Physics-
General
Easy
Question
A 10 kg block is connected to an empty 1kg bucket by a cord running over a friction less pulley. The static friction coefficient is 0.4 and the kinetic friction between the table and block is 0.3. Sand is gradually added to the bucket until the system just begins to move. The mass of sand added to the bucket and the acceleration (in m/s2) of the system respectively ( g = acceleration due to gravity)
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)
- 5kg, g/10
- 3 kg, g
- 3 kg , g/14
- 5 kg, g/2
The correct answer is: 3 kg , g/14
Related Questions to study
Physics-
A plank having mass M is placed on smooth horizontal surface. Block of mass m is placed on it coefficient of friction between block and plank is
, where k is constant and x is relative displacement between block and plank. A force F is applied on block where F = at, where a = 10; t is in second. Find t0 when relative motion will occur between block and plank
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)
A plank having mass M is placed on smooth horizontal surface. Block of mass m is placed on it coefficient of friction between block and plank is
, where k is constant and x is relative displacement between block and plank. A force F is applied on block where F = at, where a = 10; t is in second. Find t0 when relative motion will occur between block and plank
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MDR48cxo/Hj2B/SjK6dXfFuLETERkegd+uXMT10utQ22mgUqoQGRWBPn36mPM4OmjhG9ALXZyccOniZVSWlwN0KG0zaEvWDJ1OiyemTYVap8ann2zA7l07MW/BAsjlCijkcmi1GgCAXCaDnUYDtVoFhVwO/N+GpcloREFREeobGqBSqaFSqaBSKlFTXYmTaSdQceMGVCo11EoNVEolDPpGFBcXQa83NJtHrpBBobj199AkCDCZTG3yPJDWQVsyC9y6u+CVl2fgq8QdcHF1xvRnnsLpjHt7v5lKqYKHqyt0dlowxsBEBpEx2Dt0QWR4FJwcHcEYg8hEMFGEWmMHF1dXaDRqALc2UoIg8Hx4pA3RlgyAv38ABJOAnj29AQBlNyqxfXsiPFy6ISI8CsMSxuJ8Th6KiosgmASUl1egpqYagsmEuvp6VFVWQhAE6BsbcbO2Fu4eHogMDsPxXj648tsF/JTmhGuFhegfHYsRw0ci41QqykqLkJZ+Apk52XBz90REaBSqyyoAGXDx0jWUl1TDy8sLTU1NMBiacKOiEo0NDRBMAuob6sFg3nCSdk6xdOnSpVKHkNrTU6dh6rTpGDN2HADAaBJgZ2cHJZNhT9IunM/KxtD4OKjVari6uqPqRg1u1lZDZ28PrdYBVWVlEBmDWq2Em6cnAgIC4OrmBv+AAJzNPIMTP/2M4JAwzJw1Cx5ennhg0BBUlJXg4P6DUMoVmP788xgybCi6OTuhqroKtbV1eGzSY0g/nYqS8nJ07eqMmhs1MDYZ4OTkBDcPTwQHh0ChUEj8zJF7QS9GE8IZHZMRwhmVjBDOqGSEcEYlI4QzKhkhnFHJCOGMSkYIZ1QyQjijkhHCGZWMEM6oZIRwRiUjhDMqGSGcUckI4YxKRghnVDJCOKOSEcIZlYwQzqhkhHD2HwfPMGE+8P9vAAAAAElFTkSuQmCC)
Physics-General
Physics-
Initial velocity of the block
while external force on it is
. It coefficient of static and kinetic friction are .3 and .2 respectively then distance traveled by the block in 12 sec. (g = 10 m/s2) is:
![](data:image/png;base64,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)
Initial velocity of the block
while external force on it is
. It coefficient of static and kinetic friction are .3 and .2 respectively then distance traveled by the block in 12 sec. (g = 10 m/s2) is:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAV8AAABiCAYAAAD3JtBGAAAgAElEQVR4nO3dd1hT5/sG8JsECEOmoDiw4F4MxeKsSsUFYt2jjlate9c6q7Xu1lFn3avuiaOouK0LUHAUkCUgU/aGBELy/P5wVPvF6hut8Wefz3V5XcDJnfcN5tw5OefkoENEBMYYY++VRNsTYIyx/yIuX8YY0wIuX8YY0wIuX8YY0wIuX8YY0wIuX8YY0wIuX8YY0wIuX8YY0wIuX8YY0wIuX8YY0wIuX8YY0wIuX8YY0wIuX8YY0wIuX8YY0wIuX8YY0wIuX8YY0wJdbU+AvX9Bgbchl8u1PQ32jjk6OcPU1FTb02BvSIf/ksV/T4d2beHcqBGkUn7t/Vj4+9/EipVr0Lixi7anwt4Qr33/UfMWLIahoaG2p8HekYnjx2h7CkwQ7/NljDEt4PJljDEt4PJljDEt4PJljDEt4ANujLEPnBpKRQlIVwZ9XR0QqaEsVkClfrZcB1J9fejpSqHzVuMQVEolSKILqVTylvf1erzlyxj7gKlQlPkHlvVww+yTGQAI+clXMKdjXTg2fPrPuSPmHw5EVsnbDpWG86t+xt6r4SgsfRdz/2e85csY+2AVpQfj0JLlOBGbhGYAQIT8iNvIqNASzW2f3qh8E7RxrAZT/bcbS5kSihBVFTStbA3D99CMXL6MMY2l3j2Om7FqGJrWQsNGJki+HYikInNUb+yMunZWkL1w21JFPh4GnUVYatn3JbF0gnvbWjB++n1JVhz8Th2GX2gc5E+3RImScevUA1T16otP7SuiWtWaqFHVGsZ6L9+XPM4fvkGJMDKzgpWFCbIfx0JdwQmONfQQ7f8n0hTGqNGqHRwrPEsokfwgCjqVKqGSlTkUj4Jx+24ksokAqSGs7J3R6BN9JP55D9HpuSgpZwPnVk1gZ2QAdWkOHty+hYeP8wB9E9g2cEAD+8p43Vn0XL6MMY0VZV7Flu9OoLD2CCzY3Ar3j63HtvMy9FjyI6r+rXxJpURuSixiH5V9X1KFHZ6/2y9IQdgVX0SV2sGlbg08SLwLAFDH/o4txy4jyuc6vCvZoV4dF7Tu1APd3VxQxfyvBpan3sOuhYsRb9kEnt07gPwO4Hq2HdwHd8UnQfsx/2gcmk/ahnXjHWACAMWpeBCjREXbKihvloFrS5dja1JlNHc0RWJ0DIpMU5HlkIhrN+JhVLkiitMf4kbyN5g+qAmiD6zGtlOPYVrbCCl3A6HfdihmjhiA2uX+eVOcy5cxpjF7dy/UxQkEQQoz62qo51gHxufLblc9Y0s07TkVTV93p8pcRN27jOuphmji0RxZaZefL5LInDBwwSKUKuVIeHgLN/84jS1hiZCWm4uBbnVg8rTRZNUboZElkGhgihqftoBVbhCub72NxMJRGNvfDdu8f0Z44D3k40n5KlKiEa/Wh10VW5jqJuDPgFAkWdZG7S++gac0AaEXz+H0tgugziMxeoIX4DMNQzcchF9jBc6u3ofY+jOxYWoXFN+9hgRJNZjrvP5wHZcvY+y9KM59jAs7vsfJ0LKX61bvh3kzO8A0NwWBF4/gqF8xAu6cQ0HUA2SXAIHbJ+PnciswY0ALqNVK5GZ2gFeLM/h1y0EEhcWja/M6MCn38n0aGxrC0sL86XflYGNtCl1zM1gCKPprZkiOTgJ0TVClqiWkkKHHt8ORe9QHK2ZHwOkzNzgZ5SM2IR3yiwexIPoikBqOrOQ8BJ6ywc0cHVibmcC0nDUqftYDDd/w98Hlyxh7L/SMLdG0+xTYdyh7uY6hDcwAqJQlKMxOQUJkAhIi/1qe9uAqAhOeXI1PItGDhbUdLNzd0c4vEg+NDaCraZsp0hHzuAC6Zk6oaqELwAw1Ow/Et03ao0fgGazZtBqbMtTIhy4cHNzQ78sOqGb0JGoWtRv71WpYJDxGJoCKAsPyqWaMsbekhlIZh7jwDERHhiDjFbeS6Mpg9UkD1K9f9r969uWhB0BWsR4GLjyFgMC7CAi8hKUDmqKCAeA+7wK2VNmKVs1bYPrs7QjPAPLSUqCs1xKdPnOEtewVA79GUVoSUuS5MK9ZC2YSAKlnMfW7lQhRVEPj9l9impcrKshNUN4mH8GPkpGia4Xq9a1RFPUAMR0GYkStYiTFe+OXfSGIfxyJq1evIjql4LXjcvkyxt6CG0ZM7QGrpMtYOWs5gnUqo5J+FK753UFCombXjNaR6MKgnDksLcvD0tICpuWMIJPpw8jUAmbt2+BT6zT4HFmMnp5umHAsH4269ELj2maQPN/NSsi/uhcHE/WRHhyGLZMnY7PfZaTpp+CQzyFsm/kLIvT0oAhdh7UnHyH9cSqU+eaoXcPyyQcrSAmbZj1R9cpc9GzUHMOP6qPPnr04uHIROqmuY1m/lnDpNAMxld3QwqAhxh35Fe1tEuA3fxBGTzqGUlNH1LAp9+oH+Oxx8vV8/3s6tGuLEz5n+JKSH5GJ48fgqyHD+Hq+/4/wli9jjGkBH3BjH6WkwOOITALyoQfLqrXRwKEWLPQBQI6MB/fg/zAVOlIr1HR0QR3bl98BZD+8gduR6VAoAfvm3eBQocwhGHsrZZZv2p+ncPFOPPKLy1hoVAUuLVvAsboV9MpY/K8oSsddv4u4F5MNpdoaDVt1QIsGpgCUyIi+B/8bgUh+vnvJEq69e8HZUgpAhbzHEQi49AdiCwDABPXadoBrrQqQSYDoixtw8SEAY2vU/dQNreuUf1+PiP3L8hKDccc3APvOPULNbmMxa+6T8i2IvoCty35Hoo0dbKkEQdceoP3IAWhub/w8K898gNPrVuNMRB76b+fyZf+OMstXoiuDLMUPS3ZeQwk1xpezvGAPACW5iAx6AOPyNVDvvZVvOoK8d2Ldjt3wj8tBqbo8HAL+xMS589GmUhbCrx7Gr8sP4OGz8q3ghU09ez5P60h0oa9Igb/PGVwLLUCt62mYvWI4mlUwgURXFxmxl5Fo5AmHZv/2NYzY+1TPawr0DJfi9LkXT/h/jJu79sM7pgbWL5+O+kXXsXjQNOyyqIka0z/Hs46t3NQLLT/ZiXORedqYOvuPKLN8req7o0f+fSzeexMqdW10+OrrJxe1KFUgPTETKkMTaHhWh7CCqFD8qTCDx7hF+FIejT0/rIL/rRPYe20QmrVTQVmuOvot3IzKzzZcylWHq6X06TdSmFSsjTadekAhAwr2XUbYjT34aYUN1i3oC7tWgzHYRBeBJT3RvKaB8NwWL5yPxMRErN+4+Z093o9aST6iLu3AyuMhqFKnMWxNlYgMDYZ+s9EY3DIbBxYcQKqJIzqOGodONV6ORp9egk1nY1FQ1rsxCwf0GtQbn9W3+WuDQCKFvmV5WL54u/gg+NyJRb6hI0xNAYmuKQz185AQGoS4/M9RwaSsSatRkB6C42vX4WYaYOvqhd7dvFBTEoST+/fjQnAeSp9d2tDcFs29vsaglrZl3REDEB4ehjWrVqKzhwe8unbT9nS06s32+ZYqkBhyG3fSDdG2fRO87R+nzoq6hv2bl+JiVFkzMoLdZ6Mxe2JbWAIwqOyMLr0awdTEBDJVEcxifBB4OAufVDFDQtRxHFm/BzHVasKubjN4efRCuwZWkP3PYUQ9lK/jjgmjK2DNqi24+/sKjKpoi9OTmsLYuBwMJGLFu3HDrzh31hdRkZFQKPhPsL8xXT3om5lAcc8XB5IkGD/SDRaXY3Fk+UQkFy7GZBcluq7cgywrBzSd3gYWL0RtmvTC19WKXriG6wv0TFGpqgWkL/5MRwcSA0MYAHh+pcH8PGQqS1BaxQaVnn/8U46CwmikpgEos3wl0IUMpcWZSDfyQt+mrqikuoOtS5Zh73kp+m6chMZ312HA+mA4fekFt3pWb/lL+rhlZWbi/Dlf3L93Fzu2b8Os2T+gSZNPtT0trXht+SoV3hjf8hwkehXQtM80fNb+7Qc1t/sUg2dtQx9lGQt1dKArM4HZswkam8P62TJpOSgU8TCQ9YKbkxLxu6/jclw8lAmJiL3lB//Dm7Fv2EbsGPUp9KR/242ga4wKnw3FQkUshv90HFFbx2Bc5RNY0OjN533K53csWjgPBfn5kMu5dIVJpNA3sYC5PlClsi3qOTgg9ncjqDKKUb1uXdS0dIH98kDkZefg708N4wq1UP9d7Xs10IcMwJMeV0OtLoGyrOciAHVJIYJ9N+Jxq5+w1e0TlDPShzTqGgIiYpFU3gPNHZxQ28gZ9muDoVuiCyNLPn3vTaSlpSItLRWjhg+DvkwfZ3wvwMzc/PXBj8hry1fPoAfWXp8D61uXcDVJg/2ilIg9e6MwcKDb8x9JdGUwNrWEUZkBHUBHUuY5cKS+Dt8j9fHd+cVoYQlg4i48mAhkZz/ETe/NWL31FAJWzMI299MYVaeMKwrpGqJ27+VYGn8PwzdH4tK8TjCftgCtXlHAKpUKACE6OhqenV79qqNSvYcrL79DH8Kp3VJdKaTSZ9uqupDpSwGp9OWt1xcEre+BcZvuIbuojIU2n2Pmkpno26oGXvce5slJ9C/+xBDGRnaoYF327e+v7o2DsWlo3NsdxV1qwkwHQPkK+MTYGAahiYhXlkASF4tHMgNUrWrz8m6O90ytUn3wz8Un69RfcnNzAABNGjtCJpPhfkgYAEBHRwKJ5OM+E/bNdjvoGaFGyy54aTdcSQGysvIgL1VDz6wijEtSkSOXQE9fBqmkBAq1ASyNJXh4dCFWBzWFm6cCVSyerBoZ4ZewfeUcnA4va0blUMN9Cn6e1REvvoFTFeXjxpa7cDrnjb5VCSUKOVR6RjCUAhYWNeE5bCk8m9aF1/A1iEsgoM6rH07TKXswN7YH5p9OxJntW1F9bd8yb/eFlwciwsNe++tp59b6tbf5kKSmpGh7CsJcxnjDb4xIgoC/F1GDJuhY1QYPomLxUEmwLy2FWm0Ec6taqPSKE10ceq3GV/mz8dOxdViy3QJz+jSBmWVrTFs8HoarN2N1tw5Q68jQe8w6TBom8DbqXzBh3Bjoy97yiuL/smJFWTvtny4rLkbdWtUhk8nQf8BAfD977nuc2fv3+vIloLgYePkImxxplzZg6fZbSFSkoLTRt/BSb8fec6mQlq+HGg2LkazXFjPdpNiw+zbyssMw9aAj9o168ukbq3rtMG1zO0x7w0kqcxMRsH8jblT5HO5pQbiVrERKchx0azdGlVIlrGxsYW1tBthVR6tqHVCv1suvmCqVCgqFAsYqFQApABv0XLcOiV3G4nDuq8f1OX0W/fr0hEIhR2hIyCtvd+XqzTd8JB+GDu3aamdgtQoleZnIKgHk2blIjnmI1KJClEKOx2mpSM1KhJxUUOelIC1HiQrmmp5Po0BycCCCb9xHPlRQZiYiPDQSNg1s0WloR5yfF4GrvreRU/InCi2aofOAjqj+QrowJQbJeSUgAnJJBdce8zA64issXjMH2bFjMXGIK9KPXUG83Vgs6F8R+lIAEiA9NgXGVW1g9N7OwXzZug2bPvhPuN28cR1fDfqyzGUSiQSNGrugfoMGH33xAq8o35yYANwJjISyVA2VOg6XvC/Ask0rOFR++qYuLxi79p3H42rd0LtuDNYvnYrIFVfwQ7X5WLwnFuaN5mBG/9aoij/hv24Pbteb8Lx4RZXkJ+PaoWVYtO00EjJ3YTsA6JmgrtdUjMpfjUnrA1GnRXd81r41qllko/qoMfC0ffaw1CjKSsCdK+fgG5WFiln6sG7tCCsTfQCNMerX76H46eA/jn/g0FGkpqZgyuSJCPD30+gxsKdKlSgtLIa5a1eYwwQJgXdQVKMuWlsAitRohKXnwrHT55CVz0FcohwNNS7ffNw/dQBnk6Ww69IOQC78fC+ignl3tGoxGHPG7sPGS3sQrVcLn09dhM6uL+8sSA8NRHbVpujoCeiF+yKypTsMK34KzzYA8iIRG62HhPhkXD87HqfXPH0brWeIKs37YtrUKfBoYPY/M2Kv1/WLbli2YpW2p/HelFm+RRmxiCixRf/BQ5/cKDUcyblN/yrfnCykyuWIibyLULNq6DB0GGpW0UeNyu1Q99haRNy4h/jWjVCxyttPsLQ4B9mGtdGhxws75XQNUKl5SzSpZoch+ZWRnK9CwqMYWNX0gFeN8pA+3/AllBRmIT1fjnJGhijMykJBcenT8gVkth0x5lsThBn/z7AvqVjRBgsX/YQDB/bi3p07CAoKfPsH9l+kb4Ia7cdg1St3n3ui3TsZyBqdZ6xD51csrdV1DFZ0fXXart0E/Pj3icxZh37Pvs6MwPZLFeHg8SVqWxtCogMoix4j8mEM7jzK5vIV1L1HT1iWL48ZM2dreyrvVZnlW9m1H0a7/kOqgiM6tWyO9FtFIJUKqkoOQMBabE9Ih7JqFST7HcH6tUYYN6oRqtaygW7wSezwd8OQZuKHI4ys6qPXwPqvWFoLg8f901toKcxtG6H72Ffsi5PowaRWG/zTQ33Gzt4eM2bOxv3793D3ThAOHtiHh1FlnSvHPno6RZBIlCivVkFdqgJJAL2q9mhlXxkNnUWu6Prf1tnDE41dmqDrF91gafnf+3SpZtd2MKiMlv3HwNIpCmkKJWBWBRXU+rCsbwRzc3P0TE6GwqAiKpvao9bIGVgekwKjiu/rYxn/LicnZzg5OcPBwQlTJk9AUlKitqfE3jfL+ug2fCwcopORoVSDdHSga2kFu2q1YGvDp5q9iY6dPDB12kzYVqum7alojcYX1jGoaIdGFe1e+InTC186//W1pSXa1dR0lA+XS5Mm2LRlO5/v+58kg7m9I1zsHbU9kf93HBydcPjoCVS0sUGlSpW0PR2t4quavYU6detqewqM/b9iYmIC50baPSXvQ/Fxn8XMGGMfKC5fxhjTAi5fxhjTAi5fxhjTAi5fxhjTAi5fxhjTAi5fxhjTAi5fxhjTAi5fxhjTAi5fxhjTAi5fxhjTAi5fxhjTAi5fxhjTAi5fxhjTAi5fxhjTAi5fxhjTAi5fxhjTAv5LFv9Rnp3aQ0dHR9vTYO9IRkY6vhoy7KWfhYU9wMH9+/Dj/IXC9zd4YH9s2bYTMpn43178bed2WFtXgIdnF+FsUlISViz7Gb+sWiOcHTdmJH6cvxBWVtavv/HfHPM+iuJiBfr1HyCczc/Pw7eTJmDLtp1COR0iIuHRAIwdPQJXLl/SJMq0TKlUQsP/dvYB09PTe+kFlYigUqmgqyu+jaVUKqGnp6fRPFQqFXR0dCCRiL+xJiKUqlTQ03DOurp60GSbQqVSAyBIpVLxMF7+fY2bMAmjx4x7fYjeEZWqlK5cvkRzZs/UKJ+dnU1NmzgL5+RyOS1f+hO5ujhTUOBtoaxaraY7QYE0cfwY4XGJiHJycsjdrbVwrri4mDZtXE+uLs506eIF4XxkZAR9PXiAcK4gP58yMzOo+xddSC6XC+cVCgWtWb2SXF2c6eaN64JpNYUEB5Ori7PQc6SwsJAyMzNo8MD+lJqaIjSiUqkkn99PkKuLM/22Y7vgfImysjKpndtnwrmioiLKzMygcWNGUlRkpFBWpVLRH1cuk6uLM61dvVJ4bE3XIyKiosJCmjH9Owq8fUs4W1paSufOnqGFC+YJZ3Nycsj989bUqoWrcFYul9OihfM0Wo9UKhX53bxB076bLJzNy82l7l90IVcXzX7XRETvpHxDQ0Po2tU/aOaMqcLZhIR4Cg0NoUED+pFarRbK5uXl0tYtm+jI4YPC4xIRBQXepnFjRmmUjYt7RCOHD6W8vFyhXGFhIe3bu5t2bN8qPGZkRASFhoZoVLypqSn04w/fU1fPTpSUmCiUVSgUFBoaQr/t3E779u4WHjsiPIzu379HI74ZIpTLyEinn5csoq6enSg8PEwoq1Qq6dzZM7RooXgZEBFFRUVSr+5dhXPZ2dm0ds0q6urZiW7fChDKqtXqJ+vRdPH1iIgoNiaGBg/sL7weERFlZmbSL8uX0uVLF4WzoaEhdOniBfrxh9nC2fi4OBo5fCjl5oqtR0RPSnvD+nV08sRx4SwRkb/fTZoyeYJwLjExkSZPHCe8Hv3dW5fvtat/0IhvhtD3M6cLZyMjI2jBvLk04pshlJWZKZTNy82lXb/toH179wiPS0R05fIlmjh+rHAuNiaGLl44T3N/+J4S4uOFsvKiIjqwfx9t2bxReNzA27do0oRxwgVGRJSYkEArf1lOfjdvCGeVSiV5Hz1CI74ZQr/tFN96vBXgT+PHjqIxo4YL5VJSUmj9ujV04fw54TGJiE75/E6LNNgKexAaQhcvnKcpkyeSQqEQymZmZtLWLZvoxHFv4XGJiM6fO0uzZkwTzkVGRtDFC+dp1oyplJmZIZxPT0ujTRt+pTOnfYSzV65cohHfDNGoeMPDwujHH2ZTfHyccDYnO5t2bNuq0YbXjevX6OKF8zR1yiThbPTDKFq8cD6Fhz0Qzv7dWx1wO3P6FG7fCsCmLduFs+FhD+Drewbde/ZCgwYNhbIKuRyHDx+EoaEh+n8pvoPc5/eTCAq8jVVr1gnlYqKjccrnJDIyMjBg0GBUtbV94+y+vbuhVCqhKi3FN8NHCo17/fpVXL96FT/OXwAzM3OhbFJiIk4c90ZjFxc0a95CKAsAB/bvRW5OjvD/8e1bAYiKisSjR7FY8vNyGBsbv3E2PT0Nx72PoHqNmmjn3l50yjiwby8SEuIxa/YPQrn79+/hwvlzyMvNxYxZs4UONuXl5sL7yCFYWVuj6xfdRacM76OHERIcjEVLfhbKhYeFwdf3NLKzsjBq9DhYWpYXymdlZcHb+wiqVK2KTp09hbKnfE4i8PZtjdb/kJBgnD/ri/5fDoCtbTWhbGFhAY4cOQQzMzP07NVHKHv+3FkE+PtBqVRi6fKVQtmoqEicOeUDD88uqFO3nlC2LBodcLt44Tzu378HmUyGocOGw9DQUCgfERGOs75n0LatGxydnEWHx8oVy2BbrRp69e4rlDvrewahoSGQyWQYMXK00AGFuLhHOH7MG82bt4Br02ZC427c8CtIrYaJqSkGDvpKKPvHlcsI/vM+evXpCxubSkLZtNRU7N+3B40au6B1m7ZCWQBYt3Y1DA0NMeybEUK5gAB/3Arwh65Uit59+wkdfc7Ly8X2bVvRoEFDtO/QUWjcgwf2ISkpCYYGBhg9drxQ9v79e7h65TI6dOyMOnXrCmVLSkqwft0a1KhZC15dvxDKAsCe3buQl5eLMYJzjoyIgK/vabRp4wYnZ/H16JcVyyDR0UGduvXQ2UOseI8eOYSUlBSMGDkKenr6QtnQ0BBcvHAe7dzbC294/bJiGXR0dGBnZ4/uPXoKZU/5nMSj2FgM/nooTExMhLIx0dHw+f0EWn3WGo1dmghlX0V4y/fSxQuIjIyAvb093D53Fyre7OxsLFm0AOWtrODh2QUODo6iw2PG9O/QunVb4dNYzvqeQdyjWNjb28O9fUeh4k1LS8We3bvQubOH8C9+zapfYGNTCX369RfKAcC1q38gNCQY3Xv0Ei7egoICbNiwDh06dkZzwS3eLZs3IioyEq5Nmwq/wAUF3oa/30107doN9tWrC2XVajWWLf0J7dt3FH6x2LdnN5SlStjb26Nbd7GVMuxBKC6cP4cuXboKFy8AzJ3zPdq5t4d7+w7C2Z07tkFXqiv8Ahf36BGOHTsCD48ucHB0Eh535vSpcG3aFObmFnD7vJ1Q9tDBAygqLMDgr4YIF29UVCROn/KBZxcv1K/fQCi7YN5cNHRwgJGRMTp26iyU9fn9JFIeJ6PflwOFizc5KQkHD+5D585d4NyokVD2H4nso7h+7Sqt/GUZPX78WHj/hkqlojGjhtPNG9cpIiJcOL9w/o80aEA/un7tqnD24oXztHbNKkpLTRXOyuVymjBuNIWGhghnV/6ynE4c96aSkhLhbIC/Hy1f+hMlJSUJZ4mIRnwzhO7fuyuc27JpAx06sJ9u3rhOpaWlQtnQkGBaOP9Hiot7JDwuEdFXg74UPmOFiGj/3j2067cdlKfBQZtHj2JpzvczKTr6oXCWiGjk8KEU4O+nUXbnjm20b+9uKijIF8plZKTT1CmTKSJcfD0iIvp20gSN1iMioiOHD9H2bVsoJztbKCeXy2nQgH40c/pUiooSOwOEiOiH2bM03v/ve+YUbfh1LWWkpwtn8/JyafLE8RT24O338f7dG5fv3Tt3aM73M4UPjD3Tsb0bxceJ71gnIlq8cD6d9T1DMdHRwkdy/f1u0oL5cyk7O0ujsb08O1JCgtiBNSKitatX0jHvI8IHbYiIQkNCaOb07ygjQ/zgCRGRR0d3inskXoA7d2yjPbt/o6KiIuFsQnw8jR87mtLSxF/giIj69upOMTHRwjnvo4dp04ZfqSBfrMCIiHJysmnY14MpRYONCSKi4UO/ptCQYOHc+XNnqX27NrRj2xYqLCwUyqrVKurbuwclJWl2pP3bSePpVoC/RmdE+Px+ktauWUV5eXnCWS+PjhQTHU3JycnC2bk/fE+XL10U3hggIvrjj8v085JFlJOTI5z16NSeenzRhRITE4Szb+K15SuXy8mhQR0a8tVAKi4uFh6gf9+e5NCgDhUViT3JnlmxfCkdP3aUVCqVcDY87AGNHvmNRvMmImrZrIlGRbR1yyba9dsOjZ4sycnJNKB/H43n3LljO8rNFX+iHT50gNatWUVKpVI4W1RURF06d9DohYaIqF+fnsJnjhARnTvrS4sWzNNozkRErVs20+h8ZyKiUcOHUUhwsHCJBfj70fSpU6iosFCjeTs1rEtyufhzkoho2nff0s0b1zUq3qt/XKEfZs/S6F2cpusR0ZMNrzOnT2m0/t+7d5cmTRir0Zw9OrlTTk6OxvN+E+/sQxYfmz69umv0Cq9Nw4d9/a+9Sv9bpkyeSA802KXD3p/IiHCNP4ikLSkpj2nIVwO1PY1/pPHHixljjGmOr2rGGGNawOXLGGNawOXLGGNawOXLGGNawOXLGGNawOXLGGNawOXLGGNawOXLGGNawHnCn28AAAA7SURBVOXLGGNawOXLGGNawOXLGGNawOXLGGNawOXLGGNawOXLGGNawOXLGGNawOXLGGNawOXLGGNa8H/0Z2tlVKzxVAAAAABJRU5ErkJggg==)
Physics-General
Physics-
In the system shown, the acceleration of the wedge of mass 5M is (there is no friction anywhere)
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)
In the system shown, the acceleration of the wedge of mass 5M is (there is no friction anywhere)
![](data:image/png;base64,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)
Physics-General
Physics-
A particle starts at ‘A’ with initial speed
. It moves along a circular path under the action of a variable
![](data:image/png;base64,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)
force which is always directed towards ‘B”. A and B are end points of a diameter. When it reaches the point ‘P’ as shown , the speed is (Neglect the effect of gravity).
