Physics-
General
Easy
Question
A wheel of radius ‘r’ and mass ‘m’ stands in front of a step of height 'h’ The least horizontal force which should be applied to the axle of the wheel to allow it to raise onto the step is
![](data:image/png;base64,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)
The correct answer is: ![fraction numerator m g square root of h left parenthesis 2 r minus h right parenthesis end root over denominator r minus h end fraction](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHUAAAAnCAYAAAAxQgdAAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAbSkFbcgAAA3VJREFUeNrtmk1oE0EUx5cSREIRi0IIKkrpQaSUQC1aVLyJeCgiBQ2eJCJFpIiXKCh6EUsQBRUvCh4EBakfh6KCFJEiogQUj3oQD6WUQIQStJT68Qb+gWXZ2bzZ2djZ9v3gj3F2dt97M7tv307H89ynk/RXFKnUcYT02hOWFS9IxxO4zknSWIrHYQwxpJ71pB/414Y+0rtlMB5vEUuqGSE9jTj+k9TBHIyC7/+7SOOkOdIC6RPp6BLHyomlnzSV9klV79JhzbEe0mfGNQqYVD9vSEUUYYpt6FNcoji5sXiY1P60TugWUo20WnP8IOkh4zoV0ilGv80GA5s03FgUoza1wUVSmZQj3SDNkmZIB3C8i3SNVEcaOxc4P4sBVRMzj3R3C9fkcJZ0h+HfOvgxC19GA/1ekvYwbc5H2FGvgir6lBOeVG4sikHSZFxDj2CsirSUwd38jZRHCjuM9k0INodzMzhexm+lM6RF3JUcPpL2M/xT6WgI76MN8CPr66duuFUMe4MhabppZ5p0ldTdpieVG4uHWObiGvqCO6Ir0D6NJyisPY/fF0iXNdfMhywuBOlFVsi08G8i5Pw67vgmi4xYVYp/jwIqzM6hNqdfbixNFuIY6UA1ljVsbzIT4ozq0wgUB/ewIrI70PcK6XoL/xohfmQCfnAmVd2cz0j7IsaBQ9yVH5NYrCZ1h2YVh9OuK7uD557HpKrv0A+BvirFb2/h36QmhQb9i0q/3ZjQHsNxSBKTWKzSbxEDHqddpar7BueqVZI/vvfxTtLXFqnXxL9XmrS6Fa+RbAw7SWI61rELJVXtnojZPqQpz9VElyI+vB/g903SJYZ/xzTtJcYnTQ7FSYZhp9TmSTWJxUMslTiGnvg+XUzb16AkL/g+/sdRSO3V2LtL+oVBruEpSsq/sMWHCYaNKDtJYjrWsRcf6pqPfm67elq/44VeRRFSi1gGW0v6TXrs8dZoTf1T1+xjFjWc6yWJSSxOLRP2MlZMpjCop9tgXxb0LVFp7bbve3QAzrRKdwOY1I1t8mvES/ef3iqaeua/0ImXfAMF0HM8qRyGPUEQhBWHbOCSDWiCIAiCIAjCSoS79VRICSbbNYWUYLJdU0gA17ZrCgng2nZNIQFc3K4pWODqdk3BAhe3awqWuLhdU7DExe2agiUubtcULHFtu6az/AM1NMDltTkGIAAAAO90RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWZyYWM+PG1yb3c+PG1pPm08L21pPjxtaT5nPC9taT48bXNxcnQ+PG1pPmg8L21pPjxtbz4oPC9tbz48bW4+MjwvbW4+PG1pPnI8L21pPjxtbz4tPC9tbz48bWk+aDwvbWk+PG1vPik8L21vPjwvbXNxcnQ+PC9tcm93Pjxtcm93PjxtaT5yPC9taT48bW8+LTwvbW8+PG1pPmg8L21pPjwvbXJvdz48L21mcmFjPjwvbWF0aD5SwguCAAAAAElFTkSuQmCC)
Applying the condition of rotational equilibrium,
![F left parenthesis r minus h right parenthesis equals m g x](data:image/png;base64,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)
But ![r to the power of 2 end exponent equals x to the power of 2 end exponent plus left parenthesis r minus h right parenthesis to the power of 2 end exponent rightwards double arrow x equals square root of h left parenthesis 2 r minus h right parenthesis end root](data:image/png;base64,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)
![therefore F equals fraction numerator m g square root of h left parenthesis 2 r minus h right parenthesis end root over denominator r minus h end fraction](data:image/png;base64,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)
Related Questions to study
Maths-
The order of differential equation is![open parentheses fraction numerator d squared y over denominator d x squared end fraction close parentheses cubed equals open parentheses 1 plus fraction numerator d y over denominator d x end fraction close parentheses to the power of 1 divided by 2 end exponent](data:image/png;base64,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)
The order of differential equation is![open parentheses fraction numerator d squared y over denominator d x squared end fraction close parentheses cubed equals open parentheses 1 plus fraction numerator d y over denominator d x end fraction close parentheses to the power of 1 divided by 2 end exponent](data:image/png;base64,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)
Maths-General
physics-
Two condensers, one of capacity
and the other of capacity
, are connected to a
volt battery , as shown. The work done in charging fully both the condensers is
![](data:image/png;base64,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)
Two condensers, one of capacity
and the other of capacity
, are connected to a
volt battery , as shown. The work done in charging fully both the condensers is
![](data:image/png;base64,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)
physics-General
physics-
A cubical block of side ‘L’ rests on a rough horizontal surface with coefficient of friction ‘m’ A horizontal force F is applied on the block as shown. If the coefficient of friction is sufficiently high so that the block does not slide before toppling, the minimum force required to topple the block is
![](data:image/png;base64,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)
A cubical block of side ‘L’ rests on a rough horizontal surface with coefficient of friction ‘m’ A horizontal force F is applied on the block as shown. If the coefficient of friction is sufficiently high so that the block does not slide before toppling, the minimum force required to topple the block is
![](data:image/png;base64,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)
physics-General
physics-
If the time period of a pendulum is 1 sec, then what is the length of the pendulum at point of intersection of l-T and
graph
![](data:image/png;base64,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)
If the time period of a pendulum is 1 sec, then what is the length of the pendulum at point of intersection of l-T and
graph
![](data:image/png;base64,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)
physics-General
Maths-
Order and degree of differential equation
are
Order and degree of differential equation
are
Maths-General
Maths-
The solution of
is
The solution of
is
Maths-General
physics-
For the given figure, calculate zero correction.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQsAAAFHCAYAAAC2z2lFAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAFxEAABcRAcom8z8AAEVGSURBVHhe7b2HdxxHlq+5/8mes+fN2327M2fn7b4578yZmZ3p90ZSS5runp5u9Uyrpe5WG6llWpbeiN6DIAmCBAh6D8IQlvDee28I78t774Df3htIEBBFFosSQQPe7zBYVYmsyMjMiC9vREZV/S8QBEGIAZGFIAgxIbIQBCEmRBaCIMSEyEIQhJgQWQiCEBMiC0EQYkJkIQhCTIgsBEGICZGFIAgxIbIQBCEmRBaCIMTEqsliQZIkSU8lPS2eiCyeZoEFQXg4q9kWn5gsOEXov8jCAiLzQHh+QZIkSU8hcZujB9DDYtLa45PmicgiQJaYdUfQoPMjY9SNiwNOnO934Vw/P0qSJOlJp8W25cLlQRdyxz3oNAdg9kUQIms8t7LgQtkC86ic8WFXsxU/K9Djn7Pm8Fq2Dm/kSpIkaTXS6zk61ca4rb1TbERijwPdJAxvmML6VeJ7y4LDnzlvGLdG3PhTpQlv5Mzh53f0+Iier6+zYF2tJEmSnmiidvVljQXvV5jwZq6ekg5bG62omvXCEYxoLfPJ871lweMU0+4wrg258OdqMz6kHUjocqBs2ocOUxDtRkmSJD3RRO2q2RBE/oQXO5tteK/MiG0ki5IpL6z+51kWFPXMkCxuDLtUJLG90Yb8cS8Mnsi9ARjuR0mSJOn7p6U25QsvYMwRwoUBl4oydpM0SqZfEFncJFlsqrdgDxW6fNoPd3A1hlgEQVhC743gxpAbG+kiva/FhtIXSRYbSRY7m2wonvRRoVdvoEUQXnZ4HHPaFcaVQYroay3YK7IQBOFBiCwEQYgJkYUgCDEhshAEISZEFoIgxITIQhCEmBBZCIIQEyILQRBiQmQhCEJMiCwEQYgJkYUgCDEhshAEISZEFoIgxITIQhCEmBBZCIIQEyILQRBiQmQhCEJMiCwEQYgJkYUgCDEhshAEISZEFoIgxITIQhCEmBBZCIIQEyILQRBiQmQhCEJMiCwEQYgJkYUgCDEhshAEISZEFoIgxITIQhCEmBBZCIIQEyILQRBiQmQhCEJMiCwEQYgJkYUgCDEhshAEISZEFoIgxITIQhCEmBBZCIIQEyILQRBiQmQhCEJMiCwEQYgJkYUgCDEhshAEISZEFoIgxITIQhCEmBBZCIIQEyILQRBiQmQhCEJMiCwEQYgJkYUgCDEhshAEISZEFoIgxITIQhCEmBBZCIIQEyILQRBiQmQhCEJMiCwEQYgJkYUgCDEhshAEISZEFoIgxITIQhCEmBBZCIIQEyILQRBiQmQhCEJMiCwEQYiJNSGLXSSLEpKFzSeyEITVYkkWV19oWTSTLKZIFhJZCMKqodqdJosNL5IspkkW14ac+LzWjE31VtyZ4EKLLARhNZmjdsfdkC9qzNT9t6J46jmXxfwCoPOEcWvEhc+o0B9WmJDS60SvJQhfmP4ITs8JC48uSwyrCC8dC5ifn0ckEqHH56OCuEPz6DYHcLTTjvepzX1NsiijyMIWeI5lwYfOEZxH1ZwPeygUervIiD+UmXCyy4Fmgx92Lvxz1gAXFujEh0MIBvzw+7zwein5fPAHggiFqEKIMYR7zCPgc8Ni0mN2VgejxQ5fcPUaZCy4qb21GQM41ePAb0qN+GWxAYfb7Wij9uYhiawW31sWTIhsO0n9p5xxD7Y1WpUwfl1ixM5mG/Jo2Zg9BL+KMp41EQQ8dsyO30VrXSXys28jLTUVt9KzUFBWg46+UejNTvifcWUQngPoghL0umHSTWGwrwvNTQ2oq2tAQ3Mb+u5SPbE4EKCG+TQDjWBkARPOMAonvdjXasN7ZUb8e5EBmxssyBnzYNYVUm1xtXgisuDi+WlHeOyimiKMBIoqPqww461CAz6uMiOlz6lMaAvQFf2ZOYNCyaAH+okBVObeRPyeLfjgvXfx77/4BX756/exYWc8rudUom9cD6cvpL1HeBlZmA/D77ZhYrALFYU5SLuVhts5+SgoLERWZjpSUzNQUtOKkVkzvIHwqgfOEYp07XQB66Jux8UBFz6tNuMX1LbeLzchnroh5dT9mCKJ+MPzq9qNfiKyWIJF4CAh9FiCuDnkVndH3qYQ6VeUtjZakE1RBpsx/AzCfK4AHrsRg51NyE+/juSTx3DowH7s3bsXB44cx9mrmShv6MKk3gZvMKy9S3j5WKCIwoG5kW6U5qTidEICTp29ivzyWrS0NKEsLw1nqe4cO30R2eXNmDLa1RV/tYhQpDBFEUP+hIcidauK2P+DRPFVnQWXB53oJIHwoCbfSl1tnqgsFHTceJhC7w2jlqKMY112CpcM+Nc7enxUZboXZVhoB5+aMhYi8LssGO1tRh6LIikZ56/eQlFVA7r67mJieg4GsxVOtxcBMvjzMoglPAPmQ7AbJtBcdhtJ8QewY/dhnLmRj467UzAYdBjprEJqSjw2b9qGAyevoK5nFDZP8InXZb6e2v3zaDcFcKHfiT9TNPEzakO/LTWq8YnyGR9F8iFqawu07tOpr09eFhrc3jjK6LMGkDbiwiaKMn5RqFdpe5MVBVNeNT8jOL/6SpyP+GGZHUJ13jUc3PYlfv+73+ODzzYjPuU6ius6MKGzwOMP3et/PoPAR3guWEDE78LM3XZkXz6J7RvXUfc0DldyajCqs8PHYxgT3ci/dhrrPvkYn27ci9SSJkwYnWoKwZMiRALgORRF1EZ43O+XRQb8vMCAdRRNXB9yqe4IT014GtHESlZNFktwf8voC6OGooz4DooyyIw/ydfjjxUmnOx2oNnohzO4uns9H/bBPDuM+qI0JOzfio/+8Bu89dYv8Mvf/AGfbd6D5Gs5aOwZgdnhVSddXPGSsjCPgNOEwdYKnDu6E59+/DE27ElAWmkbZq1ehIIBuPQjqMi8gA0f/wHvffAFTlwvRPe4kRq4lsf3xEVtodXgx+keBz6gNvJTLZo41GZT0cSc59l045lVlwUzT83PRxoctYeQOeLGl7UW/JiE8dMCjjJsahIXT13lkGo1mI+E4HFYMD3Sj6bqEmRcP4+4vVvw4e/ewU9/+nO888cvcCQlFbWdQzA7fWRs0cVLyXwEHussumruIGHPJnz4/kfYtP80squ7YXBQvQgF4TaOozrnCjZ/8h5+9dsPsfdMFpoHZxH8nnf7eNyDBykLqS3wBKu3KAL/cb5OTbi6NezCXVtQ3Rbli++z4qnIYgm+ahvIjLVzfhzvdODXZMwf5ujUveKknsWJXKtxn3iBGn+ETjSHkXabBbqZCQx2NSE/7Tz2bf0Cf6BuyZ837cX59BL0juvhlrshLyULC2G4zNNor8hG/I51+OCPH2LLoTPIre2B0elXsvCYJlCTexWbP/4t/uPX72PnqQw09M2o26jfFa7zfFPgTK8Tvysz4o1cHbUNA45SJF41S9GEO/RcXMCeqiyW4B0fJ4umj3jUrM9/ydOprgnfL84e86ixjNVnHk7jBJqKb+HY3q34asM2HE6+gcp2ii6oOyKxBTFPMaHPj4jZhNDsNML6Ocw7nViIrM15KAsLEbjNM+isysXxXRvwpw8++pYsXMYxVGVfwsaPfou3f/sn7EtZjCy+iyy4/fOdDp6ftIXq/s8o0v4RtQW+NXpz2I0RisRX807L4/JMZMHwoeWxilajX90x+TkdqH/MnFNGPdvvxICVQr7Q6h4onncxN9SKvOspiDsSh4TzqShvGYDB5n6G80GeFLQDHLJSP1w9/w4shOiKZjTA29QAZ1423GVFCAwPYd7v19ZYY9Cx8juMGGgqRcqRHfj0kz9TN+QUbld2QmfjMQs/HLq7KM04i3V/ek+NWSTcLEbPBMn0cSoMrcqznjmaONvnUJOrfnB7Tg3+czTRpPerOUnP20D7M5PFEjzjbMQRpCjDjc8pyngtew6vUFpfZ0HBpBfm7/nBmKgHPBKEdWYAtYUZuHTxEq7dLkJj7zgsLp+S2YvMAl0F550OhCkqiFitFCH4aH8f71guBAIITk7AlZcDy6kE2C9fgK+1BRG3W1vj26jbeNT3p8uwKgMLB2GKFJ+3mv9A+G6IE1MDLcg4F48t677Ehl3HcL2gEVNGJwJ+D8yTXci/nogvPvwAn6zfjdSSZkyaXI8xk3MBeuqK8zjdBqrjr1M3nNNnFE3comhi2BZ8rqKJlTwzWfDhWHlIAuF5tBj8atT3xxSKsWl/S8ZN7nWoe808SvxdWKBQOhjwwWGzQK/TQW80w+GmqwRVYo/dhNGeZpTk3UZmdh7KGzoxNmeF5ynMyosZ1fho3/lRJW35I5h3UeUe6Ienshze6koEh+6qZY/TaBcoggiOjcKZkQZz3CHYziTB29iACHVFHsYCiSFisyI0NgJ/TxcCgwMIG/RKPC8E80HY9ONo5Dtnh3Zjy9cHcOZGIXrHdbDZzRjtrMT1pENYt34L9p+8ivqecdi9sY1xOYIRtFEkfbrbocYm/mfWHP7tjh4Hqc5zNLGan+t4EjzzyGIlHGXw/eXsMbcay2BhvEIHlPtzxZMeZeTgY97QXoiE4LIaMNTTirLCO8jLL0JtUwcGh4Yx0NuBmvIS5OXdQUVdM+5OzMHpDT7Re+ZRWRIAy2BJCCvgsYF5j4eiA7PqDnAjjDVC4GjCW1sDa/IpWE4chSs/V0UJC+HYo4tFWYwtyuLo4UfLgso/7/WSmAZpezmwn0+h996Cv7tzUVQPY+k40H5xJMLCUcfjmbA4g3N2qAMFGVdwLC4ep87fREVTJ/oH+1BTlImUhDjEJV5AZlkrpo0UvT2iqHyXb9bN8yYWxyZey6F6TelTquO3xzyYcD1fYxMP47mSxRI8llGn8+FQ++JYBgvj1yUG9Sm7x44y5sNwW3Toa6nCrYtJOLx/Lw4cogqQchE307Nwp6gSjW29GJ8xwEWiiD2c/P6oroLDjrBej4jJSGJwkyC0wV1ueCQGbqzu6irV+Dw1VYsN3kvCeATz1FXwtbXAmpQI444tsKachq+jTTXmWLkni8x0mOOPwJaS/GhZUNfHT9u1XT4P85GD1HW5CF8nbdcdRRZkZy5vaHpKRUPBiXGVz7MaSF2gblTAbcXEYCfKC7Jw4/o1XLuZirT0dNy4cQM307JQVt9BUajtkZ9AdaloIqA+L/Uu1eHXsnX4jyIDDnfYUavzw/4dI+ZnwXMji2+30QXovGFkjnrwSZVJjWXwlPGvm2zI5U+yOkLwxhK2UQUOeZ2YGx9AfWkurp5LQsLxBCSeuYi0nBK0dAxCr7ci4KMw+amaghqW24XA3QHVVfBUllHI3o8IyUNdZQlu2IG+XthTb8AUd4CihER4aqtVlPGo6IIbWmhmCs7sTJgO7KZuxEG4SgoRNj36vUs8tiwoGohYzPDW18J2/gxFNPFw3M5AgCKNef9DBEe7yqLgfeexEfu1y/CUlyKsm1sc73hmUL3xu2GaHUVHUw0KcnOQlZWNQv508sAYTHZ31IjCy/OKnCEVJW9tsOJHeXoVUfC07SyKJuY83z4HT7H2fSeey8hiJTxq3GII4ESXXX0ojedl/LbUhDO9DtX/4y/7eNTHcvlKEfR74bRbYKBKOD09jalZHfQ6IxyzevinZ1TlnLfbsBAMUFt9AranhsONfd7hoBDcpfrsPH6yBD+P0Pa8DXWwnqOGlXAMrpzbCI4Mq0aq4AY/Ow1XUQHMx+NgOrxfdQlYMAsxRAgRujp762pV3qZ9u2C/cRWB4cHl/B8Brxd6DFlw94GPo6e8WInNmngC7sIChDgaCj644atB1AnaRk4mzIf2wXxwL0kjW+WjBkYfAB87dZ4o8mIJcYT2fbotXD8WgkEtP8p3RVdtPhyEl6Iiq9kEk8kEq90Jr58iQu3v98PTAviDXRwBJ1Ik/KvixbGJtymaONltV+NyzsATqF/PgOdeFktMkKX5ez6/rLHgp/kG/KLAgC2NVmSSuYftoe82OMTdgOG78BbfoYaaqRpuaG429sE4jgC0KOB+5klOHBW4S4rgqapQEuBuxhJ810B1FTraYbtwFsbdX8NCjctLkUPEYrmXL7+HBwrtVy/BRI3JeuaU6o5wtwVLXZaHQVfm8PAQnDeuwLJvJ6wnj8FHV/15O0UvsRAgWYwvysJCsrCTLPxNDRRbPySyoAYcnhyHuyCXRHEctuRT8FLUxPMzHhjNUPcjbNSr42M6egiGLRuo23QSvmYS0ooI6xtokg3099KxqoKvpYnO2Yxq7N8FJTiLCX7q/viaG9X4Cg/I8rF7XLgODlFdTBvhT1xbKRI2qPlDXGf5bt8k1eEXmRdGFoyaN6/1//ijuv9KJ4Lnz/Mdk7o5H3Tux5syvkDdAD/14zlk5iuv9cxpFUKHjdwQHxGqc2OnK3doZlr1tTn8XikZvr3orihTA4PmIwfgys1W6628WvIVLDRHV+KyElg4ciAZODJuIUgCW6CGqqCrXoSusr6yYthOHoeFGhUPGgbuUoSwQj4KzV38TV98FPjTs0G6GjpIWIYjBzG3dxdM1O+2jU7A7gvBSlGZha5yZl8YJnq9mMKw+Ofpb5QcXpgHh6G/lQbdkcMwJSfBWV+PoMOpemysZ068LbU9r0fddXFlkVwSjsJOEZO/sQ7zVrO2xgrU8XPC196qZGn4egtFL4dJHCQXEuG9sZuV0HsiNorGmpvoPSl0XPcvRkvUzbl3vB7EfZu+B20jbLXC19YM+81rKhpyZlO3aWQoen4r4OPNX+w06wmjetanPu/0+zIT3qRux7vFJpyi190UZfDHHV50XihZMHxiRh0hpA97sJns/RZFGDxgtK3RQn1BijIcQSWVWObQc584ND1JDTmLGupeGPfsgP36ZbqSd6tQe2W34X7UINjoMFx3cuBMT6Vwv3rxChpevHpE6CrLA4rW0ydh2EpXzFMnqFK2fiuE5+jC39sD+5WLMB3YoyrsYnRBDUzrDrEUghRdOK5eVuKx0BXbUV0FN3Wl3L6g6qrxJB4zNXKjL6K+HkDnjWCGKvC4yYWh2mb0nUhE76at6D5xGq2VLagbs6JixovSGQ+KpvhLlvUqFdLzkmmP+tBS1Zgd9Y39aLtwAz17D2DwxCmMlNdgYs6KaVdI9bt1tD2Db54kQ+Ix2WFu74Tx2jXo4+NgvnQBbpJBiLpi98Mh/73bsiRqEx175+00BCmSWeA5Gtp692BRkJzVMaX916/7DMadW+CkcxfS6+hALsudozaOGOZ9fnU3ibel7rCsrBP0XI2VkHQdaTdgou6PGteh88kXgEdGbVRCljF/snrQthhNbKinqJeiCf6EKEe9OWNeFU2s5rdXPU1eGFncf7i5cdTP+RHf6cAfyk1KGPx9GacoymDDs+n5m4MeBV9BeAzAfvOqqrAsDWd+jhrYUzMVHyIdHtcI0FXUfpUaOXUhbEkJKiTmaGPx7+QNCmddBXnUxdiukpOii+DUxDf74lTJ56myL0YO8bDS1dJJlddHZQp6vAhSPl5/CPapGejyCzARH4/hffvQe/Eamms7UDFkRi5JMnXEi8uDLpzpcyKB+sZxdFz2tdvxdbMVe7O7kHj4Gq59vhuXNsfhcEoh1t0ZpajMiN9XzuK3pe14p7iEUik976DjOYv3K8z4uGQWm9I6cPzIdVzedAiXdp3CiSvl2Fs5rb5v9VC7A8coyjvd61LfuZDWMo2i7GrUHU9B295D6D53BYNNXZgwOGHwU8OineEvcQ4EgvDPzMBVWkzdG4q8dm6FkyKFUG8XxfIPmPDFDZsk6yXxWM8mQ/fln6Hf+KUSe4CjMBLzPXhd7j5Rd9Lf1UGRYp3qDvJt55XjGtxtCU3ShaLojpIEnx/7pfOqGxKhiPNR+KkLxVO1y6a86tuq/kh18OeFBvyeHjm6aKEI+HmfN/G4vHCRxUp4xHnMGUb2qPbdn8UG9aG0HU1WdRelV/sWIXXOoshdDQS2NqmrupEqrvV0ArzUj1aTiaL0hcMU4vOYhGnvDhi3bYQj9TqCFMLyWAjDlThAEYHtzCl1+5IfvdQvXtkf56tg0OmCq7sbxqtXMLN/LyZPHMdYcTkGhmbQbvSrLxEquWvGnTuNuHPsHAo27UHGngQkXy7B7uIRfFVlxIeVFjVtmL+VjKcN852j1ykUfjWXrnS3hvBVcgWOkzBOxF3H5nOV+E3mCF0FdXgzfwR/l56P/+taAv7yWiL+PqMQP8obxb8VmPBW7ix+d6sP25OLcCzuBvYfy8SHFxrxk8wJ/DCXP8egx884sis24r0SPT7LHsL+c6U4t+8cru86iSunM3CuuBcXu624NeZDwZQPNRTNdA7rcbeiHqOJpzC6fSsmjx6FsbQMHur+hUikfGTunS5u/A4bAl2dsFN30bDhCxg2fUWiuLLYXVh5fmhdFbHMTMHN8iWxWE8lwE1CUGNRS7KgLiafOx78Ved813ZY+JxTdMjjRQ+NKKlQPK2bZxV3mYPq8xtbGqy0/wb8ko7BjmabmnXMcyruvyMapfq9MLzQsmD4JJgo5K7T+ZXRP640q5HnjytNSOyyo4rCaf5gmi+02I9/IFTJQgadurVojjugIgz7ZbrKdHaoPvLDRtq5GxMcHoKdroqGjV/BTFGJu6zkG12ICAnHU5gPC/3NvH8n7LfT4aGoxev1w0llMlHXYdrux9DdaXTdLkDTvjhUbduLrMTrSMptx45aPT6tseB3pQZ8cLMbW+KzcXxbIhJ3JmNfUiHWZ/Xj03K9+tg//2bL1yRN/sGZQ+02HKXoIqHbiQs9NuR061HbOYHGrnHUDOhQOuqkbocHN4Z50lsRfpp/HD/LP4HtjaW4NaJD8bRPfVy6eMSG6v451HVNoLRjEqmdBiR32dTnefgbm/a32bGTtretwYwdpRM4lNaMhDP5iD+ZpaT0Xvog3sqfw8+Kzfg19eU/LZvDodsduH7yJgo37kTZpl0oP38Ljc2D6De4MUXnykjdGp5/4AlRV8/hhI+u9g666hspmuDkoC7b4jjFNyMKFS3MTsNdUQrL8SPU/dtIj0dJAjWLkQWto+TjclHXr1sJx0iiNx/eDzdFgHyr+WFjVfxWD52vSbo4lZL0+DMcHNHyF9N8Um1SER3ftbNTxLtWeeFlsQQPbI44Qsgg229vtFA4bcAf6ErLUQbPue80BWCmfvXD+o9c0QKjI3Ckp6rBTvPBPdSH5jkCQ4sTmbi2PIAFvqNRXwsLh7KbvoQt5bSqiAvexXA6TF0Jd28v9GfPYHLbJowfO4a7xVVoGdShhELY1FGv+p2VY/VzOHqrEYmHruDMthM4fugatl2tx4cFk2ra+3vlZnxeMo24/F7cyqrDndw65Fb2IaNjDplDTnVFq571o5UqbJ8lqMZ1Zt0Rtc88pkFPwTMd7h+PdwVtyBurxtb6ZDpuZ1A4WUcR2zfHVXjPuVl66Allq76licdF+Bvdub/eYQqiQedD1bgDVSSW8tZR5NUP40LdBPbVG/BVrRnvU+TDIfoHhdPYcr0Zx4+l4syOkzh+8DJ2XWvA9vIpHGyz4jQ1uhvDHhKVG82jJow0tGP6/AVMbliHyXUkiwvn4evv/9bdChZHaHZmURQnjqrow3Rwn+oGhmcpqtC6fnyrlcdFXHlZavzHuJcEzoOk1O172FwQjiYMdEFqpq4F/6gPj5X9psSovpRmF4kyj6TLX1b91Gb+PiPWjCwYHqIwUCVupCgjqcehPpzDJ5WnjvOodAVFGRNUwfnTrMoZ97V/dSuzvQ22c2dUaGo+EQ93eamqhIvh7gOEQVEH361wZaZRV2QTvW8bHLlZ8ExMwOGlBusMYmBkDi03c1C/bTeqN+9E9ukbOHWnB9tqDfio2kJdJxN+VTCH9zMG8PWlWpw+X4jLqZW4VNaPix1GpJLsCulq1qz3YcTig9HuhcPlg8sTgMsfVgO6fNVT4wFUsbnbxcdC+e0BRV5mARafDVmjVdhcl4ytDWeQP1EHR+Aht0ZXwHnzMeRt8VRlHnj20QtfMAxvIETlCsHmC6k7VHxru80YRDl1QfKGbMhuGkdWUQuuZdTgUEYrPs4dxX9Ql+gXdJV+hxrgn6rM2Fqtw6mCHuSdvo7adVtQ/dHnqIk7ha7adkyZXEpaAVUGHqMIIKybVV1H26njMG5Zr2TvupOH4PTkvTEiFkaI54HUVKuuJg9oqztgTQ3qduz9cOPn2cQs3iKSMY+P/anChHep2/EF1akLAy41n4LvKj3kGrSmWFOyWIIHlu5ag8gYcatvRP59uZFCRqP61abUIY4ygur24Lc+VkwVT41DVJSr23jGHVtVF8PX2rT4yc2HjZDTcm9HB3QJxzG97nNMHTmEuyWVqL+rV/fXk9pNOHGrAWf2puDy+oM4ue8CNl9vwicls/i01ootjYvdhgs9VhT2m9A2pMPdcQNGdQ5M2vwweCKqy0L/nijz1FUyeK10nKqwkWSxuT4FOWN1dGy+fffiScBjTFYSqMHmxbTBhqEZKxomHcgZdeNcv0tNgebvZ/2yzoIviyex62otzu5OwvVPv0bilhM4eLkSJ5vmcHPMh0pdAL2WAGbtPtimZuGqqYKDRGHdug62/bvg4Yld01P3zpn6AiSHXd1NsV+5pLqafI5dxYVKIPdPLQ/S+iqaoEjt0oBTfVM9jwlx12N/6+Lv4Yw7F78w92VhTcqC4a9QN1KUUU/hMX+mhK8E/Ek/niDDYxv8I7J8xeCr8jd+gYzHISYpKridDtP+3TAf2A1n2k0EBwfUvIwl+ErCFcpNDcBA/dR+6vvX3cxDw4ZtqPl8PTISruJoXje+qlocP9mQN4z4GzW4diEPqanluFR5F1dIDjnjXjToAximsvCtz6fZ5X3asngYFJSorhI3Pp5HUzjpQ1qPCWkVfchJLUbaxRzEpTbg88IJfEjH8hMS7NZGK461WXCrZQp1+VUYSDiFkfXrMLrja+gy0uEen0AktCz3BZ4DMjKkupY8RmGmc+tIv6W+n+Mb82PonPK4A3+fCgshjgT2cZVJ1R3+wtzz/U60UTTxPP7S3mqzZmXBsAM4jBy0BdV8fB744zCSfxtyB0UcPCOUp4zzFwoHVnQ4uWKpWZOXz9MV6Gt1e89dXKAkEvIH1M/H8TwGzreeugY5FKKe6bQiPqcTFw+cxY31+3CC+uKbqW/+RekcvqbIIamLrkYDJrSPGDA+Y4HO6oHZE1b36bn7wN2Gp83zIosl+BRwd4YFbiXRm2wezOis6J4w486wDckkfb7j8BF1U35NXbffFUxjc1oHUo5dR/ZXO5D/xXbknrqKmvo+DBg90PsX4KH8QvwZF+pK8mdOrCePw8wD2DxhjLqc9251U+Jb7fyFuA3Ujb1AkQ4PGPNPcbKgWBrcFWGhcYT0MrKmZbEEXy34x5v5uz95LIN/oIW7JvxlO8c67erXp3lw1EOVdBG+1NkRbKiBk0Jb266tahqyvrIKI6NzqJ92I4Pkk0gRytdNFnxSTVFLuRkfFU6rK2DqlQJk5tThduMoVXI76ihk7reFMetbgJM28bxUtedNFg+Dh4p1QWDQvtiQebLTWWrMRxv1iM/rQnLSbZzZdRoHD17Fxhst2FGjQ2K/B7cpamucdWNkfA6G+gb1GRzb3h1wJhxFoLIMsJgo5wV1PnjeTj9FE3xROdBmV4LgLsdm6n7wr4DxwPFq/kL5i8BLIQuGuxo8lnEvyqB+50dUIfhnFnlc4/pdl7r1xRGDl65GAQphHROTmMnKweiePejb9jVqky4j9U4rDtfOYn2dWVWoP1YYVbSyrs6KI202ZFD43DasxyRdER0uL0LhyHMbrb4oslgJH0v+VLjZN48Rkwcd1P2raehDVmELjhX0UiQ3u3hOKPrYUGvG0doZpOU3oz7lKgZ27MT43j3QpaXDMTwCvz8IF53rSTf/7KYf56iLsanBive5q0MXAP6Fcv7tDv6+CY7+XnZeGlkswSP3HGrW0xXqbB8PXFnVb5h8qaIMB/InvGg3BdFPV7HGSTvulHUg++hZZH61G+d3nsbuc2X4LG8En1UZ1GAcj4fcHnWr/PhDRDwoxt9h8FjfyfiMeBFlsZIw9Vt81OBtJOVpM3UpdR51ITjZ48TWJhs+K9fhi8w+HEjIwpVNh5Dz6VYUHD6NsqImtExY0EuRRJMxgHQ6f/tJ9Py7vB/QxWM7dXWu0cWjnf7G09if1e90PG+8dLJYQt0xoSiDv02cKwp/ZwZ/KI1HvXmy0bFup4o+NpdMYPf5ciTGXcfZxEycyWzE2cZppN11qK9p53kG/FOM3NWJxvNY3V50WdwP39w20bkYoPNaTucmrc+C82UDuHQ2B1d3n0TKjkQcSr6DHYXD6pzzNO191OX4kiIQPvfcLT3e5VDdUv5Mx8t0pyMWXlpZMBxl8Ff1NeopBKUoY12tRU2X5m/n4p+y50G0jyoM2F86htTyPlQ3DqJvaJauYm7Y/YufcH2EI55r1posluCRBf5Vf5vbj5lpA4aau9B0pwrp2bU4cGcAH5XM4u0SE96i88wfRHyPzvNOikR4+nY3f0SAoolHyf9l5KWWBcNVggc2edbjVQo9ebo4/44J/2wcD4SmUD+2ctqDYeofW5w+1c+dXyNT9daqLJZZwEIooD57YzVaMTRnQ/GYU33FAXc3+Dc6+MeG+XNF/G3bfKeD78YID+allcX9VYIHNfk3TLgLwvfU+ctUeWov/0oaD4KtDT18k7Uvi2/Csy5MgQU06QPqF/E+qDSpORR8t2OMRCG9jui89JHFEjzBim+dpWiDniwNnh7O3w+xVuvQyyYLhie9TWq/hsd3wfizQ7fH3OqzLuKK6IgsNHj8gm+rXhhwqrscJ7od6p4+339fq7yMsuD5VHOuCPLGvdjfyp/QtdJzNww+kcWjEFlo8GAlRxbnSBb8LUf8oaGaOb/67gKJLNYOPEdjmiKLrFEP9pAodlN0kaNFFmv3svBkEFloiCxeIlm4SBY8MU+TBX9dv8ji0YgsNEQWIguRRXREFhoiC5GFyCI6IgsNkYXIQmQRHZGFhshCZCGyiI7IQkNkIbIQWURHZKEhshBZiCyiI7LQEFmILEQW0RFZaIgsRBYii+iILDREFiILkUV0RBYaIguRhcgiOiILDZGFyEJkER2RhYbIQmQhsoiOyEJDZCGyEFlER2ShIbIQWYgsoiOy0BBZiCxEFtERWWiILEQWIovoiCw0RBYiC5FFdEQWGiILkYXIIjoiCw2RhchCZBEdkYWGyEJkIbKIjshCQ2QhshBZREdkoSGyEFmILKIjstAQWYgsRBbREVloiCxEFiKL6IgsNEQWIguRRXREFhoiC5GFyCI6IgsNkYXIQmQRHZGFhshCZCGyiI7IQkNkIbIQWURHZKEhshBZiCyiI7LQEFmILEQW0RFZaIgsRBYii+iILDREFiILkUV0RBYaIguRhcgiOiILDZGFyEJkER2RhYbIQmQhsoiOyEJDZCGyEFlER2ShIbIQWYgsoiOy0BBZiCxEFtERWWiILEQWIovoiCw0RBYiC5FFdEQWGiILkYXIIjoiCw2RhchCZBEdkYWGyEJkIbKIjshCQ2QhshBZREdkoSGyEFmILKIjstAQWYgsRBbREVloiCxEFiKL6IgsNEQWIguRRXREFhoiC5GFyCI6IgsNkYXIQmQRHZGFhshCZCGyiI7IQkNkIbIQWURHZKEhshBZiCyiI7LQEFmILEQW0RFZaIgsRBYii+iILDREFiILkUV0RBYaIguRhcgiOiILDZGFyEJkER2RhYbIQmQhsoiOyEJDZCGyEFlER2ShIbIQWYgsoiOy0BBZiCxEFtERWWiILEQWIovoiCw0RBYiC5FFdEQWGiILkYXIIjoiCw2RhchCZBEdkYWGyEJkIbKIjshCQ2QhshBZREdkoSGyEFmILKIjstAQWYgsRBbREVloiCxEFiKL6IgsNEQWIguRRXREFhoiC5GFyCI6IgsNkYXIQmQRHZGFhshCZCGyiI7IQkNkIbIQWURHZKEhshBZiCyiI7LQEFmILEQW0RFZaIgsRBYii+iILDREFiILkUV0RBYaIguRhcgiOiILDZGFyEJkER2RhYbIQmQhsoiOyEJDZCGyEFlER2ShIbIQWYgsoiOy0BBZiCxEFtERWWiILEQWIovoiCw0RBYiC5FFdEQWGuH5BQzagrhAsthGsjje5UC9zg9bgGrXmmUeZp8Vt0kWm0gWWxpSkDdeB3tg7cqCrgmYc4eRM+7BvlYr9pAwcsfdMPnC2hrCw3hsWfBVlhNbmNPS6xc1LeGnWtRHkcXZPoosGrTIYpYiCx9FFitWvP/930q08mMtX7UUfXtMhCILvceK9OEqbKhNxqb6M3SVraVo6puyeFReq56ewDFdgiPIKWcYt0c9ShS7KLLIoshC56HIYsWK97//RU9PgseSBZ+cIB1se4AqmTeCOTrABno0UoN6kZPZN49putrUzvmUJD6vsWB3i41Cci8GSSB6dwhGdxBGTwgG3md+pNcq0WuVD4Wx6rWLl9Hf+TUtV+uvWM7rGemY3Vu+lAcvX5m3Z3G5yketu7RcK4Na/oBlK5dT4jwftD0T7TOH3n0WE873VeDjqtP4c3UyLg/WUIRlhck/v/jee+/RtnHfNtV+35f3vTKvWHexHPevu5TninUp3Sszr8/LVhxTPtb38lDL6TnXQZW05ZyW8tDyXTp/M64QOowBXBxwYWO9BRvqLLhMz3stAVWnTVqdWGvJSufTE16gCPq7y+OxZBEiUeioUXF4fmPYjWS6Cp/j1P9iJ644yT1OJYjflBrxZp4e/15opMq02B3haON8v4vWdeGseuT3LT0uPld/v3csVqy7tEx75PXO9618Lyd+P/9t5bKVaTG/e69X5qme35+flvocaluLZVuZBy0bcKu/x3dO4aPKQvwwJwGv557EJ1UlONE1S3/3LL5Pre9YfKTjpPK4t30t76X17pVlaR1tOaVv7N9SuVVaWvf+tPzepXSW0nKZKGnb4OOsjut9f1Ovl7aj3uvEmV4nDrfbSY5m/Gu+Hj+h9Gd6frTDruWvvX+NpVRqr9xu5zwRFV19Fx5LFu7QAjpMASRSw3qvzISf3NHjl0VGvFvyYqdfkyDepv34Ub4Of5s2g7+6MY3/ljqL17J1eIuW/Sp3Cr/KGsevcibxq7xpvJNLj9n0mtI7+TN4t0iPdwt5vUm8Teu9Teu9c2cW79ByfvxV9gS9fwzv5E3h3QIdrUvL6X1v0/K37+VBywtoXVpH5U15vUvv5XxVHto2F/OYU+mdFeVSedC6796ZWV6X8+B1uRz0d1UOlcc0LTPg3WID3ioYxj9l5uAvr8XjL68fo+f5+EXBKH7N55W2u1jGMZUnb5u3xfvIx0TlrfZF28dsrRy0j4tlnlL7p/aF9m1xX6gcWh5c/nd4Xcrn3n5TPvxedUx5H/mY07FT2y/kfVnMQ+WrjimdD+34c35qOe8jraP2+w7lzceD16XHtynPf6N6+0+35/Bfb87grynx858XGPAO14X76saLnt4pNuJntG9v07k+2GZHo57H4b7bUO5jycIenEflrA/bm6z4MRn536gQX9Za1OuvX+C0k/qtWxst+LDShB/l6fAPGSSKHD1+Swf7y6JJbLrWhA2nirHhfBU23WzFpqsNWJdYhPVJJdh8uwfbq3XYWjyOjZdqse7EHaw/V4UteXexrUqnHjekVGD9yUJsut6CrUVj2FY2hc2Z3Vh/ppxSGTald2JryQS2UsPdyNtKLqO86rAld0At35zVhw0XaiifcrX9rYUjtO6Ier6B8th4vhpbqBxbS8bVe7gcG6hsm6400Lqj2Fo2jc3p3Srf9adpeWobtpfNYHujGV/VTZAw8vF3acfx9+knKKIqwrrqcXxdSWXP7MF6LjvlxXluutGiyrGey0fl5DKo8qV3UdkqsYH2m5/zPqr9pu3z/m3kcuTfVeXbnNWr1lufXKrKv6WY1qX92Uh5r08qVflszu7H9spZlT/vGx/TjZfq6RjTsaPlm7P7VL7rEgrUvmyrmFHl4PJxWflvm7N6aPksttyhPPh4nCrCxst12Eh5flppxC+KTfgBSeIHmXO0z8v1eMd9deNFTzxYz9L45+w5/KnChNxxr+pufZfY4rFkYSUjlUz7VAF+QwXY0WRDwYQXLdQHbKOIo5UeX7TURomjpUa9D2kjbqowFvyOoqYv66w42+tAUfskqm7koSwuCRVnrqM6owSV17JRcjARpUeTUVtcj+ZRExo7RlFxMR0le+JRnnQVdTVdaBoxqceyk5dQeiAR1bcK0Ng6jKa+KdQW1aEs4QJKT5xDdV4lGjpHUd/YR9vKRdnxc6i8mIG6qg40do6jtrQJFWdvUj4XaftFaGgeVImflyVcREXKDSpHA607hrrqTnpvOsqOnkHllSzU03qNvdOoya9V+ZbGJaM6