSXRez+Hzp+q4VRQuJz6/u0GGhYnPP7FoKnHkC3B1s/VQA9nOBWTNfMmS73S7m8zn+8Y9/yAiF09NT/PLLLzg+Pv7q9/Ol7911/XP3feqxyuGgYvNAeCgHk8Vigd/vl4pmu90Or9crw6AU5VvR6JqyBWM/5owVg86K8mdQsVG22I33ANsxH0X5VlRsFEXZCyo2iqLsBRUbRVH2goqNoih7QcVGUZS9oGKjKMpeULFRFGUvqNgoirIXVGwURdkLKjaKouwFFRtFUfaCio2iKHtBxUZRlL2gYqMoyl5QsVEUZS+o2CiKshdUbBRF2QsqNoqi7AUVG0VR9oKKjaIoe0HFRlGUvaBioyjKXlCxUe6E61x217ooyreiYqN8EV13q3wPVGyULSwWC6xWK5xOJ1wuF5xOJ2w2232/LOURoGKjbGGxWGC322EYBgKBAHw+n+z9VpQ/g36ClC0sFgscDge8Xi8CgQD8fr+KjfJdsN/3C1AeFlarFV6vF6lUCicnJ4jH4wgGg7Db9aOi/Dn0E6RsYbPZEA6H8fLlS3g8HgSDQSSTSTidzvt+acqBY9loXlMxsVwu0e/3Ua/XMRgM4HQ6EY/HEY1G4XK57vvlKQeMio3yEev1GqvVCuv1WrJTNptNU+DKn0LFRlGUvaApBkVR9oKKjaIoe0HFRlGUvaBioyjKXlCxURRlL6jYKIqyF1RsFEXZCyo2iqLsBRUbRVH2goqNoih7QcVGUZS9oGKjKMpeULFRFGUvqNgoirIXVGwURdkLKjaKouwFFRtFUfaCio2iKHtBxUZRlL2gYqMoyl5QsVEUZS+o2CiKshdUbBRF2QsqNoqi7AUVG0VR9oKKjaIoe0HFRlGUvaBioyjKXlCxURRlL/x/bJu+Sqr6W7YAAAAASUVORK5CYII=)
Maths-General
For such questions, we should know the formula of area of different shapes.
physics-
A solid sphere of radius
has moment of inertia
about its geometrical axis. If it is melted into a disc of radius
and thickness
. If its moment of inertia about the tangential axis (which is perpendicular to plane of the disc), is also equal to
, then the value of
is equal to
![](data:image/png;base64,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)
A solid sphere of radius
has moment of inertia
about its geometrical axis. If it is melted into a disc of radius
and thickness
. If its moment of inertia about the tangential axis (which is perpendicular to plane of the disc), is also equal to
, then the value of
is equal to
