Question
Hint:
We can apply L'Hopital's rule, also commonly spelled L'Hospital's rule, whenever direct substitution of a limit yields an indeterminate form. This means that the limit of a quotient of functions (i.e., an algebraic fraction) is equal to the limit of their derivatives.
In this question, we have to find value of
.
The correct answer is: ![7 over 5](data:image/png;base64,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)
![Lt subscript x not stretchy rightwards arrow 3 end subscript space fraction numerator 4 x squared minus 17 x plus 15 over denominator x squared minus x minus 6 end fraction](data:image/png;base64,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)
We first try substitution:
= ![Lt subscript x not stretchy rightwards arrow 3 end subscript space fraction numerator 4 cross times 9 minus 17 cross times 3 plus 15 over denominator 3 squared minus 3 minus 6 end fraction space equals space 0 over 0](data:image/png;base64,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)
Since the limit is in the form 0 over 0, it is indeterminate—we don’t yet know what is it. We need to do some work to put it in a form where we can determine the limit.
![Lt subscript x not stretchy rightwards arrow 3 end subscript space fraction numerator 4 x squared minus 17 x plus 15 over denominator x squared minus x minus 6 end fraction](data:image/png;base64,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)
(As with Factoring, this approach will probably lead to being able to cancel a term.)
![Lt subscript x not stretchy rightwards arrow 3 end subscript space fraction numerator 4 x minus 5 over denominator x plus 2 end fraction](data:image/png;base64,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)
On substituting, We get
= ![Lt subscript x not stretchy rightwards arrow 3 end subscript space fraction numerator 12 minus 5 over denominator 3 plus 2 end fraction space equals 7 over 5](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJEAAAAjCAYAAACU2uhdAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAwZJREFUeNrtWz1oFFEQHg4JIocgIqkkEOQIEkJARESCCHKIpAhCChERGxGrYG8ltiJiZ2FhIYiIiAQ7EbEQLMRCRAhimSZFirAE4Zxhv4Nr7nbf3vuZ584HH9zl/l5mvp03s2+GqD3oMe8xv415/RzzFXOXuY/3XQu0lsEEpsZA+fqS4jnz1gRDfGReZXbx/CTzM/4WwlG5YZ35lAzODpxjfjcR0SzzE/OgyaeZAwsTEb1lLpt0mjnwLLa0NovoNnJJQwMHSuj+goQ7xBr2kcRvMu+O5GKaMAcbHDDZuIvoCPMNsz9lJVP1W+KcU7jSfzIXlNlKio0LJhl3Ec1DQCcir6sPp2mqxjZNLu4iWkAZeyjR2golNuogMloy7SgiKWNfJtz/F5lbSmy0piwqZiOidxFzkteo/DrgJQjoihIbvWDebMO9iyb/36SkN+atfsk3fjH/MncQAU8rstU2igvvItqxIGaYVkQDM5FhGhHZSa7BIlFL/Je8jcNEZDAROV6VuVCzvSwS2XbWnkg0NMCwZbVvesl3OxMndhKvUe4o/zFX5SsiiQLj+o2ldXIJj0Vo76nsRamDZ1S/l0a+2256ZrqnCqSvZHuM2FapPG8RPCS3MyA5NZcjgDMV7zvKfEINz3QMeUAi1QaNnwi4UyFUOUfqVQj8uqe1ygUhvTJ7VLZfiIgfQai+EXMUKUYwCYrHVPagzDh+TkQnJ9hVB5CHmQ+oHPuZFh8QLUfXuoxt2DdijiLFSGuC4SK2sx/MY46fdcmJiMI2bu1GMnaoUaRsRXQcV1sXW9b9gL+1wvwa6LvnEUljGbswEZWYQWXWG3m+RX4nF4b7ceFY9dXFLJJ1yYsuRzJ2qFGkrLez/6Ea3Yhk7JCjSL7sksM4kypIB98aHHu+YdVSt3qpO4qkAdrHmVSiCyGFikSpRpF8QNs4k2oUgUSUehQptm1aiyUk175FlHoUyQc0jTOpgYTmdThWzuPkDvZv5o0AIoo5iuQD2seZ1GAFzi1AuYO9GqkK1N6r7jzO9A8Y/VSj7MjviAAAAVJ0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bXN1Yj48bWk+THQ8L21pPjxtcm93PjxtaT54PC9taT48bW8gc3RyZXRjaHk9ImZhbHNlIj4mI3gyMTkyOzwvbW8+PG1uPjM8L21uPjwvbXJvdz48L21zdWI+PG1vPiYjeEEwOzwvbW8+PG1mcmFjPjxtcm93Pjxtbj4xMjwvbW4+PG1vPiYjeDIyMTI7PC9tbz48bW4+NTwvbW4+PC9tcm93Pjxtcm93Pjxtbj4zPC9tbj48bW8+KzwvbW8+PG1uPjI8L21uPjwvbXJvdz48L21mcmFjPjxtbz4mI3hBMDs8L21vPjxtbz49PC9tbz48bWZyYWM+PG1uPjc8L21uPjxtbj41PC9tbj48L21mcmFjPjwvbWF0aD4CjZ+6AAAAAElFTkSuQmCC)
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means
Related Questions to study
A lens when placed on a plane mirror then object needle and its image coincide at 15 cm. The focal length of the lens is
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)
A lens when placed on a plane mirror then object needle and its image coincide at 15 cm. The focal length of the lens is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKwAAACqCAYAAAAwaKTFAAAUZUlEQVR4nO2c2XMT2fWAv5a629pl2ZLwInnFC2NsAhkzUMQhC0VqJpkHUqmpeUlN3vPnTFWe8pLKvCV5SCqTqoHUbCEJZmCAAYyxBxtjY+N9t7V16/eQX3dkYzZjYl9zvqouS7bcupI+nXvuvee2ViwWiwiCInh2uwGC8CKIsIJSiLCCUoiwglKIsIJSiLCCUoiwglKIsIJSiLCCUoiwglLou90AFclkMszOzuL1eolEIvj9fjRNe+xxlmWxtrZGNpslEAjg8/nweCRGvAwi7DZYXl6mt7eXbDbLG2+8QXt7O4ZhbJDRtm0ymQy3b99meXmZtrY2amtrd7HV+wP5um8DwzAIBoP86U9/4je/+Q0DAwNks1kAisUitm2ztrbGF198wR/+8AeuX7+OpmlbRmHhxRBht0EgEKC9vZ0333yT+fl5PvroI/r6+lhdXcW2bebm5vj3v//NJ598gmmaHD58mGg0KsLuAJISbAPTNEmn03zwwQdEIhH++Mc/AvDee++RSqX46quvuHDhArZt86Mf/Yjvf//7mKYpwu4AIuw20TSNeDzOu+++i6Zp/PnPf6asrIwDBw4wNDSEbdt88MEHtLa2iqw7yL4U1hmdZzIZPB4Pfr+ffD7P+vo6fr8fXdfJ5/Pk83kMw8A0TbLZLLlcjkAggKZpZLNZisUipmliGAZra2tYlkUwGMS2bdbX1/F6vYRCIX7yk5+Qz+f56KOPmJub49SpU7z33nvEYjEWFxdZWlp6Ja9T0zSi0SiBQOC1mX3Yl8Kurq7y6aefcvHiRWprazl9+jT9/f1cvHiREydOcPDgQb799ltu3LjBiRMnqKur48qVK9y5c4d33nmHUCjE5cuXmZmZ4eTJk1RXV3P+/HnW1tY4e/YsuVyO8+fPU1lZyVtvvYVhGPzrX/9iYGCA9fV1Ll68yNLSEoZhUCwWeVWbOkzT5Fe/+hU//OEPX5tB3b4UVtd1EokETU1NHDhwgEgkQlVVFa2trVRVVRGLxaiqqmJlZYWqqiqi0Si1tbUUCgXi8TiBQIB0Ok04HCaZTBKJRKivryebzVJeXo5t2zQ3N1NRUQHA9evXuXnzJrZt09XVRbFY5NKlS/T09NDc3OxG5VfxOisqKvB4PK+FrADaftvT5US0fD5PoVBA0zQMw8CyLDcF8Hg8WJaFbdt4vV68Xi/5fB7Lstx8s1AoUCwWN/zdtm1M08S2bbLZLJZlceXKFS5cuMDw8DCXLl3i3LlzVFdX8+mnn3Ly5EnefvttWltb8Xq9r6Tb9vl8r1WOvO8irNM1mqaJaZoUi0U0TUPX9Q0frGEYG/5P13X3sc/6e6FQwLZt/vGPf/D5558D8P7777OwsEAikeDnP/856XSaDz/8kOXlZX75y19y6NAhfD7fK3u9rwv7TlgH50Ms/TCf9cE+798zmQy3bt3iyy+/xDRNfvaznxGNRvH5fGiaRmVlJadPn2ZpaYlLly7R29tLS0vLazMwepXsW2FfJbZto2kanZ2dpFIp3nzzTSYmJtA0jWKxiK7r1NbWcu7cORobG93Bl/DyiLDbwO/309bWRltbG8Fg0O3qS6X0eDwkk0l+/OMfY1mWRNcdQoTdBoZhUFlZuWXa4eDkzboub/FOIu/mNnjdBjp7CemnBKUQYQWlEGEFpRBhBaUQYQWlEGEFpRBhBaUQYQWlEGEFpRBhBaUQYQWlEGEFpRBhBaUQYQWlEGEFpRBhBaUQYQWlEGEFpRBhBaUQYQWlEGEFpRBhBaUQYQWlEGEFpRBhBaUQYQWlEGEFpRBhBaUQYQWlEGEFpRBhBaUQYQWlEGEFpRBhBaUQYQWlEGEFpRBhBaUQYQWlEGEFpRBhBaUQYQWlEGEFpRBhBaUQYQWlEGEFpRBhBaUQYQWlEGEFpRBhBaUQYQWlEGEFpRBhBaUQYQWlEGEFpRBhBaUQYQWlEGEFpRBhBaUQYQWlEGEFpRBhBaUQYQWlEGEFpRBhBaUQYQWlEGEFpRBhBaUQYQWlEGEFpRBhBaUQYQWlEGEFpRBhBaXQd7sBKlIsFjfc1zQNj8eDpmnuUfoYTdP+103ct4iw/0+xWHSP0vultwuFAtlslmw2S6FQcH/v8XgYGxtjZWWF2dlZRkZGCIfD6LqOYRiYpolhGBiGgdfrBf4rcankziE8mddS2FIRnZ+5XI5MJkM2myWTyZDL5cjn81iW5Yq6trbGysoKq6urZLNZLMuiWCyiaRqTk5PMzs4yODjIJ598QiAQwOfzEQgE3MPv97vy6rqOruv4fD58Ph9lZWXu4UgNG8UWXjNhi8UilmVhWZYro2VZrKys8PDhQx4+fMjY2BgPHz5kcnKS+fl5lpaWWF5eRtf1DfKZponH48Hj8eD1ellYWGBpaYnJyUlu3bqFaZpkMhn3yGazrK+vk8lkAPD7/VRWVlJbW0sqlSKdTlNTU0NtbS0VFRVuNHbE1nVdpAW04uaEbB9RKBTI5/Puz1wux9TUFGNjY4yNjTExMcHMzAz5fN4Vr1TC0tumaboR0DRNdF1381bDMJiamuL3v/89zc3NvP3225SVlZHL5dxIXfqzUCi4XxbLsrBtG9u23duaplFeXk4ymaSmpob6+nrq6uooKytzU4vS9OJ1Yt9GWNu2mZmZYWRkhNHRUSYmJpiammJ9fZ1cLkc2m3VlDgQCRKNRYrEYsViM8vJyotEowWAQv9+P3+/fIMfm77hpmty/f5+PP/6YdDpNd3c3oVAI27bdx5RGR8uyyGQyLC8vMz8/z/z8PAsLC+7t5eVl1tfXmZ6eZnBw0P2yVFdX09DQQH19PalUisrKytcu6iovrCNPoVBgeXmZiYkJJiYmGB8fZ25ujrm5ORYWFlhZWaFYLFJRUUEqlSKRSJBIJKioqMDn822ImE5k3TwQ2jz6d36n6/pjEVnXdWzbdh/vnMMZpOm6TjAYJJlMuhHWObLZLIuLi8zNzTE1NcXExARjY2M8evSI4eFhKioqiMVixONxEokE1dXV1NbWEg6H933UVU7Y0oFSoVBwu925uTkGBwe5fv06N27coL+/n2QySXt7Oy0tLTQ0NJBKpfD7/a5UjmRbRannzZSclMAwjA3pg2maWJb13OfY/NwHDhxw0wTLssjlcoyMjHD37l3u3r3Ll19+ydraGqlUimPHjvHWW2/R2tpKOBx+LGXZT1FYOWEty3JH8pOTk9y4cYMrV64wODiI1+uloaGB48eP84tf/IJ4PE4kEnFH6GVlZRs+vJ1I3zVNc0f+mqZtS9innbuUaDRKc3MzP/jBD1hZWWF6eprR0VGGhobo7e0lEonQ2dnJyZMnaWxsJBwOu3nvfpFWCWFLp5bGx8fp6+ujr6+P6elpisUiPp+PkydPkkwmqa6uJplMkkwm8fl8T40yOyXs5ghbOih6mefY3GYnjYD/vCf19fU0NDRw8OBBRkdHefToEaOjo/T39xONRunq6qKjo4PGxkaCwaCbuqgs754U1vmQnZxuYWGBe/fu0d/fz71795ibm2NxcZFwOExzc7Pb7VdUVGw4hyNqabe/012kI6wz7eTxeFxhS3PY7VKaAjmDOOe1BYNBgsEgdXV1fOc732FsbIz+/n6uXbvG+Pg4S0tL9PX1kUqlaGlp4dChQ1RVVW1IF1RjTwoL/xlEzczMMD4+zu3bt7lx4wb37t3D6/Vy+PBhzp49S2NjI5FIxH3zc7mcG0G26vpLB1WwM/I65ysddDn3t3vu0i+sc79U/M0rcLZt4/F4SKVS1NTU0NPTw9jYGFevXuWbb77h5s2bXLlyhePHj9Pd3U06nSYWi+Hz+V7qte8Ge0rYYrHIysqKOzru7e3l2rVrrK2tceDAAc6ePUtLSwvRaJRQKOR2+Y6AzjmeJUpp9N0ceZ/n/zez+UtQOsvwPK/Zed7NUm41K/E0nDYYhkFNTQ3RaJTu7m438vb29tLb20t3dzff/e53qaurc2dJSt/DvcyeENZZgcrlcty8eZO///3v3Lp1C13Xqa6u5sSJE9TV1RGPx4lGo+i6/liUeRE5NlMq7na6ylL5S6P4s2TbLOWLCroZJwUpFovuwK+8vNxdURseHqavr48vvviCy5cvc+TIEc6cOUNLSwt+v1+JGYVdFdbpzpaXl7l9+zaff/45IyMjFAoFmpubaWxsJJ1Ok0wm3eko27YpFArPLcXztgMeH+Q86wMsjc6b522diLVV+7bq3nca5721bRtd10kmk4TDYaqqqnjw4AHDw8PcvHmTO3fu0NHRwalTp2hra3MHZ3tV3F0VNpfLMTY2Rm9vL1evXmV4eJjy8nIOHz5MZ2cn8Xj8qVMy2+m+t8tW8pbe36r6yrm/udjmVfK05ygrKyOVSlFbW0ttbS3Xr1/nzp07fPXVVzx69Ii2tja6uro4evQour4nOt/H2NVWra2t8c9//pPf/va3TE9P89Of/pSenh5SqZQbsSzLUnIq5mW791eFE3lramqorq7m6NGjnD9/nr/85S94vV7OnTtHR0eHCLvlk+s68XicVCrlToQPDQ25S6iBQMCd7N+Lwj4pldjLOG1dX19nbm6O+/fvMz8/TzQapaWlhWPHju1ZWWGXhfX5fHR3d5NIJBgYGODy5cv89a9/JRqNcurUKTo7O0kkEhiG8T/t/h22WjJ9EpsHgZtH/XsF27bJZDLcvn2bzz77jPv373Ps2DF+/etf09nZSSqVEmGf+OS6TmVlJeXl5bS1tVFXV0dDQwPDw8Ncu3aN69ev09jYSH19PU1NTaTT6cdG1a+SFxFus6SllVrPc76dTiFK3yOnbmJmZoZvvvmGK1eusLq6Sjgc5t133+XkyZN0dnYSiUTcRYW9yq4KWzqi9nq9HD9+nI6ODgYHB+nt7eXu3btMTEzw4MEDBgcHeeONN9zc60nTMC8j8ZOmyJ51Tq/Xu2FKyRmdbxbwaTMGO7VMXDqXXCwWyWQyTE1N8fDhQ0ZHRxkdHWVtbY3W1lZ6eno4cuQIoVAI0zT3bOpVyp6J/R6Pxy2OPnr0KK2trUxNTXHt2jU+++wz+vr6GB0d5eDBg7S3t3PgwAEikQjhcJhgMLjl/OnzLCBsdftFcQaHpbI6xdjbYbsphfPlz+Vybq3txMQEQ0ND3Llzh2w2y6FDh3j//fdpa2sjFos9VhC019kzwjo4a/NOAXVNTQ1nzpxhZGSEy5cvc+nSJf72t79RXV3NsWPH6Orqor293a1pdYpQnlU2uFPdr9PlOhG1tCTwZau1nue5HZxyy3w+z8jICNeuXePq1at8++23NDQ00NPTQ3d3Ny0tLYTDYbc4RyVZYQ8KC//t2pyyvVAoRDAYJBaL0draytDQEI8ePWJ2dpaPP/6YCxcuuHluQ0MDyWTSrUwqzclexSDIiWrOLlpnYcPZBrMTPCmVcKrY1tfXmZqaYmBggIGBAaanpykrK6O9vZ0zZ86QTqdpamqipqaGQCCwp3PUZ7EnhS3FiQB+v5+mpiaampro6enhwYMH9Pf3Mzg4yOjoKCMjIwwPD2MYBuXl5aTTaerr66mvrycej7vLuaWREF5eYqd9hULBTQecwvKdqNYqXTJ2Dtu2mZ+fd/PS4eFhRkdH0TSNsrIy6uvraW9vp6Ojg4MHDypZ5PIk9rywW2EYBnV1dVRVVXHixAnm5+cZHBx05Z2cnGRxcZF79+65+7UqKyvd/VqxWIxIJIJhGMDW1yR4Xhyh8vn8hpoIZ1fui1K6UqZpGrZtuzsqZmdn3WNubs7dbr6+vk44HObQoUN0dXW59a9O8fZ+QklhnXTBNE1CoRCxWIy6ujp6enrIZDKMj49z8+ZNbty4wcWLF5mbm3OXI1OplFuGV5rLbd42U9ptPquewLmuQWl0zWazzxVhN9f+lu6kdeRfWFjg/v37DA8PMzQ0xNTUFIFAgIMHD9LV1cWRI0doaWlxd/Xu5VqAl0VJYTfjSGYYBoFAgEgkQiqV4nvf+x5LS0ssLCy4G/lGRkb4+uuvWVhYIBQKkUgkiMfjVFRUUFlZ6d4unTbbXD+7+XfOxsHSnRGGYbgzB1tdRab0sG2btbU15ufnmZmZYWZmxo2ik5OTLC0tkU6naWxs5J133qGhoYF4PE4oFCIcDrv7uDbXMexH9Fwut9tt2HGcavxAIEAikcCyLJqbm1lYWGB2dnbD1urV1VVWV1cZHx9ncHCQ9fV18vk8Pp+PSCSC3+93r