A particle starts at ‘A’ with initial speed
. It moves along a circular path under the action of a variable
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAUkAAAC/CAYAAABzNi4YAAAgAElEQVR4nO3dd1yVdf/H8ddhHED2EAfiQAVRXDlyoVnmzNRCM82VWlZmtu7qZ6mVDa0M0/R25Oq21NIs09RSHBCmuBDBBbIRlX2AwzrX7w/ThoioBy7O8fN8PPzjnHNxXW8C3l3je30vjaIoCkIIIcploXYAIYSoyaQkhRCiAlKSQghRASlJIYSogJSkEEJUQEpSCCEqICUphBAVkJIUQogKSEkKIUQFpCSFEKIClSrJ6dOn4+Hhwbx584yy0bKyMjZs2ECPHj04evSoUdYphKheTz31FD169FA7hlHk5+fzxBNPcN999xEdHf2PzzRy77YQQkBycjJLlixh27ZtHD9+/Pr7UpJCCFEBOScphBAVkJIUQogKSEkKIUQFpCSFEKICUpJCCFEBKUkhhKiAldoBagSllPzsLApKy/nMygprq1o4OtpgWe3BzFNxcTE5OTnY29tTq1YtteMIUSEpSaBEH8vK557gvwcvk5hwCYvaXnjVd8fOsgSdUy1sXZ/gg1mD6ebfDDet2mlN17W7q8LDw5k1axYffPABzz77rMqphKiYDCa/prSAM1uWMG38J1g8/QGfzplIK6dMotev4IVZ7xCWFMAbP2xhRj9vbNXOakLCw8O5dOkSAEOHDr3+/qRJk1i+fLlasYSoNNmTvMbKCltvN9zqQvb1N91oOfI/LEnbjP9rx/j607U81mMG7e1VzGkiDh06xKFDh1i8eDExMTH/+Kxhw4b07t1bpWRC3B4pyUpo0Wsw3oYIihJiSMhBSvIm0tPT+fzzzwEIDQ0lLCys3OX8/f0ZNWpUdUYT4o5JSVZGkZ4CwFrtHDVEdnY2q1atIiIi4h/v5+TksG3btlt+fWRkJKNHj77h/VmzZuHr62u0nEIYg5RkJRzetYEMCyt8/O/H30PtNFUnNzeX5cuX8+OPP1a4XHFxMT169GDs2LH/uDodHx9fqZL09vZmypQp11+npqZSUFDA2LFj0WorvjL25Zdf0rp161tuQwhjkZKsUDqHf3iP4YsuYGPXlZfff5pmZnB1OzExkaeeeorExMR/vG8wGBg4cCALFy7ExcWlwnU4Ozvj5OSEhcVfQ227dOlCz549r79+8803Wb9+/Q1f6+rqSmBg4PXXpaWlGAwGHnroISq6jhgbG8vQoUMpKyu74bOXXnqJyZMn4+DgUGFuIW6bIv5UpMQfXKmMbIri3bCh0r1uXcXNwkKx0GiUzp3HKzvPGRSD2hHvUG5urjJr1izFwsLi+r/vvvtOOXLkiFJWVvaPfwaD8b5Lg8Fwfb1OTk4KoACKRqNRJk+efEfr/HfesrIyJSUlRRk2bNg/vr9jx44pMTExRvtexL1L9iRvUIdWQ2b+OQRI7SyVYzAYyM3NJT8/H4Dz588zbtw4Skv/Gh3fv39/Ll68SO3atastl0ajQaPRAFfPV16zb98+Ro8ezfz583nllVdua51/33O9pn79+mzevPn665iYGB5++OHrrw0GA48++ihTp07F1dX1+vuenp5YW8uZZlExKUkzkJWVxYwZM1i6dOn190JDQ+nevbuKqW6uV69eJCcnV9n6/f39/7H+jIwMZsyYccO5zMjISDm/KW5JStJEXblyhZCQEAB0Oh0Ajz76KDY2NgC4u7urlq2m0Wq1dOjQgeHDhwNXL1AZDAZ27drF6dOncXd3p0uXLnKLpCiXlOQ1ZWWUZOrQ5RRQmH0FfV4xONWsqzQ5OTls2rSJ7OxsUlJSyMzMxM3NDYA+ffowcOBA+UMvh6OjI5MnT2by5MkAXLp0iZKSEubPn09iYiI6nY69e/fi4uJC165dadasGa6urlhZyZ+HkNsSASgrTuGX4I/4bvcxdu/6ndLG7egV+CjDpz7NwA6NqKXSzBZFRUWEhISwa9cu4Or4RGdnZ7y9vdFqtYwaNep6SYo7U1payqlTp9izZw95eXkkJydTUFCAm5sbVlZWvP7669SrV0/tmEJFUpKAoTSb6L2/cTr77+864NOxMwEN3dBW84RyBoOBQ4cO8fHHH+Pq6kqrVq3w8PDAwcGBrl27Ur9+/esXRITx6PV6jh07RkpKCnB1qNSOHTvw9fXlnXfeoU6dOionFGqQkqwhUlJSyM/P55lnnqGgoAB7e3umTZtGQEAAXl5eaLVaOfyrZgUFBURGRnLw4EFWrVqFre3VqU0mTpzI6NGjsbeX+1PvBVKSKrt06RJvvfUWP//8MwaDgZUrV9KxY0csLS1xd3fH0lJmsVSbXq8nKyuLrKwsUlNTWbZsGQcOHGDFihUMGDCg3GFJwnxISaokLy+PTz/9lPfee4+ZM2fy2muv4ejoqHYsUUmxsbH069eP2NhYGUpk5uT4TQX5+fkkJCRQXFxMw4YNcXV1lXOMJsba2poGDRqg1+tJSUnBwcEBW1tbateuLadFzIzsSVaTgoICjh07RklJCREREWzcuJG+ffvyyiuvyBVqExYXF8f48ePJz8+nYcOGjB49mrZt29K4cWO5m8dMSElWsYKCAkJDQ4mMjGT//v0YDAZ8fX1588038fT0VDueMAKDwUBSUhLnzp1j6dKluLu70759ex588EF8fHzkvLKJk5KsIoWFhezfv5+9e/eSkZGBs7MzL7zwAra2ttStW1fteKKKFBQUsGvXLn799VcA6tWrx/jx47GxsanW++aF8UhJGpHBYCA2NpaEhATWr1+PlZUVPj4+DBw4EH9/f9mjuIfodDp27tzJiRMnOHfuHAB+fn5MnToVDw8znpTUDElJGtHgwYPJyMigXr16PPLII3To0IEWLVrcciJZYb50Oh0HDhygpKSEc+fOkZiYyPvvv4+Tk4lMMSWkJI0hPj6eUaNGER4eDly9j3r79u1y4l78w5UrV1i2bBnffvstI0eOZOrUqTg7O6sdS9yCjII1Ar1eT2Rk5PXXlpaWUpDiBg4ODri6uhIVFUVSUtI/5vsUNZeU5B1SFIXY2Fh69uxJhw4d+PXXX8nJycHW1paCggLi4uLUjihqGFtbW5577jkyMjLQarV4e3uzcOFCDh48KIVZg8nh9m1QFIWcnBzS09PJy8vjiy++YOjQoQwePBhra2sMBgNnzpwhLCyM33//nWXLlsnAYnFTWVlZTJkyhUOHDrFo0SJ8fX1p1KiRnMOuYeQv+Dakp6ezZMkSdu/ejZWVFRMmTKB///7XD60tLCzw9/cnNzeX/fv3c+LECTp06KByalFTubq6EhwcTEFBAdOnT0en0zFlyhSGDRsmRVmDSElWUmZmJsuWLQNgy5Yt1KpV66YT3LZt25aAgAA2bdpEmzZt5PykuKlrc1Vu3bqV5ORkZsyYgaIoDBs27Pos80Jdck6yEnJycpgzZw4WFha8/vrreHh4VDgDuK2tLd26dSMvL4+QkBCKioqqMa0wVV5eXsyYMYODBw+yceNG9Hq92pEEck6yQpcvX+bzzz/nwoULtG7dmunTp1f68QhFRUXs37+f77//nueee4527dpVcVphDgwGA6dOneKrr74iMzMTGxsbRo8eTffu3eWIRCWyJ1mB3NxcNm7cyPr16xk8ePBtPT/GxsaGTp06Xb/QI0RlWFhY0LhxY5ydnfn6669ZsWIFMTExlJWVqR3tniUlWY68vDxSUlJ4++23mTlzJlFRUfj6+t72ehwdHbG3tycpKUkOuUWl2dvbM3XqVA4ePMiuXbvYvn07R44cQQ76VKKIf8jLy1P+85//KPb29sqKFSuUgoKCu1rfuXPnlJ49