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALgAAACuCAYAAACFvMdBAAAgAElEQVR4nO2daWxb15XHf6S4SKJIShQpkpIoarMW29osR0ukJE5ip0mbOG1Qo+iSQVMUaKdov0w+zJcOUGDmczFL0RbFYKbATItkskwyTtzGduLY9RJLsi3b2qx9oyRKlChK4r7NBw/fxLElr9TC3B/wYOvxie+S+vPw3HPPOVcWj8fjJBG3241KpUKj0STzNgLBHZEn64nj8Th+v5/z588zMjKSrNsIBBuSNIFHo1EWFhb493//d86dO5es2wgEG5I0gQsE2wEhcEFKIwQuSGmEwAUpjRC4IKURAhekNELggpRGCFyQ0giBC1IaIXBBSiMELkhphMAFKY0QuCClEQIXpDRC4IKURghckNIIgQtSmm0l8EgkwsjICO+99x4Oh4NQKLTVQxLscLaVwKPRKNevX+cf//EfOXr0KAMDA6yurm71sAQ7mG0lcLVajV6vJxwO8zd/8zf88pe/pLu7m1gsttVDE+xQtpXAASorK/nBD35AVlYWJ0+e5Be/+AW/+tWv8Hq9JLnDhSAFUWz1AL6I0Whk//79FBYWMjw8TFdXFx6Ph/n5eb73ve9ht9vJyMjY6mEKdghJE3gsFmNtbQ2VSoVarb7n31OpVOTn53Po0CGWlpaYmpri6tWrzM/PEw6HOXDgAA0NDVgslmQNXZBCJM1FicViLC0tkZGRQXp6+n39rk6n49vf/jYlJSUolUoikQjT09P8y7/8C7/+9a85efIkMzMzwmUR3JVt56LAzclmfX09VquV9PR0gsGg1CnrT3/6Ez09PQwMDPB3f/d39/XtIPjysS0FnuCb3/wmbrebTz/9lGAwiEKhoK2tjd27d1NXV4dKpdrqIQq2Odta4I8//jjnz5+no6MDmUyG3W7nu9/9LnV1dZjNZmQy2VYPUbDNuWeBLy4usra2hl6vR6fTIZcnP8JosVhoaGjg4sWLDAwMUFtbS1tbG9XV1Um/tyA1uCeBh0Ihrl+/jsPhoLm5Ga1Wm+xxSTQ3NzM6OorT6aS+vp6srKxNu7dg53NPZtjhcHD27FmuXbtGYWHhpljvBGVlZTz22GOUlZXR0tKCXq/ftHsLdj4bWvB4PE44HOYPf/gDcrmcI0eOoFKpNtX3XVxcZG5uDqVSyZ49e0QjfcF9saEpDgQC/PnPf8bv91NZWUlVVdWmWm+Aa9euMTk5yYEDB9Dr9aSlpW3q/QU7m3XVGo1GWVpa4r333sNut1NXV7fp/u/S0hI9PT34fD6+8pWvoFBs66CPYBuyrsD9fj+Tk5MMDw+za9cuSkpKNm1Q8XicSCRCd3c3i4uL2Gw29uzZI6y34L5ZV+Dz8/N89tlnNDY2YjabN1VciWX+P/7xj5hMJr71rW9t2r0FqcW63/kej4eBgQH279+PTqfbtAEl8k7+6Z/+ib1799Le3k52dvam3V+QWqxrwd1uN729vdTU1GyawILBID09Pbz77ruYzWba29spKysTvrfggVlXOV6vF4fDgc1mIzMzM+kD8fl89Pb20tXVxdraGi+//DLl5eUiLCh4KNYVeDweJxqNkpaWltTQYDweJxQKcePGDT766CMikQivvvoqJSUlmx6SFKQe6ypILpejVCoJh8NJrYkMh8MMDw/z29/+Fr1ezw9/+EMhbsEjY10LrtVqKSkpYWRkREqwepSEQiEGBwc5fvw4vb29HDp0iObmZsxmsxC34JGxrsBNJhNNTU1cuHABm832SASecHuuX7/OlStXmJqaQqlU0tbWxuOPP05BQYGIdQseKesK3GKxcODAAd588036+vrQ6/UYjcYHvpHX62V6eprBwUGGh4dxOBxotVpaW1tpbm4mIyND5HcLHjnrCtxgMNDU1MTp06fp7OxEqVTy2GOPodFoUKvVdxVjIlErHA6ztLREb28vp0+f5tixY+zfv5/Dhw/z2GOPiQp5QVKRxTeo3I3FYiwvL/PGG29w+fJlcnNzOXz4ME1NTSiVyg2feGVlhTfffJP/+I//YGZmhvz8fJqbm3n11VcpLCxEq9WiUCiE1RYklQ0FDjdF7nA46O3t5dq1a4yMjBCLxcjKysJms2EymaRrXS4XTqeT2dlZnE4ncrmc2dlZnnzySV588UWKioooKipCrVaLiaRgU7irwBMsLS0xNjZGf38/U1NTRCIRYrHYLa0bZDIZcrkcmUxGLBZjfn4eh8PBK6+8wpEjR+67fYRA8LDc8xq4wWDAYDBQX1/P/Pw8KysrOBwO5ufnpWuMRiN5eXlYLBYyMzM5evQonZ2dGAwGIW7BlnDfSR5paWlYrVasViuVlZXrXre2tvZQAxMIHgXCERakNELggpRGCFyQ0giBC1IaIXBBSiMELkhphMAFKY0QuCClEdW8D4HX6yUcDhMMBvH7/UQiEeBm8XQwGJR+/jyxWEx6/F4qpeRyOZmZmev2QlcoFLfk6qvVajIyMpDL5SKhDSHwOxKNRonH48RiMen/dzo3Pj7O8vKylHPj9XqBm0lnCwsLd1zNDYVCLCwsSHsO3Q2lUondbsdgMNzx8aysrFvaSRuNRmw2G2q1moqKCrKyslAoFFIhSULwcrn8tnOpiBD4HZicnMTtdjM/P8/U1BRer5fx8fHbzhUWFqLX68nNzcVisUi57RUVFbS2tt6xI4BSqSQ3N5fc3Ny7phzDzZpVh8PB8vLyHR/3er0MDQ1JPw8ODnL69GnC4TCjo6N4vV5yc3OlLM7KykqysrKwWCzSB6GyshKtVpuSGZ5fWoHHYjECgQCTk5NMTk4yPj7O2NgYk5OTpKeno1QqycjIQKPRoFAosNlslJeX33JOq9WiUqlIT0+XzgGkp6dLz/FF5HK5tDHXvQgqFothNpsJBoN3fDwcDtPQ0CD9HAgE8Hq9xGIxPB4P4XAYv9/P2tqalN+/urrK/Pw8Fy5cIBqNsry8THZ2NoWFhRQVFWGz2bDb7ZjN5h1fkPKlEHgkEmFpaYmFhQXJfXC5XCwvLxONRqUjLS2NoqIicnNz0Wg0aLVacnJyUKvVGI1GMjMz0el00rnNQC6X37UeNj8/f8PHV1dXWVpaIhKJMDc3RzAYxOPx4Ha7CYfDzM3NSR+E4eFhxsbGkMvlqNVqsrOzMZlMmEwmLBYLJpMJjUazY6x9ygk8YZk9Hs8tx+LiIgsLC9KxtLREOBzGbrdTUlJCWVkZ5eXllJSUbHoP9GSj1WqlXTnKysrueI3T6WRiYkL6JhsbG8PlcqFQKG4TeE5ODlqtVvqw63S6bbshWEoIPBqNEolEiEQikttx+fJlLl++zNWrV5mcnMRut1NdXc3u3btpb2+nqqqKoqKilBLyw2A2mzGbzTQ1NUnnfD4fU1NT9PX10dfXx4kTJ+jt7SUWi1FSUkJtbS0tLS3U1dVhMpmkyaxSqdw272tKCHxsbIyOjg4uXrxIf38/kUiEyspKqqurOXz4MHa7nczMTNRqNSqVSjq2yx9hu5KRkUFJSQkFBQU89dRTBAIBQqEQi4uLTExMMDg4yNtvv80vf/lLDAYD+/btY9++fbS3t6PX67eFG7MjBb62tsbU1BTd3d10dHQQDofR6XQUFRVRX1+PyWTCaDRiNBrJzc3dNm/2TkMmk0nG4PMkIjDV1dW0trZKcxq3282ZM2d4//33KS0tpa6ujpqaGoqKirboFewggYfDYWZmZrhx4wbj4+MsLi4SDAZRqVQUFBRQUlJCeXk5hYWFGAwGYZ2TSCJKlJeXR3V1tRTbHx8fZ3x8nMHBQXw+H5cuXWJgYACDwUBVVRXl5eXk5ORsarfgbS3weDzO6uoqLpeLmZkZhoaGuH79OgsLCxgMBpqbm3nqqacwmUzbdpLzZSBhZAoKCmhrayMcDnP9+nU+++wzrl69yuLiIpOTkzgcDoqLi6XJ6ma4iUkVeKLi/n5fRGLl0Ofz0d3dzYcffsgnn3xCfn4+r7zyCgcOHMButydjyIJHgFKplPzxxKT/rbfe4je/+Q0ZGRk888wzvPjiixQUFEjrAckS+j23jbhfVldXeeedd+jt7eXgwYN85Stfua/fPX78OO+99x6RSETa4dhut6PX69FoNPe0CijYehIdzjweDy6Xi4GBAS5cuMCVK1fYv38/3/jGN9i7d2/SetAnzYInVtLUavU9L4pMTk7y2WefcfHiRdRqNa2trdjtdoqLi7Hb7Wg0GuFb7zASE9VE/Dw3NxebzUZTUxPj4+O8+eabnDx5kqamJtra2khPT3+kf+OkCjwQCKBQKDacVMTjcfx+P11dXfT39zM7O0tGRgZ79uyhtbWV/Px84V+nCAqFgry8PPLy8qirq+Pq1atcvHgRp9NJR0cH09PTtLS0UFRU9Mgs+pZOMoPBIAsLCwwNDXHixAkCgQANDQ08//zzGI1GYa1TGKVSyf79+6mvr6e/v59Tp05x4sQJfD4f+/bto6ysDIPB8NDttLdM4LFYjKmpKY4ePcof//hHXnvtNb761a9SXFy8VUMSrMMX2/Mlzj0KA6RQKKipqaGiooKvfvWr/MM//APnz5/nhRde4MUXX0Sn0z3UfbZE4OFwmFOnTnHmzBmi0Sj//M//TGlpKTk5OVsxHMEG+P1+3G63lK5bWFgonTebzY/sPiqVCpvNxt///d/T0dFBZ2cnQ0ND/OAHPyA/P/+BY+ebKvB4PE4gEOD9999nYmICu91OfX09e/fuFR1ntylut5vOzk7Onj1Lbm4uTU1NjIyMMDIywk9+8pOHEt/nkclkqNVqbDYbCoWC7Oxsenp6+Nd//VdefvllKY/9ftk0gSdykT/66CNGR0cpLCykubmZqqqqzRqC4AFQKpWoVCpWV1eJRCKsrKywvLyMy+VKmkGyWq3odDr0ej3Hjx+XCjiqq6vR6/X39VybIvDE1txXrlzhgw8+4JVXXqG9vf2RfsUJkoPJZGLv3r309/cjk8koLCzEarVSW1sruSvJQKPRUF9fT0FBAb/+9a/p6OhAJpOxd+/e+9o7dVN8gmAwyMWLF/nd737HT3/6U5577jkh7h3EwsICH374IQaDAavVSnNz830t3D0oCoUCi8XCz3/+c1ZXVzlx4gT9/f339RxJF3gsFuPEiRN0dnbyrW99i927d4vdi3cQfr8fh8NBX18flZWV6xY/J4vEQtF3vvMdDAYD//M//8PIyMgdOxbciaQL3OFwsLi4iNFopK2tLWWLW1MVt9uNz+fj6aefpqCgYNNK9T6PTCbDZrPx2GOPkZOTw+9//3s8Hg/3kmWSNKXF43GCwSATExPk5OTQ1NSE1WoV4t5hOJ1OFhcXeeGFF7Y0r16hUFBdXU1NTQ1jY2NcuXJl3U4Dnydpo41Go8zNzeHxeCgtLWXfvn3JupUgiTidTmZmZqRQ7laSlZXFrl27aG5u5tixY0xMTNy1eVLSBB4MBrly5Qp5eXkUFBRsapK74NERDAaRy+U0NDRsucDh5kLT17/+dc6fP8/w8DA+n2/D65Mi8ETdnsvlIjs7+5Hvcy/YPJ588kl+9KMfbfUwJNLS0sjKyqK1tZXJyUlGRkY2vD4pAne73fT29qLRaKTWYYKdSU5ODgUFBVs9jFtIT0/niSeewOFw3FXgSVHe8vIy/f395Obm3tO234JbWVxcZHx8nIWFBfLy8rDb7eTk5IgJ+v+hVCqpr6/nv//7v3E4HBtemxSBr62tMT09jVarFZU390GiBrWzs5O3336b69evU1dXxze+8Q0aGxvF+sH/EY/HycnJYXV1lcXFRUKh0Prdd5MxgEAgwMLCAjqd7qHzeb9MhMNhTp8+zb/9279x9OhR4vE4ly5dwuVy4XA4qKio2OohbisCgQArKyvMzs6uW6ObFIHHYjFCoRBpaWnCPblH4vE4/f39nDx5ku7ubqLRqPTY5cuXWV1dxWq1buEItx/Dw8PI5XIuXbq0uQJPS0sjMzOTcDh8T6tNgpurdXl5ebS3t0s9AhM0NDTw7LPPCoF/gRs3bmA2m9m1a9e61yRF4Onp6RgMBpaWlm6xRIKNsVqtHDp0iHg8Tjwex+l0YjKZ+M53vsOzzz676Xkg25XEKvnvf/97zGYzJSUl616bFIFnZmaSn5/P+Pg40WhUuCn3QXZ2NocPH6axsZFLly5RX19PYWFh0toq7ERisRizs7OEQiFCoRBer3fdYoikxJ1MJhONjY3MzMwAiKr4+yQ9PZ2SkhJeeeUVqem+4P8JhUJcuHCBlZWVu66xJMWC6/V6KisriUQit2zOJLh35HK5iHuvQyAQ4M9//jOzs7OoVKoNDUBS3sFoNEooFCIjI4Pp6WlcLlcybiP4EuLz+RgdHcXpdCKTycjKytpQ4Emx4OFwmNXVVeLxOA6Hg6mpKTwez33X0wkEnycejzMzM8Px48exWq34/X6ys7M3XExMigVPS0tDpVLh8XgIBoOMjo7S19d3T/tCCgTrsba2Rl9fHx999BEVFRXU1dXdtfQxKQJP9I5WKBTU1tYyPj7Oe++9h9frFXFxwQPT2dlJV1cXhw4dore3l7Kysruu7iZF4DKZDKVSidFoJBAIsHv3bsxmM7/61a9YWVkRllxw33R2dnLt2jU0Gg3t7e1MT09js9mw2Wwb/l7SpumJvSWdTifZ2dlSRc8bb7zB9PS0ELngnkg007948SKZmZns2bOHiYkJdu3aRVFR0V2bASVN4GlpaZhMJiKRCF6vVyo6HhgY4MyZMwwPD6+7ualAALCyskJ3dzeffvopsViMqqoqDAYDZ8+e5dChQ9hstruGUpNWiZBwU0pKSnA6nQwMDPD8888TiUR46623cLlcfO1rX8Nut4uFIMEtxONxvF4vfX19vPPOOwB8//vfJzMzk48//hiv18uTTz5JXl7eXZ8r6SsJe/bsYXV1lQsXLhAIBGhra+Ov//qv8Xg8/Pa3v+XGjRsiX0VwC36/n2PHjvGf//mflJaW8vrrr1NZWcm5c+fo6urixz/+8T0XgCRtCxOXy8UvfvELiouL0el0eDweAoEAr7/+OgAjIyNcuHCB7u5uqSd