87i8/ncbd9+v98d2JmmycTEhDuV9ODBA/x+/4Zou/lwrjSzvLzMwsICmUwGr9frXqgjFArR1NTEkSNHKC8vJx6Pu7tkY7GYOxviCPqqZyR2E+c1er1etK+//nrvrR/uMJuLqjVNI5/PMz09zdTUFDMzM0xPTzM9Pc3s7CyLi4sUCoUNu0+dGQdnO0zpzgZd11lcXKS3t5dEIkFHRwemaT42J1s63eVEY+fiGrquE4lE3CifTCZJJBJUVVURj8fdUkrnnPC/qf7aCxSLRcLhMA0NDWi/+93vXo9X/QJYluVeR8u5vFBpdHTu5/N5Vx7nohywcSuOcxEMwzDchRFnuq6srIxQKEQkEiEYDLqbFvdzl74dLMuiurqa06dPo9fW1u52e3aN0prV0p9Obll6GaHNS66lS7HO/2xFaVQvFbk06m++PsLmc74ukfRJ2LZNRUXFfy5A8joL+zS2Ks5+0v2n/f5Zy78i5bOxbdvtgfTKysrdbo8gPBVnj5rH40EPhUK73R5BeCbuINeyLOmLhD2NMxD1eDz7+/qwwv5D3bId4bVEhBWUQoQVlEKEFZRChBWUQoQVlEKEFZRChBWUQoQVlEKEFZTiufZ0le63d/ZOCcJu8FwRtlgs8vDhQz788EPy+fyrbpMgPBEpfhGUQnJYQSlEWEEpRFhBKURYQSlEWEEpRFhBKURYQSlEWEEpRFhBKURYQSlEWEEpRFhBKURYQSlEWEEpRFhBKURYQSlEWEEpRFhBKURYQSlEWEEp/g/Fk5gtQ4u6uQAAAABJRU5ErkJggg==)
How much force is required to produce an increase of 0.2% in the length of a brass wire of diameter 0.06 mm (Young's modulus for brass
)
How much force is required to produce an increase of 0.2% in the length of a brass wire of diameter 0.06 mm (Young's modulus for brass
)
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means
PQR is a right angled prism with other angles as
and
. Refractive index of prism is 1.5. PQ has a thin layer of liquid. Light falls normally on the face PR. For total internal reflection, maximum refractive index of liquid is
![](data:image/png;base64,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)
PQR is a right angled prism with other angles as
and
. Refractive index of prism is 1.5. PQ has a thin layer of liquid. Light falls normally on the face PR. For total internal reflection, maximum refractive index of liquid is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAARcAAAC+CAYAAAAft0tGAAAgAElEQVR4nOx92Vdb2ZX+pwnNAxJCAsQo5nk02MZQxniMy+WuSpWrUslKOunuh17d6X+hV/fqh+6nXumXzuqHpDsrnaSq41QlNbjKxjY2xsaAEQgzz4hBTBJC83D1e+B3biQQSLbBDL7fWqykDPfcc889Z99z9v72t1nBYDAIBgwYMNhjsA+6AwwYMDieYIwLAwYM9gWMcWHAgMG+gDEuDBgw2BcwxoUBAwb7Asa4MGDAYF/AGBcGDBjsCxjjwoABg30BY1wYMGCwL2CMCwMGDPYFjHFhwIDBvoAxLgwYMNgXMMaFAQMG+wLGuDBgwGBfwBgXBgwY7AsY48KAAYN9AWNcGDBgsC9gjAsDBgz2BdyD7sBRgNPpxO3bt/HrX/8aXC4XZ8+exccffwyRSHTQXWPA4NCCMS4xgMfjIS8vDw0NDZDL5bh48SJ4PN5Bd4sBg0MNFiPQzYABg/0A43NhwIDBvoAxLgwYMNgXMMaFAQMG+wLGuDBgwGBfwBgXBgwY7AsY48KAAYN9AWNcGDBgsC94I0l0Pp8PbrcbDocDPp9v2+9FIhFEIhEEAgFYLFbU9jweD5xOJ5xOJyiKCvsdm82GWCyGSCRCXFxc1LaCwSBcLhecTifcbjdCaUgsFgtcLhcSiQQCgQBcbmyvLxAIwOPxYGNjAz6fb1ubcXFx9DOz2Tt/b4LBIPx+P+x2O1wuFwKBQNjvuVwuBAIBJBIJuFzurmNHURScTifsdjv8fn/EPpHnjNSnQCBAj5PH4wn7HYvFAp/Ph0QiQVxcHDgczq7PFPr+ttK+OBwOJBIJhEJhVOKk3++Hy+WKOK9YLBaEQuELzaujjjfSuNhsNnR1daGlpQXLy8vbJnZFRQUaGxtRUlISdRIEg0EsLCzgwYMHePz4MVwuV9jvJRIJ6uvrcfr0aaSmpkZty+/3Y2BgAPfv38fz589BURTdBxaLheTkZJw7dw6VlZVQKBQxPa/P54PRaMTt27cxNTUFv98f9rzp6eloampCTU3NrhM/EAhgeXkZt2/fRkdHBxwOB/23wWAQ8fHxqK6uRlNTEzQazY6LOhgMwufzobu7G3fu3MH8/HyYoeJyucjKysL58+dRXl4OFosV1qdgMAiv14unT5/iwYMHmJycDPs9i8VCfn4+mpubUVRUtKtxAYDp6Wm0trais7MTXq83bLwVCgUaGxtRV1cHrVa7azsulwttbW1obW3FwsJCWDtsNhtlZWVoampCfn5+zB+Go4wDfUKKojA1NYVnz55haGgIgUAgbJLIZDJUV1ejqKgI8fHxADYnltPpRG9vLwwGA8xmM9hsNlgsFoLBIDgcDrKyslBbW4vU1NSIuwUejweJRAKNRgMejxe2QFgsFpRKJYRCYUzPQL6yCoUCSUlJ8Hg8Ye0JhULI5fKYdi1kEYlEIqhUKiQnJ9P/TgxgYmIixGLxC01ONpsNoVAItVoNr9dLjzNpU61WQywW77prIe1wuVwoFApotVq43W76GoqiIJVKoVAowsZ0p+fkcDgQi8VITExEMBikxz4YDILNZkOtVtM7qa1tkcUqFovpZwrtO0VRSEhIgFAojPpMACAQCBAfH4+kpCT4/X76mmAwCKlUCplMFlO6B4fDgVQqRWJiIv2MoX1WKpVvzK4FOGD6fyAQgMFgwOeff44HDx6EGZdgMAiNRoPr16+jubmZ/mpQFAWbzYZbt27hiy++wMTEBL3QgsEguFwuqqur8f7776O0tBQCgSDiff1+Pzwez7atPQDExcWBx+PFZBCAze2w1+uFz+eLeCwi7cViEMhX3ev1RjwusNls8Pl8cLncqF9kAoqiwp53a5scDgdxcXGIi4vbdeIHg0FQFAWPxxPxWTkcDrhcLvh8fkSjsLVPPp8PHo8HFEVF7BOfz9/RUJHryTiFghwf+Xw+OBxOVAPj8/notrYuBzLePB4v6nhTFEXPg0h9InMq2pHxuOBAjQs57zocjm3HCSD8vBu6MAOBAH1GjnS2DT1v7zSxoj32i778vWwvllfyMpNzr/r4utqJ1tbrHPPXPTbHAQeeuEi2xDt1gxwVtr6UrV+7WK5hwIDB68OBGxcGDBgcTzA8FwYMGOwLDjweRo5EW52DQPjxJtIRJ/S6rRswck0s0YLQo9lO7cR6zCLHtUjtAIjq6Azt09a+7dSv0Pb3or0X8S/sdDwlYx+LzyTaO9zt/b/K9ZGwF+8vlnEJbfO44kCNCwkrW61W2O32bS+Dx+NBoVBAKpVui9xQFAW73Q6LxRKRbMbn86FQKCCTyaISw7xeLywWC03oCgWXy4VUKkV8fHzUEGsgEMDGxgasVis8Hs+2PgmFQsTHx8cU9gU2oxhWqxU2m21bv4izOz4+Hnw+P2pbwWAQbrebfs7QvgWDQfD5fMjlcsjlcnA4nKgTPxAIhI3/VohEIigUCkgkkh2flaIouFwuWCyWbQQ2EsaXyWR0nyI9k8PhgNVq3XY9ic7Ex8dDKpVGjdQRg7C+vg6r1Qqv1xv2ezabDZFIhPj4+F1D3BRFYWNjA+vr63A6nWG/I/OSzIHjznU5cJ7L8+fP8Yc//AH379+Hz+cDh8OhJ4lGo8F7772HCxcu0JwPAr/fjydPnuC3v/0tBgYGwnY+wWAQBQUF+OCDD9Dc3Aw+n78rMcxkMuHTTz/FnTt3YLFY6IkcCASgVCpx6dIlfPe734VOp9uVGOZ2u3Hv3j18+umnGBkZCZuAHA4HJSUl+PDDD1FfXx81zE1RFJaXl3Hz5k388Y9/hNVqDQvTy2QyNDY24saNG8jOzo4aJvX7/RgaGsLvfvc7tLa2ho1XIBBAeno6rl69iuvXr9Ocot3gcrnQ2tqKTz/9FM+fPw/jgVAUherqarz33ntobGzccSF6PB709vbiN7/5DTo7O8MIg4FAAHl5ebh27RouX74MmUy2jUhHiHiffvopOjs7aa4M8Gdy4AcffIDz589DLpfv+jzBYBAbGxv4+uuv8fvf/x4zMzNhfBc+n4/q6mp8+OGHqKqqivhMJPrZ1taGmzdvore3l941Ef5Ofn4+bty4gdOnT0ft01HHgYeiFxcXMTo6itnZ2bDJBWx+/XJzc5Geng6pVBp2rd/vh8lkwtDQEFZXV+lrQ4lweXl5SE9P3/VLTHgzw8PDmJmZgcvl2kaCy8jIQF5e3q5fYTLZp6enMTIygrW1NQB/JsBxOByoVCoUFBQgOTk56leLoig4HA6Mjo5ifHyc3h2Q9vh8PnQ6HfLy8hAfHx91JxQIBLCysoLh4WHMzs6GfeUpioJcLkdWVhays7NjInp5vV7MzMxgZGQEKysrYfcPBoPQarXIyclBamrqjobP5/NhaWkJQ0NDWFxcDHuHwWAQKpUKWVlZyMrKisjBCQQCmJubw8jICBYXF8OIeCwWCzKZjJ4DkfhOoSCGYWJiAqOjo7DZbGHjzeVyodFokJ+fvyP7OBgMIhAIYHp6GqOjo1heXg5rg81m0/MyJSUlph3nUQYTLWLAgMG+gIkWMWDAYF/AGBcGYWA2sgz2CofeXR0Le3c/rt3LNqK1s5dtvSgzObQt4pTmcrm0g/Yg+vWqY7VXYx06Lq/azm5thP7vccKhNS4kNEgSwbYmGJKEQBIJCn05FEWFXbuVQ8Plculkwt0ctMTJF+n+HA6HTkSLhc+xWzJitCS9rWPi8Xjg9/sj9omMCWl7N1AURWu9BAIB+Hw+3L17F3q9Hnq9PmycYlnMsYxVLMl/JMmSvEcCkpC4W58ItYAkI4aCXC8QCGIOt5P3trUfJKwcLaFxaxuRKBOxJrUeNRzqJ9rY2EBHRwd6enpgsVjCojhxcXE4efIkTp48Cblcvi1MubS0hPb2dhgMhjCOSDAYhFqtRn19PUpKSiASiXacpOvr6+jo6EBXVxc2NjbC7i8Wi3Hy5ElUV1dH1VWhKArDw8N49OgRZmZmwiYqm82GTqfDmTNnUFhYGFXYaHV1FY8fP4bRaIzYp8bGRlRVVUEsFkcd30AggImJCTx69AgTExOw2+0YHBxEYmIidDodUlJScPbsWeTk5OxqYILBIGw2G548eYKnT5+G8TuCwU3ZgtraWnqsomVLk7GanZ3dZqj0ej0aGxuRlZUVcUEGAgEMDg6io6MDk5OT235PdGJSUlJ2pQMEg0EsLy/j6dOnePbsGdxud1i/JRIJmpqaUFxcDJlMtmM7NpsNBoMBT548wfr6elj7XC4X9fX1qKqqglqtPna7l0NrXEhYz+l0Yn19Haurq2ELSSAQwOFwbJMQIL8nimkWiyWMEEXCuG63O6LcQujfEbW09fX1bcbN7/eH3X+3hUd2G6SdUGNHSHrkS73bLij0vlardRv3xe/302p4u/WJgMgWEOLf6uoqurq66LC7TCbbRlDcqV/kXVmtVmxsbGx7fofDQe/aohmX0LEK3X1wOBxsbGzQBMVIbZEd1MbGBlZXV8N+x2azYbfbI+5mI4GMJyH5hR5hfD5fRDW+ndqwWq2wWCxhR624uDg4nc5tBMnjgkMbig5d3OQYEAo2mw2BQECzXbcei8hkJ4s2FDweD0KhkNb7iHb/SIaIw+FAIBBAKBRG3WKTIxqRiIjEJCUymNHYxKHPtZPMJNmNxWpcSHtmsxkffvghfvCDH+AnP/kJ4uLiIBAIovJeoo0V0VbZi7GKi4uj391OO0632w232x1R/jIuLo5mx8ai8+JyueB2u3eULyVHrJ1AjnhOp3PbuLBYLFr28jjWHj+0xoXB6wVFUVhYWMDf/d3f4bvf/S4+/vjjg+4SgyMOxrgwAPDn48To6CjUanVUvVgGDKKBMS4MAPw54uPz+cBms4/lNp3B68WBO3T9fj/9sxXEHxHpfEz8D0T3dKuNJAskml5p6KLaGiYmfSC8j1j4FX6/P6LDkKTak9BlLGn70fpFQrwvIgMQSd8VAD2+8/PzUCgUSEhI2LU94teKFBIH/hx+3u1ZQ+kGO7VB2tnJv0JCvZGuDx3vWKU3yPi87Psjc2CncSEUCjabHVOfjjIOXHJhZWUFY2NjMJlM27gEIpEIOTk5SEtLg0QiCbuWJK0NDw9jbW1t27Xx8fHIzc1FWlpa1Mlgs9no5MlIiYvp6enIycmBRCLZtR2fz4eZmRmMjo7CarWGGQSSuJiXl4fk5OSofI9gcFOOYmxsDBMTE9tkDfh8PlJSUpCbmxs1vAtsGoOVlRWMjo7CZDJtI88pFArI5XLcu3cPjY2NaGho2LU9v9+P2dlZjI6OYnV1FWw2OyxxUKPRIDs7e9dMcr/fj+XlZQwPD8NsNm/LbFcqlcjKykJGRkbExEXiJxodHYXZbN7m/JVKpcjLy0NqampMiYterxeTk5MYGxujExcJuFwuEhMTkZeXh8TExF0TF00mE8bGxujERQI2m03Py+Tk5GOfuHgojMvTp0/x9OnTber/CQkJoCgKarV6m3EBAJPJhNbWVoyNjW3L8tXr9RAIBLtObgLCRWhvb8fGxgb9RQkEApDJZGhoaEBSUlLEPoQiEAhgamoKLS0tmJqaCvsysdls5OXlQSqVIikpKabxcTqd6O/vx927d2Gz2cIkAEQiEWpra6HVamOqX0Q4Mk+ePKHlCQgoioJOp4Ner8fnn3+O5OTkqMaFZP/evXsX4+PjYWMcDAZRVFQEkUgEnU63axtmsxmPHj1CX19fWGiZoiikp6ejubk5IieF7HoWFxfR1tYGo9EIIJw4mJKSAh6Pt02uYyd4vV6MjY3hm2++wcLCQth483g8lJSUID4+HomJiTu2QYzu/fv3MTw8vG23q9frIRQKkZiYeOyNy4FLLtjtdthsNmxsbGzbfYSKRW19EUSsaG1tbVu4mYSpybW7HRvItpyIKG1ldfJ4vDCxqN0YvUS+wWq1buOHEBauUqmEWCyOaefi9XrDxKJC2+PxeBCLxVAoFDtWJdw6Xm63m+ahbN32CwQCWCwW/PjHP8ZPfvIT/PSnP921PcIjslqtcLlc23YNYrEYcrkcEolkx2clVRPX1tYiVqskYlEKhSLiOySCYUQsausc4PF4UCqVkEgkUX1IZNcRKha19f0JhUK6ptVOOxeyEyZiUaFtkDIlZA4cR1ZuKA7coUteyKvIXEZ6BHJGfpHcj0i+m2h92Iq9krnc636FHoEijTVFUZibm8P777+PH/7wh/j7v//7mNrcK5nLndog7bzK9S+S17QX72+nNkg7b4rM5YEbFwaHA0Ti8Q9/+ANKS0tRXV190F1icMTBGBcGAMKTD0kCJAMGr4LjfehjEDNCHekMGOwFDq1xIQ7N5eVlrK2thWWlBv9/RqlarUZiYuI2RytRlV9aWtoWpiaRFrVavauiPwktm81m2mkcen8+nw+VSgW1Wh21xjJxFJrNZjgcjjCtWJKjotFodlS5D30uj8eDpaUlusLA1j6p1Wqo1eqY6hETp7jZbIbdbofH48HMzAyUSiWt3K/RaGiH6k4IfVcrKyt0ThB5RjJWCQkJu4qlbx0rko8TOlZSqRQajWbHqg4URcFisWBlZQXr6+vb7iWTyZCcnAyRSBTVqe5wOLCysoK1tTX4fL6wtrhcLpKTk6FQKHaN+pCKC0tLS9sSaDkcDjQaDZRKJUQi0a59OYo41MZlfX0d33zzDe7cuYP5+Xl6MlAUBT6fj3fffRfvvPMO1Gp12LWE/3Dz5k20tLTA6/XSEyMQCCAtLQ3vv/8+GhoadlRgDwaDsFgsuHXrFm7dukVzOUj7CoUC77zzDi5fvozExMSoRDGj0Yjf//732yoVsFgs5Ofn44MPPsCpU6eiZkUvLS3h888/x/3797G2thbWJ7lcjo8++ggXL17cJkMRCX6/H8PDw/j973+Pnp4euFwu2O12xMXFQSQSIS8vD9///vdRXV29q1Eg7+rWrVv44osvYLVaw/qlVCrx9ttvRx0r8vdkrAYHB8OIaCwWC2VlZfjoo49QXl4e0VHr9/thMBjwpz/9CQaDYZsBKi8vx49+9CPk5uZGlbcwm8344osvcOvWLTidzrC24uPj8f3vfx9nzpzZ1bhYLBa0tLTgT3/6UxjvhaIo8Hg8vP/++7h06RJ0Ot2xI9UdWuNCSHSlpaUQCATbtEu4XC6Ki4shFou3TTA2mw2FQoETJ05AqVSGTVBiGIjKfSz35/P5YSn3weCm5MNO99/aDpvNRmpqKs6dO4fi4uJtRw+NRoPU1NSokQgWa1PRvrKyEnK5PIzwR1EURCIR8vPzY1LvBzbDq0lJSWhsbEROTg6Wl5fx85//HHV1dWhqakJCQgJSUlKifuFDx4rH40UkIhYWFkYdKwC7jlUwGIROp4NWq91xrDgcDtLT09HU1IT8/PxtOj8pKSlQq9UxPZNcLkdVVRUkEknYBwrYDN3n5ORAKBTu2o5YLEZhYSGAzZ1QaF9IuRmpVHosI0eH1qG7lf4eSYmOqJJt/YJtpbpvDQsSSvluaffR7k+o6dFkEkhbJC1gq/5MKI0/llSF0OfaGlLmcDhhYxINoSkUPp8PCwsLuHHjBn74wx/ir//6r1+oX2SsyJFo63iHpgNE69NuY8XlcumfnY6z5PqtaQ5krPl8fkwhZZJasHWsyXyLi4uLKt0QCAR2TFMJbSPauBxFHOqdC4u1KQP4okxGMole5YW9yv0jtcXj8V45GXAvnmtre2ShEj2W6upqpKWlbasTFa2dwzJWezXWAPZkrEM/Qm8aDu3OhcHrBdl5LC4u0oxkBgxeBYxxYUCDGBhy5GTA4FVw4DOIKLxHOo8CoFPTt56PQ9MGIl0bSj+PVY4gEo2ctBOrrMFe9SmWfpFj0otQ23ejtweDQSwsLEAmk+26cwntF/nvSM8Ziy9qp/EC/ky1j5Ybttv8IePzuuZAaJ8iyTa86Bw4yjjwQvSjo6O0mr3f7w/LRFUoFKivr0dFRQVUKlXYtX6/H0ajEQ8ePKBV4skCAYDU1FTU19ejvLx8VwdnIBDA0tIS2traYDAYwrKiKYqiozP19fVQqVS7au56PB48e/YMjx49wtzcHIDwWsPp6eloaGhAYWFhVJ8A4Ws8evQIT58+hd1up9ujKApisRglJSU4c+YMkpKSovoGSB3rhw8fwmg0hi2gQCCApKQkZGVloaOjA1euXEFzc/OObVksFnR1daG9vX2boj2Hw0FpaSlOnTqFrKysXftFajO3trZidHQ0jP9DURRSU1NRW1uLqqqqbVUaiON2cHAQjx49wsjISBi3hs1mQ61W48yZMygvL981o52iKKytraGtrQ09PT1hofRgcFNIu7KyEmfOnIFWq911Dni9XvT19aG9vZ2uPhDaJ51Oh4aGBhQUFMRUoeEo48B3Ll6vF2trazCZTNskF9xud8QMXgJClNtaWJ1MCJfLFVMffD4frFYr5ufnw6QNAoEA5HI59Hp9TArtweCmBsvi4iJmZ2e3SS6IRKJtuiy7IRAIwGazYW5uLmIZEZ1Oty2LeyewWCx4vV6srq7Sei6h9yFkvlu3biEnJ2dX40KyvxcXF8MU9olxSUlJCSOM7Qa3242VlRVazyeUj8Tj8WC323d8/2SOLC8vY3Z2ln7O0H6Ghn93AyHvzc/Ph/GHyFzKzMyMaazJHDCbzZidnd22QyGK/2+CN+KVfC67XRrrtj9UfX5rexwOh1ZH3/q1IDuFSCrxAGhF/Vg4H6T8w04q76TKQCxhVJfLBZfLFbEgF+lTNJYqaYtEcFwuV8R+8fl8iESimNi40caay+VieXkZH374IX784x/jH/7hH3Zsi8g3hJYxCX1O0q9oxdRCqw9slTgANt8hqbAQ6YhF5oDL5dp2PTkykjkQS1UFovQfSaVfKBTSrN5oYXm32033aWs7XC4XYrE4JgrDXiPScW8/8VI7F/IyHA5HRGKQUCikiUHRSGE8Hg8ymWxHQ7VTG2QSx8XFRU23jwYOhwOJRLLjNpWck6OBTEKBQPDKfSL3FIvFO1LDX7S93caaaKMoFIqoVHSyC9uJhBhrv4jkI4/H23G8yN/tdJ/d5gC5Nlo/iCHai7FmsVgQCATg8/mvPAf2CqHrlRyvQz++++W8f+lWnU4nfvWrX+HBgwe0/4DD4cDtdqO5uRlXr16FWq2O6lt4lYHeq5e0ly/7sLYVrT0WiwWFQoG//Mu/RHFxcdR2AOwJ3+ZVn/G4z4FXBSHwra6u4v/+7//Q0dEBFosFiUSCU6dO4cKFC9BoNPtC4nvpnQvZZhsMBvB4PFy9ehUSiQStra34+uuvIRaLcfXq1R1zdxgcLpCkwOvXrx97+cU3CW63G0NDQ/jNb36D5eVlWrvXZDLh17/+NWQyGc6fP7+rPvTL4qWMC9liFxQUoKioCPHx8firv/orWh/2s88+w9OnT9Hc3MwYlyME8l6PWwLdm4zp6Wn86le/Qn9/P959911cu3YNXC4XBoMB//RP/wSj0YiioiLk5ubu+b1fahYRZ+PGxgaUSiVKSkqgUCigUCiQkpICgUCwq5efweEDiXI8fvwYMzMzB90dBq8I4lgeHh7G/fv3cfbsWTQ1NSElJQUajQZpaWmIj4/H6uoqVlZW9iV69dKfKK/XC5PJBDabjdzcXAgEAlr5nMViISkpiWF5HiFQFIXV1VX867/+K1pbWw+6OwxeERRFYWJiAp2dnUhISMDly5eh1+vDHMr7HQ5/aZ+L3+/HysoK/H4/JBIJLdBz69YtSCQSNDY2HksBnOMMQiaLlR/E4PCCoijMzs5ifn4eOTk5UKlUYdwdUvGCVFjYDwf0SxsXj8dD15xxOp0Qi8Vwu92QSqW4ePEiampqdgxVkjT2SJUEY0UooYzByyOUtBYIBEBRFPx+PzY2NgAw4/sqeJU5GnotyVyPxhsKBRFMW1xcxLlz58K4Pj6fD0tLS9jY2IBGo9kmtrZXeGHjQqJEs7OztM9Fo9EAAFQqFS5cuECLGe00EEtLS7h9+zYWFxfpNmNFaG5GpPwNBrFja+7O2toazGYzHj58CAA7lsplEB2h47pVlybadaG8Kr/fD6VSifPnzyMzMzPm+5O0FrfbHVbdMRjcVFicnJwEh8OBTqdDfHz84dm5eL1ejI+PQygU4saNG3jvvfdo0RyJRBKVFWuz2fDVV1+hv78farUaKpUq5sH3+XxYX1/H2toaEhIS6KqMDF4MLBYLLpeL1r3lcrkQCoXgcrl4/PgxBgcHkZycTGvVMmP8YiBjC2wqDcYS3id+EJvNBpPJBL/fD5lMhurqajQ2NsZ8b3LssdvtNEE09Eg0Pz+P3t5eZGVlITU1dd+Eql5q5+LxeDAyMgKpVIrs7Gyo1eqocn+hkEqlqK+vh9vtRkFBAU6cOBETk5LNZmN9fR39/f1ob29HQ0MD6urqXul49aaBsDWdTidMJhMMBgOCwSDkcjkyMzNhtVoxOzsLkUiEyspK5OXl0cLhRy1EvRvrd6e/2/r7l6XMk2RYu92Oa9euIT4+fsc5Gsobs9vtGB0dBbD5IT158iTeffddpKSkxHRfAlJxEgCd0kAU+vr7+2E0GnH9+vXDZVz8fj9sNht6e3uhUqm2ZavGAq1Wi+vXr6Ovr49W9icPGS1ficvlIj4+HgKBAFKpFAkJCYxxiRHkw7C4uIjHjx9jbGwMMpkM165dQ1ZWFmQyGdbX17GysoLe3l7cu3cP4+PjOH/+PDIyMsLyqw7zeBMD6vV66WRI4rcI/YgRSgXxAZIFSXK1yKL3er10vhGRpYw25zkcDuRyOTweD+RyORISEnY0VGRNTU1NwWAwYHV1FSdPnkRDQwOKioqgVCpjykcLbZfP5yMjIwMcDgcdHR0oLS2FUCjEo0eP8Nlnn+HEiRO4cuVKVMH0V8ELG5fl5WXcu3cPs7OzMJvNGBoaQm1tLZ3uHtNNuVwolUqcPn0a7e3tMBqNtPp5NONCfC3kXMrhcLaVDtnp2t3+JtrvjypYLBb8fj9dkmRoaAgjIxi9Tf4AACAASURBVCOgKApFRUXIzs5Geno64uPj4XA4cPPmTeTn5+PixYtITk7G5OQkvvzyS+j1epSWliItLY12DkZ7XwcBIlUxPj6OkZERLC0tgcViITk5GZWVlUhPT6ePKIFAAMPDw+jt7cX8/Dwtpl1cXEx/tJaWlvD48WPMzc1BIBCgtLQUJSUlUeUSZDIZ5HI5pqensbKyApVKRedQhfoLXS4Xpqen0dfXh/n5eWRmZuLChQsoKSlBeno6Hcl5UQPA5XJRV1eH+fl5fPPNN/jnf/5nuj51fX09GhsbkZaWtq90kZdqOSEhAd/97nfh9/uh0+leaoLx+Xw0NTVhcnISAwMDWFxcRFJS0q5JaBwOB16vFzabDTKZjN41hX6NyEsLfRlbEw8jZfJu/f3WNo4iyNd3bW0Nvb29GB8fh8PhgFQqRV5eHvLz86HRaOjxW11dRXt7OxISEnDlyhUkJSVhYGAAvb29WFhYwMLCAlJTU1FRUUFrtexUp/kgwGaz4ff70dLSgoWFBdr/t7y8jJGREfj9fojFYqSmpsLv92NxcRHt7e0wm82QSqWwWCy4f/8+AKCurg4ejwezs7O0nIPL5cLExARkMhny8vJ2XJhk55CYmAihUIihoSHodDoolUrauPj9fkxPT+PZs2dYWlqCUCjEiRMncPLkSVRWVkIkEr3SMZTD4SArKwtXr16F1+vFw4cPMTAwgIaGBly7dg1paWkvVLf8ZfDCxkWr1eLy5cs4f/78ZgMvoDYfdmMuF0lJSSgrK8P09DQ6OjrQ1NQEjUazLeWdgMPhwOl0YmFhASkpKVCpVPB6vTCbzVhcXITVakVubi60Wi1tMPx+P+bm5jA7OwubzQaFQoHU1FRoNBpwuVz4/X7ae76xsQGxWAy9Xg+VSnUkjQt5bp/PB4vFgpmZGQwPD2N4eBhxcXEoKytDTU0NlEolPbmIkNHWCIdIJEJ1dTXKy8vR3d1Niyk5nU6srKwgJSUFiYmJEIlEh8LIkC+80+mEVqtFc3MzEhISMDQ0hH//93/H1NQU1tbWkJGRgfX1dfT29mJubg41NTU4d+4choeH8bvf/Q4GgwEZGRng8Xiw2WzIyspCVVUVHA4H+vr6YDabkZ2dvWNSLpk3GRkZmJubg9FohFQqRUVFBRQKBVZXVzE9PY3h4WEsLCwgKysL3/nOd2j6xsusp0jgcDjIycnBT3/6U5SUlODLL7+EVqsFn8/HysoKvF4vEhISXsq1EQte2Ljslfo8yWOpqKiAyWTCnTt3UFxcDKVSGbF9FosFj8eD1dVVrK6uoqSkBHw+H0NDQxgeHsbs7CzsdjuUSiVd1yYQCGBtbQ2tra0YGRmBy+WCQCBAUVERGhoaoNFo4HQ6MTIygra2Nqyvr0Mmk8Hn86G4uPjIiVQTo7C+vg6TyYTJyUlMTU1hY2MDhYWFKC0thU6ng1AoDPOdkInF5XKh1Wohk8no9oDN9PyysjKkpKRgbGwMY2NjaG1tRUJCAkpLS5GdnQ2FQhHVZ7bfCAaD4PF4+OCDD8BmsyEUCul6QwqFAlqtlu6n0+mEwWCga1hJJBLodDpkZ2djenoaZrMZmZmZEAgEWFxcxMjISFhbsciLJiQkoKioCCaTCe3t7bBYLEhKSoLZbMbKygoSEhLwgx/8AOXl5dBqtWHvZa8QFxcHDoeDyspKtLa2wmg0orW1FWw2G0lJSZBKpftGduX84z/+4z/uS8sxgOifsFgsDA4OwuFwICEhIWxyh1KVZ2ZmaCnK06dPw2q1oqWlBcvLy7TBSEtLA5/PB4fDgcViQW9vLx4/foySkhKcO3cOdrsdfX19EIlESE5OpnctUqkUJ0+ehFgshsVioXdWoX047D8+nw9ra2vo6urCvXv3MDU1Bb1ej9OnT6OiogIpKSnbhJdCrwc2DYxer9/mgOTz+ZDJZHRuSjAYhNFoxMTEBO20DHWGHuQPcTyvr69jcHAQHR0dEIvFqK+vR05ODuLi4rC4uIjbt28jOTkZZWVliI+PRyAQwOLiIubn56HT6aDX6wEAXV1dePLkCWZnZ5GZmYmysrIwvaKdfohGjFKpxMzMDLq6umA0GiEQCNDU1IR33nkHFRUV9G5iv6JxLNZmfSSLxYInT56gp6cHSqUSdXV1dOnf/cCBJ//weDzk5ubizJkzuHnzJpKSkuj6zwTESXfv3j2MjY2hsbERFEWhra0NFEXh8uXLyMzMpNPGWazN6MDi4iKePHmCtLQ0VFRUID8/ny7+NTAwgNLSUpqVKpPJkJqaCp/PRyvShXIDDiNCv5wejwcDAwP4/PPPYTKZUFlZibq6OqSmpkImk23bakf66gqFQtTX14c5HgnI0UkgECA1NRUKhQKFhYUYHBxEd3c3Hjx4gMbGRpw/fx5yuTyiePfrApvNRnd3N/70pz9hcnISAoEAjY2NNN8k9OhH/p4cCYPBTZHy1dVVWt7ye9/7Hs0ZUalUiI+PjymyyWKx4HA4MDIygsHBQSQlJeHtt9/GW2+9haSkJMhkshdi3b4siHG5dOkSioqK4PP5kJiYiOTk5D2p77QTDty4cDgcWgS7u7sbExMTyMjIoMubEmFpkq2bn5+PnJwc+piTl5eHrKwsiEQiekGQr8b6+jomJydx5coVqNVq2smWmJiIubk5eDweKJVKyGQyPH/+nBZUzs3NRUpKCv3SD5vvhezkKIrC+vo6JiYmMDo6ipWVFdhsNvj9fmi1WhQVFdHjshuXI/TfpVJp2DhGAo/HowvLk2314OAgJicn8dvf/hYFBQXIzc1FQkLCvjsNIyEYDEKtVqOqqgqpqalYWVnB6OgoUlNToVQqoVAotu0yQqsVkAqLRCYzOzubbjvUt7TVWJN/DwQCWF5exvDwMKampuByuXD58mXU1NSgrq4OWq02aqXGvQaHw0FCQgJ91H+RagYviwM3LsDmZNXr9WhqasLvfvc7DA4OgsvlYmNjA8vLyxgcHMTExAQKCgrw1ltvQSgUore3l64U2NraSotpFxQU0BEQwlIUCoV0xTsiQWi1WuHz+RAfH4+srCyYTCaYzWaoVCpkZGQgKSnp0O1cQheC2+3G7Owsenp6MDw8TDsez5w5g7GxMWxsbGBubg55eXkAtkfIIrXtcrnQ0dGBtLQ0ZGdnR70mGNys3ZySkoKKigo8evQIBoMBKysrmJ2dpT8EJBXkdaYS5ObmorCwEE6nE11dXfjFL36B58+f02F30p/QRUZ2vPHx8dtYrTsZZ/L/CYt5fX0d4+PjGBoawvT0NF2zvLm5GcnJyQdWeTF07rwuHArjQs7JZWVluHv3Lvr7+zE/Pw+r1QqPx4O4uDicPXsWVVVVUKlUmJ+fx+TkJBITE+kzssViAUVROH/+POrr65Genr6jb4EkXbpcLsTFxUGv1yM9PZ3eym+taXwYdi5kMRBl+YWFBYyMjNATuLGxEfn5+eDz+Xj27Bk6OzvxzTffwG63IysrC3K5nDbGkchcHA4HDocD//M//4O3336bPkJGA2lLrVbj0qVLqKysxJMnT+jFtbCwgLy8PKSkpNC+kP1OJSDO1kAgAIFAgLy8PBQUFCAQCGBlZYX+Gy6XC6/XS1d2IBSE+Ph4yOXysGjaTnOAzLGNjQ3Mz8+jv78f09PTADbD2WfPnkVGRgYkEskbJ0FyKJ6WTG7Cr/j5z3+O58+fIycnB+Xl5SgpKUFiYiJN3iLsSyLRJxaLYTKZcPv2bTx79gwajQZZWVnbvjDkv4mIONmaEqFogsOUrEcmt9/vx/r6OkZGRvD06VMsLy8jMzMTly9fRlpaGuRyOZ2FXltbCzabjdbWVvz2t79FU1MTiouLoVAowOfzt53zSWKd1+ulKxfsdiyKBCLardPpcPnyZeTl5dG1jaanp1FWVga9Xg+lUkkf1fYDFEVheXkZbDab9mmQTG+hUEinqfD5fKjValitVqysrCAzMxNOpxOrq6sQCoV0ygMQ+eNC3ovL5cLa2hrGx8fR29uL5eVlVFVV4dy5c8jLy4NEInkhdu1xwqEwLgRyuRy1tbV49OgRgsEgysrKcObMGfrsTpyvwObL1ev1KC4uBofDgVKphNVqxWeffUaLWEU6V7NYmwSn5ORkOr4fyZgc5GTYem8SxXj06BE6OzsRFxeHmpoaVFVVISkpiV4wZGykUimqq6shFotx584dfPXVV+jp6UFZWRlyc3Oh0+loBy9RFCQ7IlLB4WXO46TciVAohEQiQUpKCmZnZ2EwGPDJJ58gMTERzc3NqK2tDctV2okx/aIGiPjofvnLX0IikeD69euQyWSYnZ3F2NgYamtrodPpAAASiQQlJSVoa2vDxMQEHYKem5tDeno6UlJSIoabQ//b7/djaGgI33zzDdbW1lBaWoq/+Iu/QH5+PnQ63RuvRXyojAuLxYJMJkNzczOdWCeRSMDhcOiCaVtLYRKPP8nlIB5/FmuzxINIJMLq6iqcTiftq3C5XPSX/jBS2IE/+0CmpqZgNBphMpnAYrFQW1uLnJwcpKenQ6FQgMvlbnMwUhQFiUSCoqIiyOVyjI+P08eoZ8+ewev1gsfjgc/nw+v1wufzQSKRQCQSoaysDJmZmVGduruBoijweDxotVqoVCqo1WpkZmZieHgYd+/eRXd3N+rr65Gfnw+ZTEYbRaJSL5FIdi03s9uYcTgcZGRk4Pnz5/iP//gP+t9zcnLoYzWwaVxOnDiBtbU1dHd3o7u7GxwOB6mpqTh16lQYc3nrDthut2NkZATd3d00d+XixYuoqKhAZmYmvSt+03GgPJetIC9SoVDAbDbj+fPnSEpKgkQioY8tLNYmA7Onpwd8Ph8ajQYikQg2mw1GoxEWiwUFBQUoKCiAxWLB/Pw81tfXkZycDJVKhcHBQfT19SE9PR0lJSUROTUH/UO0OAwGA7q6ujA3NwehUIji4mLU1dXRpUAj7c5Cf+Li4pCYmIjU1FTa8JLs2FBfAuFiaDQaVFVVITs7myZWveqzcLlcqFQqZGZmQiwWw2azYX5+HouLi1hfX6ePqDweD263G/39/aAoij6WvMi9SH+VSiXNriVksTNnziA/P5/OCSJSBBKJBIFAAB6PB0lJSTh9+jTy8/PpXW1o2y6XCyaTCT09Pejt7YXdbkd2djYuXLiAxsZG6HQ6uoDfm3gM2opXqri4X6AoCp2dnfj000+xvLyMt99+G8XFxbQz0mq14ssvv8TExARUKhV0Oh0cDgcGBweh0+nQ2NiI4uJiLCws4PHjx7h16xays7ORmZmJ0dFR2O12XL58GWVlZft6/o8VoUZlbW0NU1NTGBwcxOjoKE3Zr6qqemXCE5nwJDuaOMvJsYoYA6JKt9dgs9m0pMCtW7ewuLgInU6Hqqoq5OTkQCgU4u7du/D5fLSRe1nW79bFHS1SFunvyE6ZoijMzc1hYGAAQ0NDsNlsSExMxKVLl1BVVQWlUvnSu7zjjEO5d2Oz2cjJyUFNTQ1+9rOfYWJiAunp6RCLxfTR6dy5cxAKhXj27BkGBgYgFAqRl5eH06dPIyMjA4FAAAqFAlVVVbDZbBgYGMDExAS0Wi2amppQWFgYtqgOAqGLfW1tDXNzc+jv78fY2BhYLBYqKytRWlpK6+XEalhCj4/En7T16EQqQwJ/jngQhUGJRLKr/sirQCQSobCwEElJSTAYDOjr66Ozjkn432AwwOPxQKPR0JyUF8XWxb6Tkz7S3wGgj9BWqxULCwvo7+/H8PAw4uPjaWatWq0OC1kzCMeh3LkAmxN9bGwM//Vf/wWPx4O33norrBIg0Xm1WCzw+XzgcrmQSqWQyWRh2r1EK8Nms8Hj8UAsFkMul+9LEagXRehOrKurC3fu3IHP50NlZSVNACNp8rG+JtJmqLQiyQfb7XnZbDZWVlbwb//2bzh37hyuXLkSc5H7FwUxeg6HAzabDZOTk3j06BEGBgZogqRUKsVHH32Eurq617p4Q43x/Pw82tra0NbWBp1Oh6amJpoEt5uMK4NNHMqdC7CZ45KWloZ33nkH//3f/42+vr4wvc+4uDgkJCTQYjdkQmzlcRC/g0ajof/udWrvRpqApB8rKyvo6+tDd3c3nE4n9Ho9CgsLkZOTA41GQ9PwY9HKIV9giqIwNjaGlpYWDA0N0eH6qqoqyOXyHb/gJIN8fHwc5eXltBN9v749ZAcaHx8PpVJJ75b6+vowMzMDj8eDtLQ05OXlvZYMdTJ+fr8fZrMZXV1dGB4ehtfrxYULF1BTU4PS0tKYkxYZHGLjQqI9BQUFyMnJwejoKMbGxlBdXR12Die6K6Hb/lBnJYCwBRq67d2PhUPuQbg4JBpDFM8cDgfW19cxMzOD+fl5OJ1O+qhQWFiIlJSUMF5ErJOYbOONRiNGRkZoB/D6+jrN/VEqlTv6Urbe53X4EDweDywWC+bm5jA+Po6pqSmMj4/DbrfD7/eju7sbmZmZuHLlCp2WsFfY+myBQACrq6vo7+9Hf38/3G437fQvKyuDRqOho4uMYYkNh9a4AKCJUKdPn8b4+DgGBgaQlZW1rRTCy2il7vQ3rwqyKO12O8xmM1ZXV7GwsICNjQ3Y7XbYbDasra1hdnYWSqUSFRUVOHXqFB3CfNl++nw+zMzMoK+vDzweD+fOnUNaWhqMRiP+93//F0tLS7sKbRNnrlarhVQqjfm+rwKKouB2u+maV16vF2lpadDpdPD7/eBwOJienqZL1uz1B4E8H8nPev78Oebm5hAIBFBZWYmmpibo9XrExcUxfpWXwKE2LizWJuGN5In09vait7cXZ8+ePbQ8AjJh3W43VlZWMDU1hSdPnsBoNNJlMyUSCSoqKvDxxx+jvLx8W7WEl1nUZrMZra2tkMlkOHPmDFJTUxEIBCCRSMIyX3drWywW4/z583Re0cv2JVYIhUJkZGQgLS0Nb731Fs1C9vl8cDqddCg5Li4OFEXtyTsPPT4SRu7AwAAeP36M+fl5XL58mRbEJmkgzE7l5XA4V2gIyNm8oaEBMzMzMBqNKC8vh0qleiFH5+sCmYhyuRxpaWkIBoOYmprC6OgoTS7T6/X46KOPaC3W0OPay8Dj8WBychKtra24evUq3G43xsfH4fV6MTY2Bp/PR399d9q5BINBCIVCNDc301Kjr8vPQYwGi7Wp70N8YkR4nQgekb95lftRFAWPx4OVlRUMDw+jr6+PrkLxgx/8ADk5OdDpdODxeMxu5RVx6I0LsJnJTISTHz9+jJ6eHtTX14fphhw0tvIj3G43hoaGcPfuXTr6oVarIZVK8Z3vfAfV1dWQSCRh17zMPTkcDkwmE3p7e7G0tIRPPvkE9+/fRyAQgM/ng8/nQ2ZmJhQKBX2fnY6MhPBGnOKve3GR59m6W3jVD0ioP87pdGJoaIiW8MjIyMDZs2dRXl4elhbB4NVxJIwLyVk5ffo0FhcX8c033yA3N3ffaty+DFisTeo5UYJrbW3F5OQkAoEA6urqoFAoMDExgYSEBDQ0NNCh8FfdIXC5XJhMJkxMTKC5uRkqlYpWm5uamkJbWxv0ej1dFXOne7HZbNhsNnzxxRcoLCxEZWXlvhDpXgav+o5JJKy/vx9PnjzB6OgodDodrl69ivLycmRlZdFpJodlPh0HHAnjAmxOkIyMDJSVlaGzsxODg4OQy+XQarUHIg691TAQLV6DwYCHDx/CZrMhNzcXpaWlOHHiBGZnZyGTyZCdnY2kpKRX1psl9/V6vVhYWIDNZsNPfvITWpXe7Xajvb0dY2NjdDh3a8QsFGw2Gy6XC19//TWdGHkYRLdfBKHRQbJDc7lcmJmZwfPnz2EymeBwOFBUVIQzZ86guroaIpHotQs3vSk4MsaFhKbJxHj27BlUKlXUL/J+9ofF+rNu7cjICL799lsMDQ0hGAyiubkZFy9eRGpqKoLBIJaWlpCRkYHi4mLw+fyIamYven9gM9JhsVgAACkpKVAoFLSfZ3p6GmlpaTS7meiW7MS9oSgKVqsVLpfryIZcCTvZ4/HAarViamoK3d3d6Ovrg16vx5UrV3Dq1Kk3WgrhdeHIGBdgc+IkJyejsbER9+7dQ39/P3JycqBWq1+b8nxoHlCoI7W9vR0CgQDf+c53UF9fD51OBy6XS/crIyMDAGhB8r3oB7C5YyJZ0MRh63Q60dbWhv7+fnz88cdITEyMevwii3KvnKevG6EESbfbjcnJSTx8+BBGoxFarRY//vGPUVtbi4SEBNq5fZSe7yjiSBkXYFMlLjU1la4zYzQa0dDQ8NrOy4FAAC6XC1arFX19fejp6YHD4cDJkydRUlKCrKwsaLVaOnxKCHxETX+vJzUJNVutVkxOTtLks6WlJTqDOlRfeDcIBALU1NTQuy3g8BsY0r9AIAC73Y75+Xn09fXR+VlXrlxBeXk5cnJyoFAo9lWQmkE4jpxxYbPZUCqVuHTpEj2RSMbzfmqzkGPD0tISHj16hNHRUbBYLFr1Ljc3l1ZTJ19Qch3h6wB7q8fLYm3KU6SlpYHFYuHnP/85pFIpUlJSUFNTg6KiojC92GiQSqV47733wvwzhx1kx2WxWNDa2oqHDx+Cz+ejpKQEVVVVKCwsRGJi4r4VW2ewMw5t4uJuCAaDsNvtuHnzJu7cuYPa2lpcu3aNljTcq3uEZhdbrVb09PSgo6MDU1NT0Gg0OHHiBC3BGUtx8r0G2QmZTCY8ffoUExMTAICamhqUl5fTWjWxtkVytvx+Py3OddgQ6qzlcDh0RcOBgQFYrVa6LGptbS1t7Jko0MHgSBoXYJPuPjIygl/84hfw+/24ceMGXcx+r0BRFGw2G8xmM62RajabkZWVhcbGRuTk5ISVwjyooaQoipYAJYvuRQvFs1gs2odEhKMOC4cICJe9JBnxi4uLGBgYQF9fHzweDy2InZaWBoFAcGhZ3G8KjqxxATYjJXfu3EFLSwu0Wi3ef/99yOXyl24vNFnQ7XZjaWkJfX196OzsxPz8PAoKCnD69Gnaj3HQ5UsJyJc8NDv8ZfRnl5aW8C//8i9obm7G9evXaYbsYQD5aLjdbphMJvT396OjowNerxeFhYU4f/489Ho9nbXM4OBxpE27SCTCyZMn0d/fjwcPHuDEiRPIz8+HQCB4qUVBspkdDgeeP3+OlpYWzM/PIzc3l05iUyqVYblAh2W7vdWgvGi/CNFsYmICFovlUEVTyK5qY2MD/f39aG1txfT0NOrq6vDWW2/RztrQSBeDg8eRNi4ki7eiogKTk5Po6uqCWq2mk/ZeZHGQrfbk5CTtVxGLxbh48SJyc3ORkZGxJ3lAhxVkrIg8xOuQXIiG0NDywMAAWltbsbCwgLS0NJw+fRplZWVIT09/Id8Sg9eHI21cyAI4ceIENjY28MknnyA7OztMaGk3EL+Ex+PB6Ogo2tvbMT4+DgDIyMhATU0NnVwYGlY+ruByuUhOTj7QxRrqrN3Y2MD4+Dg6OzsxPT0Nj8eD0tJSnD17FqWlpYwUwiHHkTYuBCqVCpWVlbhz5w4GBgag0+mQn5+/Y3VB8r9OpxPT09N0udi1tTVoNBpUV1cjPz+fPr/vVB/4OIFIQbzzzjvIy8t7LZILW0EMi9vtpjPgh4eH4XK5kJGRgRMnTqCwsBAymYwxLEcAR9qhS0AErr/66ivcu3cPtbW1ePvttyOGIIPBzcqCNpsNU1NT6OjoQH9/P0QiES1nGCpleAyGJ2aQYwgJwb/uexM9l+npaXR0dGBwcBACgQDXrl1DXV0dza49rgb+uOFYGBdg01cwNzeHn/3sZ/D5fHTlu9B6RxRFwW63Y3x8HA8fPqTlHwm7NjEx8Vj7VWLB63z20FQKh8OBhYUF3L17F0+ePIFcLsfVq1dpoyIUChm+yhHDsTEuFEXB4XDg22+/xddff43s7GzcuHEDUqmU1q+dnZ1FR0cHent7wWazad3ajIwMunohg9cHIgg1OzuLJ0+eoKenB1KpFEVFRSguLkZOTg6USmVY6VcGRwfHZjWx2WyIxWKcOHECAwMDmJycxOjoKEpLS7G0tISnT5/SVfJSUlJQUFCA8vJyml17mAhjxxWh7FqKorC4uAiDwYDe3l6sr69Do9Hg9OnTqK6uhlarZQzKEcex2bkQEB2TmzdvIi4uDpWVlejv78fk5CTNizl16hRdgIsxKq8PpFyJ1WqF0WiEwWDA1NQUFAoFKisrcebMGWi1WvD5fMawHAMcm51LKAh1/d69e1hYWACXy0VpaSlOnjyJvLy8sEgDc4bffxBC3urqKkZHR2E0GjE7O4tAIICamhqcPn0a6enpkEgkB5KjxWB/cCyMC4ly+Hw+LC0t4dmzZ1hYWIDb7YbZbMbf/u3fory8nE65j1TelMH+gJDg3G43DAYDvvzyS4yNjeH8+fO4dOkSMjMzIZVKwePxmHdxzHDkjUswGITb7cbGxgaGhobw6aefYnx8HJWVlSgoKEBrayucTie4XC6tsQIwRmU/EZrjtLGxgc7OTrS0tMBqtSI/Px/vv/8+CgoKaLLjYUo1YLB3OLLGhexU1tbW0N/fD4PBAIvFApVKhYqKClRWVtL1oY1GI9LT06FSqQC83nDrm4CtSv2BQAAWiwVjY2Po6emByWSCVCpFXV0dysvLodfrmdDyG4AjZ1zI5PX5fBgeHkZ7ezv6+/sRCASQm5uLxsZGFBYWQigUwmazIRgM4j//8z8xMDCAzMxMpoD4PiFUU3hkZASPHz/G0NAQ2Gw2cnNzae0bIsfJ4PjjSBmXYDAIh8MBk8mE8fFxGAwGTExMQKPR4OzZs6ioqIBMJqOdghKJhE5uGx0dRV9fHxoaGpidyx6CsHm9Xi9mZmboCgjT09NQqVS4du0aKioqaDlOxrC8OTgSoWiKouD1erG4uIjBwUG0t7fDZDIhKyuLllmIj4+nawGF7kxcLhcePXqEzz77DElJSfjRj34EsVjMTPJXRGjpjvX1dUxOTqKzsxMGgwE6OtWE9gAADk1JREFUnQ4NDQ0oLS2FWq2mtW8YvFk41DsXcgRyu92Ym5vD119/jSdPniAuLg4XLlxAdXU1rTq2k7GIi4tDWVkZnQT39OlTnDx5EhKJ5NhnOe8ltvpVCLt2cnISbW1t6OzshFQqpfOz0tPTmSPoG45Da1wCgQC91f7222/x7NkzSCQSnD9/HmVlZcjIyIBMJosawmSz2ZDL5Th58iTGxsbwxRdfICcnB1KpFAATNXpRsNls+Hw+LCwsoKWlBR0dHWCxWGhsbERVVRVtVJjQMoNDZVzIF9Hj8WB+fh4GgwFGoxF2ux3p6ekoKytDVVUVXbEwlqMNi8UCj8dDTk4OiouL8eDBA/T390OtVtO1mpndy84gBoIUhzebzejq6kJ3dzecTieysrJQUFCA2tpauqQKc+RkABwi40JS7ldXV/H8+XN0dXVhZGQEIpEIp06dQn19PbRa7UvVnWGxWJDJZGhoaIDZbEZHRwf0ej1d+pRBZIRq8xJ2bV9fH4xGI5xOJxobG3H58mWkpaUxBoXBNhyKleX3+2GxWDA+Pg6j0Yhnz57B5/OhtrYWly9fhkwmo2v6viw4HA4yMjJQVVWFTz75hJZbSEhI2MMnOR4IlULY2NjA/Pw8enp60NnZCZfLherqapw7dw5JSUm0E50Bg604MONCnLV2ux1ra2vo6urCvXv34HA4UF1djZMnTyI9PR1KpXJPdhdsNht8Ph/5+fkoLS1FZ2cniouLGamFCAhNpejr68Pjx4+xsrKC3NxcnDp1CoWFhYiPj6cLvTFgEAn7uqoi+TJCa8+srq7i6dOnaG9vx9zcHPR6PU6ePIni4mKaGr6X4HA4SE9PR2VlJbq7u2EwGKBWq5GWlsb4XULgcDhgNBrx1VdfYWpqCnq9Hh988AEKCgqQmprKOGsZxIR9MS6hqu3kh+QAORwOrK2tYWBgAMPDw2Cz2UhOTkZNTQ3y8/ORnp5OU8P3GsS5q9frcerUKfpoRIzLm75gPB4Pnj17htbWVphMJiQlJeHdd99FYWEh9Ho9fTR908eJQWzYt52Ly+XC/Pw8FhYWMDMzA7PZjLW1NdjtdqyurmJ4eBiJiYloampCc3MzcnNz6boz+zl5WSwWEhMTcfbsWXR3d2NwcBCVlZXQarVvFHM39FkdDgdmZ2cxMjKC3t5ezM3NQavV4sKFC6isrIRAIGDygBi8MPZt5+Lz+WC327G0tITOzk7cunUL09PTCAaD4PF4KCwsxA9/+EM0NTVBqVS+1sxYoVAIvV6P2tpaDA0NoaWlBTdu3IBAIHgjxKMIZd/j8dB+lY6ODoyPjyMzMxPf+973UFNTA5lMxhgVBi+NfTEuJK8nNTUVXq8XKpUKMpkMAoEAPp8Per0ef/M3f4OGhoYDKb9JCq43NTVhdnYWXV1deOutt5CUlIS4uLhju3sJLXy2srKCsbExdHZ2YmJiAlKpFO+99x4qKyuhVqshlUoZKQQGr4Q9Ny4kY9ntdmN0dBS//OUv0dXVBZFIhJKSEjgcDjQ1NeHcuXNITEw8sJwTDoeD1NRUlJeX0/Wmr127BrVafSyNC0l1IIblj3/8I1paWiCXy9Hc3Iy6ujpoNBpIpVImD4jBnmBPjQsJLT9+/BjffvstBgYG4HA4cOHCBZSXl2NgYABGoxGXLl1CSkrKgRKvWCwWBAIBqqurMTk5ibt376KgoADx8fGHpsD8XiCUs2IymXD//n10dXUBAE6dOoWKigqUlZVBpVIxKvsM9hSvbFxIZIhkLX/55ZdoaWnB6uoqCgoKUF1djYaGBroYmUKhQEFBwaEIZ7LZbGi1WpSWluL58+fo6elBRkYG7dw9DiB5QP39/TAajVhZWYFSqURVVRUqKirCBLGPyzMzOBx4JeNCkguXl5cxPT2NkZER3L9/H263