Physics-
General
Easy
Question
Two very wide parallel glass plates are held vertically at a small separation d, and dipped in water. Some water climbs up in the gap between the plates. Let S be the surface tension of water,
= atmospheric pressure, P = pressure of water just below the water surface in the region between the plates–
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)
The correct answer is: ![P equals P subscript 0 end subscript minus fraction numerator 2 S over denominator d end fraction](data:image/png;base64,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)
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chemistry-
A square planar complex represented as:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZgAAAD5CAYAAAAa5CMeAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAFxEAABcRAcom8z8AAE/1SURBVHhe7Z0FWBRtF4b5bFExsLu7u7u7O7G7u7u7u7u7u7t+C8XCQJQwwPb88xxmldilBzbO/V17Ie8M6Lc7M8972ooEQRAEQQNEYARBEARNEIERBEEQNEEERhAEQdAEERhBEARBE0RgBEEQBE0QgREEQRA0QQRGEAST4/v3b/T82VN6/foVffjwnlxcPtDPnz/Vo3759PEjPVPOd3r7ls99/eoVOb58SZ8+feI/v3rlyL/H1cWF3js70/Pnz8hZ+frnzx/+eXd3N6+fd3JSft6FX2/fvqEXynkeHh58juAXEZhA4unpQUcOHaQTx47SpYsX6Mqli/TmzWv1qF9w4R88sI9OnzpBVy5fopMnjtOxo4f5grx04TwdPXKIf8/VK5f566ED++mK8mfdTfLyxQs6uH8fnTl9in8e5509c1o5bx85Or7kcwTBUnn29Ck1bVSfyhQvQmmSJ6GMqZPTiKGD6cePH+oZPjly+CA1aViXihfKT1nSp6YyJYpSj26d6cTxYzRkQD8qrfye7JnSU9YMaShX1kxUrVJ5mj93Nv369Yt/fs+unVS/dg0qkj8Pn4PfUaRAXmrVrDFdu3qVzxH8IgITSLBjGdivD1WtUI7ixoxGMaNG5Avu3Tsn9QyfXL92lfr17kElixYkW5vofAGPGDqIzp09Q/Nmz+QLOEWi+Moxa0qROD41rFuLFi+cT9++feOfv3j+PHXv0pEK58tN8WPHoHixolPenFmpe+cOdFkRN0EQSNmsXaBmitAkUO6R5AltaeXypeoR/cycNoUyp0tF58+dVVe8wH0JwbCJFolaNW+iWDMf1CP/+P7jO40fO4oSxo1FqZMnplUrlv21cAT9iMAEEed372jKxPGUOlkiihMjKvXv3ZM8/TGR9+3ZTTmzZGTB8Q6sn7o1q1Mc6yjUrnVLNvn1sWXzJkqTIgmlVS7ozRvXq6uCIOh4/cqRsmVMS7GjR2br4tDBA+oRv1y8cJ6qVChLnp6e6ooXcIE1qldb2TxGpVkzpqmrfoEnIWOaFFQgTw66f/+euioYQgQmGMBsLl44P1+MieLF4l2RIezt7fmChsvMO1+/fqUObdvwjmnU8KHqql+eOjhQ/lzZ2SS/dFEsF0HwDeIr5UoVo7Ili5KNIjJwg/3v7l31qE/+d/cO1axaiWMt3nF2fsceCdzTUyZNUFf9cv/e/1jE4E24efOGuioYQgQmGCBOUrt6FWpUvw4lto1N6VImpZ07tqlHffLy5QuqUaUiPX3qoK54geBi21YteNc1dNCAv75e37x4/pwK5c1FmdKm5HiMIAg+QeC+QZ2adGD/PqpUrgxFj2ilfF+DXPS4uUIqMHfv3ObNnghM4BCBCQZwiTVUzGkE3Xt06UQxIv9H+XJloxvXr6ln/OPFi+chEhgEMwvmySkCIwgGgMDgHnNyesvJN9kypVMsmUg0oE8vP66wwAjM1MkT1VW/3PvfXRGYICACEwwgMLWqVVbM5Xv0zsmJqlepQNaRrahG1YpssXgnMAKD7BdDIIVSLBhBMIxOYB4/esTfb9m0gVIlTUgJ48SiBfPm8JqOwAjMpAnjeMOn73VLERURmMAjAhMMIDBwkSF9GOCiQ7ZX9EhW1K1Te/ry5Quvg4AEBkH+7ooV9Nj+ETk4PPHzgqjkzZGFM19EYATBLzqBsX/0UF1BtthUzryE0Ozfu0dd9V9g4GZDxmbxwgWoeZOGel+475MnsuVNnwhMwIjABAOdwCCjRMfhgwfYykDQfvLEcepqAALTugXFt7GmogXzUusWTalNy2Z+Xo3r16G0KRJTjszpRWAEQQ/6BOarpycN7NebywnyZM9Cd27d4nXEUAKyYEaNGMrZovpeZ06f5PscLnERmIARgQkG+gQGrFm5gnPxk9jG/ptS/PLlS38tGLjIhg8ZpK76BdXG4iITBMPoExgA93WdmlXZswD3Nb53ePI4QIGZNmWSuuqXB/fviYssCIjABANDAoMqYlQFQzRgcVy9eoXbUuDiDijI//v3b/WIT54/exYqQX7cQI6OPuNDgmAq2D98YLCo0ZDAAKQVw31tHfk/Gty/L4tCvVrV/RWYkGaRSfHlP0RggoEhgQGfP3+mlk0bUbQIVlS7RhWuGIZvNyCBQQBRHwFlkUGYUGMDS8d77Mc76DbQsG5Nqly+NF2/Lm0tBNPh1+9fNH/uLMqVNSPNnjFN78PbP4EBJ48fo6wZ01LCODGpc4e2VEu5d93d3dWjXgRWYBDDMSQwTx7bU/8+vah8qeJsJe3YttXf/miWgAhMMPBPYABqV1BcifRlXGgVypTw0z8ssALjnwXj5uZGE8eNofKlS/ANVLdmNb0CggsfNyBcBQXz5qIjhwxXOguCseChbJhGjxxOieLZUGzryDRG+fP379/Vo/+A6wv32WN7rywyfaxZtYKSJYzH3TcK5M3J97B3QmrBvHv3jvr26kFDBvWnRfPnspUEdznayRjyTlgCIjDB4NvXr1SnRlU/7V+8c/nSBSqQOwcHGTOkScE5+t759Okzt4iBwAwbPNDgRfjU4Qm3pYDAoO5GBwQJF2/fnt3pyOFDtHXzJk4WyJ0tsyIoj9Wz/oHmme3bKH+fcqNmSJ2c1q1epR4RBOMDnY17dO3MWZZpUyalRQvm0U8DjSwhMOjtZ8iCAT9//eT6FttY1so9ksmPwHi1iqmjCFAUmulPq5hzyj2YPlUyP61iziqbP6RH68C/v1LZ0lS1Yjn2algqIjDBANYHLpxzZ/898PVxYP9eFhf0LfMtMGhq+Vdg/AnyIxUa1gl2TRfOn1NXid68fk07t2/z0Sp8755dvEvb7O1C985Hd3fl7xpI8ePE4F3h1EnjlX/HV/WoIBgHaMPfrHEDslYsblgKu3fuUI/4BJsyFFIuW7yIOyrPnTWT7ytDmzUPD0/OzMS99EV96MPlhtjpqVMnKGfWDBQrWiR2aT9WrH7v7i1s6GBRDR7QV7FyolGKxLY0b84svv/w97m5uip/9umiHjl0CJUqVog+K88LS0UEJgigf9gTxQyHWyphXBvqYNeK7ty+xYF8Q6BPWZrkiTlGAnAxI66C3U6mNCkpWkQrTnnctnUzn6O7OeD+wg6pa6cOFDNKBBaiTu3t6OaN6+w/xo2k67ys4+GD+1SkQB7avm2LuuKXHz++09LFCygNmnUqu8M+vbqTq6vPgKcghBc3b9ygyuXLUGQrK3b9Xrp4Xj3iF8RD2rVuQSWLFuJ7CC34GzeowyM1DIF7rEvH9myxgFeOjoql1IkqlitF+XNnZ3c0kgLwb4Bg6VzXu3Zup3q1a3B3dHgmCijnQjyaN25o0FXep2c37qhuSPAsARGYIICdVa/uXbg2pWnDetwmHK993gq5fINd0PQpk+jtmzf8PUznYYMH8O9oovyO5spODV8b1K3FJjxEDJw8fpxaNm3Mvx9zL/ilnIcEAkPZZGfPnKKaVSvyYKSA2Lt7F+XInI5dePg7njzx61YThLAEs1nQMh8JMrjWkVLsH9isuSqWAzwKsMQ/f/7E/cd8b7x8A9HQJQvgz25uriw4uPfws5j9hN/r3bUFSwm/G4k0Xps7r78P2Wj64kL2ykYUbf/vKhtQS0YExkzAzTZh7GgOMAY2TfLihXO8I0PwH7u/a1euqEcEIWzZtHE9Zc2YhmMg2MS5KBsxUwVCNWXSeNq4fq26YrmIwJgJyAwbN3oEty4PCgiMonEnMt7yZM/EUzQFISxZtGA+JUsQj5ImiEuTxo/lWIcpA4/GwgXzeNNn6YjAmAG3b96k8WNG0qtgjlJ+/96ZenfvSrGiRaS0KZLQquXL/vqeBUEr4FoaO2o4xxeR2bh61QqTj1ecOnGcli1ZRD9//EsQ+PrVZ0dnS0IEJoQgZTk8sX/4kBMJ0PNMh7ubW5AFAr2bsHtEbzRkmI0cPpR9zIKgBUiMQXAdFfZI+cXMfFPC9xgAgH6EI4cNoUePHnG8Br3LkL58+tQJi63uF4EJAWgPbteymY9Z+mEJssY6tbOj9WtXc0bNLcWSQQLAwvlzg/3vWblsCaVNnoQzzDp3aEdOb53UI/9AFtvWLZsUy0l6MQl+wcMUvfiuXL6o98H65Ik9NWtcn4P5VSqUobvKtWsqYLQ5NmIoqnRz9cpEA3t376T0qZKzWFarXIEqlCnJUzaLFsjLhc6WighMMEHlL4oto/5nxZW/Ye1vRXolqvMzpk7BgfpihfJxBk7OrJlo3uyZIdoxHdi3l9MwEZdBRTKsJO+sWr6U4sSM6u8cG8FycXzpSJnTpaSyJYqQg4PPTDCk9OLBC8ulVfPG9OqVo3rENMB9PnhAP86+HDqwPwsOwLDBbcqmC5Nt8XXbls2KyG6g0ydPSJqyEDRQUIUaGIxmReGVvjRFrUEqJQaeobsrrJe7d/C6zX8ODdfWtatXuBI5iiKgmHV+4dy/Is+9u3fwWIJqlSpwiwxB8M7G9espQZyYVKlcKfro7qquEten5M2RlWxjRachA/vRp09BS0gxFlCk2aVjW44dzZ05XV0V9CECE0SQgjgAcyawA2vWmHPozRWHJ0+4TidqBCvKkSUjF4MCJycnLkpD14CL5w0XwgkWiGI5Y4x4LGWHP3zovw4V2NUjgQSZYvPnzlZ29aadRIJOGjWrVaYEsWPQxg2SjmwIEZgggKJJFEOiVUTl8mX/VuebM8gwQzVyvFjRKE3yRLRk0QI2+QcqlhtaeaDDLR4qggBev3KkMsWLUMrE8ems2koJtVmJ4saiLBlS064d23jNHHj08AEVK5iPUidLSEcOHVJXBe+IwASBVSuXUcK4MTmQd/f2bXXV/EHVMroRYPcJ18eUiRNoxdIlZGsTnWpVreynB5NguezZtVO5TuKxW/XdWyeaMGY0dyjGg/iit1565sKVSxe5ES3mP+lGqAv/EIEJJPv37uYdfPrUyejY0cPqqmWxacN6bhSIVObqlSpQ7uyZKV3KpPTg3v/UMwSLRrFk0VIf8bmO7dpwFiLa4zeoXZPdrebKvj27eU5/iaIF6JE/HZ0tERGYQHDh/FnKnikdm/mW1P4BvdewK0OaJbrF/vn9hy5dvMCppbBkUiSOz6/FC+arPyFYMmibX7tGVb428ufKQamSJaThQwdyTy+4Vd+8ec1JKbif9NWRmDIrli1hN3LdWtV5wJ/ghQhMACBTC91VsSubNX2KumoZwC2WyDY2FSmQm1uYd+vUgWbPnM5V/9kypaW0KRJTYuU4ahoEAcKRMkl8SqdY+amSJaLyZUrQTOWeGT9mFHVSLBqMuMiVLRMlTRCHO4qbE99/oCvBCM4s69i29d9xAJaOCIw/PHVwoErlSlOMKBFoUH+kI4d9MWV4cuLoUapXuzoVLpCHY09IbogR5T/OHkufOjklSxCXU05LFiko3ZgtHNRdLVu6mFIlTcSxupRJElDGtCkonnLNxIwageMwGFuBpqod27Yxy+xLdFru0qEtj9dABt2fP5Zb/6JDBMYAaKuPluHIlGrdvCm5uphvOrIh0G4GzTNh8j976kDnlR3q2tUraOK40dRKeU8wr6Ni2ZLUqH4dWr50kfpTgiXyUblOunXpSPVr11REpAhVr1yBunZuz12Ft2/dTDeuXaWXL1/wfeU1JM88Mw+dnZ2pdvWqZGMdiQueLR0RGD2gUBF9kmC5YLY+5uILfoFfHZM67969zQ8P/zh/9ixNmzKRpwDKyzxec5UH6JyZM/jP169e4dZFeOliLpbKE3t7KlG4ACWMHZOr+S0ZERhfoBXE6OFDKHb0SFQoby6ujhdCBnqXNWlQj+fOxI9tzTM/YBmiE4K8TO+FIkpbG2vOJkSWmE30iLRkoSR6eOfKpUucuowu0SeOG56wae6IwPgCRWGIK2CW/qmTx9VVISR8+fKZOndoyw8j+OcxzXPpkkW0cN4cP7tieRn3C63oRw0fStkzpaUEcWJQupTJqGjBvLR+3Wr10xZ07Nm5g5Me0PXi5o1r6qplIQLjjU0b1lHyhBh8FIe2bt6orgqhwbQpk3iGOQK/ObNmpN27dqhHBFPivfM7atOiKWdLNaxXi7p0bEelihbkOIvgF3S+gLWHvmyIY1oaIjAqhw/up8zpUrHZP2u6tD8JbbDrXbdmFa1cvpT7N+G9RudZwXRAnUuLpg25zX65kkX5gbl44QLKlzObCIwBEIsaPWIYZ5YhnR9zcCwJERiFS5cuUL5c2ShWtEg0sF9vsysCMwaQtolOAGDGtEnsXkGLjX17d/GaYNy4urpwc1c0PkW7/f/d9YpNzp01QwQmAJD00Ll9W45B9uza2eRHQgcFixeY//3vDpUqVphnn+AGwjRIIfSBwKxbs5L/jPRnDG2KrQh6jizp6fixI7wuGCduyj3RqX0btlww4wVZgzrmzJwuAhMIXF1cqGGdmlxHNmbkMGXFMjwkFi0wjo6OVF/50KNFtKLqlcvTi+f/xg4LoYt3gQHoTD186GCyiR6J8mTPrIiM5WbaGDMfP7rz7hv3SME8OejCubPqES9EYALPY/tHHK9Ck1hMnbUELFZgPrq7U7vWLTldtnA+pCPfUo8IWuBbYAAGtWEqJtrw5M2RhU4cO6YeEYwBd3c3zv5DanLBvDnpnNp+3zsiMEHjysWLlCNzBu7hhxk55o5FCgxiLAP79uIWFlnSp7HoPPWwQp/AgG9fv9KIIYPYkoHInDwuImMMoJVLlw52HDcopGzA9IkLEIEJOnv37KJUSRNS1gxp6MypE+qqeWKRAjNh3GiKYx2VBwVtWLdGXRW0xJDAAEwJHTFE5y5TLBkRmXDF3d1VsVwUcVEsF4jL2TP6xQWIwASPpYu90peL5M9Nd27fVFfND4sTmKWLFlAS29jcUhzpyH8sJNgW3vgnMIBjMoolgypxFhmJyYQLmJOPho2IuWCw3pnTJ9Uj+hGBCR5oDjp21HCKEdmKKpcvTS9fmGf816IEZsvmjTwgK26MqOwiw0NNCBsCEhjw/ds3RWQGckwmX86sdOqEdFIIS9DSp2unduwWQ0D/7JlT6hHDiMAEn69fPahrx3Ys5s0bN+BUcHPDYgQGqbCoII+p7JDtWjbjIL8QdiCYv2bVCvU7w8BdNmywIjLRVZE5ad4+amPB3c2VH3ZIeuGA/umAxQWIwIQMZ+d31KBOLS6T6NWti9nNkbEIgbly5TIVKZiXfco1KlegV68c1SNCWDFi2GCaP2e2+p3/QGSGKyKDwte8OcSS0RpstiAubLnkzUFnTgVOXMCcWTMoZ5YM0lopBNg/fEilixehONZRaNzokfTbjObImL3AYNwv+gDBDC1WKB/dvnVDPSKEFfA3w0U2e+Y0dSVgfv74ySKDkQkQmZOS6acJ3759o97du3CFfoHc2el0ELOaYMHkzZ5FsWDMP+VWSy6cP8fdlzHYb+miheqq6WPWAvPB2ZkaN6jD1bPZlQ9PKsbDB53AzJk1XV0JHHj49VIefnDboJXPhXNn1CNCaODp4UGD+/dldyQC+mdPG84WMwRGaBfOm4t2bt+irgjBZc+unZy+jMmf+/fsVldNG7MVGIwvxWhWm+iR+UOTdOTwI7gCAz66u1H3Lh3ZfVO8cH66deO6ekQICV89PWnIgP4U2zoKZc2YNtidFERgQpcVy5ZQvFjRuYXS5Yvn1VXTxSwFBg+0oYMGcLZY4nixaebUKeoRITwIicCAT58+scigF1bJIgXohoXO1ggtYBkOGdifLZesGdKGaHSCCEzogu7LE8eNYa9L8UL56f69/6lHTBOzExjMkB8/ZhQljBuLg2ZwAfySdORwJaQCAzDGunvnDhT1P0Vkiha02AFOIYXFRbFcYNlnzpCadu0M2VweEZjQx+PLZ+rRuRNZR/6PqlcqR48f26tHTA+zE5j79+5Rgdw5KLKVFQ9GcjPD3HJTIzQEBqDxIkQGlgyaBt6+Ke6yoODp6cGWC9xiWRRxQcuSkCICow1v3ryh+rVr8IZqysRx6qrpYXYCg4fZsSNHaGC/PhY5Qc4YCS2BAX5FRrICAwNSvyEucawjc8xlz+7QmcMjAqMdD+7f4/oxe/uH6orpYbZBfvgyBeMgNAUGoJ1Jt87tObUW7jIJ/PsPulYPGzyAxxzDctm1c7t6JOSIwAj+YbYCIxgPoS0wACLTtZMiMv8plkyxQnRL3GV6Qcxl2KCBLC6Z04euuAARGME/RGAEzdEJzNzZM9SV0AEpzN06efVyKl2sMN2+Zb5daYODh4cHZ1Mi2QXisnvXTvVI6CECI/iHCIygOTqBmT51kroSemAoVqd2bSiqFUSmkIiMyp8/v2nsqBEsLpg7ooW4AFTyF8qbk3aIwAh6MCmBwSx39KVCnnj7Nq2oRZNG1L5taxo1Yqiyg9rKQX1Uw9rbP6IfP36wC6Vh3Vp/Xw3q1KTG9WoT+ich6AkOHdhP9WpWp8b161Aj5RjOwRjl9nat6LxUjocKEBj0IhvNs8hDnw/vnalls8YURdxlf5kyaTzFjx3Dyy22I3TdYt7BvZQ7ayaLmM5oDOBeunr5Ek2fPImnjeIZ2K51C8VS7c/F5A5PHtORQwfp6pUrfD4SO/A8w/NP93zDCz3PXFy8MmxvXLtGDevVoiYN6nqdoz4rWyn31L69IesoYDICY//oIbVr05KbVk4cP4bOnz1DT5Q389HDB3TwwD7up5QjSwbKouzWTp88wR/Es2dPadWKpXyTRVJ2uEUK5KGzp0+R09u3f5MA3N3c6Pq1q9SjSydO30SBU99ePbiHGQr8hJCDzwLiopXAgLdv31DLJg05Pb1syWL08P499YhlgU0YxMU2VnQeTbFzxzb1iDZws8tM6WnbJml2qTVvXr+mfr17UoG8OVhQTp44xs8pvE6eOEpDlLX8ubJR2hRJacP6dfwzji9fsnWJDtm4N7Ioz8L9e/fQ61ev/o4rQdeTu3fu0MjhQylhnJgc14S4/O9/d3iyaUgwCYG5eP48Fc6fm/Lnzk4Xzp1TV30CwZg2eSJly5jWR8O+b9++UiPFOrGJGpFGKW+gIW7euE4pkyZUfj6dsgOW1NfQBJ/NpAljafLEcZpm9+EGxFwNZJfVqFKRnjo8UY9YBhCXqZMn8DC91MkS0drVq9Qj2gGB4WaXYsFoCjbSVSqUoczpUtE+f/qUrV29ksfAb1QFRkefnt2UzbMVt88yBLrM58qWiVIkjq9s2verqyHD6AXmlaK05ZQdKbJgdgeQAYMOvN06d6CNG/69uagAb6iYfRhiNXLYEHXVL+/fO1OaFEm4dQYsGiH0CCuBAU6KJdNCsWS8RKYCOTwx3SrooICYyzRVXNAscc3KgGfvhAYI8hfJl1uC/BqCcQpNG9Zjy2LhvLnqqmFGjxhKM6ZOVr/z2nj06t6VvTP+CQw8DRiRnTyRLe3ft0ddDRlGLTB4Y8aPHcVzQeAbRCVyQBzcv49fOpDOqhMYFC0ZAi4WncBcu+rlvxRCh7AUGODk9NZLZJQbskbl8vTE3vxFBpYLYi6wXFatXK6uao9kkWnPyuVLyDaWNbt+3ypWekBcuXzJR3NfuMLQlRwC08GutbrqF8St4UqDwIQ09qLDqAXmlaMjFS2Ql+LEiKJcyIGbJYIHmPdRyCIw4U9YCwx4+8bLXRbFSmfJPFaPmBe/fv2kqWpAH13DVwdiamhoIgKjLR4eX6hm1UqKOESgQeirqGy6AwKWCMRChwiMAU4eP0aJbWMrN481Z0YEB+8CgyaYhvD09KS0KZOKwGhAeAgMQEymWaP6bMnUrFrR7FoH4WEzbcpEdoulSpqIVoeh5aJDBEZb0E05Y5qU3Phy+dLF6mrQ+CcwVtS1Ywd1VT+IdSdLGM8yBGbxwvmUJH4cFpjLly6qq0EDAoMgf5wYUal86eI0oG8vvS/EbhDcwlQ5EZjQJbwEBsAybaYG/iEyT83GkvlD06dM4gmIqZMlplUrlqnrYYsIjLYgxTxtiiRkrYhDcFPBvQSmK8W2jkxFC+bT+/zDq1/vHpQhTQqO4VmEwEwaP/avwFy6eEFdDRo6gUEKcuvmTenQwf16X5s2rGMXQ/ZM6URgQpnwFBiAwD8sGdTJQGQcTLj9uQ6Ii84ttmp5+IgLEIHRlpXLlnJcDS6yrZuDlwqus2BiRYtItatV0fv8wwvpyyj1wDVlEQKzesVyRWBiU3wba7p4IXjT3by7yMaOHqmu+uXT508Sg9GI8BYY4PjyBdWtWZXroWpVrWTSKczz585myyVlkgR8j4QnIjDagkJw1DPBRbZl0wZ1NWh4j8F06dBOXdUPXGQWE4M5e+Y0JU0QlwVmx7at6mrQkCB/+KMTGBQAIgAZXqAgDRYMAv+1qlU2yZjM0sUL+QFgDOICIDCSpqwd6EqCQnFYMHNnzVRXg4YE+Q2AdNMShQtSXOsoNHhAX3U1aIjAhD8QmMkTx3O7GHT3DU8cFMulVrVK7C7DV1PKLlu2eBGlUG7+VCwu4ecW8w4KLfPlyErbt0qhpRbgfqlToxrFihqR7Fo252SkoBIaAoNsxT27dlCfnl159MO5s4Fro2XUAoMsmflzZnGAHrGRW7cCrrDHLvXUyRN/e40FVmAgZoYEBv+OLZs2UsumjahapfL8sES7GSFwQGCmTJpAA/r1pC9fPqur4QdbMlUqcusMuM2QbWbsLF+ymJNQEsSJQQvmzVFXwx8IDLpfBNd9I/gPLP7tWzdT0vhx+fMPTDYtpmEeO3KYPn78yN8HVmBwnj6B+a08/xYq1xx6lHVs14aKF8pPGdOmpPVrVwfokTBqgQGuri7Uqb0dWUeyoga1a3JvHUM4PH5MUydP5EIj3f/416+e1KRhPa8YzCjDMZhHDx9yMA1ZZHfu3FZXvUACgF2r5tyKpnePrpQ+VTJq0qCOUTwsTQGdwAzs35vz+o2Bx/aPqHrlCiwyzRvVp/fO79QjxsdSWC4sLjFp1oyp6qpxIAKjPWh3BevfJlpEKlOiCN27e1c94pd3Tk7KNTKNjh094qNmBhli1pGRptxeXfELml/mzZmV3a9HjhxSV73G0KNr9vNnz/hefvniBW+00VYmoF5lRi8w4MP799StUweKFzMalS5eWFHONbwL/fz5M6v0wwf3afPGDfwQu3LpkvpTXmB3WrFcKTYx0XUUpp4+0MMH8R6IDDoy68DfjXTpl8+fqytEUxQLJkPq5D46BgiGwUUJ4R80oI/RCAyAyNRQRAat/lGU+e6dk3rEeFi2ZBHf8InixjI6cQEiMGGDh4cH91JEckc+RQQWLZjPNTJoyIt2WE8dHGjn9m00VXkGnjh+VP0pLzy+fKHmTRpQzKgRuGjTUBPfI4cP8eY5oXKtLVowT131atcFUfHOkoULOJ35bQCeHJMQGIA3ZZtiKqKNdO7smVnJ69aqTm1aNqN+fXpyEPnhgwfq2V4dQtFxFE0PkyWKR7Y20Sll4gTcln/FsiV/XWho/9+2ZXMqkDs7v7FxFRFDU83+iuJfvXKZXD58IDfFivLOzZs3qHC+3LRty2Z1RfAP7KRmTJvMnwc+F2MCMZiaVRSR+Q8iU59Tmo0FFNZBXBLHs2FxCc8ECUNgZ5sraybaukW6KWsNRl8fPnSAOx3nyZGFShYpQHVqVKUWTRtRv149uFu5b/f+pAnjqH7tGrxxRlo7CtdrVqvEyRlubm58zt07t6lzezsqUaQgJVKuNTwDs2dKz+NOYAnpAxufGpUrkru7u7qiH5MRGB2fFIsFnUUvnD9Hp04e5/RlfSmnCFihqzJeaF6JDsn4euLYUbp96xb7G8GLF8/p0MEDXGeDjso4D78brbDfvtH/sMHx8qVL+BA0wTAQmJnTpnBw0NgEBsAarl65PGeXGYsls2LpEnaLYcc6c/oUtgKNEQhMvpzZOE4ghA3oyYhrFs8sxJvPnz3L40x+/vzXHkYHno8njh9j4cGz7cb1a8qz7ThvnuF6A87O71i48FzTPQNR2H5ceVbCLeYbbHS6d+nInh2Tj8EYIxj2gyJQY9xRGiPGLjAAN2i1SuU4u6xF04Y8xCy80FkuCOhDXIwZERjL4+jhQ8q9PJBcXD6oK4YRgQki165c4YAZZicIgcMUBAbY2z+kSmVLUbQIisg0aUjO78I+8A9xQSU13LUzpxtfzMU3IjCWBVzKGMWN+pzAYLICAzcX4icIwocVjo6O3DDzzu1b6ooQGExFYMCd27epTPHCLDItFUvmnVPYpaNv2riexQUB/ZnTJtPvP8bpFvOOCEz4APf9McWSePw47NoeIWEKSQRBmZdlsgKDrLK8ObKyDzIscHZ2pnlzZvl4c+Eiw8NT8B9TEhhw/epVzlZEg0yIjHMYxGTQyDB96uScioyECFO5rkRgwgc0wUyXMpnywJ+ormgL0p8nTxhHp0+d5O8RE8QgtHNnzvgbKjBZgUHRI+drHw5eG/+ggGyL8WNH057dOzlrAi8kFqA5HOp0BP8xNYEB165cplLFCrHIaB2T2aqIC7rYIssH75MpIQITPqAswyZaZH/HwIcWz589pVrVqlCxQvm5YBOd59HTrFbVyv6ObwYmKzB2LZtxzvaxo4fVFW14/foVd2HGrBjkkNdQXigyKlYoHwf6hYDRCYwxpin7xw3FWi1VrDBFsPKajIlEgNAEmY66Opd4saJxfZWpAYHJnyu7CEwYs3XzJopvE4PjIVqDtjC9e3Sjgf36UP8+Palf757Up0dXGjKwf4AhChGYAHjz5jVX8mOY08rlS7l9Ntp2rF2zip4/95vCJ/gFAoPq4p5dOysWn/+Vv8bGmdMnlRurN3/uSA0NTSAwB/bv49Tovr260/dv39UjpsPcWTO4vZIUWoYtYSkwIUEERtAcCMxsRWA6t29LHz6EX/pvcNG6BgX+7Q/Opve+AHT4xX2ITZgQdojAaIwIjOmgExj4bT98CLusP0F7IDBomyQCE7aIwGiMCIzpIAJjvojAhA8iMBojAmM6mIvAoDXHrBnTqWe3zpxNg7HFhpqn+gY1BOgVhZ/zysTpGGpDncITEZjwQQRGY0RgTAcIDILB3Tq1N2mBwQyg8+fOUtlSxcjKyornZlxQvg8MmKcR2zoyZ6ShqeDunTvo2bOn6lHTBZ9rxjQpaPNGEZiwRARGY0RgTAedwHQ3cYHRMXL4UK5ZSRI/jmLNdFH+//xPAnj//j3VrVmNU5EhSqtXrlCPmD5o1581Yxrasmm9uiKEBSIwGiMCYzqYm8AMGtCXa6JyZ8vMs1CuBdA6Y8O6tdzbDG3t0SEZDwdzQQQmfBCB0RgRGNPB3ASmV/euNG/2LGrbqjlZR45AI4cZHsWNuh/MMFq1fBnPJsJsF1RhmwsiMOGDCIzGiMCYDuYmMD26dqK1q1fR8WNHKGFcG55j/uD+ffWoTzAdtW7N6tyZuWrFctzIUgRGCCkiMBojAmM66ASmR+cO9MHF9AWme5dOPBUVVKlYlqwjWdG0KZP4e+9gqF3b1i1oltp2v2yJoiIwQqggAqMxIjCmg05gOtq1Nsq590EFArN08UL+M77GsY5CZUsWo9e+ZgSh83atapXphdpSyFwFJkuG1CIwYYwIjMaIwJgOEJj5c2ZRs4b1zWJQGwQG42LByxcvqFTRQhRbEZmlixbwmg70XkNDQB3mKDDzZs/kxIUN61arK0JYIAKjMSIwpoNOYJo2rGd2AkN//tDkiePIOvJ/VLViWfrq6cnLjx4+oMrly/CMcx3mKTCzKLGtDa1bs1JdEcICERiNEYExHcxaYBQe3L9HBfLkpETxbEjXVRg3Ptqa//HWKNNcBSZJ/NgiMGGMCIzGiMCYDuYuMJjnN6BvL4oW0Ypb7z9/9owzx44eOeR1gooIjBBaiMBojAiM6WCOArPEV7zlyuVLlCV9GsqVNSPVql6FunfuRN++fVOPeiECI4QWIjAaIwJjOpibwGC636L5c9XvvMBc8o5t2yg3vTUlVh64+/ftUY/8Qycw27ZuUVdMHxGY8EEERmNEYEwHCAweRE3MQGAgJHatmvNcct+cOnGce5Q1rl+HPn36qK56YW//iPLlzEpxY0Tl1F5zAZ9r0gRxRGDCGBEYjRGBMR0gMHNnz6TGDeqatMCsWbWCWjdvQoltY/O117Vje1q76t+D9evXr2ylLV+6WF0hevHsGY0ZOZxqVq1M8WJGo6j/WVG2jGlp6OABdOrkCfUs0wVpyskT2tL6tavUFSEsEIHRGBEY08FcBGb/3j20cvlS2rVzO+3cvpWFxLsrDKOVHR1fkouLi7pC9PbNay7G3Lh+HbeN2bdnN23fuln5Pcvo+rVr6lmmiwhM+CACozEiMKaDuQiM4BcRmPBBBEZjRGBMB1MXGLi+tATTLr98+aJ+Z1pwJX+i+CIwYYwIjMaIwJgOHOSfM4tnqJjaFMcTx4/SsiVefce0YsHcOTR0UH92sZkaEJjE8SSLLKwRgdGYVs0aU+pkifwUswnGBwRm/tzZVLFsKXr82F5dNX5u3bxBObNmoA5tW6sr2jB18kSKHsGKZs2Ypq6YDvhcY0aJQKuWL1VXhLAAtVRxrKPS6BHD1BXjxGQFpoNdK8qaIQ3vMAXjRicwlcqVpidPHqurxs3tWzepdPHCPHsfWWBasnvnds5MwwsiY0qWDD5XdDBYqY4vEMKG7Vu3UNL4cWnC2NHqinFisgJz7swZ2rF1K71580ZdEYwVUxOYJ4qVVUmxtiIr4oJRx68dX6pHtAG1NcuXLaakCeN6icz0qfyemQL4XKNHEoEJa54/fUqb1q9TNkK31BXjxGQFRjAdTElgnjo8phpVKlC0CF7igjTjsAJpz8kT2VKS+HHYkvnzG13OjBsRGME/RGAEzTEVgXlib0/VK5fnYkiIyzunt+qRsGP5kkVeIqNYMrNNICYjAiP4hwiMoDmmIDBwi8FyiapYLuiI7PQ2/FyvyxYvpGTsLrMx+piMCIzgHyIwguYYu8A8e/qEU6gRc2lUrza9ef1KPRJ+LFMsGfT4QkwGlsxvI43J6ARmhbf2OILG/PlD9+/9j7tIIJsMnSHQB+/1K6/r9tOnT+Ty4QP/+dDBA7RNOY5s25PHj9Gxo0do25bNdPzYUfL09OBz8HMb16+lfXt38/rJE8fo4IF9nAr94MF9Pie4GL3AIAB65vQpnr8xbvRIGjV8KF/UeENRAPfy5Quyf/SQzz2svJlI25s2ZRI3FMSNOWn8WF57qyYDvHNy4p8fO2o47w5x3oxpU2jE0MG0fq2MfdUCCAwKLSuUKWl0AvPMwYFqVatEUf6z4q/PjahOB/U3yRPGo6Tx49CcmdP5XjA2dAKzdrXUwYQFFy+cpy4d2nLPu149utKwwQP4mThsyADq2qk9DezXm+xaNKMd27fx+VzgXL8OpUwSn2JFjUgJ48ak5k0acvuijx/d+RwMzOvdsxuVL12cbG2syTqyFeXMkoEG9e9DZ5Vnb0gwaoE5c/okNWvcgOdrjFXEZcO6NbRuzSpaoZjj/fv0oob16lChvLk4VQ+33vWrV2ne7BmUP1c23o2icy3qZdCk0FXtD+Xm5kp7d++iPj26UfzY1vxgyZA6OY0cNphOKAovhD5w8UDMy5YqRg5Pnqir4c+TJ/ZsuURRrhWIy1Mj+rfpWLp4AYsMAv/G2IV5/pzZ/EBCqrWgHT9//uQRETkyp6eWTRvTjevXfGw4vn//TpcuXlCu48oUxzoK977T4fnVk+xaNaOYUSNQgzo1ecOnj3PnzlLmdKnYNbtqxTJ1NWQYpcDggQQRyZAquaLU9enxo0c+Rs+CD4oJuGzxIooXMzqLjXcWzJvD4lGkQF569uyZuuoTzE6vW7MaxYoWyeiLlUwdncCUU3ZIxiIwDg6P/7rF8BUxGGMFIgNXWTJFaFaG0o0fWugEBk08Be1At4c4yoa5aaP65PHFy7WlD3ho4OZFsoh3+vXuwZ9Tlw7t1BW/QKQK5MlBKRLHpyOHD6qrIcMoBQa+P9xMpYsXoQ/v36ur+pk+dTL16t6V3xwd6HibIE4MKlGkIL1S/ZK+wUNvUP++FCPKfzR10gR1VdACncCULlFEeZCHv4vs6dMnbLGwuFSpYNTiogPuXgwzS5UskbK7XK6uhj8iMNpz9colLirHZ3/l0kV11TCIy3h/psH66dW9Cz/rOtgZ7koBy6Zg3pycxYh4TGhgdALz7KkDFVUsj3ixonO1akC8cnSkmdOmkuPLf8VwCJBCYIoXLkAvXrxQV32CN10nMIjTCNoBgYF7p0Du7OzvDU9wfcGNANdozaoVFIvKeNOmvfP712+aNnkiJYgdg9IkT0xrjCTmoROYwNyrQtDBQ99LHCJQ29YtyNPDsPWiw9nZmR4+eKB+F3iB+fHjh/kLzIK5Xr2NCuTOobxR79RV/3F6+9ZHN9rACszAfn1EYMIAncDkzpaZ7v3vrroa9jg5vWUftJdbrCLHYEyJX8o1i75lmJqJPnxrVq9Qj4QfuiD/utXSTVkLUOibL2c2fiZOnzIJCWRBxrvAdG7fVl3VT6F8ucxXYD5//sQTA2NHj0x2rVrQ12/Ba5MOgUEMpmTRQuTq5qau+mX4kEG8+xKB0RadwOTJniXcBMb5nRM1b1yfiyhrVK5Ajx8/Uo+YFngvYckg2wcis3pl+LrL/gmMZJFpwZlTJyldyqT8nNq8cb26GjR0AoMgP+IzaOKq73Xt6hXKnT0zpUySwDwF5vUrx7/uMVgXeGOCAwQmSfzYlEvZMc9TTPgN69b6eSEbrX7tmmQTPZIIjMaEt8C8f+/MxZPIFkOl/mN7r7R2k0XZxU6b5CUycJetXhV+IiMCoy1rlA0ENhKwPrZu3qiuBg0vgelKsa2jUME8OaljuzZ6X+3tWvEIFFxTZikw9o8ecb42/MwD+vYOkcAkTRCXsmZMy78HKc6+X+iQi/bxsa0j06QJ49SfFLQgPAUGbrHmTRRxgeVSxXRiLgGBwktjiMmIwGjLlk0b+PO1jhwhhAKjc5EZziIDZu0ie/78GeXKmol3ZgP79w2RwMBFVqpYYfr48aO66hcUV4qLTHvCS2DevXtLLZs0ZMulWuVyJpEtFhRwf0yZOJ6v9dTKQwhWeVgjAqMtly9d5Do9a0Uc1qwMXszNu8BYdJD/w4f3VLNaJYobMypXpf748S/1OChIkN+4CA+BQYJIi6aKuCiWS5nihenObeNuax5cYMlAZGxjRWeRQVFxWCICoy0uLi7KQz8XxYwakYYNHhisbg6hJTDu7m7coga1bN7LQvzDqAQG/4ODB/Rjq6J4ofxcTBkcQkNgXF1d6cSxo1xwpOsCIASPsBYYxFzQDRmNK0sVLUTXr11Vj5gneOhMnTiBLf+0KZKEqbtMBEZbkKY8YsggsokemUoWLUgvnusvHPcOrodXrxy5lRYIrMDgPEMCgwQAu1bNqVC+nJQlfWrq0LYNPTdQxO4doxIYgIZs6VIkpYRxY9H6tWvUVf/B9EHkfusIrMAYqoNBNWzrFk34xoHYtWrWhN6GY3ddUycsBQYt9mG5YJ4LCnVvXL+mHjFv8CCaPGEctwlJq9w/mzdtUI9oyz+BCf+UaXPFweEJX8u4ptF7DPeTfxw8sJ+fnR5qzQyujd49uvKzrqMiDIbw9PRUK/ltuZGmDjwPhw8eRIvmz2OhWbJoIVvLSJz5+tVTPUs/RicwP3/+4KaWaItQOH9uenDf/26eRw8fornKw8t7rMVHJf9r/QOj8Kb36dmd3/Spk31W8i9ZtID69+nJHUhHDR/Cim7so0mNGeyoZk6fyg307v/vf+pq6MMxl7/iUphuXLMMcdEBlzIeQNjtZkqXknvuaQ0ExloRGGRmCtpx5fIlKlYoH8fbEDvWdU72Doow9+3eTbNnTmdR8I7OgmnfppW64hd7+0fc68y3wNy9c4e7LHtn9IihlFw57907n3+Pb4xOYACUdPCAvvxmFi2Qh3bv3MEuKx0/vn/nCn5kWExTxAGZQt5BLzJbm+iKQOVh9dcHzMcaVSqSTbRINEp5s7wD15iuyBM90Nq2akHNGtUPlv9T8BKYyRPHc7uLB/dC1v7bEHBjtmzWiOtcUP907epl9YhlAZEZOqg/1zxkzZBWc5GZP2cWW/n79vx7IAnacPPGDa7lQioxNs+D+vWhFcuWsrWyZOEC6tG1Ey2cP5c+f/6s/gSxx2D9mtW8uYtkZUWpkyXm8dwPH9z/G0dxc3OjyxcvsAjFiRGFC5HRp/Hc2dPsuUHowrfVhMJaFIB69xzpwygFBnxTBAANLyuUKcEPpsrly3AHZIjB2FEjqG+v7tyfCf52HVD5RQvmUf7c2SmC8iZhJ9eofm1apVg0uvkIbopQ7dq5nfr16sE1MAgCp0+VnHd+x44c5nN8g79vyIB+IjDBRCcwcN1gNxTafHT/yC3Mo0WEuBRkM96SweZp6KB+XP2dLVM62q9hnzCdwMAtI4QNx48eYS8PqvIRF+nRpRM3w4Q72PczCq38W7doSh3btubzOyhfUcyOxBDdph1Flq2aN+ZjndrbUad2dtSuTUuujTl0UP/nOn7MKEWQutK3b9/UFf0YrcDoeP/+PR05dJDmzZ5JE8eN4XYJaNvv25ePNxbnjVPEYNb0qWzF4OJHrQA+DF0MBSYdVH6C8gbNU47jg8GsjdEjh/HQHd+g6zJ6AB028EYLAYPPBi1OMIsitAPu7u7u1L1zR8X8j8CWyw0zD+gHFngBhg7sR7GiRaTsEJm92lgYuhjMti2b1BXB3MEMLiQLXFU29AFh9AIT3iAOg6LMgIJZgmF0ApMoXqxQDbp/+viRuinigh00xOW6hVsuvsHmiC2ZqBEpW8a0isiEviWjE5i14dyyRggbvn37yjEeTMkMDCIw/uDu5kYTx4+xeJdLSNFCYL58+ayISwcOMJcoXICuXrHMmEtAfP/+7Z+7TBGZfaEck5E0Zcvhz5/f3A8N0zCRJBUYzEJg8AA7sG8vx1ZCE0yF8z7n4nsA/kZBP6EtMMgY7NGlo/LQ/I/F5ZqIi798U6xv1JdBZOAuO+AtQyikiMCEDYiTrFKsRLiEwwu4WZcvXaJ+5wU62fuHWQjMy+fPOaMBk9gQAAsNjh05Qju3/xOsG9evcxWrEHRCU2A+KjcYgprIksJIhyuXAvYDC4jJeHBmJtxlSEU9sH+veiRkiMBoz9s3b6huzaq8QUBGWHiAuHe71i3oyOFDdPHCeTp/7ixvwLdt2cz3tyHMQmDgi0exJLow58qakS5duKAeCTpIx0PKHh5eZUoUpXq1qlPViuWoWsXy3LZBCDqhJTCfP31SxSUi5cmZhU4cP6YeEQKDLv0f4uxlyYRcZERgtOXL58+c0QVXcMVyJenunbBveXTs6GHKmSUjF2Gi4LN44fxUJH8eypcru2JZ3VTP0o/ZxGBQGwM3QCzl4YP2IPeDOTnR1dWFU5iLFMjDowPQOiFPjix+5v4LgSc0BMbjyxcvcVF2cRhcdtRASrngPwj8o94hekQryp455NllIjDa8ePnD55ZhXIKbHjDK86IOpkXz5/z1GC0h8Hr2dOn3I7GP+sFmFWQH2+EXctmnFVUq3plvdWuAYE3LLABLCFwhFRgvGIuXpYLBiKdOO6zqlgIGihK7dqxHd8n2TOnp2NHDqlHgo4IjDbAkzJ39kxKECcmZUiVnI4dNs0NlVkJDMCI0ZpVK/FFD7GBRSKELyERmC+fP1GPrp25niMvu8VEXEID3BcsMsp9gsJk+NSDgwiMNmzZtJFSJIrPgxMR/zBVzE5ggP2jh1SiSAGKoezQBvfvw7nbQvgBgZk2ZRIltrUJksCgLx3ansDtCcvFUKcFIXggDb9rR68OCHAFXzwfdJHRCczaMB4TYM6cPXOKMqdLxWNLZs+Yrq6aJmYpMODSxQuUR3ko4eE0ZeK4AH2FgnbgvUerGDQgvXnjurrqP6jfGD5kIE8cReIGsleE0MdNsWTQZgejDQrmyUEXgigyOoHZsDZ8spvMjTu3b3MAHZ0pkJAR2LkrxorZCgw4uH8vpU+ZjBLGickt/IXwAz2R0M31wrlz6oph0DXBS1yi8IRT351chdDFxeWDIjJ2bMkUgiVzIeDPSAcEBm62XTtCtwbNEnn9ypGqVCjLgt2mRVNyef9ePWK6mLXAgNUrllOyhPEoVdKEtH3bFnVVCGt0AnM0gGDlN8VywYAlzDXJlS2ziEsY4QqR6diWs8uCIjJiwYQO6ErcslljzpKsVrk8vXjxXD1i2pi9wCAjDJ1D4c/EJDa04hfCHp3AoIDVEBgCN2KoTlwySSpyGOPu7vq3K3XBvDkUkQnYXaYTmBVLF6srQlBB92vEiuEWQ2lEWI0VDwvMXmDAr18/qV/vHvwBYmhPcGsxhOATkMDA1zxy2GAWl2wZ09DhQwfVI0JYghTmzu3teGhb4Xy5ArRkdAKzcpnPFiJC4MHYEWyAM6VNSadPnlRXzQOLEBiAjBmkLWN3VqV8GXpqYBCZoA3+CczXb19p5NDBFE+5yTKmSUG7dmxTjwjhgcuH99TBrhUPb8NU2csXz6tH/CICEzLWrVnFqchoc7XDDF34FiMwwMnpDdWuXoUzZpo2rB/gNDYh9DAkMGy5DB+s7OCi8Zhfc7zJTJH3zu945jqLTL7cdMmAyIjABJ8jhw9S2hRJeHLv/Dkz1VXzwqIEBjy8f59KFyvMlgyCmp8/f1KPCFqiT2AQc4FbLG4ML8tl+5bAzZgQwoY3r1/xiN4oVlZUKF8uuqTHXSYCEzwwfTdvjqwUO3pkbgeDtHxzxOIEBpw/e5oL9zCPf9jggTxzWtCWfwLjFbiHuIwePkQRlyiUMXVy2h7IAUZC2ILU2WaN6vGcdgSgfU8MFYEJOo8f21P5UsX5fsCY4i9fvqhHzA+LFBiwd/cuSpcyKdfIIMj2R/lP0A6dwJw55RXEnD5lMhdeZmBxEbeYMfPK8SU1aVCXovxnxQ9G72MrRGCChsuHD9SscQOKEfk/ql2jCgu4OWOxAgOQWokAG2pk1qySka9aAoGBxYg08cUL5lPieLEpQ5rkgR69KoQvcJc1bViXYzLeRWbBvDkiMIHEw+ML9ezamd3zJYsU4JZW5o5FCwy3MJkw7m8MYP++feoRIbQZPWIYB/KbNa5P6VMloxyZM/iYFioYP66uH8iuVTNuv1S+dHFyfPmcx+fCfSZ1MAEzafwYfu8w8O3i+cB3SzBlLFpgAGIBA/r2JGvFZM2TPQudO3NGPSKEJhPGjmGBSRI/DqVLmYxmTJ1MrxwdydHxJVcty8v4X5isiAdjpXKl+EHZqF4t6turO28YVq9Ypn7Sgj6WKUKcOJ4NpUmemPbs3qmumj8WLzDAzc2Vx4HC/MewsocPHqhHhNDg06ePPJUvfuwYlNg2NmVKl5pKFClIRQrk5ToLeZnOC58bhl8lS2hLtjbWlDVDGipboiht3rhO/bQF3+zcvo3SpkjMbuHFi+arq5aBCIwKprOhRgb+0ZpVKvHOWggdIDB2rZqTrSIwGLOKaaF4SGEOibxM74WUZWwOkKCRIrEtdy3ftWOr+mkL3sH8+tzZMlGcGFFpzIjhFpexKgLjjbt37lCpYoW44V/Lpo3ITWbwhxoQ8HNnz9CjRw/pqYMDOTg8kZeJv65dvULnz52hJ4/teZqs4BP0FCtVrDAnQWC4m6enp3rEchCB8cXpUyc5AB0zagTq1a2zRV4Uhvjx/Qe5ubrSs6cO9PLlC/ry5bN6RBB88v69M89uf+fkZNZ1HoZwfudEDerU5CLVRvVr8/thiYjA6GH3zh2UNnliso0VnUaNGGbyQ3+Cyrdv3+j161c8HOz40SO0acM6mjNrBvXt1YNaN29KTRvVowF9eynWiMSqBP3s2L6VGtStRfVr1aAOdq1pzMjhtGzxItq9awdbskjR/fDB9Oed6AMbr07t2nBLqoplS9BTZUNmqYjAGGDl8qWc8ZQ4fmxaNH+uumr+LFT+X+vWrMaDj/LmyEIpkyRUrLmI3NLC1iY61w1lSpeKunRoz0IkCPp49PAhu5sRo0EyQLxY0QjdzNF3CyUBGGleq3platW8CV2/ekX9KdPn1+/fNGLIYIoZ5T8qmCcnXb18ST1imYjAGAA1MlMnTeAbI3WyRBbTyqRb5w48STJ5wniUPnVynstSq1plDuwmTxRPEZwEHLAcPKCf+hOC4Jevnp5k16oFJU0QR7lubDmVuVK50lykmSltKk7XTZogLtlEi0h7d5lP2u7cObM4WzJ96mS0d88uddVyEYHxBwwCGtCnJ7c4yZIhDZ08bv7Dym7fvEGnT56gq1cukbPzO3J+946FFg8JCC3SLdOlSkqbN65Xf0IQ9INpsrB6kW1mq1guJYsUpCOHDnJM5uGD+5xhhd50uM7MAbiSUyVNQIlt47AHRBCBCZD3zs6KGd+U544XzJODblz32ezPnMGclnGjR1KieDbcVnxA755UQHkP0Cj02TPL9SsLgQOD/eAOy5czK9WpUZVdZfmV6+fA/r3qGeYDRntnz5SObKJHpikTJ6irgghMIHB86UjVK1fgjBC4i5ycnNQj5guqtju1t6NY0SJRxtQpaN/e3bRn1052bdStWVU9SxAMgyF/aJKJCvb9e/fQ0EH9KV7MaLxZmT93Fv35/Vs907RxevuWShYtyFNA+/bsLrFJb4jABJLbt25yiwxkU3mYedrl48ePlB1nFQ7KFsmfh06dOMHr48aMpJjKGnoqCUJgmDp5Il8z06dO5mzMqRPHUxLb2BTfJjpPMTWHVHcPDw/q3aMrtWrWSOqBfCECEwRcXV3ot5nsugxx7cplKl28MFlHtqJqlcrTrVs3eB3V+I0b1OHU7ePH9M/VFwTfnDxxjNKnSsoBfh3oW4b58xCezh3sFAvgjXrEdIHIfPr4Uf1O0CECI/zl2NEjnJocQxGX9nat6cXz5+oRoju3b3HsJUv61PTWDB4IQtjg6uJCFcqUoDTJEtHN69fUVa9xwUXy5+b+f/VqV6f79//NmBHMBxEYgdm0fh2nksaJEYVHuH50d1ePeLFzx1ZuoYMiS+luIAQFFOUi9X3G1CnqihfYtMBKRkEi6mIwK0gwL0RgLJxfv37RzGlTKVnCeJQicXxatGCu3oZ879+/p31799DpUyeUn/mprgpCwFxXLJd1q1fSw/v31JV/OL58wX3/4C7LmiE1bdog6e/mhAiMBfPxozsN6t+H4saMym3Xd2yT0cVC2IP43qABfXmENjY68+bMtLj2TOaKCIyFgjhK21bNOZhfungROn/2rHpEEMKeHz++09xZM7w6RVhHoaED+5Grywf1qGCqiMBYIGg0WK9WNS4ebVy/Ntnbm/9scME02LJpAyeS4Nps3aIpj3YQTBcRGAsDzffKFC9KMSL/Rz26djLbjraC6XLq5AkqnC8XW9dVKpalmze8UuUF00MEJgDgC75w7iwdOrCfLpw/R5cvXeQeSvj+vLKu8xW/ef2aW2CcPHGcz8Hr7OlTXMEcmF3Y/fv3lJ/fxz+Dv+f27Vv0+/cv9ahPfv78yf+Ggwf28bl44e+5fu0qB+0NcVD592G6HprxTR4/zuKm6wmmw//u3qHaNSpzH8BCeXPTiWPH1CN+wXWMnmZHDx/i++KKsonCPYHrHUPRfv70us6fP3vK3Sgw8wn3J86DmB06eCDACbaof7t18wbt37eXzp05zb//3v8Mp1Z7enjwWAI8Jy5dvMB/xj16V/n/QiNdS0EEJgA+f/5Mc2fPpNrVqlCqpAm50BBdYOFigs/4i3Ic3FJ2WZiXUqJwAYpvE4PixoxGObJk4HYruKADYs/uXdSxbRvKnC4VuwfQXHL9mlXqUZ+gFcWCeXPIrmVzri9A9lerZo1p9crlBkVj7eqVlDpZQm71Io34BFMAQ+06tG1NsaJGogypU3AqPZHfhzPS5kcNH8rtnJIljMup9ilxTzRtTKtWLKOvX73S6vGQR9wRI7sTKJss9A3DCGgkuly9cpnPMQQ2bhvXraUmDetR+lTJ+R7F2AoIiD5cXFxo9szp1Lh+HUoYNxY3/MRUy+3btph9sbZ3RGACCVpAtFQu2NjWkZWLrC5nvujjsLIbypwuNQvE8qWL1dXAc0nZgVWrXJ7rBlDtfPbMGfWIfpo3bkCtWzRRv/PLb+XGmDZlIlst+XNl5262gmAquLu708ihQ5SNnTXPIpo8cRx3OdcHvAioq8E02vZtWqmrftm2ZRPfn9gw7t0d9FEBqNcpW7IYPwsK58vNo9YNAfHDbKUhA/urK5aFCEwg+fXrN1sosaJFpD69uhusBUGTSGRlobX9saOH1dWgAWHCz8eKGpFKFS2sXMC31SN+mTBuDI0ZNUL9zicQwcED+vKwsPKli/OESkEwNTCqe+H8OWyBwzPQV7n/XD74zTCDZd+8SUO+R2HRGOKtIkRpUyalbBnT0q1g3hMYYYFRBHFjRKWaVSv56HrhGzT5nD9nlvqdZSECE0hw8fbs1kUxqyNxcPzbN/27qHdO76hcqeK8OwpuW/L1a9dQ/do1qESRgjxNsmWzxryT0weab44dPdKP2e3q6kptW7fk3VzzRvXp5QvDN4AgmAK7d26nHJnTc/C/SYN6PKvIO3Bnw4UFgRk6aIC66pcP799TulTJOFvtyqWL6mrQmDJxPLvkypQoQjbRIlH3zh3/uuK8g/ty/NjRNGv6VHXFshCBCSSBFRi07ob5HBKBWbZkMY0ZOYwTBuBuw985TLlhfvz0azXBz6tPYByePGZLqkeXTuTu5qquCoJpc/7sGSpWKD/VqV6FHB4/Vle9CKzAQJhCKjBopzR9yiTu35cikS3HdGYqIuL7PsT348aMEoER/Me7wKA1t75gI3BTLIeQWjBLFy/iCxisW7OK/cWIoSxZtIDXvGNIYJCp8kS5AXHTCYI5geva8aXfrC/vAjNi6GB11S/osxcaAjNZsWLArBnT2HUHt/bOHdt4TYcIjBAodAKDwF6bls3o3v/u0mP7R35eSJMsruywkK0VEoHRBQUhFJMmjOV2LpgOeHD/Pl7XYUhgBMHS0AkMNoHdOnfQe3/idfniRR56hvZIIREYxD8BMjf7q6PV8+bMyok6OkRghEDBAtO9i2JJWFPBvDk5LbhNi6Z+Xk2VCxxCkDFtylARGADfLrJiEI8pVigf3b/3L/9eBEYQvIDANG1UnzdjRQvm1Xt/4tVMOQep/dkzpQ8VgQFwjWN6p3Xk/6hS2VJ/LSwRGCFQeHeR9VKE5s8f/Q90lw8uoeIi853W+PbNa85WwayWhnVr0Xtnrwp8ERhB8MK7i2z4EMMuMjdXt1BxkXkXGGD/6BHHPZFY07Ft678DyERghADxHeT//l3/3O13Tk4hDvLrExhw4/o1KpA7Oxd59enZnf78/kML580RgREEBe8C41+Q/72zsyYCA44ePkyZ06biYk9kmv38+YsmTxgnAiP4j2+B0TKLzJDAAMxkQQFmwrgxac3KFZxfP1G50EVgBEsnsAITWllk+gQGoMwgSfw4/AzYuH4t18zMmTldPWpZiMAEksAKjJYWjI4VSxdTYlsbypE5HVWtWI6mT50sAiNYPKFlwaDbOJJp0G/s86dP6qpP/BMYMH3qJIoXM5qyGUxFDerU5NZOlogITCCBwPTq3pUFpme3zgZdZKjkL1OiKAsMmlH6Bg0yZyiCsHD+XL6Q9bF86RIaNnig+p1fvnp+5ePopRTfxpoLuQTB0vny5ctfgfHv/kFLmXQpk7LAoLu4d7Zu3kh1alTlbs7pUiajFk0bkoOeZrVIg540YZz6nV/c3dyoS4d2nHWKXmTz585Wj1gWIjBBwLvAGAryI30ZPb+Qpnz40AF11QuMg61VrTLVq1WdL25ko6HDqm9wMXbr3FH9Tj/YrSFdGm1gEEQUBEsHnc2RRRYragR/BQZdlLEBxD1449pVdZXo0cOHbPkcPXKYnj9/RutWr6LUSRNxU1nfHZCHDuzvr5UE4M2oU6Ma2SqbwHnSKkbQB7qoPn/2jHbv3MHdkaNFtKJsmdJxd2K0/9a1x//48SM9uH+fBvTtpeygInFKcfMmDbgtuKuLC/+OMSOH093bt3mndefObSqk7JIqli3FFyLAV1TvIxUZu6ed27ZxRf4PA+Njnz11oPKlS9Cg/n393ACCYCngHkQGF+5JxCcjWVlR3hxZ6cC+vdyGXzf2wtXVhW5ev0ad2tnxPYpkme5dOtK9e3fJ3d2NW/tjTIB3eijHcd/rupTj96Hlf66sGbkT8749uxUL5wkf08d15e9DQ8wp/lg75owITAB8+vSJxo0eSU3q1+H8+RZNG/HXRvVqc/YWjgMUb9m1as7djfnVpCGf17xxQzpy+CCb5d7rVwD8sqiXgYiATRvWUeMGdXgXhp9tpvwezCr33XPJO5g1sWP7Vp4RIwiWiIeHB/Xs2km93xpQC/XeQ00aevV5enrweZgZgxR/3Js4B+fCpYaU4nNnT3NWpm+QAYZuyLr7C6M7Gtap+ffvws8HZMmcPH6cdm73WeFvKYjAhCOrV66gUsUKk7OzYQERBCH86Ny+Lc99EoKHCEw4AbN+YL/eNHPaFHFvCYIRcvH8OXahochZCB4iMOEERrWiI4Cri9+5FoIghC9v376hsaNGcEKAEHxEYMIBBPPHjhzuJ6AoCEL48/nzJ5o9Yxod0lNmIAQNEZgwBhllSEM+e/q0uiIIgrGAEcdLFy+kg/t8istTfzLFBMOIwIQhmOuPAstjR46oK14FnLdu3uCvgiCEH2hOiQ4arVs0pe3bttLWLZu4dm3SuDF0+OB+9SwhKIjAhBHv3jlRp/Z23GkZqY9IfUarCaQ6YhSstHoRhPBl47q1XNuC2rIKZUvyvVqicAGqWaUiOSv3rxB0RGDCCOTCI3ce8/VbN29KLdV6mo7t2tDLFy/UswRBCC/gRfj69Su/PD08+IUaG3QIEIKHCIwgCIKgCSIwgiAIgiaIwAiCIAiaIAIjCIIgaIIIjCAIgqAJIjCCIAiCJojACIIgCJogAiMIgiBoggiMIAiCoAkiMIIgCIImiMAIgiAImiACIwiCIGiCCIwgCIKgCSIwgiAIgiaIwAiCIAiaIAIjCIIgaIIIjCAIgqAJIjCCIAiCJojACIIgCJogAiMIgiBoggiMIAiCoAkiMIIgCIImiMAIgiAImiACIwiCIGiCCIwgCIKgCSIwgiAIgiaIwAiCIAiaIAIjCIIgaIIIjCAIgqAJIjCCIAiCJojACIIgCJogAiMIgiBoggiMIAiCoAkiMIIgCIImiMAIgiAImiACIwiCIGiCCIwgCIKgCSIwgiAIgiaIwAiCIAiaIAIjCIIgaIIIjCAIgqAJIjCCIAiCJojACIIgCJogAiMIgiBoggiMIAiCoAkiMIIgCIIGEP0fzCAZZ31SOIsAAAAASUVORK5CYII=)
A square planar complex represented as:
![](data:image/png;base64,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)
chemistry-General
physics-
A square box of water has a small hole located in one of the bottom corner. When the box is full and sitting on a level surface, complete opening of the hole results in a flow of water with a speed
, as shown in figure (1). When the box is tilted by
and half filled so that the hole is at the lowest point. Now the water will flow out with a speed of:
![](data:image/png;base64,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)
A square box of water has a small hole located in one of the bottom corner. When the box is full and sitting on a level surface, complete opening of the hole results in a flow of water with a speed
, as shown in figure (1). When the box is tilted by
and half filled so that the hole is at the lowest point. Now the water will flow out with a speed of:
![](data:image/png;base64,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)
physics-General
physics-
A non uniform cylinder of mass m, length
and radius r is having its centre of mass at a distance
/4 from the centre and lying on the axis of the cylinder. The cylinder is kept in a liquid of uniform density
, The moment of inertia of the rod about the centre of mass is I. The angular acceleration of point A relative to point B just after the rod is released from the position shown in figure is :
![](data:image/png;base64,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)
A non uniform cylinder of mass m, length
and radius r is having its centre of mass at a distance
/4 from the centre and lying on the axis of the cylinder. The cylinder is kept in a liquid of uniform density
, The moment of inertia of the rod about the centre of mass is I. The angular acceleration of point A relative to point B just after the rod is released from the position shown in figure is :
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOEAAABhCAYAAAAgA8aiAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAFxEAABcRAcom8z8AADAwSURBVHhe7Z0HlBTF9v/9v/fzPeNTFEmKSFQQEESCgoCoIJJEJAlIRlGCIEjOWSTnpJgw6/NhjmQEFRTJIAKS85LDwv3Xp3pqt3e2Zne6ZxD09D3ne6anUtete2/VrdDdl0hAAQV0QSkwwoACusAUGGFAAV1gSmWEZ86ckf379smxo0dDIQEFFFAshE0dOLBfjh49IufOnQuFJlMqI1y/fr3Uq1VTXp4xPRQSUEABxUK/b9okzZs8IZMnTpCTJ0+EQpMplRH+8vNyyZfzZhnQr08oJKCAAoqF1qxeJcWLFpbuXTrLsWPHQqHJZDXCW3PlkIH9+4ZCAgoooFgIIyxx5x3So6sHI7wt9y2BEQYUUJwIIyxZrIgywucDIwwooAtBgREGFNAFpsAIAwroAlNghAEFdIEpMMKAArrAFBhhQAFdYAqMMKCALjAFRhhQQBeYfBvhoAH9QiEBBRRQLLRu7Rp/RtirRzdJSDikkCCHDh2y4KAcP35MnxDn2p7GKw7q8k6cOK6v7Wkig/qePXtWjhw5bI33Dng87pvHgwcPyunTpxU/J/S1LY1XIA94PHzYD48HlRIclcTEREucP8SDx7NnE5XMjljjvCM2HuHh1KlTcvLkSd/8cO+jR4/qa+T1w9IlUqJoYWWEXaIzwhU//6zPjnbr0ll2794le/bsll27dqXCzp07tNKfPn1KX9vSeAXlwPzhwwk+ytyp60sD7Nu3V/+3p4seDo8JvnncsWOHVk4UjGtbGm/YqeUBj3v37tH/7ensgAdjNPFoHxAPHhMTz8j+/fvUdXxkFguP8MDggrH442en6rRPqzoc0NfIa8H8eVK8SCHp2S1KIzQj4ZBBA0IhAQUUUCy0Yf06KXlX0ejdUTMS9uzeVVszvcr+/fu1i0ePxcOJBw4ciBn0fAz7uJ5c29KkB0YERk3qZ4v3AofHI0kPYNrSpAV44FkxRnK//NhgeIxHu8eHx5Oaz4uBR/ghH/lt8X5geGR098fjfm0n2AvX2M+S7xfrR5miHgmNEXZXVovLs3fvXu3m4WsjvN27d+shNlYwVMMo/rsZtr3CUaYDSW5zLHB4POSbR3jAjWEO6ZcfG5J5tMd7QXx4PK75jCePTufunUf4IR/82OL9AL4YGDAWPzzCA/XBXrjGfhYtnB+4owEFdCFpw/r1/tzRHspqGY4Z8vft2+cbe/bs0b0nQzzXtjRpgdGYSTargVzb0njDXt1L4cLAnz1NZMADDYkr7YcfO/bo3tMfj3v1aODwg6z2hsV7R6w8GpnxTpV4ySwWHqkDdaFOfupDG9AWtInX9qC+3y9e6M8dxQidQigMpv2BSmOEuJ4OA/Z0kWAEmqyg9nTRAvcAPx2BOg1lTxcJ8JBSQe3pvAC+UhqhPZ0N8JOsoCicPZ0XxMqjkRnzz3jJLBYeqQN1STZCe7pIoA1SGqE9nQ3Ud/Eij0YYbNYHFFB8yfdmfWCEAQUUH/JshO7VUYZehm/bKpANrCYx7J86ddLXyhKbnQz7LO9ybUvjBaye4XLixuDCeF1FpQ5msz4e9QGGR1xPd5mO+5JyPhENHPfI8LjHF48s81MnrpEb/y8UsXYAP7jn/Hrlx4ZwHm1p0gJtQr3Qba96jUx8r446+4Qc2zkY2i9MH+yLMP/D93b2SOzpIoE85GUJ3E/+cDCPYEmeY1788t+WLhKoA42GQsSjPoByKI9y3WWaI04pcUSOnTglZ86mfGHsucQzcvL4UTms0iAjc1wPWcXKIwsJNkUxdO7QJvn+fzNl0rC+0rtrZ+nRs5+MnPKGfLlsm5yUBNn0w1fy3zffkg/ef1dmz10tu48lhnKmpON/LJN5n38oH773jrz37leycs9xISXyhx86FX698mNDOI+2NGmBNnH0kj1tb/mRydIli70dWzNGOHhg/1BIQBeS9q9fJLNnjpHhfbpKt86dpFf/F2TaW5/LT5v/5Deknzsgqz8bJ51q3ydlS5eT2s07SJ9+yhCfbSTVSxeRUqUrSYvuo2XWrBHyfP37pHienFKwVEOZMHezpFK7Eyvl9U6PSvnC+aTw7XdLg26vyA97T8rZUPTfjXyfmDFnR9lwZAgOB2f06L0Z4p1zlanTeAXlMOzjOngtc+fO5LOjuJ78t6Xzglh53LFju14Vxo3h2pYGOHyHvZl533L5aFQ7qVO+uJSt9Ji07tRHhg7qKZ2aVZVyRQtJuYcbSPfxX8ivOw/Knr3K9baUGw7uQ+9Mrx6pfagnI1AKOrVNlrzaUSrnzSx5iz8ifV7/TlZsPSSn1QB9OmGb/Pr1GHny3qxy1aWFpOO0UdKzxQOS79//J9dcmUHKdJglKw+mNK+9X/aUGgWuk2svv0IyZS4n/b7eKEdCgz3yR+f8yi8aHtMC/CefHY0ss0jgnpwdZQTnGl4WzJ/rzx11nqJI0AaBUMLBMEtlOe3AtS2NV1AOLoN5isKWJhKMO+d+isKWzgscHpWb5JNHXEWUAcUybqMNDt+nQxJQg872OTKlfWW5I0s2ubdxP3l7/irZduiUnDunXLVtK+Xrya2kTJYrJGu+WjL+hz1yUM0vbeWGg/ugBHRUkdqHesJzMh2T3756QerlvUxuuL2mDPn0D0n9IvfTsunD7lIldwFpMnygdGlVVe7IeK1kz3yNZLm1toyf58pzeo3MbFlGbst4tWS5IaNkv7mGTFixR5XgEPJH5/zKLxoe0wL80+mmJ7NI4J7cm5NgXMOL56cogtXRC0znfpfZvapJkeuvlML1RsicradCES5K/EM+6lJJ7rytogxfelBSf2IkjrTne5neuphk+OdNUrPP+/L7mVB4OB3bLqsWL5BfNn4iI5qVlVsL3ifVyhSRIpkzStku78na0FrPvm/7Sq07bpHSZUtJobw5JHu2KjJm2U41n/z7UrBF8RejY0tHSYNiWSRj1vIy6LtterHCRqd2rpQlC3+UzQmRrCI+dGDxdGlT4lL5542VpNdbK6OYt/0kkxoXlxzFnpIJg9vKE6WzSIY89WXqkj0qbou89fS9kj9/NRnxwtPycMnckjVz5cAIQ79JZOaEXZ/vpP1r/Nzt27fpnX9cq+3bt2tfOVZs2/aHdntwHbm2pUkP1If5H/WzxXuBw6OzCuaHR3jgQU7glR/ud+IkI16i/DjiMSl5s5orle4u321Nf/Hl5NEEa5k2wCOrg2nxSN1x6Rw6K+tnD5I6t1wi/y5QS4b+b1MoPA06t0QmKCPMXvBJ+XDJVzLz2fslj5obVhrwuSz/7AV54q6bpXSbd2XlJ4OlTsnsckOmlEbIHNrROXv93IAf5A8/tng/gH9cST9yBNSb+mAvXMPL/HlzQnPCrt5Gwj69eiQpFQsLNI4z3zqiwmIHxof/zx4c17Y06YH6OIZsj/eCWHmEBxofeOWH+zGPENkrH3SsIHdkukyyVR0my7annn2FE3uytjJtiIZH6s58yKFz8tsnQ6V+bmWEOR+WPu+sCoWnQSEjvKlAU3ln9QHZ/2UfqXl7BslSuIrUKV9IChSqJiPn75ITS0ZKraI3pjJC2sHonK1+bpAG+cOPLd4PHL30J0dAnaiPWZCDl2U//Rj6IEywRfEXoIMy+/kHpEiWyyRL+Z4yZ8uRUPiFoyM/viady18j/7o8vzQa+rFsC4VHph9kYsgIZy1TE8ETP8mYRiUk97VXSqYM16lRcJasPqxmsUuHSo0iqY3w70jr163154526fxcaIjdoYd9v9i6davuUbg517Y0aeGPP7bq1SrcKK5tabwAF4OTDPR2jvtgTxcJ8MAqLD2wH35sMDzi/q2e0ljK5vqPXH9zVRmzeIdYlmVS0OGEg9rlwatAVvBnu0e0gCeW+JPo+Gp5v9fDkudf/5RbyrWWl37YF4oIowOr5MvXpsr737wifRuWkZyFmsmbP5E2UX5/va1UynOlXJmtorzw7WZnJXTR4CQjHLt8VxKfjCDhfHAdC4+0LzwxwvvRIdoEeSN3rzKnvvPmfufPHe3bu6e+sXfwYKvzcCvgpjSes2ybHB4ZqfMzvKOk0eW3wZ3vmBLGCf3Z4pRpIiF1fXBVoufHhtRlwiN0etPb8twDeSXb1RmlTOuZsuKgfWnmwK8fy8yJ0+XTlQfkqFLcZH781Cm5PtTF6RAMnZEjGz6VYfULy41XZ5DCFVvL5M/XiXuMTlj7iYxqeZ8UL/G4jPnoVRna/F7Jkb+xvPHTXifBwaXyxsB20mHwf2XtgRA/8wdK9TuyyPXXV5RRP+1OMkLa1dTDXT+M0y+Phie/MiMPeZG7n/zLl/3kzx0NVkcvFB2TTR8PksfvyiZZM+eRKk+Plq/XHUrehjizT3797xBpXqGolH2sr3y5Jb2xMh50Rg5vWyrvD39Sqt2VTwoULCHVHm8pzyv36rkWtaVGhdJSqVZ7mfzp1/LJ1I5SI/8NyrhySpk6/eXTtftU3c/JiYQDcujIKWd19dRqea9zZSmc5WrJmOEmuadGB5m1fF+6o/5flXyvjuKOOkOqs2IUDbZu3aJX1ths59qWJi2Qhx6PTVI/+cOB64E7wEgMH/y3pYsE6sDJB9yYeNQHUI7ZCDZlmrAkSjws23/6QEa2qSr35M8nd5Z6QBq0bCNdOz0jLWs9KA/c96A06DBWPl+xU3bsV+7ozth4NK4a11u2OP+tdOqg7PhthSz+8gN569WX5fU3Zsl7H8yW7xYukw3bDinH85wc3bVJ1vyyXFYoLF+xUXYrw0tFZ4/Izt/WyKoVv8jKX3+RX35ZI9sTHANl5GBVnlGHX6/82BDOoy1NWqBNqBeb71zb0kQCMpk751t/7mi/Pr10pdOG82Ij93+UAdcqdVw4bPHOyh1lpJ/fhtR5cENwY8LD7bDzc+5cNPzYEC2PTlg4nTi0UzavXirffPS2vPXG6/LOe+/Lx5/NkZ9W/Sa7DjlnTM6dPZMGj9HUOaXM6AT5ny6p+54+rfKF/saLqIfhh197nd3wzmN4XMr/qUGbGJlxbUuTjNTx2JTjjnrcrA9eg39xEU9OnEmMt8oH9GfQ2jWr/bujznDK6hKuXTIY0tmMxMq5Do9PD1u2bFaVOSo8U8e1LY3Btm3ORjyuCTCbom5QR+LorVj5dFalUqeLBO6x/8B+lT/Rc95I+EO1Hb0ie0dc29KkB/jhmbrtyqXexWH6XTu162lL6wY88Bwb+W3xfgAPZkHELz82ODxGPnDhljtp0ElHN7bqA/u4reE6Ew3QO856wlN6Ohg9nFVuDhAYu6DOc777Vu7y447279tbM5iMUyn+s1qEy+AOSxvu/LgbZ7UAwss14NA08Y7bdlKOq8rDHB/XoI4rfvk5CWyG8kvcr2qewXzEHZ8eKI98q1etVP+95Y0Eyly18leN8PpGC+pDvbznD/GzGn5s8d4RD37CQR3XrF5tlRlhK39doRWbjgw3EAVH7+gs0RF0w5sOumHKiqyDfkB9qJc7DF5K+nVHKRAYMv8NYCA8zAZD7rC08hqi4RcvXCjDhw2RBnVrS5mSxeWuOwrqSW7xIoX1y3O4vrPw7Sq8kO5t8L2dcA8IlUMZ1ng/UGVSH+C5PiE49fGb/+LjxwCF1HJSZRUrrORJeanKdOqPG1etciV57tl28vKM6apjWqWNx002HYoGhmxxfmErj87Ulzv6fKeOoaF/q3bxsGhniN3qCZs3b9aPc3B8h2tbGjdYzdy8+XeZPHG8PHR/eSl4a15dHzqGGzNdL5muvVruu/ceqVGlshbOQw9UkFtVXJbrr5G8t2SXiveV0+FVH6oY4CIEsqlUobwULVhAst5wnZLbtVKu9N1S/eGHkuIfrviAZM+aSTJl+I9kU2kK579VyT+n3JYnp+5w2z3dWhYsmK/1EoO06VF6QBeNOxqNXkYD7MO4o46L62zsz/nuG915eXZHB/Troxk0QzZk/kcCw7ANhs4pN8IWb/JzH0a/QWoUzpPjJm105cvcI+2eeVpefGGY3FP8TrlBGWE31aNMnjxJxo4ZLePHjZXOz3WQ/EpApK9auaKMeHG4Dic+wMUDZDJm1Cip/GAFyZEts+S4MbPqZHNLg3p1tMwmjB+n0oyTker69nx5tIHSAQ8ZOEAG9O8ndR97VG65MYtkzZhB6cXd8tVXX2q9cusg0HqFPiUPdqmI6ZBSSD1ShethOJy4yPFuQOixOwy3umQxH+4oRkhh7gLxxW1w4iKv3J1LPKXmdCfkTIRGMfcBL02fqg0q4zVXSZ1HH5FRI1+UKVMmy0vKFSlTqrgO79Wrh7z80gyZNnWKjBrxojxQ/l7JeVNW3Vvemov343STqSoPhjp50sQAFwmQyZMtmkm+nDfL7crDqVenlnZDc2XPJk+1aiGTJk6Q6dOnyfixY5KNUOkiBkx422daS+6bb9Tps2fOKPepDvrn5cu1IRk9TdJDtm6OH5cTJ0/KiWNH5UiC896ew4ePKENQ80vLQaTkMlLqNsQ90rIBA9KYejhhZ71/JDTcHWU4DR92w8HQy9k+XFbIVESvqJ/bL8ve6Sst6raWcZ+udw7qhuJhjDzO6wx2yHfffiMPli8rtyiDoqERUO+ePbQApk+bKqVL3qWNsGePbvLyyy/J6FEjpXLF+3WvWlm5MIyIhfLn0y7qGBWH4CdOGB/gIgAdIp3jHbffpqYNN8vzz3XU8un6fGcpdFtebVzt2z6jOtxJMs5lhAwIY0aP1HkL5Mutwzu0byvNmzyhPJ/rpNYj1WT9+nVaT9FD3j4HHdu9Qj6Z1F96KT1+vnNX6du3j/Tv3V16dm4nHdq2l94jX5VvV+6UE4wMSg9xI9HD8CkXUyNcVjbquXbHRQPqxULT3XfdGdtIGG7t4TCWn5rOyfFf35EeD90kV196lRSt3U8+3pB6I5i8DPn9evfSAnq2XVt5okF97XpQ+X59emujMyNhn149ZYoSas0aVbVLU/aeUjJs6BAt1CoPPah7Wt4g/ncwQngAjBK2+D8LsdZjqvJaqql5H1MGZIvbychIec+2a6O9H+Z8TDVwWwsqw9RGSJgyVBZp8iq5Pv1UK+0ZjVQeUOmSxXW+N2e9rvXIrYfnzh6R1bN7SZXcueSBluNk8ZYdsnPzSln80QTp2bCcFMqcQfKWaSJjvv5DPzidcjRNqdvERTsSpoaPkdAYYVzOjiZuli+G1ZHiN2WSXDlvVL58IWk8/DPZZnEF1q5ZIxXVhP1BBdwPhFOrRnXldtygJ+4vDBuqjK2kmhNepQ2saeOGkjN7VilxZxEZqOYLuKYoybOqN82nDLn2ozV0j0qYTSkudlBvlNTMbc3/P9sY6ewA9TDtyX9b2kigzszpWZy4/dY8en6HvIijPOJbNW+qF9ZYsOnapbM2QkY6PCJWxPMp76zJEw31vJH7k6+DMl7mh3VqPaINJJx2LBwjdQrcKjV6fSzuV1cl/PyudLvvKvnnZfnl8YEfy65Q+Pki30bIsTWzf8JQHQ5GLnqH5P/OHkkynZOEH1+RNiWySsknnpchgztJlSyXSJbSrWXmkuQDyaaHmaCEnDvHjdKuzdPy2muv6t6OsJo1qml3s2rlSlpACIZVNIRUTPWOA5SbgUCnTZ0qM5TbisIWuT2/iiuorkfpuSTxRoGdtA4IM0riDufeKcOmasE7YVOdMOUeE4ZSoBD8N+H8TxGm8vCf9En51S/lpQybosMASj9k8EBp2qSR1K1dS00PnpPhSpHd5ZKOEcbk5drGT2re3fzYwlT56h7kG6PasK/yUJo3bSxPNKyvDWT0yBE6na57mjxSRyesY/t2Wq/q1Kqp60jZgDTIjeuG9evqNBgr7unNWTNpMAISRzlMTchPvpEjhkuRgvlV+oIyf95cravoZUizZPvCsVJPxT/a91M5HAqFDnw/U9qXukIuz1pWOr38g/BaK/SQvG4dNzAjpC0uPVAn31sUXk7MAE4vuN8YJolb5MuhNeTWLCWkw6y1cnj7VzK0Vk656l+5pN6gj2RTqK1gLuFwgjRr3EiyZ7lBT75xLceMHiUjVCMz6pUqXky7MXpFTQHB5Lo5m7RUvefgQQO1wg4dPEgG61W0vnoLI4/qVZl3oMiMlENUOnryQSrNQDXKE0YelIlwHTagvw5/YdgQbcxcD1JhlElPTp24doehGLhG7vBRSknDw5i/jhj+QlIYZY9V5Q1XIzwjg7k39504cby0aNZUz2+NIuKalyxWVDp1eFbzCVjAgH/DD9coKO2h7xEKHzZksIXHoWnySLsxH69R9WFlEDcltT31YAvhBSUjjHFAv2QemYe/GMYj5WGojerX03kbN2qg6jlA14d6kYZ6IR/aqGKFckk8A+7JdIM3PZAGwCPorcIq3Ftaj5Zd0Velq5wUcihkhIXyS82eH8nuY4dkz7bfZcXX06RHnZJSIGcRqdfjVfkpdFYd3WXLw5nLJes680zmhGxn+DlZE9OcMLazo+fk6M+z5LkyWaVw7UEyRz9WdlyWv9JOKtzwD8lWvr3MWpby/Sm4kf+57FJtbNdddbnu+Ss/eL9c/5/L9V4Rq2FuIyRdNuWK3KjCmTMWLVRAu6o6rTJmJ811+j/7TbffmlsrB4rAXOOGa66UOwrcpnthenrCcG2u/88VetWtR7euqrwrVf4Mct2Vl+nR9zllAFxT5rVX/Fvvbb3zztvSuOHj+r8Jb9msiZr3JIdluPLfeoSvpUZ1rgmDLzq6Svffp/nl3tSzR/eu0l/NxzFAwowyGp74zXzdNXqkQIFx0/hP3tvUNZ3KENW53KTaBZ4yKj5L3VVUz6OTeFT3u79cGenetYuOd+p4mebnuQ7tQjxm0GWY9nbXg3l5i6ZN9JYB+Uz+9m3bSM1qVZLCaMuO7dvK66+/pg2Jet6owqkHBkS9uD//KRt+WLhBrkbWgHogb3jMnzunHnHpcAhDxtdffYU89MB9IU0ypIxw0XhpWCiXlKvfTabNGCG9n6otlUvmlTw58kqFJ/rLB8t3yxHXuHG+yPPZUbc7ak6Bp8YJPcwyTDunxp0jRUnuaOJOmTf+cSl4bU6p0XGqLNTHkn6RH94aII1LXiOXXn2nPDN5nuwLJccNaNP6SSU0xzAK3ZZPr4bVe6yWcjvzSImid+jRGUEhFAwJ15S5QjHlutDrPnhfOSms/H82c0lLGgTKiQx+2W+kd6cxyFtYKfn95e7Vq66MDoTdWeh2fe+a1atqwyxcIJ8ur6Cax3BiB6XlmjBW6nCRZs16Q55+sqX+b8LbK4Nr3So5jA6ATqWJGgW4JowVQd7tinvGgQTuTT37K/e647Pt1bw2u1ZktzJiAGzFwGfpEnfpkbzM3SW0S0bee9U1Rsgoh0sHTxhzlUoPaAVP4lHdr9Yj1aWP4pF4p455ND98gwQeWQhBD8LrADDCespFbqw6Gl33UP4unTupsPr62uExn36J9GuvviIVypbRxmbuR4dIvfhPvZAx/Nxf/l7JETJ47mXkCD/8YswYITwy5cifN5c2zkerV9G66eghWqWMcPFEaVwgixQqV096jJgqH3wxVxbP/0im9XlCKt1+k+Qp/LB0nblQdoZe5cP0K7WuO/puD08NbADbcOfBpjw9RRHN84Q2d9R5ZYTjY57Z+KkMrZFLsuUsKpUfqydP1K+tlbhB3UflkXJFJF+GK6RogxflW71Cc1YOqaG+sZpv5MmRXffYzONwN1AojGSwMpJSxe/UPaIRTjM1V5qk0jCXMGlxDQmjN4YHXCXiERrxJh3/3WHAhLnD9XUUYaZMd3h42MQJtrCU9THATWPlL6tSWoxAj/rqF97hDTfSzbfJxzVhOtxVngk3/8PDwvnhGhmwZZBLjbiMns6oc72+JuyZ1k/pNO78+r6h+rjDmL9htMgNQ8X7sKVFfp06PquMP2eSrHE18TSYextZmjridjeoX0cf7ODbKeiqPkWjF0iT54Q1e3+SYmFGZI8smdFGyma6RG4oUleGf75dPwu5d88e5UL6f36RvHQC5gA3YTE9T+jfHT0pqz/optzOTFKxw6uyJmzRKuGH6dK29FVyWY7q8sLHG8RMo6lgjmxZ9KsWZ778UpLw6PHKl75b94gAQbKKRsM/1aJ5kvAQqNsI2aZgm8XEGQUz1+6wSOG+w8L+6zAP5cET7nA51evT0+fPk0uPOFUqPajmkM48NK38Xu4VKYx7oPjMu4sUvE1vBQD26VilJB31tOUND8N4WP3EheaXfO68XLOohCt+hxoZGYkZ8ZG1Gf2fapUsa1Mmc+9ypVUbqfZ57ZWZIU0y5FqY6fOJhH9nKmHZG/JsiUvl/64qIk2GfS77Q+Hng/78LYpjv8rbHe6S626sIF1nrQkFuujkKnmza0XJ8c9MUrXPB7IhtL04b948PUeoX6e2Nr7p06bphQzcTHpFzoritjAiPF7nMX3IN1d2euQnU/T69I4V1HwHI4QHwhDaXw3Um+NbnTt20HMtOid4mzzJ2/ZALDAGwsIJo2K7Ns/oEWfcWGfLxJbHBgyHTXnc1ApqCsARtalTnJVcgEHhhuNeYoDci7SMvHS8eDXIEzef+1Iv8rAWwKLRQ2pezegTTnt+nCQNlBHW6v9Vyre5nd4rC2e0lQoZL5HLs5WVji/9KOfz8zq+38DNahQZgHmymGcATZgbHM4+cUrNcE8dkt9mD5bHcl0il2S+W56ZtET2hr06M/HIJvmgV1Up8I9L5Joi9WX47E2yO+GkHDpwQJo2bqR62tz6RMy4sWO14WGArHay2sh+IWdHeQkViyQF1CiRL9fN+gQF2woImy0L6l9c+eD6yFuo5/wrwhiBOX7Hf1u6842kOvisB53k6NGjpFSxoo5LqubHdLKUNWXyZL0aXfbuktrY2rZprd1t5sy4voQ91aKZ1gtGYubWTFFYXWXzn5Gyr9JVdBT95JdR8MyxXbLo5bZyr+q073qst3w4f6F8v2i+zPvmf/La4FZS487skj1HIXmk4ySZu/WsnFP6bcqw6Xh0OBpaJ+FdsE45rKwuX+bxvaNmTkjP6zxIuV0/dMlk08wRw4Hvu+/gEZFDa2XO1A5St2pVqVWjlrQZ/Lr8GNZBndz0rUzv3lDqPFJDp2k3/D1ZtGG/HNq/W95/9x394Qwm3+wLMvdgLsiiAi4q8yQWBXr16K7/t+IcojJCsyjACNqgXl3tvjR8vJ5ypxg5/poj4d8JGC2yqVmtqmTLeJ1eQGLhj7khLiWr4Ewxmio3F3kx4ptja7jjnA9+qmVzPQXBG2LRrs3TrfWKOQc8FigvimOP6OeePSicGjB2LJHXejWXho/WkLp16krzVk/Lc21bSrN6j8ijNR+TZq27yOi358rGBGd1kC0K83CxTcejwzZtJzyIbeaD1Mv3Kw8v1Mt/x4weodyQjHLd1VeouUgBvUr50ksztMDcZ0cJY5Rr0qihFg6uzLPKbeMEzR0Fbk0xH2SOFuACQhkismDR7Z4SxSRThqulTKkSet7LNgfyY5UY42OUY//UfYCb/UfcTxZoGA1ZQc+bM4eUVLL++kvnSYqLmXy7o717dg+9xtt5tTcv8HV+7eCZQYZhNt/5T76jOo58bqgw4gxC+Q3YU2mmesQMV12mer380qlDe73hy1MT9KAYIXMBlr0xTMCjMIyaTPy1S/NMay1M4vgNcHEA74VO1Wyws7XCKanHHqkukyZM0DJ+ecYM3XHylAVGyEopUxPyc7a4sDJAdINtDowVF9LoDq9L4fUbjg4qXXPrmQVOvjDdDAN6bU7ScG1LkxIpy+E+vI0AV9zzFgXuqPnIonnPR1pgKOZUAYbItS1NNOAVgz8vX6YrXL5MKb0y90D5ssowG+lJOyNk7Zo1pHWrFnpTnNW2+rVr6U1rs2HNftyTLZrr+AAXF55q2UIeqVpFzedza3mxDdGgbh0dTjzy5PQUUwo63BxZM2t5smfMni97pHS6H37wvv6AD+/eMbqD3pmP+rjfTxMLeP8Qr/DEwLm2pUkL2A+vt2DR0fNIeDF8i4JhfOTwYfokBxN13JBiqgfk3KjzWIsDlqgZBbmmd8VY3fF+wcKPsyxvj08PellflWGL8wvK9MtbrPzY4IdHNuiREwcHOOnklie/lIkXxGjHHJBwjn01VVOPN19/TRvEX4l8n5hJ60u9vOCXVR+Gfa7D4/2Achj2cS+45r64Fqw2rVA9ycyXZ8hk5aZMnTJJpqr5hRucoeyvXNQZ2u2ZosImpkrjFVMmTdTvNHmDw+Tq2pYmLUyZNEHvXb0y8yV9bUvjDRNlmuJ9llLC6VO98wgPLyn3/I3XX1X/Y28fkMSjcjPPH49OXT+e/ZHs279P6wguXiQdQskdvUwd7we8pNmcgPHz5V70mCfrPbmjK1es0O4ox5fYe+FA7K5du/SvAYe16Y1glmt3XDQgT3g+5wA4DXw0VRzMmyVfoH3tsKVk3GDopP5UmLdlZsrCl08RpgR9llcgKOLaHc793WltII2h9NI7c4e060w8cxyIDhDhHlZ1jhZ0qHxGDfKaNxI4eG/IzWM0/NhAnuPK9YPcy/ws/WNUnNJy60U40Bv4pOPm5IwtjQEP8IbrmQ3oPsfZaHO3HZCXMtxpbWDF1bM7unjRQm2E5vuERrm5NqBRHGVEcZPDowECwngxOCMsQDlmUmsrkzATDtEzOcaRHE7H4E4bDSiDsqDwvG4ezX96Rc4Huu8dCfBi+IkEyqE8Jv5pl5laeBeazpwJLYC4eDT80E7RtFE4wuXILx4RZAw1Epz0zgKNLd6A+lI/jJVrWxoDykytl4ZHR2bhedygzp4XZj6e/T99OuG59m1l7drV+nEMDHHdurVxwapVK3WvduDAPn1tS5MWqBNGw9m81atXWdN4AWVQFjxSti2NAe/xpIdFIFzb0ngF90fJduzYliY/Gzas14rjJoTMIhYd2vkk+F23Zo0eZdzEflh4m8HDsWNH9KgRD/lQ/m+/bdSdFG2QnoyiAXrHazAwVj866PDIyLgzXR6pMzLy9CgTD0cyEvbq3lWvVCJorB6X0A/4riArVua/Wb2iUd3hkYALQj3Mf67NSETZ7rTR4YAuk1/+U4bp2dz3sYG0GAz193fv1OCexg1P6/7Md+i5IX4XzJ8rXTp1lKZPNNBh55NQVvSh7dNPyfy5c5LqceL4iVR1dvhxPiGWXntGhwN6bsU96byN3GJBrHI0MouGR+rsa05oFmYowBm19msl8AoqiLFRYa6dcMo7EPrvTKYjgQan8Wkwrk24abj08oeDPPTqEHlNGfxGwyN1YLka4bnrEwsoxxHo0TTLZBSio1i/bp0WJquHPIfIq//Gc5Zz4gSZcp4wfOgQfVD6ykv/n36ciPvztLhjGCnr6fBzOpXM/ALZMIflXhijI7PYgO6xAOgYofc6GpkxT0yPR+rs2QjNPqFZmGFiaZtwRgMmr9wU9zGaSXA4cP1oKHri9Cba0QAXhEZnTgpv/Leli4Q9e3bpUZOOhWtbGq9I5jFBX9vSAEZvFHHVypXS/pnW+oQQ+2ws9V9yySXnHVde+g99bpdtBQ5Ss4qOIobX0+HnlO7s4iUzPCZkhi56lZkN6CKeB1OQWPSSuWJ6PPpamCEDI+GQQQNCIQFdbHRGKcA85RYO7NdHPwzNSDVy+Asy8kVvGM0BdzXSTRw/NlXcxHFj9fbAmJEj9PZPq2ZN9WLdnG+/Vfc/v3PQvxt5Pra2YP48PRLyyApDreOqOe4joFdiNKAX5Nod5xf08mYZ2MwBY4PjWjr7RY6raU/n8MNIS9q00nkBPNDL4vLEhx9HDoyE4bRl8++hK3+Eq8R7O8OJRZelS5aE/qn/e52R2E3wF0ub0ea0vXc92q/dc0dmtnjvQE7wg9ziJTNAm/3041L9ZoCe3aJ8isK9OopwWN1Zt25NElgN4ngQcyNnZSg5zi9YoTJDu7NaZU8XLdasWS0bN27QbiO//LelA/BgVkfTSucF8ODMfc0KsD2dF9hWR9MiXCHnK1M/h0JS05dffK6P/PHRHUNMHd596039YHSt6tVk2Y8/hGJSE4YaS5vR5nz51qsecc/Nmzfp/LZ4P0BOGA2dXbxkBpAZ36LgZFDUT1EsWrjAWR3VJ2bY9U/QCpUMcyrhjL5OGecPMM5knp7ImXjb03mBmczza4tPhnMQwBk1bfHeAQ90AChJvPgxm9DR0K6dO2XooIF6z/fdt98KhaYkFnga1a8rUydNDIU4q6CjRwyXlk0bSzs176xVvarM+ebrUGxqgj9bXaMFbU7b+9Ej5pzxlhn8ILd4yQwgMz7dx9vko36ekI1FfXY0mBP+JQmPgve1Mt/bsX27njuG00HV43d7vpP+3BgeDcQ8861Zb+gnWH5ZvkzmzflOfwtk7nff6viA/JPnOSFCYyQkAys7uBzO8TUHuIyMLuY9je64aMBRH0Y85n/OsR97Oi+gnvSKzGGdVSl7OhvggZ44eaXPns4LYudxj64P9TJtjByiGQl5mLRhvTry28aNsmjBAj3fchPuEWdsefES79E0NFcZXaPH66p54Pf6/xeffaqfVknLCFGoWNoMHhl1vOsRRxmdbQJ7vHcgJ7ZVkFu89BIgM88HuJPmhKqXTJ4TJp8AwB/ndAc9qDMfSHlCID1w0oRhmsl1vE6dUE/cCD7YsVb1OrY0kQAPySdmvOWNhFh5pB7Uh3qZNo5mTpiolHLhgvl6lJv90Ufy/aJFoZhkmj9vjn7C/btvk42LR2743sOwIYNCISLffPWV1K1VU80XF4RCUhMGHkubwSNzQq96xD2RNflt8X6AnMycMF56CRITT+tPPHgywu8XL9IjYZ9UD/U6YN5Ab8HIw7U7LhqQB2ViNdRP/kigx4FBc84vWlAHekDye80bCbHzeFjXh3qZ/OZUT1qEXKZNmSxDBvaXH5cuVe2R8vVFWzZv1idsJowdEwpx6H///VC/v4cnGL747DP5Whkg3wTkk3PDhw7Wp6h270r9xQY6vljaLJzH6OEctndkZov3jmSZOfvStjR+gMz4JLgnI2TJ+mJ5njAgb7Ttjz/09/+WLF4cCkkmFnZ4IRJHz1gMcdPm339XhvelnrtwGGCN6rlnTJsm1R+uJK/OfEmPwihmQP7I8ysP+UYgIyEuDU8n43Lge4c/MewXbG9QEXp2P0/gUyfmo+zlmBfpxALKoCx4TO9pbOrLfBg3yE/dbeD+zorcgTT54UA03kckov64PTyHd1KNiPTAnC6ByMczenVqVpdNmzbqsPSI5yDZ2/rsk9mhkNRETx/eZvBA++COx0M+lM+cEf5og/RkFA0cOToenR85euGROns+MWPcUd4xQ0VTumqxAyVmyEfxuLalSQvUie++sejhuA2xweHRcW3SK88YIArhp+42cE+MxLxCwZbGQdruKPV3lvsPyaaNG2XD+vWyYZ2zCb9o4UL9SokvP/9c/0+Ptqi5KPNDXu/PFkf4yGnIkWHKejr8nNHtlF57RgPK4P7G9YxPmbHJ0eExUZVxIor6+HjHjDm2Frijf106rFxPFhgQOEbJJ+ImThgXik2fcF1xUXfu2KFXCuk0A/JPnldHw987ypDKkOsHvJufnoCRxvl0sD1dJLDcTm/LqpV5j2Ns2KaVyrie/Lens2Pbtq36AANuDNe2NF6RzOP+NHlEDsYdZUR0wx0WTtT19983JQnfnS8SbGSLR7bhbQgPjBB0AvGSGS4dMnN0MZb3gjpAF+lo8PL86iUjaTQ8Umffn0Zzv4GbVTY/YN5HL0oDcm1LkxaMGwLDXNvSeAFl0PAoEnx5LRMeMBiMwQ8/NkTP47GIBnKhCNmG15n/tA/t5LV9baCMWGRmQ6xy9MajjyfrsVqMMC6fyw4ooIC8u6PffP2V3qzny6cM/bhtDLkGDN+sJtILcO2O8ws2pVmYYP7CtS2NF/BKDtwA48Lw35YOwAMnMOjV00rnBfBAD8nEPF78IAv4wTWLRz0dOe6PSo7wgOsJT/Hgx4A2ZwXXqx7BP88Bkt8W7wfni0dGzMWLFujnP6M+wP3D0iV6JIz0kVDmGCiDmh3oa1sar6Ac3A0qHJ8ynY+WQvzy357OuTfChNJK5wWUiYsZT374hdLjJ1pQLy1H1e7p1ZH4xMSzmqf48OMAou29l5ksX3u8d5xPHlns9PaR0JA7GqyOBhRQfGj9urXe9gnZrOfV5KzmjBszSn+LTv+GMHb0SJk0YZw+BMy1Oy4akIejVbzQ1U/+SODFtjw94LVM0k8cP07nt8X7QTx4pD7UKx5tFCuP5IcXeIpHfQz88kh6ZB1vmWkeJ8eXR14g3b1LZ7ktT07p06NbdEb487Jl+htyWTNeq+eGfONB/7rAFgavKg8PjxaMtMAW5xfUh3rZ4tJDrPzYECuPsfBjQyCz9HG+eOTjN3xHsb+a4kVlhH9s3SqtWzaXFk0a6WfLIqOBJexCItb6/N34sSGQ2Z8Pp46tmjWRd95+M2ku66ZURshiAquU8XpqPkCAAA7YAbDt9aYywoACCujPpcAIAwroAlNghAEFdEFJ5P8DvsGbcpp0y9EAAAAASUVORK5CYII=)
physics-General
physics-
A U–tube of base length
filled with same volume of two liquids of densities
and 2
is moving with an acceleration
on the horizontal plane. If the height difference between the two surfaces (open to atmosphere) becomes zero, then the height h is given by–
![](data:image/png;base64,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)
A U–tube of base length
filled with same volume of two liquids of densities
and 2
is moving with an acceleration
on the horizontal plane. If the height difference between the two surfaces (open to atmosphere) becomes zero, then the height h is given by–
![](data:image/png;base64,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)
physics-General
physics-
A narrow tube completely filled with a liquid is lying on a series of cylinder as shown in figure. Assuming no sliding between any surfaces, the value of acceleration of the cylinders for which liquid will not come out of the tube from anywhere is given by
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)
A narrow tube completely filled with a liquid is lying on a series of cylinder as shown in figure. Assuming no sliding between any surfaces, the value of acceleration of the cylinders for which liquid will not come out of the tube from anywhere is given by
![](data:image/png;base64,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)
physics-General
physics-
A cylindrical container of radius 'R' and height 'h' is completely filled with a liquid. Two horizontal L shaped pipes of small cross–section area 'a' are connected to the cylinder as shown in the figure. Now the two pipes are opened and fluid starts coming out of the pipes horizontally in opposite directions. Then the torque due to ejected liquid on the system is–
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)
A cylindrical container of radius 'R' and height 'h' is completely filled with a liquid. Two horizontal L shaped pipes of small cross–section area 'a' are connected to the cylinder as shown in the figure. Now the two pipes are opened and fluid starts coming out of the pipes horizontally in opposite directions. Then the torque due to ejected liquid on the system is–
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)
physics-General
physics-
A small uniform tube is bent into a circular tube of radius R and kept in the vertical plane. Equal volumes of two liquids of densities
and
fill half of the tube as shown.
is the angle which the radius passing through the interface makes with the vertical. The value of
is:–
![](data:image/png;base64,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)
A small uniform tube is bent into a circular tube of radius R and kept in the vertical plane. Equal volumes of two liquids of densities
and
fill half of the tube as shown.
is the angle which the radius passing through the interface makes with the vertical. The value of
is:–
![](data:image/png;base64,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)
physics-General
physics-
A cylindrical vessel filled with water is released on an inclined surface of angle
as shown in figure. The friction coefficient of surface with vessel is
Then the constant angle made by the surface of water with the incline will be–
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMQAAACwCAYAAABQFcG8AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAFxEAABcRAcom8z8AAD8iSURBVHhe7X0HQJRX2vXu/v/3/d+3Jdlkk41JjL137AoCUuyKXbErWLArRewiFhQRUbECYm90sGFHATtWbKggiAoKKE2Knv+eC5MlRiMqZQbfs3sjOu8MM/Pec5/+PH+CAgUKfoVCCAUKCkAhhAIFBaAQQoGCAlAIoUBBASiEUKCgABRCKFBQAAohFCgoAIUQChQUgEIIBQoKQCGEAgUFoBBCgYIC+CAhXr9+jdycnPy/KVBQtvFBQuQIMqSlpiI56TlSUpLx6lVm/iMKFJQ9FIoQT548QcjJ49ixfSuOHz2C1NSX+Y8q+JKQm5Mr90NZxgcJkZubi5iYGKxfuwb9evXA2NEjceTwIbx48SL/CgVlFVlZWfI+x8REI+LiRZw4flysY7hw7hzu3r2Nx/HxSE5OQkZGBt68eZP/LM1GoWyI6OhoOC9bhpZNtFCtUkUMHzIQfj7eeJaYmH+VgrKG5KRkXDh/Hls3e2LW9Gning9C7+7d0KeHCQb17ysORnPMnT0THhvXC5IcRVxsbP4zNRsfJASZH/vwIdasWoVWTRvjz3/6E77/5z9g2rc3fLz24lHcozIvRr80ZGa+wumQENjNmY1unTqI+66F1s2boK1Oa+hpt0LrZk3k4ain3RK9TLpg8oRxWLN6FY4Jdfru3TtIFAelpu6JQhNinaur/FL+Igjx32JVKv8jBvTphc0e7rh/716ZEZkKgKioKCyyny/ud1PUqV5VbPqucHRYBO89u7Fj21a5+SkdRo4Yis7tjdGqWWNoi2t7dusCWytLbN+6Bbdv3dLIPVFoQriuXAmdls1Q6edyaFy/DmpWrYTqlX5B986dsNZ1Fa5euYz09PT8ZynQRFA9vifI4Cq0AX2dVvil3Pcw0m+DDevW/kYlSn35Um74fUEBWCqIMnTgAOi1bgktsS9aNG4kVatFC+bj6JHDePQoTqOkRaEI8VAQYsVyJ2i3aCpF5tRJ4zFqxHA002qAGpUroINRWywWX8D5s2eRKQwsBZqJhzExcvN3MDLED99+jfq1qsPWxhIXLpyXzpWC4CZPSnoutYPQU6ewxdNDSofO7YygVa82Gjeoi8Gm/eDhtgF379zB67eer64oNCGcHJdKlYk6pYfbRgT6+wkdcxYM9XSkpGjTsjnmzJiOY0eO4NmzZ/nPVqAp4Im/cf1aDB88SNgITVFN3NN2BnpwcXbC7du3PnjKM0Z14dxZrF+zWrzGQEGmGqjyy0/ysHRaugRnw8Pw/Pnz/KvVF4UnhPhQ1BWpM+7asV2Kwhs3rmH1yhXoaGyIWkKFai0enzh2DPYFBiJJAz68AkLc35horFm1En17dsfAfn1hNXUyRgwdjAF9e2POrBnikDtcKDf7q8xMPHkcL2NVM2yspfFd6adyUtW2sZyKI8GHkJycnH+1euKjCUHGkxDpaWny8bt3botTwVXqjbWrVUHDOrVgNmww9uzcIZ+nQL3B+0cbkO5USv9lSxykt2j71s3Se0TDeaNQo548eZz/jA8jUxDjvJAWtC8MdXVQ8acf0KB2TVgLop0/e07aKuqKTyLE9m1bkJiQIB/nh6PBtWPbNmlcNa5fF/VqVpOnjaeHG2JjH/5O/1RQ+uB9o2TYsNYVvcRhRt1/8QJ7XL0cgZdCGtyMvIFlSx3EY11hNWUSrly+LPdCYUEV68H9++L116BHt86oW6OqVMGWC9X7+rVrePXqVf6V6oVPIsQ2cXowSlkQcXFx8PX2woSxFtKgqlaxvFCvjLBm9Ur55SpQL9y7F4V1rqvRr1d3qQbPnm6Ls2fCpdpDZGSkw9trL0w6d0SXDu2kKzUh4al87GNAUnjt2SWlTUdjA3QSxLObO1sa6tlZWflXqQ8+nRCPfy9CU4R+ePzoUUyztoROi2ao/MuPMNRvA0eHxbhx/ZoQpYoHqrRBaR0d/QBuG9ZJNamT2KQMwJ0JC5WqTkFcvHABFiPNpA0wbvQoBB88IF2uHwuSiyqU/bw5MGjTWrpylyxaIKVRdlZ2/lXqgSIlBJGSkoLQ06ew0H4+dFu3ROXyP4rnNcF8cSqcPRMm82MUlB5IhnVrVguVVpBBnNazbKch9FTIOzc6tQBKEUp6ehF57bWrVz9KdVKBZDsTHo55s2eiYztDYa+0h/MyRzy4dz//CvVAkROC4Kannujs5CROICMZzGvaqD5sLKcg5MQJ6b9WULKgzUD1xX3jeikZ2gt9njlKYadPIyP93ZKbMaVLFy9i9gxbNG/cUBrI9EZFP3iQf8XHgfvi8qVLghSzoNuquVTHtnp6Iv7Rb9Xv0kSxEILgh79z+zY8Nm5Aj66dpE+agZ7xFqOxLzAAz54rsYqSBLMNpDewRzdxDw0wc5oNQk6e+EMViPc+LS0N+/cFYZBpPzSoU0umcezavg0vhSbwKaCkCD54EGZDB6F108YYOsgU/r4+aqNOFxshVKAHauf2LTDt2wvVK/6C2tWryMzJvXt2y5NGnV1wZQVUS9zFwdRXGNDGbXUxzcoSp0NOys1eGDyKf4Qtmz2lW5bu0+GDBsiYwqeWAHDv7NyxTapt3FOWkycg4uIFpKam5l9Reih2QnDDJyYmIMDfDyOHD0OdGlVRq0ol9O/TC5vc3XD/XpS4RkkMLC48iovDxvV5BnQ7Q30ZMGNNQ1pa4TcfDfGHD2OwYvkyGAi1qblWA0ydNAHHjx39JPcpX4/va+UKZ7mfOgmbwkW89o3r1/OvKD0UOyFUYISSonL82DHQqlcnPzGwI1a7OOPK5QjFA1UMeHD/3q+SgZ4dy8kTpZr08hM8RcTVKxFYYDdPpoG3aqYFi1HmCArwl5v7U0DX64xp1mjbRltqEAF+vtxw+Y+WDkqMEAQrq+iBmmlrg9bNG6N2tcpoZ6AvU43PnT3zO7efgk8D71l8fDw2uW1EH6GWkAzTrKbKPDPeg08F6+kvCdVm/pzZYhO3RqN6tTFkQH9s27xZSpCPVX95SNI+MRXaQhthZDOB9FPcukWJEiUEoQrrL7CbK29U9UoVoNuqBaZbW8mUAXXPddEExEQ/gIf7Rlnya6Cng0njx8rvlnGiz8WrzFe4cP4clixeKO6frkziM+nUEa6rXGQAlvvlY8BouY0ga8umWrCeOgW3b90s1Sh2iROC4EkSeeMGVgl1iYYav9RmjRrke6ACkZSU/NFfrIK87/Xxo3hs2eSBfr0FGXS1ZdrFYWEAq3LPigL8PSwiWr3SBV07tpfeQ9oByx2X4JJQg0i8wkoLvi9mM3TpYAzz4UMRKFSwhKcfHxEvKpQKIYicnFzcuXNb+sWZYUlju0HtGhg60BR7du9SK9+0piAu9iE83d2kCsK0/InjLAQZDhZb2jXLRT03ucsaaxrajELT2GZpMd28hQHrJAL8fDBqxDD5vlcw3VxIidJCqRFCBaaRe+3ZA/MRQ2UOVM3KFaRHZLM45WKFXpqTo16hfXXE6zevpWG7bbOn2FQ9pZE6efy4vFSLYm4Z9Pz5M2kMjxs9UqZ7N9dqiMED+skKy7DQ09K2+JBdcOLYUUyZMA7du3TCzOnTcFFImdJCqROCYN8nGlc8XZo0qIeqFcujS3tjmZZMKaLgjxH/OF4eIAP69BantLZUPQ+I77OkCnLYVIA1E3NmzkBHI0Oh/taHnrALzYYNgYvzcpw8cUKmgbxPDT64fx/MxbXtxd6aYWsjDffSgloQgnj5MhWnQk5i1gxbmRjIJgY0CPl7mT+TodRrvxMMfG7bslmqG/rarWQS3gGxwYrCgP4YZGdn4XLEJZn7NNpsOAyF/cKkQNqIk4S0WrHMEXt27ZTJnxfPn5cxh0ixwsNCMXfWDOlg6dyhnazQY41GaUFtCEGwZSZzZ5gdywAQSaHTojnmz5uDc6zXVtMc+tLC06dPsHXzJlnZpq/TGuPG5DklSstTx9Rxqm70Im4WtgUlPvOV2rRuIdUputhpLzKnjTX4dnNmYqQwpNmYoGHdWtKoZuOCZ89Kr9+XWhGCYNQ6zwOVV5paufxPspmBrbWVjIxSZ1WQJxl2bN8m4wCGem1kkOzAvn1qU7fMTc2ION2xDAj2790TXTq2h4mwEwaL98y6a9ZHsG7mX1/9TTawcHZyxP37UaWaEa12hCBysrMREx0DTw93WbHFL42VeBPGjsH+oMBPKlQpS+Dn3751Kwb275svGUbJhEl1UyvZloiVlezMwaxaHy8vrF+3FnZz52DEkMFyP1X55WfZ1mjKxPHC1jguVK/SdaKoJSFUYPnprp3bpUpQq2plWYZoNnSwTAz71BRkTYf0Jgmbgd8J7wdLdbeKvz9LVH/JmZaahpuRN2Wf4B5dO8tMBTZDU8VK1OGgU2tCiF8u9OEk2fJmtPkIGaeoV7O6jMAyrZzp5aV9opQUeB8YsKJrlXp5lQo/yRqFsaNGSmlx6cIFcZ9iZAsgZqEyI4DPUSfQxoi4eAnzhYTQFXZFyyaNJBkYRac0UYf3q96EyAf1UZ4grMttITYBuwaadO4gC9YjIi59sGdQWQDdlnSt8nP/9P23+Obv/4N6tarL5gC0I8aYm0kj1mHhAmlonxT6+6cm3RULxD66fu2qdJiwhrutrrZ8v3TX8tBTF2gEIYhXwtAKFXooe4rqt2ktO3swGmtvNxfnzpxRi1z64gC/f+rhO4UBTRdm+R++kzYVXZrcWFxsI8nUFy6ma5gKA9Zm6mRsctuAM+FhUvV8+bL0xhdQWtElyzpqulfZ8I6GNltdFmVKSVFAYwhBMIefQRvHJTxljFBL6KD0TkyznCr922Wxt6yKDOx7xf5GTJun3WA/by5WrViBlc7O8mdLoXqYDRsqH+tkbAgjcVjQi0Oby3HJIrn5SqOjIlMzrl65ggXz58mGEyTDpPEWOHI4GMlJ6iMZVNAoQqhw62akLIdkajMlBT1Q9LQwIKXqF1UW8PTJE3jv2YOB/fugwo//xndf/x3GbfVkW1Gmcp8VkvH8+fMICw0VG+wwdu/cJSPDVpMnyUAdU7R5YHTp2A7WlpNlPy3Wur948Wnlnx8LZq1y0IrDooWSDNw/UyaMl2pSYav1ShoaSQj282GlHVuzDxtkKnXpujWrykEubNnOCj1NR9Kz5/DavUuW27YQxmeVCuWlhKCk2LZli7CdImQQk0NNzp07h/CwMDnhZ/++fdi7ezc83NywZPEiTBJ2Vx9KjXaGsl09u14cP3602Dckq+JuCPKx1sVIkJjt8mkDHgkOln1g1RUaSQgV2F7R39dbjvlqVLcmalSpiL49TMSG8cQDWa+tmSnkLO4hsUcIMmjn2woMajWqWxvdu3aShLh0KUK2dQk5eRKnQkLkoo1FYpAg58Xiv7F23WHRIkksPZ1WsoaBWbB7du/Endu3ZNFPUYOBtYhLKptBV+ybJpg8fmzefMJSLgD6EDSaEHxvHOvFCPY0yynSA1W1ws/o1rkD1rqulrMOPraKq7TBJtF7hWQYNmiANJzZJWPBfDvMmjEdbbVby6i0s9MymTBHApw+depXQvBnFSlIFik1xHWHDh7E5k2bhNo0RfZEYqo220suX7ZEeumKkhR0g7MpHb1dxoIMVNksJ02QNgxTc9QdGk0IFdLT0xAeelqqAzTa2PKGG2f5MkdcvhxRqhVYHwO6Vr3Eic60BnZSp+7PyjTaRmzI0K9XT+i2biVO+LHiHmxByImTOHv2rCQCJcXbi/9O++LChQuCKKFSWkyfZiNzitiUmh4feu1OnjiGpCIwcKkmXRaqnCSDUJMYdKMBTcmgKUM6ywQhiCyx6ennZoNekoFtNJn9Kd2y586qvVuWG9J7714pGTjLr3uXjvK9H9i/X7aU9PPxkflcndu3k1Vqs4XE2B8UJI3q9xGCS6VKkRj808/XR6gyC4XkMUGTBnVl+S67ctNL9zl2BdWkGzeuyzhDu3ybIS/odlijMpXLDCGI169zZV0vi1NoRNJfT4PU1sYKRw8Hq23HwKdPn8JLkEGV38P3zj6o/n6+UgLQeKZXyd1tg7AFBsvsUNld3d1dkkG13kUI1eLjzBgODw+TtScrhNrF7FKm2nOxcRkLc1TNjj8G3CNM0afN0N5QX7xeU2mnkAxsbapJKFOEUIGZoJ6bPGTlXS1haLONJhMDgwIDxPuOl6JdXUCbwdfbW07uYaE9e56SDKwtDhd2gOpk55/Bhw5ijlBx2Ge1jTjZZ4hNzHJNbvYz4WekNHgXGVRLJS24jgmJsGvnDun54Zg0ktBJSNfrV6/Ie15YSMkgbAYnxyWSDLQZrKbkB92EKqtpKJOEIFjTu2fXDgwZ0A/1alVDo7q1MGLoIOmqjYmOzr+qdMF2ntzQZkOHiO+2idiUeZ24/X19ESoIUNA+yDOSQ7Fh/VrZw6hFEy306NpFqIhLpOFMO+FDUoKL16g8UfyZc6itJk+Wm5lq2oZ1az4qyY5FPlTBOhi2FURtJjt8kAzqlI7xMSizhCBSxE0JCvCTblnWVNSvXUMmBnKWGuemfYp6UFRg2aW/n48kKWc+d+5gDLu5sxDg5yc3PwlR8MSnhOBGDvD3x8IF8wV5jNCkYX1hcwzEzu3bESYeY6CO1xUkwPuWSlKQFLRdxluMQVsdbVn2ySKdD6mXlAzXhZrEfLL2ggwqb5I6B90KgzJNCILpCrxJ7GdKXZmRbdZrM9rLjoHiA+ZfWXJgeaeP916hw1MyCJvB2FDOcqPByw3Kjf32ac+/cwOHCJLQW0SSN2lYTzb4ourE4SYkDKXKh1QnLl7D16Sk4N/XrnEV72eYJKaqNuF94Dd26+ZNOC5eLPcD3wObBMh0jFKq1isqlHlCEHS7crOwORpVg9rVKsnCGrppOTWHI6RKCiz7ZJeKEcMGC5uhkfg+DWRNMb1ItAN4wr9vQ/PfeQ1jEByezo7cPJk7GBuITTwBWzw9cfz4MWk8U8pww3+IHJREXIeDg+G6aqWsU+B3s2iBHaLu3v1dN0XGGa4JO4Mu7Y7ivdOAJoGYwl0WEiy/CEIQTPy7cuVyfnO09rI4hfUEbPHIVOmSUJ+Ycerr442RUjJoyeQ7jrLiKLLTYuOStKcpBd6xcVVLqjpiAzPYtmb1agwZZCo9abw3rBlx27hBEoYqFAnxtqR5e5EwfE1KFtourK+gy5Sdubd4bvpNfyUGORndpmubRjhnPLBz99EjwaWaTVuU+GIIQbwR/2NbG7cN62WNL+sq2J907ChzHNy/v1g7xknJ4O8r1SQWxhgb6GH2zOmyrJJE4In+odNctbjJqVYdPXIEq1auwIB+feSwdLbwYSUdT29fH998iZLnqfqj1z4lXo85USeOHZNxBDahJsmYMHlBqFQqSMnguETWupMMUyaOkz2VPrV5sjriiyIEkZubIzvc+QhDkgYk5x3UqV5FzmWmx4epIPzMRQnm7zDnin5/koGqxixKBqEmcXOrDNx3bdZ3LW5ubnI+h6oOW79w8Ai7qtetXlXmPc2ZORN7du/GcbHJSTheK6XFO4ihIg7/3L1zByyF+kUnBFPs/YRE44w4dhJnEwApGVq3gI0lg3lHylx7oC+OECpQGrBlC+MTDevURM0qFaUHavuWzXjwoOjmnpFg9HRx3jNPXRY1MQjmvXdPvmeocEbw24vP4SanvXD08GFZp0z3LYN2VAfZvY92BavsOMaMyX7nzua5Wn/3WmLx37lOHj+O1S4usicW7RPGF4IPHZCSgaomo/+MXTB/rKTSyEsSXywhCBqBp0+dxAwbK5kYWI0zK7p0kp0h7gqDMivr83KgqEpwfgL7lpIM7Qzb5gfTvPJObNWp/dYGLexSkYKLXiE2G7CcPEnWQdStWU0G79iraf1aV+wLChLX50kjKV3E4u+nusTX4eK/R1yKkK1F+4rDga1F2Wt3gsVotDfQl2S2tbYsk5JBhS+aEASr8Dibwm7OLHEiNkPVCuWlX53+dZY9furYWFaDkQyjzfLIwMZrtjbW2Cs2G0kg3aOfQYaCi4l7lBRUh/bs2iWHJJp06SgLp+g46Nmts8x9YjMC1kycP5dXQ0E7RHqZ8olJtSkyMlLaU0wX5wHBWhM2GSPJmJtEyVDSXQFLEl88IQh+RiYGMjbB/P0alSugrU4r6aYNFxvmYzM1GaVl/6hRJIPYkMwqnS7I4C0kg0r3/xQ16Y+WPOGFCkZ7gaogDWv2baIKxXb1TLizGDUSzsuWYce2bQgICJD2Bw1pPp+E4PsiUWhH0DhnM4Pv//kPOV6Zk37YeKwslukWhEKIfDDyevfOHenf79a5vbApKkgd2mbqFKmjF7b+lzENSgZ2waABzR6n06ynyrRubtp3Bd2KalFS8PVJCnbxo1uWqRQ0hEmMpg3ro52Bnsybmjt7FtatcZX9VgP9/XHwwAGpVlFdWjjfTh4M5X/4F+pUq5KfqFc0A1fUHQoh3gJ7G23ZvEkOHGGqBzfRBIsx8PP2/sMO1gTb5XAjMh7QXGxAqSZZW8FLGNDsfvEh92dRLf4ekoLqEWdtOCxaIJsN0Aag+sYTv3uXzsI+GCDtAxvLqZg7a6ZUq1hr0aVDO6EuVZAzO0abjcCB/UEaU8/wuVAI8RYYfGJpqtfe3RgpjGEtoYfTv8/eR0wM5MyKd4H5O8ymtRhpLjcdvTzWU6fKNIuQkLzkPKok79rARb0ogUgKLlWdNctO2a1k8oTxcsBJp3bGaNOyhVTpaGewBoM5VYxnsLNHhR9/kA3RSOYvadC+Qoj3gE2DDx7YL12MjNzSa9O7e1c5s+L2rVu/aY7GRD0W8kjJoNUQutotYSVULRq4PKmZxk3JUBLSoeCSdoUgBd2tNLoZk9gtVCR25qDkMmfbml7d5VwGGs///uYrfP/132VmMG0ITjCNU6dmZyUAhRB/AAbUOLOCZZZt27SSiYFMc2ZxTWTkDSlNaHvQKzN2zCipp+sLY5yuTwbFuCm5IUtKMrxrqaSFKjhHUjDtg4a3j1ADN3m4Y96cWejcIa/PVVMhDScJtelAUKBUAXM1rCb9c6EQ4gPIzMiQ8w6WOiyUKQsM4LFElYanv68PvIVqxV5DdNkygsuOdDt3bJfuTBq4JS0V/mgxDkFiMEjH5mHsjEGViD2bmPTIe6uKM6SWkdykj4VCiEKAUoCDABkN7mXSVaoUbA/D7h4sqmH7SBbuW02ZLG2GU6fyAmbF5U361KVSoVRpGqyDYFp8ewM9GLfVlfPdONj9c2ZZazoUQhQSb968lm1t2H2b0ds8nfsfcsoRCTFl0gQ5wIQnMBPl1EkycPH9kKB5qlOoeK/bMXXSREkEI30dTBOSgdHuspiO8TFQCPGRYKtMqkqjzIZLtyQJQXcmZ+Mx1sDNd4YRYCEh1IUUfB98PyQDvU6spWaPJsYa+N6n21jhhCDDlywZVFAI8QlgYiAL/umBaqbVUNgVldC1Yzs594CG6ulTeZuvNI3pgqugG3bXrp2YKuwcFRlYD8IItKZXuhUVFEJ8IliFxyxRpjTQh8/uHlSd6M6kz59dLWQtgiBGadkSKjWJ74OSgca+teVUGAk1SZWo9yWkY3wMFEJ8BuiWZS8jNhRj7hP7QLFFzISxY2XaNV2ckhTiZH7Xhi3uRTLIjFqx2ACZRj8bDxsKm4HEZR6TpvVNKm4ohCgCXLkSkd+XqK2chUc1ilFu1ijT5x8eFl6sOUxvr18lg/idISdDZDKfzdSpMJYp3G2kAc0aiVQN7o5RXFAIUQSg+sSC/HVrVsuW8xwOyY4YzDZlVJhRbJWkKAlDm2RQGfV0rTJBsV1bfWk3zLDJy1otqxOXPhcKIYoQHD/LwvzBA/qhUb06ckAkm4mxe3eAv580tBkUK05JwdeWdQ6CEJw89CsZ9HRlzIGR97JUA13UUAhRhOD4KE798fXxkoPUmddUp0Y1dGxnBLu5s2XLSpW3J48URSst+Joqe4W1FzSa2xu0lW3pWalHycDIu4L3QyFEMYCtIJnfxLRq1lSw4IgJf9bitN69c6fcuHmSomhiFSqbgRKIi7+Dc/eYd8XCIFtKhpMn8EIxoD8IhRDFBOro3JzzhWSgi5Mp1XJeAmc7bNks3aCMGBeFXaEiA1+TuUl0BbOzB8nA7h40oDMzFclQGCiEKEawRuLC+XNwZpc7YwNZo6xVtzZGmQ+Hu9tGuYFV+v6nkkKlJpEQdK3aCGnATn7MrWIEmmRQXKuFh0KIYgbrJliays4X9EBVr1geDerWwpCBptIrxdJNEkIVwPsYYvD6vKDbCTmGa4atjSCDoSwT5c8kQ1ntjlFcUAhRAiApODWVPZ9kx8AqlVCraiXZ1n6Fk5OwNw68ZWy/mwAFF6+TRBLP8d6bZ0BzfpxsdWNjLfsrKZLh46EQogSR8OSpbFDGSUF1qleVrTTZB8ph4UL4yP6ueSf+H9kVKgOaqha9VKyAmzltmmyPz8AgZ8hRMqQrQbdPgkKIEgbb87M0lU2FG9SpJYztCnLs7rzZs+AjTnpuepac8vR/mwxcKsnA5ePtI9vbkAwdDA0w03aazFpV4gyfDoUQpQA2R2NrG8spk2SsgjlQhro6Mr1iy2bPfGM7r6U9JQK7eavIoDLCKRkYW2CzALpXqSbx2tRUhQyfA4UQpQRmmJ4Tm5utX2SsokpFOXhkwjgLeHq4y87eJAQ3v0pNUv3MJsmsbqNkIRnYUp/FPYoB/flQCFGK4PARumUXL7CXc50ZwGNLGHYiZ2Lg4UPBslsGg3gclMIuguzkMX2atZyCxFiDSjJ8KX2TihsKIUoZnIh6MzJSJgF27dRelqayrT17J61Y7iTdspQUNKA5ZYgSpUsHkkFIhhkMuimVbkUJhRBqALaz4RBIDnIx7dsbdWtUk4mB0gO1aKFsNckmySQDK/PYmpJxBibqKekYRQuFEGoEztfetWO7VJnYQpOxik7GRphuYyOHMjKGYdK5g+xUTjIokqHooRBCzRD/6JFUjSaOtfjVA8WCI07z6dvDRJIhLPS0YjMUExRCqCGSnj/H0cPBMjGPnQB/KfcdKv9cTn73HKzOqUQKigcKIdQUKSnJsr+T8zIORtdDhR+/l3MeWP55OSIi/yoFRQ2FEGoMfvfsGOi+YZ20HxrUqQk97ZbSuGbHDw5mUVC0UAih5mCs4vHjeHh77cHwIYPRsE4tGatgP9nDwYeQVMhBLgoKB4UQGoLExATpfmXHQM7WZn9Zjuzau2eX9E4pKBoohNAgsOCIo63YYZyDTkiKQf37YPvWLXhw/74M8in4PCiE0DCwNJVuV0apOTO6fq1qsiP5qhXOuHH9mkKKz0TxEuJNDl5nZyAz7SVevHiJly9TZZ5+uvh76otkpCQ9ly5GTuvh4s/UiZOSU5DyIhWpGa+QmSNeJv/l1AfiHb3OQs4r8VleJiP5WSKeJz5D0ot0pGa9QXYxv2FGtulp4ogspnBQhWJe0zLxd3YSVFpTfjqKlxA5Sch6eh13LpzA8UMHEXzgII4dCcaxwwfEz/4I8veBv48XfL259sKPf/r4wM/XH4FB4vpTETgXlYzHmfmvpy54kwWkx+J5VBguHNkLr42r4eG6AVsCzuDYvVeI/7x574UCZ1bcjLyBtatXok9PE2lsM2aRV0d9XCkQ+kQULyGyE/EqNhRX963DZgcbzJs6FpMnTMLEqbaYOXchHJycsErc0NUrV2D1iuVY5bwULkvmYuH0CbC2GIkJVvMxa8MB7A6Nwq3oR3iSmIznadlSapQq3giGvriJuDBPeDtaYLJJG/Qw7ox+Nh5wDHmJqyUYRH4YE43t2zbLGu0mDeqipbAt2JWcRUgsRlLwcSheQrzORG7SDTw+sRo+c3pgVPsGaFS/BeppD0Df8UvguGk3fA/ux759gdgfKKSCzzb4eCzEyml9Yd5OC3ottaHdZzwG2zphuasHdgSewuFrzxEjNlzpqlGCkekP8Pj0RvjM7obhTf+NRtXrotlgJ9gEJeN8CQ7tpPoUFxcrZ1aMtxiN5loN0Lh+HZgNHSIlr0KKj0PxG9VCSuRc34LwpR1h3uo7fPvPSvhbzYEwsd6OnaE3cO9xPGLFDY2LjUHMvRuIijiIU7sXw3VKdwxr3wQ62s3RpEVLGBl3Q78pLpjnfRfhcW9Q6qMAc5Lx8vJenHbojgktvkKdStVQp+9STPFLwtlS2IPMej0q1FE2KGvdvAnq1aohJ4lylHCMkCK8jwo+jOInxBuhyz7wQeTanpioXw7f/asG/t5oPAY4HMOJ+8l4lZOD7JxsGYDKzsrAq/QkvHhyCw/O7MH+NVNgZ2aE7q1rQbu5DvSHLMSUrZEIiVaHm/sGb2KO4+7GwZhn+C80rFodtfsuwdRSIgTBLhtnz4TDft4c6LdpjdrVq8jWN24b1iEmOjr/KgV/hOInBIS+HReEKA9TWLWrgB9/rI9vWtpg+MpzuPBEGKfvxUthf5zF9cOb4bXOAa4uq7Fqx3EERCQhTl2ynlOvItlrDJy7lUOzmrWkhLD0T8K5UtRS6Ha9HHFJtuc3NtCTpOA9YwHStatXpTGu4P0oAQkhCBEbiLvu/WFlrCLENIwgIZ5m51/0LggpkJOK9KTHSIh9gNiYGDyMT8CTpDS8SH+FzFdZ4ubmS5bsHOTkvkaueK8cjvgmNwe5UupkCanzSlwnVnYuct7Ws16L52Vl4lVGuqxHTk/PQEZmFl6Ja3N/I4TEE3PF673KQGY63cZpSEsT10cdw233YbDv8AOa1KiFuv1KnxBEttj0HBDJRmisn+DMCkM9XSxaYC/dtUrD4/ejBAghvvyHAbjj1h+Wxr+g3I8N8E2rGTBfexXX3umNETsx6wWyUx8jMTYSN88exQm/XfDbuQVeft7wCz4I38Ag+Ozxgr900QYhIDAEIREPEJWSgZfpCUiJOoPrp/djv783vHdtg6+/MNzP3MeVp1Je5SEjBomRJ3AmaDu8PFzh5roKrqvXY4OnF3bvC0fYnWd4JA7TN8hCbuJ1xJwLxOFdG+C50hEu4rtwdHTGykU2WGphiAHNvke9arWhNWAZrAOEUa0mdizb82/e5I4+PUxkBR57yzKlnF3AXyr1FO9ECRLCFJbtKuKnH2vj2yZjYWofiP2X7onXicfjeK5HiH94RxjVobh08gBOHPFHwO41cJtnjqkmLdCppRbadOuHHlPnYqLtDEy3GILxg3ujf+9h6D/MHnabwnA8Pg0paXfx5OQq7F1gDosBvdG7ez+YTV2M+TsvITgqF0nidM9MuIz7JzfDb/VMLJw6ChPMBsN8UH8M7d8bA02HYOjomZi1JgC7wm/g0tXTOO/rhM12IzFpYE/069YZvbp3R6/efTCgZwf0M24A7erfoEaVOmhKL1Og+hCC945TU71278LwwQPRsE5NeQ+nTpqAI4cOIUE8Ri+Vgv+g5AjhPhBWHaqiwg8V8V1VPeh0H43x1mJDzp+HhXZzsHDeDNhNHw9L834YMWgw+lvYYpylNexGtYdZq+9Qp9w/8U3Drmhu7oAZ9nOxckpHmOsLQ/aX+qjSdDSGLgtB8GOhKiEKz0/MwQazZmhbqyaqN+yGLpYecDkajatxgnhX/BGyYSoWjeyFQb1NMWjsTFg5rMEq1+Vwc5yAOWYd0FNfFwYdTdF3nBUmTDLD+H6G6GlkDONuIzFEkMthzUa4ua3EuvmjMb1vM7Sr/hVqVK6FxoOcYC0IUdoq09vgzIqgwACMGz1SZsoyXjFy+DDs3rkDcbFx+VcpIEqOEB4kRHVU+nd5fFexKZq27YF+g4fKwSIWI4fDwtwUZv2MYaJTF82baqN+5ykYONEerrMGwK53VbSo8Qu+aTIc+pZ74ekbiEt7bbHeohUMalZDpVom6DBpCzaE3MDN2wdxbvNozOvZBDpaRtAxXYo5e64iPDYeT28H4bSrGaZ1aoQ2jfTRptd02HicREBkCuKT4/Hq/i6EuPTBaO3KqPn99yhfqQp++aUCqlWsi4b6w2E63wdupx/iXlq2sEkSkXRhKw7P64JRTb5GvSo10cB0GayEyqRuhCCYznHi2FHYWE6RfaAa168rO3ts2eSBu3fvKMZ2PkpQQlBlqozy5arj23r90XXCKqzdHYRjRw7np3P4Yf+u1XCzH4/pk6Zg1BxPOLvtxuktVthk0RD6dSri6wZDoD/tIHafjcOLhyGICpgGxyEtYFi/PrR0+6PPlHmYPt0C00310Mu4CzoMX4E5O6/jYtxTpDw7hVveU7CwjxZaVm+MeobWGO10FMfuvUSCzIcT/0nZhyvuAzBO+xdU/Z+/4Nu//w3/+78/4acqHdBp0nq4nHmM6y+liZ2HR8dxZ/0gzDH4DlrVaqJef0e1MKrfB9Zhh4eFYoHdPNkhnDlQJp07wsXZCdevXxNXKLGKEjaqVV4mW5ituoiIZ2/dgKwEJN05gythp3D87F1cu3YRSccXwdeqGYzrCkLUMYXetEPYcTlH3LpXwPNQ3PSajhVDW6Jr02qo17AxqlVvhGb19dFpuAPm+D/I1+eFNX17LQ7O0kbPej/hx5om0Jnoh7UnE5CYloLMxPt4GHkUEd6z4DpBH10aVkLlr7/Cz99+i2+/00JtHUtM2XQGYcIi/9UoJ+LDELvVDA6d1MvL9EfIFTbD9WtX4bJ8Gbp36ShTyEmOhfbzcf7cWTlq+EtG6RCilSDEakGI5+84kXLS8SotFS/TspCZdAe54Q7wntIUhnUqCEL0h67NAWy/mJF/Sqcj+8ERXFk3FPO7VUTjSt/jf/5WE5UbDsXQxfvh9+g1ZNei7AfIODobW0dUg36171GucX+0n70fG45F4aYwmm8ccccupwmYOVAX3VvVljp27aqVUPPnH/HjT9po0GkR5npfx235OwtAEsIcDp3LoamGEILg1NTbt25JD9SAfr2hJSSFTstmcvLQ6ZCQL1p9KgVC1MM3LawwzDkMZ+I+kKb86h4Qvgh7JjaGQW1BiLqm0LU+gK3n0/6jtiSEIXLDMCzq+jOaVv5WEKIyfqrZC92ttsHj8nM85L1Nv4dkX0ts6FceOtW+ww9aXaBrsRKzXfdgp+ca7HKdg8U2ozB2yBCYjxiOSVOHY1R/XRjVrowK5dqgYTcn2PvfxIO83/gfPArDw3xCaIqEKIhHj+KkYT1y2FA0rlcHLRo3wsRxFjh08ID0QH2JKH5CUMmIDUSUsCHyItUkhDWGrziDc/GCLH+ETEGIM4uxd5KKEAOEyhSMHRFUXKj4RyH2+Ep4jG2Hobp1oafXEo3FTW1SUwtNdUdgoH2QUK9SEJcQhYT9s7B5eHW0rfEd/lmhMWobjcSgKYuxdMUauHu4Y9M2L+zwP42QM6cQed4Nvo49MaSxMKq/0kIdI2Gb7L6MazkF7AdCSIiHW0Zgccd8lUnYEFYBKSWa3Pc5oMv16dOnMi1/8vixaNmkkVChamPUiGEyWZD1KV8aSoAQYgs9PYS4rYNg26GiDMz9s9UMjHS9hKvPPpDHnfUQuLQM/lZNYUQbov4wGMw+iYDbQrK8isLTi2uxbVofDDbuCBPTSbB0XAHnZVMxx7QVOtO92NYC/RcGY+eJi7h7agUC5wmVqP4P+Op/K6J8w37obbMe6w+eR9ite4h6lIpEqSmkCdtkD86s6oqhjcrh33/5CRWECjZw+REEio/8m3HniWF44DYYdgbfQKt6LdQf5ALbQ5m4rGExr5cvXuLksWOYaWuN1s2aoEHtvMRAlqZGP/idXCzTKF5CvMnFm6znyLy5Axedu2KMzg/49ttq+GuD0ehrfwjBt5KQnvUar39nSoh/eJON3KSrSD08E5vMaqN1lXL4a/XeaDV+OzwOhyLy1Fp4zewI0yb1UL/pMPS22w/v67GIjz2CS5uGY3anymhYsTYqNB+DAdM3YvtuF+xxHghzg1qo9s8KqFzHBN2s3LAuJAqXnyQi8XkyklNS8CL2DKIO2MF9qj56NKssjOvvUaVKK+gMW4wZwo44cZ8VfUlITnqMuLDN2D+zHcwb/D/U+LkiqpnMg8WOOJx8lC2r5t5hIaktXmVmIuLSRSycbweDNtqyv2zv7t3gvnGDIMV9ORbsS0DxEiInEZnRx3Fp21Q49q+FNr/8X/z3//kb/vyvZmjQYy6sN53Bibsv8OJ3NZfZ4v8PkXh5G47Ym2Bss69Q+av/xp+/rY+K2gMwcKQZrIe3Qa/6/8BPf/0B/6wzBn2WXcJxKeHvIzV0NtYNqobGf/8z/uvPP+Cn+l3ReegUWNtOhO3ozuijUwdaVeuhkXYv9JnigPnrPLF5myd2ujthzbzRsB7YAaYm7dG1Vzd01GsK/VqV0LB+a7ToMQEjZjlhmcsKrHacC4fx3TFCtxK0vv0Tvv3r3/F17R4wmLwHa0JicU9og5pmmubkZOPqlStwdlqG9uI+16tZTTZWXrF8Ga5dvfJF1GsXLyGy45B+0wfH1k7CDNO26NamCVo1b45W2sZoN3A6LFyOwDviOZ5nvU0IsZVe3cajcDfsmj0I4zq0QDudFmip2w6GnXqgb8+uGNitDTrrNUFrna4wGuiIWVtvCGOWyYKPxVO3Yd+SYRht1AxtG9ZD6zZdYNhnJqbMXwPPzY5wW2KG8T10Ydy0KXR0O6Jz3+EYMWYkxpv1wlCTdujSoRf6WczCdJe1YnPMwQLzThis3xS6rXSh37EXevYfgMG9xXvoYoBu7fRgqNMceto60DEchL6T1mPVoTu4JnSr37hoNQj379/H+rVr0KNrZ9men7MrHBYtwIUL58q8W7Z4CfH6BbISbyDq/CEc8dsLn71i+fjCz88PAYdO4fCFaNx6koGM3x084h9yn+Plo6uIDA3GsQAfBPn7wT8gAIEB/gjy80aAz25Zh+0dEIx9x6/h4t0kJGTS5M3Em9T7iLt2GqH7fbFv73Z4e/lhb2A4Tpy7hXvRNxF96zjCAzZiq9jsi6bbYJbtTMyxs4O9vT0clrrAxd0Xe09E4Pyd+7hz5ypunPLGwU3LsGbBdNjNmoFZcxdi/sJlcHF1h+duH3j7+8ueSf7+wTgonhfx4DkSBKc1Vcng8fRA2A7bxX0e2K8PGtUR0r1Vc1mvzWh3WZ5hV8xGNb9aYSO8zhUr729qg5wkpMbfQlREGM6fPI6Qk6cQEn4Fl+8+waPU12+pO8KeeRmPxKgIRF4Iw5kzl3D2ajSiBJlT1epDFS3YVNnHay/MZHt+IWmFwT1l4njsDwqU+VHcG2UNxUwIdUcOcjNTkc6WOMkvkPwyExl/dKznZiI7/SVSU9ORKqTRl2BmJgpSHDywTzZHYw4Ua7ZHDBmEPbt24FFc2UsM/MIJoaAwSE9Pw+lTIbI5mpFeGxnJH9C3FzauXycTA3Oyy87RoBBCQaHAKsFLFy5ghZMjunYwlqTo2rE9Vro4IzIyMv8qzYdCCAWFxpvXbxB15w7cN6zHYNN+sraig5GBjF1wmmpZGAusEELBR+F1bq7sIbtyhbOUEHVrVIW2LE2dJscGZ70qgbaFxQiFEAo+CmzqcPzYUcy0tUHfXt1l+8za1SqjRZNG0gMVfPCgRg9yUQihoNDgRicZ6HHirOxxY0Zh8YL5ck4F90YzrQYYbT4C+wIDpMtWE+u1FUIoKBRevEiRG33sKHMZj+AMbfeN63H92jWcOnkCc2ZOh27rFjIxkPbFjq1bNXKQi0KIMoU3wKsUZDx7iCePohEd+xRxiRl4mfl5ATQZi9i/DxYjzdGsUQMY6rXB0sWLZOMzFS5fuohFQloYtGktSFFTtr7Z5OaGu8IIZ18sTYFCiLKE7BSk3Q1FZPBmBOx2w8ZtftgWdBVn76TgxSdygnXY+4ICMdpsBJo1bABjfV04LLTHtStXfuNVYrZsZOQNWZ/dpUM7OTGVfzIxkFJEU7JlFUKUCQhdPTsRqbFncC5gG3avW43NHuuwfs1arF7hga3+4Qh9lImEjzyoObzmgJAMY0aaCcnQEIa6OlIyXL1yOf+K3+PevShsXL8WPbt1lk0M2hnoSzuDHihNaI6mEKIsIDcNiD+MO4dXCQK4w8E9FEcv3sTd0L044ToNK51WYcmBBzgek1dnWBikZ2RIA3rsqJFoKtQkZrwuWbxQnvasyX4fcnNzZErHzu3bZHO0xg3qQq91S9haWcoiJEocdYZCiDKA1xmPkXzKGcErLGCzcCvm70vBTSakJp9Ggp8lVs6ywogFh7D+ZCKSC6E6ccOfOhUiezi1atpYSgaSgTUR3A+FQULCUwT4+WKMuZkwwhvLNWHMaPj5eCM+/lH+VeoHhRBlAFnPr+OquxU2TDCFtZMPVl95g2iWhuQK3T3CCe6zJ2HQ0BVYsOUibmaxW+37wft95/Yt2NvNEcazDjoaG/xqQH9MNw6+TnJysuy7NcPWRg6cb9aovpQabGxAUhSWXCUJhRAaj1SkPTqCg3YjMbf3QExbdQDb44QGJfdaNPBoO/baTYBZ+8mwWhKEI0m5+KPWAQ9jYrBti6ecW9fOUB+L7O0+q1ouLS0VYWGhcmYF7Ql2DKQHasO6NbgtiKduUAih8YhFyr0d2DF5KCZ0GAXbdScQmCIMYvnYM8GXIBxwGI9J+oMxbvp2bBOi48F7DmZ6igL9fTF29Eg56nfenFm4cP68rGf5HFAFo+2xysUZ3Tq1l83RmPaxasVy2R9KnfpAKYTQaHBnR+LZFVesMx+I4UaTMdPzLI6/BvIa/Ij/5h7DSZdxsG1rgpETNwh1KhOR7xnLQekwf+5s6VodL/T9kJMnimzELyUMNz8TA/v16gGturWlSrYov2OgutRrK4TQaLAM8TISzjph5bC+6Kc3GpNdAuET+xRRT58Kw/YOnj7YC2/7IUJCtMeQcWuwLDwdV9+xx1OSU3DowH4MGzQAHQzbYu3qVXJuXVGDow/2CBtiqPg97BioL2wL1lmcDQ9Xi9JUhRAaDUGI15eQEOoAl2EmMGnWEwMnLoKDlx92+PthX8BW+O6wxwKzjhjQ2gB9BSEcTglC/Ka5VB44hounNWfSWYw0w5HDwfmPFD2eiL3D9vxUzZo3biDTyKcyMfDQQaSmvuPNlSAUQmg0SIgIJITnE6KJCUzHzseCHV7Y7OUFPx8P7NkyF/OGtke/FgboM24tloZm4NpbM92ZwbprxzZp7Pbo1hlrVq1E1N07+Y8WD6iKHT18GJaTJ8gWmkwM5GiEoIAAIUVKb28phNBoUGW6ioTzzlg9vC/664zAeAcv7Lz9ENfEPYuLvYyYm1uwfdYAjNHpiMHj18PlfCZuFOiPw/sbEx0DO2FAM+YwsH8fcVIfKJEAGhMGz4SHYs6MGdDTbiUj20MHmsqgXvyj0olVKITQaNCojsLz6xvhNnoQzI3GwnbDaQSLDZ+neAgbIPMADi8dg8m6fTDKchPcb2chqkBaUVLSc3Eq+2NAvz5CdWkEW2tLKR1KKnWbv+fi+fNSXTPSbyOHzrPOwk0Y3zcjb0jpVZJQCKHxSMCLB77wsR0G625DYbXqMPY+kQ5XgXggcQ/87cdhjJEFJtv7IeBpLh4XcLsyL2nOrBkw0GuDXt27yhgEYwclCbp7b9+8CddVLjKtnMY23bKcYUF3LaeqlhQUQmg8MpH5NBxnl4+G05BemOjoB9dIIE5uemEH3HHF1rkTMajPYsxeF47LGW/YzlmC5aCBwvgmEQx0teUpzWEqpYV7UXfhsXEDTPv2QtNG9dHeQE+ocrMReiqkxDxQCiE0Hm/w+sV9xPnOg9esQbBc4An7Q6m4/DQDGYmhSDoyH2vnz4DZTB+sORCNZ7l5ihaRlvoS69e6yq58PU264MC+oBKXDgVB9YluWR9vL4wyGy7b8+u2aoHpQo07dvRIidg1CiHKArJf4FWULy7tmo3FsxZi2hJf7Dh0AkcPeCJgmRWWLnbBQr9bOBqd/mu2Kzcfs1IX2s8Tp3E9DB8yEJHXr+c/WrrgsBa6ZTk+mJONmBg42ny4TAyky7Y4oRCiTEBYybn38fRaAPzWOGGFvSPWe27CRrf1cF3sDPdtBxH8IA2xBYLBrGJjwh77tbZsqoVJ48YiJjo6/9HSB1Wk0NOnZNCubZvWsg/UiMEDsWvHdrn3iqvgSCFEmUEWctLiEMtB88EBQjrsx74DxxB87BIi7sbjqbBLC5qm3HBMzZg0fqws+2RN9JMn6nVP09LScO7MGSx1WIyORgbSA9WrWxfpgYq6ezf/qqKFQogyhwxkv3yKhOgYxMYm4Fn6u9O9ExMT4M96hVHm6N65I5wdl+LZs8T8R9UHNPyZA7VmpYt8nw3r1ES3Th2waoWz+PebyMws2qEDCiHKJF4j91UWsrNf/2pAv43Y2FhscnfDiKGDZf7SZg93pKSoZz8l9o59cO8etm7eBNM+vaBVrw6M9HTkzApOPWJHwaKCQogvFAy+LVuyWEam2WAsKNAfqanqPfeBLfj37NopEwOpPtG2mDtzBsJDTwsyF00iokKILxSMN0yzmopeJl1kyjdTKIpa/ShqcC8+f/4M+/ftw3iL0TIHiukmlpMn4diRI0USq1AI8YWCzYk5CIUz5FYud8KdO7c1plUMN35eYuBE2VeWxGDmrJ+Pj4xjfA4UQnyhCBNqBrNb2XTMbf06uZF4rzUFGRkZOHf2DOyFdOPUVDZQoy3Eeu3Y2IefnIulEOILxamQkzDp3BH6Oq3hKYzrZ4l52U+ahOzsLGlUL128UPaaZbpH354mWLN6JW5GRn5SFd5HE4IidtfO7Uh8pnlfoIL/IDwsVCbS0TDd4umB5CTN7dh9//49bHLfiH69ewibQktOT129coVMXPyjHlLvQqEJsWyJgyQEmejltQcvXqi3R0LBH4N1zD26dZFJfTLDtZQr1T4XDCp67dmF8WNGoa2QemyjyRoPEv9jmhgUmhDLHZdKQrAGduWK5bh69Yq0+NkiPen5c/GzsjRhsT0l7xlbVDLFmvMdqGKwKXHe4+9+njou7ru8z5Ms3a7sJ7XFcxP6CtuIg1zatGwu51gwaZENFDKF3fEhFIoQsYIQK52Xo3XzJqhRuQL69+kJJ8cl2Ltnt+zOxtGt3kJqKEv9l5+vNwL8/bBk0UKhLmlLFcNqyiS5kfg4M03ffo66L18fb+wLypthzuxdBhvZ/6l6pV/QuF4ddG5vJPbrUqlafQiFIgSTvpyXOaJh3Vr4rz/9CT//+1/QadlU5tGb9u2NPj27S4+FstR/8TAb0K83jPR1UbVCeVT6uRx0WjRD966d5OOsVnv7OWq/hCHN9z2wf1/x+XrB2EAPdapXwfdf/x1/EvuViyoUXc0fQuFUJiFuVru4yLFJf/uvv+C7r/8mv8haVSvJX1yrWmVlaciqLe4X7xlPzwrl/o1fyn2PahXLo6a4l/Lxt67XpFW3ZjXUq1VdfsYqv/yEH7/7Bv/vL3/CXwQhaGhfunghf1e/H4UiBPU1BkLs7eZijPkIjBs9UhovDIZwogw7RMuflaX+S9wvdrdgIzJmunJNGDvmN4//5npNWdyD+e+dUWx+rskTxom/m8t2/utcVwtbOCZ/V78fHyQEkZuTI6ODjx/HC2kRLSUG1ajoBw/Eup//p7I0Z92X948bhPZhjLin775O01beXvz1s8U+lHuVKzEhoVDepkIRQoGCLwUKIRQoKACFEAoUFIBCCAUKCkAhhAIFBaAQQoGCXwH8f2TBesyY3AszAAAAAElFTkSuQmCC)
A cylindrical vessel filled with water is released on an inclined surface of angle
as shown in figure. The friction coefficient of surface with vessel is
Then the constant angle made by the surface of water with the incline will be–
![](data:image/png;base64,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)
physics-General
physics-
A solid uniform ball having volume V and density
floats at the interface of two unmixable liquids as shown in figure. The densities of the upper and the lower liquids are
and
respectively, such that
. What fraction of the volume of the ball will be in the lower liquid :–
![](data:image/png;base64,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)
A solid uniform ball having volume V and density
floats at the interface of two unmixable liquids as shown in figure. The densities of the upper and the lower liquids are
and
respectively, such that
. What fraction of the volume of the ball will be in the lower liquid :–
![](data:image/png;base64,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)
physics-General
physics-
A balloon filled with air is weighted, so that it barely floats in water as shown in figure. When it is pushed down so that it gets submerged a short distance in water, then the balloon :–
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)
A balloon filled with air is weighted, so that it barely floats in water as shown in figure. When it is pushed down so that it gets submerged a short distance in water, then the balloon :–
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKYAAACmCAYAAABQiPR3AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAFxEAABcRAcom8z8AACWcSURBVHhe7Z1ndFRXsu/f13vvu+/DnTzzZrzG4xkHDAZMDgZMMNnkHE0yWeRgck4SIogMRuSoiBLKOeccUY4og8iuW/9St0ZAAy0kZKm1a63/kk736XO6T/+6dlXtffb+P6RMWRM0BaayJmkKTGVN0hSYypqk6QTzyZMnFBUVRZYWFpSdna15VJmy+ll5eTl5eXqStZUVpaak0IsXLzTPvG46wazgA5iamFCnr78m57t3NY8qU1Y/A4xzZ8+mbp060bWrV+np06eaZ143BaayRjMtmF3rA+ZhU1Pq1rkzuTg7ax5Vpqx+lpaaSvPnzaOe3brRjevXFZjKmoYpMJU1SVNgKmuSpsBU1iRNgamsSZoCU1mTNAWmsiZpCkxlTdIUmMqapCkwlTVJa1AwfX18NI8qU1Y/y8/Lo8ULF9YPzCOHDgmYN2/coDw+oJJSfRUUGEgzp0+nb7p3f38wj5uZUZeOHWWEUd8+fZQ06gd9+y3179uXBkD9+r0szeP9eR/sh/11HaclqnfPnvTFp5/KNbnFDu+9wDx5/LiA+bv/+R/6PfSb37R4/QH67W/pT7//Pf3/P/6J/vrnP9PfoL/8pUZ47K9/+hP95Y9/pD/zfn/83e/kNbqO19KE64brgh/ue4NpduSIjJtbsWwZmZufF1Bbsk6dPEHnfz5H5ufP066dO2j8mDFyfVp9/jn98+9/p48/+og++fhj+urLL8U7zJg6lTZu+IlOnjgurzlz+pTO47YI8TU4deok7d+7lwZ99x31+eYbulnfGNPK0oKev3hOxcX3W6RKS0voYdVDqqysoLjYGLpy+RItNzKi4UMG05CBA2no4ME0YvhwGjtqNP/9ni/8QBo4YAD/P4wWzv+RTIwPkJubKxUWFdKjR1VUVlaq8zyGrJKSYiorL6WY6GiaN2dOwyQ/ly9dpPt88LS01Bal9PR7lJubQ5mZGeTn60Nn2ePNnjmDunTqSN27duUgfgZ7zl104vhJunz5ClnctmRor9Khg4dpzao1NGHsOI6pvqHP//UvAdXE2Ji8vDzp3r00ysnJluPrOq8hCp85IzOd/P386IcZM+qX/LRkMAFjBisqKpIv4LXqXzlfzF6sObNmc5NuTiEh4RQXlyiKjU2okXY7MDCELphfpFkzZzHMnejrdu1o8qSJdOXSJYqKjKSsrEzKyEjXeX5DkwKzAQRYAI0ve8kN69dT9y5d+EL2oLVr1pKtzR0KC40U8BISkkXxUHxSjbSPQ2FhkWRpZUu7du2hMdzUt/rsM+rauRNt3byZAgL85TwtwXMqMOspQJKdnUUODvY0+4eZ1K5NGxrYfwAH7mcoKCSMklPvUeq9DEpKSaP4RA2Ub1BCUgolJqXSHXsnMjY5TNt27KE5c+ZRm1at6Ou2bWnRgvnk7u4qzTq+OF3vx1CkwKyHxFMylNevXaVRI0ZQG86up0yaTJYWVgxYCt3LyGIw0yghOUWgk79vUSIrKSWVAoND6fTZ87Rj137ab2xKRstWsBfuSl9+/pncMejq6kJ5ebkGDacC8z2FmBIXDxn3kEEDqW3r1rRk0WLOpt0Z1hyGMpOSGbI6K5WPn55BLm4eZGx6mHbu3k8mpkdpzep1nNUPY+/5JS1dvJhCw0Jr3oOu99fcpcB8DwEIDC6wuH2bhg8dQp9+8gktXbKUgtjT5eYXUho33SnchL+v7jGYCdzsW1jbSnO+fedehtOMtm3bRePGjKNve/emnTt28L4pBpsMKTDfQygJBQcF0fSpU6W0M3XKVHJz96S8gvsMVZaAmXYvsx7KYK+bR6HhUXTmnDlt3b5btGefCR08eITGjh5Lg74bwD+MWxLjGiKcCsw6ChAAhkv8GTu2b0/fcaJjY2PHUBZRZlYOpXNc2RDKyMyW43n7+tMBToS2sLes9pxHacPGLTR00GCaOW0ahQQHSaZuaE26ArOOQtLh6+tN8+bMpj7f9JK6Y1ZWLuXmFQhIDamc3HyOO9PIisHfvde4Bs7jJ8/QMk6IUCM1O3qEEhLiBU5d77e5SoFZB+FioTR07swZuVDr162n2Nh4/qyllJ2T90GUxzEraqCnz5yXeBNwGnNzvnHzNho2ZChNHDdO6qf4weh6z81VCsw6CFAG+PvR3Fmz5HNaWdkwOAVUUHhfvNuHUD6HCPDGPn4BdPDQUQZyh3jNPftNaPGiJVLMP8s/lFQDS4QUmHVQYWGBlIcwQmjU999TRGQUf84SgROe7UOpoOg+ZeXkVvcI7dlPm7bsoENHTtBGjjVReF+1cgWFhoZI4V3X+26OUmDqKVwofPF79+yWmuX6tes4e06vBjMvnwEqYO/GEBUWNbAKqZDBhBISk+hn80sM5nZJiDZu2kZ9e/ehSRPGS9E9Pz9P53tvjlJg6ilk4pGREdIt+E2PHnTt2nXxYkX3ixlIQIkmvUgAKioqbnjxeUpKS8nLx0+a9C3bd3O8uZPmzZ0rI+Nv37opw+R0vffmKAWmHsJFQlHd09NDvBPGUIaFR1JeLQ8JcEQMZjEnQw2t+/dL5C8SImtbewFzzz5j2rx5K3XjOBODiuEx8V51fYbmJgWmHtKC6eHhRpPGj6cpk6fwRcsW76j1lIASzfr9+6VUUlJGpaUNJxwPYMJzFpeUUlRMHJ39+YL0o+/bd4B6dO1Kxgf20z1+r4Yy8kiBqYe0YGJkz+xZP3A2vFgyZmTj1Vl5bTBLGKRSKuPr0SAqK5fj4biFDCZ+DEiGPL18yez4aTLlZh1D7DZt2ECx0dHV3aU6PkNzkwJTD9WA6eYqo3uMlhoJmIDkbWCWV1TUqKyOqnkdH6c2mDhXcUkJpaalk7OrBx07cYp6dOtGq1eupPDwMAXmq9YiYkwPd5o2eTLNmDZdMvJ3eczyikqqqHxQD1XqBLM6+79PySn36Oy589KUY4BytPKYr1tLSX4mjBtLo0eOoJjYOAZEC8nbwXzw4CE9fFiltx48qKLKyodvBbOIt++lZ9Lp02elyI4yVkqK4RTZFZh6SAumB3tMdAFiUDCK67Xrlm8DE7BVVT3SW9i/8h0es4gz9OTkVE56DsgEE8fMjhrUDWsKTD2kBRN90tOmTJb7nN3dPSg3rzrO1AfMRwzco0fvVlUVvCZu/X27xywuLacYzs5XcWyJUU4XL5hz1q7qmK+ZIYMJiSdKTeHs9yfq1KEDHTQ5SOkZmVK+eReYDxg0QPf48WNZ2hB/X5X2cX3BLK94SAEBQTRq5EgZm2l35450mep6781RCsw6qCA/j67wZ+vVowdNnDCBYuPiqbSsvE5gPmYAnz59Rs+e/VtPnzyVx/UFE4nP/eIyGUSCjByTJOAOSgxg1vW+m6MUmHUQRhcFBQXS/HlzZQIDaytrycoBZV3ABIy//PKLCIt2AtS6gIlhdqgK7N+3X+LLo0cOU1JSosFk5JACsw7CxcKA3JMnT1Dnjh1p9apVlJiYROUMUN085lOG8oWA+fz5c3rC23UBs5Kz/ICgYJo6eYrMhuZgbyfeEu9P1/tujlJg1lEFBfkykmfsqFEyjYunhydVVDyoM5jPnj3X6FmdwSzn812/cVPql5g7Mjg4SA0UZmvRYMJjxsfHkfH+fbJU8dHDR/ixHIk16xJj1pa+YGr7ynGb70/r18uUj0ePqFsrtNaiwYTQbLq6ONPQQYNo2pQp5O/vTw+rHukFJrLvN+mdYLJXxvHs7Oxltg+Urby9vSS2NKRmHFJgvodQyI6JiaYtmzZS925dydzcnOGrEm+mC0yAVlX1mOFkjwmv+QYB3reBCfBxjn1791HrL76QqQ3hvZGU6XqfzVkKzPeQXLSMdLp714n6fdtHZuCIj0+QpARjJl8HEz0/8IYv9/C8ruoeIl09PzhuaXkF+QcE0oTx46UqcOniRYO710crBeZ7Cl4Tsd2K5cuoT69edP48e02G6s1gVgP3Lsl+0lf+MpgYkwlviRIR5iSfNnUqRYSHUzpDaWjNOKTAfE9pvZStrQ317dNbZuWIjIqWJri0rOwlMBFjoqnXW+x5azfl5ewpy8oqyMvTi4YPGSqzvx0yNZXY0hC9JaTArIcABZrSVStWSKH7wP4D4tkAU20w0cTXSQwn/gJMQAnvmZ2dS2tXr6FP//EPme4wMDBAukkN0VtCCsx6CGAATitLS/quf38aMWw4eXv5CEwCFYNZX8GD3uds3MbGVhYQ+Iq9JWbfQChhqFBCCsx6SjvMbN3atTL777o1awn3AVU+eEClpeWv3b9TV1VxJp+SkspechZ98vHfZQptjHJCJq7AfNkUmLWEC4heF0tLCxo0YAB9y4mQtbWNlHfKyyurk6H3FF6P49jy8XAnZJsvWsn0NIbuLSEFZgMIXjMlNZn27t5FrT//XFaniItLkARGWxh/Hz18+Ej64lcuXyFrAy1eMN8gux91SYHZQCoozJcR7uPHjKa2rb+kY2bH2LPlchJUwc/pmKGjqHpyhNceryXEl65ubrL4Uu+ePcjS4rbBN+FaKTAbSEiC4DnNz/9MnTt0pMEDB8q01wAznyHD4N7awuh33GmJCbNefQ5CzRJTZh80MZH5ibZu2Sy9TWjGdZ3f0KTAbEDlchMbEhJMSxYtkmX4Nm7YKPMNlXASBAAh7URZmJwVt+BmZObUPAZp98EIIldXeOAxNHL4cLkRriXEllopMBtQ6IXJyswgWxtrmd8Ii0jdvHlLwMzOyX9p3ktMZ42byXCnY+3HIYCJiVt37twlM8thPUX0Mhlin/ibpMBsYMGrRUdF0vJlRtJDY7R0KYVHRHLzXCTQZWXniuAtk5JSNPOtVz8GYR/cAXnnjh19168/q5/ErtpQQdc5DVEKzAaWFiC7O7ay9jjW/jl96rQM8gV4mVmYWz2bs/g0zriTGdB7NY/BS2IfzFIsmfhnn9EyBhu3TRjaeMt3SYH5AQSIANPK5cvpHx99RPPmzJX70JHMZGRi4n+sAZQi8WdKKsPM27jjEs/jHiLz8+aSQOHLuHr5cvWXxMDrOpehSoH5AQSPCdnb3aFhgwdLnHgGhfHcPPGKWMcnMSmZYuMSKCk5RbYBJmaQg7ec/+N8Wct8ycKFEhbgWPiidJ3LUKXA/EBKz6juRzfev5/atWlNc2fPEQ8J+