Maths-
General
Easy
Question
In Figure. PS is the bisector of
and
. Then
is equal to
![](data:image/png;base64,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)
Hint:
The correct answer is: ![1 divided by 2 left parenthesis angle Q minus angle R right parenthesis](data:image/png;base64,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)
Value of angle TPS should be calculated
Hence Choice 2 is correct
Related Questions to study
physics-
Two identical blocks A and B are placed on two inclined planes as shown in diagram. Neglect air resistance and other friction. Choose the correct statement:
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/494028/1/963307/Picture84.png)
Statement I: Kinetic energy of 'A' on sliding to J will be greater than the kinetic energy of B on falling to M.
Statement II: Acceleration of 'A' will be greater than acceleration of 'B' when both are released to slide on inclined plane. Statement III: Work done by external agent to move block slowly from position B to O is negative
Two identical blocks A and B are placed on two inclined planes as shown in diagram. Neglect air resistance and other friction. Choose the correct statement:
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/494028/1/963307/Picture84.png)
Statement I: Kinetic energy of 'A' on sliding to J will be greater than the kinetic energy of B on falling to M.
Statement II: Acceleration of 'A' will be greater than acceleration of 'B' when both are released to slide on inclined plane. Statement III: Work done by external agent to move block slowly from position B to O is negative
physics-General
physics-
Figure shows the roller coaster track. Each car will start from rest at point A and will roll with negligible friction. It is important that there should be at least some small positive normal force exerted by the track on the car at all points, otherwise the car would leave the track. With the above fact, the minimum safe value for the radius of curvature at point B is (g = 10
):
![](data:image/png;base64,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)
Figure shows the roller coaster track. Each car will start from rest at point A and will roll with negligible friction. It is important that there should be at least some small positive normal force exerted by the track on the car at all points, otherwise the car would leave the track. With the above fact, the minimum safe value for the radius of curvature at point B is (g = 10
):
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANMAAACjCAYAAAAQJSsYAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAFxEAABcRAcom8z8AACmlSURBVHhe7Z13XJVXtvfff97PvPfOTCa9TeZmSu6dzMzNTD6TSTKp9t4ooqgoYFfsgiJ2FAWsFEUQQbp0UHqX3qv0fui99/J7n7U5JLElUQ/lgf3183zO4TlbDjw8v7PWXnvttf4POByOTOBi4nBkBBcThyMjuJg4HBnBxcThyAguJg5HRnAxcTgygouJw5ERXEwcjozgYuJwZMRziam7uxuFBQVISkpAclIikhIT8CArE80tLdIRHM7047nEVFNTg6DAADg52OGaiRFsrG/hnreXIKwkQWhd0lEczvTiMTENDw9jaHAIg0NPPgiJRIK83BxIysuYqHJystHc3Iyo+/cRHhaC7q5uNo7DmU48JqaszAxYWVrA+palcNx67LCxtobR5Uu4ZKAPk6tXcOzIYVwwOA8HO1vonjwBVZU1MDM1RkR4GNJSUlBQkC8IrUn63TmcqctjYrIwM8N7b72O9999C394752fffzxd++yx/9650188P57+OLTf0Ju2WKob1gHixtmaOXzKc4U5yExdXR04OTxo3jtpV/i7ddeZqJ65/WX8darv8Fv33yNff3o8bu33/jB85Gv33n9FfZ/6Pmbr7wEheVLUVJcLH0XDmdq8pCYiouKoK2liX/+/W/4w+/eYaL49ycfY8GcmfifP/wXE8abr/xa+vjoMXKeREdWif7P73/7Nl791X9iw1plNNTXS9+Fw5maPCSmzs5OFuqm6NyJYzqYM+MbbFRVwTnd01iyYB5WKcphk+p6du7RY7P6BqiprMXcmd9gs9oGGJzTw5effYJ1q5XgaG8nfQcOZ+ry2JyJonktLc3Iz8vDRUN9rFyxDKvk5bBt00b4+/kiLS0VqclJSE2hIxlpqSlIEb5OiItFcGAANPfvxbzZM6CspAgV5VUICQ5GeWkpi/b19PRI34XDmXo8JiYiLSUV+npnmTDWrlqJBYI4yOoc1zmCk4LF0j15HKeOH8PJo/T8BHRPncCBPbuwfcsmKCmswKxvvsTCubOwbfMmYfxRnBDG6emegtk1E3h7uCMmOgrZ2Q/Q0FCPYel7cr6nv78fjQ0NwocaD9qIiSeKqSA/H9dNTJgALl8wZI+XLhjg3BldQRhHYGp0RXh+GqcFURno68HM1ASG+udw28oSVy5dgM7hQzC/fg3mZtegdWCf4AKqQn39OqxYsgjzZ8/EssULoL5BRRDhcTg7OTIL19TYKH13TnlZqXD9jeHm4owh6doeZ/LzRDHRH7C8vBzhoSHISE9HVlYWc/vInQsNCYZEeC02JhrRUfdRWJCPComELdy2t7cjOTmZWZ6+3l5mfdxdXVBSUoyqykrB5QtiN8itmxY4ckgTSvLLsVpRHls3qrM5VlCAv3AjlWFwcFD6k0w/6Hf3cHfDV5//i7nW1VVV0lc4k50niomor6tDgJ8fmx/RDV4qzHvy8/MQGRGBmuoqQWRpbN5E4fT6+jqUlpSw8HdYSAg6OzvQ3taOeGEelZeby26QurpaljlBQm1tbUFyUgJ7nXL6zM2uM1HJL1uCg/v2wNXZWRBv7rScYxUL13DXju14941X8enHf4e9zW1unUTCU8VUJ4jJ08MNMVGRqKyoEKxLCUqLSxASFCiIpojd7GmpqegVLBB9epK4ooWxlJ/X19eHooICpAvn6Dl9r6LCAgwMDDDxJSUkICUpkYmM5gUx0dHM4lF+n5YwT6OIIC323rxhhqyMDJZYOx2gDw8bayu2NPHem6/hnddeZtFQsv6cyc9TxdTW1obEhHjkCu5bS3Mzsz5NTU2CQNJRUSFBXW0Ns0Z0o9fX1yMtLY25d729Pez/lgmv9QtCosTXMsGqdXS0s7ExUVEs6tfR3iF8v0bEx8chUxDMoCA0El5mRjoLVOgc1mLBD5prWVqYM0FPdWiuum+XBj780+/Zgvf7v30bM776AnY21tPa9RULTxUThcgpqkTWZHh4iLkadPT3D7Abn57TH5glxgrP+4Sx/QPSP7gwnsYQ/f19TEgERagSBatE1ok+hVloPS0VPYLI+gULV15exnIDae5FrmJ0ZCR0DmlhlYIcC3bQ/I1+nqkKiclWsExbN6oxN48s9EVDA7YkQXNQzuTmqWJ6dgShdbaisbENfdIzBIltFBIfWR+iS7BYFMigrwcEIbJ5mWDNerp7hHEDqK2pQaxg6UKDg1g2OiXUqq1fizuODqitrWXfY6pBHxR0PZwc7Fk2yZZNauyDpVc498PryJmcyE5M7QWItD6DY7o3EVbS+ZPrR6MWjegVrBS5inQjkZWioMRo1JDmZK2trUhKTMThg/uxaN5s5gIWC/O2qQpF8yg9a8fWzdIzHDEgIzH1oTLGBseW/i/+8el8bL8aispn8EpGhUVHZWUFc+eahflZe3sbqqoq2TyL5m8VknI2f1gwZxb2aOxguYRTETdXFyYmWgTncyXxIBsxtaTD+9IBbF2rht3qCzBP8QBskpsFx+/ZIFHRPI0sFD2ORghraqrZHIturJrqaraPas63X2Pfbo0paaG4mMSJDMTUj8r75jgqTJqP3w5ChNMxrJ0xC5sMAlH5w8nTMzI0NMyCEBSsIHF1dnUKc6pilgs4koxrhWWLF0Jz/x52firBxSROXlxMnXnwv7QNqxS24aJ7KEJcrkJz2WeYveoYPApls+hKwYi8nBzm8nV1dbEbrK21TZioO2DJ/LksZYncw6kCF5M4eWExtaS7Qn+rAlQPX4eXfwjCgz1geVoNcvPkoW3/AJ3Scc8Lc/0Ey0RrVGShqL4ERbgo+hcXGwNjweUjQenrnWHrVlMBLiZx8mJi6q9EtMUuKC9Zh/N3S9Da0Ynunk5UxNtBe+lnWLjZCNG13c88d3oa5PaNbPeIY1kYtCBMbqCdzW22GdHS/MaUSEHiYhInLySm3spYOByRx9KVu2AaXP7d+lJHYRBMt8zHgpW7YRpSjE4ZLZHQ+hNZJQqVUxrSqLWqrKyE5r49WDB7JkumFTtcTOLkhcQ01NOOBkkhCksqUN/W850FGuxtE84XobCoDNXN3RiU8XojLW5mZWUiISGOWSoKpUeEhWHn1s3YpLYeubnZ0pHihItJnLx4AGICoPUoslBknRobG1BXO5I3SLt9lRXlcezIIZZcK1a4mMSJKMU0Cs2PcnNy2N6q8LBQVqvvooEB5s36FlT3j7InxAgXkzgRrZjIc6ytrWECSklKYlnlZKnqamvZVnpFuWVsTUqMcDGJE1FbJgo+UHFLiuiRFRroH8lmz8rMxEr55Wy7PQUrxAYXkzgRtZhGoa0dtBExJTmZBSPIIhmeP4dlixYg8n6EdJR44GISJ1NCTDR3onrmJCo6aFt8WVkpy907fvQI2zIvJriYxMmUENMo7W1tLPWIDkqIdbnjhOWLF8Dn3l1KpZCOmvxwMYmTKSMmSjuqFQRE2+yp+0ZCfBz8fX2xRV0N+3fvYts3xAIXkziZUpaJtnZTQIIsE5UWoyM8NJRF9mj3KmVQiAEuJnEypcREVFZIWAO2AD9fVuAlKvI+DuzZjS0bVUVT5YeLSZxMOTHRvInV8CspZmtPFHxIFdw+5ZWKUus0+W9OLiZxMuXE9CRoPYoWcvfv2YWysjLp2ckLF5M4mZJiorlTaWkJ8vJyWVd4agXqYG/H2uL43PWWjpq8cDGJkykpJqrZRy1sGmjdqbGRFdGkzYRbNqqxOnyUcjSZ4WISJ9PCzSModG5jdYtlRVBS7GSGi0mcTFkxUUEWqhmRL7h45OaRuxfo74+F82az7vDUJXGywsUkTqasmMgSUZIrRfPIrSOXr6qqCtpaB6G+fi1rPDBZ4WISJ1PezSNBUUWjUe56e2Lx/LmsfvdkhYtJnExpMZF1oh24ZaUlrPorrT3RIi5F9S7oT15Xj4tJnEx5y0T1IkZTjBrq61FdWclcPeoIT83bJiNcTOJkyouJoB25VBqMwuW0edDby5NF9QL8/aQjJhdcTOJkWoiJmgBQxVdayCVRhYUEY9G8ObhkaCjMpyZfV0IuJnEyLcQ0Cm1vp8gedTXUPLAP2zZvnJTJr1xM4mRaiIlcO+rKFxsTw7pmUD8ob08PyC1djODAQOmoyQMXkziZFmKiqB4luCYlJSIpMYE1tva9d5e5eiZGV9DXN7lKgnExiZNp5eYRVA6MGlbnZmezfU57d+0U5lGTqyUNF5M4mTZiIutEXd0jwkJZe5quzk7m6q1WlEdYaIh01OSAi0mcTBsx0bwpO/sB60RILT2pKyFlQSxduAAW5maTqos7F5M4mXZuHkHpReXlZcjOysLuHdtZJ/fq6irpqxMPF5M4mVZiIlevuqoSOTnZLL2I5k/UznPbJnWkpiRLR008XEziZJqJaaSbe/aDLGSkpbHI3nVTEyyaO5tF9yYLXEziZFq6eQTNkSgBlvY40XqTqfFVVitiMsDFJE6mnZiorxO5dJQ9XlRYiM6ODpw5dQKHNQ9AIsyjJgNcTOJk2ompra2N9XOiJFcq6k/PqXKR8kp5JCTES0dNLFxM4mTaunlES0sz0tNSWYPpJQvmws3FRfrKxMLFJE6mpZhoUyAFIigToqGhHk1NjezGpQ2DP9yVO1FwMYmTaSkm2spOBVZysh+gqKiQpRPRnGn3zu3s64mGi0mcTFs3j9acCLpZJZJy3LhuirWrVyJqEjRH42ISJ9NWTLSFndabaM5Elonqka9RUoS9MH+aaLiYxMm0FROlD0Xdv896OFHyK7WeWa0oxyJ7bW0T2wfX1cUZr/76P1gFWi4m8TCt3TxKfiVoW3t8bCwr7E9bMqhG+UTi63MP//jrn6GtpSn8jFxMYmHaiomERHXIqV1nXV0di+h5erhji7rqhDeVLpdI4GBni9jYGOkZjhiYtmIi94k6C+bm5iAvNxelwrwpNDgISnIr4Op8Rzpq7BjqaUZlXioSoyMRG5+CvIom9Ajn+9vrUfqAdgTHIzEhFnHR8UjPrUCbOJoeTmumrZiI/v7+7/Lx+vv6WUBizSpFGF25NKZ5eoOtpUi6awkjfQOYGF/BhROHoHPmBgJz6lCe7AVTTTXs1daFof45GBiYwNE/DTWTI22Q8yNMazF1d3ezrRhUjJK6DFJdvVMnjuGYzmHBalVIR8maIVRFXMcBuflQ0/VAYUcn8n0vYPP8+dh51QthPlehs0kVuo7JyCkoRWVdC7r4tEkUTG/LNNCPB1lZbNt6bHQ0cnNycOXiBWhs24y01BTpKFnTh/IoG5zZtRsXXNPRiV7keelCZcZsbL98Bz6uZ7FvjQpO20UhMSkVmXnlqKmpQGFaBIKDwxEXF4MEwTWMiY5BYkoGslJihZ89ElExqSio6cDgyPIZZwKY1mIiyDpRp0GK7lEgwsHOjq03BY5htdfB7mbUCvO1mvoGVCQ7wWDrciio68I1NRdpfkY4tGYt9p8xgpmRPvROnMS5s6ehs2UJ5s2Wg9ohA+ieP43ju5WxUlENB46cwrmTB7F1zTocMgtHVQ9X00Qx7cVErl11dTVbd6oUbnAqurJ+zWpY37KUjhgjhrsgiXPExX3rsXGXHpzjKwSbNYRWSTqig8KRWtKIjqYcBJrsgMLcL/HN7LlYunAzdIIbkdBWiYQ7+7Hy22XQss1GZU44zDWWQm7ndSQ288nVRDHtxdTT08P2NcXFxrA9TrQlQ3WdMs6dOY2O9nbpKBkz2AFJrCAkze3QPG+P2NJW9PV0obWqFEXZ6cgsqEYHG9iHooDzUJv9Mf7+6VysVDiAS+mDKEIP8oPOYNsS4ef0b0F3dRqctBShsP0a4lu4mCaKaS8mCpGTdaJscdp9m5ebgwN7d0Nr/14WnJA9fWhIc4aeylwskNfAZecwYQ4UALfbt2Fz3RimJ7dh014DeKSXoKwgCq4XNbBu+SIsWTwH8+eoQ9OvHrFN1Uh03IuVXy3CIYc8VOaHwkRtJuYo6yKgogvc0ZsYpr2YKDyelZmBtNRkJh6K6jk7OWD3jm0sKCF7mpATeB06qspQ37obOkd1cFxTAxp7T8Lsjj+i7l3HuWMncPmmPRwtL0Nf9zxMzK1gfWEvdmkcxXGXfAQ9yEfcndPYu2kPDJ1ikJMTCstDm7Dz0BX4F3SAB/8mhmkvJmHyAkl5Ofx8fFjWgZ/vPTgKj5Sn5+XhLh0jS4Yw0NuFjrY2tLe3oa21lfWPamltR1dvPwYHetHZ2oi6KgkqKqvR0NKJnr4+wQ3sQEdHJzp6BtDbP4D+HuF5ewe6evrQP9CH7o52dHR2oXeA26WJgotJgAr503Z2qgdRVlYKNxdnLJ4/h23LGM3f43B+Ci4mASqyQo2kW1tahU//dta688hhTbaAW19XJx01ftD7U9EX6icF6b4rzuSHi0mAJb02NKAgvwBFBQUsVE6lvyiLnOZT4829u9748IPfQ3P/Xr4FQ0RwMUkhV4/C5BTRo6Zo5Oqpr1dhya/jjYvzHbz8y19gs7oqF5OI4GKS0tLczA4KkXcKE/30tDSoKK+CzW1r6Yjxg++0FSdcTFLIItH8iBZwqcvgg6xMbNygAn29M+jpHt++t1xM4oSLSQrNm8gyUTCCbuDOzg7onjyOQwf3s5Jg4wkXkzjhYpJCCa/JSQnIykhn0TQqB0bFKXft2Ib4uFjpqPGBi0mccDFJGZJ2yIiMCEeAnx/L03N1uYMN65RZh8HxhItJnHAx/YD+vj5mlajASntbG5ITE7FKYQXMTE3Gdb2Hi0mccDH9AErtkUgkrAka5exRLXJaazquo42mxkbpqLGHi0mccDH9AIroUb4cBRxoK3thUSH0zuhij8YOVh9ivOBiEidcTI9AgYjGxgaWp9fb2wsPN1cWIh/PxVsuJnHCxfQIlD4UER7GMslpATc5KRFrVyvB1mb8Fm+5mMQJF9MjkJuXn5eH++HhzBrRsUZpJc6fPcPSjcYDLiZxwsX0BLoFi0TFVRoaGthBpb8O7ts9bou3XEzihIvpEcj6lJQUo7i4iM2fBgcGYWN1C9s2qbM6EeMBF5M44WJ6BEoros6C1HKmuLAQ2VlZbOftKgU5FowYD7iYxAkX0xOgGnpMUA31bEt5UWEB1DeowPjKJeG1sd95y8UkTriYngBZpeCgQAT6+7OoHvVr0jqwD9paB9lrYw0XkzjhYnoCNG+iPL2MtFQEBQawrhjbt2zEZnU1ZGakS0eNHVxM4oSL6UegfUxU+quoqAD2tjZQWbMavj53pa+OHVxM4oSL6SnQXInWm7KyMlmxlewHD7Bh3RoYXb405hWLuJjECRfTU6BUItosWF1VxVy7e/e8oaykwNp0Vkgk0lFjAxeTOOFi+hEoqkdNzyhXr6y0BCZGV1hRf2pBM5ZwMT0f9Pcaj2jr0+Bi+hGYRfL2QnRUJGprqtmOW+WVCqyzIGWYjxWTTUxDws9Avy9tS6GDfqbhIeGQvj5ZKC8rHflb1dZIz4wvXEw/Qm1NDfLycpCfm8sSYO+Hh2HtKkVsUl0/RkX9R5gMYqJP+a6uDqQk3Ye1+U0YG5vg3OmjOK17Hg63b8HLygR3o7PRMEnaGg4K81gqz6a2fh187npLz44vXEw/A1ZspaWFzZ8Mz+tBftkStrV9rJhQMQ33o0mSAVf3ezh6RAdKKxZg/rzl2LJZHWsWzcQSOUWsVViCpTO+wPwVyjhveBFJ8bEsw34iofSvXTu34f1338KhgwfQ1tomfWX84GL6CRobG4U/VDFKSkqYpfL39YHiimWCq3eZuTxjwYSISXDb6gvz4ermjD1b12KpvAq09u2GocZqaF2wgY/nDZw9dAxntfZAU9cYN528cfWSPjauU4TCiiU4qH0CmVk50m82vvT397HiN5/843/x5ssvYfY3Xwkfdr7SV8cPLqafgNKKqHQyiYoyyRMT4lmbzu1bN0MiKZeOki0TISZJSQFO7d2JeTO+xKr5M6BlegdpafGItrgCz9QcJHpchp6OFvRMnXA/tx49/W1IC7THob0HobrnOJauXCO4vxsQFhw0Zh8yT4NqHKoL7t17b72O3739BrNOhzX3s+WN8YSL6WcwRFEi4R/d2M1NjdA9dYIFIsaqBNj4iWkAA501iIlPx4E9O7Hgm8+hskMTFseP4V5hNarrkmF71RaRsR4w1zsBvcu3EZRVhrKsCHjbmMHK1hUhsRkoqGpCbHQoNDbIQ27xPFy2uI26ljHquvgINLcLCvDHRmEe+9Vnn+C3b76Gv//1Q5b6lZ39QDpqfOBi+glISJmZGQjwHyn/lZKcBLNrpli2aD6cHO2lo2TLeIlpuL8dsXeNobJuPdSVVsDq1FYYOgfB6oIVYooLUZpsC+NboYjytIS1ZwQSi9oxONCAvEg/+PuFIbW4UZgrNQrjAuDpYIOLptbQ1DmFRcvloG9gMC55jCQm6kVM5ax1T57A67/5FbaoqyJHEBJ5E+MJF9NPQH+sCsGdy0hPQ25ODkqF+dODrCxs27wRJ48dZUX+Zc3Yi2kQ/R11CAwMxtrls7FwgSIiArxRE3IB52zuQE/PFdllVWjMj0N8TjUqigpR0dwz0pFwqBNN9c3oHhhCT3k8fB2tYWPnCt/g+0gTrFlRYTbOH96GOV99Bs0jx1FaPrYL3D/E1soKL/3H/4XOYS3pmfGFi+lnQtkQVOV1FGtLC+zasRWpKSnSM7JjrMU03NeKSI+rUFmjhA3KijitbYyymgrUxptCz9wBlg6paGztxWBfG6pzIhHo5QoXF0+4efshwNcbXi534H43GHGJcYiJSUD6gxxkp0TA380BDnb2cHT1gqn5TcgrKkH70CFUVVZI33lssbK8ybqHHDmkKT0zvnAx/QzohqZ1JmrR6esjHPfu4srFiyxEbm9nIx0lO8ZOTIJF6mlGaEgIlJfOhNwyJYT4uMDTxBLRZaWozPWGvXcicks6BItM4/tQn2GFo6sWYvkOYxx2iENkvHB4GEFbVQkbdeyQWtuNjrIEBHu5wfOeH0Ij45GRlY30pEicPKiBr/71MXR0DVDT+P0H0ViRl5eL21aWLEg0EXAx/QzI1auvr2NJrwnCzUTb12Oio7B/7y7B1dMRXpPt3GDMxNTfhlg/M6iuXwOVVQo4e9wUuQU5iLQygkt6Oepb61BV046B795yAF0SBxye/zlm73GHbiLAnNrWGFxd9zk+masJr+x6dLZUoUxSiaK0cAR4CNbJ3h4urm7w8QuEibERFi5ejlvWNrKP8g31oSIrGh7uPojJbZKeBHrq8hHlZQMHB3vcEeZytrfvwC8qBw1jl7TC4GJ6BkqE+VJSYgJrO9PQ2IC7Xp7Q2L6VRZNkyViJqSA3HVtWz4PCcjn4eDvB7ZoVovLykB1gD/fUWrQ8drMNoLPcEdoLv8CcndbQCSpBfHwovK4fwZY1KtC6FoSi1tGfbwitJcmIDvZDUHgc0rJyUFiQi5gQX6iuXI6Fc2bCyi0Azb0ySkIa7kBDcTIsdXZg/hJ1GHjmj76AktCbOLlxJTROGMHC3BzWdh4ITy1D6xin7XExPQPUojMiLBThoSGsBNgdRwe25nTB4LxMy4CNhZhqyvNxVvck1BUVcOWYHmIfZCL4ljHcBItUV12BiqYe9D12swlikjhBe/6n+GK5JtYbOsHa1grXjm7EqqXy2G3ogbTaXkFGD9OSH4MgD2Hu5OgIdw9PuHt6YfcuDcit2YiohDTpqBdkuBtttSWwPb4PX38pj5MuowvGXchyO4MD6tthFChBQ1MrOnu/v4bkZYwVXEzPAN3YFL2rraaoVQHS09Nw+YIh9u7aIVM/XdZi6mitx9VzR7BKuJnDPR0Ra3sdztFZSPK2hWd6Pdqe+oktFdOCz/D16nPYbp2AuLxyVBenIMhoC+TmLsV+ywRUP9QLbhBNhUmICg3C/fgMFFU2oFc4W1ZeDm2tAzh2RAuS8rKRoTIg3s4Yy2Yq4NR3YmpCsuNRbFu+ElpGd4Rr6Qov/1jkFBUgM8wB1w0MYWZlDaubN3HrpiUchdddblvA2uI6TK19EPqgHn3PqTcupmektLRUsE5huB8RgfS0VISFBGOLuhouXzSUmXWSnZiG0dPRBFdnJygvW4DD+89DUl2IfMENuuaWAUlhMSTNT7JIo9CcSXDzFnyBefs9cSZpGKMZby2hp7Dq0w8wc58rchukJ5/EcC/aBQtSkBYLI/3TWDBrBrSP66Ky9sf+088n1uYqlj4kphZkB97AmT0HcOGWICSnazivuQP7tU9BV3sLVnzxJZQ1r8Luhj60lWdhgZIGzt24hRvntmPp18uxRd8PZb3P5w9yMT0j5WVliI6MFMQUzhZxo+5HCJ+2h6G6bg1io6Oko14MWYlpuL8VIR4mUN+oBjN9XXgamSKsuAzFuQG445GO1o6f+Age7oQk8jzUPv8z/r5YC2sMPeF6zwc+TuYw0FCEnLwazrlnopFMz2MIFio/FsGCJXRydIKrYAHu+fjCxvo21qio4rKRsWDlXzxL4jsxueZKzwjeQ0M5CnOLUdsp/H5DVYi22InlM+djhZIq1OTkcdghF0MNqfA8LI+FyqfgVy/8nvEW2PHlvyCnYYH0jue75lxMLwB1aKe8vdTkZLbmpKd7mrXxfFFkJaacrCRsVJiFDWs3Ijs3EVm+N2ARkIuqxlpIyhrQ93STNMJQD2qzAuFsYQwTcwdYu/ohIMAXvq62sLa0gWdoBqo7nhYiGxDEFI+IQF+ExqQht6gUFRWlyEuPh86+HZg34ytcumaJupYXyzaPszViYjo9KqaWYiT5ChYp/AFGbF8bMl11oDxbENNKNWxWUsKxOwWCN5iOeyfXQ17VEGHtXSiPvwmNrz+DvCCmtE4upnGjpqaGhcgpPE6LtpS6cslQn+XrySKyJwsx1dfX4IzuKaxdMAfXT5xCpKQCheneMLvuj+KmPumo8aGtJBn3fV3g4izMYVxc4ObujlPHj2P+UgVY2TlhYPB5YtbD6G2WwP74dnzy50+xTtsS8fk1aKlIhuuJDVi1XhNm/tGICbDGxQPq2LxTGyd1tkHu6xnYcikIxQ8CcWPTLHy1ZD/s0/KR7n0KCn/5AN+uPg1/Sbfw3Z8dLqbnoLq6CrEx0YKLd591yaDeTUmJiawx2pHDWi+80/NFxdTf3w3729ewZLkc7GyNkehmjNvhJSgrzkawowcyGjpGUoPGhUE0F8Qh3M8bgREJeFBcjXZBOy1tHewDiMoABPj7PkeUbRhdDSWIcLfBZcPLuGnrhbjcKnT2d6E6Ixgut63h5OaNu862sLV1R1hiBjLjvXDLxAx3glNQVJKJcAdTXLvlgZgc4dqk3IPVpQsws/VBek3PYxHKnwMX0wtAtcipsD9tGqSSYLetbkFJYQUcHeykI56PFxHT8PAgIoV53LqlM7BNbQP88gpQkOIFc4sgFFY3o0FShrruvnEU0+MMdjWhpiQLng5WWDp/HuSWr0B01IvPNylKSLtsc3IoGDGMvu4OdHQ9HrofK7iYnhO6yakEWFFRIdvCTgftq6FgBC3k5uU+/0a5FxFTRWkGdm7XgJrSHLib68IyqBClBZkIdPBAZlPXuN1YjzOMtrJ0xAZ5w9vTE14e7vBysYOJ/nEsnvEllBXk4RUUjZYX8EDdXZ3ZBsFLhobSM+MLF9NzMlrgnzoM/vCGz8nJxl6NHdDXO4vm5mbp2WfjucQkuEmdLfWwsbyEr7+dAwNrexQk38XtG97IqmhAbVkp6nr6J9Aijbh7IV5OsDG7AqMrV3DTxol1srcwt8Ba5bVYoqQKv/A46fhnx+qmBcsaP6x5QHpmfOFiekGo6iu5eaUlJSxsTu1ozM2usWAEZUgMDT377fs8YhpsrUeQlTE2qazA3t3bYeqeheqidIRYGsEtswEPratOKMNoLU5AqKcdHJ29EBqbiQrBHGWkJ2HnenlsWKUAr4BwtPQ8+3Wz5lnj4oYsEwkpV7BI+Xm5KCwoYNVfTY2uYv/uXYiKjJCO/Pk8j5gqcpOxS34eVFU3INbPEU43PZBeWoC8aBc4h0nQ/sS1oIlmEN2NpchOCEeovzeMjY2hrLwOixTXwsLOGd1dz7ZXjMT0yq/+HxeT2KG6ck2NjSjMz2euXowwoT56WAu7dmxjYfRn4VnF1NBQDZMr57B8/nycOGONmrJMxDqbwe5+AWobKlBW3oq+gefMkRlD+upykRDkwkqH2Tm4ITSxEIkPinHh/EmsU1yMs7pn8ODBz597UlGVV371CzZvnQi4mGREXW0tEw1lRlAhRAqZU+j83NkzrPRUQtzPF5SXMEEnMe3ctkV65uk0N9Xhov5JyCksw6Wzp2BnZI+MWgmKMvxx524WWnsmn4hG6ZRkISUxCbnV7dK5XC9ayjNxz9kG2zX24OtZC6GupgZPd7enbnOhkDoFgYIDA6C5fy/eePnXWLtKCZEREcz9Hk+4mGREXW0NCvLzWC+nUajZNK1HHTq4Hzu3bmF1JLo6O6WvPg5FB1OSknDujC7efu1lKMmvQFhICHKyswUL9cjCpjAXqywswKUL5zHznx9h/56DSMyMRbj9NdxJqUZDWyMqy2rROzBx8bufzxDaK7ORFOwBV/tbsLZ2gGdoCjz8w3H0iBbU1yrguLYmPDzckZUQhby8AlS1fu+3BgcGYtmiBfjwT79n1Yn+8N472Cy4u1ReYDzhYpIxJKDy8jK294nC47SgS4K6oH8em9U3wMzU5KklwjLS07Fv1058+vFH+N1br+MvH/wRSxbMhcWN6+jrfzhmnJ2aiEOC5Zo3fx6Ob1XFHZNriCrPR1a0Mxz8S9A5KedIT6MPtVlh8Ha0h09MHuq7pNZ0qB2Z9+9C+9BhrF6vjs3rFbFDfi5U1qlj/8kLsLppDhcnB5w+dRKff/IxfvvGK4KYXscH77+Hs6dPsXSv8YSLScZQbb201BS25kRtPMlSVVRImMWhzPJ1ykqsDFWk4A5SV/cf0tTUBIPzevjzH99nn7Bvv/YbLJo3G1GRkdIRYJVl/f18sGeLKmZ9+w1OXLNCZUoYoh1vwCWzBjX1ZSgoaED/82ToTCDkrtFyA5PRcC+ahXlfXIAwn7p1E/Ze4YiIisD1C6exbed+7Nm/Dxvk5mLWl//GEkUV7N68EgqLvsUHf/qr4B6/hOWLFyL+GdxqWcHFNAbQjUEZ0WShyNVISkpgAsvLzYWVpQWWCy7JhrXKsLQwZ9G/H0JpSZRF8c7rrzBRGZ4/x8qNUTcO2jNlqK+HubNmYPZHf8JZHW34VAqqaS1E+l0z3AioRMf41n8cE/rqchDjaQnzm84Iz6pAQ00+Yj1uwsLuHhIqetDfUYYQe2PoX7JCUHopGtO94WZ5CXNW7cFf//tP0NM9JVyv8TfNXExjBKUaUYGPKukkmPY6ketHO3X1zpxmjdMoL01b8wBr85manMRy+lpamgWR3cA//vYhmzNRswDahGh9yxIqyqswd+Y3WCyIcfuSr+FnaYKgOvruLZCkeeOOX+mEpgnJiuGWCpSWVaCRfTB0oTzuLlzcgpDF0sCHUJfmC2cnb8SVj5jfugR/3HP1hcm9KCaklKREdn68kZmYqqurWR1uqtzj53Nv2h90HShPjKoZ0XW5cc0UR7Q0hbnTORbyXrFkEeum8W/B1//oL//DilpSvTcSzXm9M5jx1RdMTCQ8xRVL8dGH/41/fvQ3Nm6logKU53wOvX3bcdrSC76+zrC/ZYhzejfh4XmXuYFP+plEcwjXztfHBwH+/ghwNsNVYb55ycwRvgEBCHAzge4BDRw4chWufgEI9rPHlVPaOHrEEMbW1rhyyZAtltM1f/T73hP+HumChzBWyExMlBby3luv4S3BZ31XcFGm/fHGq8KE+FX2SF9TdI6uDT2+/epv8JZw0HMK5b720i9ZJVLy998RzpGLR69/N0Z4jcbQWJpHff+9hOfS96P/885rI4/vChPxh34WsR2j141dO+F60e8lPGfXU/h65LqMjqPXR67Jw//v4e9J1+bl//wFdm7dxNzwsUBmYqI1FuqNQ64L7Trlx8OHmspadn3okYrMq29QYY8bhUeqk01f0+uqNE446Lz6Bul46ZiRcyP/b3S8mor0PaT/79H3Ff8x8nt993vS1/R7r//+d1VTGfl6ZJxw/rux3x/kVlOKl5mp8eQXE0ViqA8sP/gxGY8+6eNYdnzkAQgOR0ZwMXE4MoKLicOREVxMHI6M4GLicGQEFxOHIyO4mDgcGcHFxOHICC4mDkdGcDFxODKCi4nDkRFcTByOjOBi4nBkBBcThyMjuJg4HJkA/H+Xib73uapm2QAAAABJRU5ErkJggg==)
physics-General
physics-
A collar 'B' of mass 2 kg is constrained to move along a horizontal smooth and fixed circular track of radius 5m. The spring lying in the plane of the circular track and having spring constant 200
is undeformed when the collar is at 'A'. If the collar starts from rest at B' the normal reaction exerted by the track on the collar when it passes through 'A' is:
![](data:image/png;base64,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)
A collar 'B' of mass 2 kg is constrained to move along a horizontal smooth and fixed circular track of radius 5m. The spring lying in the plane of the circular track and having spring constant 200