4fn6+yB//EhOJROjr6+P999/H7/fT0NBAS0sL+fn5fPrpp3R1daHT6fjud79LVlbWPQk86cWSaWlpVFdXs7a2xp/+9CfOnDlDU1MTlZWV0o64c3Nz/Nd//Rd1dXXU1tbe01ePIHUIhULMzMzQ0dHB4OAgCoWC5uZmGhsbsVgsDA0N0dXVhVar5cCBA/dVxL4p1cDZ2dnY7Xbm5ub4+OOPMRgM7N27l6qqKmw2G5988gnnzp3j3LlzLCwsUFZWRmlpKdnZ2aJgOYWJRCJMT08zNjbG8PAwQ0NDaDQaXnjhBXbv3o1cLsfhcHDq1Cnkcjm1tbVUV1ff1z02TT2FhYU899xzXL58mStXrqDRaKioqECj0fDSSy/R2NjIO++8w9tvv41Go+HIkSPU1NRgNBpJT08XQk8REruu+Xw+XC4XH330EX/5y1+QyWR8+9vf5uDBg1KxjMPh4Ny5c/T09PD973+fhoaG+77fpqlGLpdjNpv5+c9/zm9+8xtOnjwJ3JyEApjNZl577TWee+45Ojs7+d3vfodOp+OZZ57hmWee2TCpXbBz8Pv9DA4OcuzYMY4fP05DQwN/9Vd/RWNjIzqdjvT0dABp36bu7m7+9m//luLi4gcycptqFhUKBSaTiSNHjvCXv/yFDz/8EI/HQ1NTEwqFgqysLGlSWlpayuDgIDdu3ODSpUvk5eXx1FNPsW/fPpG0tcOIxWLMz89z9uxZurq6cLvd2Gw2fvrTn1JeXo7NZrslKnLq1Cm6urqQy+X87Gc/o7i4+IG7am36975cLqeqqopAIEBnZydnzpzB5XLR0tKC0WhErVZjtVqxWq0UFhZiNpsZGhpiaWmJM2fOcPnyZQoLC6moqKC8vJysrCxRMbQNiUajLCwsSL71zMwMkUhEMl67d++mpqaGrKws0tLSiEajLC4u8sknnzA+Pk5WVhb19fUP3dNySxzbtLQ06uvrycjI4NixY5w/f55oNEptba20vTNAUVERRUVFtLW1MTQ0xOnTp+nv72d8fJzp6WlGR0cxm81YrVaMRqP0Zgm2hnA4zPLyMvPz8zidTqanp5mYmGBqagq5XE5rayutra2Ulpbe4m74fD4cDgdXr17l7NmzVFRU8MQTT7B3796HHtOWzdzS0tLYvXs3NpuNDz74gA8++ICJiQmef/557Hb7LTve6nQ6GhsbaWxsZH5+nkuXLnH8+HHeeusttFotTz/9NK2trZSVlaHValGpVCiVShQKhaiKSRLxeJxYLEY4HJaOpaUlrl+/zpkzZ+jo6ECr1fLUU0/xwx/+kNraWslwJYjFYvj9foaHh/nkk0/4+OOP+clPfkJLS8sjK7BO+kJPWVkZBw8epKam5o7XJV7k9evXef/995mdneXQoUMcOXLkjkv4iWohv9+Px+ORLHtnZycrKyuUlZXR0tJCY2MjlZWV5ObmJuPlfekJh8O4XC4uXbokHYkGPG1tbdKOxVlZWaSnp6NSqW5xJWOxGG63mzfeeIOuri4sFguvvvqqtMvxozJMWy7wBKurq4yOjtLT00N/fz9+v5+XXnqJurq6dffPjEajUmej+fl5FhYWWFhYwOl0srCwQDAYRK/XU1paSlFREXa7HbvdTnZ2djJecsoSCoVYWlpiYmKCyclJxsbGmJycZHl5GZPJdMuRl5eHxWIhLy8PjUZzx/mR0+nk1KlTnD9/HqPRSGVlJXv27GHXrl23fRAelm0jcPj/dgBdXV10d3cjk8