swTNfTNoMXhRPGPEobYy/Kb4FMkxCUc7q1A6oUfrsJHKWI+yU5dpPymvi2moTiugcqSqfKpu5qG+aYC2OYqavCqU03q83zV51Wof62m/K69mqf1T5ajtVuXjfSlPvk55nFXlaGgfRkPLIKoo79KjKWp7teUtaL6rQ0NTP8rP3KBjekwdj0Zat+muXv29jPIt2Xec8ihG08AMGrrGUJ1eiNL4ZNrmedSUNKJpkPJo7EflhTSUHUlC1aUMVDcOIHfYjrhuN10czKoBxVEXpGjqxa7H96d2TrQvTQY/Erud1AMw4I/lJqrjHsy4w6srC86cZVE87cVOkgT387gvP+YIwUfdE76b4A+/eClAiQdtHcGIkkYSCWJDgxWHOp0onfRgfGgahvQ0zBw5hLmzKTDm5kKfmorp/XsxE3cYluoqeCxWOEfGoLt8GZM7v8ZcchJsbe3wmK302IHZkycxvXcvjLdvwzk4BNfUNCyVlZhNOIGZ48dgKi6GY2QU9u4eta1ZWqa/fAW25lY4R8dhra2D7vw5zCYmwJSbA0ffABz9A1SWHMo7AbpzZ2GtrlHr2lrboL9ymcp2BPobN2CndV3TszCXlattzRw5DFNeHjzTc/AGw5j02nFjqApf1iRjXW0K0kfrMOMww2cyw1pVjbnTpxbzunwJxqzbVI7zqnxcTntvP21zDObiEsydOoW5pCRYSkrVPtrbO2C4eQMzJ2hfrl+HjV5z+Sy0L3MpKSoPLodzaASOgUEYsrIwHRdH2zsNa0MD3HoDHL190J09i6ldO6C/eoXWHablRvp7PeUbj6ndO2HMy4Frbg6OsTEYc7Iwc/QwZk8cp/NSC7eO8ujpg/7SJcwcPgQD5WHq6cddgxtp437saLZRdGVVF4kJVwherg8vaD2+P/F+cHKH5lEw6cXHJMaPqyxIG/WowfyF72CLx5ZFCcliT4uNKpcZ1+66YKKQZi0QoaM3ZA+pwc5tFL4d73ahnrpc5rFpeDJT4YjbB9e5JPjys+G5dQO2A7tgP3oAwbpKwGnDwsQY3FcuwLpzC5xnEhHqbKd+m5UeO+BIPA7bvl3wZmdifmQIC3PTCNRUwHkyHo7jcfCXFWF+YhTh/h54eVsn4iiviwi1t2B+chzBxlq4Lp6B89Qxtf3I3X5Ehvrhu5MNZ+IxuM4nUzmq1bqhjja4r15SZfOkXqV1BwDdLAKVZZTvEdqPA/AX5AL6OdrreViCTmSN1SzOs6hPQf5kHexeK5XdglBdFVxJCXBQXu4r5+HNyYTrQooqnzfzFiKD/bTNMQTKiuE6nQBXciIC5SVqH8NdHbT9a3AkxMFz86p6rfalgfblbJLKw3cnFwtjI4gMD1Let6nMh+BMOolgcz1gNlD+fXCfS4Zt9zZ4rl2kdYdpuRGh5jrK9wgt366OAYxzmJ8agzcvE/b4A3AmHEWwvkatGxmgPC6fh/3IPsrjEvwD/ZizeJE3HcT+VpuamJU34Va3yNcq1bN+aq8WfFptoYvBU5RFqSaLL0gWVwZd0HnoIH+HDT9vsIXVDE6KltQMzi4Xqmd80I9Ow5FxCxZqZDaquC66kjlu3YTpwB6YqXJ7a6swb7chNEaRATVw465tsJ45DV9HOyJWKz12wMIRwb49cNKVOTg0hNAMCai6EtaTdAU8Hg93aTGC46Pw9/XAyduiq6b9yiX42loQnBiHt6EOtosUPZw6obYfoAofoIbqys+BNfEEbOdTqBw1lMc4fO1tsF+9rMrmoMYaGBxAaHYGnooyWKgRWWi5uyAPEboaz89HYPA7kDFSjY21ydhcl4Kc8TqY3RYsWC3w0b7ZqPHye3jfnNm3YbtwVpXPmZmmyhEcH4OntAS20ydhSz4NT1kpgsND8LMkU6/DmkBCvHlNveZ1vfW0L2eTKY+jVP5cBEdGELg7CCdFBeb4I7AmnYK3qQFhowGB/j7Yz6XAtPtrOK5dpnWHETEa4WuqV/ti2rNDHYMwiS9Esnbm3qY8DtFxPUbbqaU8jIt5XL4A85EDKg93Xz+mTB5kTwZIFLblGZye79aAnnci8wuomPbhcxIFyyKDZKG6IU9TFhxZrDlZ2EgW/Stl4SVZTD1AFjdIFrtVg/RQg4pwBEFXSPtVkgVdBa0pJAuKLJZlcQKm/btVY+OGdE8WFHFww1spC7UtakiPL4tq1RiXZXEYdpKFn9ZblkW8KrNrpSwCJItRksXSdO8VsmARWkkW/J5osnBTZGElWViTTz2mLHKUABZlwQ39MOWRuCyLvmVZ2K9dQWB0GGGTYVkWe1fIgiIcV96iLCwkC89DZOEiWUyaSRZT98nCuzane/PM5HK66H1BkcVnlEQWTwCRhchCZBEdkYWGyEJkIbKIjshCQ2QhshBZREdkoSGyEFmILKIjstAQWYgsRBbREVloiCxEFiKL6IgsNEQWIguRRXREFhoiC5GFyCI6IguNl1kW6SSLDSQL9U1ZK2TBMzhFFi82IotV4GWWRdpIJb6qOY31dUnIYll4RBZrBZHFKvByymIepoALuWP12Nl0kRrOZRROtcDqtdHJtko3ZA0gslgFXjZZhOdmlSy84SAGrZMon26jStWOIfssfAGvjFmsEUQWq8BLJYs7eWrZAsmCT12YuiPBSJCOQRAhWjYfDiNiMcNbI7J40RFZrAIvqyweSDhCsjDdk8WjPqIusnh+EVmsAiKLZRZUZCGyWAuILFYBkcUyCxGRxVpBZLEKiCyWEVmsHUQWq4DIYhmRxdpBZLEKiCyWEVmsHUQWq4DIYhmRxdpBZLEKiCyWEVmsHUQWq4DIYhmRxdpBZLEKiCyWEVmsHUQWq4DIYhmRxdpBZLEKiCyWEVmsHUQWq4DIYhmRxdpBZLEKiCyWEVmsHUQWq4DIYhmRxdpBZLEKiCyWEVmsHUQWq4DIYhmRxdpBZLEKiCyWEVmsHUQWq4DIYhmRxdpBZLEKiCyWEVmsHUQWq4DIYhmRxdpBZLEKiCyWEVmsHUQWq4DIYhmRxdpBZLEKiCyWEVmsHUQWq4DIYhmRxdpBZLEKiCyWEVmsHUQWq4DIYhmRxdpBZLEKiCyWEVmsHUQWq4DIYhmRxdpBZLEKiCyWEVmsHUQWq4DIYhmRxdpBZLEKiCyWEVmsHUQWq4DIYhmRxdpBZLEKiCyWEVmsHZ4rWcyRLL7Lhp83RBbLiCzWDiKLVSD4EFkYSBZOasBWkoWdZOGmxupcIQsvyWKeZBEmWThIFqYVsph/gCxC1JDC98nCQ7IIkSwCD5BFiGThI1nYSRY2kgVvP/gAWfhIFiFqjP4YZRGmZXiILECymL9PFg6ShYvKbydZWKnMLpIFl4O3uVIWXpIF72OA5OC8Txa87v2yCD2mLCIkC/8KWbgpjwjJIkyycN8niwjJIkiycGiycJIs3FFksQaq8beIPA+y+IpkcZW7IV7qhqwBQnRQB+xBnCdZbCVZHCNZ1Mx6YSRZuKgB2+L2w0Gy8FBjdZEsLAd2wXr0IDXSKiw4rIiQLJwkC/PurbCTLAIkiwWbFQGShY2lsH8X3NTYwtSQIrPT8JEsbInHVMPzkizCE6MIkizUtqghOUkWAZJFeHIcfpKFg2RhP3VcbT/EjZQk4KGGYqe8HSQLP8kiTI0xQLJwkiys1MCdJIsgrReZm4GPZGGjBsZl9pAseBmFFtre38c8VSarCT6ShY1kwe9xkiy4/A6ShY2jIZIFl4O36SVZ2EkWdpKFj2TB+xgkObiULGhfSBYsD17XR7KwkyxsJ+JU+cMki9DQINwkCys1dDvJwk+ymCcphEgWDpKFefd2auhXKHobxryZJEKysCXEwbL3a5XHvGEOEZKFJ5fzOAjbyXjaTi3lYUSIZOEkWViP7IeLZOEhWUxbPMiZDmAf1eM9JIuccTeMvrC282uLebJCxayPLu7PUBbr6yxIG3HDGVw7wdukK4xrd13YRft3uteNVr0P7skpRDJvInBkN0LnEoE7txFJuwrf/u3wx+0FGioAjw2YGkH46ll4d25EKCUB6GkDXLS8ux3BxKPw7duOhZx0YHwI0E8DteUIJMYhcPwQUFag3o/Bbsxn3kDwxCFErp4DOpuBmXGgqRahi8kInjqKBdo+hvuAkX6gIAshyjt8/jSVoxKYHgO6WhG5dp7Ktg+RW5cX1zOSGKpLEEw4hACXuTB7cdlDoXPqMAN1FQgkxcN/dB/t2znM56arcgSofPO3bwJDVA7eZkUhQqfjEUo+AVQWL+5jD3XDblE0kHAYkVQqB71W6zbVIHQ2kfbxoCo/JmjdkQEsUN7++H2Ux3GgrR6wGYG7vWrfvLs2IXL9Aq07DNhpeUsd7QuJes8WLHAeFh0dpzEs5HEeexE8eQRorKEKq+Vx5Sz8R/ZQHufpGPfB4vCieC6Ew+12HGqzoXjKC3doLXZCFmnU+7GhzorPn5YsGCfJt2zWj+1NVvy2zIi9rTZUUojTbw1iUEsDj5EGbSEM2sO4y8kRJal1aF1af4C6Cg/K6/ukYcq7yxxA7rgXO+lK84cKE9Y3WHF5wInqzkk038hG/eETaEy+hJaMO2i+moG6/fGoP3ISbSW16J00oadrGE3nb6Bm50E0nr6IzroO9E6Y1GPDiRTU7YtHy618dHcOoWdgCu1FNWg4fgYN8UlozS1DF72/s6mHtpWFhmNJaL5wE501bejuHkN7WSMaU66iISEFrbT9rtZ+dLcOoDWzAI2Ud1PyFbSX1NG6o+iobaf3plLZEtF8JZ3WHUDv4DTaCyppe8looDK33i5EDy3rtwQomgp/83jQMe43+9A7algs48mzKq8mKk9LWr4qRz2Vr4WOSVcLlYO22ZZfhkZar/HUBXpege6Ou7TfnXSc0tU2m6+kobO+c7F85Q1U3ku0PAltXA7a7972u2hPv4PG+NNoTrqIruoW9NP2u1v60HTmCmp3H0LzpVR17HpHdOioaFTvr9tzRB2D3qEZdPeMoTU9D/VxJ9U220sb0Duso2NKedB5qT+cgObLt9DWMojyCRcS+334c40Vn1RZcbLbido5v+qGDnJaeTxe0KT2g1KPhbvWLvyq2Ij3qV6njTwlWXhoA5W6AL6oteC/3ZrF/3l9Gv8jS4c38vT4l5iTDm9SUs/zDfjxHSN+UmDCTwqjJP57gRE/ovWX8nnzXn7fP3G+r+fq8A+Zc7RPM/hfL0/hP1+bwX9Pm8X/vDmGV5Na8UpcJV49UYfXUtrw6ukmvHKkAq8crcQPL/bgzcxJvHFzGK8mNuCfD5Wp9V6/0q+W8+Mrx2rU+q8lt9F6I3gjbQyvX+heXB5fjR+e68TrtPz1a4N4LamFllVRXo14/XI/3kgdxeuXevHqyQa1/g9p+69fv4s3rg/R83a8SstePVFP+fWovF+/2o9XT1H5jlIe9Pg6rffGLdre+S7Kl7bHZab3cRnepH3mc/DN42FQy9/MoLJzGY/Te3jfqTyvnaF953JQmbmcqhypI6r8r9J6rx6vVc/fuDFE5Rig49S8uC4dL37N675+qQevJdRRuavxOq37Ju3fv1B68ywdgxO1eIOO4b9cHcSPMqdUPq8m1OOVQ6V47VQjvR7GG+kT+CEdD873lcPl+OFZ2pf0cXWcfkjl4/17hfLm8/JGxgQd07t4jcrO+/AalYeP8z9n6/A3GQb85+tz+E/X5vD/punwSg7te/7SMeA6uvT8xU5v5OrxX2/O4H+jOv3zAoPqDfA443fhwbKgvmwo4KNIcA4jg71oayaTNzWhtr0XOXSlPdRowNtFBvwgaw7/eJuT7jHSHP6J35M5jb+9Poy/PteN/3K6DX9xsgX/6UEpoRl/kdiG/5LSh//n6hj+Ln1G5fNP38r3+6bFcv2Anv8P2q8fkAR5G/9EAvlHSkuPi/vL62p/5+eZsyqp5fQ+9agtU0lbX+Wj/rb0uJTH8va5LPcel9ZTr3n9pddLedJyLhMv5+1rf1/MQ9vevXLw3xbzVs+19Zf3f2V6wLoq38W0ctuLj0t/X9wWv1bLV+bBj1riv//drQn8zZVB/NWZTvzvia34i4QWqgOtdM5b6XUH/upsP/7m+gT+PmMx78V8FvdjabtLx255/5aW8baXXlOiv/9D2iT++9Uh/N9nu/B/qO1RveJtct0604O/vjyMv701hf+P89fy+fZxecES1S8+Vn+fMacu0Lupe92g86vhhO8QWDxYFguRCHwuK8b6WlGQeQ2njx/B4bhjOH3xJm5XtqFqyIjqGY8aZeX+3r00HUOi9UqnfSiacCCjcwJnytpwOKsGe25VYNcD0s7UUuzJqMbhom6cb51D9oiT8vCh5EF5f9dEZSrS9qGEysbl48TbKZ70UHKjmEJXTkXqNaUJ7VEleq9axutpiZdxnvyoLSta8R6Vj1quvdbKUKTy4vc/aF1t+ZSW7pWL86ak1uXtLb5vZRnVttVrzmMpH62M9x2LxaTt+7i2XS3/e+WgvJaORdGK48N5f6Mc2rpL5eByF447kN2nw7XGASQWNuJgZhV23yzDzpuldL4rsO92PRLK+3Gt04BcOt+8b8vv52NEj7yMy7a0fGWiv6l11H5QWWh7eYMG3GgexumSFhzIrKRtlWEHbWtXeg0OFXQgpXECaYM2FGjve6L161kk7Twu1evqOZ/qltj8EXXnb55s8bjCiBJZeGE1zOBuL/W5a6tRVV2LprYujEzOwe7yIhieB21T3UV43ERvRSgShtvtgtFowNT0DMYmJjH6gDQyPoGxyWlM6c0wO73wBiOUx+L94wfl/cRThI4FyTMU1pJ6Tekbr3k9SkvL1PKl969crr03Wh5Ly1eut7TsG8tXrHv/ct6OWr60TEv3r3v/vt6fVr5n6X33XnMe2jorl6vXvJzSQ8oRDIXh9Xpht1mh081hcnIKo2MTGBkbpzSJ8alZzBmtsLv98AXDVNdW5LuyXKFv5/2Ncqh1F+j9Yfj8Pjgcduj1ekxMTal6NTxO9Yvq1qTOCKPdBZc/pObb8PueWv16SimiBimW9fC4omAea8xCEISXF5GFIAgxIbIQBCEmRBaCIMSEyEIQhJgQWQiCEBMiC0EQYkJkIQhCTIgsBEGICZGFIAgxIbIQBCEmRBaCIMSEyEIQhJgQWQiCEBMiC0EQYkJkIQhCTIgsBEGICZGFIAgxIbIQBCEmRBaCIMSEyEIQhJgQWQiCEBMiC0EQYkJkIQhCTIgsBEGICZGFIAgxIbIQBCEmRBaCIMSEyEIQhJgQWQiCEBMiC0EQYkJkIQhCTIgsBEGICZGFIAgxIbIQBCEmRBaCIMSEyEIQhJgQWQiCEBMiC0EQYkJkIQhCDAD/P7isZ97q7Iz/AAAAAElFTkSuQmCC)
For the given figure, calculate zero correction.