eyrR0dFGSijuFQaDQSkrK1MuXLigtG7dWjl16pTake5Jsif5N7m5uXzxxRdoNBqio6MZPXo0dnZ2d7XOZs2a4ebmxtmzZykpKZHDJlFpGo3m+uH3zp076dOnD1FRURgMBrWj3VPkwg1Xp7c6c+YM+/btIz4+nvfff9+oj1JISkpi4sSJjB07FgcHB4YOHWq0dYt7R1paGn379iU4OJjGjRvj5eWFlZWV3LBQxe7pktTr9SiKwtKlS9m6dSvt27fnjTfeqJJ5/zIyMmjSpAkAqampODg4GH0bwvxFR0fz6quv4uzsTI8ePWjfvj3333+/FGUVumdLsrCwkLVr15KRkUFsbCyfffYZLi4uVbrNsWPHotfrCQwM5MUXX6zSbQnzVVZWRnh4OEuWLKF27do8+eSTdOjQQYqyityzJZmenk5gYCDnzp0jISGBhg0bVvk2T548SW5uLs8++yxRUVFVvj1hvgoLC0lPTyc4OJh69eoxbdq0uz5/Lsp3T1640el0LFq0iLFjx/LZZ5/h7u5eLdtt0KABDRo0oKSkhEuXLlXLNoV50mq1eHh4MGzYMBISEjh06JBcFKwi99yepE6nY968edjb2zNhwgScnJywtbWttu0XFxcTHBxMcnIyX3zxRbVtV5in0tJSDh8+zIIFC3j11Vfp2LGjPJ7YyO6ZPcn8/HwWLFhA27ZtKS0tZezYsdSuXbtaCxKu7gH07duXyMhIsrKyqnXbwvxYWVnRuXNnXnrpJaZNm4avry8xMTEyn6kR3RN7kiUlJWzYsIFt27YRHByMu7u7qie5CwsL+eqrr9i/fz8LFy6kTp06qmUR5kFRFEpKSkhMTKRVq1Y0a9aMkJAQeWyxEZh1SZaWlnLixAkSEhJYtWoVa9aswc3NTe1YwNXhRwsXLiQvL4/Zs2djYXHP7NSLKpaUlERsbCwfffQR//3vf2nUqJH8ft0Fs/4vt2XLFsaPH8/KlStZvXp1jSlIuDqdWpMmTbh06RIXLlxQO44wI97e3vTo0YOpU6cyc+ZMTp06pXYkk2bWJTlx4kS2bt3K0qVLq+0K9u3o3bs3ACEhISonEebGysqKPn36EBAQwObNm9WOY9LMtiTz8/NRFAUnJ6cae3eLra0t9vb26PV6eRCUMDorKytsbW0pKiqipKRE7TgmyyxLMi8vj7lz5zJx4kTc3Nxq7LON7e3t6du3LzExMYSHh5OamirTYQmjsba25v777yc3N5eQkBApyjtkdvcx5eXl8eGHH+Ls7MzUqVPVjnNLvXr1wmAwsGzZMi5fvszmzZtva3JfISpy3333UVRUxPr167G2tiYwMFBuX7xNZrUnqdPp+Oijj3Bzc2PSpEkmMfzB1taWhx9+mPT0dHbu3MmZM2fUjiTMiFarpXv37kyYMIElS5Zw5MgR0tLS1I5lUsxmCFBWVhZz587F3t6e559/Hjc3N5O68yAiIoIrV67w/PPPy0BgYXQGg4GYmBgmTpxIUlISu3fvpkWLFmrHMglmU5JfffUVJ0+eNPpckNXN2dmZ0NBQWrdurXYUYYZSUlIoLi6mffv2ZGdnqx3HJJj84XZJSQnx8fFcuXIFV1dXky5IgNDQUHr06KF2DGGmvLy8aNKkCWVlZaSkpKgdxySYfEnm5ORw9OhRdDqdWdzed+2iTXFxscpJhDnz9/cnOjparnhXgklf5srOzmbFihWEhYXRtWtXRo4cqXaku9a0aVMCAwPZuHEjQ4cOrbFjPIVpW7t2Le+++y46nY6BAwdiY2OjdqRKK8q9SHTEPs5e/uf7Tbo/RucG155NXsSVuGiOHT5L5p/vuPr35MGAulhZ3N61CpMtycuXL/P5559jaWnJmjVrsLGxwd7eXu1YRrFw4ULmzp1LQUEBzzzzjNpxhBny8/Nj1qxZLFq0iMLCQoYMGWIyfz+lhTmcj9jBktX7OBxzgQL3tjz+WA+CWg75W0mWknflPGEb5rFm31E0Lfsz4bUAHmhV97a3Zzl79uzZxv0WqsdLL71EnTp1rj/vQ6vVqh3JaFxcXKhTpw7z589nyJAhMuO0MDqNRoObmxve3t5s27aN4uJiWrZsqXasStE6eNC8bSC+tXKJijpBUtNRrPxiFv2aO/DXPqIWV6/m+HrmkVDiwZDnZvFC31bYWd3+GUaTPCeZmZnJxo0bmT59ulkejmo0Gpo2bUrXrl1ZuXKl2nGEmbKwsKBVq1Y0b96cP/74A71er3akStM6uHP/gAcJDGiM/flkkvXF3Pig3VKyrtji2+lx+ndujb215R1ty+RKMjMzk/Hjx7NgwQKzvjPF1dWVrl278scff3D27FlycnLUjiTMkKWlJf369UOn0/Htt9+SlpZmMvMIaOt345G+bWhs2MryH6MpLvlXTeancCJZwbW2D3Wd76wgwcRKMjMzkwkTJjBu3DhGjRqldpwqZWFhQffu3WnevDndunVj69atakcSZqpJkya89dZb7Nmzh7Zt2xIWFobBcON+WY1jZU+XoSN5oFltwr/fQ2zJP8s9L/EcJe4O+LZvg+NdNJ3JlKSiKJSWlpKbm4uzszPW1ta3/iITp9Vqsba2JiMjw6QOhYRpsbCwwNHREYPBQFZWFoWFhSYz0YqVd2ce7lIfh5Pv8em2Av5KfZkTYQlkXqhL0yZW3M29dzW+JA0GA8nJyRw4cIDXX3+dqVOn0qtXr3tipmVHR0f8/Pzw8vIiNTWVS5cumcwvrzAtLi4uLFq0iAsXLvDxxx/z22+/mchYXU+GjBuFt6c7az+cT/Sfwz7L0tO4XHQZ1y4BNLjhaxTKinO5GBdHXFwSl7IKqOgEQ41vmtTUVBYsWMAbb7zBww8/zCOPPHJP7EVeM2jQIPbu3UthYSFLliyRW8lElXF1daVBgwZ8//33zJ07l/Xr16sdqXLa9OJpfy+0kZtYHZ4FhhJSk2JJyC3CJ6DxDYuX6eLZu/kTXhsxkYlPvciMjzdyOC2Hmw2rr9ElaTAYOHLkCBcvXmTr1q0EBQWZ1KBXY3BycqJZs2bMmDGDffv2cfr0admbFFXKw8OD7777jqlTp5rIBcMWBE3vR32bc/x33o9cLMwg9vRJsjweo4PXjUvHbX+bd5anMnZjCCE/zyPQ+jjL1m4jLqeo3LXX2JJUFIXTp0+zd+9e+vTpg4eHR7U//rUmcXBwYPDgwaxbt46iovJ/mEIYi7u7OyNGjODLL79UO0qluHcexVP3aSnZu4qVYYdJOHMJn/tbcOPw+Av8uOAn6o95h74+gJsvgwb5k3/sd8JjLlLeCYYaW5J6vZ6PP/6Ydu3a8fjjj6sdp0aYOHEiu3fv5uLFi2pHEfeAGTNm8PXXX5Obm6t2lFtzaccz43tQrA9j6YdfEmbZjYeal3MH0ZVw9h+3oHXTvw7D3T3q45x9majEDArKOTlZY0vy3LlzREREMHLkSLMcMH4nnJycePvtt5kyZQrx8fFqxxFmzsvLi6eeeoq3336by5cv3/oLbsPChQs5evSoUdfZYOjrjGtWRub5eDy7DaRBeTeq5eaQo/Gl7g3zceeTn19CWTkjn2psSebl5WFhYXHPnYO8lQ4dOhAaGkpeXp7aUYSZs7S0pEWLFkRERBh9CFpkZKTRixePQGZOfxwXpwE83MPlpotpNK7Y38advjW2JIOCgli9erXaMWqc5s2bEx4ezsCBA9WOIsycpaUl/fv3Z8KECcybN89o6507dy5ff/01w4cP5/Tp00ZbL2hp/PQaToZ/SPeb3YzXuAnNDEe4kPTXW1lZV8jLtaN+XQfKmwKixpWkwWDgzJkzGAwGOnbsqHacGsfS0pLWrVtTWFjIiRMn1I4jzJy9vT1NmjQhIyOD6OhoMjMz73p0hV6vp6ioiLy8PMrKyoyU9CqN1h4XZ7ubT29m0Z9HJhjYuCOEMgVQykhPjSe3bSO6NK5