FLvpVN8QhJFx8TJQlPVzTmAzaRTJ0/LNRzYvz/dvn1LEp6WFFtqpcD8QMKFxbC08LBQud23X59v6eqVqwIhlvOLjU+gqOgYiuO/8JgZ3Ix7+/jSmFGjJGnC1C+AuyVCCSkwP6BwcXF/0M0bN+j7YcNo8qRJ5OnlTSmckcfExVMYZ+v4m8agevv60YIFC6T+uXjRQhnW1pLKQ69KgfmBpb1RzNj4gNzVuMzIiAICQ2QZ6JDQcM7MU8nT04cWzF8giw5MmjCBHBwcWkzX45ukwGwEYW50zOCxaP586tCuHe3ZvYdCgsMpOfke+fj40+pVq8VTYhptG2trab4NaVaN95ECsxEE0FBCcnSwl/WBMPfR1s1b6dZNC1qzeg1n7Z1p8sSJdMfWVoDMzs6UkfG6jtVSpMBsJAHM1NRkToAuS7yJedOxUGnvnt9I7InZ2gBlS/eUWikwG1Fa6K5fuya3Yvzht7+hcWPGkKOjgzzXUjNwXVJgNqJwsZHUoJmewl7yv//zP2W5PQz8VZ7yZSkwG1lo0lF4x9QyAHPd2jUyE7Dyli9LgdnI0g7GmDp5Mv2///ovTn5WSdauwHxZCsxGlgJTPykwG1kKTP2kwGxkKTD1kwKzkaXA1E8KzEaWAlM/KTAbWQpM/aTAbGQpMPWTArORpcDUTwrMRpYCUz8pMBtZCkz9pMBsZCkw9ZMCs5GlwNRPCsxGlgJTPykwG1kKTP2kwGxkKTD1kwKzkaXA1E8KzEaWAlM/KTAbWQpM/aTA1EO4SACnIYSJXfFXC+baNaupsLCg5i7JhpKuz9GcpMDUQ/ByuJMRng1/66Nivi74i7Un/+9//Af9tH4dVVSUE1a9eHXfOovfX0FBvsyX1NzhVGC+RbibMTk5SaZt2b51K61ZtYo2bvhJtOEn1vr1tPEnFh7jvxsYMvzdhOf5ueptPKfdXk+bN26U7d49e9Kf//AHmT9z25Ytmtdrj4X911Vvv/L6fz+vPfeGl97LCiMj2rN7F/n5+cpnaK6AKjDfInhKLFS/e+dOWR+8fdu21KNbN+rcsRN17dyFL1YP6tWjJ3Xp0FGmefm2V29ZFKBD+/bUs1t3+rZ3b3ldF96/J19YzLrRk1+PybWw75CBg6gXA4oFUgEqVlXDvjgWHoewIhq2cS4sP43nO/PrsfYPHuvIr8V7wfto/9VX9PHfPqIRw4eRlZVls17LXIH5FgmYcbG0Z9dOmc5l4YJFtHvXbtq0cTOZmBykI4eP0PZtO2jb1u1kdtSMjh09Rtu376RdvM/Jk6fo2LHjtH3HTtq7dx+dPn2GjvI+27dtl1V6T506TaYHTWkbb5uYmMiMwwcPHpRjmR48xNtnycS4evvwocOyP46zZctWMjU1JTMzM9qxfQdt3rSZjI1N6KCJKS0zWkZDBw/hL3KmgJmSkqzANGiPyWDCo23etJU8PH3Jx9efEpNTKDg0jGztHCkiEgtD5ZN/QBDddXHjC5pNWGAqMCiEfPwCZBprbAcFh5CHFxYorV4kwNnVjbz5WFieD7MJe3h5U2hYhCynknYvnby8ffk1obIgVWJyKjk4OfM5wwlLs4Twue0cnGQqw7j4RN7Xn25bWNOM6TOpX99vZW1L5THZDBlMeExcmFWr1lAAw5acmkbhDOMde0cKYZBycvIoNDSC3D28KCklRZbbw1TWADgl9Z4sgh8RFUNuHt6cmBTImuZ+/oECHlZHy2cQARggzMsr4Cy9mPz9gyggMJiKeV+B2M2D94mQBapiYhPI1d1T3ksSAwuY7R2cyemuKy1dvIRDiF5kaaHAFDNkMHft2E7dOdbbyc0y1ucJDY8QKL19qsGLiIgiFxcPjbcrkHnVndlzYqFTrF0eyVC6uHqI58RqvNgP0OJYWE8ynF8PT4qlVEpKS8nXL1DmzSwqKhbo3T29yI+9cXpmFiUlpZKrmyfv7ytQRkTGkLWtPXtyHwpiUJcwmH05tlVgasyQwdypAROxXiKD4XTXhZthdwEwJjaenJ3d2AMGiTfDKhROzq7sIaPZU5bz6xMZLG9ZBQ3rSsYlcLPL0CWnpDKEZRQZHSOeNoO9Yll5JQWFhPLzfuxZ8wVaf/aa8KwyTzuHCO4ePux5vTh+TJNVLxBKuLH3jI9PIm9uzqUp79NHNeVaM+gYk7NyXBgkLX7+wdxsOlF0bCw314l0l6GEt8OqE/CeLgwsmuD7xSUMxj32ZN4Uy/s9ePCQPWQGQ+Yn8WIpQxsVEytNMhYMwBLSUdGx5MmeEMcC1GHsWeEJ0/h5LMUCL+rMnjeJocQPwMHRmWNad4kxo6PjydrajiZNmCQLXykwNWboMSaSn/XrfmLv5E3BIWEUn5jI/3sJmNo1Id05hvRkSNGcpyOZYSjhOcsrH0gzjSY6luNDQJrMcMGzwutVPXoszTJei+a+gp+HJ8bc7MnJaZL8wJNi/3j20ljmz5VjTsSUiGUBJjy4hYUNzZk1h8FUHrPGDNpjapKf1Zz8IAGBp0QGfYeb0di4RA2E1U1sJje3gAsxZDAnM4gTsY4kEpWw8EiqqqoS0Dx4Xyyngu0M3t+Xs3d42IrKSok9ASkgRqKEGNXB8a4ACG8K4AEpQgkI23b2TuTGsafRUiPq20fFmDVm6DEmPtf+ffvFWwEaK5s73BTHCUS+vgES5yUkJUsciKbcm+NElIWQ7GAbpaOqqkcMWolAGBcXTw8fVlEBQ4rST1x8PFWyp0RZCaBFwtNyTAqP6Ojkwj+AePG6PnwuZ26+4WnhdZEUWdvYUWBgCCuY5s2dp8CsbYYM5q4dO6hH1250yPSwlIdsOAtGDTOZPVxwSDjd5SY1IiKasnNypc6IjBxeExk2oERpCDFlKSc7yMjhAcsrKqiiolIycsSSDx8+ZGhLBcrwyKhqz8nHR7gASLHOJLy1C3tFrEuJ9c4RUlgxlDgHPKednRONHzue+nOMaWWpen7EDDrG5OQHXX6bNm2RWiSyZiQfAMze4a54KyQnaKpRBEe8WMyeEbVJNOnwguUMIZboQ5Edzz199kyAQ+3ywYMHAiliUJSiSsrK5HjYBozZOTniMV1Qy2SI8QPA4lU2d+zFY1Y3575085Yl/TBTk5Urj1lthp78oF8aBXZfzsqxJiTiQ8R1yLIRV6L3B00uHkeZBxk2YEEPDppoxKWANJ8To2fPnwtowZzQwKsizoQnBaT3i4sZ3FJp+uEJATWycGT7eD4nr0AAR6+Pr3+A/AgQGtjecZQylqpjvmIG3ZTv3EHdu3SVfnE034AOnhEeDMvvRfM2oEQzXlBYyPFigjTBCRwfwlOi+xIxZ0ZGBnvKp7KN5h0QPnn6RCD1CwiURAmeE14Tz+ewZ0SvD46FOim8KLwjsnEcD2UmhBK2dxzkBwJwFZivmKEnPwATMSaSnbucEdtzlgxvhSTEkSFFPzm8G7ypNnkpLi7h41Rn2EhicFGxwKl0RTJ0z5+/YG+YSv6BQZTHr0UZCZBiXUmsa47ECF4Wtc3snDzxvihPAUK8D/T6oJaJikBcHHtkhnXmjB9UU17bDBnM3ewx0ZQb7zfh5jNQeluiY+MESgzagPdCySglNY08GTpAWlB4X7JoZOto5h8/fiJNPuJTJEaPHz+mDH4N4lMA9+jRIz5nunQ/opcHiZB/QLD0GsFTAlSUowRK9to4N7JzdHXifxTYLS1tadw4lfy8ZIYeYyL5Wbt2vRTRkZFj1VyAgn7rRG5ekSUDUHQvwnNicAaa4JCwcMmw4fECGFg08+XllVKER3ITw/GiFlo3Dg3QPKP5Dw4OE0+IQR9Z7F2xLzxnYlKK9DABWIQPqG1C8Jy3LWzox3k/Ko9Z2wzaYzKYGPi7du06yYrRKwMI0ZxHRcVSFjwhezIkKPBsKO2guUYCA8+JAjtKO6EMKZIddFfCcyKWROKDLBvNf2JSskCJEhKOl8XxZQG/FudE1yXCARTYcWyACCARcyK0cGBIETKoGPMVM+gYU5KfzrRnzx5Odu5JFoxaJsDKYE/p4xMgCQlKSNnc7GLgBWJDgIUMGyUfJDMYd4lSkI+fPwVyolLK1yw3P1/GbKL0hFqnNsaE5ywrLROPiu5GNNcYJALPiZgWMaV4TvbgyNCD+RwIIVBgVx6zlhkymBj21qNrVzp86IiMq0RPC+qHSEBQ0oG3QgkH4KDphndDD1EpQxnG8MKT5eRiSFuZdE0CzHzO3mX0EB8H2XQB/4+xnJ7enCglJornTEhIlswfWT+6MQGzg5OrnAuhA3qBUEcNYm8MUDG4ZOKEiSrGrG2GHWPukEEcW7ds59jOR5rhtPR0bpojuEl1oUhObjDYN5IBQtyJ5rW0lL1fbILEiRjggbgSRXE0wxgMjCYdBXg094hJkRBhNDs8I0YWSX8574sk635JiZSokGhhkDDiV4QGTpyhwxujOgCvbWFpTTOmz6C+7DENEcybCsxq1U5+MB7TyGi5ZOUoCYWGh5PjXZSJgnnfdIk7ASVqmUhskBA5u1RnzMiwkZnjeewLiNGFiWFsaP6R0fuhlyckvAZSxJyAD/FoHMeWiCNRHkKMiR4mZOQ4N+JO/4AQDi0cxGMaLVlCA/r1M7imHDff2Vpb07NnzzTEvW4tsClHuag7zZs3jy5cvERnz54jYxNTMmFdML9IV65cle2DpofJ0tKKrl69Rnv3HqAzp8+QtZUVmZtfIFPTQ3T2zFmyuG1Bly5doQPGB+WGs1u3btPx4yflZrKbN24JUMZyo9tRsrKylmObGJvKzW3Xr9+gixcuyfOHDh2W586c+VlugDt06Kjc/IZVfbFYv4DJoYEhgDlj2jQaOGAA+Xh704sXLzTEvW4tCsy42Bjas3u3TFCAAbgd27eX22dx22ynDh2oayfcbtuJH6/ehmftwtsd2rWXx7HdmR+X22x5G9cHt+/iOLgVF9udvu4gt/DiVl1s4/ZfvKb61l/tvh3//VreF89jG++lQ7t2cm7c7ovXTJk0WX4QhnKXJFYq/n7YME4EYzS06TbdYFZUMJiH5cKdO3dWZoTAwXWdtLkI07YkJibQz+fO0TIjI5o4fjyNZG80euRIGjNqlGj0iBGi6u2RNKrWNvaTbdl/5L+3X3l+jOZ4+F+2cSx5js/1yr415+Jt/I/Hx2q2sSj/uNFjaPXKleTq4iJNeXOe8ADX39vbS647PltOTo6GNt2mE0wM2zrHTRx+xbt37qIkziyb669VK1wcfLmhISF018mJHOzt6O5dJ/m/yYnfl5OTIznY2ZG7mxsnXjE1n+HVz9UchPeNFsvR0YGGDh4sXhM137eZTjCfcbZka2NTHYvNmUN+vrh/OkvnSZubcIEwN5DMXdTEhfdoKHMX4bqjRIQQauH8+RrS3mw6waRffqHgwEDq1aOH3HNiY20lF0nXSZWU3iWAiR/YyePHpVSH+ZreZbrBZMvKzKTvhw6lz/71Tzp16oRMr5fWTJsSpV9X8PiYsnHLpk3Ug5PC40fNNJS92d4IJuLMLZs30xeffiqEN+fgW+nXE7wluEGcPHP6dPquXz+Jm99lbwTzF27OPdzdaUDfvjRpwgTy8vSUzKq5BuBKv44AJYScpT+zNGfWLI7x8zSUvdneCCassrKS5s+bJ3HBBXNzccfKayrVRdrZlXds20bt2rShfXv3vrWwrrW3ggk7bmZG3Tt3lglJkSkqMJX0FVpXlBlDQ0No4vhx0hVpb2enIevt9k4wo6KipBCNecbj4mIFTNWcK+kjlIiQm5w6eYLat/2Kli5eTPl6NOOwd4KJW1MxBXOvnj3I/Px5cc3Nvdiu1Ahi54Xad1BQoPT5t/r8c7p04YKGqnfbO8GE3bG1lamep0+bRpGRESoJUnqnsjgfSUpKpCOHD0n/PzLy+Lg4DVHvNr3AzMvNpZXLl8vggmNHj8oJAaeuN6SkBKeVm5dLri7ONGTQQPq6bVuysbLSK+nRml5gonRkcfu2TKg/Ytgwcnd3q8m2dL0xpZYtVG8iIsIJq3VgkYM1q1dTLju3upheYMJKiotpz65d9FXr1rTcyEiadPQ563pjSi1X8JbZ2Zn087kzMkxw8oQJFBUZWSdvCdMbTFhWVhatWLaMunTsQKamByklNVl+HbreoFLLFMZUODrYyzC//n37kZurq7S4dbU6gQmLiYqSMXXf9e9HFy+YS586ygK63qRSyxE8JVpQf38/GYiNgdIX65CFv2p1BhND4uzt7WWBpVHDh8uwf8SbCs6WK+QaaDkjOa5cumQxtWvzJW3dspkeVFZqqKm71RlMGKZEMTE2ljIARmBbWtyWof+AU5WRWpYAJeqVkuysq052fpw7Rzpj6mPvBSassLCQNm3YQG2+/JKGDBxIZ8+cqSkjKThbhrSeMiI8jDZt3ECdO3SkcWNGk6enJ8eVdUt2XrX3BhOWn58vnhNvqPc339DePbspJgYri2UrOA1cgBKDf9Gzs3LFcurSqSMtXLCAgoOC6MmTJxpC3t/qBSYM85CfY2+JEUidvm5Pa1atpMDAAAmEVZ3TMIVWUQrori4y6zHu8ly/bi3Fx8drqKi/1RtMGAYVX718WSaA+vSTT2ju7Nnk7HyXsjj2UEmR4QhjJOBwcLfp5cuXaAQnv61btZKB5KjONKQ1CJiwx48eyc1G6Bn6+1//SqNHjqDr16/JGuEYLqe6MJuvtM12Nodovj4+Msdoj25dqU0rzr43b6ac7GwNBQ1nDQYm7Pnz5+Ti7EwLfvxRbuwf9N0AOmhiXLMQPGLPzCyVHDUXaZMbtHoRkeF088Z1mv3DD9StS2e5DffkiRNUUFCg+fYb1hoUTNgvL15Q8f37dPXKFRo/ZowUWmdMnyauP5yzN+0cPPCg+IsPr0BtGsL3gO8D3422hUtIiKe7To60bs0aCdUwLeL2bdskyX3b3EP1tQYHU2to2jFRgtmRIzRk0CC5FXjurFkyEwYABZTaC1FbeEyB+uGlvc6vfgfax1D6s7e3o/Vr18oNZPj+MMLMx8tLEt4PbR8MTK2Vl5dLXLJ961YaPHAgxybdaMK4cRybbJL7iHDDGy5CDscw2majtieFdF1YpbpLez1xbbWtForjSGiwjdKPxe1bZMrhF4rk6N3ryd8XQjMr6eFr2ATnbfbBwdRaUVGRzMGzjQEdxvHJ123byegTTLCEO+e2bNpIZ06fIgcHewoJwUJMCQJpUVGhCPMn4QIiCFfSX7hmGFhRUFhQcx0BZ1RUJHl4uEvItW/vHlq6eBGNHztWFu7v3OFrmdx2HsN5+dIlSk5K0nyLjWeNBqbWsHKYp4cHHTl8mNasWkWTJ06U2AXzJOFiDBsyhAPsmVK03bZ1iyRPp06elFnn0C8PcBHzKL1bTo6OZGtrI9WSC+fP0/FjZrR/717a8NN6WrhgvkxuBa+IWeYwHRAm+lq0YIEMb7xx/Rp71nTNt9b41uhg1jZk8fg1Otrbk9nRo7RCMwvboAEDBNRWn31GH//tbzLpApIohALj+FeN+9yV3i6Mg8S1RK0RsxKjSvLZP/8pdWaMcYAzGD1iJDfZc2nXzp2ccd+g8LAwKisr03w7v679qmC+Zr/8QkWFhRTg50eXL16kbVu20uyZM6svNntWeFfRpElK+kpzzQApZllDAnP82DH2qE4cd6Y1SPfhh7CmBabGMLAU83OjRwnJU2lpqQjZoFLdVQrx9YM3xCQWGB2G1qopW5MEU5kyBaayJmkKTGVN0hSYypqkKTCVNUlTYCprgkb0v+ZBWH+Tn6VLAAAAAElFTkSuQmCC)
physics-General
physics-
A capillary of the shape as shown is dipped in a liquid. Contact angle between the liquid and the capillary is 0° and effect to liquid inside the meniscus is to be neglected. T is surface tension of the liquid, r is radius of the meniscus, g is acceleration due to gravity and r is density of the liquid then height h in equilibrium is:
![](data:image/png;base64,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)
A capillary of the shape as shown is dipped in a liquid. Contact angle between the liquid and the capillary is 0° and effect to liquid inside the meniscus is to be neglected. T is surface tension of the liquid, r is radius of the meniscus, g is acceleration due to gravity and r is density of the liquid then height h in equilibrium is:
![](data:image/png;base64,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)
physics-General
physics-
The spring balance A read 2 kg with a block m suspended from it. A balance B reads 5 kg when a beaker with liquid is put on the pan of the balance. The two balances are now so arranged that the hanging mass is inside the liquid in the beaker as shown in figure. In this situation :–
![](data:image/png;base64,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)
The spring balance A read 2 kg with a block m suspended from it. A balance B reads 5 kg when a beaker with liquid is put on the pan of the balance. The two balances are now so arranged that the hanging mass is inside the liquid in the beaker as shown in figure. In this situation :–
![](data:image/png;base64,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)
physics-General
physics-
A block of mass 'M' area of cross–section 'A' & length
is placed on smooth horizontal floor. A force 'F' is applied on the block as shown. If Y is young modulus of material , then total extension in the block will be:
![](data:image/png;base64,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)
A block of mass 'M' area of cross–section 'A' & length
is placed on smooth horizontal floor. A force 'F' is applied on the block as shown. If Y is young modulus of material , then total extension in the block will be:
![](data:image/png;base64,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)
physics-General
physics-
A steel rod of cross–sectional area 16
and two brass rods of cross section area 10
together support a load of 5000 kg as shown in figure. The stress in steel rod will be : (Take Y for steel =
N/
and for brass =
N/
)
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)
A steel rod of cross–sectional area 16
and two brass rods of cross section area 10
together support a load of 5000 kg as shown in figure. The stress in steel rod will be : (Take Y for steel =
N/
and for brass =
N/
)
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)
physics-General
physics-
The figure shows a soap film in which a closed elastic thread is lying. The film inside the thread is pricked. Now the sliding wire is moved out so that the surface area increases. The radius of the circle formed by elastic thread will :
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)
The figure shows a soap film in which a closed elastic thread is lying. The film inside the thread is pricked. Now the sliding wire is moved out so that the surface area increases. The radius of the circle formed by elastic thread will :
![](data:image/png;base64,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)
physics-General