![](data:image/png;base64,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)
physics-General
physics-
Three capacitors
are connected as shown in the figure to a battery of
volt. If the capacitor
breaks down electrically the change in total charge on the combination of capacitors is
![](data:image/png;base64,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)
Three capacitors
are connected as shown in the figure to a battery of
volt. If the capacitor
breaks down electrically the change in total charge on the combination of capacitors is
![](data:image/png;base64,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)
physics-General
physics-
The charge deposited on
capacitor the circuit is
![](data:image/png;base64,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)
The charge deposited on
capacitor the circuit is
![](data:image/png;base64,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)
physics-General
Maths-
If
then y satisfies
If
then y satisfies
Maths-General
physics-
In the figure, a proton moves a distance d in a uniform electric field E as shown in the figure. Does the electric field do a positive or negative work on the proton? Does the electric potential energy of the proton increase or decrease?
![](data:image/png;base64,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)
In the figure, a proton moves a distance d in a uniform electric field E as shown in the figure. Does the electric field do a positive or negative work on the proton? Does the electric potential energy of the proton increase or decrease?
![](data:image/png;base64,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)
physics-General
maths-
Solution of
is
Solution of
is
maths-General
physics-
Two charges
and
are placed 30 cm apart, as shown in the figure. A third charge
is moved along the arc of a circle of radius 40 cm from C to D. The change in the potential energy of the system is
where k is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAATgAAAEFCAYAAAB3m/sZAAAgAElEQVR4nOydWXNb533/PwcHONj3Hdw37ZRkR3KcxbEnaTNpJxftTC/a19A30VfSi172rum0yaSJk7RO/7ZjW7IWUgspLiAJEMS+rwf/C/V5AlKULcuSuD2fGY4t8hA4AHG+57f/tOFwOEShUChOIZajPgGFQqF4XSiBUygUpxYlcAqF4tSiBE6hUJxalMApFIpTixI4hUJxalECp1AoTi1K4BQKxalFCZxCoTi1KIFTKBSnFiVwCoXi1KIETqFQnFqUwCkUilOLEjiFQnFqUQKnUChOLUrgFArFqUUJHKBmfioUpxPrUZ/AUTAcDuWXQNM0+aVQKE4HZ1LgNE3DNE0ajQYATqcT0zQxTRObzYau60roFIpTwJkTONM0aTab1Go1yuUyuq4TDAap1+t0u12SySQ+n++oT1OhULwCzozADYdDKW73799ndXWVdruNz+cjHo/z5MkTqtUqP//5z5XAKRSnhDMjcJqmUSwWefjwIffu3WNvb494PM5gMGBnZ4f19XWazSbtdvuoT1WhULwiTr3AiUSCpmmsra3xq1/9imq1SiKR4OrVq+i6zp07dzBNE6/Xi81mk79nmua+ZITFYkHTNCwWlXxWKE4CZ0Lg2u02lUqF5eVllpaWuHjxIjdu3GBubo5CoUCr1cLpdBKLxXA6nQB0Oh3q9Tq1Wo12u43VaiUSieDxeJTAKRQnhDMhcPV6nQcPHrC6ukq322V+fp6bN28SDAbJ5XJUq1XcbjfT09O4XC4AWq0We3t7ZDIZSqUShmEwNzdHMpkkGAwe8atSKBQvwpkQuHK5zOeff06j0eDdd99lfn4em81Gr9djd3eXhw8fsri4SDKZxOVy0e12qVQq5PN5stksmUyG4XBIo9FgMBjg8/nQdf2oX5pCofgaTrWvNRwOGQwGVCoVVldXGQwGXLt2jVQqxWAwIJ/Ps7u7S71exzAMgsEgNpuN4XCIpmk4HA78fj9utxuAYrFIpVLBNM0jfmUKheJFOPUWnIilVatV4vE4sVgMj8dDu91mfX2dUqlELBYjEolgt9sBsFqthEIhAoEAU1NTJJNJdnZ2KJfLWCwW1dqlUJwQTr3A2Ww2XC4Xfr+fer3Ol19+Sblcxu12k8/n0XWd6elp4vE4hmHIdi273U6n06HT6bC9vc3e3h6RSIRAICCTDMLSUygUx5NT7aJqmobT6SQajTI/P4+maXzyySd8+umnrKysUKlUcLlczM7OEovFsFqt+3pS6/U66+vrfPLJJ9y5cwdd1/F4PEf9shQKxQty6i040zQJBAL84Ac/IJlMksvlSCQS+Hw+Njc3sVqtjI2N4fP5pMDB05q3brdLqVRib2+PfD7PvXv38Hq9hEIhGZdTKBTHl1MvcMPhELfbzaVLl4jH4+RyObxeL51OhydPngAQCARwu9376tssFgs2mw23200ymWQwGFAoFNjd3aXZbGK327FaT/3bp1CcaE79FWqxWDAMA5vNhtPpJB6PY5omOzs7Mobm9XpxuVz7BE7TNOLxOC6Xi1gsxsbGBhsbG+i6TqvVwu12q6kjCsUx59QLnBAg0WI1HA7Z2triwYMHPHnyhEAgQKPRoN/vy98ZDAZ0Oh3ZquVyufD5fHg8HpxOJzabTXUzKBQngFMvcKN0Oh3y+Ty3b9/mk08+YXl5mYmJCdl4L9qwut0u+XyeWq1GvV6nWCxSq9Ww2Wz4/X58Pp/MuCoUiuPLmRI40zTp9/vSLZ2fnycej6PrurTWABqNBhsbG2xublKpVHA4HIRCIaamphgbG8Nut6tOBoXiBHCmBE7TNAzDIJFIMBwOmZubk1nRUYvMNE263S6tVotWq4XP5yMWizE7O0swGFTJBYXihKANz1BZvmma9Ho92u023W4X0zTRdR2HwyGzopqm0e12qdfrtNtter0edrsdp9OJy+XaV0qiUCiON2dK4BQKxdlCpQIVCsWp5VQKnDJKFQoFnIIkw+iO01FhE+PFBccxbibOV5z7YbtZDxudLo4ZfY3i56PZ4MOOUyjOEide4MRF3O126XQ6DIdDrFYrhmHIbKe46I/bYmdN0+TMOvHv0fITIVj9fp9eryeLkXVdxzAMDMPY93iDwYButyuPs9ls8j1QIqc4i5xoget0OjQaDer1Oq1WS9a4GYaB3W7HbrdjsViwWq24XC65UOZVMmotCSvqoCBZLBYcDofMwA6HQ3q9HpVKhWq1SqvVkpNPgsEgXq9XCpPogd3b26NardLv97Hb7YyNjTE+Pi4FUdM0KpUK6XSaer0OgNfrJRwOE4vFpBiK5+50OlJYrVYrNpttX4fG6Os67HUqsVScBE6UwIkLS9SpZTIZHj16RC6Xo9Vq4XA4ZCuVruvouo7T6SQSiTA7O/uMxfNNMU1TTvMdvfBH28BarRaFQoFCoUC5XMY0TTweD9PT00QiEVlUXK/XuXfvHg8fPqRUKqHrOvF4nKtXr3Lu3DkpXN1ul42NDb744gs2NjZoNBp4PB7ef/99ksnkPotve3ub3/72t+zs7AAQj8e5du0aPp8Pu90uLcJisciTJ0+o1WpYLBaCwSDRaJRIJILT6ZQiJixf0zQZDAbyZjHq+ioUx5kTJXCCZrPJ7du3efToEbu7uxiGQSgUkr2iFouFXC5HLpfD7/czHA6Zmpp67uO9iEVimibtdltu2mq1WlitVmKxGF6vV7qA4twePnxIsVjE4XAwOTlJIBAgHA5LK28wGNBut2k2m3Q6HZxOJ1arVQrlaDxRWKB+vx/DMHC5XBiG8czodF3X5XEATqfzmS4N0zSpVCosLS2RTqfp9/vE43EWFhZYXFyUltxwOKRarbK+vk6hUKDb7RKNRkkmk4TDYbl9TKE4zpwYgROi0O/32d7e5ne/+x0rKysEg0EuXrzIuXPnCAQC2O12uYehUCgwGAxIJBLycUZF4aCQjAb7LRbLvrhVp9OhUCiwtbXF9vY25XIZr9fLO++8I4dgiljg2toad+/epV6vEwwG8Xg8Mj4onk/Xdfx+P2NjY0SjUbxerxQP4Z4Oh0MsFgvRaJTLly8zPT1Nv9+XM+xG3UXTNAmFQly/fp1WqyVjkdFoFKvVimma8rV0u12KxSLb29s0Gg0ajQZOp5OZmRlCoZB8/lqtxp07d3j48CHNZpPZ2VmuXbuGw+GQ28fE32U0ESJiieL9U+6s4qg4MQIHT0Xmzp07/OlPf+LRo0cEAgF++tOfMj09TTAYlN0Ig8GAyclJarUahmHg9XqlKycspFH3S7hgg8GAXq8nY2aifcs0TbLZLB999BFLS0vs7u7icrk4f/48/X5/n6vm9Xp5//33uXjxIt1uF4fDQTgcJplM7suSCkGJxWIMBgM5e87tdkuB0TQNm81GKBTC6XTS7/el6Llcrn3uqaZp+P1+ZmdnGQwG+xbn2O32fW5lMpnkJz/5CW+//Ta9Xg+3200oFCIajWKz2aQgGYZBOBwmFArR6XRIp9Pous7U1BTRaFQ+d71eZ3l5mVKpJON+0WgUj8eDYRgqwaE4Mk6MwAmrTEwC0XWdCxcu8N3vfpdwOCwTDEKQUqmUFIRgMCinhFQqFer1+j6LyjRNOp2OTAy43W5SqRSBQACbzSZjfrVajUajIeNqwWBw3x6H4XCIx+Ph+vXrz5z/qOUoZtTF43F5voKDFo/VasXj8eB2u5/JBB/8f5fLhdPpfKak5OAgz0gkQiQSOfQcDz7e9PQ0FosFv99PqVR6pg9XLNZ+/PgxT548we/3Mz4+zuzsLBMTE4RCIXmcuJEctJJVLE/xujgxAtdqtdjd3eXJkycUCgV+9rOf8e6778rg+cHhk16vV7pxDocDgEwmw71791hZWWFvb08mIuDpBBGxwX5ubo733ntPxrp0XSeZTPLXf/3XvPfee/R6PZxOJz6fT8b44FlxGuXgRTxqfX3dZJIXtX6+rTs4eo5iDt7U1BSxWIzLly9jmiY2m41AIIBpmvJ40eNbKpXY2dkhl8vRbDZxu91ySfZgMKDRaFAqleREZLfbjcfjkRlmheJVc2I+Vc1mk93dXYrFIqZpMjY2xtjY2KFz2TRNk66epmlywfPnn3/Ob37zG1ZWViiVSnIsuWEY+P1+YrEYExMTRKNR6QIKS8Pj8eD1eqV1NHpxn0b3S9M0rFYrXq9Xvm7xmoUVJo4T7rphGJTLZbnoRyR8NE2j3+9Tq9VYXV0lnU7T6/Xw+XxMTEwwNzdHPB4/yperOKWcGIFrNBrkcjkZM3K5XM+984taOFH3tre3x8OHD/n973/PL37xC3K53L4aMJ/Px82bN1lYWOD9999nfn5eWm/i8UZdt1FO81y453WCHIz9BQIBvv/973Pjxg3pwosR8eJY0zRptVpsb29z9+5ddnd38Xg8XLp0CY/H84zAjXZ5iOc5jTcSxevl2Avc6BDKQqGArusygD0aED8M8bNGo8HS0hKPHj2iUqnsG0/e6/VoNBq0Wi1M08Tv9xMKhfa5YIqvRyRm7Hb7M7WC8PRG4vf7uXjxIj6fj3K5LOOQIk4HT/8e1WqVjY