Question
Two cylinder A and B having piston connected by massless rod (as shown in figure) The cross-sectional area of two cylinders are same & equal to ‘S’ The cylinder A contains m gm of an ideal gas at Pressure P & temperature
The cylinder B contain identical gas at same temperature
but has different mass The piston is held at the state in the position so that volume of gas in cylinder A & cylinder B are same & is equal to V0 The walls & piston of cylinder A are thermally insulated, where as cylinder B is maintained at temperature
The whole system is in vacuum Now the piston is slowly released and it moves towards left & mechanical equilibrium is reached at the state when the volume of gas in cylinder A becomes
Then (here g for gas = 1.5) What will be the compressive force in connecting rod at equilibrium
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)
- PS
- zero
The correct answer is: ![2 to the power of 3 divided by 2 end exponent P S](data:image/png;base64,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)
Related Questions to study
Two cylinder A and B having piston connected by massless rod (as shown in figure) The cross-sectional area of two cylinders are same & equal to ‘S’ The cylinder A contains m gm of an ideal gas at Pressure P & temperature
The cylinder B contain identical gas at same temperature
but has different mass The piston is held at the state in the position so that volume of gas in cylinder A & cylinder B are same & is equal to V0 The walls & piston of cylinder A are thermally insulated, where as cylinder B is maintained at temperature
The whole system is in vacuum Now the piston is slowly released and it moves towards left & mechanical equilibrium is reached at the state when the volume of gas in cylinder A becomes
Then (here g for gas = 1.5) If work done by the gas in cylinder B is WB & work done by the gas in cylinder A is WA then
![](data:image/png;base64,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)
Two cylinder A and B having piston connected by massless rod (as shown in figure) The cross-sectional area of two cylinders are same & equal to ‘S’ The cylinder A contains m gm of an ideal gas at Pressure P & temperature
The cylinder B contain identical gas at same temperature
but has different mass The piston is held at the state in the position so that volume of gas in cylinder A & cylinder B are same & is equal to V0 The walls & piston of cylinder A are thermally insulated, where as cylinder B is maintained at temperature
The whole system is in vacuum Now the piston is slowly released and it moves towards left & mechanical equilibrium is reached at the state when the volume of gas in cylinder A becomes
Then (here g for gas = 1.5) If work done by the gas in cylinder B is WB & work done by the gas in cylinder A is WA then
![](data:image/png;base64,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)
Two cylinder A and B having piston connected by massless rod (as shown in figure) The cross-sectional area of two cylinders are same & equal to ‘S’ The cylinder A contains m gm of an ideal gas at Pressure P & temperature
The cylinder B contain identical gas at same temperature
but has different mass The piston is held at the state in the position so that volume of gas in cylinder A & cylinder B are same & is equal to V0 The walls & piston of cylinder A are thermally insulated, where as cylinder B is maintained at temperature
The whole system is in vacuum Now the piston is slowly released and it moves towards left & mechanical equilibrium is reached at the state when the volume of gas in cylinder A becomes
Then (here g for gas = 1.5) The change in internal energy of gas in cylinder A
![](data:image/png;base64,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)
Two cylinder A and B having piston connected by massless rod (as shown in figure) The cross-sectional area of two cylinders are same & equal to ‘S’ The cylinder A contains m gm of an ideal gas at Pressure P & temperature
The cylinder B contain identical gas at same temperature
but has different mass The piston is held at the state in the position so that volume of gas in cylinder A & cylinder B are same & is equal to V0 The walls & piston of cylinder A are thermally insulated, where as cylinder B is maintained at temperature
The whole system is in vacuum Now the piston is slowly released and it moves towards left & mechanical equilibrium is reached at the state when the volume of gas in cylinder A becomes
Then (here g for gas = 1.5) The change in internal energy of gas in cylinder A
![](data:image/png;base64,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)