is undeformed when the collar is at 'A'. If the collar starts from rest at B' the normal reaction exerted by the track on the collar when it passes through 'A' is:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAPgAAACXCAYAAAA4c5aEAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAFxEAABcRAcom8z8AAFLqSURBVHhe7Z0FYB1XkrV39x+eycxkIDNhTpzEzMzMzMzMzExxHDMzMzPGzMzMzGzJss5/v5Je4ji2ZJCtZ6fPbo+ch/26b92iU1X/Iw8ePLy28ATcg18gODg49F8eIhKegHuIdNy7d083btxQYGBg6CMeIgqegHuINKC1T5w4rnVr12jViuU6e/ZM6DMeIgqegHuINAQFBWnalMmqU7O6mjdppK1bNoc+4yGi4Am4h0gDAj529CiVLVVCtapX1Yb160Kf8RBR8ATcQ9gIvqfg2+d149ReHduxXpvWrdaa1Wu1bv0mbd22Tds3r9fGNSu0YvlKrdmwXbuOntWF2/d17wliZgj4zBnT1ahBPbVt1VLb3ed5iFh4Au4hbATd1v3zm3RiST9N61hFNUoWVJHiFVSpTkt1/v579ejcXG3rVVDlUsVVrlIDteg1RTO3X9C5W0EKT8bv37+vjRvWa8yokZo8cYKOHTsa+oyHiIIn4B7CRnCQdOecbu+ZpJW9S6pQ0lhKlLmqyn07Rys279DePdu0ZdlEzexZWVVyplKaNEVVuMkkzd97QddDP+JxIDNG9Pz8+XO6ePGC7t69G/qMh4iCJ+AengBOyM8t0s6RZZU/7peKlbmhqo04oPO3Q5++d1JXt3ZTp4LxFPfD2IqapZOGrj2q86FPPw5o8C2bN2vShPGaOX2aRdQ9RCw8AffwBAiUzizUjhFlVSBeFMV2Al59+D6duXHPPRfkrPgjurh7kL4v5TR4tBRKWryvJmw9pSshb34syH+3bNZEH779lmJH+1qzZ84IfcZDRMETcA9PgIcEPEtj1XAa/NytO7p/9YAOLh2kUS3yq2CalEqfp44aj9munRcCQt/7eJAHb1S/rt788x/0+Ufva8a0qaHPeIgoeALu4QnwgIA7Ez1mkkLK12CQxk6epFnje6tP01Iqmzq6kiTJrDx1B6jfyjOavGCFJo0f82MAbeqUyT87pjuTHNO8QN7c+vff/qJP3n9HTRs10KyZ0zVt6pRfvJ6DzyGttmb1Kl25csWi8B7ChifgHp4ACPgiJ+DlnIB/oajfJFGybKVUqXIV1a9XQ7UqllTpHBmUO3dhlWvSS22GLVGewqUU/avP9dVnnyh96hTKnT2LcmbN/OORK1tm5ciSSUkTxnOv+0Ixo36ltCmTu8d//jrfwfszpk2taO61DerU1t49exTgBeXChSfgHp4AD2rwKIqRsqyKtZ+pZeu3au++Pdq7a5O2LZ+gEc2Lq2qu9EqeqoCiRImmd996U1E+/UjVq1RSpw5t1a5Ny18cbVu1UJtWzd3RQu1a81irX7yGg/fXrVXDbQRRVLVieW3fulV379wJPT8Pj4Mn4B6eAA/74I1UfcRBXXhQvgLP6PjkJupSMLa+eOcTvfufdxTFae/c2bM683qSkVg2bdzw47F58yZjrvXs/r0qlC2tmtWqaOL4cdq6dbM2bdr4s9dy7NixXTOmT1XKpIlUuXw5bduyRXc8AQ8XnoB7eALck86GpMl+HkW/H/q8Q9AN3V7ZTaNqJFd050+///a7SpQwoZo2bqgjhw/bSwiq+Q4QEBCgxg3q6603/6qvP/9E053vDXj2wdf6Xn/wwAFlTp9GFcuV9QT8CeEJuIcngM8H/0nAq5mA+4JcQbp/87B2DKupltm/0pfvfaD33/1ASRMnVvOmjR/LUCNNRhT9n3/9s7785MMfBfxxOHzokCfgTwlPwD2EjfsBun91ny6u7KmpjTMo9Rfv6pOY2ZS5SncNHT9Vs2dO0fSxAzWsexM1LJ5ZBTJlUuqsZfRN9PhKljihmjVpqKNHjoR+2M9B/Xf92jX1xh9+a1H0KZMmhj7zaBw6eNAT8KeEJ+Aewsa9W7p/aqUOz+ikkQ0KqEjm1EqbIbfylaiuRi1aqV2rxmpes4wqFcqpggVLqnKT3mrVf4HSZsyl5Inim4AfO/poDQ6TrUe3ru51CZQtUwb9sGRx6DOPhqfBnx6egHsIG8H3FRxwXXcun9L5Ywd0YO9u7dmzT/sPHtbR48d14vgxHT98QIf27dX+/Yd07NRF7Tl4QsWKFFHSBPHUzPngj9Pgwe6zT506aXTVzZs26eLFi+6x0CcfAU+DPz08AfcQ4bhz64bKly6h+LFjqHKFcpo2ZZJWLF+mObNnacrkSUZ+GTywv3r26Kbu33+nbt91UZdOHdWpQzv727tnd/f8AHsdEfj5c+do7ZrVzoSfZFF00mQ7t2/XfY/oEi48AfcQIcDcvnnjhi5cuGCdWQrmza1oUT5XlgzpVKtaFTWsV0fVKldS+TKlVKxQQeXNmV2ZnDaO8fWXeu+tf+rDd/6jONG/UZoUSd170ipPjqwqUjC/NYMgj96kYX3VqFpZsaJ9rcL58xoLbu+e3VaJdvPmDft+D7+EJ+AengmkrhAqjrt37+jMqdNasWyZBvbrpxpVKit+rBj6+N3/OgGOopxZM6lMyWKqWqmCGtSto9Ytmqlrl87q5TQ4z/3nH3/Tpx+8a0SW4UOHmF/evm1ro67WrlHN8uTFChYw8zzKpx9bSi1DmpTWBWZAvz7ue3/Q+bNnFRgQoPsPpNU8eALu4Rlw88ZNp6W3aMSwoerft4+6ftvZ+qoVLVRA+XLndNo3m2JF/cpopXlzZnOv6a15c+Zo0cIFWrlihTV52OO0797du1WxbBn99Y+/1UduM8AsP3P6tPY7f37r1i3WjHHZ0qXORJ+r2TNnug2huxLFi22fjWWQJWN6Zc+cQUUK5FODOrXMtF8wf56OHz2qoHue+Q48AffwRCCgdebMGe3auVOzZs5Qq+bNlDp5UiVLFN/5xYntb6Z0acznbtm8qT0Hz7yZ08LHjx0L/ZSfIyjovtPAfZU1U3q3OeQ34Q8LBOsw3+Gwd2zfzsz+IgXzue9KYoKfPnVKVSpXRgPcpkNBCptFQMCvm6/uCbiHxwLzGzIKvvU2p1HRxAhi8sQJrDjk688/DaGOViirIU77EghDqA7s36/ihQsqSYK4ata40WPTZODChfM6cGC/jhw+ZN1dwoIvTVa2VEmtcpsBGwfaniAcwblSxYv+uLHw/f379DY//dbNm79as90TcA+PBO2T9u/bZ+yyju3aWHAsXaoU+uyj9/TNF59a1VfHdm01fuwYrV65wtJlvuqua9euqlzpEiZoaHOE/nGYN2e2mjgtz3fs3bsn9NFH4+SJE8qaMZ0qlS9nUXRfuejVq1e1b+9e/bB0iYYNGaymDeurZNHCKpg3j/n9w91j+9xn/xpF3BNwDz/CZ4YjPAgevjUaO+qXnxnTLE6MaFa6ib89euQInTp50mn5X4rNpYsXVaJIIcX4JopKlyimyZMmOpN5tVa5jcB3YEIv+2GpCeI/3viTPn7/bUuTYQWsWrnyZ6/lWLdmjRWj4AqQB9+6efMj8+BUmO3etVMjhw9TjapVzJxHs3fv+p1957mzZ51VEhj66tcfnoC/wsDsRIvhZ7LYOdCimNVPYpLyivvOD4YyeuP6dWeGbzUNWKVCeaVKlljRv/5S3zjhpuST9BWkFSrAzp8758zp648NZCHgJYsV1sfvvWNRdEz6NCmSKbX7DN+RJqX7b+c7R43yud77z78sTRYvdgyrCX/wdb6Dx5MmjK+vnfVQp0Z1Kxd9lIDzu32/59jRI5rvNqraNaoqm/PzixcupLFjRuuI8+W5Ru7Foe96feEJ+CsMFjIRaUgjrVo0U5sWzTWwX18tX/aDrl4JryMaQa4gHXT+L2Y4tdilSxS1qHTqZEnMx6aNUrxYMVSvTk1NGDdWO3dsf6LOpzedzzt00EDVr1PLmjPw9+GjQb06lhaDpooGf/etfypfrhxWfFK/7i9fz1Gvdi01dM9zLieOH3+iWWZXLl82q6BPrx7OtC+rQvnzWoBw5YrlunP79WfCeQL+ioKFu3zZUmtamCt7FqVMkkjpnJYrlDe3Gjeop3HONybifevWzdB3hABtf9aZ4Wjr2bNmqnPH9k7bFnEaMplSJE6oxPHjOKGObgEyzHGCZGvXrjGhfVKgHaGVbt60UZsfquv2HVtC68G/7/KtSjgzneg3/jwkmc0bf1kP7jv4PDQw5/M05JbTp05p0oRxKl+mpPLnzmllqqTUuBavcwDOE3B/h5nh90xz3r59W7dv3dK1q1e1cME883Mxc3Nmy6Ka1aqa9qtSoZzloUlZEeBCw1935ira7sqVy9rl/NNRI4apWuWKFnGOGzOaM8eTmJ/auGF9lXE+c/w4MZUlYzr16tnNSj0hsjyNEPBKhJx67zAP95vOnz/vBPaQ+54j9rs4z0e+9oHjSV2QBxF0P0jXr12zDaRTu7ZW3AKjbsyoUXYOZrK/hvAE3M/Bgqf/GKWUPb7vqi6dOpk5XqJoITNvoXDOnjXLijV2bN9mAj1rxnQzQ9kASGHB4aZhIe2QShQpqHSpkiuNE24IIh3attGQgQP1XWhAjUh50YL5NXLEcB0+fOiptOTT4n7wfQuccY7169a23/Cigd++Z/cuDRs82AKACDnBxJDf+vqRYyJUwElXYEZBhFgwb55Onz4V+oyHZwGaZemSJRZdJtpMRBgON+kn/GMCWH179bTI94PAt4ZpVq92TSWME8tp5eIq7gQbeifBsgJ5cpnpjcm6etUqzZw+3Ugj5JiLOSFHuIk2v2iweeFb/zW0HnxqOPXgEYlz585p1MjhKleqhArly+N89J4WY3jdiDHPLeC+qCWk/yWLF9kF++LjD4yLPGf2zNBXeQgLwU5LYnriV2JOhxzXNG3qZNMyKZx/DUurtDOjGzhNx7+hdhKBrl61shYvWviLiDImJ1qfwBVklPROM1O4QRAO3/iy8+GJdvMdcL3xuckZc8/4/hepuX1g3eBW/Otvf7ZIPaOEXxb4fRSpLJg3V3VqVrP8epfOHS1f/joJ+XMLeEBggNavW6tvO3ZQfreYqCD619/+os8+fM9K/TyED3zPdWvXamD/vtZdtHXL5vq2Uwfzh7NnzqhO7duZ2b3FCSY+JHTQODGiKkfWzCbsaEHMc3zlB7F7lzNFhwy2QNb4MWPMuoIsgmDB7lq5fLkT7lKm2RvVr2cNFxD8lwWfBn/Sji4vAlevXrGIeotmjc1cb+OuPQw5ilZeBzyzgKMxoCROnTzJ8qP4e5iRRGHf/teb+uqzjzV9Wtg9tjxIp06esDQV5jRRa4I/eXJkN8GlX3h65y/PmD7NAkQAi6lpo4bmKzd2QklAjR7jUDVhnj0YfLp29ZrzLQ9rn3sc98kHAnakjurVqmlmf+3qVZ2pvlK3bt0KfcXLAa4EsQHKQJs0bGCR9Z9wRzcvHtORrWu0ae0qrXHnu9a5E6tWrtbGXUd15HKgAoIiRgixdjZu2GCVbsUKFdDQwYN0+NDBpw7k+SOeWsCJ6GLCkcro2e175cmeTTmzZLaI7ZLFCy3XSJdMTC5PwH8Ci+We01hEweFcY47jB44YPsw2R/xqhLuuE3T848Tx4hj5A5JIt+++tbbBLESEk8AaJiXsLCwnCi7wrdHyd277JgKGfCemKILkW6z33L93bN9u6THILKTUYJk9ijTyosE50cWFABd89Z9ScbgHZ3Vk7QSNalxRTevVUf3GTdTCXZemDVvou+HzNWfPLV0LeDYB9JF7+M1YMpB2zp49aw0mIOhQ0ILlg9v5MlyVF4mnEnCijHCOKSwoW7K48ZEb1qtrfhx9rxcvXGiLlfpeT8B/DgTvoLN4GLA3asRwt4AGqYfbIHM67UvQi7pmCCoUXhBYS50sqWJH/8aEHhZXqxbNreADhhYRcgQa/3WmE+rOndoreZKEtkDJjz9u2bNBnDx50jjkeXPmUJMG9c1Mf5ocd0SC8xnmtCXNIchPQyUNAdHsg9o2vZs65M+rBp0Gqvf0pVq6dLnWrN+qnYfP6uwNt3GFvPipgGAzqphIOtcbt4CKtnatW1kgkqo0ylzz5c5h9+n2rZ82zFcRTyzgp06e0qIF850p2MGEm7wp/iK1uviPBEgwM+nD5ZnoPwGLB58OM7y9W0S1qlVVZWfl4M5kSZ9Gn334ri0meNksPkD/b8b9sIGSEmN4AALZs1s3I2YQKINxxuMjRwxTl86dlMRd9yGDBlj0+3GmJf734IEDLfCGv0mtNdorssDvZc288fvf6OP33n7AB4dGuk1rx3RQ44xF1W7MUs09clnnL17XHftp7n8CrurCqbO6cO60Ll44qWPOFTl0+IxOu9fcDrqjG5dO6cyRwzpyzL3mRgCNn3XTbY6LFy4wVluLpo1VrUolM8nJ+eNaMmaJGFK6lMnMoipXuqQVsGCxvqoIV8Dv3LmtI+5CMfQNthG+YbVKFTRxwnjt2bMnJMDmhB5fjpQM/a3f+fc/fpUCjmDduXvH/N3Lly+Z38y1ozECQ/YolChRpLD5vOSao3/1pT557x1lTp9W/Xr30nFnHQEqoyCqlC1V3AbxUQ2Fli9cIJ81KMRSouADoa7i7kUZt+GyQOmGcv7C+UcKOMEzpndmduYnGwellNdC/frIAgKOFeLri/5TFN2J4/11Wjm8tWqlKqF2o+Zp5t4j2r//gA4fO+U2sYM6vmeV5o2ZpNnTp2nBD7M0c/J4TRw7VbPmLdP6XVu0bsUCLZwy3m0a0zV3zX7tO39Xx06dVlu3yUIOItNDF5lPPnjHNpeP333bOPFwC5o1aqhSxaDtZrSOMhs2rLeN+lVEmAIe6EwoKnn4kTmyZrI0y+AB/UNohsaBHmBmDVo7i1ukrZwfniNLRv33n39XlF+hgMM0I1IND/t75zejLWkoiLbFr6MF0crly3TIaehxY0abYCeOF1cJ48ay19CQ0DYFp424rrlzZLUuJdu3bVX9OrWNToppjw8NzRRiSlK3aSRy78fMpQrr3mMWItVhuE90Q8HEJyCHLxqZQMBJ+/2d8cEfvm8B29BnnIZermWD66hM7FQqUqmlWvTqq8G92qp5jZpq3qqZ2nzbVFVzZVGhQtVVtV0/jRvfTaM7lFPLkrlVrERV1ekyTP0G9dGoNuVVvkontR21Xtuv3tSaTZvU0H3nV86F/ODtt/T+f/+tDzjcvzkIWs6bO1uL5s83QaeZxbcd21td+avoj4cp4EHuB+Gn0PuKETRjx4zSemeOU2Dfvm0b5cmZ3Sp9SOfgx2DOkFP9zz9+XUE2FiqBIqwcNkPaFKGx0dJoYrQFwRuEzGeGr1uz2phkHGhnhL1yxfImuPjh7du0MhOclBimdMO6dUzzfPdtJ3secgsCQQqNWmoYYY8ip/j8bvqgYWFBlCEOwOORDYJ/BAabNKjnfm9r27hCn3H/f1iHN0zX+K7dNWjwRE2aPVvzJ/VX35p5VS5/VqXNkEVZY36u1LlqqXz3RVq9fqrWDyql9vkSKm6SkqrWZ45mL56spd8VUZ50ZVWixRStvn1f1+4Ha4LbXIlhoMFNwJ1gwytg86MA5uDBgxYInemsAzIaBfPlNivswQDmq4JwTXS4yAg0F59AGou4WOGCFuXFT6Sx/ULnm9NZA/I+i9oXZCP4Bh7nE76qQDi42SwCDkzqoYMHWZorcfyQIg3cGBoKfumuwxfO/Kzo3BvaBhM1BuReuVZVnFAjoC2bNTVtUbd2DbOOZs+aYcQT45S75/AVMa2HDx1sgU4Av5oNg+PBSPmDYI721ClT3IaTSymSJDRXwDcrLNLhzvfKpUsWfKQwBq58yOP3FXT3mm5cuej87mu6edf9PvfTgq6d0PkpddSqUAZF+ySJssf9SgXr9Fb7JTd18eph3VnRRmMa5FeKXO3Vc/FBnbm4Vccm11X5TGVUstEYzbtyVwfPX9Co4UOVy22eBDFNyJ1pjpnO/cIq9XEBuE7Qg7Gc4O4fdoLvDxvj0yBcAYdhdfz4cfOPateorlRuESZNENcWMAKM6YKWx4wh4kv9MD44Ak5UlwgtPqlPc73qQIhOnz5tnO/58+ZqjtO4cLzpK4Z5161rF4t2U4YJxRSGGCZ0gtgxVTh/PtO0+OfkoRFwAl50F6UzKFq+TImipplpTzSofz+rEKO/OL5hXed3hxBanpxpdfDgAVWtWMHOA199txMkf7kXmLy4FWxgJYsXtUCj4d4dXd89T8unjlH/Mau17cwNBfD4zTO6MKWmWhTOrG++SKO8Cb5Rsfp91XH5XV25flJBaztqQtPCSpnvW/VddkQXrm7Xian1VSFzWZVqMEoj9x5Vu+7dlds24jgqXCCvVeGxXj99n66uNS2m5CMMUQyzxZn0WFiZ0qXWCGIc5148hTciEaaAs1vt2b1bfd2uj9ZOmyq5mXid3cJFq2Oujx83RnWcWUNAImvG9Na3mmDFpx+8Z5Fi0g9tW7e0NrnsjlPdRoH2YneMjNzrsyIwINA09egRwy3NBAML87l08WJKmSyxNSIo7nxcrBgfqNOm+2fZkiWcMOczzQ6Vd5X7/XDFyUHDIsM3Z3HTRwyhp+f3lctX7NrThhhiy/ffdtaSRQvNYnhSoIlmTptq9d2QYehyEplR84fB4AKsP+i4MZx5PHliaBT93i3d3DpaU7vUU7kyLdV9wkIt2bJB6xeO1eimxVWzdEFly5VPeeN+ocxFW6rumL06fGS1Tk6tqZ6l0ipemhpqOWWrtu5bqW39S6hYquxKla2GyrRopwxZMiu3uxbEi4jam+XkhJyoOeucZhY0g/QBOi/rFwHn3sEkfJUQdpAtMEAznB/Nj0uWOIHRGseMHqmdO3eYcKN58BPJwbIB9O7Zw0xBivd9jezpwoEGI79IPpdgUM1qle1i0kebKDNpCH8y4zkXtCTnRaSZ3DOWSh/3+zCZ2cgQRBrwY/aSXqGtEdoYU/3UqVO2OfJvfHFSMvhwbVu2MOunZ7euRhRCkAmUEfzq0La1RdnZJJYtXfJjbprzuODMSnjTT3uNqM5q3rihuVOtWjQ1Mok/RYPR4AQlCfoRg5jrXJiQJwIUeGyxlg9rp8YVa6tV90EaNGaoxvR1rkytOmrbub2+79deDYrmUqlKndRq5Bp3f+Zr18Sm6lutkAoUbaDO07do2YYVWtilmHIlSaxPPo6tuPESKqtTRBC06PbCtSX33q51a5tPzubMfXvwOqOEFrmNldgS9fIw7yI7+/A0CMdEDzZTkkUyyu3+FCns3LndNDHaObn7wfnz5LQh7ps3bzTqKrTD//7zb9acr2njBs4kHWvdODt37GAVS0SHYWfFixndtFc953NiDcDH9pcoJeymXTt2mAlO0Avtyi6OC4IfPHrECDN9McW/7dBeedwmRwALggRpqK5dvtXZs2fs/TQILOVMb/5NDjZD6pTGIyBlRXyD2mwaLnA9CPYQpMPHxr/24Vk3P6492Q9MTCwnf/Mf+V3k5qlmg5H3k3YMtnloNy6c0PGD+3Rg3z7t37ffra+DOnToqE6eOaNzF87oxKEDTnOf1skL13Xn9lXdvnRC544e1MFD7u+12zp24pimjOyvrGnTONcxim22aG2Cjr5rQcdYCkywJKCnPgzO8eq1qxo4oJ8FlJs3aWTu2bPek5eNcH1wRtFsWL8+pM545nTzN9FcLBoEloZ6CP76tWusdJF0EGkygktjRo2wwAm7JcwhNgt41eygjLMh2pwxTSrbLHxN8R7kTL9soN3MDB85wvp+kQvFfMR3ZVOKHT2q/TdaB9Dgb8iggdZxFMske5ZM5uuSXaBwg+o6tHdO9/jwoUNNQ9FNBO1PfALu93En5Lg5XEsOrvHzui4E3CDEtG3VwlkFCX6skvJHEA+AEkrNOyy8RyH43l0F3Lmru4FPLlQn3HUd665x+XLllC1zBgtYEtuAHvwwOIcL58//ovvNg8A3xy1j7UNjDfKzzfJxCFPA2aV8UWIWPRFfNBBmJcLMjsuuB8ONnl5EIWECvf2vMIgu7h5BnmHBEZGvXrmS1SHDrW7etJGV77E4X7S24bchoJcvXTI/ixtPPTAsJ+qDiTfgfuTLldO5F3GMiEETQqZ3oH3ZuGgPPLB/P7suEE+wZGD4wQv4rnMn+y1DBw9UDmcWEpTEl4YQBJONoKUvWIYrQFP/k8ePu38/v/mHBcIUEXgLsLSW/bDErrm/gXvAdFHy/HRCpbLrecE1pV1U/359rP8apbLcGzZb3/V+Fly+eMnSiwRSWzRpbL76q5AXD9sHd0JGlRHaLH3qVM4cz2VRYrQ51FUEHNOKwBtBHHKtT0p0YdfkhuIXYr763ls4fx717tHdLfYTpoleFBCq3Tt3OZNtku30I4YNsYWAjw3BBAoo7Y3oAYYGxEdkJlaC2DGcZi9i2uCS2xymTJ5sPAEOdnk45WmdKQcVdO7s2U7bb7RungnixDQTPsY3Xzkzr7FZPb5NjIXOvx+X6npa0CiinfPpfVYWFpQ/guIbOsng3nDdcWGeB4wjZpMmgEYX18zuM/l8NhBISM8DavZxqerUrGFMRAKevgo/f0aYAs4OtXrlSmMbEW0kKMROS5CNBnmUGxL5xW8koLTC+arPQnQhaIHZi68OaSZvruwWfcdkJ7gUkWARHHJWxxhnkTC1kvwyZBM2qQRuoVFnXaFcGe3bt9deT2xggjOhC7mNB3eiZtUqtnAIyhAoW7J4sWlm3AxmaSH4ECOyZEhvUWHy0Gj8Vu768R4i8Pj0bA4vQgOwScBZwArht3E+/roQ2eTr16kZIfXgrBOEjg0NOjWdaQiKsl5J9UYEsK5gKdasWtlaXdEX3t8Rrg9OB0sGv9E8gIAIJIxePbs7U7SIaW1qwSFw7HJCD1OLdNCzVJOhuDCX8dvxUX19uCOyThktyW+gGo5OnvQmK1Y4RMBJlWCGI+AwypYvW2bxANwFBDy/M9XpqDJv7hzLnxIgpEEDhTbwuhEoYgtMxSSYU9D994xp0+x7SbEdOnhAO5wmOXOGeVkRs+AeBbT3pIkTjJwBK+vQoUNOU/qnv4iAI5D/+Msfje33LB1d2NBwrxYtWuDcvYrG0yicL69RgclmRIRF5AOxkfXr1tk5c7+x7vzdTA9XwLkJaKEjh4+Yz4yPmTFtKlWvWskKIaBNIoSY6phZ+N7PWmyCdsVst9yo+x78p5rVq1g+OCKEghE6aO7c2bJYUGy0M82JBZCXbuH8/yTWMjiGsmfOpHKlSloFGAy9iePGWowAa4Vij0YN6lnaEB+XfDamOSY6ZmHULz+3nCqVdrQm9gFzlN/wIt0OQOOCRg3qGy+BjedFbibPC9YWHACqD2k/haXzNGCqChsmliUpymQJ41t8Y7mzkGAMRjTXni4vyAKkLtYmmwiz1fwZYZvo7gchFPjI+I1UQpUvW8qCSfhLRMXxXaHxIdwZnODTMP95y0UxX7nZ+Zypzk1DWLAQnhfEDlgADJen7PXEieP2OOWc/fv0Mq1Mmq9Pz56WDsOknuK0IT3PcB0YjctiCtHSucyKgVmGP4/ZTWEJ/hntf9j0IiMjYPzpnNlMmxFo82eg/TauX2911xMnTNDRMIYUPgysMcxvZokb0yxtamuUwX14kS4JFsGI4UONwIQbuc3PiS/h+uA0p6cxACkthIObQTUZvjkXF3YWKSTMaoJRRBn/i4n+HAIOiFJ3//47a++bMklCq6LCFHsekwsiA/z5Gs76II3lM6/OOi0wzlknGd0igYSCKU2uGoIPEVPiA/w2/HAi5tQJk9uGiUaGAZC3ptiD3DjXJ6LciqcBvweOAvwEWgH7zs1fwb2E6ERHGQTdx9MPDxCPCFJyT3AT2ZhJCWJNvQyTGVcUC5N2z3A4/BnhCHiQcaQpr6PIgaj5vn17NMz9G/ZVvJjRrOMn5i2dQeBfY6q+9eYbz11NFhIs2mbRdRhxTKvEksDUfVaQh4a2CWmFQKFvMRBhXbp4sfnk+P1YJjTfw4/FLGfQHRYLzQnix4puxSN0YuGaPNiymM/D7AwMDIhQ3+9JwHeTR6Y3G2k68ux0LvFncK0IOpJdgBEYrrC4a4rLgZYmmo0rlD93DouFMMroedbG02Dt6lVqUKeWuXm4rf6MsH1wd0HRSviYmLeYzQhAtozpTRNSITV65HD7wYzRoQYa/9zSZJ8+nwYH5G4J4JE+w+fB94F59KxAwOlDRgR0z0P1vfj5FHtgolMQMnLYUNMOfDeD7rgOmN2Y7zQI7Of8WzSkv/DpmZgJWYRGjAgLbsWL5hI8LxBwyCN/++PvrKqLiH9YIAjLvcGCYjNmigvZHFKtL3NDxTVgLSIDROr9GWEKOBeNFBb+L3nhCmXLmE8MFxvK3uwZM5wPssUEhxlZ/GBM84js6EL7ojatWloADD+YRfysgaO5zrRio2B+NGb3gwEvYg0M7yPOUKNKZSPuZHfCTbR0//799ho2BOIDbAYUyzy4QUQ2IO1Qjw9ji8q2lzEl5HmBgP/Y8OGjBxs+/ByBbvOCCMTQQfgFdJStVL6MaXxISi8bpMew3pInjm/WoNUNvGSL7UkRpoBzAzBXmeqIYMDoIorOjaAVL77md506WX9uikkwWyGCRGRPtps3bmrF8mXm22MdkEZ7FN3wSWAC7rRb5Qrlf6HhMG9h6yHQMNb4PeRTKYR40NRl0/ORUvwJXCeiulQ8Ed1nI/R3sL5QDDRbwA1jIs7DYDM/6vx0NCW+dgq3DiGy4G/fuP70BTgRAaxIWIpYg3Wdq8Bm76/WUrhBNrQzzC6KRAiqIWwIPf2/MJGIXiIUmCw0YMR8isiuqtxAgmBNnVlMpB6T7lmCR9T2EgEncAZjDT/uQSFlsaElMAHJGBBYhGfOQvLnVJMPEHJgGZLfJzDIb/F3sL527thhXV0IgDIB9EHcunnLXMOWTZtYmjJbpozq1b2bpR+fl5n2PGBNEkzNmiGddYNdu3p1pJ5PWAjbB3cgr9q5Q3tNGD/W2gxRy006iOATAkcjRsj3RDWhZcICi+i2yZifY0eNsqaDRO3pE/ckwD8+efKE1q9fa+YdxA+KYb7r3NEWFvXIDwNtbUP81q83s/1VAf4pjfsh7Qzo28cIOv4OBAVLA+GmVfS5B5opUOREYBNXkOwGKVPKkdm4IkNrPwwIYASaqQSEoPNjai44UIHXTmrvljX6YeF8LXa/i9+xZPFSLV+7VdsPntPZawH0jX0pCFfAIejDjjp4cL8zAUdZeoDopa8TCbRI2GHUdpM24rmIbpuM+YMmhUFEJw6G5j2ulzdaAY1L7IBdlmIPcvcEnnAfSHWhMSAsPGqh8BhVZXwn/ONXBTTuhyNPZJffd9X9Pn8HVhNZEgJszCSn0hCrCv7A9GlTrUqPhpT8Lmi/3FN/iXvAkmO9ExeCUHQJNy74nu5eOqRDy4erS/1yyp89q/IXzK8CObMob/Ycyl+ypup1majJa47o1O37eoriuGdGuAJO1Qw7LLOrEGrK5dDo7EqwwBgpg2lYukRRM9Xjx44Z4QKO0EEmoYUR5Zh0lGHn/4WAuv+GtELVT5uWLSw3T6UaxA/M8kED+htrjYj4q1Lu9yRgI6IWH64CltWGdev81mR8EHC7uS9v/uUP+vj9d6wwhPZf/fr0so2KAh+6ycJspJzTn8D5MLiCUuLWLZu5Dfao7h5brhWD6qtRiTxq0qKjBk6erwVLFmvZokma3KeZWpXMqOzpMqtwvT4auO66zr4EqkSYAo4A4QOxU8GtZiwRRApM2L1OuOlHRsADU6W8871Jk/1IdImANNnDmDtrlrUXpncWC8GHSxcvWcXQLBoHhA5mIJVHaSYuBBxxYgf+tkgiCtwn7kn2TBmslzqZB38HlGR4/SgFsi6fvP+u/ZssACxCauhbON+bXgT+GMCi9RVdekoVL6aalUvp6Nbp2jSmsZrkT6a06Uuo+7gVOvljdepd3Tq2TCsHVFXFVFGVMW8t1Z92QYdfgpEVpoBjLtFkHypq3969LPWCuQ5JpHevHqEUwTQWACNFQ5cTKssigujyKKxasUIVypS2RUDlEYsE9wCN3bhhfdvxMfVoLwxllKDaoUMHRAfUx5l2ISZ5kB38m9lhly5dDDkuXjQtw3O4BPw3aTL+Ur3E41gWIY+HHGhOHsfM/OnxS6G1yCHfhWnKQe6a7+Q5q0sP/U7ey+uIIdj3hXUu7jlYf7gjbGi0zqL5Bh1l+N2POxe+n8yBPe4O/s1jvzyXKzbP7Pad2z9+H4/jcxLDoPb8x892fzk3rnVY1wWrcOniRc7aKGAkFzrZ0OILIaeqjG6n3b7/Tju377CMie977VycsPNZvs/1nQuf/dO5uNeHnguPP8k9ohEmv53P53ra4+7wXRdGCvuuC73u6LBK74B8eXKrVN402jKyorqVTaWk8TIoZ4vZWrjzIekNvqIbJ3/QtNZl1bpRB3236LJOvAQmc7ganJuxzWlHmEK7d+825g4+La2aCFohRJs2bDANyUA7CAgQXSLSRPeB76lfu5bFAShSgBNfpWI5ZXJmOIUe+Gr0DSc/Sq6agNnjdn9+G1VW+KpwoGlcgY9HMI6mDjS1wEyEaUXAiog6GoYSTB6nDzyPU2TDf/P6Is4lYGQybkKI1ZPbBgOSWlzqTDViA5SqslFCHqItFGQehiFgdRAg4zuINcCTx5dGYHE1+Cx6oBOIGjp4kDUz4DxxmYiFbNm80UYgRYvyhXJnz2KPk86kI+5P55LfgkJYP9S6V61Y3j6H19JAklrqVatWml/JeXMuBO6Oud8Dx53fzrnwONeFtTFssLsudi7u8fx5zI2Ccvot1F73Ol7PcwSiCHgyOLFg3lxmiTE9lXbFCDcHPcpZOzG/ieKsw1l2zbBIfL+fnDlBNqr0+C2+e9ShXRu7F8RbfPeIvzDciE3A7vPdI9+5cH05F17Hb6VTD+4bGRoUmu+6QE2mpTORcrtH7rVkKngfay5G1KjKkugrja4S12nnBEqQroqazT+sXdcedrDv636g29wObNOBPQd08EKgbr8EwyRcH5zdmN0NASZ6ThqseJECRuVEc8JVp+oqZKRtcjPNI5Lo8iCIfIc0hshkA+3pLvPFxx9aM0dquxF8+rRzoydNmGCCRrXP1MmTjXHHgeYnOo4GRtBwOZo7U5AZ2tzIFs2a6G9/+r0df/x//2NRe0o9azqL4E+//V8jZfzxN/9jAkHnENoz/cG9jtf/9Y+/s1bJCEqShHHtdX/9w2/1n3/+zZhxjBUa5c6hiducalWvpq5uM8ICgY31zr/ftLpovoMGCLt371T3rl3s+/hcPiunM10ZB4yV9Off/Z/+7r6T90CpbdempeVlmexK+SXsMM6FTSRJgjgh5+Iee+vvbxiXACH/8uMP3Of8P/3l97+xLrgI1ITx4/T2v/7+wLnEtEAq18d3Ln/iXNx1gUfuOxd+P59F5xo2FeI1vJ/X8xybP3ETmnD+6bf/ZzPkac7p096+AwFH8FlvKA/fuXD+BEmxVLhuvs/lHsE2xHqEJs138jh/2cDYUDkX3s/jdi4d2rvru0vJEsaz1/H5uJXcB3jxrGG7Lu53ffHR+5ZSpTWZ7x696a7vP974k2WL3vnPW0r85Ttqkfp95YiRRMnztdeQfZd1MvID/YZwBZydkd27YtnSlvMuXbyILQK6jG53Fxuh52bD0eb5ONGjvjABJ5CExiTQxuJ4/z//dn//ZTs4GhFB57s/eOctY9ShTdmA6KbCaznixoxm5YSmfYYMNrbaV59/4n5DJv2wZIktZH4DB+2nKpcvZ33T6EUHASZujKi2AIk9sIGw2/M6Xo9pidY4sH+fxSx4XeyoX1tXUyLEECJI+7Ax0V2VdsrU2c91FgfZB1pO8x1UrbFg4RpwvnwunwVB50TodFCmcPAc153nPvngXRMQ6qpjOA3IZ4Wcy37TXnYu7jGi0txPfFvOg9dSAci1o2EFZKAk8eO6z/edSw4bczR08GD3233n8qVtcGhkaL9oXIgq/G3tNv4zp8+ohttweT+v59oMGtDPhA3Nx+O89rMP33Pn/N8fhRthp+V24vixLRU6b86cn87FnT+NQNgkhrgNPORzv7FrT2yIbitMg+Gz+T7+MriReW9s/ryf19u5OCuDOEXh0HPh88nOEFPasmWzpeU4Pw4UCTXgBJrh+PNa3EA+h066H7uNMdaHb6lizLeVJkoqpS7aTeOPXdGzUbEiHuH64NxwzBWCaKQDaJdM4A3hKFOymDXkZy4ZjCRM4wplSuo/L2g+OAuN3TdxvNimFdntidgTxefGU3n2j7/8ybQDiwXSCqQc/Dx2XQ76l8Nig/hC8QwuB77UuLGjTQAZOEAnGY7VbpHBO8aXZXGuXrXix8eZL4aPTDNJ/tsedwcamUoy+Ov2emfyIjgE+EjNEUeAX79owYIQNtaNG7p44YL5zXDdeQ+PM7aWfmXw/O2z3eNonbswu5xLASdhvTs2bVhnpjtsMK475i9uBkVCCCDngtYLOXfOZbVtbvST4z7yON9L3h8fF4uH833wXGhGCD3zF+dy946NbOK1vsexavBlcZFCvjPkPSedSYzvy3VBeFk/dMiBompa3B1s2vFjxTCXAlMZn/cX5+L8as5lzaqH7pFzdXCzfN/JXzbJkHv08Ln47lHIdeHzffcIfx0as+9xrhEkItw937lwrxY6gadLT6rkyRTrg7dUKcZ/lfbzZEpRsLNGHLqsn1N2Ig/hCjiaEfMKYeHGIBxoUbqDklvG7yUARx4cEgw+04uaTYYJTfoLVlN+Z3ZR+IJJjQlFZ84+vXqa+dvMaUk0CTz5o0ePWGS9iXMhODBb9zsNCyg7PHf2jPPHTvwYlHqRIB7Ad7LQiQE8NYJv6/bxddrshHf52n06EVrnssu5BLWqVzEthTY74oTO34GQduv6nVGg//XXP+sdt1GjrZk2ylry9zw+GwQuX27noiX96n01T/mecnwdXfEz11PHlWe130+ylOGa6OzGRM7xQ2ldRKABnrbxcGtVdwK/wLq64DMRtKB5P37Ti5guCluOBQDXmrp0BAZB8QkLf4kZ+A57/KHHOHjs1cN93T27VbtH11S9gnmUr3R79Vl1Rkduwo0PNGuE9sDkZeEnEPn1Z3B+aH+aNOBb02oJ3j9a0t/PHRCXYqxz/rx5lTN5NI0oH1sVU3ypGAlzq2SvNVp19OEqwyDdD7iuaxfOOHm6pMu3gnTv/otfh+EKOKbJooULjANOEI0gCZFFzECCXmh1ItcEMnzthV+UD465jT/F9z9L/65XG2d0auMw9SmWUBmivK8ocbMrW8Mpmr3roq4F39f27dss+PiqCDibL1kFSj0pWoLHQEzjecqBXyZwHxDwYnQ5KpxFW8bXVd8q6ZXi62hKlK22xi7e+nM66p0zurBtkka1rKqWrXup74qLOnU9kgUcEx3NTN03jRLoE067Ihov4MsQka5ft7ZVkUFOoOosg/Or3qYe/AUIOL2tiQcw+gh/37Txaw9+43UFnZqjtUNrqnjSJMoQ61MlThhH0dJUVYvxm7T1qrSfiH6OrNbdFWHB8vJ3IOQMHyS2Q+svYiCvCkgFDujfR6VLFFfD2pV1cud87ZzdU10q51HBjBlVq1FbDZo0W7MXLNSiOVM0dXg39WxdW7Uq1lDT78Zpyo5rungnkgU8IDDAcqn0nyrjfgipHgIWWzZttsAU3TTQ6OQpGQDAJEZqqUnVRLQPjjlOHICUELPKiQ0EvwQTJ9Lh/O7gm1t0Zm5jDa+RTSnTVlbVCgVVv2QixYuaUNkajFHPpae0cMlSZc2Q1qLUbMoR3W76RQArA5eLoKitl6kRqxBeJCDgEJvCYurcqYMFLnXnpI6vHa2RbSuoQqnSKlShrhq3aq22TaqpbsVSKl2+gVoMXKKFuy/p5ktau2EKODssTfPhApMLpaMojR9IlaVzggaTrXePHsZ9JmI5b+5sI2tEdDUZlgTmGxx0Uk6DB/QPqZZ6JX3pp0PwrTO6ubGn5jVKp9rZMyt7vQkaP3OkFvYvo4Kxv1HCDA2UuEAbpUyRQl9+/J6l+8gIwMLyd4QIeB3LKePavUpuF8Qvuv8wXXbE8GGWIcHPDrx5SRdOHtKOjWu0YukSLfthhVauXq8NW3dp94GjOn7e+eF3ghjw81IQfpDtzh0ruMcsxzxHgEnFkMpg0iJ+OCwfCCNEcCFpkLqKSBOdhQBllpx02hTJrNgeoX/9EazbZ7dqa59iapk5vvLmqKKmMw9qz+XTOrOmv3oUjKvU8bPonU/TWIrsv2/+xfq7MzaJaid/B/eVPndv/P43xmh7nsEHLxuk8eArwIAjZXbjIYspOPCObl+77Hx1d1y/IyfTkYJwNTgLhZ21KpTQtKlUwP0ofCaituxipDTatWppaTMILwwOiOhqMjjYPb7/Trnc5zMQkPzlrwL3L+ncjkkaVMqZ4tHiK3Xupuq+ZJs2uuu+a+lIjameRFlifq3334+pT7+KoxjRQ6LRtatXs3y+vwO3C5otlE+KlKhneBUQdC/IlBruIp1VCXD6a8wjTAHnBtBGh+aDRZ3mZgIoiX9ymDSCoFyOkT/QNelNRQlpxXJPP7ooLNwLumfMMFoRob1pBwxr6VeBKxu0d3ojVUweXbG+iKcE6YqoYu36atK8qZrVKqfq+RIrxTcf6ouYGZWgeA9Vbd5VpUoVMxZdRPSRf9FAgVC6SwNMuAkvsp95RIJilqmTJlm7cBpwkkb214BvmALOSW/dvMmGAdJRFcYQFD84u9TpUuzAnKahgwdZn3R6jcMHj0gfnOIKeqWlTZnUdnkYWpBFXn8E6+aOcVrQPrcyJM6uJPlbqlq3SZo4dbrmzpqhOTMnatqYrmpTPJmyJUqm+Lk7qUHfqSrr7kv6NCmNdebvwM2CAgrFFDYirMBXARCJmK6bKlkSdXHuUECA/6Ykw/XB8ZOg6rFLMeQfTjH134z/oZqMml4YZphXzRo1tKb7EUV0YYeHQkmaDnINlWQw1l7/2Bra4LIOzGivHsWSKVHWZirce4umnJAepE8E3z2h7UMqq1nmWIoVt5DKdp2qvLVbKHGCeG4DmGGMOX8Ga+vHrqofvvfYrqr+BtxTip6yZU6vIQMHhj7qnwhXwDHTqb4aP3asTQ6lNTJkk0kTx1vBCRF0zOZcWbMoXszoxi2OCKILwg1Hm4KLJAnjWXSYAnt/6UP+QhF8S7q1Rou6lVGF5ImVtOwQNZx3QhucvP6s/WPgVV1d3kVDKidVwmiJlbXhBKUo20Hx48TWELcRw7n2Z4RE0evqn3/98ysVRV/mlBnFNKWKFvb7TSlMAceEoga7VYumYsY1PbKotqKsEFbZ+LGjbX4XVUkhHU9r21+ILs8r4Nx8qp5wA6h2ojKI0sdfA7nl3o3jOrmwlToXjam4H0dRlEwtVWrgRk0/els37/1kvty/c0Fn5rZW39KxFP+LLxU7cx1Fz1BJCRIltesFtdef4YuiU676KkXR2YgIKtepWc3qIPwZ4Qo4jDGK5DGThzpfe/u2bRZo69u7p6XLkjhzkLbKzIla9sMPNr/seavJuPH4Y2we8WPHsHG9C+fP1907/s/OiggEXD2mg1PbqlftfCqUv5iKVO6qZsPXa9beG7r5Y6e+YN2/e0GnVgxR7+rZFOPjD/XhpwkUJ0kO5cpTQKVLlrCFyMRWfwXW4eCB/d36yWZFS0/aLTeygFUJvZautdC2mZ3H9Fl/RrgmOhFrAiH42RzUgpP7S5wgjrVGorMKBScQXRDCogULPFeQDQ1NII+yUGaEQ4+dOWNaCFPoV4Lg+/eMMHHlwmmbfXbm/BVdvHZHNwPu6+cEqCAFB9zUxFFD9JW73v/917+VN08edWjfzijDHdu3tfJHf4XPDaPElE4t/s6+Y0OiyQW94hiKQY0GJbP+jHAFHKILbDYmKlKCSTsgBJveaPjE69evMzMFjV6iSMHnyoMHu//DrGRsEGZ/Eae5IdAwA/pRPcw9hGDypElWD/7GH35jLawWzJ9rJbXETGjs4K9xCyxErAyCtfQToG7dn0GJ6IK5c51bUcMKnuhB4O8IU8DRpvSuYka2FZw4jUq3CwIj+Mew2KgPb9m8qVtQ6S0vSEOFpw2y8T1U59B9hTGwtOCBBjvECTc7O4PePTwemLZwovELRw0fZo0PaFcE04phAQwR8EfgilGlSFsrmi36uw/OdaS3QC3nOtKwgsySvyNMAQ90/saMqVNtJhitfsqUKq6xY0Zpn/M7Nm/caIuHKjL8ZFhsNIKgB/mTTBfFPGMHhwFEt4/ZM6eHDM5zGwWU10ULF+rcufP2Gg9hAzORsl46ktAVls2SJpGF8+W16jLiGVxvf4Mviv5TsYn/RtHpo0+Qt0TRQtaHjr57WLf+jjAFnEVBiyE6a/bt3ctMcRoVMnsaoj3D4Di4SXNmzdCmDeutV9eTVJPdcYuSNBsklto1qovRNDTtp7aczp6PmzziIXwE3A3Qzu3bjbIKdXXi+LF+2RPeF0V/4/e/9fsoOvUYA/r2tr4HcP2JbbwK6zNcHxwmGX2oaKxPDTgRxAJ5c7mFk8hMQuZ8kTYj+U8TCBrjWZDNmeiY8YAbSe+xkM4wB7VuzRor/YTeymcRsKANLn78q+DX+DtYdrSfgoEI2wofF+60v4Gg1cgRw62VMxmTjes3hD7jP0CIsWRnz5ppAzgrlStr7axfFYQfZHMmNJF0oudoZ7pP0outnvOdqDAjeg6LrW2rluaff/XZJ3rX+eBocOrHmQzK5kC/NrqckkdnzBEFBnTPZBhgx3ZttGHDOmso/zqNFHpZIHVDDzOu34PsNaqc8M2Zp83YJn9ktrHxkymgHBjGpL+5ZGxChw4dUrvWrWw2fvfvu7o1f/CVsS7D9cEJfLVo2tiisqStaKo4ypnVFJvQQ5rGeaTNaPpAfy0Elu6YmFwhkfB8VpBCuovgGX9pNUzrXwIVLEKKSW7ffgmDml5ToJ3ZfBmSQN91n5CQ0unnXKtEcWPZCCcsMX+qekJImBwSMvuurlmAJ0+e9CsyE5YQbmT+3CFTfBYtmG+dbV8VhCng7F70ivYJJzXgFJ2QymIWOEKK38zkDooFaCeL8NIg/qN337aOmYXz57H+36QV8Albt2xhnTuoIGKSiIfnB4JB5uJ3//s/quPMcVwigDDT/pe6Afp7c7/8aSQyAk43W1wz+ps3aVTfpuf4ixZno6FnHPEmiC2M6MLFfJUQrokOaw1fmSkTdHUheogfXqxwAetrTbkcCX/K/uiSWb1KRfPBP//4A+Oo08scMgMVYMyKIpeISUkZ6Kti5vg72IRxnb7+/BMbAuETcHD61El1bt/OuAvZM2e04Q6UZfrLlWc9TJo4wdw++A/73HrxFwHH5cH3zpopvQ2PoCcgvQleJYQr4ExRxM/Gj2ZIAKksIomMiRk3ZrRN5mAowMKF860yCOqqdXRxPjjRWy+H/eLB5kofNhYg7s6DGycDATZu3GB1BEzqQBsRDwkM9A8zEyotbiDR9DFufVEg4y8mOoMWsDphBbZu0dyv674fhzAFnB9Dby+mmdBkEZYU0W588rmzZ5m5ws0hgMPCIQceO9o3PzLZZkyfGvpJHiILCDuWE2OMCLbR045hfAcP7DcXzB9w5vQpW09kYq5euxrplh3ff/rkSfXv18cyPCg1aNhBr5hwg3B98HVOuBvWrWPBM6ZOMrgOs5sWt8yOqlOjmpnq+Olwn/n7JEQXDy8TwaaN2rRqYT3zKN4ZN3aM38RAMIWpWoSBx5ikyBZwrNbxY8aoZNFCyubMc2IcDDqI7PN6FoQp4PygtWvWqGWzpsYJR5NjjpMeYzxQtkwZbAws5Hui4fTjrlq5wgtpm+zh+UCKjKkhBEEJGJF3ZiKNP/i7zAIrX7qUBg7oZ0GtyDSDuU7EnZiimyNzRuvgSzbiVTPNfQjXB8cngsiybetWWyDDhg62klAaMBBoo08bvh99ymmpnMtp8Ihum+whbJCnJZVD6SV1+o9bjASI2Jzpb5crexabcc7ijWwQpI0XI5oaN4zcKDrXjSAy8+/oL4/iMlcm8NXlZoSrwclPQ0JgIia5Shofpk2R1CpqiDAS1IHCCtGFLpMho4sitquqh7BBRRZFPrhGWFYPRtEfBhpq3OjRxlHPlzOH1RZEdvCIWeWk8cgARJZVEXQ/yAhdbJKY5YyH3rRxo2V8XmWEKeAQXTBXGJNKEQjjeRn8R9NFzHECbMwHJ4VAmiNrhnQvpG2yh7BBmumj9962qqwG9eqEKeCAqDvDEZiNTgdWClMYJxxZoO0wVWVkXc6fOxspmw2jk/v26aXCBfLZuaxcvuy1aA8WpoCzk0JoQYDz58ll0x9nz5xhfdjgmTPMPnO6NFZtxvhahrG9iMkmHsIG/ASmvlBTTd3+k2hAiid6dOsaUpqbO6eZ+PS5jwyQqYGNh6UYGZH906dPaZyzZKD14nvDrEPgXweE64MTWCPIRo6S0UXstv379nGCnN8istkyZjCGFFVndHwhiOMF2V4ucKXQeveDQkcmPwEQpOMnjltknaAbZb+jRgwzIXvZbYAZ6k/Klamop0+ffmkaHEvnuNvUIHHRKRiuwOhRI/26C87TIlwBJ4eKbwK1dEJoZ1UaO7AomCYKN5eBhATimjSob4R8S5ORB5/m5cH9GSxwasVxs6gzoGEmOXJSoOGZ+REJqM+F8+dVSufmwZqE3faiwQZHxP77rl2s3z7rmlgG1sSrmA57HMIOsrmdlEYCa1atUrcu34bchKSJVLJYYfXp2cO6uUBQoKABv6VYoQKKFe1r/fONP+mzD9/T6BHDjQ8dmQGcVxkIGb3oNm/eZJr1RQSfWOi7neXV3S10zHUCTO3btLba/pchaIBqxKhffqo//+Z/jWtx48aLzc+joVnTDFygBJRCnamTJoYMtHzNEKaA0weN1Bj1xNQVw2eGsUYTRMxxtDbcc6qVUiVLbFxiWD9sAkkSxFX71q201Zn1r3okMrJAxJvh+B3atrGOttCF2XAj+nqyAdP3DrYibESyIWhSqs8gw7xojUYWJlbUr/T3P/3ezGSIJi8CbJAMziAt15wKSbeZ1axaxeJMlK2+jghbwN2NnzFtml0Igg/4aJjjaJQ+vXsqX+4cihszqt2cis7EYbQRtb3syKQZCuTJ6RZn61diVrU/IsBZP8vd4qfOHreoRtVKlsEgNUmENyIFz7f42bzRaGzmVdxfCEwvmvFGmixO9Khm+dH770UJOBp68KABVtoMQeu7Lp0tS4Rwv0ZW+c8QtonufjTFJHRPZdej/nva1MnWKrlcqZLWGJFAW9IE8SxHThR225YtNgkUc55JJxQRvEx/7nXDyuXLnYUU28pB48aIqvxuU2VsDiW3tJcOCAzQrl07bEYWBI358+Y8lyl/0fmgixbOd/e4oWVEIMUM7N/PCCAv6j6eOnnC2oD169PL3L6I/h78aqxNLCHaerN2sVZ2uN/0uk/KCTfIhhahZpeWtqTBCEbgqzWqX8/88DzZs1p3FnZ7CBRMN4kfK4Y1fPjyk49Uwe3ItHri/Zib3vHkBzwDiBdslO/860198PZb+vCd/5igFytUUL16dtfatattBC/X+82//EEN3Ub7vALC+5lO+r3TcHmdyU5umOAbVWg0ZKBCLSJBKTEuH7+ZLrpBQc8fs6EwBMuDqaVTJk+yGBGNQaHEwi1H6H8NsaFwBZwgD/XG0FOzZUxnPhL91Iis79i2zdILyRLFNyFPkSSRYnwdxRYbCzFqlM+dho+ppAnj2Wv46x1PcTjLKG7MaPr0g3d/FG7++jbPBO7a4jqhaXkNBCOsq4jQgPj55IeXOI1KGTB1B5QJo/mgLROACxGQ57dt2chyZsnkNq5oxsSj4ORZwJngthA4hMyzcAGWSANlyZDOuBy9u3czRUM9/K8l8BumgGPqUWdMYA3BxsRZMG+ezjiNDkgzlC5exFhsaVMlV6J4cfTZR+/bQmMxRvvqC2O0/eONP+rvf/69TZH0jic/3nQHLYXf/++/bbCBT8Ax199zj8WO/o3q1appJjSafpD7S2AsIodEoAWxwLAS6MrDGCs2eybPQFU+fOjQcwf9QqLon+nPv/0/I5s8axTdqtI2btDI4cOs+xDjkOg2xNRbtDbtvgP9eNTvi0CYAo4m4OI3rFdXo0cOt8YPD4LyvlLFCltAhnQDxQIEMAiYfPz+28aPRvjZ+QuEsuH85SiQJ7c7pzxWVBD2kVsF7fWP/pwXeXDdqEf+4uMP9N5//mXCjaZG00FMadywnjHXzjpt9aKBRpzrvouYCtqcJgj056PYiHOglht2HD3ZA5+SjUYUnWYUf/vj78wiedIg262bt8x93L93r21CNCRp3rihXTdq34kD0UqM7IO/jxh6UQgnyBZs5hI3F7PmYRohAk5OnBQZQbZ9e/Zo2dKlZtLhNyLglCWyy/MZpGL85jh9UqdOHrfJLcePH3vMwfMndPLUaZ1+1Ge84IPcN73CCWS+7bQ2hTyY7o0b1Dc6JawvioFeRiMCTFrM8tOnToUUHjkNCTkmXqzodv/pzUd3XPrj07qLyDTrBSuQ91rE/zHWPL4989+xTGBCPpx14b0cfA6fh+KhPpvZ8cOHDrY0LpmehHFjW0MLBLxXj+7WyeYSG46fdK+JDITrg4eFQ06jFy2Yz3LemERcTJhvG51PNaBvX5V15hajXp4nqvuiEHj5iA6vnKq5k0dpjLNOSAGOHD7UjhEcI0Zo5IjxmjZvjbacvadn8wqfHyuW/aBkTqiJYbBx0iZrq/MjGQwRWeA+U2mFxiRfXql8GfNxczg/mg66FcqWsjbDPE/mhXJWBi9ASfUJakDAXTPt+W8aQdJrfPy4Mc4fXx/6LSEgSwAvnHjA7t27rNyVJo1cCwKNmdOndVZOCgsGVqtS0Vh5c2aFdBv6tWrtB/FcAs6N6eIEmNLRYYMHuRsRUpF0P/i+Llw4b1RVdnv/IrqgRpwm2jhFk5sUUOVSpVSqUh01btLYWlHBu2/WoKbqlc2rQjmLqlSdXhq744pORsJPoJpvy6ZNZhZ/27G91dz7U1onMPCemeWkttjQiVQXypfXKK8Ie6liRc2yo/kmbb3Gjh5teXaEmWIlTPulixdp+bJltpGhyZmzxoElOG/ubE2ZPNH66/fp1Uvt27Y2Dc8mki5lchPuwvnzmbAPceuP+AMmO0MsPYTguQQcE+zSpYs6d+6cNd5/UFOzS8PEoq+0mWd+A87lqg4t6ad+pZIqX8nGqtN9hhauWq8NGzZo8+aNWj1/jMY2zKoCGfIoc8WBmnXsmi6FvPmlguvLMACmu6IB/WujDAH3HE2JSY5mx02bNWOGWW70y0+dPKmZzglix7CoPzPucDPoKUCXV/xkuOAJYsc0mjO1DJQm83ySBHGMJUkmhtQr5jfPEezD94cmvW/PXjPXb7rvJ6XLuvPwE55LwF9NIOB3dH73Ui0b2llDJi3T/G1ndeHqDV2/cVN3bh7RkXVOY5RIqpw5qqrU9+u171rkLBoWq+94VUA8gBzzvr17TSNPd1YcJBY0eI/vu1rfPspa0ez4zjWrVTWNTJaAjAHxhto1ahiVlEmzXb/tZAQYyFZTJk2yWfQMvjzq/Pyrly97Y6XDwa9QwMF93b16ThcO79Hx8zd1+cdhH878vbxSu6Y0VNXUSZWnbGu1mLDe+tLt2LlL23bt1Z7N67Vp7SqtWbdJm3ce1snzZ3T5/BGd3rdZ29av1trVa7Vh8y7tPnZJF28GesaiAxYcATrG75JahR1J7psMDTxw/HUCiP9440/KkiqJRvXsqFED+zi3b7AmTZikRc5c37BhrXZs2aitW7Zpx57DOnz6qq4Fcic9hIVfqYCz6Kifvue0o89jc+ZvwAFdWdNF0xtlUbpEeVW+VVf1nzJAHasWUY2a9VSjWUd1aFBDDaqUUoWK1VW90fcaOmm85k0bqAnfNVCL2pVUpUwZVa3WSM36LdDCXed13X24J+QhQo4lgkmP60EkHJfDl4qFJPXZRx+qVLbkmtWpvFpUKKj8uQuoWMmqatSqvTp1bqtOzeuqUd16atziO/UYMU9Ld5/Rqev3FORd4MfiVyvgDyM44KoC9o/R2i551DRLIiXJ2VKdx07XisV91CZfPKWPm0gp89ZSw17jNWXGQA3/topKp0ulnJlyKE+xWqrSpLeGTJmhSf1aqFPJTMqarZoaDv5Ba645u8BbgGGCjADm/MKFi7R18RjtG19LdXMlVILEOZW11lCNW7BOO3Zt09b1y7R85hANblNVdYoVUPHKbfXdlE3acilYgZ4qfyQ8AQ9F4NWDOjiuhnrmi6qcCVMpW+NpmrL5oI5vHqv+xWMrdZRYSpKvtXqsPqGTtw5r75x2apzqE8X6OJ6iZGiusn03asOZm7q4aZRm1Uml5FHTKHeTMZp4MlhOyXgIA5judOadNWu2tv8wWmfn11e9LDEUI35+5Wi/RptO+jIHQQq6sk97532vvjWyKFPClMpWrou6zj2s4zedJg99lYef4Am44bquHJmvCbXSqlC0T5QwRXHVnbhXm64G6+r+JZpeM7GyJcqsrFWGaf6ZG7rhltKpVcM0oEh0JY+fT0kqT1KnVTd1gv4I+6ZpbcdcShc7lXLUG65RB+6br+jh8SAtRp7/w3ffUZ3iqXVkmrN+csRV7ESFlLfzOm06/kDjCVyrO/t1ZGV3tc0VVyniZFO26iM07+g1XfYspV/AE3BwfaeOLmipupljKOZnSZW8SBeN3n5e591TVw8s08w6SZQ9aXZlrzFKiy/cEsvt7LoxGlE6plIlLaKUtWaq26YAnUHR7J+h9d/mUfo4noA/KaCqxvj6S/31T39UxTwJdHhq1ccLuCFQN44u15xG6ZU/blTFzVRD7Rae0p7Iawzrt/AEnMWye4oWtcuurLHj6POElVWw3RJtOnfTIrRXDyx3JndS5UDAa47Wkou3TcDPrR+v0WVjKk3yokpVZ7a6bw7UGaLxB5yAOz/eBLz+CI06GOwJeDggyBY9yud644+/V4Xc8Z9AwKWA8/u0u09hVU7xib5JmFtlhuzVmhOeI/4wfuUC7pzjeye0a2pbdcgWVQliZFfCMsPUcs45nb6BR3dPF3fN04SqCZQpfgZlrDRIM49f1dWgAJ1cMVQDikVT8oT5lLTyBHVcedX8wMBdE7S0VWaljpFYGasP0MDtd3TFf2bu+yVoCwb7LepXX6lJhczORK+uBtnDFvB7lw7oyLDSqpnuU0WJm0UFe2zR8sPeTvowft0CHnRTwcena0a7fMoR/WvFyNRUxfpt0tQTQU7rOofu5l4dmNNJTbJEUZyPvlLc7PXVctZu7T+wRptG1lGlZB8r6qdxFCV9I5XqsVzrTx7UngXfqWf+bxT3E/dc9oZqMGaPznkqPExQkkpL7tWr1+jg+qk6M48gW6wwBfzu+T3a0augKib/UF8nyKkSA3dr1XHPCX8Yv24Bv+fM8KOztGhAA9UqV001uy3QiM2XdNDJI/Ktm0d1etNUjevWSu0bN1OHnmM1Ye0xnTy6TQeXj9LgTs3VullrtewyRgNnbtX+C8d1eNtczenZQh2bN1arHuM17oejunbLE/CwQE0DNQtbt23XjeNrdX5BQ9XNEjMMAb+ta4cWakrtNMoV/UvFSldZLeYd187XY1ZBhOJXrsEDFXz5kI7tXK1VK9dp65ErOnszGMM9FMEKvh+koHv3jJxx7577N8SY4Pu/fDx06ACtpn/x+tBP8/Bo0HQxbYrkatq4iXb8MDpEg2f1afD12nzigRZRwYEKurZNe+a1U6NMMZU4WjplqthPkw9c0XnPBf8Fft0CThHMvbsKuH1DN27c1O3A+7rnSeNLBw0RE8aJrUrlK2jl9D5OwOupfrbYipWwoHI7Df6TgAdJNw5q3+xv1aNscqWOHkspCrdWiyn7dPhawAMbswcffuVBNg/+AHjpdAJq1ri25g9vrWXf5lWxRJ/o408TKkGBVvp28ATNmj1NM8YP1cheLdW6SiGVzJFN+cs2Vdsxq7T6ZIDuenzVR8ITcA+RDkYl9e/bWxPHD9AP47toUpNCqpA9lVImS6MMWYuofK36aty0rhpVLakyBfOqaLGKqt6yn4Ys3qu95+94BSdhwBNwD5EO2ibv3b1bhw/t07kTh3ThyF4d3LNTO3bs1K7de7T/0GEdOXJIhw/s0749u7V330EdPnFO568798rT3GHCE3APkQ7aK/Xs9r313d+2dZsXlIxAeALuIdJBa+7UyZKoWKH8NuGTfm0eIgaegHuIdDCgknloHdq11bp1ay3F6CFi4Am4h0gH/eaWLV2izZs22QBEr69axMETcA8eXmN4Au7Bw2sMT8A9eHiN4Qm4Bw+vMTwB9+DhNYYn4B48vMbwBNyDh9cYnoB78PAawxNwDx5eY3gC7sHDawxPwD14eI3hCbgHD68xPAH34OE1hifgHjy8tpD+Px06rypZzpyyAAAAAElFTkSuQmCC)