LeVN217iS3LNnD48//jgHDhxQO0qNtmPHDkaNGoVer5eJU0WV6tq1K126dGHIkCF88sknXLp0yWjrjouLq/ZbIPu98Bkd967lq/0xxOzdzNc/6ejy0Cg6+ruXu3yNKUm9Xk9eXh7Tpk1jy5Yt+Pr6qh2pRvP396dhw4asWrWKsLAwteMIM2Zvb8/kyZMJDQ0lKSmJ8PDwOy62lJQUYmNjr79+9NFH0el0xopaKXYtxvLR/EAOfzid6R/vxKn3cJ4Lug/XmyxfYybd3bVrF0ePHqVt27bUr19f7Tg1np2dHa+99hp9+vRh3LhxdOvWzazm1BQ1i52dHXZ2dnTt2pUDBw7QrVu3O3pk8y+//MLXX39dBQlvg8aKup2eZvnOpyu1eI3Yk9TpdGzYsIF3332XKVOmyCSzlWBhYUHLli159tlncXBw4KeffqKwsFDtWMLMPfXUUxw9epSYmBij3fn18ccfG2U9VaXGlOS1P3APDw+Tel62mlxdXZkyZQru7u789ttvFBQUqB1JmDlnZ2dsbGy4cuXKbR9ynzp1ijVr1tzw/kcffWSseFWiRpTktm3baNKkCYsXL6ZevXpqxzEZWq2Wpk2bMnz4cLRarZybFNVi6tSprFix4rbHTiYnJxMaGlruZ8OGDTNGtCqheklmZ2dz7NgxmjdvzoQJE3B1vdnpU/Fv1+YBbNmyJS4uLkRGRpKfn692LGHm+vbtS2JiIjExMUZb5549e4y2LmNTvSS3bNlCaWkpw4YNw9bWVg6174CFhQWTJ0/m+PHjhIeHqx1HmDmtVsu6desYMGCA2lGqhaolmZWVxfnz52ncuDF16tRRM4rJ8/b2pl69ely4cEH2JkWVa9euHba2tpU+xXPq1CkGDx7MSy+9hKIoTJo0iR07dqAoCo0aNcLS0pKAgIAqTn1nVCtJRVEIDQ3lzJkzTJo0Sa0YZmXGjBmEhISwatUqGWAuqtyePXsYMGBApabus7W1ZdKkSQQHB9/wWXx8PElJSfj5+VVFzLumWklmZWVx8OBBOnXqhIeHh1oxzErdunVZvHgxixYtMupdEUKUp3nz5nTq1Invv//+lss2bdqUxYsX3/Rze3t7Nm3aZMx4RqNaSaalpRESEsKTTz6pVgSz5OLigpWVlUylJqrFe++9V+OH8NwtVUpSURQuX76MjY0Nzs7OakQwa6NGjWLVqlVqxxD3gDp16lBaWkpaWpqJPOrh9qlSkoWFhSxevJhnnnkGJycnNSKYtRdeeIGNGzeSkJBAWlqa2nGEGfP29ubxxx9n8uTJ5Q4UNwfVXpJxcXGcPXuWqKgohg4dWt2bvyc4OzuzaNEigoKCmD59utpxhBnTarUMHTqUbdu2ERYWRmZmptqRjK7aS3LQoEEMHz6cJUuWyD3aVWjkyJFERERw/Phxrly5onYcYaY0Gg0tWrTg559/xsfHxywnyq72WYBSU1MB6NmzZ3Vv+p6i1Wo5fPgwFy5c4LHHHmPdunV4e3urHUuYIUdHRwYOHEhaWhopKSlqxzG6ai3JgwcP4uzsjKWlpdxZUw06duxI27ZtKSoqYvbs2SxfvhwLC9VvshJmSKPRYGtrS1paGqmpqWY13WG1/sVMmjSJb7/9lp9++qk6N3tPs7a2pnbt2mRlZcnYSVGlrt2muH37dpWTGFe171Y4OTnJFe1q5u7ujpOTExcuXFA7ijBjWq0WW1tbtWMYXbWVZE5ODqWlpTRq1IhGjRpV12YFEBAQQEBAAFu3bpXbFUWVcXR0xNXVFZ1OR3FxsdpxjKbaSnL58uX069dPHjGgAltbWwIDA8nNzWXnzp2VutdWiDvRpUsXoqOjOXPmjNpRjKZaSjIjI4OtW7fy5JNPYmNjUx2bFP/Svn17RowYwY8//khUVJTacYSZ6tWrF3q9nmPHjpnNUUu1lOSiRYt46KGHaNGihVzVVolWq6Vbt26UlZVx4sQJszocEjWHra0tzz33HJs2bSIxMVHtOEZRLSWZnJxMhw4d5D5tlVlZWfHqq6/yzTffyEUcUWU6d+5MYWHhbT/eoaaq8pK8ePEiGRkZWFlZyV5kDdCqVSusrKyIiori+PHjascRZsjS0hILCwtOnz5NWVmZ2nHuWpWXpE6nw9raWs5F1iCurq5kZ2dz8eJFtaMIM3Xtd8xYj51VU5XfcbNu3Tratm1L586dq3pTopI+/fRTevfuzblz59Dr9fI/MGF0137Hhg8fbvLjoqt0T7K4uJjCwkI8PT2pVatWVW5K3AYvLy969+5Nv379WLVqFbm5uWpHEmbGy8sLrVZLdnY22dnZase5K1VakkePHiU7O5vmzZtX5WbEHXj//fdZuXIlx44dY8mSJWrHEWZoyJAhzJ8/n7lz56od5a5U6eF2VFQUTk5O3H///VW5GXEHPD09AZg5cyYPPvggEydOlGcNCaN67bXXaNSoERqNxqQf8VDlF27s7e3N8n5Oc1G7dm1Gjx7NvHnz1I4izIyrq6tZjGipspLMz88nPT29qlYvjMTa2ppBgwYRHh4uPy9RJQwGg0k/mK7KStJgMMhdHSpK2LeaAQPqUKdOY9o//DrfxZQ/O/m1eQDLysrk5yWqhKIoJj2wvMpK8vfff+fkyZNMmTKlqjZhnpQyCvOOs3L2CFq3scGmzWDmbD//1+eGMk5vX8jT3W2wda1LwJRgdqSWYbg+HE2hbO9M2j26lmGL00lPiuKbp9zY/epb/HTWUO4mmzZtytixY3n33Xer/NsT95awsDB27dpFUFCQ2lHuWJWek3R3d6dOnTpVuQnzUphJ6r4P6V7nIT7b5s4LcyJIDdnK2wObXf28NJ/0H16n04RP8Jl3nrzkE7zjG8WbY2ay4Xg+pQCk8e2KHxj7zRaeaQJoHfB/ZChdAj3YE3KQ8gZj2Nra4u/vT3FxMbGxsWZxl4SoGa5N02fKjF6SiqKg0+koLCw09qrNW9EVov/3JkP6L0f7/Lus37aEKY+2xt39b4uc/47J//kfzmPX8HZ3b6zt3Qjs3ZeOWZtY9/UmzuWX/rmkN3Vr/+1Hq7XBUbFGm5XHzX4qnTp1olevXsyfP5/z58/fZCkh7ozBYDDZTjB6SRYXFxMcHExYWBht2rQx9urNlJ6k/cuY9u5Gcrq8xYpPp9La88ZlzuwL4WSOJUEPd/zzPWs8PJvRqq2W8PAQIk5eppRa+PiWsW/jb5zRAYYSsmPPcv5SHm4BzXC5SYJatWoxevRo7O3t2blzJ5mZmbJHKYzCysqKgIAAfo2Ie38AAAzaSURBVPjhB7Wj3BGjl2RRURHvvPMOERERjB071tirN0+Xj7N86XoOaVrxcvA4yj04yT/P3r2nyMltSUtfy+tvax0cqVvfm9KYOM7Ep5KPC93GvkHLKzsIXvYBH8yZy2fLQyjx6sjQrk2p6CG+tra29OjRg5iYGGbNmiXPxBFGYWdnx/PPP8/atWvVjnJHquycpI2NjUyNVkkph7ezJzIOl17D8I1czMdTpjDlxVeYtW4Pp/P+XCj/IvEp+RSVuOPu9rcfm7UWB3snnHPy0ekKKQFo/CCz50yjbxMPPOrUo8VDjzBi4mO0cC9n4//SvXt3MjIyWLRoEXFxcWYxQYFQl0ajoXbt2mrHuGPV/txt8W+pROyL5GJSPu7dHHAIaEOgqy+a3zaw5v9eJCryWd54aRqddZkk6vXc/MEL2WTl6NAXATbg1KAlwxq0vO0016a5AigoKEBRFLMYECzEnTJ6SZ47d87YqzRz+eRm6inSB/L0uN4EtPfFvj20auWFxcUneGfDD7Ro/wAtezrhqdVifdP1OODoYIf25gvcUkFBAUuWLMHJyYnPPvuMmTNn4uHhQfv27e98pUL8KT8/n4sXL1K3bl21o9wWox9uDxo0iP379/Ppp58ae9Xmzc+fto08sNNoQKPBpUlz+o0ZTYfEdBLPJpFtZYWthUUFPzArrCwtsbiDn6her+err76ifv36JCYmMmvWLF588UVWr17NwIED7+KbEuKqJk2aEBQUxJw5c9SOctuMvidZWFhIYGCgsVdrxiywsLRAY6Hwj9N/GlucazemYdM/X3vWx8fRAVvNGc6eL4P7rr6t5Ou4mJ5Cckd/2vg3prJTVBgMVweW5+XlsX//fjZu3EhsbCzufxtz5OfnB8Aff/whk5SIu1KrVi1atGhhkg+hq7ZHyoqbaUrnvv40Lgrj1+OXKbk26kYxUFpUSImnB/Wa1seFljwQ1AxP92gOn7w2/6OCLjeD5IQ0fL298a5zswE+/1RaWsru3bvZsmULnTp14ssvv2TFihX/KMhr9u3bR9++feUxtOKeJSVZAzR/8CmCurnx+48/cPJiDigKJZfjiNy3jyyPTvTs0AwHIODRFxnZ0Y9t678hKaMQQ0ke5yP3ERHXkEf6D6FdM4dbbqukpIQ9e/bw5ZdfsmDBAkJDQ9mxYwfe3t7lLu/r60u7du1MdoybEHdLrm7XBC7tGfvKVGJnBzPv42L6tqlPaXICsZdcGTxlEr1bOF5dzr0bL86aTtyHW/n8gxL8mtpwPuosTZ58jTFD7+dWgywKCwvZuXMn27dvZ86cOdStW7dSc0guWbKEoKAghgwZgp1dRSMthTA/UpI1hEv7J3hvTl1+2hrKhbR07JxbM3RUIO386mP/t+XcukwiONibzf/7g5RcS3wfeZEhD3TG0/6mq74uJyeHtWvXMnToUPz8/LC2rtyl8AYNGlBaWkpubq6UpLjnGLUkk5OTjbm6e45z616Mad3rlsu5+vRj4sx+t73+vXv34uPjQ6dOnbC0tLz1F/zJxsaGoKAgFi1axOTJk3F2dpYbBcQd0el05OTkqB3jthj1nOS4ceMIDg425iqFEZ05c4amTZvi5+d3fcB4ZWi1WqZOnUqtWrUYMWIE3333XRWmFOaqZcuW1K9f3+R+f4xakhEREYwaNcqYqxRGZm1tfVsFCVdvK6tXrx5t27bljz/+4Pjx4yb/BDxR/by8vGjevDkpKSlqR7ktRr+6Lc9wNk8ajYZu3boRHh5OaWkpW7ZsUTuSMDEWFhZYWZneZRAZAiQqzcXFhS5dutC4cWNSUlLIzs6WCTCE2ZOSFLdt0qRJXLp0icWLF5Obm3vrLxDChElJitvm4eHBO++8w86dO2VEgzB7UpLijtjZ2WFlZUVWVpYccguzJiUp7oi9vT1BQUGsXr3apB8XKsStGK0kU1NTr88sI+4NY8aMISwsjLi4OLWjCBOSnZ2NTqdTO0alGa0kp0+fzieffGKs1QkT4ODgwIwZM5g4cSIDBgxQO44wAT179qSwsJDffvtN7SiVZrRBS9HR0SxevNhYqxMmYsWKFRw6dAiNRoOPjw+BgYGsWbNG7ViiBtq/fz9jxowhKyuLvLy8W39BDWHUc5JardaYqxMm4MqVKyiKgsFg4MKFC6Snp6sdSdRA0dHRPPjggyQmJl4vyEGDBmFtbX3TYWRR/3uW+5/7kOg0dQ/NjTr8XSY9MA2TJ082+jqdnJxMbuICUX0URbnhOe4VPdfdUHKK8N/Ok7xmLyv6D+ejwc2xUekys1FLskOHDrc1u4wwH/b2lZirTdyz7Ozs8PPz48yZM9ff8/Pzw9nZuZzOKONi6B8cuZRCjn0823YeY0Z/H2xs1OkWjWKkQW4vv/wyH374ocw3KIQo1/Hjx/nggw+uv54xYwbt2rW7ccHCJHat3UGuRSrfrPof29ICWLf7G4J81OmWP0syh4j1KzmQVv5Cnp6eeLboQucOTZEDaiFEVcqL3s2mfafx6f0g+SvfZNLi7TSYfYw/XgtQJc/1o3zFUEpGzM/MfeU9lm6I4LKioCgKSk4iEWve443XXuHNpVuQEXFCiCpTnEX0mSQKbBvT1MefwJEP4+/hRMTqHzirUqQ/z0k60+nJV2gYUIfTv5xF17o/E14ZQ3OAwkwSTvTBec5w5rwfS76bH2uH+6sUVwhhzooyE0nLvoxLi0fx1IK1/wP0b+nMgZ0r2Rz5Dm+2qf5Mf10v0miwcqxNbad/LWHnRqMug3h57FDKUs8TunAHMdWbUQhxTyggOe0MFzLdaN3eDWsAO1/GTxyEjTaZZZ9tRo0BZpW+uu3sWhsUBUNmLqZzQ5EQwmTk53Jh90Zmv7+HuZ/P+qucinLRFZVR8vNq9qU8xgiv6o1VuZFHikLsuWjQWuE4/CE6VXEoYZquDSr/65+CTBAkKsdAxqUznDrfkM3nMrmYnEzytX+Xc9k1zYmSghB+2pNQ7cnKKckyCnVXSE1IICEhgYSEQ4QveJFxbx3Bu9Ew3pvco9pDipqtVJ9JyvndLH1/PA/08cHHxwefxvfTuf9sVq2PIjVTj3SlqFBZCZcvHCO53Xge8rzx4z6Pv4ijUsT+j74ktLh6o5VTkpmc3LuU18aMYcyYMYx5YhpTFv9EVMNuvPzB87QslZmoxd/kJvLj0ik80uc/JNYdzbKN8cTHxxMf9QMfBGWzYe5oJs5bzuEE07lXV1S/3Pjj/PC/UzTrdpMrM4ETeLdbCdmZm9m26TzZ+SXVF065rky5ErddmdKygdJv0lrl7LW3MzOV0yEblDmPd1FqW2mVnqM/UY4kFShCKAVJStgno5VaWl9l4JrIchbIUWI3T1Y61rVTmo9cppzNq/aEosbTKWf3bFQ+HOmnuNR9XHl55S/Kwbisfy1zSYnYuFCZ3gsFtEr9Jg8pby3ZokQm51ZLwlufk3R1xe+BEcxYNov+tYsJ37WE4D1J1VDfoqZLO7ic/1vwE3q/sQSPbV3OEk74PPQST9xfl4Tv3uedX+KrPaOo6UrIiD1JTqOhPDuuGdqL50jO+vckzjpSo9Kx6fIGb7zxMmNGdMSQn0F6blG1JKz8vdtu3XigM3y9v4xLWTKRgUjlwPrdnL6cR+fpQ6+OqS2PUysGPOzL7B2/su2zH4gd/jJNqzOmqOFc6DLpPbpUuEwTBr/7PoOrKdG/VX5ejYth7DkGNtZWeNd2r8JIwiTkxHHibDb5RdCisXeFi/o0b42FhSVl0aEcv1xN+YQwkr9K0lBGfvxRjsYBOuBv12cuHtvOc49MY0uKlnpdnuX5gRX/UYh7QJGewrIyKvPADjs7BzQaDYqSR2FhlScTwqj+PNxOYOHAjsw+WECOXo/lDy/Q5ddXsfyzQstK9Pg29eXJ9WFM6xdAK0dr9RILIUQ1+rMkG/Hijsu8qG4WYUo869HEwR5bDZw6Fwu0v+miCfFnMRjKsOrxGL0aVl9EIYxBHikr7lArHghqiqe7FYcPn6TgpsvpOX3iGGVl1nh2bY2cqBGmRkpS3LHWQ6Yx4j5frLd8y3/PZpazRDG5SZvZ/GMmHi3GE/xs92rPKMTdspw9e/ZstUMIE1WrIW2aWpN49lc2/noZb+8meHq6UcsaiopyOR/5C+vmzuc3jQ8vf7GSUX5yLluYHqM9vkHcu7IObWf96nXsvOJK68Z10DpCoXUpORkXwcKH7kFPMKJDI6wsNGpHFeK2SUkKozBkxXP8yFFi466QBeDgQL3GLbmvTQvqOdjKeR1hsqQkhRCiAvI/eCGEqICUpBBCVEBKUgghKiAlKYQQFZCSFEKICkhJCiFEBaQkhRCiAlKSQghRASlJIYSogJSkEEJUQEpSCCEqICUphBAVkJIUQogKSEkKIUQFpCSFEKIC/w9+8pwJv29dSQAAAABJRU5ErkJggg==)
force which is always directed towards ‘B”. A and B are end points of a diameter. When it reaches the point ‘P’ as shown , the speed is (Neglect the effect of gravity).