Two cylinder A and B having piston connected by massless rod (as shown in figure) The cross-sectional area of two cylinders are same & equal to ‘S’ The cylinder A contains m gm of an ideal gas at Pressure P & temperature
The cylinder B contain identical gas at same temperature
but has different mass The piston is held at the state in the position so that volume of gas in cylinder A & cylinder B are same & is equal to V0 The walls & piston of cylinder A are thermally insulated, where as cylinder B is maintained at temperature
The whole system is in vacuum Now the piston is slowly released and it moves towards left & mechanical equilibrium is reached at the state when the volume of gas in cylinder A becomes
Then (here g for gas = 1.5) The mass of gas in cylinder B
![](data:image/png;base64,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)
Two cylinder A and B having piston connected by massless rod (as shown in figure) The cross-sectional area of two cylinders are same & equal to ‘S’ The cylinder A contains m gm of an ideal gas at Pressure P & temperature
The cylinder B contain identical gas at same temperature
but has different mass The piston is held at the state in the position so that volume of gas in cylinder A & cylinder B are same & is equal to V0 The walls & piston of cylinder A are thermally insulated, where as cylinder B is maintained at temperature
The whole system is in vacuum Now the piston is slowly released and it moves towards left & mechanical equilibrium is reached at the state when the volume of gas in cylinder A becomes
Then (here g for gas = 1.5) The mass of gas in cylinder B
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOcAAACYCAYAAAAfgP40AAAgAElEQVR4nOy9d5RlV33n+9knn5sr56qu1NU5qYPUrVbOQkggA5IRCAYwYHgeGxNsv/ds1mB7Bo89tmc8mCDSPIMBIyQBLYSQCGqplVNL3eqcKud440nvj3PrVlV3dd3bVSVbSPe7Vi/p1tq/vfetOr+zf/uXvsLzPI8iiijiDQfpP3oDRRRRxPwoKmcRRbxBUVTOIop4g6KonEUU8QZFUTmLKOINiqJyFlHEGxRF5SyiiDcoispZRBFvUBSVs4gi3qAoKmcRRbxBofxHb6CI/1jYiSSelUFynQsXXlLi5yKEvSUuutglL1RQCISQkIJBhK5f+KJZFJXzLQrbcYgnMrzcM0Gw9wxNI2dQXfvCJllKWva/d0r3otdbjJwAScJYvxGtpRWhaYtauaicb1HEkxkOnerjcy/arHzsV3z0ue9Snh5HnOch9vCfbyFAFDC/m51mofHTc+Yb93rOW8h8FzzWAzyX0j/4FNF334lSWZVn5vlRVM63KBxZYSIQI61M8nLdevYE38+7a6HSlNHluWPHMy4nJmx+1ZWkKaxwUYXOiqg677wZ16M37nDvsTiKBOtKNS6rM5CFQJz1RL80lOHp/jSDSYdrG0xWl2pE1Pkfexc4Mmbzo+NxTEWwvUpna6WOJotzFOXZgTQvD6YZTrlc22jSGtWI6nPdKwnbpWvS4ZHOJB6woVxje5WOLs+aLfu/ccuja8rmwdMJNEmwoUzj0lrjnO8D4E5OYp0+ReLxveC6eM4irgtZFJXzLQpXSNiyhitJ9JbU80RpDLtM5taWAGtKVQLKzMMsLJfSSZu+/eMctTz6SjXe1R6iJihjynOfUNuDZMImdizO0/1pTikCuynAlfUmMV2a80BXjlmEulI8dHyKqZjGZIPJVfUGIVVCOuvBdz0ombCpOBlnb0+K/qBCssHk+qYAuizmeDZrRjO82pnk+dNJRiMKN60IcEmNQcksBVUdsJMOHJ7ileEMxxWB0h5kU7lOhTk9zt+E4nikEw7S4UleHrE4rUnobUE2VeiUnqX09uAAqdDzJJ99xj++l2C9F5XzLQoBTJ85eixKMlDCd+IOYTVCqDzA6lINRfJHqB60ZFxWKhP8+GScU45HqRLm+qoAjWEFbZaCakC17XFlTYZDr0zw7ECawYxCZTTK5gqNklnHcpvtkajP8BttlL0jFkl0qiJhLqrUCSjnKmi95XJ9o8VLz4/x7KjFiKWyIhqlI6YR0aXcCbrK8RisSvG0OcHDfWkkYRINh7ikxkCTBJLw9xkGLoomOHZ0in19aWRbx4iECVfpRLQZpdMA0/XYEUty7PAUTw1lsNIagWiEzeUa4VljJdPE7upEKGeZH4uA/PnPf/7zS56liN86JG2PnimHR7qSrC/TuGlFgBcGM7wynMHxYEuFjpFVECFAk31zbtLyeGEwzZ5TCdpiKjVBZc6DDKBKgqqAQokuMZp22XMqyVjGpTYo0xxRENnjU5EEJYbM1kqdV4YtnulLc2TM4uIqg4gmoZylnZosKDdk6oIynVMOv+lJcXTcZnWpSm1ARsrOK0uCqoDM2lKNFwYzPDeYpi/hsL1SJ6DOnbc5ohBQJLrjNj89lUTJyjaG555bshA0RxR0WdAdd/jRiQQBWVAZkGmYNdadmsTqPEPyqSfQ165HX7seORxe1N+oqJxvUcxWzsawwvWNAdaX6ZyatDk6btOfdOiIqQRUkbsvKjKUGzJBVWL/cIbTEzaygKawSlCZa7JKAiK6TFiVcFyPl4cyTGY8TEXQOuu+KgtBUJUo0SUStq/4XVM2laZCdVCeo0gCkIQgoskEFIHjeTzemyLleARViRXhuYofUCXqggpDSYeDoxmOjNk0RxRKdBk1O68kBFFdotKU6Y07HB+3GU271ARlSvS560tCENNlSnSJ/oTD0XGbKcujwpSpMGVkIYrKWcTSMVs564MK1zSYrCvXSNkeXXGH/cMZDFlQZkiUGBKSEP7DqUlEdRkPjwMjFoNJF1kIVkQUVEnkTi8AUxFENImYLnNywqZzymE04z/4YU3ynTnCP2nLDBlZEgwlXZ4fyCCAiC5RF5QRYsbpIwBDEUR1mYAi0Tlpc2rSJmG7lBlZJZH8eTVJUB2U8TwYSDo82ZdGkwQxXaIqOw4goEqUGTKmIjgxYXNqwmIi41IXUgipYo7ZHsq+SMKaxJFxi64pm0nLpSHsn8BKYqqonEUsDbOVszaocFmtQWNYpT4kk3E8nhlI8+pwhnJTpj6kENL8O50sCUp0ifVlGicmbPYPZTgyZtEWVYnpMuZZJ2hIlagPK8hCcHgsw6vDFikbGkIK0Vmmq6kIKkyZckPmmYE0R8cs0o7HqhL/VJbPMnHDqkSFKVOqy7w0lOHomE3c8ujIOrOUrILqsqA2qGAqEs8Ppnl1JIMmC1ZE/P1Oh0VMRWJNqcaU5XF4zOKJ3lRuPyWGhDzrSwU1iXWlGmMZl0OjFs8PZojpMhWmRDgTx+3qLCpnEYvH2cq5q8ag1JCJaDMP/aNdSU5O2IDgokodKXuCSZIgkDVPJzIu+3rTPNOfoi2mUR+S55w0AIoQtEYVQHBqwmbP6QRRzTclqwIzjhNDkagwJepCMgdGMrw4lGEw5bChzHfQnB26MBSJlqiKwOPkpM0TvSkkBLUhhQpz7rxlpkRbVOXpvhQHRizG0y47qw1kiZnvNete+dJQhid604Q1iRURdU4oZnpse0xFINg/nOGXnb4y13hJggNdReUsYvE4n3IqWcUrMWQU4SvTyQkb2/VoDCsEVCn3cAZViVD2TvpUf5qxjIsmS7RGVd+0zK417VAq0SUCquDkhM3JCQvHg6qAQqnhn2CSADXr9BECRlIuzw2kAUGJIVEZmOsBnTaJSw0ZSUBfwuGloQxa9nSfVtDpE7TMkFAlQW/Cv4NOWS61Af8OOn2C6opEVJMoN/0XRNeUTdx26YhpaLKYc4IasiCq+eNfHbbojjs4k5O0TPVhP70Pc93SlPOcUIrtevQnHHoTDrb775xi9VsGz3HAssDzEKa57PMrkiCsSjRHlHNOo6XC88DOxuEGkv5DPZRyc+GLlOP5dy5N4tiYxXeOTOEBrVGVgDKzl5TjURuSieoSz/SnAbAdl1rVRRYeQpYRqu8A8oCAItESUXiyL83DZ5J4HlxWZ6CflUwQViXKTYnnBlweOBnH8Tz6kw5BZf7fQ1CRqAkovDqc5KHTCdKOx2DSmZOk4HpQakiU6RKHxyz+9UgcVRJsLNcJzUp+sFwoM3xn0oGRDA+cSGAqElfVmTRHFcKqf4pKQtASVblREvQnHB4+k+TxkRTNE2k6nKXrzhzl9PDfPo/1JHm8J03KdpeW2/xmhufhJpM4U5PgeqhV1YXln10AgqpEa0Th7tURSpdbOcmmowk4PJrh+0emCM+KFU5DEv5L4oneNGcmbVZGVaqDc08wy/VoCqu8NJTmwVMJnutNsElNogsHSTeQo9E568pCEFIFrw7799WXhjIEVcHZejeedqkOyLw6nGEw6fBYd4q60PzxQw8/O6nMkHh+MMPxcZvnBtJENYmzf3Vx2yOmSbw6nOFLr0zQGlWpO+s7eZ5/D9ZkwYtDaV4ZzvC5i2Lc2Bigo0QlmE2UUCVBU1jhDzZGSdgerxzweKw7RYO9jMrpef6p+cXnx3iqL03a9Sj2m14AHrjJNG7cAkAR6WVXzrAqkbY9Mq+DBaPLguqATFgV9CdcDo5mzokrAtiubwIHVcFY2uXQmEVXfG6CvOeB4wGe7zAaTjm8PJlBdl0kXUJKp+eOx59TlwWu5/lrz5Ov6niQcTwCqiDleJyctOhNnD853/Ug7XgYsiDjehwetfx5z5rY8SBte8R02Z933KI3fu68rue/IGThr/+lVybY15viugaTO1eGKDVkdFnknGQfWhPmpBphckrHPM8JfyHIKaeL/+Y5Om4hBFxTb7KuTEMuVnzOD9sh+eJhUgdfACFRcs1HWO5flib596TwefJNlwJTETRHVf5oU4yRtIO6QDa3m31xu55/Upzva7qubyrbY2NkHnkab3wcraWN4JZr5x3vuP5zN58C5eD5KYH+PXeBcWfN65/Q2a80j8z0CyXfvIdGMuzrS7OvL01HTCVuudx7PM6RMYvdtSbbqnTaoiqKJGiOqJRW6IxVaEjLYOnMOjk9bM+/Q5QaErtqDG5pDiz7XefNAs+ymDg0xOTQCwhJpnZVCCEvPWXr3wuq5Icu3tkaXPa57b44Qz8+hD3Ui9mqU7ZqcQ6RNwIe604ynHJ5diDNDY0BErbL0/0pHu1K0pdw6I7b7KoxaIuqlOi+IykQVBhehvd0TjkFy26VFVHEmwayEFxSrbOhXOPwaIB7Dk7wq+4UT/enebQzycfXh9laaVDmLrEGfRbmOIRmK6hXdAUVUcQ5CCgS68o0/nRrCdc2pnmkM8m+3hT/91OjXFJtcJ0WZ7ftsRxughnlFLMVs4giipgPkoCw5qfvhVU/kaIlorCvN82B4QyJZJx4X4ItlkdsiWvNjXNmtdMZGyd9tI/kUBpHLKyqcnkFckUlciQC+Fn59tAQzuCA7yHIAykaRWttRygKZBOH04degwKKVIVuIJeWolRVIXQDPA/PssicOI47PpZXHklCrqxEKStHCvn3IndiAntwAGdocEFRz3GwTpzAnZhAii71z/DmRDKZZOD0aQ7u3Zt3bF1dHZWVlYRCIQAcx6G/f4Djx48VtFZFRQUNDQ0EAgGEEFiWxcTEBMdPnCCdSuWVDwQCrFmzBsMwEEKQTqd55ZVXODqlMTkZxENiMOkwabmUyjICqArIVJgm68s02mNJfnY6Sc8Jl6f6Uqy2XVwP3CVEPM4xawFSB/YzfPBndJ98As1ZuK9M6O23EX3XHZhbtwOQPnaUyZ8+wOS/fR8vk8m7AfOSnVT97T8ihyMIVSVz7Cg9H/0gXiKZf/P19QSvvZ7Yne9DbWjEs23ssVGG/vtfk9z3RF55VIXIu+8k/LZbMTdt8b/7odeYuPf7TP34/jzC06EmgbnjkvxrvQXR3d3NT554inu++s28Yz/5iU/wO79zO5s3bwYgkUiy58EH+fSnP13QWu985zv54099io6OlaiqytjYGM888wx/8id/ypnOzrzyq1et4rvf/Q4NDQ2oqsrg4CAf/ejH8Jo3IW27DTuylsd7U9SHFHZUS7nqF0lAhSlze2uI3bUGzwXHeeGMXwRguR6W67HYFl/zKiceeK4LjoOXRznlSBS5omJmwrJytMYmPM/NK+svKpACwRlPpwfY+dcFkIIh9HUbkIJZj6MkIQVDIERB8kKWUBsaUcrKZvZfXo4ciRa29+yaxYvA+eG6Lrad/3c5MDjA6OiMtZNOp0mlUgXJAkxNTTEyOoKbtdYSiQS9vb2k0umC5shYFvF4HNu2UVXVj/s7DkyMwMQQVsjj/pMJjo1bXFpjcFtLkMawQjCXLQSluszWKp3GliCG5qcKqvPEjgvFHG/t9L1TqasnWHUNsctXobGwaWru2IlSWp77LJeWYmzZSskHPoxnW3k3oDVnu5NN1+FVVRH7wIfwrPynrlJTh7F2fU45hSQh6TrhG25GX9mRV17ICuaWrcglM8opl5cTuHQ3Qs3TJMJxSR87Qub4cc7tYlMEQCwW45JLagms3ZB37Pp166mrq819NgydzZs28od/+J8LWmvlypXUVFcjZ1/yoVCIVatX86EP/ScmJyfzyleUV1BaWpqTD4fDfODuu+l0AhwKNvKKJ1gRVpjIuOw5laAn7nBxtcHmCo3WqIomi1wxeCDih1IkwZwSuguFmKad97MrXG7+SR+yJPjwmjDvaAkW45zngWdZTDxwL5M/vt+Pc379//xWxTlfT9h9vQz9/d9g9/Zi7riEsk8UpmBvRDzWneRfDk/xnSNTfHFnKSMph192pTg6ZrG6VOXqepNrG/12LVFNQh7oJbHvcYb//m+IvOtOIu+6E7W2Nv9C82CuWSuywRRvyb2JiijiTQVJCFbFNDZWaNzYFODe43F+ejLB/3x5nAdPJ3jfqjDXNZjULaPSzH/npKiYRRRxNhQJIqrEqhKN962S2FCm83hvkucHMtxzYJJn+9NcLk+xK+Xg5A9U5F9vvh9a/X0kxl9h4sVhtDxqqrW2obW2IZeUAuCMjmCdOUPm6OGCenYqVdUEdl7qh1IkCWd4iPivf4lXwCVeCofRVrSgrmhGCgTAdXGtDMmnnsTu680rLyQJrWMVakMTckmJv/+RYTLHj5E5cXxhYcch+dILOAMDKNXVedcq4rcTZz/9IhvnXFuqURdUqA8p1ASTPNWXZv9QhqlUArc/xSbbo2SJa5+bvicgc+IY4wceZOD4Y2jOwk6dyB3vJXrHXTnltPv6mHr0Yca++TW8s6oR5kNg126MzRf5vBKShHXmDIP/5c9xk4m8slpLK+Hb30OktBQpEMBzXdxEgrFvf53E44/llReqSuzDHyN8w8055bR6e5j4yX1MfO+7eeUBP1ZatbiO3m92WJZFenSMiVOn8o4Nh0IEQyFMwwB8L+/U1BTDIyMFrRUwA0SjEXRdRwiBbdskk0nGxsZ8r2seaKpKRUUFqqrm5Pv6+hkctEkmPDw8xjIuCdtDybbXjOkSl9UZbKrQ2Fmd4ntH4xw77PBoZ5J2281eDZcxzpnLEirQDyQ0DWEauc9SMIhSWlpY+QCAkHxvrXThmcJCN1CrqhFqlotCkpB0A6QCHTNCIEejiEAg9yMpGEQylr9w+q2Inu5uHnlpP//2vR/mHXvrbbdyyy23cPGOHQBMTk7y45/8hC/+ty8WtNYVV17J3e9/Pxs3bkDTNAYHB9m3bx9f+tI/09/fn1e+pbWFv/3bv6WxsRFD1/0458c+xni4jviqq7AqtvHDY3FUCS6vMwmpM89rSJW4pMakPapxMDTB4WEdQ87GOR2PxTGlnOMQ8v+rtrQRWXMHlcZ1+c3alR0o5ZW5z3JZGYFdl1EZChdm1lbX+AqeXVxtbKTiz/9LQWatXFKCvnotUjarRAgBuk7s/R8kdO31eeWFLKFv2IRSNhMKUsorCN90C1pr+8LCWbM2vf/l3N6LmAUPLMtmbHSMk1P5M3TGx8exrblW2tRUnJMFnLoA64eHcGYxpXmeR8ay6OrupqurK6+8bhg4s55X23bo6upCrg2ieg6257GvN8VY2uH5gQxX1RusLfObZEsCAoqgLiSjV+hU1RoEsk3Jzm5MdiGYk1s7rYdKVTWB1W1E2kJzuSMKgBQMobWvRGtfuagNyWXlRG5/96JkEQIhywQvu2Jx8oAUCmNs2oKRzRg6HzzLAk3N3m2LyjkfQuEQa9au4fb65rxjt27dSmXlzEte0zTa29q4/fbbC1pr29atVFZUIGUtsEAgQEtzMzfddBPDw8N55evqaolFoyjZcFggYHL99dcxHqyhu6oWyYHaoMxQymXP6QQ9cZvdtQYby3Wawgoh1VfGMkPCjKoMy349qbyEF/e8J+d0KKWIIhYNAdXV1bxzxyV8ZBFxTtM0ueaaq7nmmqsXtXwsFmPHjh3syJrJF4qysjL+5otfzMU59SNT/P76CEMplwdOJvjXo3Ge6E1x84oAv9MWpD2mEVTEskY55q3nzHacKKKIIrIQwi9Ov7zOZHuVzuO9KX56MsF9x+Ps6/ULsd/WHKB1GRp7TWP+UMqZU0yeOMGw04nGwvdGY/NFGJu2oFT4JokzPET6yGGSTz5e0L1RXdFC5Lbbc6EUu6eb8e9/t6D0PbmsAmPzFvSVHX5VieviWhaTP74P62SeUAiArBDYuRt95Urk7L3THhok9dILpF54bmHZbPqedeYMWtOK/GsV8VuP6e4RJYZMqSFTG5B5si/N/uGMT/A0abFTmmLbpI36esQ5BX44IX7wV4we/VXeUEr0ve9HbWqeUc7RUVIvvcjoN7+Oly6gVOfSywjfdEsu9c3u72fsW18vLJTSvhJh6Kj1DUihMJ7n4WXSTP38QRKP/TqvvNA0pEAQpbIyp5zO6CiJfU8w/i/fyisPgCShNjUVNraI3zrMZ0UGFMHKmMqKsMKqEo1HupI80pnkqf40g6kE3mCKLfZ0EGW5QinTl04hQJIQskJeK1qW54ZBst2BhSKDnZ9hUJwdQhGAIiPkAmQVBaGoc8I2HuT2nheyDGcvL3wvbn75mZKxokNofngUXpUihECSpDmeb9d1c1UmFyrved6cf4XIz/4Hfk1pxnawsuk+juvheh5ettRBkwVbKnXWlGq8vTnI1w5M8MKrLg+eTrLScvG8pXVEmPcJ1FetoeTSZmrL/hN6vmLrqmqUqpkMGaW2jvAtt2Fu2VpgsXUMyTRzCq61tVP7lW8WVmwdCKBUVSPH/GJnIUnIgQDlf/w53A99NK88koRSV59LoAC/Iid21wcIXbNwKMZzHBKPP0Zi3+PFUMp50NPdzZOHv8NDD/4i79ht27Zy3bXXsnv3bgBGRkZ49NFf8vVvfKOgtTZv3sTNN9/Mtq1b0XWd7u4ennzySe67/z5GRkbzytfX1/PHn/ojmpqaCAQCDAwO8md/+md0u0H667eRrt7JP70yQV/S5ap6k5pZfW41WdAYVvj4ugjHtBg94wFCz0rLW2w9DSkSRW2tw2xfRCjFNJHMOtTaukVtSAqFc4XbFwwhELKC3rF6cfKAZAaQmlag5rlHepaF1dOF9Or+Ra/1ZkcymeT06dPsPXA479iWluY5NpoQgsGhQfYW0EUBIBqNznlJCgGZTIbnn3ueru7uvPKrOjpwXTc3RzqV5tnnnkOpXYnS6NMNvjSUwfGmODFucXGNwYYyjXLDD6EEFEFbTKW0Sqe7SkdXxJJLxua9c/qxlEXPWUQRABiGQV19HdvDpXnHbtu2jcbGxtznQCBAQ0MD27dtK2itDRvW09TYiKL4j3QkEqGjYyVbLrqI2gJKtlY0N1NaWoqm+fk8uq6xYcN65Mb1jK9o5cU4VAZkOqd8npdDoxa3NAfYWK5RG1KIqD7RUkSTUMLT9ZxieZUTKOpmEcuC2ro67nr7Nj7+e7+fd6ymqrlCZwBd17nxhhu46qqrClpLkWVUVc0lIYRCITZv3sw3vn5PQaalJESufxD4PYm++pWv8ERfhu+fSKEfS/Anm2PEbZf7TyS472Scvb1Jrm8I8LsdIXbVGMte+zyvcmaOHmb02f30jh9E8xa++wWvuobg5VeiVPrJ3/bQIOn9LzPxwL14mfydEPQ1ayn92CdzDb4yJ44z8j//DjedP5SiNjQSuu4G9I7VSOGZUMroPV8m/eoreeWFqhB+x7swNmzMpfDZgwMkHvs1U488vLCw52L39mL396EtwYx+M0MSAlVVCc7KXb4QKIqSOwkvFEIIZFnGXCTBlBAC0zTxm3RkEAgiusRFlTpNEZXL6wx+fibBC0NpTk7aXFytc2NTgFUZFzX/9AXhXLNWgD02Suq1A8QPP4qVJ5SiVFdjbNycU053fJz0kUPEf/loQaEUL53yG4FJEkKWccfHif/qlwWGUjpQVzSjNq5ACmdDKekUqReeI7H3N3nlhaahr13vxymnQyljY6QOvkr80TzKOY1iD6G3DGQB1UGZqqBMS1ShzJTY1+uTDD90OsFQ0uESkWDThI2R35+ZF/O8ljwk00SpqEKz2tDchZVTPrstpOchNB2tuaWwPkDVNXO8usIwUFta8ApoZ6hU1yC8WZEozwPHQamuQWttyysvFNWviJntVfZc5Eg0v7zn4U5O4sTjFEMpS8d0uONsz7fneUvyhhcqP984PxTi5czi6SdNlwV1QYU720NcVKHzaGeS7x+L8/CZJCfSUySHU1zseMtbMgb+L8dYtZrYdeupbfokep7qK8kw53BTqiuaiVbXEL7l1oISdIWm+Q26ZodSvvqtwmRlGWGYSNkaQKHIyNEY5Z/504LacoJACgQQxkzJm9bcSsl/+gjRO+9aUNKzLKZ+/iBTD/+8GEo5Dzyv8CRtx3Fypug0XNfFcRwURVnwdzwtOztGOb3+tAdWWqAkcTqeOtuE9jzPrwlNW6QsP06bcTwc12OaU1Bk+TmrAgpXNZj88FicFw8M83hvio22i+N52O4ylYxBNqSuakiRMEplCOUCL7lCURChUK6M60IhVDWXbbQIaZAEcmzxNehCVRGqihSOLDjOsyykSAShLdcN482HgYEBXv7xj3ly/8G8Y1taWth96aVceumlgB/nfPLJp/jRfT9CEtKCxonnebS3t7P70t1cdNEWdF2nq7ubp59+msf3Ps7k1NSC5cWe51FZWckHP/AB6uvrMU2T0dFR/vbv/o5jU4KTJWtIV17CVw9M0BW32V1rZinn/ZS+qCYwFZXb24JscsMMDZgElSwD+BKsqsXdtosoogBMTk7yyonTfHffs3nH3nHHe9g2K2ziuh4nTpzge9/7fkFr3XjjjWzfPhMft22bkZERfrpnDz09PXnlOzo6uOM978mZ1/F4gj17HkRUrkDe1orjeTw7kCbjQm/c4ZIag1UlKuVZjk5dFqwu0aitNemvMRCKyIZSCtr+vJj35PQyFs7EBPZAgnzdHqVA0O/fM202uC5eJo0zOVmgWavnMnzAP5GcsdHCZFUVKRjyac2nX42ehzM+jpfJ3yIFIZDDYYSmz9m/m0zgxuMLinqWhT05RcoFR9WYzLiIYhtRAGzLY0poWKqBGYlSE85vyVx5xRVs2rgx9zkajVBdU01NTU1Ba3Z0dLBp0ybULMV9ZUUF27dvp7GxoaD0vZqaaqqrq3PeXVmWqKyooHzLDtwNW9k/DHUhhRMTFi8PZXisJ8Xdq0LsqDaoDSoYsq+IQcUnJR6Wsqmgyx3nTB85xMij++jufgo9j0Mo8u7fJXzrO1BK/cbMztgoyReeY+Sf/rEgb625dTsVf/GXfuK7EGSOHaX/zz5dkENIX7WG2Ac/jNba5nd69zxcy8X89GgAACAASURBVGL4f/wNyWefyisvNI3ST/4h5tbtMw3KxsaY/Mn9jH/vXxaU9TwYy7i8atZwas0mwoemFtVq5c0Id8JhKria6lWCq26s4u533JRXpqqqKseTAn4Y5bprr2XD+vUFrRmNxoiEw7m7pWEYdKxcyde++jWsAhyTuq5TWlo6N8751a/w0qTCnn4FfTTFH6yPIAnBr7qT7Dmd4AvPjrGtUueW5gA3NgVy3d+XC/N6a91UEntwEOvEcYSz8BezTp/EGRzMKac9PEz68CEyx48W1OBLqa7BTSZ9x4ws46VSPkFQAaEUhERq/0so1TVIwRCe4+AlE1jdnWQKIMARmkb6yGG0FS0zDcoG+8mcOpFX3hUS/bE6nq9p4cmStSjHE0WnbRZexsEKtLGlzKO6voKOjvzd98+GEIJoNEo0Gl3UHiRJwjAMWlryd2GYD6qq0tzcTGd3EmloCiEE1UGFtqhKbcivRtnbk+TEhMXXD06yfzjD5bUmqy2Hhb0VhWMes9Z3qOir1xCsddDchQM2WnOrn0AwLS/LKOXlBK+4uqB6Tn3VambHCaVolOCVVxWUhCCXlyPMwFknlsDYuNk3VfNAKDJKeQUos2x3SUZtaiZ49XULyrqAkRDEdJ1qawojJBfe1OxNDjdpk7bjxJxk3ufnjQ43+28aVQGZmqDMxnKNhpDMr7pTvDCY4b4TCfoSDrulJJsnbPTXI84phEBvayfavpnq1WGMC7xHaS2taC2tRN/z3kVtSGtppfofvrQoWaEoyNEoZX/wqUXJA+jtK9HbV1LygQ8tOM6zLMIP3Evrj+9HnDxM7f9zS5GOIQu7r5ehJx8i09ODVrONeCK/FSRL0pyMoOlSM6tAIqNpeVlRELPkbdsuKNIoCZFrqymEwPM8UqkUiUSKTDbTLe24ZByPgCoR0QS3t4W4pMZkX1+KL70ywU9OJng5PsHtwwmus1zK86yZD+dJfC/mvBSxdPR0d/P4a4fZ88CDecdu2bKFG2+8MdczaGhoiId/8Qu+fs/XC1pr0+bN3PK2m9m1axe6rtPZ2cmvf/MbHnjgAUYLKBlraGjgc5/7LM3NzQQCAQYHB/njT3+abttkuGkH6YYr+YeXJ+iacrguy40CUG5KXFFnsDKq8MuuFK++NsbxkxaZLP1fxvUWnc537p1TZAtVC6jFzLW+nF0kOy0rxLmF1GfLu66fUTT7xPE8PNv2f5bPweJ5uI6DJM81KT3Hyb/+rCJc4bvV5v787H3Nh+z+i5gfqVSK7q5unpnK3zJm7bq1GMbMVURRFJ9j89n8YRiAquoqTNPMPYfTp/CBAwfo6spfMjYxOTknWSGdzrB//yuo9R2YponjeRwatfjhsTjHxm121hhcVKFRGZApN2RKdRlTkWhPBxns1DEVCYlcvsKicK5yeh7u5ASZk/0kExm8BYqtPdtGKitDqaz2G0kDzvgYdn8/zuhIXjey5zhI4Qh6x6pcOMSZnCS1/yU/+yefcioKIhBAa5pNx2CROXoYd2Iir3J5rodcVoZSWZUL5zhjo9gD/TjDQwt2Q/Acm8yJ4zjj43OKtYuYgWmaNDU1sbs0f1LJpbsupaWlJfc5GAzS0tySK77Oh61bt9Lc3JzLMIrFYqxft46dO3fS29uXV37FiibKy8tnSsYMnW1btyIa1zHaspLnJwTNEYXxLAXg4dEMg80BtlToNIYVSnSZ9phKXb3JaEOAlOr3rF221pgAwnPJHD3K2KFH6Tn8EPqCHJsewRtuJvLOd6HsvhyAzKHXmLjvh0z+bA9Y+apSPMyLd1L13/4HckkJQtOwThyj7w8+jpdMkM/9KVdWYl68k9KPfdLP5bVtnJFhP5Ty5BN55VEUQjffQuS22wlcvBOA1CsvM/GjHxL/+YN55GdO3iKz9fyoravjvdt28MmP/195x57dokTXdW644Xquu+7agtaSJGlOil4wGGT9+vXc87WvFdymZHbqYGVFBV/5ypfZ25Piu0fjGPEEn9kcJe14/OhEgnuPTfF4b4prGkzu6ghzTYOJLgs0SRDSJDLL4Bucx6yVsqati1cAw7RaWzengbS6ohnjom1MPrSnMHZoSUKOxWY8vh5ZRu0CusVXVBK+5VbkbBhHKApKaRlCVgqSF4qMuWUrWvPMG1tr70CtbyhIfnr/RcwPga80iy37OlvhLnj9sxTuQiHLcnZ9X9MMWWJTuUpDWOWqOoMHTyc5OmbzX58f4xedSd62IsB622W5yDzm9dYqVTWYJbsp2VGHnqc1ZmDX7jl0BnJpGeZFWWbrAoK/WksbQp9117gAZmu1cQXGWbTzQtcJ3XATWnseOgX8qhSf2XrGLJ1mtiZfCKDIbP2WgySg3JSpCMisCCuUGn5rzBcH0/ymO8lw0uESMcXW0QyR1yeUAmpdPaG2DsrWXHgoRWgaWms7ZX/0mcVtqLZu0bLTWDSdAyCpGoGLdxG4eNeC42YzWxfjm0vHdPXI2VUlnuflPT1nm61ny5/9s/PJz7eO67rYjouTdY462SIbTRaUmzK3tgTZWK6ztyfJD47GeXYgTc9UnNRAiiuXgWXsvN+66IQsYqnwXLcgrz/4zbiss3wUjuOQSqXytse0bRvLsvyYZvbBdV0Xy7KwLKsg+UwmM0fJp+OcE1Nx4skU4JG0XTJn9bpsCCu8szXIP19Zzu+vj1ATlHluIEPS9rCzJWOLxXkbfC1F45eKpRTYLrU4d1Fr/ruu9tuD/v5+XrzvPvY+93Lesc3NzVxx+eVceaVPQjU0PMzjjz/Ov/3g3/x74wJ/U891aWtrY/fu3ezatdMvGevq4okn9rF3795sydjC8pVVlXzkwx+hsbGBQCDAyMgIf/3X/5VjUx5nyjeQrruMf9o/wfFxmyvrTdaXawj8UElAldBlwduaA6y1IwwNBgg/Ky0vkZG/Uw9naIjk+GtMHBwkLRZ+66iNTWgtrbnetfbgANapk1inThb01lSqqjAv3omUrQxxhoaY+vWjBfWtlQIBlJraXA8hz3FwU0lSzz6NXQAno5Akv83JipmO9XZ/H5kTx7HOnF5YOEsBaA/0o1QVVjnxVsNUPM7BE6e595kX845973t/l9mvOQF0dXZx/wMPFLTWDTdcz6WXXpqz+IQQpNNpHnnkEboLLBn7wAc+kFPiRCLJI48+ilzdilq5EcfzODiawQG6EzaXTpqsK1WpCSqYikCRBC0RlcoqnaEqHVv2TfRlLRnD88h0nmbitUcZePWn6HkS38O33U703XfOKGd3F5M/+ykTP/jXgroRBHZeir5hk99dXpKwOs8w9IW/KCjxXalvIHTtDShV1bkGX148zti3v0Hiifz9ToWqErnjLsK33JpTzsyZ034o6P5788oDfmPqqiLt/HxQFYVYSYzmciPv2GuuvoZNmzblPsdiMerr62leURgPzbq169i8eRNatvi9qqqKXbt20r6yPRe7XAgrmpqoranJlYwpikx9fT3lF12KvXEHL/YJOmIa42mXHxyN83hPirs6wuyqMVgR8SkAJQGGLCg1siVjwFKqIc41ayVxQWahXFGBUt8wM2FtPca6DUzc+4MCd6AgRyKF0SecLVpWRuCyK5CylQtCUZBjJX5CQyGQJIw161Dr6nM/0hqbUKqLyrYcqK2r467rbuT9d92dd2x5WRmBWV36ZFnmmmuuZuOmjQtIzSAcChGNRnNOHVVVaWpq4itf/nJB+bmaqhKbVVdcUVHBV778ZV6ckHigR6APJvnYugimIvhVV5J/Ox7nv78wxsPlGrc0B3hHS5Co/jqXjAkhUBsaCTffQuXtF6PnMWv1NWuRS2aKaeVoFHPrdir//AsFVaUoNbW+Yi6C2Vopr8BYtRrJDExvHqGqxN73wbxVJeBX0JjbtiPPKkuSYyWErrsRta5hAUmKzNYFQFVVzJIYZQWefmcjFArNqfG8EAgh0DSN+vr6/IPngaIo1NfXcaI7idQ3hcAnxl1V4qfsrSrV+HV3kpMTFt9+bYqXhzJcWW+y0baXnPCe28PZPxD47NJGSxORdZELD6XoOmpjE2rj4pi3lsRsDSAEgWy20qLEdR1j3QaMdRsWHFdkts6PqakpTh48yMC9+a8ITU0raGxsyLFbZzIZzpw5w8sv53cmAdTU1NDe3k5ZWRmSJJFIJBgYGODgwddIFnBFCocj7NixnVAohCzLJBIJ9u59nMNJjfF0KWSrNEsNicqAztpSjbqgzG+6UzwzkOKRziSDSYceKcH2UYvw69Ma08fsjpNFFHHB8KCvt48H9j3NV7/93bzD3/e+u7jzjjtyyplIJPjFL37Bpz/z2YKWu/mmm/jkJz/Bjh070HWd4eERHntsL3/5V39Fd4FcKd/+P9+mtaUF0zQZHh7hs5/7HFpNG8r2t0Pt7lycUxJgKoIbmgJsrdR5YdDgKwcmeKo/zdGxSfoH4rz9dSkZmy7OWOLEbxksMdBchA9N1VCUGV+BkKT8hQ+zIMsyWrYeE3yHzmx6hbwQAiWXrjcDV1ZxZA3P8+hP2IxnXCpnFefHdIkd1QYtEYXHelK8dGCc3pMOtuthO8tdMuZ62D3dTJ08zdDDxzDypO/p6zZgbNycc6rYPd2kXjtA6qUXoYDcWrWpmfAttyEMHSHJF8RsLUVL0Fetwti0BTka89uUpJJM7vkJ1qkTeeWRZMzNF6GvWYtS45PdWF2dpPa/RDofe9g0s3XnmbyMZG9VlJWXcXVrG01b8xcGbNiwnubmmd+jYRhccvHF/NVf/mVBa7W1tdHU2JjLpY1EImzatJHPfvYzTE5M5pUvLSulsrIylwcci0X51B/9Ia9ZEV6UG8gk4TtHpuiJO+yqMdhSqaNKfgglqgmimoYmSzQng/R3mgRVCUla7pIxPJ8v5OA+xl79Mbq9sJJE3vO7qE3NOeV0JsZJ7X+ZsW/dU1APocCu3YRuvBnhaiBdGLO12tJK5J3vQl+5CqIxvxYz2+y5IDoGVfOT5evqc8rpjI+RfHIf49//Tl55IMtsXVTOcyCgpKSE2h2X8LZP/OcLFtc1jY0bN7JxY2He2rMRDAZZuXIlK1euzD94HoTDYe6++24eOp3gzKFJnGNxXhzKMJFx6ZyyGcu4tEdVqoIy4Wxjr8awQmW1wXidyZTil4stb8mYkPxKC0kGWUF4C3tr5VgJSvmsxPeSUtTGJj+cYRdQGaKqCMOcqb28AGZrOZKtBc264IUsIQIBf85CmLFVBbW+YS55bkUlcllZ4czWQhT9QW9iBBRBSJWQhWBntU7nlMM3XpvkvhNxfm9thLc1B9lQpuUeA0Xy76OJ16NkTAjh9wDaWEtd1e0YeZitldq6uVUdJaUEL7sCrelbhWX5xGJIs/rOXgiztRQKodTV+20xAYSEpKqU/dFnKfngR/LKk80Qms33IsdKiNz+bgKX5El8n81sXdTONz00Cd7REqREl3luIM0DJ+P84Jif7H5ZrcE7WoLUBJVlYxiD8ziE5FAIpbESc30UQ7nwqhSlonLRlApLYrYGEBJ6x6rFi2saakMjakPjguOKzNZvLQjhkxetL9NoCCtUB2Se7EtxcsLmgRNxuqYcdlTrrLct6paJ33ZB263ogyxiKUilUox0d3O8gD5AsWiU8vJySrPtbizLYmhoiM6uroLWioTDVFZWEovFkCSJVCrF6Ogo/f39ZPJ25ADTMGhpacEwDGRZJpPJcOjwYU4OO0yN6pAtoQ5rEutNmXWlKuvLNX5+OsEjXUnuOxHn6LjF1WqCKyctzNelnjP736JiFrFUdHd3s+epZ/jWPd/OO/bqa67mjjvu4Na3vx2A4eERfvjDe/nCF75Q0Fq7L9vN3e