0Ndnd3SSaTxONxOUVZZGcVihfhWAvcaI+p2FBvtVoJBAI4HI6v/aALcWy32+RyOSqVinQ7DwvCi9IKeDZmpvhqDvYBj35fuLuBQACPx8O5c+fo9XrAU+EbrakTruzS0hJffvklU1NTXLhwgdnZWSKRCC6Xa19SZxRl4SkOcqwF7kUYLdIdrcMS9Vkizibq0QSjLqeu6zIg/m27Hc4qXycu4u9gtVpxOBzPFUTRLdHv98lkMqyurvL48WP+4i/+gqtXr0qBE7V3o8+tBgsoDnLsBW60bszr9dLtdqU1JjoARo8Vlp4oxRCV//Pz86ysrLCyskKv16Pb7cqdqalUivn5eWZnZ9VC59fIi8TRxM1menqat99+m0wmg9frlRa7uHm122329vao1+vy7+j3+/F6veompZAca4EbvRh8Ph9jY2N89tlnbG9vk06nmZ+f31fEa5omtVqNdDqN3W4nHo/L2M/169cpFAqsr6/LfszhcEgikeA73/kO7777LouLi3i93qN6uQr+3OEhkha1Wo1+vy9HxotCbVFcvLm5SavV2neTEsklZckpjrXAjeLz+Zibm+PSpUsMBgOWlpZotVrMzs5KkRst4fB6vbKzQdd1YrEYb7/9Nu12m4mJCTY2Nuj1eszOzvLBBx+wuLhIIBA41VnRk4Cw8oT17fF4pDs66n6K/tzhcEg2myWfz8vEhWEYOBwOJXAK9H/6p3/6p6M+iRfBarXuWwyzu7vLzs4OxWKRXC5HPp+XVlk0GiUajUrBEkFun89HKpXC5XLhdrvltI3333+f8fHxfV0JiuPBaPfGwd5W0ftbLpflKKlUKiW3pFksFtl+J7pa1N/3bHFiLDhhlV25coVEIkE2m6VUKtFqtTAMA5/PRzAYJBQKEQgE8Hq98oMs3BqPxyN7KdvtNuVyWQrhaFGq4vjwvPpDsf7RbreTSqVot9sYhkEqlZLWm2ixy2azmKZJPB6XrWwHH19xOjkxAicaz2OxGJFIhKmpKcrlMoVCQVbTB4NB3G63bME6rFDV4XDIroReryeLhZVrerIQPboul0sWCY8OMxhNRjx58oR8Pk8kEiEcDssBAmIiiuL0cqIEbvT/7XY7kUiEYDC4r3FbCNvBO/PoWCExOeSwMT+Kk4OwxESZycFBnKZp0mw2efjwIZ999hmNRoOpqSneeecdbty4wfT09JGdu+LNcGIEDvaLnBjMeJAXEarRaRsHZ8IpTg7i73ywdWwUu93O9PQ0jUaD3d1d/H7/M8t6xMisg3V06oZ38jlRAid4kfYsxdng6/7eXq+X733ve1y4cIHd3V36/b5MMglxa7Va1Ot1TNNE13XZciYSFYqTy4kUOIXiRRBxW5/Ph8vlIhQKye4Wt9stXdpcLsft27dJp9NomsbVq1eZn58nkUgogTvhKIFTnFpGY7G6rmO32w89pt/vU61WWV1dleUmgNxvobLrJxclcIozTyqV4r333sMwDO7cucPS0hLtdhuv18vs7Cx+v18J3AlFCZzizON2uxkfH6fVamG329nc3CQYDO7rhhAFw2Lq82hvLKjY73FFCZxCwdO6upmZGRKJBN1uV65gFJNPRrequVwuEokEbrdbLhdXbuzxRAmc4kwzGqMbXdoj0HVdWm8bGxv8+te/BmBubo7FxUVmZmZkh4zi+KEETqH4P57XpzraFSFaBCuVCj6fTw7hVBxPlMApFF+DaAW8cOEC//AP/8DDhw/J5/P0ej1qtdqhKxgVxwMlcArF1yDq6cRuiFAoRDqdfmZ0vmj/E6PvR1vIFEeDEjiF4gURcbpz584xMzMjv2ez2ej3+3J0U7fbxe1243Q6MQxjn9gp3ixK4BSKF2C0kV8syhkdsNrpdCiXy3zxxRek02k5gXpmZkbu2VW8eZTAKRQvyWhSYjgc0mw2SafT3Lp1C13XmZ+fx2q1yj2+ijePspsVileA1WolGAxy8+ZN3n//fYLBINVqlZ2dHarV6lGf3plFWXAKxStA13W8Xi/nz5+Xo/KbzSZer1fu2oUXG+eleHUogVMoXgEi02q1WhkfH8fn8zEYDDAMQ66iFMNWR2cQiiGtKgnxelACp1C8IkRMzuFw7FtuLQqFTdNkd3eXhw8fMhgMCAQCpFIpwuGwbPlSvFqUwCkUrwHTNAH2JSGGwyG5XI7//u//ptlsMjY2xo0bN3A4HNhsNiVwrwH1jioUr4GDDfjCuvP5fCwsLMipJWtra2SzWTmDTvFqURacQvEGEDV04XCYq1evYpomGxsbWCwW+v2+tPgUrxYlcArFG0Ls9hUTSBYXF/F4PPj9fqxW6z63VsTtBCrz+nIogVMo3iBWqxWv14thGMRisX1Z1H6/T6/Xo9frMRwOMQzjudvjFC+GEjiF4g0jmvFHd/gOh0P6/T6NRoO9vT06nQ5+v59AIIDP58NqtSor7iVQAqdQvGE0TXtmQKbYy9rpdHj06BGbm5u4XC7m5ua4evUqfr9fWXIvgRI4heIYIJIQuq7TaDTY2tqi3W7T7/eZmJjA6XQqK+4lUGUiCsUxwWazEQgEuH79Ojdv3sTr9dJqtSiXy7RarWcyraMdEYrDURacQnEMGO2CmJiYkEW/hmHg8Xjkv0d7WQ9mWhXPogROoThGaJqG0+lkamqKRCKBxWLB4XCg6zrD4ZDBYCDdWVVG8vUogVMojhGiad9ms8kmfYHYASGW3vj9fmKxGC6XS231eg5K4BSKY8bzrDHTNKnVaqytrfHw4UNisRgXLlxgYmICv9//lb97VlFJBoXihCDq51qtFo8ePeKXv/wl//qv/8ry8jKNRkP1sx6CEjiF4gQgkgsul4tgMEg0GsVisVAqlWg0GrL7QbEf5aIqFCcEq9WKx+Ph0qVLhMNhNjc3aTQapFIptbnrOSiBUyhOCKIQOBAISEuu2WzKLgdRNjIahzvrI9KVwCkUJ4BRkbJYLBiGQTwel98TJSS9Xo9+vy/FUDTyn1XrTgmcQnECOUywBoMBGxsbpNNpAoEAsViMSCSC0+k8gjM8HiiBUyhOEZVKhdXVVXRdJ5FIcOnSJRKJxJndy6oETqE4BWiaJpMQTqeTzz77jC+//FK6q1NTU2cyFnc2HXOF4hSi6zrhcJjZ2Vmi0ShWq5VGo0Gz2TyzJSTKglMoTgmaphGJRLDb7QwGA7LZLF6v90xabgIlcArFKULXdTweD+fOnSOVSqHrOn6//8yKnBI4heKUoes68XiceDwuxzDB0yyraZpyerAYoHmaxU8JnEJxyjhMtEzTpFgsUigUqFaruN1uxsfHcTqdslbuNAqdEjiF4gxgmiatVotMJsPS0hJut5ter8fY2BiBQODUFgIrgVMozgDCLW02m9y9e5fhcIjFYsFqteLz+Y769F4bp1O2FQrFPsTS6fHxca5cuUI0GiWTyVAoFJ7Z9XCaUBacQnEGsFgs+P1+5ubmsNlsPHz4kPX1dUzTPNU1ckrgFIozgIixOZ1OxsfHcbvdzM3NEQqFsFpPrwyc3lemUCieQdd1vF4vbrebsbEx4M/buUzTZDAYyEkkpyGrqgROoThjaJomt3RpmoZpmvT7fTqdDu12G4fDgdvtVgKnUChOLkLARI3c+vo6KysrTExMcPXqVTweDzab7YjP8tvxygTurE8OVShOKqZpUi6XuX//Pr/+9a+5evUq4XCYyclJGZ87qdf2oQInpoN2u92nB1mtz1Q7C5+93+/T7XYZDAbouo7NZpPz4U97G4hCcRrQNA2/3y8Lfre2trh16xZutxufz3eis6yHCtxgMKBWq7G+vk6/3ycajRIKhfB6vcBTcet0OlSrVbmEttfrYRgGXq+XUCiEx+PB4XAogVMojjmihGRycpJLly5Rr9cpl8u02+2jPrVvzXMFLpPJ8G//9m80Gg3effddrl27hsfjQdM0KYDLy8t8+eWX5HI5Op0OdrudyclJLl68yNzc3L6Z8QqF4nhisVhwOBzMzs7y85//nEKhwHA4xOPxyA6Ik8ozAmeaJqVSifX1de7evUuv12NhYYF2uy1N1WazyerqKisrK+TzedxuN6FQiF6vR7FY5M6dO7jdbrm78eveoMM2AR3keY8x+rvi9w4ee5JNbIXidSNCSX6/n4WFBeLxOJ1OB6/Xi2maJ7oRf5/ACdczk8mwtrZGuVzG4XDI7TxCKMrlMnfv3iWbzeL3+/n+97/P+Pg4u7u7fPLJJ9y5c4fx8XHOnz8va2qeR7fbpdvt0uv19o1xsdlschVar9djMBigaRoWi4XhcCjjfpqmYbfbsdls8nEGgwE2mw3DMPbFAxUKxeGI3lSHw4HdbpffF7VxorTkpF1L+wSu3+9TrVbZ2dkhm83idrvx+/1SVMRXpVJhe3sbgImJCRKJBNFoVA7bq9fr5HI58vk8sVjsma0+QiiHwyGFQoGVlRVu377N7u4uDoeDixcvcuPGDZLJJACZTIZsNku5XCYUCmGxWPjTn/5EqVQiGo3y1ltvMTMzw4MHD1heXmZ7e5upqSneeecdxsbGTnUzsULxKhBW3MGpIs1mk1KpRL/fxzAMfD4fbrf7xFRNSIEzTZNarcbOzg61Wg2bzUYkEsHj8cgXPRwOabfbVKtVisUi0WiUZDKJ2+3GarXKCmmAUqnE7u4uPp/vUIHrdDrUajU2NjZkLG9jY4PhcEi1WpXLbS0WC0tLSywtLbG3t8eFCxcIBALcv3+f9fV1XC4Xpmmi6zrr6+ssLy+ztLTE1taWtDxdLteJr+dRKI6Cfr9PoVCgUCgwGAyYmpoilUpht9tPRLeDFLher8f29ja3b98mGo3yzjvvUKlU5FYeUfHcarVoNBoywyJeKCDLRGw2m7TiJicnn1F70zTJ5/PcvXuXra0tOp0Of/u3f4tpmnzxxRfU63U+/vhjDMPAMAx+9atfsby8jMPhIB6Ps7CwwN///d+ztLTEhx9+yJ07dwCYn5/nb/7mb7hx4wZ3797ld7/7HV6vl2g0SiAQ+EpXWaFQPEu/36der3P//n3W1tZ46623uHnzJqlUCo/Hc9Sn97VIgdvZ2aFarWKz2YhGo9jtdux2O91uV9a8maZJr9eTcS7gGRUXW7S73S6tVkseJxBubrlc5sGDB7RaLcbGxlhcXMTr9aLrOisrKzQaDfm7hmEAT81li8VCLBYjHo9jmiaffvopzWaTSqVCKBRidnaWmZkZMpkMH3/8MZlMhkajgc/nUwKnUHwDhsMhuq5LD63RaLC3t8fe3h7RaPTYW28wInB37tzB4/Fw+fJl3G43e3t7tNttOp0OrVaLVqtFu92WiYDnBRtFfO2rGnZN06Rer8skxdjYmLTWzp07RzAYpNFoMDExgcPh4Kc//Skej4e7d+8SCAQIBoPysUSMMBwO43Q6cTqdOBwOmQFqNpu0Wq1TPfNKoXhdOBwOJiYmqNVqDIdDDMOg1WqdmMoEKXAffvghbrebQCCApmkUi0Xu379Pp9Oh1+tRr9cpFApMT09jGIa01A7rbjBNE6fTic/nOzT2ZZom7XabUqmEy+XC6XRiGAYul4tEIkEgEKDX6+H1eun1egQCAbxeL4ZhyOyoiK/pui6zruK/8FRge70enU5HWqEKheKbYbPZ8Hq9zMzMYLfb6ff7eL3efZnW44wUuGw2K8emCL87nU4zGAwYDAZYrVZcLpecJSVeYKfTYTAYyN8T7qvP5yMajUr38iCj7m6/35dxOo/HIwsMRTJCPL5IU8OztW6jbWGjo1/6/b58fIVC8eKMZlYTiQTBYJBerydLs05CJlUK3D/+4z/Kk+12u2xtbfGb3/yGZrPJ5cuXuXbtGpcvX2Z8fJy1tTU8Hg/NZpN0Os34+DihUEi2b9XrdXw+HxMTEzidzkPFyGaz4XQ66Xa75PN5Wq2W/Hmj0aBQKKBpmhS4UWET7u9ov+uoRQnsO171xCoU3w5d12W9KXBi6uGkwP3oRz+S3zRNk5WVFVZXV6lUKly4cIErV65w/vx5AAKBANPT02SzWdLpNBMTE2iaRiaTodlsEg6HicVi+P3+QwP7o/Pha7Ua6XSaVColM7DVapVCoYDT6aTf71Mul6nVanQ6HZrNJtVqFcMwqNfr1Ot1LBYLlUpF/luUoPT7fdrtNu12m36/D6iuBoXiZREGhPCQms0m7XYbXddl+Oi4lY48txdVuIRiXIrIfmqaRjAY5ObNm3z++ec8fvyYe/fukclkyOVymKbJd7/7XSYmJg59QlERHQ6HWVxc5N69e2xubmK32ymVSjLWZrFYMAyDXq/H1tYWW1tb1Go1crkc6+vrOBwOdnZ25HO6XC7m5+exWq3kcjnS6TT9fp9KpUI+n6fdbp+ItLZCcVw5GALK5XKsra3hdDqJxWKybvbYC5ymabhcLqanp2k0GsTjcVwul7c6u7YAACAASURBVPy50+lkamqKZrMpY2+5XI7hcMjY2BgzMzMkk8nnvlAhkpcvX8ZisbC6uspgMGB3d5d2u004HCYcDuNyuWQdnt/vx2q14nQ6qVarMpOTSqXodrvY7Xba7TaFQoFcLofb7ebKlStyu3e/3z/1CzYUijeBELhKpcLjx49pt9vEYjHeeecdXC7XsQoJPVfg3G43ly5dotfrEYvF5KgkeOqP+/1+Ll68SDAY5MGDB1QqFSKRCNPT08zMzBwaexNYLBY8Hg8ulwu3200ikWBzc5Nms4mu6zgcDgKBgEw2JBIJaU36fD5pVYbDYW7cuCHNZIfDIefSzc/PMzMzg9/vJxgMyikoSuAUipdHeHLw59bOx48fs76+zuzsLOPj48eq3vQrLbipqSmGwyFOp/OZtLAQKVHD1m63Ze+q0+nc15z/vOfQdV12GAQCAbrdLoZh4Ha78Xg8GIZBIBBgcXGRdrstF9WKN1BkYkVBsMvlQtd1xsbG5PdsNhsulwuPx/O156RQKL4ecR3G43EWFxcplUqUy+VjaUA8V+AMwyAcDgN/zkg+88sH+k9HM5Yv+kINwyAUCsni3VGrT2RbhdCKGODXCedorGD03ycl86NQHFfE9WO1WolEIly+fJlisUgmkzl28Tf4CoH7uhM9KBwvy8v87qjAHZwFN/q95/2OQqF4ecT1ZbPZCAaD/OhHP6LT6RAOh4+dEXEit2od9ga+iCC/yHEKheLFsFgsOJ1OmYA8joW/J1LgXobj+OYrFCeZg57ecby+zozAKRSK10+9XieTyVCtVgGYnJyUrutRoAROoVC8MprNJpubmzx+/JhOp8N77713pBv2jkZWFQrFqcRisWCz2djZ2eGzzz5jfX2der1+ZOPKlMApFIpXhmEYBINB2Vkkhm8clcApF1WhULwynE4niUSC+fl5arXakQ/IVAKnUCheGWLE+blz53A4HCQSCTl1+yhQAqdQKF4ZogtqZmaGRCKBw+HA6XQqgVMoFCcf0WMuWjhHh9GO8qbqUpXAKRSKV4oQOTEUYzAY0Gq16PV6DIdD7HY7hmEogVMoFCeb0QVTpVKJTqdDKpUiEolgs9leu8gpgVMoFK8NMWy2WCyytLREJpPh5s2bcteqEjiFQnFiGV1ktb6+zq1btwgEAkxMTOByuV578kEV+ioUiteK0+kklUoRCoUYDAZsb2+zsbFBt9t97c+tBE6hULxWDMMgEokwNzfHxYsX8fv9b6yzQbmoCoXitTIcDrFYLFy5coVUKoXD4cDn8+FwOF77cyuBUygUrxVRCxeJRIhEIm90GbsSOIVC8doZTSaI/SqHrRl41aKnBE6hULxRNE2j1+vJNaFiC9/rsOiUwCkUijfKcDik3W6zvb3NcDgkFArh8/leS9mIEjiFQvFG0TSNer3OrVu3KJfLxONxrly5wtzc3CvvblACp1Ao3jimacqauLW1NVwuF6lU6pV3N6g6OIXiFSEC56ZpHvqldvM+xTRNnE4n58+fx+Px8ODBAzY3N6nX6wwGg1f6XMqCUyheEaNLyJvNJvC0yFUIm5iwcRzX671JNE3D5XIxPT3N3NwcT548wel0vpYbgBI4heIVMBwO5VigZrNJvV7HYrHgcrnkhev1enE4HHKM0FlF0zScTidOp5NLly5RrVaZmJh4LdNFlMApFK+AbrdLqVTi1q1bbG5u4vV65bq8wWCAw+FgYWGBeDx+5gVulMnJSVwuF263G6/Xq7KoCsVxYTTmlsvlePToEffu3SOfz7OwsABALpej3W7j9XpJpVLyd866mwpP379AIEAgEJAxSiVwCsUxYjAY0G63efz4Mb///e/p9XqMjY1x+fJl+v0+9+7do1qtomkapmmiado+YRwVujfZwnQcOPjaAZlksFgsr+R9UAKnUHwLWq0Wm5ubrK2tUSqVmJ+f5+rVq4yPj1MoFDAMA7fbjc/nwzAMTNOk1+tRq9Wo1Wqykt/r9WIYxplNQrRaLWq1GtVqFbvdTjwex263f+vHVQKnULwkomB1eXmZ7e1tPB4Ply5d4vr161gsFkqlEjabjWg0SiqVwuVy0e/3qVarbG9vk81m0TQNn88nx3h7PJ6jfllHQr1eZ2tri5WVFQKBAF6vF5vN9q1dViVwCsW3oNFosLy8TLlcZnp6mkQigdvtpl6vU6lUyOfzjI+PE4vFcLlcdDodstksuVyOvb09stksw+GQiYkJFhcXuXLlylG/pCPBNE0qlQq3b98mGAwyNzeHw+HAbrd/K5FThb4Kxbeg3W6zsbFBo9EglUoRDAYxTZNiscjOzg57e3vouk40GpW1XiKrGggEAMhkMnz88cc8evTozBYDiw6GQqHA9vY2mUyGarX6rQdjKgtOofgW9Pt9CoUCoVCIYDCIy+Wi3W6zsrLC48ePKRaL2Gw2QqEQFosFp9PJ5OSkLAAeHx/no48+4t///d9llvUs4na7iUQiJBIJarUaa2trBINBQqHQt3pcJXAKxbdA13Upaqurq9jtdjweD41GA7vdTiAQwOfzydo3wzAIBAIYhgHA2NgYyWSSQCCA3W4/kwkGQMYq33nnHWq1GrFYTC6O/jYogVMovgVOp5O5uTnW1tb47LPPqFQqTE1NYbfbGR8fJxQK7bNCRhcii4xqIBDgnXfe4dy5c2dW4DRNIxgM8sEHHwBPXVar1aqSDArFUeL3+/n+97/P2NgYrVaL2dlZ/H4/a2trDIdDxsbGZKwN9td+9Xo9yuUymqbx9ttvMzExcWYFzmKxYBjGKykNGUUJnELxkpimidfr5a233mJqaop6vU4qlaLdbvPJJ5+g6zrXrl3D5/M983uDwYBms0mz2cRutzMzM0M4HD6zAnfwdYsJLPBU/F7WklMCp1C8JBaLBbvdTjgcJhAIMBgMcLvdpNNpcrkcbrcbv9+P0+l85nfr9TqlUgmPx0MkEiEWix163FlEdHk0Gg16vZ4skn4ZlMApFN8CYV3YbDZarRY7Ozvcu3ePjY0NkskkvV5v3/G9Xo9Wq8Xe3h6FQgGn04mmaZRKJVqtFna7HbvdjtV6di/N4XBIv98nnU6zu7vL9PQ08XhcTmL5Jlbu2X0XFYpXSKPRYHNzk08//ZSPP/6YdDqNx+Mhn8+TTCax2+3SKsnlcqTTaVleUqvVqFQq+P1+JiYmiEajZ1bgRJlMv9/nwYMHfPHFF3znO99hcXGRsbExXC7XN3q8Y/suHlYPJL53WJOuQnGUCMus1+vhdru5cuUKU1NT0hoRlMtl7t+/z9bWFrVaTS5aabVaXLhwgfPnz2Oz2c78xBHTNOl2u1SrVTY2NggGg0SjUdxu9zd6nGMpcGLawmAwoNfr0W63MU1Tmqci42Kz2dRsLcWxQNM0DMMglUrhdDqxWCz4/f5nZpx1Oh0KhQK1Wo1+v0+5XJZjggzDIBgMSoE7i4hpK+L9C4VC1Ot18vn8vhvFi3IsBU6Mlmm1WmSzWZaWluj1ekQiEWw2Gy6Xi0QiQTAYxOFwnOk7neJ44HK5mJycJBqN0u12ZVzOMAzpVmmaRiqV4ic/+QmdTkcG0+FpLC8UCskb9ln+TAuxn56eptVqsbu7K4XPNM1vlFE9lgInxsmsr6+ztrZGOp1G0zS63S6dTgfDMDAMA6/X+1KPr1xcxavGZrNhs9meKQkZRdM0vF7vS39uzxI2m41EIoGmaXg8HpxO50vFJY+lwNVqNZ48ecL//M//kMlkmJubk1M/t7a26HQ6TE9PMzEx8dLPoYRNoTjeiBl5oo/3ZVq3jo3Aibhbv99na2uL27dvUygU8Hg8zM/P4/f7yefz6LoufXGLxXJoMParkhHiec5qjEPx8pz1wP+bRNM0aRWL+kDhvn+Tv8OxETh46prW63XW1ta4d+8ekUiEK1eucPnyZaxWK4PBgEAgINeO6bouRbHX68l4huj3O2yJ7GAwkMeLr8FgwGAwOLPTVBVfjYj9iM8JIJNdFotFfW5eE6MJB0DubRDv/Yu858dK4FqtFul0mu3tbdrtNqlUivPnz+Pz+ajVajQaDQaDAXa7HcMwsFqt9Pt9SqUSm5ubLC8vY7PZeOedd0gkEvLDN4ppmrTbber1OtVqlXq9LrO0Z7X2SPHVjCa9yuUypmnKUeQul0t9bl4T4sYyapBYrVY5deVECtzm5qacZZ9MJkmlUmiaRqVSYW9vD0C2v1gsFnq9nqyV+eMf/4jdbmd2dpZwOIzdbt83uaFSqbC9vc3Kygqrq6sUi0U6nY7MfMXjcfm4CgUge0b39vbY2dlhe3ubXq+H0+kkGo2SSCRIJpOynk1Zcq8OcWNpt9sUCgWy2SzBYJDx8fEX7k89NgKnaRrtdpudnR0ajQaBQAC/349hGDSbTXK5HJlMBofDwfj4OC6Xa5+Ki9EzmqYxGAykuyqadrvdLo8ePeLDDz/kiy++YG1tjXq9jt/vZ319nR/+8Id873vfY3p6+hsXEypOL41Gg42NDf73f/+XL774gidPntBsNvF4PExOTnLt2jV+9KMfMTU1hcvlwmazHfUpnyqGwyGtVouVlRV+//vfc+HCBYLB4AtPHTk2Agd/rl7u9XpYLBaazSalUknOtm82m3KBh+jh03Udn89HPB7H5/NJcRP+Ojy1DLe3t/n888/58MMPefz4MaVSiW63i2EY0pITexqVwCkE2WyW//f//h+//e1vuXPnDru7u3Q6HRwOB2traxSLRVmLubCwoATuNWCz2eh2u6ytrWG1Wrly5QoOh+OFGvCPlcBZrVZ8Ph82m416vU42m8Xr9dJsNqlWqwAEAgFisZj8UOm6TiQSYXZ2lng8LndQjmZSG40GS0tLfPrpp9y6dYtCoSCfs91u02q16HQ69Pt9Ll++TCqVYjAYKHfjDCNCG8vLy/zmN7/hk08+YXt7W8aF2u02lUqFTqeDx+PB5/MxPj4uBU4Ew0e/RjP3ozdgeP5O1MOy/ocdK34+usNA/Fy4zqOPNfqYo48nKhOed5z4r3APR3/+Iucozu+wxxx9XGGkmKaJy+XC4/FgtVqpVqtsbW0Rj8f3zdl7HsdG4IbDIV6vl4sXL9Lr9aQLWa1WiUQi5PN5yuUyuq4TDof3BXYtFgtWq/W52axGo8Hq6iqbm5u0Wq1nft7r9SgUCty5c4d//ud/5re//e1r2bKtODnouo5pmty9e5fbt2+Tz+dlBhX+fGHX63U2Nja4e/cuTqeTdrstb8Y2mw2Px8Ps7CzT09N4vV663S7ZbJaVlRU2NzdlZb6maXKnqtfrlTHj3d1dstks3W5XPre4oft8PtnHKpbc1Go1eZ5ut5tUKkU0GpWP2Ww2KRaLNBoNWW5ls9nwer34fD48Ho8sqi8Wi9RqNbrdLsPhEF3XcbvdslhZJPnEPtN2u02/35e7JzweDx6PB7vdLqsdut3uM7PexLWr6zo2m43BYCANDnGObreba9euyR2yL5rYOTYCB8iat8FggMVikYFbYY4Oh0PZgwr771rCNT1Y3zYcDun1elQqFVqtliwdGT3OYrFgmiblcpnbt2+ztrYmP3TKijubiAB3NpulWCxKi370cyNuqK1Wi1wux9raGrlcjt3dXQAcDgeRSASHw0E8HsftdtPr9SiVSjx+/Jjbt2/L8iQRNF9YWMDtdjMYDGg0Gmxvb3P//n1arZZ8fuGtiB2qnU6HfD7Pw4cPyefz9Ho9hsMh4XBYipLH42E4HNJoNEin0+zt7UmxcTqdpFIp4KmQWCwWut0umUyGnZ0d2u02g8FA7k1IJpM4HA4pcMVike3tbcrlMt1uF13XCQQCxONxKVrD4XCfuIpzFK2XYncFIMW1Wq3SarXkjWRychK/308ikXjh2XnHSuB0Xcfj8XD+/HlSqRQWi4V2u8329ja1Wo3Z2VkikYg8fvQD91UFvGKr0fPaaDRNw2q1kkwm+bu/+zuuXbsm3V/F2UTXdQaDAf/1X//Ff/7nf7K5uUmn05E/H63REgKxuLgos/riZuzxeJiYmMDr9cqG/GQyydtvv00sFpMWnMViYWpqCo/HI91Er9dLOBwmGo3SbrflzVb0YIubsK7rOJ1OQqEQmqZJ8fD7/XKGmkBsActkMnQ6HUzTxO1243A4CAaD8voZDAbk83nS6bSsFTUMQ648FG1UwnjIZrOUSiXa7Ta6rtNqtdB1XZ6TWIR99+5dNjY2KJfLwJ9vAjdv3pQ1rs1mk9XVVR4/fkwmk6Hf78vlPtevXyeRSOByuV6o4PfYCNzolBCxgm0wGLC5ucmDBw+o1WrMzMw8d/P3qM8v7ogCl8vF7OwsU1NT3L17l3q9vk8IrVYriUSCxcVFfvjDH3Lz5k3lop5hhsMhVqtV1r5tb2/TarVoNpvS/RMXl9frZX5+ngsXLjA3NycD4sKlE/VyQpCsVqucGJJMJvcVrrrd7n3JMzFUQtSCjQqcKHQHsNvtBINBZmZmSCQSDAYDhsMhDoeDcDgs49WapklrUtd1WRwvREZUJsBToyAcDtPtduXj6bqO3+/H5/NJF1HXdbxeL4lEAo/HIxOEHo9HZjuFENvtdnw+H+FwGJvNJgX/oBBbrVbcbjfBYJB+vy/FVVhvwkV9kW6kYyNw8OeAo8imttttdnd3+fLLL6X5fphVJYKXwkUdrTgH8Pl8XLlyhXQ6zZdffikLNgH5R1tcXOS9995jYmJCxgwOuiSKs4MQmfPnz/PBBx9QKBSoVCqUSiVpdXk8HsbHx/ne977H1atXCYfDh7pOo6EOUXwuRiMdPGbUIrFYLCSTSeLx+DOPN1pzJzbAR6PRZz6vo6EWEb8Wfd0HjxutLXO73Vy/fp2rV68e+tzicd1uN/Pz88zOzj6TZBg9DiCVShGPx/eFkkbPTVzbfr+ft956i2vXrsnzPOy4E1foKxgMBnKayNLSErVaDcMwyOfzMog6WsCbzWa5f/8+T548YWdnh8FgwF/+5V/y4x//WFqFsViMmzdv0uv1ePDgAdlsVmbApqamWFxc5Nq1a3LF22h2R3F2icfj3LhxA9M0OXfuHJubm7TbbZxOJ8lkkkuXLvH222+TSCSktfJ1vGhs92Bm8ds+njj2RQL03+S4UdH5Kl60OPdFn/tFOLYCJ2bBFYtF4vE4NptNZmFEpkYEgkulEltbWzKDdevWLRYWFuQfXQRar1y5wtjYGBsbG2QyGRqNBn6/n9nZWaLRqDSVFQqBSHwJoVtdXaXT6eB2u5mcnHxmabNqyD9eaMNj6IP1+30ajQaFQoFyuUyn05EuQSwWk+NTxLHFYpHd3V12d3ep1+tYLBZmZ2e5ePHivjuBiGU0Gg2azaYs9PX5fNjtdhkXOCoOmvjP+/dh9U+j3z/sOMXLIz43rVaLarUqe1FdLpecU/a8yTaKo+VYCpyIox1WjHiw32+0RGQUEev4qv7ArxMC8bgHkxavi9Ex7a1WS7riDodjX6B4FNGiJuqGRDB3tA9XoTirHEsXdbRE4zALZfQiF+JzUKe/bQ3bcDik0+nQ7XZxuVwvvZfxm9LtdimXy2xtbdFqtWQmLRaLHWphmqYpuz4ajQa6rhOLxYhGo0rgFGeeY2nBHRXCxRCLQQqFAt1ul+npacLh8Gt9bjG1Ip/Pk8/nKRQKlEolGo0GwWCQyclJpqenZV2ROM90Os3Ozg7FYpFer4dhGDidTiKRCHNzc/j9flXy8g046GYqd/9kcywtuKNAuMOaplEul1laWiKXy2Gz2YhEIq9d4Pr9PvV6nUKhQLFYRNM0+v0+GxsbrK6usrW1JQtHbTabTK7cv3+f9fV1bDYbDocDm83GxsYGTqdTTrcwDEN1ZbwAo+VGok3oYE+p8Bi+LvyhOB4ogfs/NE2TVtSTJ0/4wx/+gGEYXLly5Y1YP6IiPhqNysbiWCyGz+fj7t27pNNp8vk8ExMT6LpOrVZjZ2eH3d1der0eCwsLhMNhTNNkeXmZcrnMxsYGhmEwNjb23CkXX2ehjPYMftXvjG48Oqxh/Kue4zgghKzf75PL5WQf5ujQBbHoKBKJSEt6VAAVxw8lcP+H6FktlUqk02kePnzI2NiYrLB+3RkyUbluGIZMbLTbbVwuF3t7ezQaDXmew+GQUqnExsYGlUoFl8vFzMwMyWSSdrvN3t4e5XKZzc1NHA4H0Wj0ueUvolq/3W7LRAU8vZiFRShactrttnSDRTO6qHQXx1osFjqdDu12G3hahOr3+194ftdRI7Lyjx49Yn19XVbqiwnSVquVSCRCMpmUN6DDRuMrjgdK4P4PMQKnWCxSqVRkW82b+uCK4sbRKm3RDJ1MJvF6vUxMTMhWtVwux+rqKu12W46OCQaDNJtNgsEghmGQTqdxOBxcvnz5uQLd6/XIZDKsr6+zsbFBsVhkOBwyNjbG9PQ0k5OTaJrG7u4uDx48oFgsMjs7i8vlolqtsr29TaPR4PLlyySTSXq9Hpubm6yvr2O1WpmamuIHP/gBsVjsxJRR9Ho9tre3+eMf/0gkEuHSpUvE43Ha7TaPHz+WcdGf/OQnXL9+/Znhq4rjgxI4kPGsXC5Ho9GQfXcOhwOn0/lGLLjRGrZGo0E2m2V7e5tMJiMnQ4hx6qLTI5fL4XQ65XnC075E0adYLBYpFAqy+fqgS9nr9SiXy9y/f5+NjQ25qKfZbHL37l22t7dlbG9zc5Nbt26RyWTQNI3p6WksFgvValUWv87OzsoR8/1+n8ePH5PP57lw4YJcanzcRUCECqxWK+12G7vdTiKRYGJiQs4i29zcJJvNcv369UMn2CiOD2de4ISLlk6n2djYwO12ywvR4XDIAZxvAiE6+XyeTz/9lLt375LNZhkbG+P69ety3pbIoDYaDek6CctvNADearVkPd3Bi3AwGFCv19nZ2eHOnTvUajV+/OMfEw6HKRaL/OIXv2B9fZ3Lly8TCoUol8uk02m2trZYXFzE5/ORSqWkwC0vL9Pv91lYWJCN18vLyzx48IC9vT3Gx8eP9b6L0a4X0RAei8WYnp7m/Pnzcpiq6EfNZrMv3HqkODrOvMDVajUePHjAl19+yfr6On6/n0KhQC6XY2FhQc69elN36dH1dM1mU46h6Xa7RKPRfQ3dIss3inCVRocOHHbupmmyu7vLysoKnU6HQCBAKpWSAxJv3LhBLpeTk13EKJ/BYCDLUFKpFLFYDI/HQ61WwzRNIpEIsViMwWCA2+2mVCqxt7dHqVQ6MXE4MehBdC7s7e1Rr9dlS6CY3ptKpWQXg+J4cmYFTlz0pVKJ9fV1MpkM5XKZZrO5rz1MdAS8CddKuJHCLZqamqJWq7GxscH9+/d56623WFhYkE3d4rxGBWy03EUExQ+7AIfDIXt7e3K4ZywWIxgMEg6H8fv9fP/736dcLpNIJHC73dhsNhnb83g8cneFmAJrGAZ2u51AICB/7vV60XWdSqVCrVYjFou99vfw29Lv96lUKlQqFbrdrnRLxbDGUqnEzMwM3/nOd+SIclUucnw5swInxpQXCgUcDgdXr15lOBxSLBZJp9PA09HQb7I/VUw+iUajOJ1Opqeneeutt/jlL3/J8vIy1WqVWq1GIBDAZrNJ8T2shEPst/B4PIcKtGma0joRtXLicaxWK2NjY/tev3iMw4LpooVutHNi1JIcrSk7rowWeedyOWq1mhTuWq3GysoK9XqdRCJBKpWS02VVBvV4c2YEbnS+m5i6ure3R6fTkRu5dF3nyZMn1Ot1KpUKbrf7jbsgYkS70+kkGAwSDAZZWVmRQjw6aFG4gmJpDjwV7mazSa/Xk9NgDxNpEWN0uVxUKhW5WWy0/1XTnk5XFceL93H0v6Pz9Q8uIBldHCKC8cc1kyrOTezgHA6HzM/PMzY2RjAYpNPpsL29TbFYpFwuy4k2yj09esRn6zBL+kwInPjwinFL5XJZZhidTqfcadloNGS8TcSv3kSWTJzfwcEBYqN3OBzm3LlzJJNJOdI6EomwsLDA2toalUqFQqGA3W6n1WqRz+dpNBokEgnGxsbkKJ9RNE0jmUyysLDAH/7wB1ZXV8nn84RCIex2O91ul1qtRrFYlIkMMQhAWGTi/Eb/LZajiO+LjeRiMutxFjhxsyiXyzgcDi5dusT09DTBYJBr167x0Ucf8S//8i9y+GowGHzh3QCK18PodS0mAo1yZgSu1+uxtbXF8vIyW1tbNBoNvF4vCwsLGIZBv99nd3eXe/fucefOHQqFgtxKdO3aNRKJxGs9x1arRaFQkEM9RalFq9Wi2+0yNTW1b1yz6DUtl8vs7e3xySef4HQ6GQwGssVsdnaWycnJQwcFWK1W4vE48/PzfP755+zs7PDRRx+xvb0tl5Vo2tOR0qI3N5PJyIUpk5OTmKYps8+ilWxlZYVqtcrGxgbZbJbd3V2Wl5f3LSt5U4MLvgnCehOWvcPhYHp6momJCVmsHAwGaTQaslay1+sd9WmfecTfTSxxP7MC1+/3yWaz3Lp1iydPnjAcDrl48aIcbd5sNtnd3SWdTpPNZun3+zIIPzc391rPb7TBf21tjd3dXelOixq4iYkJuZlJlDJMTEyQyWSoVCo8efKEdruNxWLB7/czPT3N9PQ08Xj80Omouq7LJv6ZmRmq1SorKytUKhXGx8flTP2xsTEajQY7OztyQYmIU/r9fkqlEq1WS87ZEwF5cbzVaiWfz8tujH6/fywFTmxVy2azlMtl4vE4oVAIr9cruzg6nY4UflX/dnwQawZH1xQIzoTAiSB4KBTi4sWLpFIpdF0nmUwyNjYmtwWJseYzMzNy3nw8Hsflcr32c7Tb7YTDYbk1fTgc4nQ65To1sbdSXGAWiwWv18vVq1eJx+Ps7e3RarWk+5pIJIhGo18pJhaLhUAgwAcffMC5c+doNpvYbDZprfh8PlwuF7VajU6nw1/91V9RLpel8Pl8Pi5cuIDdbqfRaMjyCbvdjmEY/OxnP6NcLuP1epmenpbu9XFiNDYrUtelLgAAAo1JREFUWvTERipRt9doNFheXubRo0domkYoFJLrABVHi6ZpsrD9sL/HmRE44dZdvnyZwWCA1WqVS2SFCIh1ZN1uV16IYnnv60ZsRrJYLHJ9m8vlIhwOywznaAZTuI+pVIpQKEQqlZKlLX6/X2ZPvw6Hw8GFCxdkSYrYf+nz+aTQihhcMpncN1RTbBwfGxuT1prYCjUYDEgmk7JZXSwMPk4z6kTcrdvtUigUWF5eZnl5Wf7txbLxra0tPv/8czKZDNPT01y4cEHuYFAcLeI6EBNznvn5WZkHJ9zU0bal0ap/EeTv9/uYpvmMkLyqJRhfdX7i+YUoiH7Yr5tKPJqlBPbVyH2T5xYJjtGxQMC+guHRySCj79voezr6mKPHio6L45JkGA6HctP88vIy//Ef/8H9+/eZnJzk/PnzLCwsUCqVWFtbI51O43a7uXHjBteuXeP8+fPH0iJV7OdMWHDw9CKz2WyHtl2NZvaOKj4kROWbWjgv+3vf5DEsFssba1d70whxtlqtzMzM4HQ6icViRCIRWbKTSqVIJBLE43GuXLlCKpWSG+AVx5szY8EpFAcRY+lFHWC73d5XGiSEX7Sm+f3+/9/OHaNAEAIBEDwQ//9es8sWWfbys7cq8gWNIzg/RyH+k8DxWvsb3FrrGsH3sXuM8ZlzXtuROYvA8Wr3nxlPywv2s9vbWQQOyPJKCmQJHJAlcECWwAFZAgdkCRyQJXBAlsABWQIHZAkckCVwQJbAAVkCB2QJHJAlcECWwAFZAgdkCRyQJXBAlsABWQIHZAkckCVwQJbAAVkCB2QJHJAlcECWwAFZAgdkCRyQJXBAlsABWQIHZAkckCVwQJbAAVkCB2QJHJAlcECWwAFZXwDnfxI2PvN5AAAAAElFTkSuQmCC)
Two charges
and
are placed 30 cm apart, as shown in the figure. A third charge
is moved along the arc of a circle of radius 40 cm from C to D. The change in the potential energy of the system is
where k is
![](data:image/png;base64,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)
physics-General
physics-
Figure shows three spherical and equipotential surfaces A, B and C round a point charge q. The potential difference
. If
and
be the distance between them. Then
![](data:image/png;base64,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)
Figure shows three spherical and equipotential surfaces A, B and C round a point charge q. The potential difference
. If
and
be the distance between them. Then
![](data:image/png;base64,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)
physics-General
physics-
Charges +q and –q are placed at points A and B respectively which are a distance
apart, C is the mid-point between A and B. The work done in moving a charge+
along the semicircle CRD is
![](data:image/png;base64,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)
Charges +q and –q are placed at points A and B respectively which are a distance
apart, C is the mid-point between A and B. The work done in moving a charge+
along the semicircle CRD is
![](data:image/png;base64,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)
physics-General