physics-General
physics-
The blocks A and B shown in the figure have masses
. The system is released from rest. The speed of B after A has travelled a distance 1 m along the incline is:
![](data:image/png;base64,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)
The blocks A and B shown in the figure have masses
. The system is released from rest. The speed of B after A has travelled a distance 1 m along the incline is:
![](data:image/png;base64,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)
physics-General
physics-
Two bodies of mass
are connected by a light inextensible string which passes through a smooth fixed pulley. The instantaneous power delivered by an external agent to pull
with constant velocity v is:
![](data:image/png;base64,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)
Two bodies of mass
are connected by a light inextensible string which passes through a smooth fixed pulley. The instantaneous power delivered by an external agent to pull
with constant velocity v is:
![](data:image/png;base64,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)
physics-General
physics-
A small block slides with velocity
on the horizontal frictionless surface as shown in the figure. The block leaves the surface at point C. The angle q in the figure is:
![](data:image/png;base64,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)
A small block slides with velocity
on the horizontal frictionless surface as shown in the figure. The block leaves the surface at point C. The angle q in the figure is:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOsAAACxCAYAAAAlH0pEAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAFxEAABcRAcom8z8AAD4cSURBVHhe7Z0FeFVn1rZn2vmn8818M+1HBSjSUgoUWmgpFC0uQYq7u7sUCQ4BgrtbcPfiFtwtOBQpXuhQJLRI6frfe50cCCFAdoTkhPe5rn1BcjTn7Gcve9ZafxELxZ9//vn4CI7n/d7C4lXDktXg/v37cuvWLblz+7bcvXtXHjx4EHSL6P8DAwPl5s1fZc2a1XLp0uWgWywsXi0sWQ1+/+03uXzxknTw9paxY8bIb4awAGt67drPcvr0jzJx4gT54IMPZMeOHXqbhcWrhiWrwW+GrBDyq6++klQpU8rJEyf0948e/Sk7tm+TKX4TpVTJEpImTRpjeQP1NguLVw1LVgPc4OvXrkmzpk3krb//XRYumK+/f2B+v3D+fGnVvKkh8WeSN29eva+FRXTAkjUIDx88lAnjxsrf3nxTevr4yG0Tw/56478yfepkSf15SkmQIIFs2rQp6N4WFq8elqxBID71X79Ovk77laT7+mvZvMlf9u3dI5NNrJogfjypVKly0D0tLKIHlqxBgKznzp6RLp07yVtvvSXdu3aWmdOnyagRwyRu3A+kY8eOQfd04dGjR0H/s7B4NbBkDQbKNju2b5ckH38syZImlY7t2mgcGz9+fNm3b688+vOR7N27V6ZPny4rVqyQM2fOBD3SwiLqYckaAiSaWrVoLn/5y1+kkFc+KZA/v+TOnVst6UZ/f3n77bflvffek0SJEkmcOHGkdu3aWqO1sIhqWLKGwC/Xf9FSTYoUySRhgg8lUcIE0qOHj942Z/Zs+ec//ymrVq2SgIAAWb16tSRMmNDc3kNvt7CISliyhsCdO3dk966d0qplS/nrX/8qb7zxhixdulRv27Vzh7z9n//IxIkT9WfQpUsXyW+sr4VFVMOSNQQePnwov964IZs2bpSUKVNK+vTp5fTp0+oGX750Scs6WFc/Pz+5efOmNGvWTLJmzRr0aAuLqIMlawg8+vNPuXfvnkoOIem1n3/W3/O7e0GCiBEjRmjdNUuWLJI4cWKpUqWK/t7CIiphyRpGYHGDd94cPnxYM8Lr16+XCxcuBP3WwiLqYMkaRkBUrOsff/wR9BsLi1eLaCErJz4nPdbqVR283p9/RkzIQLvc7du31TX+9dcbEhh4V5sA7gYGyo0b/5X//vKL1Q5bRBmihayBdwPlzJnTcvToETl+/GiUH8eOHZFz584qqSCTEszEpOE5yBZv27JZ+vfxlcYN6kmNqpWlbauWMnhgf1m5Yrl5raPyyy/XldS///570EXCNq5bRBzRQtbjx49Jl47eUqViOalepaJUq1xBqlbiKB9Jh+v5eN7qlSvq73r26CrHjh6Vc2fOGLJtkU3+/rLRf4OjY9NGf9myeZOMGDZEShQpLJ+nSCofxf9Avvo8peTNmV3KlSohTRrWF9+ePWTu7Fmyd88eJS4W2RLWIqKIFrJu37rVnNzZJPGHH0ja1J9L5m/SSfYsGc2RSXJkDX5klpwc3wY/sjz5v7kth/k3+GOyc5jnypY5o2TJkE7SpflCEsePK0UKealF3Lhhg/j69JDO3u2lk8Ojc4f20qWDt1QuX1ZSp0wuSRLGl48+jGue/wNJFPd9SRTvffks6cf62vVq11Rd8a6dO1UVZbXEFhFF9JB121bJnzuHIenX0qxxQ+nn21vGjB4p48eO0Ta1SRPGid+E8eI3caJMmTRJpvqZY7I5pviZY7LrX/PzFPP7yZMmmvtNkEkTx8uk8eP08ePM84weNUIG9OsrrVo0kwxffynFCheUbVu36GNyZs0iX6ZKYY7PwnWk/DSJfJwgnhLVfShhDVn599OPE8k3aVNLpfJlZNTwYbJ/396nRsVYWIQH0UZWrzy5pEDe3CbWGyDLli41v9umVmjP7t2yb+9e2b9/nxw8cEAOBRyUwxyHA+TI4cNBxyE5fCjA3BYgAeY+Bw7slwPm/vuM27l71y7ZuWOHIeZWjSFHDh8ueXJ8K0ULFdDXXbNypbRp1UIa1q3t/KjnOiqWLS25jIX/PHlSJWjCuO/JJ4kTqDucL1d2qWrce16jT6+e5vWHyqIF83XixJ7du5S4uOMXzp+XWzdvavLLwiIsiDY32CtPTilauIBaxa0mhjx+7JicOnlSfvzxRzl79oyc++mcntCXLl6US5cuyeXLl+XKlStPDvMziqKLFy7I+fM/yU/nzmkXzI+nTsmJEyc0ecW8pBlTp4mXuSgUKZBfCfPz1avmNU6Z1zrh+Pjx1Ak5feqkLFm8UFo1byK5smWRZMaKpjCuLy53hTKlpHdPH1m5fJmc/+knfS/Tp06Rgf37GuL6KHmHmIsTf/OyH5bqxeXnq1fkjz+eruFaWISGaCVrse8KGXfWTy0hJzZkO2dId+GCIemli4aUl+Xnn69qqeSX69e1NPLf/7pKJNfNz8SCkI/7cX/ITdYX5dFJQ669e3bL7JkzpWC+3PJdEFnJ6JINJlPr9KDOSjYZC9mvT2+pVa2KVCxXRjp6t1P3e/WKFRJw8IBcNRcTYlQI3qNrZ6lfp5a6+z17dJPhQwbLMHP0Mv/v0LaNzJ0109zvpL4vC4sXIVrJWvy7ghp77txpyGqsHRb1J2ORLl68YCzpJSUihFSiGpKi2f3111/lhvlXSRtE2KvGOnF/HveTsciQ/pSxgHv37gkia57HZIVwEbViZ8zFYOH8eTJq5HCZaOJk3Pdr164/k0TCNa9fu6aULVFMWjRtYu47Vi3q3NmzpWf3rlK5Qlnp1qmjLDe/c8saLSyeh+gla5FCMm3KZI0zqbtCNNxaXFw3UbGikJSeUWqX7gMRPb/n9mtK2KtKWJd1PafuNLHv7FmzIp2sjC6FXHpRuXRZ5w2HFnu6yVqzaiUZ2K+v7Ny+XS8yvN/d5gKFNe7Vo7sMHzpYL1QWFi9CtJN1+pQpmlQ6a6whRCMOxY10u75YURIxgXfuqGIId5Gh27fNz/ye2+lBhQDEspCd+PW0Iev+fftkzuzIJ2tYAVkbGBeYeq+viVk3bliv7++iicO3bt4sY0aNlEED+mmGm99bWLwI0UrWEpB1ahBZz551WVVD1sdW1VghLCiqoSdx5j39V9VEQRaW+xHDYl2JXUnu4KpClrlzZkuh/NFF1v0ar5YuXkTFEpRxFi9cIIsXLVCS1q9TU60q/bNceCwsXoToJ+u0KZoIIjFE94paVkM6rKq6v4aQDNa+d+93rVXibpLkgbCBgca66sjQG8HI6nKFcSsp/cybC1nzRitZvyuQT8s9bVu3lL6+vTUr3Kh+HSlsft/bp5u+r5smFreweBFiHllN3Hk1yAUmmXT79h21opD14cMHqrWFtJDu7t075vZQyGqe55yx1DGDrDWlSEEvqVKhnHRo19ZY1P4yoF8frcOihGrfprXMmjlDL1IWFi9CjHCDlayGXE/IGsyyGstJjIolxaJC1Pv3cYV/U/eY24lbn7GsJgZGLBG9ZA2KWStVkN49e8j6dWv1ooTVR+yxauVyJW392rW05GNh8SKEiawPjTWDMGQ/ESlEtA0s1Jg1KMEE2SjFuGLWX9Q9vHPHtd3NHbfyLy4wWWGsrzvDyuN4f8Ss1Fo1ZiXBFG0xqyFr3VqaER4/drT5G08H3eJqE0TM0bpFU02A8d4sLF6El5PVnNeQ4uSJ47Jg3lxNkGDFIgI3WV2lmymu0o0h1wVDsksXyQZflmvGul7/BcLe0CQS7wFLykXDbVE1uRRkVa9dCxJHUGsNVrqZEwWlm7DCbVlrV6+qiaRDBw/KffP6HHgDyCVbNG0sxb8rpLVaC4sX4aVk5cRmq9qsGTPEu8330rNbV9W3Qp7wnvRPk3WynqhscYNkT5JMVwwBTeyqqiWXGMJda71508Sp5mct21BnNTGuWtUgF5g66ylDVgZyz54V+aKIsILSUZ0a1TQbXSlI6TR0yCA9+vXxlW6dO0mj+nXFu+33cvzY0aBHWViEjpeSlYTOurVrpF3rVtp72rJZE5k3Z7ZK5LgtPHhMVrfcMISCCcK63WEIi+XE1YWcrsMlOXxMVJUbBiWWDFFRMJ00728PcsNZMwxZn8gNXyVZjx09Ih3at9HSDXFzse8KSukSxfQoZX5XvkxJVTAtXbxIy1UWFi/CS8lKjIgkEJF6pw7tVdfap3dP7WgJb+zqJisnLy1rO3ZsV3kgKiYSMOeNdUQ4gHifpNHPhpDEpJDWffCzi6gui8r9eRz1WlzgE8ZtJxYm0xpdZMX6I9bnYrfKfF4rV6yQ1atW6rF29Srx91+v3UNclHhfFhYvwgvJSiKHk5/JCIjWZ06fKosXLdRxJvSL4paGBzsNOWmRK1aooPhNmijbtm2V44Zcp4x1VdkhhHVrhA0R3R03LuJe1X/dnTcklLCoEJWMMoklrP6xY8fUvWa5FK14RQp4mZ93yINX3JLGheGPPx5pku7hwydzp2wzuoVTvJCsJGzoNR02eJAMHtBPDh7YL5s3bdLxJUxNICEUln5MTtjgB03gWNYiBfPL2NGjZP36dVqTpJxBryru44njx9WVpRsHS0lMC5HJGvMvckJug5i0xB0396dPlMfzPMSLjG6hHS1/bvNaxrLSz4qnAFFCvqfoOoIjxI8WFk/hhWQ9euSItnIhQsftxYrt2rFDalWvqtvA161e/dJYC2sHYRgoNmzIIM2KUltM92VqneBADZKMaId2baRj+7bSybuda3xKR2/p2qmDdO3c0RydNBnTvYvr6MahvzeHuU8Xjo4d9HE8nufxbttG3yMDzdJ9+YVkNK+lg80G9Jeh5uLDe3lVBxMwZs2Yptn0JcYzCXksW7pEXeUd27bpBRHXmM+exB4SzFu3b8kfxipbvN54DlnNVd9Yny2bNkr1yhXEp2sXdSmpEyJGb9OyuWYxB/TtIwEHDwY9JnRsMFbz20wZJBHTFBJ9qId7dhEH41H4OaqO4ONX+Nn9Hl7JEfR633yVWr0IVExkh0MeDerW1gtJz+7dZMiggSbsGCqjR47QixxTJggb8CKI0UmwPdFLo+y6Z93q1wShkhWVECfG/LlzpXzpEtKoXl0ZY2JU5h0NGzJQWhpLWLFsKZ1OSKLkRVhrrC9WNM6//iFx47ytRzxzfPje/0l8c8R79x3XEXRbZB08X7w4rufmdfS1QtzH0fF/rn95vg/fjyMJPnhX/+Xn4LcHPz545z8S19yeJmVylRxCzBZNGj11NDcHIv86NatreYcMOTF2vlw5zL+5dBxN+dIlpXaNqtKyeRMlNERG7LF+3Rqt5VKuun0n/KU0C89AqGS9cydQZyKNHD5MLSiu5YRxY3SQGS7diKFDpG6t6jqhkNILiabnxa6s+ke0XrLod1K2ZHGPPYjT+RsgUbo0n8uniRMai5lGCuTLLSWLFdHbn31cCSVaw7p1dJM685gmG2sZ/GAw3NhRI6Vv717S7vtWGmKUKVlMs9fUZ70MYfOb13SRN7eUKVFMk30QHbd/YD9ftcA/LFksW7dsNi70IU3O3fj1RoSVZhYxC6GSFanf2NEjNRYcN2aUcYc3aYmE31P3JENLL2bBfHmlt08PnY+LoD40oDgiIXTi+DFVQXnqQWmJbPIEc7FiIFrqz5JL3Zo1TCw6XbXNjHAJ7XH83STDyFaTwdaSU/DDeDDE/ZSfVHllXgfRCXOKKfH8YOLZRQsXqlfDLCeEFY3NBbSC8WwK5csjORjhasKMfDmzSylzMWnWuJFaXn8TfvB89AE/+uNJQs3Cc/EMWflCSWxQnqlTo7qsMScMRA2J1StX6snarFFDtbavQ9cIDQaEA2WKF5UvPksmNY2FQyCCQCM03DYexy4Tb+KlMBOKODMsQGxyJ/COq5vIEJrPn4w4F4V1a1bLvLlz9DNnKwBeT9PGDdUi04ZXvkwpqVa5oibtSA5SduOCQq6BiwblOAvPxFNkhai4TsRBVSqWN3FSNdWzMsYk5FWZrCWZzmbGHSMzi2ootgMtL1pf3ODkSRJLnuzfatYaCxoaKD8xnZ95S/MNwRB8hAV81iSM3AfkdbcG0nFEUgnSQX4uFFxc/f391fp29G6r6igGpGdKl1ZnM+NSozybZkIW/oafDfndCaoHD+4/LmVZxGw8Q1ZOCEo0iB9WLF+mMj8ywyGB1C8g4KCxvKs048uiptgKiIImedXKFVLIK+/jTHPKTz+RiuVKa7Y2tBOexA9CEjqLNm/0V6VSVIDaMd8TNWis74rlP2gcS1seCSz6ZmmAJ3lVs2pl6dqpo0wysTJeE6tMwmrxLaIXz7jBnJhcuTk5aUsLjaiAkxNi32EekrlvWMQRngo+DwQXrMPAWpFZphRERjh39qwmppyvZHlkPrvgoMUPAQiJH0hx8+armwbxq3ktZifTM4sr3KheHZ0mSVIQrTJN8dSjSW5R46WuS+yMteW7tYh5CDVm5YC0L/vS3PfjCGlVYhOwPLQGNm5QV778PIWSFLIyiT9T+rTSv6+vZr1D6nvxNvbs2qWJKZRWz0vCRQX4TnCV0Scjy+T10UYvnD9XBvXvJ00a1BOv3Dkla4b0Uih/Pl0zgjQTl/qesdQWMQ/PkNXiWWBxmJuEFSVWReDhtqypP0umyR2mKDJxMTguqhs8Td1gNtBFd2cNnhDExW2fMW2KNmYwuxg5ZmGvfJow69O7l2agSUaxItMi5sCS9SXAu6AxngQNGWDWZXysyqi4kjRxAkn7RUpN4NCNRPY2OHCdiQ/ZWEdGlhJWdMLtCZFEZPrGpcuXtPOnb++e2lXFNr9M6b7S0tS0KX5y5FCAlt6YfWVd4+iHJetL8MCc2BcvnNfBbpRD2Eb3dWpXNrhsqeKqWaaEsnzZD88kakjCMR8Y2eZxQ1xkgjEJEJD9sTQ9LDZx96D+fTXbjcADNRXD3Cb7TRTWhXC/RxHcHG8RMViyvgRYISwmVpFsMKWawl55Ve+La0yZizIWDQshFUPEsLi+tPTd/PXmM7fHFGBxea9kr39YskgvQKWKFdF+Y2SOzDhm2RalKGJgrHNkgOchiYkwBAEHPch4IwhJaM1ENBJTP7PogCXrS4D1eaj1zftyxsRxkydN0kXJuL7Eo4gXmGtM+SRkkg3ZH4371D/9N6wPVVwSk0AN95fr1zRzzftFCdW0UQMpUbSwlCxSWDuj6BC6QeY7gglFPis8DeSRM6ZNlV49uqr2GR1604b1tYuKz5cyIt+BrQJbsjoCV/oF8+dJq+bNpEzJ4rJk8aKgW0IHVoKWPqwx42Wog3oKuPjQG0xyrFnjBlKkUAEpbkKA1uZvJ/5miwCqNZJW4QEXOHqj6TCiOQFhjU+3LtKjS2f9vNBJ9/LpIYsWLtAMNRfM1x2WrA7AeJn58+ZKy2ZNdY4SwpEXAb0w8Sy7WRcumKeLtzwFWD6ISAhAyQdSVSpX2rWYuqCX1miZHcU0jz8eOtsvy/NevHheevt017Wf6MuZqUymmjUiXATISPf17SXft2wuc2bNlN8C7UpMS1YHcEpWZh7v37tHVUWUQhCPeCJumL+DjfNLFi3Q7qC6tWqoZ1G9ckXp37ePbFi3ztH6DzyUDRvW6RACenzp2UXd5SY8/xA/87xMElmzepWKNV53WLI6gFOyEueibELJRL+pp6u8IBPdR1Mm+ylRKfVQo23f5nvtzMIi/nb35QooBBp+E8erq4v7+7wxrLResqmAyZc20WTJ6ghOyUp9FveROcGUdmLDWkcsHO48EsWB/ftp00Be4xpXKl9GhgwcqAPbb916cYkKKz1qxHANDyAtibjQwMUNb4Rar63zWrI6glOykhhhL2vPHt3N4+bo1MbYAkhEfXZAv77aKJAzayYpX7qU/r0bTPyJlX2eJ8EoIB3CN7C/JuyIVS1eDktWB3BKVoQEGzf6axmEIWjUKGMLqJFi8RgTyzC91i2a6eaDnN9mlmaNG8q8ObM0Ng0t8cRnweA8tunNnjlDk1ShgSYSklG8lpMEVmyFJasDOCUrmVRKHCrkN7HeqxTyv0og/Fi7Zo26tVUquNrxUEItMlaTDQshQZac2jOjbliB+TwZ5uVLF3Ui5KaNG+XuXds0b8nqAE7JyknMJH76ghnVQqIpNgKrd//Bfa0rQ0LWgtCKh4VdOG/eM0okxtswsobkUpvWLXQjA0omrCiuM2oqVqSsXbNKFVTMrGaq4+sOS1YHcEpWrCl6W2qtzAd+XiIltoDkEzOkUCTR+ECjft2a1ZXAZHTdYIsenwVD+Ljf0EEDtRGeSRpIDylz4R5Ty61VvYpMHD9W7nho2SsyYcnqAE7JypIsJjJMGDdW1q9dI1cux/45VVhGdL6LFszTOV7lSpeUurVrGMJOUEWUe+UK42RozHcrmIYOHqiKMCzuQuM+M6sapRizqWkvDNkr/DrCktUBnJJVFUC/3tDY1dVqFnunabiBS8zfzeb6/Xv3arMDtVi01GiLWW3C7Y8euZrjWYsyd/ZMnVXVtnUradGssaqWEF8wG5kJFmiIbenGktURnJIVQcSObVt1ax6dJC+rP8Y2EIfSHojel40E+fPkEJ9uXTU7Tj8tIJZltxEqJRr4p02dYlzgmXofSl9oiG0i2AVLVgdwStZjx45I984dpUuH9jJr5nRdP/I6ASvLONZ9e3ZL/Tq15LNPk0i61J8by9lCDhuXGLUT99HOJuN1YHHdBz8z08qWbJ7AktUBnJIVa4pY3ad7F5k3d7b2vL5uIGGE1UThlCje+5IkQXzjFudQt5fh8Na9DTssWR3AKVkvXbqo84KJvdhByzaD1wWQMNC4sKzZJG5lxlOKTz7SCRtpUqWQQubncWNGy/nzP1ndbxhhyeoATslKBpNuEprOUS+9TiclCbWjRw5rNjdvzuySN0c23cn7bcb08nXqlLqsrFaNajJ1ip8uw7Z4OSxZHcApWZm6wM4ZejWZhB9yoFpsBDEmFynKNMOHDFYlU+kSRXW6Bgu6qL0WzJ9HKpYrI6WLF9XNepRqaImLrHExsRWWrA7glKycsN5tWmvfJtv2Tp96IgyIjSAVdO/+PW1YYBNByaKFdZn1yGFDtdZMkzkb9xrWq6vdNvUNgbNnyahbAxiUjvdhE0rPhyWrAziOWS9e1MQSJQkEACRbYjOYy0QHDZv2yP5WKldW1UkH9u+XlcuXa+20lLGmnTp465C5ObNm6bwlyjrNmzbWecYxbQJkTIIlqwM4JStlC3o3dWfq+Z80joutIKF09cplVSCxGJq9Or19fHSL3t3AuzqS1benj1pWLCw1aNroSL7hDhctXECJTeMDYgmbJX4WlqwO4JSsrGskXqVRG+VObI5ZIRgrRtipwwJp73ZtZM/u3Sp+YPja5k0bH5OV/l5cXmqprLJkyXSNKpWkYL7cOnCckldsvrCFF5asDuCUrDqK1G+Sbjhn015MH0UaXrB2Ev1ux/btpLixkN5tv5dlPyx9rAMm4cTtj8navfvjmU2QfM+eXbpL9pu0aXTHLNsAzp/znOFyrwqWrA7glKx0j7gmIgzQaX1kPGMTSAZhHXdu3y5tWjaXsiWL64Lt1atWqLQS/S94EVlxd9lksNyQm880X67s6kZzf57bJpyewJLVAZySFVcPlQ7uoCdPN3weWFzFmNJ+fXx1rUiThvVNDDpbLlx4+qL0IrK6wUxllj2zbT9frhw6HobnDgy0u2PdsGR1AKdk5SS9fPmSHjRT08cZKxBUSyW2JMZknCiLrSaOH6cZbyxicISFrOwUolmffbEkp3CH+/XprSTG+loLa8nqCE7Jeub0jyoMGDJogK6dCGlxPBUM9UadRFN4iSKFpIIh1vSpk+X4sWMqwg+JsJAV0ONKSYfJhzwviaq1a1brhc5mhy1ZHcEpWU+ePKHWgZMUlU5smG4I8Uic0VRfv24tY1FLanKIuUr37oW+hDmsZAVMhGAxNS41i7EYIk799XnP/TrBkjUYcLW4guvxJ4drC7wbTslKlhQxxJbNm+TYsZi38tEp+CyYfczajJpVK2tsOWLoEDm4f7/8pn2nobuqTsjKczBvadqUydKofl0db8o0CSZFPu/5XxdYshoQYyFgoMeSuignFt0iDKy+eMG1xQw4JSv1RTpvOBABcNJ6KnB9r1+/Zv7mBcbq1ZMqFcuLd9vWsmPbNrWGL3JTnZAV4ErrIPDhw6Rg3txSp2Y1DSNe9/nClqwGkIqyCldzRoswUnO0iZvQ87J/1S0wd0pWJiXQw3ruzBm59vM1fR1PBBaNyYybN/lLR++2kjtbFmn3fWud5hAWoYdTsvJ6JOM2+ftr3FogTy4d9YKwgrj2dbWwlqwGkAolDbEXJYgeXTvr5rL1a9casrmykcApWZluyBjN/n2Dpht6YJ0VYlA+oYzSukVTqVC2lLRo2kh+WLJYXdOQmd/Q4JSsbpAJJtlUuUJZba+jZs30xHu/v57D0yxZDZjzQzKIgV75zUmBVd23Z4/WRm/e/FVM5Kr3c0pWNnljpbkIMKyaqX+eBi5k6HWHDBqoF7I61avK3DmzHY1VDS9ZEUvs27fXXDy7SC5jzWmzo5sHTfHrCEtWA3SokLVHt866t2Xjhg3qsuKKBe+xdEpWEkoHDxzQcgQWmpPPkwDJWK7Vq0d3KVW0iNQyRKVcA1lCK9E8D+ElKx4NwosVy3+QhnVrq3VFQ7zdxMm/G+v6urnDlqwGbrIyv5Ys597du4NueRpOycoYUtRLWCaGXHvS+gy8iUOHDsmYkSOkasXyUq5USRk/doz26DptEg8vWd3AHWYDe8mi30nOb7PI2NEjNbvu5IIRG2DJahCcrFy5d+/cGXTL03BK1osXL2rsy3T5rVs2m8dfDbolZoMkDvOiaEAoY/5Oyic9jSt/0rj1uiQq6H5hRUTJyjgcdrq2btFcsmXOKA2MlZ0/d7bHeSoRhSWrQVSRlYVLo0YO1zrhyuXLnrstLabhwvmfdIJ+vVo1pFC+vDKgb1+N4QPDSY6IkhWgs0bOWMmEKXlzZZcunTrIlSuXI+wKE+54ijttyWrwhKxdI5WsTIrAAsyZPdMjJkWQ2b1+7boufiY+xaq2bNpEtmzcKA+NyxnekzoyyMpzkJHu5dNDMqZPq6TdtnWr/Hrj2VEwxLq/m/uz9JnwgzY8wP0g562bN9XL8fX1lTRp0kjXrl09grCWrAaPyWpcvRpVKmuMGRqckhX3DRXTL+ag4yamx1gkxFAnsWuV7Gvb1i1k544dKuiIyMkcGWSFgNR02crnlSe3Tkxk8zp18JDvDVf9yJEjUrhQQWndsrmKUty/p+a9YtlS/a7ffPNNqVWrlmzZskVvj+mwZDW4f/+eEpGlwAgjnldicUpWFD8IBzasW+daphxDJ0VwskNIRq8w3K1sqeLSpEF9WTB/rjaQv0idFBZEBlld+FNXbTRp2EAK5M0llSuU083pPH9InDhxQhImTCjvvfeuIecyrc1ysVy6ZLF89eWX8sH770mKFCn0Qu0psGQ14GTlhMQS4iY9L9vplKzMXmr3fStDgOYy1c9PTgdbexhTwN+Om4ibTk24sFd+lRKuWrlCY0Knmd/QEHlkFZ3DTOKrepWKkiFdWunn21tLSfdDeC23bt/SJor/+Z//kZIlSsgF4xLz3Q4aMED+9re/yV/+8hfp06dP0L09A5asDuCUrCSUGAj2JBsc82LWO7fvSMDBA+JrYsFSxYq6xoROGK9qq4cPI8dtJxbm73dPN+zl4yO3b4WvER+RBhdBmtPTpflCJ1OsMDF2yHwA9dnV5oLzXeFC8u67cWTRwgWq/65Vo4YSNWXKlNpn7EmwZHUAp2TlhGGlIUkOLII70RETgEXFkzh6+LDWLatWLKcKpQnjxmmZJKLbAyAoLiYWFLXTvNmzNRYukC+3tG/zvbbUIVcknr93L+yvpckjYyEXLpgvBfPl0amIPbp00iaM4MCa87cNGzLIWNd/SNYsWXR0TJIkSeT/GctKUskNLkwR/XtfBSxZHcApWTmpqLViYRHChxZbRRc4OSERJZpSRQur8IGFxmwOIL4LmbRxCgQgdM7QxTRl0kSdI5w1Y3pJlTypZpkZ+k0NesXyZeEaJLdnz24dzFa4QD4pWfw7WbNqlX6+7veN+05Sb/26NSa+zS1/e/NNSZw4sfz1r3+VLFkyazKN76ZsuXLy+eefS6ZMmZTAK1eujLGtjJasDuCUrFfMSbh0ySIV8ZNhZsFwTAAnMlMrUAU1bdRAihuLin55z+5dkTYnirrorp07ZOTwYVoOy5whnXyS6EP56MO4kuHrL/XiQEMAlo+JGk5BhneRsa7E11kzfSOjR40wXsypxxdEN2nJFtepUVVyZssi//jHW+oC+xg3/CdzoUplSJozZ05ZsGCB9O3bV/+fOnXqGJsdtmR1AKdkJQPc7vuW8r1x/6b4TYoR6zMgKhcNxqVAGDaSd+7QXjb6u/TQEbWobkB6iNK1UwdJkzK5JEkYTz5OEE/J+nHC+GphmcSvyijjEjsFpCRr38m89yzGYrcynzH1Yff4UzfQNrPMuVyp4vL2f/6tZF26dKmsWLFCkiZNqhdUN/A2+I7D0kkUHbBkdQCnZCVORYROrMSUQ2qu0Q1IRLyH2IE5Ry2aNtaZxpEt2KBMwnOOGDpU5wEnMVY1cfwPlKwJ474nSRMnkBpVK6krHN6mcmJieo7Z/VqxXGkZNKCfXLt2LehWF/jMWd2BhS9TqpS88cZfpXnz5rJmzRr55ptvniF3TIYlqwM4jll/+824axdUyfTfX6J3UgQWk3Y/tpDTl5onx7fSsF4dmWvIElUnLK+JyIL1GF+mTKHLlCFrYvPvFyk+1b5hGgPCW+tkMzpZ5u7meQp75ZVmjRs8s7CazilG0fA6R4ynM3HiBFm2bJnGpvHixZP169fLWfOYU8br4ThtLHFMFa9YsjqA45jVWIwfFi+WxQsXmvhtp1yPxpj1jz8eypZNG3XCQ4kihXV86JLFC817pN0tatw+yEocjIwzd/Zv1aJiXZN9nEhyZM2km+S4UPwRTtEFmWFq11jXQvnzaJM6rjeNCObVH9+HhBlrPIJ3Pe0xns6HH34oqVKllMyZM0v69OklXbp0am23bdsWdK+YBUtWB3BKVq7y48eMkTGjRurCJrfs7VUDAX7Awf0yoK+vOanzSs2qVXQCA9rZqAZeBVMlypUq8Zis6b78QmpWq6KfSURiZLe3QLyty60Keen3Q/LsZaorHou6rFu3rrJhwwYJCAiQ/fv3y4EDB2KsqsmS1QGcktW168bPWBDXrhsUQa8SnJAklI4dParDuCuULilFCuTXsgnbxkkoRTVwKRmZ07RhA/kkIdngeLqAio1xlIkiRFZzQMpTJ06oS8+sJvbtQN6wJIn4bBiKt2njxpeSOybAktUBnJIVQQAxIq6gq/n81a7PgChHjx6R8WNHS5kSRTURw0wo9qVyokaEKE7AkO4B/fpq43iKpB+rphe9NFnpyHgHV69elYH9++pwNfbtTJ3ipxP+XwYITV6BrPLZM6e13BSTYcnqAE7JyqAxlDonzZUf/epvd+8G3fI0IA3EQuHEfbB4/PxnBK72tLRR9J80YZwuesL97da5oyHv0WfcvEePnsxLjgoC8zch92NwN5vO6YSBII/+iBxrRtxLN06bVi3NBSGT9PXtpcKGsPwt7ntAXC5gMRmWrA7glKy4Z/379JY+vXrKovnzjVsceozIiULGkrrs/n375MTx4/pa9yLgpiKhYwtA9coVpYiJ5RDRM8qT6QohT2Lqi1wgeL2ocAe58KBmYpVj4wb1dKVIZHYg8fx8fpMmjJdc2bJK29Yt5fixo8+9OHoqLFkdwClZGYNCrIhIfuE81mc8TVYoQzmHE/eUue+hgwe1f5Tly/4bNmjyxCkgPu4lrWCMQWFuUeP6dWXjhvVyI6gvFXJSf+T90WjPbbilqKxwWSMbXAD4G2kYQDW1ZvWqSI+X+bvXrVmtiSYm+ZPUItMdm2DJ6gBOycqk+mNHjshRc5ChZORpcHAS/9cQiz7aevXqSvbs2bWE8NlnKSR58mQycOAAx24pqye2bN6sQ7GzZ8mk4vnly5bqFna3q8t8JVriaCEjMYMckEFx3bt00oVTUQFeF/ebJcmohqLC5dy3d6+0bt5UJ/j79vLR2mpsgiWrAzglK9bjkolVdX0GKx/vPyuKQDTwYfz4kipVKqlWrZq09/ZWfeo7b78jf//7/5N+/fqFibBKhjuBSsKO3u10BWO1ShVlzqwZ6iK6291YcKzllKWLpYYhaNmSJVScwKqKxQvn6/sNLyAj1pu/m8QNFwgsdXB3/pbxFvgcsf6hWVda4Hgcz4Wg4a55Hv7P77GeLwL5gcED+kutalV0LM02D5kAEVZYsjqAU7K6ssF7ZO+e3doqFzIbjHUpXLiQJDBkZb6QG2wCYHtagfz5JVmyZGFSGHFCBxwM0JIIAgTmH9OkjTY2ONl5Taw8UyBKGBeZ5BOby5kUATkgfXjAazAylB1BbCJArMBCLn4mfmTmEa437j5b4TZv9NfPxN0pAxFJClFmQpWER0KGlskQjB09d+bsS7Ppl81Fcf7cObqQOX/unMYVXqJ/j0PnJMbCktUBnJKVBFM/316a3HGtfHw6ZoUgyT5NJjmN++ueIsHJxbKnkcOG6sjNuHHjyr59+/S20MB5SIKF1+rVvbuUK11SSxjDhw5W0oTsoYWs58//JEuMRWd6IVI9WvicutshwfMSJ+N+416zXa57l86a7Gn7fStNKpEA4vNoZVxV/jYGhkNE3iPZcj6jgf36SueO3voc/B+rP3TQAPVAnpegc4Pmci6OuP6Z0qVVPTAXpnuheDSeCEtWB3BM1pMnZYCxkH19exoXc4GKJIIDdy/Zp59KhvTpZO/uXbqpjQkKdMQwYqWuIdN7774rq1atCnrEsyBZRPZ4+pQpmlyhiwal0p5d5vlCiQvdZKW5oE3LFoZEg8KVyAoJLOPY0aN0NhJEpJuG0a5cEArmz2Pc0iq6noTyUfMmjYzlL6cdM5R0cMtZk9HFkBSyQ9D+fXylq7kv8XTThvW1Qf74sSNBrxY6uGgRD/OZkxVu36a1JrPCO0ImpsGS1QGckpU465yxphwkdULGaHTlpEiRXOLH/UCqV6sqbdq2kZYtWkj5cuUkX+5cUqRQAXn//fdkiXHnQgPkxr0cO2aUlC9TUpcPQwDGnvDaoVnL4GSFGPSTsjkgonCTlckNvj176AoSWgJnTpumyasmDerJCGNdDxzYr8olPkc8DlZz4CqvWrFC7zNuzGi9qP189aq6yxCXJnOEHbjTLwNuNX2udWpUk6qVKmjNNbpknpENS1YHcByzmhgMYTm10zMmniM7HBzEohkzZpB/vPWWJEnysSRPnlyPRIkSSuJEiaRQAS/597//LV988YU0a9bsmdgVt3rO7FlS18SdSO2wRExGIH59HtxkZd8p3TdMh4gMsj4wZEUDXbpYEfGbNEFXaEJg9L+UjiAd5RQ+E94fqi6GndGiB7mYVdWsUQNZMG9e0DMybPy8cWWHik/3ri6X2cSvLwMXKOJ/mgeKf1dI6teuJWd+dN7cHhNhyeoATsl69uwZGW+s3uiRI3R4V2hXeC+v/JIoYQJZtXK5/GysL3HsSmNliNe88ueXf//vv6V/v37aMI2bB8joQlwSKGQ+C3vl08Fhmzdt0vjvRUkiyEocR48nFou4LjLcYDdZkfvh2tI88NC8Fg3hTRu53FguXBCVRNH+vXtVLNKgTi2Z7DdJpk2drJMgIbRbucVFBZJiHcNKVjbWkxWm2Z/PpWTRInLEeBqxAZasDuCUrFg+kirjx41RoUNo0/TatvlepxcMGTzosWgBpVGFcmXlX//6l/Tx9Q265xNQSyWZ06p5E8mbI5smbCAFruPLAJH5O8gAQy4a0SNjZ8xjspYqbtz2heaicVcvDC6yNlDZIyomas1KVhOjEpdDVoiKWILEEIkkN7i4TTCfHTVTJ5aVBvS1a1Zpcz1ZYcagvuwi5gmwZHUAp2RFYM6A6WU6KWK3TvMLDk5mTqRv0qeTd+PEMXHZWLl04YJsWLdWPkqcWAoVKqi1WfdJxomIRd1hYrnvW7Ywbl5BqVi2lMyeOV2tI8/3MvAcZE0ps1A+wdpFRlO8m6xlShbTPllI+ZisDevLxMdkvRuMrD3URdY5VYakkBWLiPt79cplneFE/MvYGUgblpiV/Pjv936XgIADUqlcGcn5bWYt50D8l9VpYzosWR3AKVlxBckIM2MIqxqyjAIJqT36r18nmTJmlDfeeEOnxTdp3FjiGPIiiAAQDJD5pQZJlpVdpdUqVdBdOtQjORGD7vZSQCKSXbduueLHyLA4kBV3X8lqPpfHZP3hBxXwYxlDkrW3T3dp0aSRxq/79u7RbDDEpMyD29zbp4dmjckuu7LBYSErdP1Ty1FMVMyZNZMuBkPq6A4jPBWWrA7g2LJeuaKJHFw7Tshfrj87g4kTCPd36+ZN4jdxohQoUEB3sDBpj64ZN+jgIfZCa1y2VAmpaKzGkEEDdFMdJI5ukJmeZywYddVNOnzNuJ2GrFtMHN3HvGdKV9SS+T0XCIjHVriB/froxQzl1JJFi4x1HiGD+vc1BBuifyuEw90fZ2J/arJhBZ9px/ZtddyLJt7Wro1QY0RMgCWrAzglK9pUkjicwOzQOR1KVhKriQVyX/WJt6ir4qq6QUIJze64UaOkTPGiUjBvbhk9YrgcDjiosj635Y1OYJ2xjgvM50ODAKNVSBQhzKB9DXf7+rWf9e9EKXX18hXdrUPijbGgZIlZNbl9+zb9XHkM7itT/IltGd1Cq2FYQVhAWYpRpXT6ILv09C4cS1YHcG5Zr+peVo6AAweeImBYcc/EXyh3cCPLly6hml8sBR0ygcadjAlEBbwP9L6MsmGlIuTld8TYaJNx93G9+T0HIcG1n69qfEosj1uMNR0/ZrQmzyAxA8jpoPHp1kVje2rVYQVJM9aWUA5C0cVzv6ik5QmwZHUAp2QlI8rJS6x2cP9+7VelAyf4gfqIEg8nOiewm3z8i8WlfIGF4aTN8W1m6eTdXjZv3BhrVDlu4jIPidi2cwdvmT5tqtZdsYyouKgF/3TurCN3/7e75jnXr9NOIq+8OaV7106RUk+OTliyOoBTsjJzCcE8ErtqlStqrMnj3EeZksW1ORxZHImi48eOqYsIICoWh2wq8WnRQgWkZfOmsnrVCrVc3B5bAGFJwNFT6zdpogwwcezggQNk9MjhGj6QFcYqOvEiyHAfNWEI3UTZMmeU5k0bySXVQHtu+caS1QGckvXE8WPSzVzZUdJ8m+kbXcqkRC3uImup4kV0GRSa3sYN6up8pDWrVsqPJs5zq4wYAJY7ezapW7umlkTQ0cZGkM2mfowQn9ovGWXISyIqPMuceT5i5HlzZsu3Gb9RyePBg/s1UeepsGR1AKdkPXjwgCY3ICQWlF5L1D0LF85XiR3ZU6bIN6xbW+uB2Qyhud+40aNkmYnbEAzky5ld11xMnTxZpy1ghWIr+NtwdUkE4RoT45KQCs/f7A4jiHVpGURZtXLFslc+YTIyYcnqAE7JSkKErg+IicVEwE5CBbkf/6JwgtAkU0aNGG6el5UWhbWYj3zQK3dOqVCmpEw3riD12ogMUHtdcWDfXiljPJmyJYuJ34RxroxyzMjJOYYlqwM4JStWgfGWJIMQCTxPQYPluHnrprq95cuUkq++SClpUqbQdjd0sWRTLcKHE8eOSYN6dXQXDnVbykuWrK8BnJIVks2eNUNmzZiuUxN4/POA6B0xQfUqleSbr9JIzqyZNQtKBjmk8ski7GBSBs3sjLBhiTPfg4dy1ZLVCdjSTfKjVfNmmsmlHvgiIIIYOniQxqo/GKuJ+xsaiNPO/HhaJk+aKKWNu0aMSwcKtVR21DhNrlg8AYm6Qebzr1erpibxmIDoqZ+nJWsY4E5WIP+bPWumNG/cSEoVL6pW9sH9B/Lg4QMlVUhQjli0YIGqeuixZDJESPDcLLCaMHaMTkXIneNb6dTBW+WJrgnxlqgRwSXzHdC43si4wtUqV9Cme0vWWAqsHmRavWKFDjFDq+qVN5dkzZBemjdprPrWaZP91L1CpB4cFOGZy7trxw7tsbwVbIuZGySaSEBBVBYrtWnVQhVPKH9ic+b3VYHQY7YJQ+j8KVX0O1k4f64la2wEXynlg6OHD0u7Nq0lU/q0kuKTj+SjBHF15f5XX6SSXNmyaAZ3mHF3qQcGB6WWXcaVpaiPRjb4pAcsNT8j8m/VrInky5VDG8nJHtOXaokaOSB0oUWRiRRk12dMm6oNBp4IS9aX4JG5CpMo6trJW8nKxm5WF7IUOEnC+ErYimVL66Y4MrrBgZSwl0931bZSnA++6JeTaNMmf2lhrDOLjWnQnjVjmooeHgbN+LWIOAglNvn767yprBnTa88trYueaF0tWcMA5H3uTWypkid9TNaEcd/VXaPt27SSdWtXqxY4OFzTDX21c4TYlf0zWExE5vSl9jAkZr0FTeR0lZyNwVu3PRUsUaZcQ7tchrRppI9vLw09YkJboVNYsoYBKGoYtYLGN70h54fvx1GyJvggjmTLnEFHt9AAHpJo6FNRzFy5fEWv8Gx2uxMYKAGHArTmhwSxcvkyMmrEsKC2sgceG0/FVFD2QgjBFMX0X6V2Zdl37gxXB1R0w5I1DIBEuKckKtgximX9OEE8SfpRAileuKCWA+4iNA8RZ0JWxo0y3gXdKyfI4cOHdJdolQrldMZu/769VcXE4y0iH64E4RUZMnCAXmjp4mEoW2iZ+ZgOS9YwAGuH+8ocW8QQyT5OpLFr+i9TS8O6dSTg4MGgez6N69evaZsWM5X27t6tIvXpUyfLdwW9pFC+PDrGhJm5JJusRY0auMMO9NZ8X8g3GZXqiQ0RlqwOQAzaybudZoA/S5pExQtcsUOuxXCDbeesfkCsTwKK2bk1qlZSorZt1VK2b936TAbZIvJBDXyq3yTJmO4r1QgzIoa41dNgyeoATL+fO3um1KxWWb5M9ZlOIWDVxfMWA9MwTT9l104dtH7KUuP8uXNoqYaZv5ExVdAibKCZPUeWTDptY9zokTpQzdNgyeoAxJX0V/p07SIZ0n6pWV6s6vNI505u6IhO4z5jkdn5snb1Ko2ZbC311WHRwvlSyCuvVKlYToeyIUP0NFiyOgCxJfEPIzfTpflCG5r54lmtyLzb0A7m3TZuUN+4YGkl7ReppKiJV9mQhls2dXLoj7FH5B2UxFCYueus+XJl1yQTkyGnTfEL9THPO5gJxTBy1lFGByxZwwFGjaT+LJmKIlIl+0Q+T570uUeqZEkleZKP9L4cJKZSfpok1PvaI+oOlGefJIovn5jPP3mSxOY7ePH3FtrxmXmOr9N8bi60fkFnwquFJWs4gEVM9nFCeedf/5D33v6XvPef5xxv/6+8/87/Stw4/5H47/2fHnHjvC3vm9+Hen97ROrB5/z+O/+WD8zB587nH+/dd8L9Hbz9z7ckQdx3ZYzxrKIDlqzhAJ0b6IEZF8IulZAH0/K98uQy/89h7pNVB3ZlyZBeRRD0qebPlUPvE9pj7RFZh+uzz24+e9zfLBnS6cH/s2fJqO4w35HrCO3xzx55cmTTgQAsfY4OWLKGA+h6GdHCKkeGVz859uv+0YPmYF3Drp07ZfXKldp8zt5Rv4njtcNm544dejv31cc89Rz2iOjB589uoTWrVujs4PFjx+jYHBJ9LAmbM3Omyj35Dg4ecH8PoT9X8GO/OXhMdAkqLFmjALdv35KAgIOyYf06XRJM3+sUv4l6otD1wUSIkFvQLSIXSEwgFr3EkJVdOdS6afBnSzzfCQJ/BgR4yqR+S9ZIBCok1uRv9F+vG8hr16imo0SosyIkr1e7pq5zYHX/5IkT5Yax0HYIWtTANZF/prRu0Vw/bwaId/Ruq9pgvodC+fNKpXJlVdSCsswTymiWrJEIBqKtX7dWenTtopMK+ZeFTBs3rNeuHOb+ssmbrWjsHMW1ii2T9WMa2FTHoi9G8HQ33wPrR9jCztLqObNm6nwryjk0/TNA4MKFC7o0KybDkjUSERh4V6fIM7Tbt6ePIekGFe+zgpBJ8LqV+9QpFfLT5zp3zizdrGYR+XCTlXUchB64xIhX2HbHoG/GxELaUsWKSOeOHXTszo0bMVv6ackaSeAkYMVjrx7d5DuvfGpRQxvNQvfNhvVrNeHR09yXrWkWkY/HZO3orQk+pkTyHSmCGjO2b9umG/5on2MMLCFMTIYlaySBGOno0SPSrXMn7ezYuX170C1Pgx2hbIVDEcMYF6YeWkQ+gpN15vRpcujgwWf6jSFw/76+OiCA7QjB9+HGRFiyRhJI59Og7tO9qzRr3FDj0dDAFZ3BatOmTBGv3LnURbOIfISFrEeOHJbBgwbI4IH9Zf68OTG+bc6SNZLAkDOSSCxPrlW9qvavhgZOGBYmoycuWbSwzmayiHyEhax4QqyVhKxYVkvW1wQIJRhH2rp5UylepLCsXrVKpxSEbCpnnhPTDlnuy9BpduBYRD5CkvVwQMAz60uohTOTiX7jJYsX6cjZmAxL1kgCe1UvmFjUp1tXlRMSCzGoO2Q54MyZ0xojkdggK7x/796gWywiE26ydunYQWbPmCFHDh16JtnHUur6tWtqq+NucwGN6cuWLVkjEUw35MSobdxgTgKGgiM5/MmQmIMN6PPmzpa6NatrM/qK5cs8sgnaEwBZUSu1bd1KBvXvJwsXzJP9+/fLUROnBhw4oKUalE0IJCaMG6urTZgRHZNhyRqJoN/1x1OnVDlTuXxZ7V1lTf6kCeNk2tTJOnqUif40oDPR8KI5QTxxJKYnALKSxGvaqKF+3uzJxSXu3rWzeLdtLbVrVNXfEa+yMeG+iWdj+hwsS9ZIBF82mV4I6565xMjRQcbdZRYTbu/woYM1hkJo/rsd6xJlYEoHi5RHjxyp9Wyy9Fqm6ddH+vn2VlHKhPFjdQgeAglPgCVrJAPCkshAuXTy5AndW8O0ginGJdvov0HOnTsrgXcC7UTDKAbfwaVLl7SrhsSf/4b1+vnz77atW4w7fERFLKElAWMqLFmjCJwAxLCcEGfPnJHTp0/raNLff7fW9FWAzx8BChdNJkj+cv26+fxdxw3zc2BgoA5d9yRYslpYeAgsWS0sPASWrBYWHgJLVgsLD4Elq4WFh8CS1cLCQ2DJamHhIbBktbDwEFiyWlh4CCxZLSw8BJasFhYeAktWCwsPgSWrhYWHwJLVwsJDYMlqYeEhsGS1sPAIiPx/L48TcGYcg/YAAAAASUVORK5CYII=)
physics-General
physics-
A bob hangs from a rigid support by an inextensible string of length
If it is displaced through a distance
(from the lowest position) keeping the string straight & released, the speed of the bob at the lowest position is:
![](data:image/png;base64,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)
A bob hangs from a rigid support by an inextensible string of length
If it is displaced through a distance
(from the lowest position) keeping the string straight & released, the speed of the bob at the lowest position is:
![](data:image/png;base64,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)
physics-General
Maths-
The angle of rotation of the axes so that the equation
may be reduced to the form ![X equals 3 square root of 2 text is end text](data:image/png;base64,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)
The angle of rotation of the axes so that the equation
may be reduced to the form ![X equals 3 square root of 2 text is end text](data:image/png;base64,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)
Maths-General
maths-
By translation of axes the equation
C=
By translation of axes the equation
C=
maths-General
maths-
In the adjoining figure
AB = 14 units, BC = 12 units and BD = 13 units. Find the value of sec![theta](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAANCAYAAAB/9ZQ7AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAJNJREFUeNpjYMAE1kC8DoifAvFBIDZnwAHMoQqZoHxRIL6LS/EFIJZGE9sBxHroCl2AeD4WA5YDsRe64GwgDsKiGOQsN3TBa0D8HwcWR1YI8tAnLKZiFQfp3ItFsSkQr8EVZOigHogT0QV5oMGGDASB+BwQs2EL4ytAnAdlawDxcSD2wRUhelDTfwHxJSD2Y6AEAAAtDR3FA6PhyAAAAE90RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+JiN4M0I4OzwvbWk+PC9tYXRoPpXIFCkAAAAASUVORK5CYII=)
![](data:image/png;base64,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)
In the adjoining figure
AB = 14 units, BC = 12 units and BD = 13 units. Find the value of sec![theta](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAANCAYAAAB/9ZQ7AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAJNJREFUeNpjYMAE1kC8DoifAvFBIDZnwAHMoQqZoHxRIL6LS/EFIJZGE9sBxHroCl2AeD4WA5YDsRe64GwgDsKiGOQsN3TBa0D8HwcWR1YI8tAnLKZiFQfp3ItFsSkQr8EVZOigHogT0QV5oMGGDASB+BwQs2EL4ytAnAdlawDxcSD2wRUhelDTfwHxJSD2Y6AEAAAtDR3FA6PhyAAAAE90RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+JiN4M0I4OzwvbWk+PC9tYXRoPpXIFCkAAAAASUVORK5CYII=)
![](data:image/png;base64,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)
maths-General
chemistry-
Glycerol has:
Glycerol has:
chemistry-General
physics-
In the figure shown, the system is released from rest. Find the velocity of block m m A B P A when block B has fallen a distance
'. Assume all pulleys to be massless and frictionless.
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)
In the figure shown, the system is released from rest. Find the velocity of block m m A B P A when block B has fallen a distance
'. Assume all pulleys to be massless and frictionless.
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)
physics-General
physics-
A block of mass m is attached to two spring of spring constant
as shown in figure. The block is displaced by x towards right and released. The velocity of the block when it is at
will be :
![](data:image/png;base64,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)
A block of mass m is attached to two spring of spring constant
as shown in figure. The block is displaced by x towards right and released. The velocity of the block when it is at
will be :
![](data:image/png;base64,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)
physics-General
Maths-
Hence answer is isinx
Maths-General
Hence answer is isinx
physics-
A block attached to a spring, pulled by a constant horizontal force, is kept on a smooth surface as shown in the figure. Initially, the spring is in the natural state. Then the maximum positive work that the applied force F can do is : [Given that spring does not break]
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)
A block attached to a spring, pulled by a constant horizontal force, is kept on a smooth surface as shown in the figure. Initially, the spring is in the natural state. Then the maximum positive work that the applied force F can do is : [Given that spring does not break]
![](data:image/png;base64,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)
physics-General