mwWCxUVVVRW1uLXq/f8MX7fD5mZmakP8D8/Dw+n08q4E0cWVlZWCwW6Q9iMpnIzs7eFv2vt5pAIMDc3NwtBmNpaQmfz0csFpNcE5lMRmZmpjRPKioqIi8vb8PEuYmJCXp6ehgcHGRlZQW1Wk1jYyM1NTVYLJakvJ6k+eDxeJxIJHJf1eFyuZyCggLy8vKora3lnXfeoaenh5mZGVwuF+Xl5RQWFqLT6e4YE83MzKS8vJzy8nLgpuDn5uYYHh5mfHyc8fFxxsbGCAaDmM1mcnNzMRqNGI1GDAYDer1eKmLNzMwkPT0dpVJJZmYmCoUiZaI1Pp+PYDBIOBxmbW2NcDiM1+tlbW1NmiS6XC7p8Pl8aDQaiouLKS4ullaa8/Pz73qvYDDI/Pw809PTDAwM0Nvbi8/no62tjUOHDmEwGJK6iJc0C+50Onn99ddpa2vj4MGDG7bX2oj+/n6OHj3KsWPHKCsr45vf/CY1NTUYDAaUSuUDda+dn5/n2rVr9PX1MTAwQF9fHy6Xi6ysLCoqKigoKMBut5OXl0d2djYlJSVoNBqUSiVyuRyZTCb1XUxLS7vt3FYRjUYlC5vI0IxGo5LlTTw+OTnJwsKCNIdZXl5mbGyMGzdu4PV6qauro7q6Wjrud5v1xGplKBTC4XBw4sQJ3nzzTQoLC3nxxRd57rnnMJlMyXobbiFpAp+bm+PHP/4xL730EgcPHly3OeLdCIVC+Hw+nE6ntDgkl8vZv38/Bw8eZN++ffcdGkxMVD9/rK6uMjc3x9jYGHNzc9LucCsrK0xNTeHz+cjLy8NsNpOdnU1paSkajYaCgoLbzm1VqHJiYkIS7uDgIOFwmPHxcVwuF8vLywwNDREKhbBarRgMBrRaLSUlJWi1WoqKiigpKcFqtaJWq6VIVOLfe/0WTuRyd3Z2cuzYMXp6eqisrORrX/sau3btIjc3l8zMzE17j5Im8NnZWX70ox/x9a9/nYMHD1JUVPRQzxcOhyX/OhFbXVhYQC6X097eTkNDw0NtcxeJRPD5fHg8Hunr2u/3S+JP5E8EAgGCwaD01Z44l7guEoncVlidk5NDTk7ObWEyALVajV6vx2g0Ajc/0G63m8XFxduuTVjGyclJQqHQbY9rNBopYqHT6aT5xkbn9Ho9KpUKrVZLdnb2A7eIW1tbY3R0lPPnz9PX14dSqcRisdzi0mi12k3/8O+YDCalUilFQebm5rhx4wb9/f1MTU3R09PDjRs3yM7OpqCggKKiImw2G3q9/p5dGIVCgU6n2zAV0+PxsLKygs/nk6I0brf7tnNfFHhiHhIOh297zsSHxOl0Sudisdgda1YTz7ue75ubm4tWqyUjIwOz2UxaWhpGoxGtVktmZqZ07lG4UYlFnampKcbHx5mdnWV5eZlQKITBYMBut1NbW0tFRQVarfah7/eg7BiBfx6LxYLFYuHxxx/H6XRy4sQJOjo6uHr1KiaTSQoJJlY4c3JypCjJw8RX9Xq9lAdTWVl5z7+3uLjI4uLiHXcES3xIEgJXq9XSxPeLyOVylEolpaWlmx7xicfj+Hw+3G43brebpaUlZmdnmZiYYGxsDK/Xi9Vq5emnn2b//v3k5ORsiwzQrR/BQ6BUKiksLOS1117jtddeY25ujs8++4yzZ8/y7rvvIpPJqK6upqWlhdbWVgoKCiT/LzE53Axyc3N35IJTNBqVjlAoxMjICGfOnOHcuXOMjo6iUql44oknePnll2loaEhaqO