Maths-
General
Easy
Question
The number of values of c such that st. line y = 4x + c touches the curve
is
- 0
- 1
- 2
- infinite.
Hint:
Equation of ellipse =
![x squared over a squared space plus y squared over b squared space equals 1](data:image/png;base64,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)
The correct answer is: 2
Equation of ellipse = ![x squared over a squared space plus y squared over b squared space equals 1](data:image/png;base64,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)
, a = 2 and b = 1
Given : straight line equation = y = 4x + c , where m = 4
We know that
General equation of tangent of ellipse (y) = ![m x space plus-or-minus square root of a squared m squared plus b squared end root](data:image/png;base64,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)
Substituting the values in above equation
y = ![4 x space plus-or-minus space square root of 2 squared 4 to the power of 2 space end exponent plus 1 squared end root](data:image/png;base64,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)
y =
comparing with y = 4x + c ![rightwards double arrow space c space equals plus-or-minus 65](data:image/png;base64,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)
Thus, we have 2 values of c i.e. ![plus-or-minus 65](data:image/png;base64,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)
Related Questions to study
Maths-
Tangents are drawn to the ellipse
at the ends of the latus rectum. The are of the quadrilateral so formed is
Tangents are drawn to the ellipse
at the ends of the latus rectum. The are of the quadrilateral so formed is
Maths-General
Maths-
A tangent to the ellipse x2 + 4y2 = 4 meets the ellipse x2 + 2y2 = 6 at P and Q. The angle between the tangents at P and Q of the ellipse x2 + 2y2 = 6 is
A tangent to the ellipse x2 + 4y2 = 4 meets the ellipse x2 + 2y2 = 6 at P and Q. The angle between the tangents at P and Q of the ellipse x2 + 2y2 = 6 is
Maths-General
physics
Here are the graphs of x→ t of moving body. which of them is not suitable?
Here are the graphs of x→ t of moving body. which of them is not suitable?
physicsGeneral
Maths-
A cubic polynomial f(x) = ax3 + bx2 + cx + d has a graph which touches the x-axis at 2, has another x-intercept at –1 and has y-intercept at –2 as shown. The value of, a + b + c + d equals
![](data:image/png;base64,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)
A cubic polynomial f(x) = ax3 + bx2 + cx + d has a graph which touches the x-axis at 2, has another x-intercept at –1 and has y-intercept at –2 as shown. The value of, a + b + c + d equals
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAc0AAAGqCAYAAABptB//AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAGdeSURBVHhe7Z0HYJXV+caf7D1JCJsQ9gZBZQjKEkFxb6ut1VrrqHVUraP6b2u1pdaqddW6tyhFFFQQUaayZ0ICIYSZQRYhe9z/95zciwERbiDJ/W7y/NrPe7nfd5OTb5znvO953/f4OCwghBBCiOPi63wVQgghxHGQaAohhBBuItEUQggh3ESiKYQQQriJRFMIIYRwE4mmEEII4SYSTSGEEMJNJJpCCCGEm0g0hRBCCDeRaAohhBBuItEUQggh3ESiKYQQQriJRFMIIYRwE4mmEEII4SYSTSGEEMJNJJpCCCGEm0g0hRBCCDeRaAohhBBuItEUQggh3ESiKYQQQriJRFMIIYRwE4mmEEII4SYSTSGEEMJNJJpCCCGEm0g0hRBCCDeRaAohhBBuItEUQggh3ESiKYTNqKioMJsQwn5INIWwEbW1tdi1axcyMjJQVVXl/FQIYRckmkLYiIMHD+Ltt9/Gyy+/jP379zs/FULYBYmmEDaBluXWrVsxe/ZszJw5EykpKXLTCmEzJJpC2IQtW7bg888/R3Z2NgoLCzFv3jysX7/euVcIYQckmkLYhOTkZMyfPx/5+fkoKSnB119/jXXr1sHhcDiPEEJ4GommEDagrKzMiOayZctQXl5uXLUrV640liatTiGEPZBoCuFhioqKsGTJEmzatAnV1dXOT+tITU3F4sWLFRQkhE2QaArhYfbt22fmMhn4cyTbt2/HnDlzsGPHDucnQghPItEUwsPs2bMHCxYsQFpamvOTH8jMzDT7mLcphPA8Ek0hPAQLGdDKpFs2PT0dNTU1zj0/wGNobfKYnTt3/sh9K4RoXiSaolE4MsJTEZ/HhwE/33zzjZmzPJ4YrlixwqSgFBcXOz8RQngCiaZoFHx8fIy19NFHH5ngFf5bHBtW/2EA0HfffXfMknkcgKxZswYLFy5EQUGB81MhhCeQaIpGY8OGDXjqqaeMVSSODYVw9+7dRgw5p0k37LHIycnB6tWrTUDQ8Y4VQjQdEk3RaDB1gmXg2MGLY8MczA8//BCbN292fnJ8eG4//vhjLFq0SMIphIeQaIpGhRYUq9kwWV/8NKWlpSbwZ+jQoejbty8GDx6M/v37o1u3bggKCkJAQAC6dOmCfv36mX085vTTT4evr685v0IIz+BjdXKK2BCNAq2gxx57DNOmTcN1112Hzp07IzAw0LlX1IfCxzlNDi74CHIOOC8vD2vXrsXjjz9u9t1///0YNWoU2rZta77DY4KDgxEeHm42IUTzI0tTNBqhoaGmg2ckaG5uLiorK517xJGEhYUhISEBiYmJxrrk65AhQ9CzZ08jjLQ0k5KSzGfc7zqmXbt2hwRT410hmh+Jpmg02NnHxsYatyOLjiunsGEwMpYpJTx/nLOktXmsaFlFKAvR/Eg0RaMREhKCNm3aHBLNY6VRCCGENyLRFI0GRTMuLs5YmCwwLtEUQrQ0JJqi0XDN01E0s7KyNKcphGhxSDRFo0HRZKAKLczs7OxWLJoK0BGipSLRFI0Go2cpmrI0FaAjREtFoikajVY3p3nIoKxB7rpPsOKl+/G/r9fjqz1AqQKHhWiRSDRFo8FCBq6UE6ZKtHjRNAYlrelt2PL1m5j17N/w4cLNWJQFlEk0hWiRSDRFoxIdHW1emW/Yct2z9eYsD+xG+Zf/wtcLF+ClrT7YXhqIUD/mUDr3CyFaFBJN0aiwNirdtKxo03JrpLoUsRQleRlYmXYAu/KAoOAgBAf6wc96qqSZQrRMJJqi0WGBA6aeFBYWmiIHLXJFjtoKoGg+9uVn4BPfyxHW6Qzc2q8WvSNrUFGj+FkhWioSTdHoREZGIiYm5lAZuBZZI9W3BOmLspGeXIEew5LQp38C2gTVItCnFrXWnyvRFKJlItEUjQ5FMyoqyogmrc2WJ5r7Ubx/O5au9see7HicPSISA3oF4WAlUFF94vOZrlqyR74KIeyDRFM0OhEREYeJZsvgB+HPW/wFUt54Fvu7doTfhIlIQCCinJHCJzM8YMF7RiBTLLnxPeeHhRD2QaIpGh0KJt2zjKCle7ZlzGnS6rPMyLIsZGZkITkrEG0G9UWfobEIQxCCax3wsw7x9fOH9X8E+NV960iYjsM1NLl25t69e83GQhCsoLRjxw7znqk6PM712b59+8x71/GujT+DwVY8VgjRPGgRatHoLFq0CEuWLMGuXbswePBgXH/99QgKCnLu9WLy1gOp/8PHeadjdehkXD/KFz2NIViCrW/fjS9eegUpF8xC4rRzcUdvWFJaBx8wl6OV1jfPy6ZNm5CZmWksSj8/P/PKQQY/mz17NsrLy3H++eeb9TVpuTMq2TX44CuP5yLfPXr0QK9evUwJQyFE0+P3qIXzvRCNAl2yrAiUnp5uFkweOXIk/P0t88vLqdmzEnu/fhozVudgzsYDKN68FDs2LMSi5d9g/vzFWJmyF2n5Fdhf4MABn2iEhIYhIdz3sPQT5q7S+k5NTTXbgQMHzOaKNKZFmZGRYaoqxcfHG3GkZVpUVGSO4Su/z+/w3HLRbx5HV64QoumRe1Y0OvXnNNnJtxRnRnFZJdIydyB93ntIfukGTH/4dtz02z/g7jv/hKc/Wok5mbVYteAjLHjtL3hu/jYs2PFjtynzV13ua24sBuF6z88phLQ8aVmyli8/4zH1j3O9Z/Ul7ufxQojmQe5Z0ejk5uZixYoV+Ne//oWkpCTz2hICWiryM5CbshCbdxVje54famp94ONfAx/fg8j89lOkfbcC+3pdiYTRl+Pcs07FGX0S0C/+cEGja5WuV1qUtBhd7llCS3PDhg146qmnzIDjzjvvxGmnnWbq+R7NPesSTrpmJZxCNA8STdHo0AW5evVq3HXXXWbe7bXXXvP+OTc+JpZQHZ1SpL19F+b9p96cZi/A5TCtP6d5LCiUS5cuNWJJC52DjYkTJxpxFELYA7lnRaPD+TXOtTGwhVZniyjc/pOCSUpRXlmNyhqgqrIc1v9RVu9PdkcwCc8T5zI5juXG9y2+6L0QXoZEUzQJdMdSPOlKpHi2XOgyrbKEsgzlZdUoL69ARSVQfQJZIEwdcQkm4blzuWSFEPZAoimaDFqbDGxhJC3n8VoyPs78TD8/X1Ow3W3zUgjhVUg0RZPAwBSmQjAClC5apki0TKiOkeg86hpMuOtfuHryKTinExDm/Rk2QoijINEUTQJFk5YmA4BycnJauGiGoe3AszH8yjsw6fReOL2tA8F+J1dSTwhhTySaoklwiSYtzZYtmkejzjcrD60QLQ+JpmgSWAGoXbt2xtJk7dSWU7hdCNGakWiKJoGi2bFjR1MdiMXFmcgvhBDejkRTNAl0zyYkJBhLk9VvmKwvhBDejkRTNAmtJ3pWCNGakGiKJoG1Utu0aWMWVqZoskScEEJ4OxJN0SSwoDhX9GBlIBY24PJWQgjh7Ug0RZNC0eQC1CziLuEUQng7Ek3RpHBOkwFBrKHK1BOKpxBCeCsSTdGkMHq2a9eupgj5zp07UVpa6twjhBDeh0RTNCl0z7LIAcnKymrxhduFEC0biaZoUhg9S9GkpSnRFEJ4OxJN0aTQ0uScJkWTRQ4kmkIIb0aiKZoURs6yyAFFk+tqKhBICOHNSDRFk0LRZJEDkpeXh4qKCvNeCCG8EYmmaFIYPdu5c2eTcpKZmalcTSGEVyPRFE0KLc0OHTqYCkGc05RoCiG8GYmmaHJobXKpMAYBtYQ8TYfz9adwHO8AIYTXItEUzQKFk9WBKJoMBmJgkLfig2KgJA0bv/kCn7/7PmbO+AgfLFyDuWkHkVdWa1nVzgOFEC0OiaZoFmJiYky+Jlc7oZu2pqbGuccLcWxH6daP8MaDt+PWa67C1Zdfhivvegq/eDMZq3er4pEQLRmJpmgWKJrt27c362qyBq13iibnY7dh8/wtmPlOOdqcepElljfit/dMwVkxexDx8b+xeHEqVhcCFbV13xBCtCwkmqJZYNoJA4KKioqwd+9eLxVNLqSdjrVrCrFsYxJG3PAQ/vTky/j79Mfx57PCMTn1LaSs24pPdwAHq+q+IYRoWUg0RbMQGxtrRLO4uNh7Lc3yAGBPPAZOHInzHj0bfXpEwt/sGIykPp0xbgIQGVeJA5ZBWqtgICFaJBJN0SxQNOme9WpLszrY2tqj+8BeGDGiAxJCnJ9XFSLXPxa7+w5A525tMTgWCNKTJUSLRI+2aBZclibnNL1WNMMslezYFqGBgYi2/mkenqp9wOZ/44sMf/y15o/o0WsQft7bsjgDuVMI0dKQaIpmgYFALNxOS5PuWa9MOWEuib8ffH184VtZiv1r3sfyl3+Pp/7xFl5Zkof9If0Q38YyM5001EXLQhABAQHw9fU1xSD4np8JIeyDRFM0C+z84+LiTIGD/Px8VFdXO/d4J1WVJchZ9gLmv/8O/vh+Grau243wyn0or1fxyPcn8jU5YGBZQVrbfHXBakmszcvPeAzzWfmZ6xi+1t+8OddVCG/Fx3rw9OSJZoEF23/2s58ZF+2LL76IgQMHOvd4H7VV5TiQvgi7tn6PTds24+M5O7A8NRSjfnU3LrhsCi7q7ouwo7homadK9/SuXbvM+aBF6efnZ/bRCk9LS8Obb75pxPLaa68154hWOo9ziScf2cDAQAwYMADdu3c3nwkhmge/Ry2c74VoUmhZLVy40FhTQ4cONfOcXKTa67BEy8cvAMFx3ZHQewwGnhqDNhmrsefbBViJPsiN7Ikze4UiJvjHjpyCggKkpKRg48aN5nXPnj1GRHfv3o2dO3dix44dSE9PN1ZmVFSUqaCUk5Nz6Bgez+NYIIJLrnGe2CW6QoimR+5Z0WzQWqKLNjIy0qytWVhY6NzjZXBu8xDWI+R/JoaNn4Rf/7Ifosr3IvX79dhVXoGjOaBpQVLwSkpKzNyla/6y/kbqvx7tPd3btNh5Dr3d1S2ENyFLUzQb7NxTU1ON9RQSEmIKHnTs2NG51xvhzAZFzA/Bvjlo49iN99LbIjugE66emISu4T/2z1ZVVRmLmy5X/u1dunQxG5dP4/mgKG7evNm4YsePH28s8l69epljOnXqZI5zvXbt2tV8h9Y6xVcI0fRoTlM0GwwC+uSTT7B27VojHuPGjcN5553n3Ovl7PoUJWs/xdkLB2Jf1AgsuH0gurU5uuv5yEfOZT3S+l6+fDl+//vfGyty+vTpRjiZ30qO9qi6viuEaB40PBXNBq0humcjIiK80D3rOOaSYCVb12HZ7M8RExiCIQMGIuQYqSIuN6trc3G8lJMjv8dNCNG8SDRFs0ExYK4mA1wY3MLUE+/BEqnaSstczkdBzh5kZOywtp3YtScdu/d9h2/WbsOy7UDvjh1w9sBghAQ2XNAYIEUXtiudhNY4A4KEEPZBoimaDYom5+FobTJKNCsry7nHSzhoqeKaZ/Hiw9dh5BlnYsyZZ2LsqLE44/Tz8JflYci6Zg6mnDMOV3cHIlQRSIgWiURTNBsUTbpmaWnSNet10bM+/kBgJCKi49G+fTtrS7As5w5IaJuIHoNGYehZgzCoewgi/R3mwVKwgBAtD4mmaHZCQ0PNfBzdkUzB8BrCk4Cht+Km/3sVi79ZgIULFmDB1wux4Jtv8J/7LscvugFxJmWyzjWrGUchWh4STdHsUDSZNkHLk4n6FE/744DDx3pc/AIRGByK8PBwawtDmHkNR0iQ9bm12/c4AUNCCO9GoimaHeYVsvwbo0O3b99uysfZHx83LUd3jxNCeCMSTdHsMI2CUbQs/8bqOF7lohVCtGokmqLZoaXJajj+/v6mniqLmAshhDcg0RTNDuc06Z6laNI9y+o3QgjhDUg0RbND96xrdQ6u2sHi5UII4Q1INEWzU39Ok5WBNKcphPAWJJqi2eECyixCTvcs14nUnKYQwluQaAqPwGCgsLAw816iKYTwFiSawmOwBm1iYqLJ00xPTzcFyoUQws5INIXHcC3EzEAgpp5INIUQdkeiKTxGdHS0KadXWlpqomglmkIIuyPRFB6D7tmePXuiuLgY27Zt85IatEKI1oxEU3gMimZSUpIRTc1pCiG8AYmm8Bgu9yyjZ3ft2oXq6mrnHiGEsCcSTeExQkJCTJEDwghab0k9Oe7SX1obTIgWi0RTeJTY2FiTr+lwOJCXl+cV1uZxl/7S2mBCtFgkmsKjsJQe5zajoqKwf/9+s9mVQwZk2RZgw2t46k934+qf/QK/uvEm3HD/C7jvjY1Yn1vuPMhCFqcQLQ6JpvAotDCZq9muXTtkZWWZjZ/ZEWNAOiqBPZux9fsvMPvjD/DeO2/g7bdexqvPv45/PjcXc1ZnYqd1mLGXZXEK0eKQaAqP4uPjg65duxrh3Llzp9lsS81uYP+neHtRHh7bOBHX3fMSFi3+GHPm/QUPTw3F8JUv4bVX5uKPn+xCwUEFNQnREpFoCo9C0eQyYQwI2rdvn9lsS0kJKvfuwf6aSFQnjcG4887FmDMuxvgzf45rJ/bA5PaW6G9OwfylmcgpV/qMEC0RiabwOG3btkWbNm3MfGZubq7zU/tRUhyKPXu74swRA/D7m3sjLsa5A53QedBQTL5hIHrHOeCblYuc6hpINoVoeUg0hUehpclcTc5p0jXLcnr8zI74hUUhPLE/unXphD7BPgh1fk6CEzqg18BeCG4fj+rgQIRZf0OAc58QouUg0RQehQIZGhqK+Ph45OfnG0vTrmknwdGRiO/bA9FR0Qiy/n34w+ODwIBwBHfuiIguHdA2wN/5uRCiJSHRFLaAwkk3LVNQuDC1XSNoD+eHNpbtSkH62s/QOTYUwwYORnAgZVUI0dKQaApbwEWpu3XrZl63b99urE7743IjlyJ1bxEW7whGnw4JmDrAF6EnoJm+vr7G8na5p+u/F0LYA4mmsAUUy969e5vqQKmpqbYucnAYjmygaDbWHmiPWT6PYlD3AbimOxB5AhOaLtEkfOW/aXkLIeyDRFPYgsDAQHTp0sXUo2VAEGvR2pZ6nuOqnGxse281CotC0G3qZCT1an/ooTqag7m2thZlZWXm7+PAgKUDCwoKzMb53MLCQtTU1JiNx/AzWt38nMfyO3zPn8FjhBDNi0RT2AKKJgscBAUFmQjaAwcOOPfYEGMM1lpbHvam78K89w8ixBGJK6/ogHYJP5iYR3OslpSUmEFBSkoKNmzYcNiWnJyMHTt2oLy83ARDceUXfsZ969evP+y4jIwMs6SaEKJ58XF4R8SFaOFQKLZu3YpZs2Zh3rx5+O1vf4vLLrvMudcu8FFxSqH1Nvvzv2Pjlix87zsFfUcPxLhT2yHS2vWDQ7Xe8U7WrFmDGTNmIDs7+5ClSDcs4TmgZblq1SpUVlZi+PDhaN++vbG+6a7lo8qNx7PQ/QUXXICxY8ea7wohmgdZmsIW1HfP7t6927gg7YdLAGtQtjcZm1dtw86SAHS8dBJ6WYLJWgd+NYWoKc1D7sEaFFX82NakW5UuVrpjuRQaLU++ut5zP124FMeKiorD9rs2l2u3tLTU+VOFEM2FLE1hK55//nk88MADePjhh3H33Xc7P7UBfExckaxbPsCe9fPxvuM6BCaNxS9OAyLq9gB73kbhzjy8UHodunWMwZV9nJ87oei5clFdQT8uS5NzluvWrcMTTzxhjrvvvvswcuRIk4rDYymmhI8sA4RYRYmrwwghmg+JprAV77zzjhHM66+/HjfffLNxQ9olgrTqwD7kpX6DVZ+9hGWrNmNxh98huuspuLRTLsKCfXGwtAJ+yYtRFNAG6ePvx8gB8bi8vfPLbkDLcunSpbj99tuNNfnMM89g8uTJJqJYCGEP5J4VtoLW08CBA42AMFjGTi7Ikh3LkPz2Dfjve9/i8bn7seS/D+Gzh8/D9b+8Hldccy1+eeNvcN2TaXh6fgL69vTHqQ0QTELrkn8vLUpunONUsI8Q9kKWprAVK1aswIcffmje9+3bF9OmTTPuSTtQnrUZe9fMxPc7qpGSF4ZAlMPXUY3KWgbpMKgnEBWVSejYsx8mXNEfiWFBh9WnPR6cp/zuu+9wzz33mOjh6dOnY8KECaYurxDCHkg0ha1gBO3ChQtNagXdkrfccotZb9Pj1J/TdJcGfkeiKYT9kXtW2Aq6Z1kZiFGkrAzEV1vQUME0nMh3hBB2RqIpbEV0dDSSkpJQVVVlEv2ZcuG1SDOFaHFINIWtYPoF19fkK1MwFAgjhLATEk1hO5iTyOCfuLg45OTkmNqrmnoXQtgBiaawJQz+6dGjh1lbk0uFuRL7hRDCk0g0hS1h8XaW1cvKykJmZqZEUwhhCySawpZwXpPWJkWTAUESTSGEHZBoClviEk26Z7kMluY0hRB2QKIpbAkT+umiZRAQhZMpKEII4WkkmsK2MIKWbllWx7H1otRCiFaDRFPYFq6xmZiYiIiICKSnp9t0jU0hRGtCoilsi7+/vympx9J6rEnLoCAhhPAkEk1hWwICAtC9e3ez0DItTRY6EEIITyLRFLaF7lkWOGA92m3btiE7O9u5RwghPINEU9gWWZpCCLsh0RS2hXOanTt3NpYm00643qQQQngSiaawPbQ0ycGDB80mhBCeQqIpbA9Fs0+fPiZnkwtTe14466oTHb1GkeMnPhdCtAQkmsL2UDT79+9vSuklJyd7fI1Nh3N1aR8UoDw7Dau/XI616zKxsxwoc/ho7WkhWjASTWF7OKdJ0aSluXnzZptUB6oFalYj/atX8dg1D+EfT3+Br/KB/TIzhWjRSDSF7YmNjcWgQYNQXV2N9evXe9zS9DmQipKVr+LlvzyHu6Z/jHl5u5BRWoGSaktKJZpCtGgkmsL2REZGmspAPj4+JvWkqKjIucdDFG9D6dav8f6spZi3PhMlCEZQdCiCrKfJz3mIEKJlItEUtodiGRcXZ2rQ0kXLlU9qamo8t1xY7GmIGns7Hn/pUUy/9xqc6xuCziXldNiipu4IIUQLRaIpvIb4+HizMV9z586dRjg9gSMkHoGdRuK006biZ+cPx4CgAERXVJuoWS2VLUTLRqIpvAYWOujbt6+pDLRlyxYzx+kJ6qJj+buLUVRchgrL4q2xrGGiyFkhWjYSTeE1dO3a1UTR7tu3z0TReko066Bd6UBtbV1epkNqKUSrQKIpvAZamixywMLttDSrqqqce4QQonmQaAqvoV27dkhKSjJ5mpmZmSgrK3PuEUKI5kGiKbwKBgIFBQWhvLzcBAR5LIK2CeCqLn5+fiZamBvfs2i9EMI+SDSFV0Fh6datm0lB2b59O/bs2ePc4/2EhoYiODgYvr6+RjT5PiwszLlXCGEHfKyRessZqosWT2lpKf773/8iJSXFBAaNHTsWo0aNcu5tTjifmoKUuV/ipUtmofL8yzHwyTswpT2QeJQKB0yPoVs5LS0N69atQ2Vl5SEr0mVZstIRBwIzZ840lvTFF19sijqw9i7382cwT7VNmzZmnVG6qjl4EEI0HxJN4VVUVFRg8eLF+O6777B161ZMnjwZV199tXNvc9Iw0aRIUhDfeustTJ8+3QQxUQiP5MjHsf4xrn0U0ksvvdRsQ4YMMZ8JIZoHiabwKmht7d69G19++SVeffVVY43de++9zr3NAx+YOinbjt1LPsezZ3+IqkuuxeAXbsTUcCDeecQPx9W1u7Cw0KTKfP/990b86WomdMcSLnnGog1z5swxlua5556LHj16mEpIFE9amfw5nNelcDKSuG3btua7QojmQaIpvArerhSO2bNn47777sNFF12Ev//97869zYSjFo7qPFRUr8Pyd7/CmzfPQ8XEc9HvkVsxuWdbDIr2Q6BlbTY0dZPW6JIlS3D77beb+rrPPvsszj77bM1rCmEjFAgkvApaXJwL5FwexaSkpMRYnhTSZqMmBcWb38GT1z2I398yHe9Z4vneF4/hyWsn46+vfYt3twHFlc5jGwCtSwonLUoODvieFqkQwj5INIVXwuCYxMREIy4MrmnelU/84BMQgdCIbkgcOBJnnXsOxow9Dad2iUeHiAAE+1PcnYc2AIokqxzxb+LG9/xMCGEf5J4VXgmXCHvjjTeMWDKSdOrUqWb+r3mwLMEaS9AqqlBdY703Clk3g+kXGAw/yxIOsIajDdVN5p0ywOmee+4xkbYMGJowYYIp6iCEsAeyNIVXwuAY1qGlq3bjxo0oKChw7ml6HNZj4+MXiKDQMIRZ7QgPD7e2uteQQH8E+jqMYGo0KkTLQ6IpvBIKFFc8YQRqampqs4rm8S3IuiMaamkKIeyPRFN4Jaye07NnTwQGBmLHjh3NKppCiNaLRFN4LSEhIYiNjTW1aPPz8838JiNPhRCiqZBoCq+Gy4WxKk5ubq4pT8e0DSGEaCokmsKr6dKlC4YOHWpEc82aNRJNIUSTItEUXo3L0qR7dv369VpjUwjRpEg0hVeTkJBgomhZt5UF3LkKihBCNBUSTeHVsKwek/9ZUo/Vc7Kzs80KIkII0RRINIXX4+fnZ6xNltXbsmWLsTiFEKIpkGgKr4ei2a9fP7MoMxenpnAKIURTINEUXg9dtBRN1p5ldSAWcBdCiKZAoim8HoomBZORtNu3b0dGRoZzjxD2QOtitBwkmsLroWiyBm3btm3NupqsDMQUFNE02FUAWA2K15+b3SpD8R7leWOUN9eAtWPlKraJec4sSck2iqMj0RQtBq58MnjwYFOXloUOVI+28aEgudb8tBtMN+JgiRs7fbu1kTnE33zzDRYtWmS7Ihw8V2xfcnIy3nrrLSxfvty5RxyJRFOcEHzI7DZaZtoJRZMroLCkHgOC2JHasYP3RtipLly4EHPnzkVxcbHzU/uwe/durF271gyYMjMzbXfdKyoqsGTJErMVFhY6P7UHPFe8plz8gGu6cppDHB2JpjghOFLmiJ7uJrtYHrQwKZpRUVGmOtDSpUuNeMrV1Djk5eXhlVdewVNPPWUWzLYbTDWiJUdh54DJboM65hHzfly9erV5dvjc2AWeK4omy1Hm5OTomTkGrVY0OSqdNWuWuYntdPMStoedEh/+d955Bzt37nTusQ/btm3DJ598ggULFpgOiqNoT0MLc9iwYWblk1WrVuHVV1/F66+/bjoCcXKwU+U1poXEjW5au8GiFvQscKNA2Q0OLDnY5MbzZzdLmNeYfQ/Pox2vr11otaJJ9817772HFStW2O4B403L0R5Fk220o2iyTV999RWWLVuG9PR0W5xDf39/tG/fHvHx8eb8MWfz008/VVBQI8AOlR0pl2GjG9zX135dB/N12T5uvBfsCAPWuPH8MTjITrA9PIfc7Hh97UKrPTN0RdBC2rNnjxn52cmVw87JNWJ2jUrtBh8w14Nvt4efojlgwADz3m6jeW/FjtdZCE/QakWTlhHdTK45OTvBjp5CSSG3a0dFweSImSN6u41KKZpcLoxuWo6ahRCisWi1ounq9Nmp2lGYXCN71ybcJy4uzgQEUTw5+JC1KYRoLFqtaDLSksLJ+Q/m99nJWmJ7GNTimpvhHJLdYJs46GAbeS4jIyOdezwPF6YeP348OnXqdGgezhvgOeS5dM0p2em8sk28L10DTb63G7wnAwMDzRYSEmK7eU1eS7aJG59vO7WPbeE1dZ234OBg5x5xJD7WKNyjw3B2aq6NTWlqq8ollB9//DHuvfdeXHDBBfjd736HNm3amJvF03ObbAOT8jnfyjZu2rQJ999/PyZNmmSiF+3QPm6zZ8/GjBkzjDCdeuqpGDNmjDmHdggI4oN/4MAB/OxnP8PixYtNOydOnGjbBapdAzZG+X7//fd44IEHTPv/+te/Yty4cWbNUAoVn5HmxvU8cgqD5QnZNkZ2//e//0X//v1tcU4pkrzvPvvsM5OUz36EUdR8timkdojs5j3JHMhf/vKX5pw+8cQT6NOnjxmEEE92w3yeGTvB68uUnZkzZ2LKlCm46667zH1nh/PXnLh0iOfFNYCtj0dFk1GijL789ttvTU4dy581tVXAk8ETwXUXmcBLVx47fp4gnhxP3ryE7WMHxSAgdqLMl6LlxPk5T3SaR8L2cWPHyfbxenGEGh0dbToAOwRU8fqyHRxwMODrtNNOM+3jezvOE7vaw46fYsnOi/cAV21huykKPMaT9yZ/NztWPjN8bnv37m2uu6fiAXiNeb/x3Ljuu3379pn7km2lVcfBBp9r1/Guzo9t5rnm39Fc9yvbwWeag2FeS15behLscC+yDTwPvL6M8+Bzzf6GtZxd+1oTPA80AKZNm2aMAQ5uXPcR8aho8sZlnt/nn39u0hdoYTWHK40PD8WIqQi8cZkMf+RowlO4blKeG1e+GTtOjlTtcPO6HnJXdC87I14zbnzvyY7dhWvww2R8CiXhTd+xY0fTRjsMPo4Gry9H9XwO+D4mJsa4ydhmO0CxYdt4/jjYpGA15z3Je891LmjhcpB9tCR8Hsd7gK8uD9aRUFS58b7l38BjmvLeZXso0q6iEBQll5XpaXie+Lfz+vK88rlmf8N+kTTlebEjPAesY33VVVdh8uTJJj7CNqLJX80LVL+IsatTbip489Jlw8T8v/