9/P9deey2madLV1c3PfvYzvvLVrzJQQBFEW3sb//S//hcdHR0Eg0EGBwf5vd/7KFawFHfjDbDybXPGCyHYXmWwpkTj5hVBvvnaJI90JjkxOMmp3knem3kd4py4LplTJ5l4/iB99zyP7i4cDglcupvA7ivQshlBVlcnyRefJ/6Ln/tZNHmgr15DyUc+htD9UMqFMFsrVdUEdu7C3LbDv/c6Dm4qxeg3vkr64IG88kJRCF13A8bmi1Cz+cFW5xnie3+T39tbZLbOC8/zsDIW8UR+ao36+gZqa2tzn4PBALquF9TzFiBgBmhoaMiFQsLhEHV1ddi2XdAcmUyGUCic41pxXY9kMolcWYJaVoPreRwes2iJqrm2mLKAkCbRUaLy8fURLq7Wee21CeK9/uFmZdtjLl+cEw93YoL00aPE9z+CnSeUolRVY27bkfvsplJYnZ3Ef3UBzNaOy7Tf6cKYrVeita/MvQQ8fEdN6qUXSez9dV55oWnoa9air1k7s/9kksyxI0Vm62VANBpl27ZtSB1r8o699pqraWycueebpsmGjRv42Mc+WtBaWy+6iIaGhlycMxwOs27dWt7/vvcxPDKcV766upry8rI5yn3nnXfQbdZzNNqCFYc9pxLELZcd1QbryzQCioQiQUSTWF+mUR2QaUsFOH3CIKD4bsKluArn9dYKw0AqK0dtbs3LbK3U1vrlWllIgYDPLN3SWhDTl1Jb54c+st7aC2G21ppbUOvqZqgXhEAoCmptbWHM1qqGUlODCARn9h8KodYUIF9kts6LiooKGndcwu8uIs6pKAoX79jBxTt25B88DwKBACtXruTP/uxPFyUfi8X4k899jofPJPj/Dk1hH5niid4UZyZtXhu1uHNliJaISoUpE1B9RawwZWJVOmuaTEZUP0FBWUJB5zwlYzJacyvRHe3UrbwbIy8FYMDnK5mesKqa8A03Edx9WeHM1po2N5RSKLO1oiAFgj51PNmUL9Ok7I//pDAKQARSKHRWg7FqonfeRfjWdy4oWWS2fmtAlwWGIlBlwTtag/RM2ew5leCRziS3twW5tTnIJdV6TgkFPrXDcjwR83Z8F4qKCJnIFVGUCw2lyDIiEPCbPC8CS2O2xufcnFWXd8HisowIhZFC4QXHFZmt3xqYNk0VAZfVGpToEi8NZfhlV5LHulMcH7e5uErn+kaTlqjK4p76+TG/t7Z4EBTx74zl6L53tgVzvq5888mfr/ue67p4noskBI0hhYsqdVaV+PfLvT0pjo1b3H/CZjDpsL1KZ61lUeV4y9Ig7zxxzv/YBl9FvDlgWxaTExNkenvzjpUkiUAgSDjsZ3s5jkM8HmdsbAxFURZULtd10TSNYDCY40uxLItEIkE8y1CeT14IifLyMtSs/8NxHAYGBhgZSpGKu4B/v9NlQXtMpT2mcmmNwU9OJbj3WJxvvjbJU/1pbjLi3Jp0UF8P5RRQdD4WsSzo7unh168c4N4f5m/StXHjRm679VZuvdWPcw4ODvLTPXv43//7SwXc6T02b97MbbfeyjXXXINpmpw+fZqHHnqI++5/gNHRfCxjHo2NTfzFn/+/tLe3EwqFGBwc5OO//wlGHJXJtkuh45ZzpFqiKnevCrO7xmDPaf8eev+JOENdk9yRdinL+60XxvmTEIoKWsQS4Wf5DHN4Kn+x81VXXUlN7UwXQ8MwsCyLI0eOFLTW6tWrqamtzYVSQqEQ1dU1dHd309nZmVdeEv7JPR3ntCybkydPIhrWoZTW4ngezw2kqQnKtMc0JOGfopWmTEgVBFWJtqjKEXWMTPbr2q7ft3ZZKQARxcOziKUjGAyysmMlb6vO048Jv/tee9tM+CoUCtGxsoO33XxzQWtdtvsy2tvacnHKkpISNm/exPXXXUdfX36WscbGRqqqKnOd+kzT4MorrmCidj099auwxuDhziQAu2pc2mMqUV1ClXzF3FCu0RxROGoHOXxcx1QES20mUjRri3jdUFNTw7t3XMLHFxnnvOqqK7nqqisXtbau67S2tvKP//gPi5IvLy/nH/7h7/llV5J/OTSJPTLFb3pSvDqc4bGeFB9bF2FzhU6FKSFLfugkrPlK2rYiwLAqUCX/32Ixv0OoeHIWUQTgp+jJkkCXBR9fF2Eg4fDSUJrPPDHM7lqTm1aYXF5nEFHlZafMOUc5PWAo6fJ0f5p/fmUcdSl9Ft7E8ByHVLyKVNUlCCERfWXignreFAJNElSYMtc2mIS15Zv7uYE0LwykGcu4uYdvoT+zly2BcrPNrRY6DDwP7AmbicAGqFyB7jUT2j8+79i042E5foGyKuffg+V6JG0PQ/aTAs63j7TjYbvk7oXzjXM9cFx/rCz5zaDnU65jYxYHR/wU1qTtsblCoy2q8PRAmpeG0gwmHQ6OWOys0VlTqhE9d4pF4xzlrDRlVAmOjln0J5xiyPN88Dxcpwan3k/9U48ufxpfWBWsKtHYVWMQzt+0vGA805/ingOT9Cf8uqagKghr0nlNMMfzSDswlnaznQHOn5bmeZDOOIwF1yGbDgEpQPDw1Lxjx9Iuo2knl/rmp8GdZ15gMuPSPWUT1iRiukRInf+FNZJymLQ8XA+qA/K8iud4HknLoz/pokk+tZ+hnLt60vaYyPjf+4XBNCtjCjetCLCqVONnpxO8Opzh2LjF6UmLq+tN1tkWJba/9lIxRzkFcHW9gSbB0XELU5aKCQnng+fh6gaulgHXRYnOdHNYLoRVn+p8KfeW+TCWdhlMOtiex1jaQ5NlKk2ZMmN+0yxhefQmbE5OuAQUmZqgQuw83c1d12My5TE+pCAciBoKzbH5/ZVnJm0mMi7DaYe2mEp9UDmvpeZ50Jdw6JyyidsedSHfOzrffk9OQHzCZjztsqbUz3/Vz5rXcjzGMi4DqQyW57cjWRFRznnpZByPKctlKOlyeMzip6eSRHWZD6wOc0Wdyc9OJ/iXw5N867UpHulM8vbABO9P2BiFkastiHNOzu1VBm0xjYTlIi3zQ/Gmgge4ETw7y6qt6cv+IlMEBBSJsLa8E2uyby5XmBI9cYeMC4ok+OjaMGFNOufvbrseAwmHv35ujMGkQ0yX+MONURRpHlPQg/G0w68rVH5yIg6qzK4ag43lGsGzTrqRlMNTfWn+5oUxJCHYUqlzQ9N5EuA8GEg6PN2f4puvTRJUBNurdC6rNc7Z73ja5ednEnz94CQp22N3rcHltcacl+e0mfztQ5Ps7UmRdjze0RKkKaJiKrPH+SZy3Pb41yNTvDyU5udnElxZZ1Bmytm0PYWn+tL8sivJCz0ZlDNT/M7rUc9ZbsqUm4un6i4cLqnxIcaH+ugfHGEs6ZCZlfYkhPB7AikqmhEkUlpJWXkplSUmCsUDfSmQhZ/MXW7KrCnVOTSaYSDhMJJ26cjSDcyG58GE5XJLc4CfnkowkHCIWy4byvV5T9CU7RHRJY4nBIdGLY6MWVzXYNIUVpBnKVLa8QgqEk/3pehJOIymXUo0iZqgPK/ZHLdcqgMyLwxkGEw6dE3Z1If8U3z2eCsbXzw+bvHyUIbxtEtIlWiJnnuCj2dcpjIu+/rSnJqw2Vyh0z7PSW+7HpbjMZ7275g/Oh7n9rYgKyIqZaZMbdBvXXLY1XHP+DKO5+F4i49zyp///Oc/v0jZJcIlMdLDwKkDHH5lH7/51T6eeHo/+4+cpndkmL7eXnp7uunq6qLrzGk6+8YYmcrgKRqarqPK0pJ6gr6V8VRfmtdGLEp1mdtagzgevDCYYSTl0hpTqQ7Ic5RICP8UrzQVTkzYHBjxW0SuKtEoNSSks45PRRJUBxSGkg5Hxyye7U+zqVyn0pQJzDo9lawXNKxKPNOfYTjtUGrItERUNPnc+58mC0oMibG0y6HRDEfHbdaWqpQaMqYyM68sBIbs30l/05MiYXuENYk1pRoSc0/7alNmPOPy8lCGQ2MZ2mMaTWEF7ayHSwhBbVBhMOVwYMTi+cEMm8o1aoMKAUWizJBZW6axQkph9HVRdfAZzLXr0dauR41EFvV3+g9UTgktGKOkPEBTWR+Pff/n7HtxjKHwWm748F1ct3s7O9e30lopI/qf54k99/HAnid59IhHZXszZdEAYbWonYvBU31pDo5YlBgSNzYFiOoS/QmHhzqTrIyqNIUVImediJIQxHSZKcvl1KTNw2eSbK3UqQsqcxRuNspNmYTt8UhnkowLdSGF5sjcc8RQJFqiCq+NZHh12OLkpMVV9SZh9Vyln95HQ1ihK+7wTH+aM1M2G8p0aoNzjcCgKlFmyhwft3h12D89L6810JW5vWQVWaBKvvf2oTNJoppEdVChLjR3PoHv1TZkQdrx+PHJBBWmTFVAzo2VhSCUSVA92oP77D7M9esJrFuPHP7/2zvTp7jO7A4/d7+9A2qaRQubJKMFaWQsW4tXeaxZYjt21YzjqqQmmcqH+ZL/IP9NUkmNU2NrKmOXl7GtsqwFS0hGSAKJfRE7TdP0ftd8aDQDNFi2xIQWvk/VrQLq5e1LcX99Tp9z3nO++4TTRmyhOIs9ckXJRJIWuPHJZQZmFexdR/nlOy+xb0eYaDBIMFJFtL6JGmURMz7M1a5+poSd1MQqaaoNfHeHMo91WSnOF+uL8yUVUaBjukDadAmqAod3qCU1raIAAVnAduHiVB7TcYnqDwIzpULSZAHbgXje4faypW4IyatG5QkCy4eSYS5n0zVvEFREavwyVescJhYopkcMp/jZ8vJUnt0hmZhfolKTVu8rCFRoIkNLJoNJC8uFlohCeEVaSgB8soguC9xeMJnK2MgCHKvWSj5TCxRjAKIA9xImExmLoCJyaIeK+mBtOoUzMU6u4xL6oTa0Q48uzs1NzD3SHcgIehi/JqMqEqKs4vNrqKqCqvkJVNRRt6+dEy8d5/ihKgIzPXRd/JbekRkWNiEi5gE1fonjNRqv7fExmbW4MJmnN2Fi2KX5gN0hmRPLgZi7CZOLUwVGUta6qQNdEmitVHir2Y8owNXZPJem8sWBQCvWCcDT1RonaovnJT8aydIdN0gZ6/+DFVHgaFTlzC4fiijw9WSOazOFYsxixTpVEmiPaZys1QkoIn8cznBnoWhFVxJWRQ5UqrzVJTxvqgAADINJREFU5MdyXDpmCnRMF8hZpa8fVkUOVqr8em+AnOXSMV3gm+k8xmbkTtaw9eIEQCqeHt/QSxUJ7Kynenc9ta5FYXyUuYVFFjah/aBH0R2rD8r8S2uIap/ErXmDj0ayJA2nRHSKKNAcUfjtgRCqKHB9tsBXE8Vo53qPZ11A5uxuP+3VKsNLFh+NZpnP2ZhrNt6hSxyPabxY7+PmvEHHdJ6hpY1b5OwOypyq03m+Tud23OTCRJ6pjIW9Yl9RKIrphXqd4zUadxZMvp4s7rv2YEelLvLu/iAHqlRGUxbv9aeZyRUHEq2lxi/xj0+F2F+hMJgsBocSBWfdtY9DmYjz4TiZDIV0hhQCri+ArqroT8zdlz8BWeQn1Rov1fsQBXh/IMNQ0iS7jvWo0iVeqPdxqk4nnnf4YDDDTNZa19KKAoQ0kX9uDdESVuieN/h9X5rZbOk7a2ulwtstfhrCMl9N5vl4NIftbHyyeGdA4t+OhNkZkLk+V+B/BjLkrNLVbTtUzuzSaQnLfDic5fJUnvyae5XF4gmT13b7aAzJfHk/R+dMsQJoLYpUHKT7RpOf+qDMxakCl6fyzOc315Ur/8fbMXGz4/R0dHLt2iAzapTmE+3sa6yjuvzv/onhwczJs3t8PFujMZuzea8/Q99iqfWSBAgpIm82+TlYVbQev+9LM55ev42qKgq0RVVO1GpEVJH3BtL0LpglbqtPFmmJKLy7L4gsQMd0nguTeTLm+g+9XxE5UKXy8i4dXRb4bDz3l0jy2n0PVqn8pjWE5bpcnsrz9WRulVdQnHMicLJW43SdjigIvD+Y4VbcKLGID9aertN5rkYDXP77Xop7CaPEI3gcyiueYqXJxkfo6exEDCmEXRMzm2BpdoCrf75G55hI5OmfcvbsMxxpqibkBWs3nYNVKs/X6XTPG3xxP8dTlQq7gjKxNblvQYD2mMbdhMlA0uTccJanKlWiulSS+xSFott6uk7nfsbmP+6muDCZI+oTOVatrVpXqUm83uinN2FyZ8Hg3FCG3SGZhlDpCQ9p2W19dZePyYzN5+M5Ph7NElSW0yYrUyZ+mV82+Lk0lWc0ZfHpWI5j1cU87cp994QUTtRqf3GtD1aptEQUWtbJkTaEFU7W6txLmJyfyHF8ukBNwKK+ZOWjsaXRWgDcHK41zbU/nefO8BQT6TTpxTkm+nrouXGZy+c/5oP3P+br3iSZmuM8+6vf8puXmtkf86FKoleM8AisjNa+UK9TvUJ4ynK6QBFFPh3PIooC1bpE8zqlcppUjLJmLZcPR7LULCfj64Lyuv+XmF9CEuDCZLHFZFSXOBpVVxUQyMvF/omCQ/+iyaXpAsdjGjV+Cb+8vqtUH5BImy7fzhtcmy1woFJhb0RZlatURIGwJpK1XO4smNxLGLRFVar01fsKAgQVkagu8dl4jqXlAoaj1VrJQDkBiCzX+H4yliVjuYSMDK3ZGXJXHj9aW1bi7J0LIbf+jN/9++94/aXTvPr8KU6feo4Th+upcBZYHO3lemcXA0tB/JWV7KwLo3vq/MF8lzih6C6GNZG+xaJVNB2XE7UaqiSU5B7DqohPFuiaMxhNmeiySHtMQ14nwCcKArJQ7JLeOWtg2C7VPok9IaXk5EiVLpGzXC5N50kWHHYG5HUrfKBYIKBJAroE5+/nEQWo0KUSayciUBuQmM7adM8b9C9atEVV6gLyqntVRQG/IjKXs+lLWiQKNu0xDb8illQuqaKAKgosmQ69CybmUoojhRnovIL/8OOJs7zcWlFDCVRRs3s3u8IqO0QHx6ynrnoHkbBGKPQZ753rovvT96mOhYlUx3h1j9ea8ofiui6ubeHmTKy4hWWutkgSUGc4/Dqc5Q9zGcaG4LyS5MV6nQpttZBV16WlYPNPlRk+HMnS15fgqpigPaahr2PpdpgOP9UsbpEkPmFzyVrgJ06EgCKsqkqK2i7PCHl+rqcZGo3TIy+y3yyO2VuPmOlwUjR4QUkSH0vQZek87YaKszWX93WBKsfltJRjTsnQMVSgO5QilvKxK7R634jl8EagwKKdZuq+xWedSd5sDlDjL829Rg2Ht4MF5q0UmdlZupfmOGQ8fKr7wygvcZYgIioBgrWtHHlRwEwn6P/qMh8OXeLGzZM0HTnBmT0Rz7X9gYiWiZBK4iaS5BKTpKXS0ReuC6cMh/nhLMNLJtODCkt7/MjrhMg12+W1vMPSYIa06TA1pLK004e1Qc/jnS68OlI8buUqAkvTIVxFRFqz9e6czZtxk8/v5xDvK8zf0wlFNn5k6woOb0zmuTlvIPZLJMb9uJrE2veIfTmbn80b5IezWHGN+ZhGxZp6WteFw47Ly6NZuucNFvokUi0BAoFScbouHHZdXh7Kcn8yTnZhDOd7THV/GGUuzr8i+BuI1jZztFnii9kMC/NxZqYXsYkg4RXC/xDUbArf5AjSRD9L3eeYS2w8Zu/nK762gbkN1snAP6z4PrN8bcRzyxeA+SdY2GDdoeXrARu9/gNOLF9QtJQb9d1rW74etu+p5ev7vP7La3/wmFPPy0Sc36NPrpvFKGRYTDnYjkokEqGyKuQJ8xF4raWCVqkJbUqi4dS/4re++13edIoHk4Oq+J1dEKB4/rFguwQVcdPbdjxR2Db+504i73j0BplbL07XASePaTlY61b8uIBBcuQmA7e76JwUMSvaeGpfE21NAU+Yj8CeaJBafSfCrhCKcPChIrIdF80GXd64NcgDLNvFdIprf7TidAHHQYpG/zpk6xHYQnG6WIUchdQsSzOjzCbzZPIuTmqWsf4BKit0FiUQXBPLSDJ+9TxXvx1kUNxLY/sveOH4AZ5uePQ//MeMpqtougrRyu/9O77vuW4Tu6n86BFcd6vaR9ssjt5h+OZXXL/8Ef/5x9v0TttQUUvz0UM0Voep1AREI8Xi9BhTKRkq9tLS/jJvvX2GY007qA1IT0CJk4fHo7GF4nQxs0tkkvMsxmcYn0mRLrgga/hCQfyagiKC4FiY+Sx5W0LQQoQqq6mvjxLxKWxiQzqP7Yw5wf3RKS5fydN+9gj1sTC+J8Dl3kK3VkDxR6jwR6ioa6Hx8Nbdicd2xsWY7Wek8xs+OJfF3L+bU+EQTU+AOj3b47GNKQYTE4N3uHfxCy52fMX5nmmG4+YT0TTdE6fHNsYGZ4a+nrt8e/0WS/lBrn5zj8GheR6/fudvjydOj+2LZWCNX+PeRIK+lI+YnGWhq5O+gRGGCuU/csQTp8c2xcE20kzfvMaUEUZqfIbTexTk6Zv09w/SPVnYlK7sf0s8cXpsT9wCRm6O7it95MIHaTv79/zqZIyYNMJI/wDXu+MYrks5t6HyxOmxLXHzM+RmbnBpIEYw2syZVw/Q/trzNFWppAfvcvvat9y3XPJlbD09cXpsQ1xyc5NM3exkbEcb0V2NtO2pp7LtFY41V1CdH2Gq9zqXxkwSZaxOT5we2w8nRWJykt7rE6gHDlHXUEdtsAKl9mmebdtDc3iJ5Ngdzl+fYTZZKFvX1hOnx/bDvM/ExBQdtzT2H95JXcyHbQrYbpSDx1ppbvBhLIxw8fMbTMwtUShT47n1p1I8PDaZ3GA3Y33ddCyk2f/Jf5G+GuC8DLgO1sIo9+ZMlEyKRMfndL+9j5aWag74y69iyBOnxzbCBjfDaM8o8xkfja+/wyttEap88rKL6ILTTFTTCdsX+UPvVbruvM6hvY207i+/44eeOD22D46Bmx3i7lCGpLKXM+++w981ylRpK2XnEK8xqCwM8eWtbvpv9nHvUCvpfQGCj9e4YNPxPnN6bBtcI409doGeVAWp8EFe2asQLBk8LFLVso99z7bT5rdY7L5B390+xi1Yp2H9luKJ02N74BbIJae58cnXLKoVhFv2UyMW54quRQg2ULnzKKdaNcLZm/T13OLLmyly1kOb5fy/4onT44nHLSSIj3Rx48InnPtzD3eHx5mJzzIykSRn2qtTJW6B9OIi8zMJso6LnZtk9NYVvvjfj/nyaj/D8QzZMsmteOL0ePIxUySnhxnu62PYqkGwspCaZnQuTcFyVljD4hGyXDJOcjFFIXqQhqf2sStgURjqortvgslkrmxSK1vYCcHDY5NwbWzLxDAMDMPGFWUkRUVVFBR5bcdAF8e2sAwDo1DAdMFFRBBlVFVFVWUkSSwLq+WJ08OjTCmHNwgPD4918MTp4VGmeOL08ChTPHF6eJQpnjg9PMoUT5weHmWKJ04PjzLFE6eHR5niidPDo0zxxOnhUaZ44vTwKFM8cXp4lCn/B4ycOUJTDhDeAAAAAElFTkSuQmCC)