G42NjXj//feRmZkJgUCAgYEBpKSkoKamhnbgHjRYLBb4fD5KS0sxOzuLnp4eDA8PQ6FQQCQSHdndC9mprK+vY2JiAs+ePUNfXx/8fj9qampw9uxZpKamgs/nM0cgBvuGlzYuFEVhfX0do6OjePjwIQwGA4RCIW7cuIHq6mokJibSoWVgs55zQkICXSfosIDD4UCj0eDUqVMwGo1ob2+HTqdDTk7OkfuSk3pAbrcb09PT6O3tRWtrKywWC2pra2lBbGJUjtrzMThaeOFV7vV66RCzwWBAR0cHHA4HamtrUVZWhry8PCiVyjB2bTAYhFqtBoA9Z92+KlgsFjgcDpKTk3HixAncvn0bo6OjSE1NhUAgOOjuRUVo1rLdbofVakV/fz/u3r2LxcVFVFRUoKqqChkZGUhOTmZqAjF4bYjJuJBIg9/vh9lsRmdnJ+7duwefz4fs7GxUVlZCr9cjOTk5IoOTHD8OK4jmS2VlJZ4+fYrnz58jNTUVpaWlB921XUHeCzEsvb29aGlpoUlwb7/9NmpqaqDT6SAUCg+6uwzeMMRkXCiKwsbGBjo6OvDo0SPMz88jISEBZWVlqK2tRVJSEng83pHeapPdS1NTEz7//HNwOBzk5eUdWqNIokAOhwODg4Noa2vD2NgYuNz/1979/STZ/3EcfyLgFMVioZE6NQlBUJYCQsZKZ7VytlUntY5ah/5HtQ7cXAe1OquWrbVS2vwRqMMlhpZpWjp/zCFgU+w++A6W3759s3v3deeP9+MPYLDr4rX3dX0+7/dHg8/nw+v1UlVVJZWK+GN+Gi7pMYYrKytMTEwQiUR49+4d8Xgch8NBU1MTR48eJT8/f1eHSppKpUKv19PQ0EB3dzcfPnwgEolgs9nIzc394zt3v9+uv7m5STKZZHp6mlAoxNjYGLFYjNLSUnw+X6bbOzs7e9dfF7F7/RAu6VI7Ho8zMzNDOBymv7+f2dlZrFYrbW1t2Gw29Hr9nmti02q1mEwmmpubCQQCPH36FJPJRE5Ozo74nSqVKrM6F41G6e/vZ2BggMLCQi5evIjL5cqMQtgJ31fsb1vCJT3HY3V1lVAoxJMnT4hGo3g8Htrb27FarVuOiNiLN7BaraapqYnZ2VkePXqE3++noKCAvLy8P7o0nUqlSCaTTE5O8vjxY3p6eigtLeXmzZu4XC4OHDjwrzR+CrFdW8JlY2ODsbExAoEA0WiU7Oxsrl69itPppLKycl8cyaFSqcjNzaW2tpZwOEwgEKC0tJTy8vJf/mn/e0L+P/Fd1tfXicfjTE1NEQwGefv2Levr67S2tlJbWysDr8SO9UPlsrq6SiqVoqamBrvdTk1Nzb4Ile9ptVqsVit+v59nz54RDocpKipCp9P9dCzDPz2uIb1n5cuXL/T29hIIBFhbW6O8vByv15sZqLWfrovYXbYciraxscH8/DzJZBKDwYBOp9uX09zTrQqRSITOzk60Wi3Xrl3DZrP9sE/n+92wg4ODLC8vY7fbsVgsf6uaSH/e0tISr1+/JhQKsbS0hMFgoLa2FrfbndmyL9WK2Mm23J1qtRqTycS3b9/27DuV7VCpVGg0GioqKvD7/Tx8+JCRkRFKSkowGAyZKiU9wHpqaorR0VH6+/v5+PEj58+fp7CwMNMEuR3pfUQrKyvMzc1lHskWFxdpbGyktbWVI0eOyOAmsWvsiuNc/6T379/T0dFBLBbjypUr+Hw+srKySCQSLCwsZGbNTkxMUF9fTzKZJJVKce7cOVpaWn75IjgdVIlEYssGxeXlZTweD36/H4vF8ltBJcROIOHyC6urqwwMDHDr1i18Ph/Xr19nfX2dYDBIV1cXsVgMq9WK2+3m2LFjzM3NcefOHfR6Pe3t7ZjN5p9WgenVuaWlJUKhUKab3Gaz4fP5sFqtmaXl/VxJit1JHtp/QafTYbfbsVqtTE9Pc+/ePWKxGJ8/f0an0+Fyuaivr6eqqoqcnBz0ej0ej4dgMEhvby9FRUUUFBRsCYZ0qMTjcSKRCD09PUxMTHDo0CHOnj3L8ePHMZvN//cMbCF2OqlctmFtbY1wOExHRwfBYBC73U5dXR0+n4/q6urMKhL8Z37Kp0+f6OzsZHl5mRs3bmCz2TJtBCqVikQiwdjYGK9evWJ8fJzNzU3MZjMnT57E6XRKqIg9QSqXbdBqtVRXV2M2m4lEIlRWVtLS0kJFRcUPu2E1Gg3FxcW4XC66urp4/vw5ZWVlaDQavn79mmkrSE/ZLysro6mpCZvNlpkzLMEi9gIJl21Qq9Xk5eXR2NhILBZjcXGRVCr1P5sCs7Ky0Gq1OJ1OJicn6e7u5syZMxw+fJipqSlevHjBmzdvKCoq4vLly7hcLoxGIxqNRkJF7CkSLtukUqlwOp3EYjFu377N8PAwxcXFGAyGH0JBrVZTUlJCXV0dw8PD3L17l83NTebn58nPz+fSpUt4vV5MJlNmg6K8rBV7jYTLb8jOzsZsNuNwOBgcHMThcKDX67fMA/7+tMl0Y+fLly+prq6mubkZh8NBWVkZRqNRBmKLPU1e6P6GdLd4X18fDx48wO1209bWhtFoJCsra8sB7gMDAwwNDbGwsEB+fj4ej4dTp05lHoGE2OvkLv8N6eNIbDYbFouFvr4+iouLOX36NDk5OSwuLhKJRAgGg4yMjKDVamlsbKSlpQWj0bgjTjwQ4t8i4fKb1Go1RqMRr9dLMBgkFApRWFhIKpViaGiIaDRKKpXC7XbT0NBAeXk5Bw4c2HOzb4T4FXks+ptmZma4f/8+4+Pj6HQ6EokEo6OjnDhxggsXLmCxWDh48OCOHZMphNIkXIQQipClCiGEIiRchBCKkHARQihCwkUIoQgJFyGEIiRchBCKkHARQihCwkUIoQgJFyGEIiRchBCKkHARQihCwkUIoQgJFyGEIiRchBCKkHARQihCwkUIoQgJFyGEIiRchBCKkHARQihCwkUIoQgJFyGEIv4CzGYu7Y+9WrMAAAAASUVORK5CYII=)
A point source of light S is placed at the bottom of a vessel containing a liquid of refractive index 5/3. A person is viewing the source from above the surface. There is an opaque disc D of radius 1 cm floating on the surface of the liquid. The centre of the disc lies vertically above the source S. The liquid from the vessel is gradually drained out through a tap. The maximum height of the liquid for which the source cannot be seen at all from above is
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)
A point source of light S is placed at the bottom of a vessel containing a liquid of refractive index 5/3. A person is viewing the source from above the surface. There is an opaque disc D of radius 1 cm floating on the surface of the liquid. The centre of the disc lies vertically above the source S. The liquid from the vessel is gradually drained out through a tap. The maximum height of the liquid for which the source cannot be seen at all from above is
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)
A ray of light strikes a plane mirror M at an angle of 45° as shown in the figure. After reflection, the ray passes through a prism of refractive index 1.5 whose apex angle is 4°. The total angle through which the ray is deviated is
![](data:image/png;base64,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)
A ray of light strikes a plane mirror M at an angle of 45° as shown in the figure. After reflection, the ray passes through a prism of refractive index 1.5 whose apex angle is 4°. The total angle through which the ray is deviated is
![](data:image/png;base64,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)
A rod is fived between two points at 20° The Coefficient of linear expansion of material of rad is and Young's modulus is
. Find the stress developed in the rod if temperature of rod becomes 10°
A rod is fived between two points at 20° The Coefficient of linear expansion of material of rad is and Young's modulus is
. Find the stress developed in the rod if temperature of rod becomes 10°
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means