zlL+ak3HjjjaaD4olpzk7gaLAN7AxYPIDlyjgyvfXWW42bjhfT0+1jp8U2zp8/37jD2rVrhyFDhhhrjh0BRd7T8PryfrrvvvuMi5ud4+WXX4577rnHDEB4v9kJ14CNIs8ycHTdsY10y48cOdIENPEYT1x71/PIDnXXrl2mbRxsTp8+HQMHDjSWcXPBc8BBLs8Dnwt6qP73v/+ZSkAUJM4T8vry+nfo0AFdu3Y1zwwtUOYS04Jin3P66afj3HPPNVYEj+E9S3FtyvNLq5xWOu9BQjd39+7dbeGe5TPNc8Dca7q32e8wJuBXv/qVedZbm3uW9wH/bvYbvJc4sKqvSx4TTf7aphbIY0Hf/U033WRGEw899JBtRn0u2CmwcDIrFlHcmUJhJ+hOf+ONN0ync8YZZ+DMM8907rEPv/nNb/Diiy+aAREHRo8//rhtrLajwY6bc7AcJHHg9Nxzz+Gcc85pFu+LO7BgxG233WamNjgYobXZ3NB1vWHDBmRlZZlBBgWcfQmvK8WR7kWeL66vOnr0aLOPYuk6noMpWlEciHDr2bMnhg8f3iznmOJz0UUXmfe8LzntYid4fb/44gtThYztvPnmm517RH085pP0pGASjuQ5ouBIlA+aJ0bxPwVdihzB07fOEbTLxWgn2CaOTnn+XO21G64RMt2IdCuytJ4dz6ULtpH3pcvq4Xt+ZgfYJgo5rzmtTr5vTuiR2rhxI1566SX8/ve/N4FIe/fuxdSpU/Hoo4/i73//O6644gojlt26dTPFLSZMmGAGHddee635DgefDz74oAkS4qD02WefxWOPPYYvv/zSDASaGl5LPs/ceP54Hu0C28J+kOeZ7eOrODr2mMgToglwdUqM7uUcBV1PWr3hxKDF5nJKuV6bC5a6/M9//mMKxXNwRrchIzuvueYaM9/kSn+hS42DcW6uaYT68N+cTqBnhEJKi55WJqdqWKeYv6f+HGlT/J0u0Wzuc+gOHKixba7Bujg6Ek1xwtjxwa8PrSK63caOHWuCgLgkE+e/RMOhEHFOkde8ua47O27ORXKwQ0FjyctevXrhhhtuMNMqnO9llKMLHu/yYNEy/ilLjvfCWWedhZ///OfGEuWxjLRmJD/vD9f3Gtsbxp/HeVeK/JGC7mnYNnpkOI/HAaZrICJ+jERTnBCuzrM5O9GGQtHkXDU7VxZydxWXFw2HgsmO3mWNNMc1Z1Q956HT0tIwYsQI/O1vfzNC54rqPBIGbbgijl3BVceC1iiD2B555BHjymX8wLx584xAN4WlxXuR6QvcKJ52ml/n+eIcL4O7OJCgm1scnVYrmnz42alylGnHTt81UmYb7TTf6oIj08YeiTc2jLRksAoFkzl7HD0zcIQBIzy/wn14rXn+aKGxU2Wn31QwYIfixTlo3vsUGUa6UuAoij8lNswrPOWUU4zLlfOa7ggn7xEeS5ctfz7vD3okNm/e3OjzehRzRsFzo/Db6flhWzjoSExMNOeiR48ezj3iSFqtaPIm4cPnzoPlCdg+to1ttNPD5YKuHHai7HQ4grZjGxmd2LdvX2MhcRTNzooDEUZOu/LlhPswpYiu0TvvvNOcz6aClt6TTz5pxPPSSy/FlVde6Vb0OFM4eI2ZTsLjG/Js0+17yy23GOGlq5bL8jHwqDHhs8IBB9Pc6Aa1GzxfHJTQyqQLWxwdv0cZetYKYUABN45KBw0aZETALh0/b16OSl2dPUfP9edu7ADbyLZRlDhSZ36cndxNhCNnRlGyE+C5pEeB7lnOW7FTbcqO/0SgZcPF0WllMfL37LPPNpVjmtKqawh8PnhfsvOvEyR6aBrvmWG08Ntvv42VK1ca8aJ1yfxfzrH9NA7rfz6mFa6BJrfDnmU3m8n7l6LBvoBWLkWb1cI4ODzZe9vVhKO2z4LOLk91P/V/N9vl2kjjXuGWQasVTV9fH9PRs9On+66uE7AHfEDZUbZrl2BZS51N+/gg2wmeO47s2anYUTAJ20YLgueOosnRPYNK2CEyOIg5pnbC3qJZA9RWoLSoFCUHK1FtnU/roYFfI/WoTF1i/iVzBDm4Yd1gzmNSxI6N1cE7qoGqg2YQnFd4wIjvwdJKlFRZ+6w2Bvq7/2xzcErBpouWbnyXR4VW9sngg2o4qktRXFCEosIiFB8swYHKGpTV+iPAOon+Vn/kKer0sRqVxQUot65DOYLhsD7kaZNg/hj7KEVTwuHSEbRv2wYjrYeSVpIdOvyjNNESoxhLmLpZnWbYUfc3PxzVH72th+GRxtb90p/61ez86K7lXBJD6pnszle7BjHZg/rXOx84MB8fP/IXPPzLJ/Hemv3YbGlVY509FvJ45plnTLUeBvuwti0t2p+m7jeb/5ZtBzY9i6fv/xlOHzkWZ54xFmdddBum/OFLfLB2/w9tdLOxHAQyHYXeiHfffddUHqKonxwZqN7xLl645WpcNex0TDprPEbd8hSu/GAnkvf/EHTUWOezodTW7MXGV+/EzMfvwgtLC7E0x7lD/IjWYWk6R1LFmRuRsz0Ve2tiUBkUhrYRIbapBOSDg0DJLqSsXIcN1paybRu25FVjX200okP8EOJvhzEfR/WV8CnZjt1bU/Dtig1ISU7Btoy9SMt1oNwnEHGRgfDEoPmQiw55KMq0OqJVO5BvjeJrIsIQbA0NaRHRm8DyhLQgGCBEC46vdrGS7WdpWue0pgI+BzKxL3kevpr9Cf7z7Lf4bmsVYqecjS7do9HNMjhP5nKz2ASjVlmDmhbiJZdcYixMVu05NvytNfCpzceBbRuweul6LNmci30HShAWVoyi/QewbZ0l9FGRCO7dBQmhAbAeI7ega5L3Bee/169fb4LxCN35x2/XkTDgrAAFKRuwbuE6rNq4B9nlB1ATUoxd2RXI3lmF3kmd0CMxBkHWfeoRK6Z2JwqTP8cHz/wTX6zPR1a/n6NzpwgMOp6R30ppHZamIQfJH/0ZM/94PZ7/chvm7ASqbBWUuh2lWz/AK/fejJsuvRiXXXA+Lrh9Oq56dSNW7bZHdQ4zCq7YD2x9D3OfvxsXXngRLrroQlx45Q2Y9tu38PdZqcgyR3qKEqB8CVa//288dNmD+Pc732OxNRYprjd853JWjA5kkQOmoLg6RPETlO8DtryOj154Gpf87n18nb8fpR1iERDsh8YoPPfdd9/hX//6l3Gds9Qhrw9d6W5RbYli3lzMX78DD645C6N+8QI2rPkWK9a8i7f/MBrX5X2M7z/4GHe+loyUPT8u7H48mH7BZQM5mHn++edPsDBGnrWtxdz/ZeCDjzrhrPtfwuspS7Fg+Yt4aZwvJi94AksWJuOtrdZ96qF6Ao6Ub7Fr7kuYtbkc8w60hY+fLyLsVVXUVrQO0SzbjrJVr2Pewq/x5sp9SNtfhXJrAGgPzxzdPtuR8tUWfPJ+GWKGnouLbr0Wv7p9IkaF70Twxy9gyZI0rCuy9MqjIm+N6mvSsX/HWrzzTQB2BY7Br3/9K/z2dxfiyimdkZg6F+tnzMDf5qZjRT13U7PgqIVP/npkL3oVTz3yIh556XMsKtyHnSWVKOVUnPMwwqAgugBpcXJ+U6knx8E/Ekg4DYPPPg+/uvk8DI/uhO6V1QiqdRgb6kSha9yVE8n5Qga7sbwdXaPu4qhwoHSnAyGh8Rhx9lAMHt4DAYHx8McYDLN+3tSJ4YgLyEfm+kzsOdBw9ypd+Qwk4xQOrU9axAwka5BLnycpPwht+/RG30tGod/gHuiE9ogMnooR/dvgzF55qPUpxk7r+a5p9ufbGkhUrkNybgUW5PVHu4hAnBpfiyDLIq+2X5abbWgVolm5OwUZi+Zi5dYCrCmPQ41vAMI5kvKAG/HHsGbrVqxaWYDFa5Mw8teP4vF/v4mnn/kbHh8XhnOSX8WmNVvxSYZ1i3uyslVtNVCwBjt3puH1jAEIPf1OPP/c83j6qf/gub9cjds7pMJn9Vw8+95GLEq2LIDmxGH1TAWWaK77Ai+8uwRLMvaiHBEIigj+kcuLHTStGboCaTkwL08cg6BYoNs0jL3sLrz0wq34zahe6F9SbolmLY5eb8c9uGLKRx99ZFbWYGEBumQbGmxTWR2E3KKu6NmtL265rBt6tHPugB/C4vtgzBWD0a93JIIOHMDBqmrQX9PQcTJd44ywp6AzUOnrr79uWP5mSYh1b3bC0Emn4bzfnIJOh+oyBMDRtgPizoxAx64hiA+07tPm7o9K9wIZ3yKlPAopCZdiZPeOmNapEiF+DlRKNH+SFiua5uFwWDd3+TdILyzAjLLz0a5tEn7WowptQ2pRYRcDo9xS771tMGD86Zjy0ET06R5lPU7kFHTv0xFnjQMiYitQZA2UrcG9x3DU+qAoMxx+jk649pohmDDelccVj6jYYZh4eV+cOszqIDJ3I2e/1Uk59zYLPv6WNTQOief9Ds+9/hD+cPVUjLc+ji+vMh37kc8/U1Fo2TAXjekNmZmZzj3ip2GP7po3PjlYLJ3RqQyu4ZztqFGjzFJeDSUgNAxxAwaiY7dEUC/rhw35hEagXdceCOnSFZXx0YgJ8Df7T6TtrF3M+WXOhdM7wVe3rU3OgSa0Q5R1zyVY/6xzaVsWXuZ7WJQdgacD7kef3n1xXV/rOW8Ol+ihZtcgL7sYc2eUwq8qDFOntkP79kGorqpt8MCitdFiRdM8HBWFOLhhI3blVqOkx1j0SOqKEXE1iPB31M1n2uHuqA4Gqjqgx5DeGDWmM9q5nvzqA8gLjEN2/37o3C0OA2KAQA9eLYc1ei/37Yzotr0x9fROGFg/dS6gIwad0Q99hlJIay2jtNp4pZrn9Fq/xccHjvDOiEyahEkTpuGqiQPRx9oTblkXR7vMjKRlZRumozCJncEe4nhUoLqy0hps1qLG5CicmHTSwueycmvWrDHLcjEPk0XUTwRfSwjD2rZBaESEGWge1qLKMlQX7UdoTDg69OqBNmHHisQ9NrQ26aalsLOgO13KXKLMLaw2IjwEAb5+CKypQlnuVmQvfgtrP3oNH6yvwDK/qejUoSPaW90Ag9WafMqIJ8lRhZq877BjSxo2HEi0zmEnjOoThMgwX5RxlMlHyhwsjkYLFU3eeeUoKi7AnE8cKNwXhsvOjUXPHsEoLnegxjLZzHNvB0KtkWiHtggLCAKD1cwFqc4Ckp/DlzsC8Hjtw+jZaxB+aalApAdTNX39/BDXrxc69utttdMH1jP+A3zao9shrGMi0KUDoiLCQC9U85ziut9S91/OWx3EgdJKMLzHMo4NR7aDokmXINMavvrqK9OBnwhN3b+1NGhZck6QAVhc1uu8885rsnVYD+TuxtrlsxHlU4KzThmImKgTF03Cog4XXnihEU8ufP39998797hPVWkednx0K179029w7sPz8eW3uxESXIOggHrdcDM8NJUHS5Dy6kvYtnIRcMFERA0ZhJjSKgRW1Zh7Wvf1sWmRosn0g9It87Bj0RfIjE6CT89B6BMeiNggB6otwfSkm/NHcCLDGo2aSiGVpchb/zFWvPoAnnvqLby6LB9ZwQPRNv6HakAeC16ymukXFAj/oCDL5uQ/6zWkqhJVmZa1VpmHpH590e6YFVyaEtqVlqVb63IxHb0H4rlmkAfds0w3YeUXltVz1+XmOsoHWSjJ+B6f/2cmvpy3EZtLDo/UFYfDwQnnMVksYOLEicbSbPyiIrwH9mF3QRFm7TsDkbH9cM0QoONJVq3jQIsufdbB5aLWrCrF+6YhdaF9/IMRnjgavUaNwTnnDEJS8C6EL3kHXy1Lwdpc6zGq+ak7thEp24maPSuxOXAoipPOxZmnxmNoEF3dISatLdDfsohDIhBsjeVd6JY+nJYpmlUV2PrFV0hZshQBY4YibnRvRKAGARXVzXBXnjhVFQeRvehpfPH2a/jDWynYsmY3wquzUVFW7jzCar5t2v9DQ0oOFmLFmlUoK8rD2UP7IqnDYXaobWEuHgM8COeq2Bm6g/nLayyFPLAcGz5/HdNveQLPv7IQiwqAfPf70FYDByNcdHnx4sWYM2eOCaxhDVuKZ6NTfQDImofM/RVYFPl7xHc7E1M6AbEnOV/I6FmmxbCQOd20FEymy/DVXfxDotF5yiO45NEZePWFO/HH4SXouuTf+OCTZXhueTEKmyM8Pv0LlGyZjfVdpmF/73MxxJLEQJSjtPAgiqzfX15VjYqSQpTWy9CxcZfpEbxHNN01sYo3wzftI6S2H4+ssX/GlFM6YpxJao5GWLC/NZryRVB4NELDrdGjM9m58UdS7vzEumPqH+kXHIH24+/D+Xc+hGcfuxQXJO5F5Ky/4d3Z3+H9LbUobaqUQrfOLY+pqxBzOFtRUpyCDwsuRXbYhfjlEF8MZ8TDCeNOW0jdce4efTTY+V1wwQXG2vnwww9NRKdb5K1C0bf/wkN3Tsf1f/ofFtUUIdcaodODoQ7mx3Aw8t5775kAGhZUZ9oPLbdGo95NUF1RgJUvJmP36hKcdc0w9BvZxbnn5O4VFyzNeP7555tUJd4zXOPTPer9dh/rAUk4B2dNGI1fTIuDI2c7Vi/bgJ3lTZ8zXJCxAcvn/gdz//kr/PO2K3H5xdNw6UUX45Ir78FjX+7Bh6vSMe/xK/Hck//GA3NzsTlXo8Aj8R7RpIlVW43a4n0o2JOGLSnJ2LR5M5KTk7F500akZewB85fLdmxC4ep3sKGgAqvL26IgeRuyd29ESsoqrMssQuaBKmSlrcaOlCKk5lSgoprO3MbGB46KIlTs347M9C3YtMnZzs2bzGtGViFyy3xMLtSh320Jl29ACGL6W6O/ix7Bz++6EbeODMMpefOwbPFqvLM8G7lMLm0KeG6rSlCVvwN7Mqz2bmZbuW02W/ruXGSX+qCyti568geqgG2rsCc5HbsSLkJo33NwansHoqy76sQ7qLrf4CjLQ0lOOtLTUrDRdf6s65yyJRWZuSXIr/A5aZFiigPn1GhBMBjI7SjainxUW+dq0/ZspGaXWw8Ri5gHIsBqzMm0p6XC1B6manBwQsFhxGyj4jrpNduRk7oeq7dYtpNfJ0w5IwE962WxNMa14T1D4ec9w7xNtwdah36768loh65DhmHq1L4ID6xCzr5slFlC3NRB/SX+MShBOKLyN6B629dYsXIlFi9fhdVrk7Ftfzn2FZZhf/oaZG7fhi1W/3igojGGGi0Lr3LP1pYXonT5v/DpE1fg3ClnY9SY8Zg4YQLGjjoNl954Fx5bWIFZm4uwcvHnWPL0z/H2jcNx/jln4tQRZ2PChOtw95tr8Nr6Isz9x/X476O/xm8/3I7P05vmNq3dsRDb3/8N7v3luRgxZhzGj5+As8aMwsRJk3DLs1/i7TTLYKlwHkwO87v6AwHjMHzi2bj5+r6ILNuDLd+ts0aiFSeVG3csarLWIuuTu/DE7Rdg9NhxOMtq7/gzx5jthsfewosbgJ31XDZ1D38+lr2bgZUf7MeE87ph3MWMnq37O062g6pO/hjrX7keN145BSPOGGfmwM4cPQJTzr8Yd7+1FrMsfSs7yUvH+UyuoMHC7SzUzZzB1NTU41cJij8D0ZPux/Pv/wMznr4Bl1mDna4l5abDa+pOz5vgfB/PJwckDALieWZhiYYUMDg+P3Tqu/43A5s/egPFF52NNj+7AgOtzw5fx6bu2JORAd4zXJuVdYwpoDt27DDzm+4vWl3vyQiPQtuOSfBP7Aq/hDi0s362m5X+Tpi2o2/B5IcW4uUZX2Ph119h/vz5+GbJF5g769/4v6mdcPXpPTDlkU/wuz/8H/55flsMa98iZ/BOCq86Iz6+/vCN6IDYTn3Qr/8ADBo0EAMG8nUw+vRIROdIB6Lb9UTkoPMwZuQonD26N4YOGoC+AwZgwIBe6NY2DAlhfojp2BMJXXogKS4YMcEn273/BEFRCI7vgcSe/THYtHMgBg4cbKLvuneIRnyIJY1HPfuuRzoQMUk9cfqIXgiODkFRRQX8LGvUzQJjDcYnIAwBbbqhU/e+pr0Dec4GDjLt7tm5LdqHWX9SvfbWFKYha+lMpJUFoqj7SAzrnYABVuOO7JBOtIPyCW2DsISe6NHbef6s9gwcPBj9uRSZdR3bBDXezcsoWubiMY2AxblZ9/VYOAJC4RfVHR0ShuKMYUnozNQHRnFwn/nvicEOmdYY588I39ulLi4zDP0DgxHo5w9/H38EhoQiyLoGdS09+l/NIgCs+kOLjKkl3BiF2igcmlKwWlBThBprkJqW58D26LHoe8bpGNknEGbGtGY3sH81Nu0qwoacI7w7JwELZHAAQMGkFX1C5Rj37kD6+i2Iiom17vNeiGjKOtjO8xUY2R4xXQahV7/BGDx4kFkWsW+PUzB81DAM7BCKxLgIdBgwFr37RSExNtC63j5uz4y1FnwcDaoJZQNqa1DrqP1xySmro/G1RNWH0XMOHsP7hI+HDwICqlBVnYlFf74FS75eh4zLZmPIuNG4qQ8Q2lT3qdVGh2mn40c3nY+vq3M8zgO861OUrP0Uk74egH2RI/D1HYPQrU0TBdlYjXTwvFnt5bmrD5dXMm2u197d897EppkvYetZv0f42AthDUrRpjEVnefPslTM+XN+5MIMnqzG/LiCCk3hjVj87Cy8/dvFCL33Lgy57xKcaxk2ccdQWEbOstrLiy++aASLtVC5HNuxoWWRgpS5X+KlS2ah8vzLMfDJOzDF+lriCeqcK7jknnvuMYEz//jHP0xqDC0bz5NtPXur8Z9zX8OKVT5IfPtfOGNCB5x1jGvOUoVcsJrzfzynzIttCiqTZ2LvwqcxI+x27O95KW4fCnRyZZikv4vStO/xZOXN8G3fF3dY+0w1sJOE14f3DK8Ra+WyNm3DrlMu1r10Nxa88S42nfshEs+5GL8dAMQ0RkHfBlONigNr8OU91+L7nUHY9/N5mDyyHa5IdO4Wh+FFlqaz62Tn7RdgVic5bLNuXD/rr6EYcb+/Pz/3tzb2YMHW/mhEhgQi1DLvgsOjEWYNQ5tMMIkPhcYalZt2HL75Ww319eFc6tECa36gdNs6LP9snvUghWGIZVGHcmjfJFitsMSC7fU7anv9TCqm0ajaUmDTa9hZWIRNpzyIPiPOwUUdXIK5z1LTD7ByYzLeTwZyTqjOvPOM8PzRqjmiLXXtoWDWHec6f3WvjJOPQHhYCO0iBIeEIywSCDN3+eHH14dRtFxXlWkoXJOR1gOT2JsSuispksxX5MYgGb4yaIauPgoNS/zxMwabcD9XQOHGeTS+FhYWmpU4mnTc6ygGDizD2lkv4o9XP4ZXF87D7P3z8doff4F/P/E6XllnWXdHKf/ESktML2HhAs4BnkjFn+NRWbgLGbPvx1vP/AG3PbMIz1nC/N6ff4s7f/VL3HzDtbju59fhml++h1ueKkaRdb/0tAbJjWW4817hIICuZt4rHCActbxeSab1vLyJt5+8B5ddeTWuuuZaXHvtFdb2Czy5IgCZ45/GxDNPw+XWeKIxxPzEqBswV5YWofSgtVXWqozeMfAi0fyRWdEA6Do7iJLyyrqQ6tKDKLPu70qPTkDx77GEqtayWCoKUZSXhV2mU9yHrJxMZOWuwqK1W7FsayV6WVbPpIGhCA48mXNwLNz4uVbHXFtTifzNX2P1rGewaEsGVkWdgbIDFfDbv9dqcx5yVizF3vlzsHRjBr7LB4pPaALW3b+x7jjX0T60TKuzrY4rA5m7spBnXe+cfduxO60Yuw6woMXhxx8J5zb79uuH+Pi2Jp+QgUdNCUWPi2GzugwT5bnx91KwWcycwslCAGvXrj10DF/rv2eQFgW1SVdqcZRb92cmMtduxKJPNmKPdQ9WxlsDorXzkbZ8OdZmO5B7hDebIs42fvPNNxgyZAimTZvWeG7ZelSX5iN/06fYvCUNi/a3RW76ZpR+9yq+/HQG3v7gI/xv5kd4d1EhvsroiS4J4TjNGkDVryNwsnBOk9MGvHd4LY96z1QWWkblemxYPt8aRMzExx9/jI8+mGlt85Dm0x+xl9yKMad2Qt8Ih2lbEw5/jgEHzCGIaF83bdUhyh+RHhNw++N97tkTguq4HV/d/zMs/GIltl23GMPPHo07+v6QduIxDmwBNs/AE28uwXOfbzNWnb+P1QlanVXCKRdj0Nk34KIxfXFq91BEWtZcsxd1dlJTcRC7Zt+DebPexvPzSrD5YCgcMUloF+pAdGAlqi3RqsyPgH91T4z9468x5dYJGGe19+TWu3cTFmyvXINdSz/H04+9jy8WpiDVuqurLWuz46lnYeItz+CC8X0xrdNPzSPXdfSbU9OxePFSfDHnfzh70kTceuttzr0u+KjUlXXwOQn3LC2SN998E5988olxB9O9x1fOpRYUFJjOlxYkUzNoBQcFBZn9rkeVVig9KnQhU5QuuugiN9zJJ4jD+jur85G7Kwe7dhag3M8XNdbf56isQHBMR0R16oP2lhi5Oln+bbS6uKj0xo0bce+992L8eFYCbnx4T5bu24Ss/FLsLQm2OjPrvFjPeo11mniueM6qqyMRHBaHxP4JiIsIAhNdGusRYqAT/0YODr744gtMnjzZLCV2GNVcm24ftu3OR2ZuqfX8MgKdxTd8ENGhJ+I6d0KHUEYweBIOiEtQlLkNxRXWnR3fD9ERASZuQPyY1rEItaEKB7Nz4BPaHlGnnIdeXePQK8pzInSISmbEp2NVag6S95YhNCQIIYGBCAwIR9KYK3DaBedgXHfrBvav6wTqOuzmx2FZmcXbvsGenHyk+w1AZGx79LIUMTzEH77+QZYV7A+/4CSEtj8D46YNxfi+8Yizvtc8YxLrrNRmo3jPPqz9fj8qrE6y/ZA+SIgJRcc28egybDK6W9e7p9W5/+T1tkQ/omIXsreuwFsfzkZu/gHEtWmD9K2pSNm2A3m+cXAEBRtxsC6DBf1X+7F/azpWf7gFNb37I2HyCPSMAKKPY83QimTUJd2ztFYYuUs3X2ioNRCxOntaj3xl9RnmBdKSiYmJMS5BHsdX/puLIlMsWVmHRegbH+u8+vjB4ReOsJgEtE/sis5du6BrZ2tLTELHdnGIszr8IL8f7koGU82cOdOIP4Nl6Jplexsd6/zwvguK7oQ27bshsWtnE53bpWsiEhO5WZ9Zr0lJ7dGlUxQig/zh7xTSxoSDGtbTnTt3rqlRe+QC2g7fQPiEtEFsQickdeuGbt2stpnXbugQF4noAFZ15pk+Mp2r+WDsh6/VzpCYdoiKb4fYUD+EWv2NZ3oa+9NKLE1Si+qKMtRU16A2IAx+LBdlB+c0rSRLkMoqqlHhjMB04RcYjACro6Y17PGmWrdJbVWp6fArqp05kq55xUN3kNVQH38EhViibzWabW6+x67aal8VysuqUM0yehxgsJO0LDL/oDBwbvtY19tRXYHyxX/F3I/fwm9ez0BuCUzFmpLiYkR26o0x987AZVMH4qpuLmv1xC1NtosuVVeagitClvOZdLs++OCDZm71scceM4XlGWBCy9JVss38XbRYrI3f5Twv99uBzz77zAQysWjEXXfdZUTFPhHATQM9A3/+85/N4ODiiy/G0KFDzYBGtEzs8aQ1NaZTr+s8g8IiLUuOHaizwzf/9RQOq3O3OhT/EISERRgrov4WERqMYGsU78vjnN/wCFRFq4P2DeT5i0aksXiirE6CVk/9Nlt/Q5T1t1jnl+kxzTlOZTIOi0OERkYi0mrLIavM+ndY0PGvN6ODgxNHo8/EG3DDzbdh0NDhxl161pln4M7bfo0LTmmL3pbB1BiGCsWOLldaJtxomXCjRck2u1JP+Dew86UVyf185cbv8JWWKX8Oj/X02JfuZLoquewXrWOm8VDsW7pgEnoLWI6Rgxeu4JKVleXcI1oirUM0j9rR1X3YnB37j3HHJcMjPOe6MZyIUjSGujQA987jMY5julK3s9H3wgfxu98/jJ9ddRkGDhyIW27/Hf543524YXQCTouzrMIjf4Dz3+aF//nJX3B86OZjEJApOG+JIN+7G8Xb2G7HhsIUDM7r0e08ZcoUM9faWuAghmuCcpCzevXqBpTWE95I6xBNIdyED0RCQlvLWupsLLk9e/YiJyfbMlF/cJ3X2XSMfIlARGQYgn38ERxkWYGWJRpunqhjW7UtEVpXXPKLc5lcsJnzma0FiiYtTVrWTAfiwIGDHU9b/6JpkGgKcRS6d+/urBK0HZ98Mhv78wqceyyrzlGGmoPp2JO+DEsWrkFaWRZS0ldi7bzvsTK9GDllPiaC07O2X/PB2rJMjWFUr8s1S7dxa4J/L/92BnUxp5bznMzFFS0PiaYQR2Hw4MG48cYbTXAO00Oysy1r00V1Kg6mvI9nbvwTHnr4FcxCGj5f9h88f+OF+MdbS/DhdqC4LsanVeBKuWDk6NSpU20TlNTcMCJ20qRJxtrmOaG7XbQ8JJpCHAVaDkzlYEUbzjEywCUvv7BuZ0AsAmL6ov8Z03D+5dfiptt+g1/84ir8/KKpGN8vAUmNnERvV+h+zMnJMUXZOahgHVNGjraG4J+jwSLuo0ePNqLJ9Vklmi0TiaYQPwGLDtBFy/kqFh1fvmyJiRK1ukeE9rgY1/35H/jnB2/ixWefx2uvvYv/vPIKHrz8FEztDIQdoyZrS4GCyUo4FAlG/rKsHJfM8nRQkqdgFC2Dx5hOxMpOLHMoWh4STSGOAavZcFkyFlLnih0VFeXOPcei5QaA1A9uoTC8/fbbJv2F+Yn2KCzvWZjbS4uT+amc62WAlAKCWhYSTSGOAfMk6XJkDh7rxXJB8eO73VqupVXfimS5vE2bNpli7BxcUDBaO3RNM3KYwVAMBuL5kWi2LCSaQhwHuhyvuuoqJCUlGcuKLsnWDOvL0vJmegVL1fXo0cOU9WutAUBHcsopp5hAMi6+zXultbqrWyq6y4U4DnQ/soYqxYEri7T2dAIWMvj0009NEj+jRVlYXtRBgeTcLjcu6/aTS4YJr0WiKcRxYEAQc/DYEXKJq8zMTJOXWFxc7DyidcFI2S+//NLUx+UKK3RFih/gPdK5c2fjluWaqJzXZA6raBlINIVwE1pU1113nRHLV155BTt37nTuaR1QBDhgoLXNJH4WgGBKjvgxdOkPHz7clNbj2qKt7V5pyUg0hXATCsSFF15oiqpzwWjmbrYm1xvzVTmXyb+dwVFMx6EVLn4MC+xzhRreM99++61ZUFy0DCSaQjQAut5GjhyJM8880ySwz549+9CSXS0dWpqLFi0ylhMLlDORXxwdzoPz/DB3k9WBWI9WtAwkmkI0EFpZTLFg8jqjI5mP19LnrLj2J4NauHC2q1oSXbTi6NAC5wLhLPrAoDEWgnCtnyq8G4mmEA2EQUG0ItgpUkRofTHRvyWTlpaGBQsWGMtpzJgx5lUcHxZ8YKAUc3tZVcrdpd6EfZFoCnEC0MqaNm2aCQ76/PPPsWTJkhZtSaSkpGDOnDlGBLj0FwNcxPHh+aJngtYm19pkxLHwbiSaQpwgp512mrE46XpjIjuFpSUGBtH1zEAWBj4xlYJzupzbFceH7lneJ6xHS9FkjqvwbiSaQpwEdL3dcccd5v1f//pXI5wtCVpGixcvNvO3rHLTtWtXVbhpALQ0mXpSUVEh0WwhSDSFOAnopj3nnHNMtSAm/a9cudKUl2sp7N+/36yVyTk5Fq5n2TzhPgwIonVOy5wDEBY7EN6NRFOIkyQ0NBQTJkzAlVdeadIxXnzxxRZTLchV/YeW0nnnnWcsTdEwWMSd+ZrceD45qFKFIO9FoilEI0BL84wzzjCRtYyopXXm7VVgWDuV1X/ojqWbkUteqZjBidGtWzdThpGCyblhiab3ItEUohGg+61v374mf5PWGEXz66+/9trCB0yNYERwamqqWbWDiytrLvPEoWAOGjTIFDnYsGGDRNOLkWgK0UB+anVELo01ZtQIjBk9GmGhYdi4cSNmzpyJ3Nxc5xGHL+JsJ+q3i8UaPv74YyP67NxZb5fuZ3Hi0BPBdTYZhcxIaw1AvBeJphANxKemGCjaga0pG7Bi5SqsWb0GqzamY1PmAfgGhWDQsKEYfupw48pkrdb6+Xl27Sxd7SooKDC1ZblxEMA8VLqdVf3n5OB6o3Rvc26Y85qKovVeJJpCuMkhW6xwFcqXPIF7f30FRo4+E2dPnIRxVz2ES//8DT5NK0JkWAQuu/JyjD/rLFPw4LPPPsO7775rIlDtDDvzDz/80AQzhYeH49prr8U111yjxaUbCRaEcEXSssKShNM78XvUwvleCHEMfFAKlKUjbXUyvvwuFzlV4UjoFIOk7oGozCpEzvrdKIlpA99uXTEoJgjx0ZGorKk11htdtLQyuPoFrY6jwcIIu3fvxrx588yxrLyTlJRkBKwpqa6uNiXeuBoHg1Ti4uJw+umnm6R8RgYTum/lUjw5XEUieL7phaCIMsBKeBcaQgrhLhW7LXPsK3y8vgKv778Qv37ov5j72Rz873/P4tmrO+Hc3I8w+8MF+NMHqcgsqEBUfAIuu+wyExzEVS9mzZplVkWxW/1RRvm+8cYbpm2BgYGmtixzT9lmFxLMkycgIMAEVXXo0MEsYs65Y+F9SDSFcJPqA77IzQxFr17dcckVgy0LkxZgiLWdiiGnDsI5U+MRU1uAnNTd2FtZbb5DsRludZSTJk0y84N0yz388MOYO3euqUfqSVj+7/XXX8c//vEP004WL7jgggswYMAA5xGiMeGAZMiQIca65Oo4Wi7MO5FoCuEm5dUROFjTE8MH9cIVo2MRFejcgWDEde+NEef1Q6d2wfCzxLDc4YCrfHt0bCxGjBhh1uDkAtYMDuIaiwwQ2rdvn3HXESbBU7ya0qqjm5ViTStnxYoVph10yTKykwXoWVeWbRSND12yDAZiPVoOWDiHLLwPiaYQbhLSJhbthw1B+7YJ4KzkYWn+4VFo17E7fDt3gSM+Fu0sAQxw7iLsMGllXH/99XjggQfM/CVr1b788stGvAjdoS7hbCpYqYirsjz77LN46aWX0L17d/zpT38y1X4YpCKanvj4eHOuy8vLTR4sX4X3INEUwk38AgMQHBVh3Gx+1r8Pk7ai/TiQsx1tEmKR2LMHIq1jXbhyIBlUw3w9ukHHjh1rBIsixmhVzicuW7bMVBNixC3Fk4s9M3DoZGHUbnJysimH9/7775v6uBRtVqkZNWqUSSnh2qCq9tM8MACIAV4MDKJotpSSi60FiaYQjcDeHalYt+obdI8Lw9jBnSzB+0GAjrQcmXJw+eWX45FHHjHznBSxP/zhD3j++edN2ToGClE0KbYnW1GI36dgzpgxA//3f/+Hp556yggz51j5bwYpieaF0dB9+vQx9wVFU2tsehc+1oNpzxIlQjQbfATccYnWHec6uu61zHqThs/f/hSz5qbglCt+h5HjT0XvcCDoKENS5uZt3brVBIJwTnPTpk2m42RaCt2zrF3LABFamZwH5RxYZGSksQJd4ss5UIoql5xiagiPIUxT4aokWVlZyMzMREZGhvlZXMuRFit/Jl2DFGrOYar4umdg+hHntRcsWGDmNu+++24MGzbMuVfYHYmmEAYHHFWlqLSE52B5DWosA48axcfD188fAaGRCAr0RzD9svUpTQcyZuHZbyMwc8dg/Om63hgz4KcDaRj4w3zI1157DfPnzzdCRsuTBQTorqPwUeTcsTBpLV599dUmRSQiIsKkjuzZs8eIJa1Lbtu2bTNrfjIqdsqUKaY+rvAsdL/zOj3zzDOmVCGjl+myF96BRFMIC0dNFSrX/AdLF8zB43OykZ5TgQhLIStLihDddQBO+eU/MXlsL0ztCPgfsiAdKExdjqWPvYH0vqcDV16N8zsFI7F+BNARUBTpHmURA1qFtBiZv0fR5FqLdM9SULnCCOc9aWFyZQwubn20It9cborRrhRNuv34nsUJ+HnHjh1NwAlTHPgZXynQwvOw22VA2Jtvvomnn34al156qXOPsDuqCCQEcdSiZu9q7MpIw+K0g8gvqUagvw9qKssRHNUW7U85Bz26tkHPSMDXeEkdqM5diq0rN2LZhmC0OW2oJXLd0cGyRA9lohwFiiAFjoLWs2dPExjEgBwu7kyLkC7YhQsXmnlNznvS/cpjGKgTGxtrjnNtTJKn25UdMIWX+3kcA4wGDx5sgnxOPfVUcxzFVIE+9oHXmVWYOEjiteL1pNdBJQvtjyxNIQwOOCrpni1H8WHu2Vr4+gUgIDQKwUE/uGdrysuQ8txtSM6vxo5z/ophfTpifLz1nbrdJwQtzeXLl+Oee+5BYWEhnnjiCZPbSSuRVibdevXho+t6fNkJs8Ol5eqyXimSEkr7wkhmroJD0aSLnWUL5QmwPxrWCOEM6fEJDENQRBvExbdFQkJbk4SekNAO8XFtEB1abz6zaAtKNn6ITUGDUTjgZxg/qiNGugSzdA0qd36L+allWJ1ljnYbzmO6hJACyA6UFiLdrkxToHjW3xjUwzZy43uuROJy1fK7Ekx7Qw8AvQt007PAxJGDImFPJJpCNMA+rK2pRv5372LT/P/gu/Dh2NdtErqXliPUEt6yg4XAmrnY9t3n+DS1BKvznV86ASicjJJV4nvLxSWanONmeUUGgAn7I9EUwk0OZizGuuem4onpf8f1Ty7Df//vNjx/y7m46LxzMGnCWJwz5QKMvPpr3Pe6L+I6Av37OL8oxFFgkBZTf5iCwkhniaZ3INEUwk1qyotRlrcDBWiDg9H90c63CDFFG7EjMwOp27Zhx87dSDvYAQeD+2Fol0D01tMljgEDf5iXy/lo5ulyE/ZHgUBCuElt5UFUHMhBUVktDlb5wddRl0tZ9wDVzYvW1oYgKDQcse3CEeLna8rtuQvntpj0zkAgVomZPn06JkyYYNJHRMuEJQ7vvPNOk1Z0xx13mGhnzlcL+6KxsBDuwOCcQEsI45LQrnMP9EjqhqTu3c3GFI/u3XuY1549O6BLx0iEUzA1HhXHgcFaTDliMBeLUjB/V9gbiaYQ7sD8k4ZyIt8RrQpGSffq1cvk7bJ6E8sfCnsj0RRCCA/hEk1G0rIGsUTT/kg0hRDCQ7AQBd2zrOTEerQsnyjsjURTCCE8BCNnWYyCdYGZcsKcTW7Cvkg0hRDCw7DiE4OBWC6RLlpG1Qp7ItEUQggPw8L7LHTAV5bUYx1iYU8kmkII4WFCQ0PNqjeBgYGmpB4L9gt7ItEUQggPI9H0HiSaQgjhYcLCwtC3b1+zpBvX2FRJPfsi0RRCCA9DC5N1aGlxMnpWomlfJJpCCGEDKJwxMTEmGIjuWQon11gV9kKiKYQQNoFpJ0lJSaZg/9atW7Weqg2RaAohhE1gkYOBAweiuLjYzG1KNO2HRFMIIWwClwVjFC2LG7CAe0VFhXOPsAsSTSGEsAku0aSlSfcsS+sJeyHRFKKBHG+VTC2jKU4Uimbv3r3NnCYrA8nStB8STSEaiA/ygcIV+Obtl/DCI3/C9L/+DX9560u8sLIAew7WHFpGU9opToTY2FgTQVtdXa3UExsi0RSioVRuR0HyHMz81+P4658ewR8evB8P/+Ul3P3WWqzaUew8iOIqRMNh6km7du3Qpk0b7Nu3D/v374dD7gvbINEUwm0oiBuwfFYy3nrFDz0uvhsPvvJ3PP/yr3FdnwPoPfPv+HbBJszPAkpr6r4hREPhcmEsdOBaY3P37t3OPcIOSDSFcJtSoDYLmXtqkVHcB8Mvvwk3//L3uOnGe3HH6EhMyvsSmemZWLjHOrLa+RUhTgDmaiYmJpplwrZv3y5L00ZINIVwl9IgYFd7DJs6Bpf+bTJ6d7H+bUhCux6dMXoKENehFlWVCgYSJw4tzV69eqF79+5IT083BdyFfZBoCuE2wUBAO3RM6oyB3aLQJtD5cWkGMqujsaLzeHS19o3pAIT4OfcJcQLQyuzcuTN27dqFHTt2qJyejZBoCuEuoZZoto9DaEAAIpwfoXgrsObfmLMN+Ef1vejWvT/O7wqEBzj3C9FAaGlGRESY6kCsQZubm6vUExsh0RSiIZh8EmsrL8ber6fjs79fj1v/+DZeWJiNyrBOiIuJrDvOolYuWnEShIeHm1q0vr6+xuKsqqpy7hGeRKIpxAlQXV2BA2lfYdOKpfh4dQ7yt+9FZEEqcnJ/yKvzbWDOCTtHWhncCF/5mWidBAcHm4AgrrXJYCAuGSY8j55IIdwuQ/DDcf4hUeh8wVO49q9v45NXb8dtA7IQM+OPeO3DRfjXqmocOEqd7eNFQLJzZEfpEk++52eidcJ8Tc5tco3NjIwM5OfnO/cIT+L3qIXzvRCtFMuyc9SiJm8Lsretw7LVm7FuQzLS0lKRvGkj0nfuRZ5PPBxBwYgMoAXogI+vHwIj4hHZYRA69YtB7K4NyF+3DCure2F/aDec1T8CbYIPjwaiELKmKAM7XBvdbszF45aSkoINGzZg6dKlKCsrQ9euXU3tUVoYe/fuNcdy27lzp/k3YYcqa7RlwmufnZ1t5jWLioqMgHbp0sW5V3gKH2v0q5kX0epx1FSgYvHj+PKTd3HHO3uQmVuGgAB/M48U06k3zrh3Bi6bOhBXdgMCjqJRZSuex7q5r+CWb4ejoOsUvPbERIxuFw5XgK2L5ORkzJgxw7xSDCl4LtFjJ8kOkikGLKHGtANWhaHFQcF1ParcxzJrV199NaZNm2bmvlwuXdFy4Eon33//PRYtWmQGVNdddx3OO+88517hKWRpCmFByXFUl6M6KA6B7Qag98BhGHn6aRg2ZCBGjB6D00eOxoDOEegYWn+ukiJW948ARxaiq/bgrR0dsD8kEddP6IYu4UdKJlBSUmKE0c/Pz0RIxsfHm2APvkZFRRkBpdVJgRwwYAC6deuGDh06mP0s5s1XCikjK4cMGWJy+fz9/Z0/XbQkeC/QRZ+amoqvvvrKXG9uwrPI0hTCbX4QyR+R8T8Urp6N8787FTmxo/DlzX3RNdZV/OAHKJo5OTnG3UYXLKGAEhbn3rhxI/7973+b42677TYMHz7ciCUtSVeuXk1NjelQKaisUSpaNi+88AIeeOABPPzww7jrrrucnwpPockQIdzmp12g+cnfY8H7M9HGPxinDh6C4KAfCyah5cCaoj169ED//v3N1q9fP7NxSSjOWdEdS+uxY8eOxkXLffWPowXKf3M1DNHyoQciJibmkJdCdo5nkWgK4S7VJUDhNmzfvBILv/kW33yzGEuWLcDS5R/ik9V7sbqiDwb17I5z+wOhP/bMGmhVUjg5DxkZGWk2vufGjpEuWx5DS7L+Z4yidR3PTpSvFFfR8omOjjZBYeXl5Sb1pLS01LlHeAKJphDucjADWP8SXvnzTZgw6RxMnmJtE87BpLOuwD/XxqLoF3Mx5ZwzcXkiEHECFYEY4EPXK6E1QXes69+i9cKBU58+fUygGOc3JZqeRaIphLsERAJxA9H/9Im45OILcdGFF+KCCy7BhRdejvMmT8K409ugdwc+VHXus4Y60Vxut/qvcsUJiibd9BTNrVu3SjQ9jAKBhLAJXGz4u+++wz333IMDBw5g+vTpmDBhgoJ9WjnM1Vy5ciU+++wzM6/54IMPGstTeAZZmkIIYWMY8MUAMFqYjK52RV0LzyDRFEIIGxMQEIBOnTqZADEWxKAXQngOiaYQQtgcRkozX5fzm3Tjs1qQZtY8g0RTCCG8AOb3MneXc5yZmZlamNpDSDSFEMILoIuWVaAomlz1RKLpGSSaQgjhBbDeMIUzNzcXu3fvlmh6CImmEEJ4AUw9YvF+zmmyqL9E0zNINIUQwgvgnGbnzp0PzWkKzyDRFEIIL4D1humiraioQH5+vioDeQiJphBCeAlMOeEC5FwcnXObctE2PxJNIYTwEpivyXlNrnqza9cuU+xANC8STSGE8BJYFYhpJ7Q4Oa9Ja1M0LxJNIYTwErg4ORcq5/zmzp07ZWl6AImmEEJ4CaxDm5iYaBamZoGDnJwc5x7RXEg0hRDCS6Cl2aNHD+Oe5dqaWVlZzj2iuZBoCiGEl0BLs2vXrkY09+7dqzlNDyDRFEIIL4LBQHTPlpeXm2XC+CqaD4mmECfLj1ZoqvtACzeJpiI0NNSknnB5MJbUq6ysdO4RTY1EU4iTxceBisJ9KMjYjL25Rcgp80GNpZg+zt1CNDbM0+zevbt5z4Agrq8pmgeJphAnyiFTshQ7F76AuQ9cghc+WooPtwPFVc5dQjQBTDnp3bu3sTS3bNmC4uJi5x7R1Eg0hThRaErW5AOZn2DFwk/w5lepWJ5eiJxy62NVNxNNiEs0SWpqqpnbFM2DRFOIk6A2NxPZC9/F8tWbMa8gBIU+oYgKtB4s+WZFE0LR7NWrl7E0mXoi92zzIdEUooHUeWVrLMXchP2F2zCz4HRUhvTFtMRadAmrRZW1S0FAoinhnCaLHLBge3p6OsrKypx7RFMj0RSigRgjsrYUSF+N3Xtzsb3tBCQkDcLUTrXoGFKDqlqJpmhamHbStm1bU+ygqKhIc5rNiERTiAZTY/2vCF/NLUfaugBMnRiHU4aGo6LaYVmZkkvRPFA4Y2NjERUVZYocFBQUaKmwZkCiKUQDqc5dhz3LvkBqWRQOJgzAwIQwdI7xNRamCQDSfKZoJjp16oT+/fubSkG0NiWaTY9EU4gGsnPBAmx4/11UDkxC1LkjEQ1/BJdWmH2yM0Vzwjq048aNQ8eOHY3l6eOjEVtTI9EUwl2pq9xnKeYXyPTvgK2D7sSwYadhSjQsyYxCeFAggv2BoJBwBIcBEUHO71i4K6TBwcFmkWFfX1/T+fE9PxPip2AE7cSJE9GnTx/jppVoNj0STSGMP9UBR1UpKksKkJ+Xh9zc/di/39pyc5FXUIQDNUBNVjpq17yBtHIfrE+YgsDSEoSWZ+PAwe1IzylGXjlQtH8PCixt3V3wg5usfjdWU1NjaoUy2tG1VVRUmK2wsNC42HgM3WxMI+BnPIZl0o78Do8TrZuEhATjnqWbNjw83Ay4RNPi42CijxCtHEdNFSrXvIylX8/BE3OyLRGsQESwnyWiRYjpNhin3vJfnB64BokLLsLzKwLx9o7eSIqsQlxwNSod1SjJzcLB/HyUBsQiauBEDLr097hqwmBcPSDA+RvqYJ3QlStXmmR0CiMtA9fGz7Zt24YPPvjACOMVV1yBfv36GQuCnSGP50brk6tcsLPs3Lmz8ycLIZoDDUuEMFhjR4dlHVKYLAuOVlz9rbamGtXBcahtNxxd27XFkJgShPhUorSq1tpvfccae3L06bB+Rm2tdTx/3FGGo4xw3Lx5M9avX48NGzYc9srPd+zYYazIqqoqszJ/cnLyof2uY7mlpKSYnyWEaF5kaQphsESvshSVFeUoLreE0tJPTg9RBH39AhAYFo0A31r4VxWhvLIG5dV0uvrCL7AaPr77seblv2LJ+zOwdcJz6DL5Rtww2IEesRyTHj7HtG7dOsyZM8dYlS5XmmseqrS01FiiCxcuNMLJAA8msDOR3WVp8nHle1qfZ599NoYOHWq+K4RoHiSaQhgb8XBxaxhl2PrOXZj30n+RfOEnSDxvKu7oBQQ699aHCwenpaUZUawvmtw4f0nL8uWXX0ZJSQluuukmDBkyxOTi1RdNHssgoZ49e5rloYQQzYdEU4iTggE/OZal+QAWvPYWUqe+g65TL8ct/YE29SJo3YHu1uXLl+Puu+82VV6efPJJExkZHx/vPEII4Wk0pynEScExZy2qyw+ivKgaJWUVKGPt2RMYitKadLlq+cp/u6xRIYQ90BMpxElBkQtERMd+6DJ8GPokJqBbBBBwAk8Wg38YdETnD7fq6mrzmRDCPkg0hTgp+AjFIGnSbbjw8Rm49bLRuCwJiDg800QI0UKQaApxsjj8EBQRh6gO3RAXHYboQIdZT1PBAkK0PCSaQpwsPwq8dc5Lmv8KIVoSEk0hhBDCTSSaQgghhJtINIUQQgg3kWgKIYQQbiLRFEIIIdxEoimEEEK4iURTCCGEOAaszMU1blmxS6IphBBCHAOuX/vFF18gKytLoimEEEIci9TUVHz11VfIzs6WaAohhBDHIiMjA0uXLkVeXp5EUwghhDgW+fn5yMzMRGlpqURTCCGEOBYVFRUoLi42y/VJNIUQQohjQLFk5KyiZ4UQQojjEBkZibZt2yIkJESiKYQQQhyLXr16Ydy4cYiPj5doCiGEEMfilFNOwZVXXokuXbpINIUQQohjMXDgQFx44YXo0KGDRFMIIYRwF4mmEDbC4XAc9iqEsBcSTSFsAoWytrbWhLXzlZvEUwh7IdEUwiYEBwcjOjoaERERCAsLQ3h4OIKCgpx7hRB2QKIphE2gSHbs2BHdu3dHUlIS2rVrZ8RTCGEffBzy/whhG1iqa9myZaZs14gRIxAXFwdfX41thbALEk0hhBDCTTSEFUIIIdxEoimEEEK4iURTCCGEcBOJphBCCOEmEk0hhBDCTSSaQgghhJtINIUQQgg3kWgKIYQQbiLRFEIIIdxEoimEEEK4iURTCCGEcBOJphBCCOEmEk0hhBDCTSSaQgghhJtINIUQQgg3kWgKIYQQbiLRFEIIIdxEoimEEEK4iURTCCGEcBOJphBCCOEmEk0hhBDCTSSaQgghhJtINIUQQgg3kWgKIYQQbiLRFEIIIdxEoimEEEK4iURTCCGEcBOJphBCCOEmEk0hhBDCTSSaQgghhJtINIUQQgg3kWgKIYQQbiLRFEIIIdxEoimEEEK4iURTCCGEcBOJphBCCOEmEk0hhBDCTSSaQgghhJtINIUQQgg3kWgKIYQQbiLRFEIIIdxEoimEEEK4iURTCCGEcBOJphBCCOEmEk0hhBDCTSSaQgghhFsA/w+TFvKF3rOxSgAAAABJRU5ErkJggg==)
Maths-General
Maths-
Consider f(x) = |1–x| 1 £ x £ 2 and g(x )= f(x) + b
, 1 £ x £ 2 then which of the following is correct?
Consider f(x) = |1–x| 1 £ x £ 2 and g(x )= f(x) + b
, 1 £ x £ 2 then which of the following is correct?
Maths-General
Maths-
The value of c in Lagrange’s theorem for the function f(x) = log sin x in the interval
is -
The value of c in Lagrange’s theorem for the function f(x) = log sin x in the interval
is -
Maths-General
physics
The relation between time and displacement of a moving particle is given by
where
is a constant. The shape of the graph is
is....
The relation between time and displacement of a moving particle is given by
where
is a constant. The shape of the graph is
is....
physicsGeneral
Maths-
If P (q) and Q
are two points on the ellipse
, then locus of the mid – point of PQ is
If P (q) and Q
are two points on the ellipse
, then locus of the mid – point of PQ is
Maths-General
Maths-
If CP and CD are semi – conjugate diameters of an ellipse
then CP2 + CD2 =
If CP and CD are semi – conjugate diameters of an ellipse
then CP2 + CD2 =
Maths-General
Maths-
The normals to the curve x = a (
+ sin
), y = a (1 – cos
) at the points
= (2n + 1)
, n
I are all -
The normals to the curve x = a (
+ sin
), y = a (1 – cos
) at the points
= (2n + 1)
, n
I are all -
Maths-General
Maths-
The normal to the curve x = 3 cos
–
, y = 3 sin
– ![sin cubed](data:image/png;base64,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)
at the point
=
/4 passes through the point -
The normal to the curve x = 3 cos
–
, y = 3 sin
– ![sin cubed](data:image/png;base64,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)
at the point
=
/4 passes through the point -
Maths-General
Maths-
The normal of the curve given by the equation x = a (sin
+ cos
), y = a (sin
– cos
) at the point Q is -
The normal of the curve given by the equation x = a (sin
+ cos
), y = a (sin
– cos
) at the point Q is -
Maths-General
Maths-
If the tangent at ‘t’ on the curve y =
, x =
meets the curve again at
and is normal to the curve at that point, then value of t must be -
If the tangent at ‘t’ on the curve y =
, x =
meets the curve again at
and is normal to the curve at that point, then value of t must be -
Maths-General
Maths-
The tangent at (
,
–
) on the curve y =
–
meets the curve again at Q, then abscissa of Q must be -
The tangent at (
,
–
) on the curve y =
–
meets the curve again at Q, then abscissa of Q must be -
Maths-General
Maths-
If
= 1 is a tangent to the curve x = 4t,y =
, t
R then -
If
= 1 is a tangent to the curve x = 4t,y =
, t
R then -
Maths-General