If a spring extends by x cm loading then what is the energy stored by the spring ? (If is tension in the spring & K is spring constant)
If a spring extends by x cm loading then what is the energy stored by the spring ? (If is tension in the spring & K is spring constant)
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
Assertion : A random variable X takes the values 0,1,2. It’s mean is 0.6. If P(X=0) =0.5 then P(X=1) = 0.4
Reason: If X : S
R is a discrete random variable with range
1 2 3 x , x , x ,.... then mean ![equals stretchy sum from r equals 1 to infinity of x subscript r end subscript P open parentheses X equals x subscript r end subscript close parentheses](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIIAAAAqCAYAAAB/TIN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAbSkFbcgAAA9hJREFUeNrtWk1kXFEUvsYYFRUqKiK6qYiIyqZqVESEqIiICllEjaqQVRZVpaoiqpsuIqoqRFREVKmIiopQFRGRTVQWXVSoLKqLbiIqIiqk55hvuF7fvPfmvft+53x8m/dzZ86537vn516losU48R1xiditXe8lzhMXiLeUINN4ThwhthMXiRcQxhzxnvbcM2Je3JVNdBB7LNc2IIYRy/V+WRWyi2Fis+XaDPGYuGtZASaJOXFZNtFAfEVsJd5GPsArwQDxBGK4T3xNvCPuyjZaiCXiKIShXx/DvWviJoFAIBAIBAKBoM5wEZACEUKihWBti6cJXKa/ifpHx7VJnfUhoqSKoJTyD7QEOyIFdwr/YGLXiJdSLIQh4oeMrNYrsCdSdBJ/YXL3iFcT6pwzbQU7waT3aff3VXkDzYodYpvDuHxvndiYIFs7YE/kaIYI2Mk/IY4koc3imIIq74Qe4r/yjuiWg1NXq9zjFvpnYlMChb+lYtrpbUB4YDEcq2RtMN1V5UMzdnnOY+IU8anD+1M29vDKt6H+33lNCtie6Tj/wCzEcA5HB01IX9pcf1Hj2NOYcCt47El88YMO7+cQSipb6I0QfWtISbgJmwcdVrJIyroxbay3Bsb7avnqHvgokXgSh22+6AMs64cevuwu4iMkxCsueUNQP5uwuQV2xYJOrYrYq6GKcMKAVp5yXP/iY4wDOKaCm0gCK8niqfJ2YIaXWz6TeSNkP5qwOQe7IsdlOJxFcKTMnj/ghKwXCV+TD4eca/9rB8tsS43lLCeYy8RvKppTVkFsruBvHKHhozaG6UTxIYzq8vFukbgZsK9R0FaCJYQIt/GC+jmIza5CCAtPNANNZ6rdiMmzyD/85CyLLs84hYYCKo7KhDRh5QuzWghqcyyhoVcTwSfDY19Hdt6A0LPnY5nks5ITLs9USxbzEIG1Hh81lAiHZXOltxNZssjl02+I4AfxisGxOatftzhhCHHaDt9xn8PAmVbauZWG1Z7Jo9ooVnlnLYSGjSmbXctHk2BH7UIEpzXGMi8xebVKnf4eWbVdQrhgU9YdeaherA2lPJbmHpfybNOgP03aHGlDaV4LCbVu25redCqiGvALLie3VbrgZvM27AodSTqP4CUh9NK46kiREJxsjnTTKUlC8JIQuqEfcT8tcLKZ7ehTdQgvCaEXzBgQVNw2T8COuoSXhLCWL62UUptjOaomEBhBO8q2fXFFfWMZ8UyOtqcMTl0styoiyp6CIES4dbGClqGClCBo506EkBF46dxJaKgDmOjciRAyAFOdOxFCymGyc+cUSgQh4B/YzFR75LHdBgAAAV90RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW8+PTwvbW8+PG11bmRlcm92ZXI+PG1vIHN0cmV0Y2h5PSJ0cnVlIj4mI3gyMjExOzwvbW8+PG1yb3c+PG1pPnI8L21pPjxtbz49PC9tbz48bW4+MTwvbW4+PC9tcm93PjxtaT4mI3gyMjFFOzwvbWk+PC9tdW5kZXJvdmVyPjxtbz4mI3gyMDBBOzwvbW8+PG1zdWI+PG1pPng8L21pPjxtaT5yPC9taT48L21zdWI+PG1pPlA8L21pPjxtZmVuY2VkIHNlcGFyYXRvcnM9InwiPjxtcm93PjxtaT5YPC9taT48bW8+PTwvbW8+PG1zdWI+PG1pPng8L21pPjxtaT5yPC9taT48L21zdWI+PC9tcm93PjwvbWZlbmNlZD48L21hdGg+bnzFDgAAAABJRU5ErkJggg==)
Assertion : A random variable X takes the values 0,1,2. It’s mean is 0.6. If P(X=0) =0.5 then P(X=1) = 0.4
Reason: If X : S
R is a discrete random variable with range
1 2 3 x , x , x ,.... then mean ![equals stretchy sum from r equals 1 to infinity of x subscript r end subscript P open parentheses X equals x subscript r end subscript close parentheses](data:image/png;base64,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)
Infinite limits in calculus occur when the function is unbounded and tends toward infinity or negative infinity as x approaches a given value.
Infinite limits in calculus occur when the function is unbounded and tends toward infinity or negative infinity as x approaches a given value.
A wire of length 50 cm and cross - sectional area of 1 mm2 is extended by 1 mm what will be the required work?![open parentheses straight Y equals 2 cross times 10 to the power of 11 Nm to the power of negative 2 end exponent close parentheses](data:image/png;base64,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)
A wire of length 50 cm and cross - sectional area of 1 mm2 is extended by 1 mm what will be the required work?![open parentheses straight Y equals 2 cross times 10 to the power of 11 Nm to the power of negative 2 end exponent close parentheses](data:image/png;base64,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)
The work per unit volume to stretch the length by 1% of a wire with cross - section area 1 mm2 will be.....
The work per unit volume to stretch the length by 1% of a wire with cross - section area 1 mm2 will be.....
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 0 over 0 or
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 0 over 0 or
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 0 over 0 or
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 0 over 0 or