9h2NEC/yJGo5Fnn32Wxx9/nJ/97GdMTEzQ39/PtWvX+MMf/kBWVhaNjY20trZSU1NDQUFByoT+kkGikqajo4PLly+j0Wioqanh8OHDlJeXk5+fT0ZGBhqNZtuuIaSUwBUKBVqtVvL5DAYDNpuN+vp6nE4nLpeL+fl5Pv74Y959913C4TCFhYVSA5nCwkKsVutd+92lEvF4XHKRZmdncTgckk8tl8vR6/UUFxfT2NhIbm4uVqsVs9mMwWDYET3LU0rgXyQh9kSxhMvlYmhoiKGhIaampnC73VLZlNPp5OrVqygUCtLT08nJyZF84YQfr9FotoVf+SBEo1HW1tYkH9rlcrGwsIDb7SYQCNySNBUOh9FoNFgsFkpKSigvL5fWAnZa8trO/Gs9IAmxtra2SiG3sbExRkdHGR0dZXx8nKmpKVZXV9FqtZjNZim3IhGN0G+TsGgAAALISURBVGg0UrveRLw4LS0NhUIhWTSVSoVKpdqUD0MkEmFtbQ24aY1DoRCBQAC4GekIBoMEAgFplTKxOul0Opmbm2NpaQmtVovVasVms1FVVUVFRQU2m23dFeOdxM4e/UMgk8lQqVRUVlbeFhFZW1tjZGSE3t5eent7+eCDDxgaGmJxcRGtVktxcTEANptNykPX6XTs3r0bQPpQJFylxErnoyCxf08iZLi6usq1a9eAm4KenZ1lampKcj0SLkdiW8fy8nJ27dpFbW0t3/ve96QU451mme+VL63ANyIzM5PKykqKi4t59tlnCQaDhEIhgsEgi4uLUkgvsWro9/uZmpri3LlzwM2dnt1uN36/H5VKxa5dux7ZNiTxeJzx8XE8Hg/hcJjMzEzJBUtLS8NgMGAymZDL5ZLvnMjuS+TKq1Qq0tPTpW+gVBU3CIHfEblcTnp6Ounp6bfUfyZy11dXVwHwer34/X7Jb3W73cDNwtrEKmgsFsPr9T7S7l3t7e1STxmVSiUVB8jlcjIzM6U0VbVajUajkVyrL8vE+fMIgd8HcrkcjUZzz1tqJzIqZ2dnH1mj0cR+mluZ87KTEAJPIokGpA+bhyN4cFLX+RIIEAIXpDhC4IKURghckNIIgQtSGiFwQUojBC5IaYTABSlN0gQej8cJBAIoFIodn5Em2LkkTeCxWAyPxyPldAgEW0FSLXgoFEIul4ucCcGWkXQfXNQ8CrYSMckUpDRC4IKURghckNIIgQtSGiFwQUojBC5IaYTABSmNELggpRECF6Q0QuCClEYIXJDSCIELUhohcEFKIwQuSGmEwAUpjRC4IKURAhekNELggpRGCFyQ0giBC1KapAk8PT2dlpYWrFYrKpUqWbcRCDZEFk9s1/WI8fv9nD9/nj179mAymUTrCMGWkDSBCwTbAeGDC1IaIXBBSiMELkhphMAFKc3/AjO9ymB5DEmQAAAAAElFTkSuQmCC)
physics-General
Maths-
The area of the region bounded by y=
and the x-axis is
![](data:image/png;base64,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)
The area of the region bounded by y=
and the x-axis is
![](data:image/png;base64,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)
Maths-General