Physics-General
Physics-
A bead of mass m is fitted on a rod and can move on it without friction. Initially the bead is at the middle of the rod and the rod moves translationally in a vertical plane with an acceleration
in a direction forming an angle
with the horizontal plane. The acceleration of bead with respect to rod is
![](data:image/png;base64,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)
A bead of mass m is fitted on a rod and can move on it without friction. Initially the bead is at the middle of the rod and the rod moves translationally in a vertical plane with an acceleration
in a direction forming an angle
with the horizontal plane. The acceleration of bead with respect to rod is
![](data:image/png;base64,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)
Physics-General
Physics-
A lens when placed on a plane mirror then object needle and its image coincide at 15 cm. The focal length of the lens is
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OH4uLiMd8rPhZyuRyDwUB7e/uINfmDwRwpqHa7nYGBAfR6fdDLGe7ComU3Ly+P733ve/z973/n4MGDPPvss2g0GsxmM4cPH8ZisXD79m127NjB4cOH6e3tDdkjSxQKBdnZ2TQ3Nw/7us/nG7IMZ3DIYFRUVFi2ToSaJGvMkchkMvR6PatWrSIzM5OMjAxOnDhBUVERarWa/v5+Tp8+7T+fTUtLw2AwkJqaGrQpVuRyOVlZWVRWVg77+khBfHC9x+Ohs7OT9PT0oJTrcRNWwRzkdrux2+3MmjWL0tJSf/Da2tqoqamhpqaG6upqKisr/ZMjzJo1i6ysLDIzMyc0i65CocBoNI44VXWg55eDwXzyySfHXZbHWVgGMzY2liVLlgxZn5aWRlpaGiUlJVgsFlpaWmhqasJkMvln7bDZbCQmJjJ37lzmzZtHRkbGmJqbBu9X6u/vp7+//77z2Ycduh80GMyRLgynurAMZiBiY2PJzc0lNzcXr9fL3bt36ezspKOjg6amJioqKjhy5Ag+n4/c3Fzy8/NZvHhxQOd706ZNQ6fT0draet8V9VhGobvdblpaWpgzZ864vt/j7rEN5pfJ5XJmzJjBjBkzmDdvHjabDYvFgsViobm5mZs3b7J//37efvttcnNzKSoqorCwkKysrGGbn6Kjo0lPT6e+vp4FCxb4149lnKbJZCIxMXFMpxUmk4mamhoKCgomPBjGZrNx6tQptFqtf2COlEyJYH7ZYPunRqMhOTmZ7OxsCgsL/W2KX3zxBWfOnOF3v/sdAKWlpZSUlFBYWOi/Vyk6Ohqj0UhVVZV/u4HUll9+T2VlJYsWLRpTu2t6ejpffPEFW7du5fnnn2fbtm1jHtvqcDj47LPP+OCDD3j66adZsWLFmD7/qEy5YD5ILpejVqtRq9XExsayYcMGNmzYgMvl4r///S+ffvopP/nJT6ipqWHZsmWsWrWK4uJiUlNTOXHiBL29vSQkJATcPDXYDXnjxg22bt065rGdmzdvxmw28/3vf5/f/OY3vPnmm2zatCmg/dbU1LBnzx7+9a9/sW3bNl544QVUKlVAZXC73UEbuR8I8TiVAHV2dnLu3DlOnz7NpUuX/D+UTCajs7NzTNtyOBx0d3cPO8fmaLxeL319fXR1dQGg1WqJiYkZteYdnOa7u7sbh8NBfHw8cXFxAc/MbLVaefnll1m5cuUjeZyKCOY4OJ1Ozp49y5///Ge+8pWvsH79+oAPyV6vl88//5y9e/eO6+lobW1t7N27l4MHD5Kamsobb7xBaWnpqL1dTqeTy5cvs2/fPs6fP8/y5ct54403yMzMDGg86OAQxqSkJPGcH6lSqVQUFhZSW1tLc3Mzdrt9TPfKnzhxgq997Wtj3m9fXx/l5eXcu3ePH//4xzz77LP3PU1jtDIvX76c/Px8KioqOHDgAFeuXCEpKUmSA5VFMMdJrVZjNBqpra2lvb094B4ch8PBmTNn2Llz55j32d/fj8Fg4K233kKr1Y6rhoqIiCAvL4+8vDyuXbuGzWYb8zYeBRHMCTAajSgUCpqamkYc0PGg6upqoqOjxzUwWqvVotPpgjaCauHChUHZTiiExSAOqZo5cyaxsbHU19f75x8abTl16hTPP//8uGq7qXQ//9T4liGiVqvJzc2ls7OTu3fvjhpKu93Op59+yosvvjjZRZc8EcwJWrx4Mb29vbS3t+PxeB66XLx4kaysLP8ziYSRiWBOUEZGBqmpqVRVVTEwMDDseMzBpaysjNWrV0/oOUNThQhmEDz11FPU1dXR3d09Ym3Z3t5OZWUlzzzzTNjfW/8oiGAGwdKlS7l37x61tbX+HqEHl3PnzlFQUIBWq53s4oYFEcwgiImJYcOGDZw+fRqn0zmktrRYLFRVVbFs2TJJNmZLkQhmkJSWlnL37l1MJtOQ2vLmzZtERkaSm5sbsqfoPm5EMIMkOTmZ0tJSDh06dF9t2dfXx7Vr15g3b964Bm1MVSKYQbRlyxZMJhPV1dX+YDY2NmKz2ViwYEHAz0MXRDCDKjk5mU2bNvlrTbvdzpUrV4iPj2fu3LmTXbywIoIZZK+//jrNzc1cvXqV1tZWuru7KSoqEtPAjJEIZpBpNBpef/11PvroI65fv47D4eDpp58O6+m9J4MIZgi88MILREZGUl5ezje+8Y2gPbBqKhHBDIGoqCh27NjB3LlzKSkpmezihCXRaRsCCoWC1atXs3r16skuStgSNaYgSSKYgiSJYAqSJIIpSJIIpiBJIpiCJIlgCpIkgilIkgimIEkimIIkiWAKkiSCKUiSCKYgSSKYgiSJYAqSJIIpSJIIpiBJIpiCJIlgCpIkgilIkgimIEkimIIkiWAKkiQe2ScExOVyIZPJ/Asw5N9gEsEUJEkcygVJEsEUJEkEU5AkEUxBkv4PZ2J6g1gvgFEAAAAASUVORK5CYII=)
A lens when placed on a plane mirror then object needle and its image coincide at 15 cm. The focal length of the lens is
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)
Physics-General
Physics-
A thin rod of
length is kept along the axis of a concave mirror of
focal length such that its image is real and magnified and one end touches the rod. Its magnification will be
![](data:image/png;base64,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)
A thin rod of
length is kept along the axis of a concave mirror of
focal length such that its image is real and magnified and one end touches the rod. Its magnification will be
![](data:image/png;base64,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)
Physics-General
Physics-
A ray of light makes an angle of 10o with the horizontal above it and strikes a plane mirror which is inclined at an angle
to the horizontal. The angle q for which the reflected ray becomes vertical is
![](data:image/png;base64,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)
A ray of light makes an angle of 10o with the horizontal above it and strikes a plane mirror which is inclined at an angle
to the horizontal. The angle q for which the reflected ray becomes vertical is
![](data:image/png;base64,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)
Physics-General
Physics-
PQR is a right angled prism with other angles as 60o and 30o. Refractive index of prism is 1.5. PQ has a thin layer of liquid. Light falls normally on the face PR. For total internal reflection, maximum refractive index of liquid is
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49y+jRo3F1dUUsFlNTU0NeXh43b94kISEBR0dH3nnnHXr16vVCo0V9yOVyfvrpJ0xNTZ9pV44/I/niiy++aC5FzM3NuXXrFnl5eXTv3h09PT1EIpHaJzc3l5iYGFxdXXF2dkYsFmsc054/FRUVXLt2jejoaK5fv06vXr0ICQnB2dlZNeL+90cikdC3b1+N9tp6BZaWlqSlpZGWlsbjx4/p3LkzRkZGrfad7ty5w969e8nJySEzM5OTJ08yePBglEolR44c4cKFC+Tm5hIVFUVJSQl9+/YlNDSUDz/8kIqKCuRyOc7Ozg320blzZ7KyskhMTMTY2BhdXV2SkpK4cOECCoWCadOmMWfOHGxtbZt91iKRSPDx8WHgwIHPLdvssXDx8fGsWbOGkSNH0r9/f7UnRXFxMcePH6empoZJkybRuXPn5z5/VVUVycnJXL16lf79+zNo0KA2sUaorq4mIyODuLg4kpKS6NevH+PHj8fe3r5Zzl9RUcHFixdJSkpCX18fT09PBg4c2CpryGvXrqGrq0uvXr2orKzko48+YuLEiVhZWXH48GFCQkIYNGgQN2/eZP78+fz8888cPXoUsViMkZERAQEBjZZNhqfhY8ePH+f27dtIJBKcnJzw9fVlxIgRbbIeArRAURF3d3cGDBhAUlISffr0oVOnTtTU1HDv3j0iIiKorKxk/PjxGoU+/pxTM2TIEAICAkhISOCPP/6gvLwcsVjM4sWLKSkpITo6GlNTUxISElQ5J9qkpKSEqKgokpOTcXBwwM7ODh0dnWcq+SuXy7l7926jUxxjY2P8/f1xdXUlPj5eZagBAQGNls5tKn8urlJaWopSqcTGxoaHDx9iamqKo6MjYrGYfv360blzZzIyMpg2bRrXr1/HwcGB3r17P9OUq6ysjNLSUvT09BgxYgTjx49XTRXbKs1uQPr6+sybN4+lS5dy7do1zMzMiI2NJTk5mSFDhjB+/HhsbGzULuiSJUtwd3dX/VDdunUjPT2dnTt3MmzYMGxtbQkPD+d///d/mT17NjKZjJEjR3L27FkqKiqadT78PMhkMi5evEhUVBTW1taMHz+ePn36UF5ezrp16wgPD2fMmDENnqO8vJydO3c+U1KeWCzGzs4OKysr+vfvT2xsLFu2bMHT05OJEyc2WMmnqWzcuJG0tDTkcjnDhw+nf//+qhJZurq6qt/A0dERuVxO3759VaW6GqO4uJioqCjS0tLw8PBg3LhxuLu7t4mZRWO0yGrUxsaGoKAgvvrqK7p164aHhwfvvvsujo6OGm+Az5w5g4mJCXPmzFHzvuzatQsHBwdGjBhBly5d6Nu3LzNnzmTMmDHo6uqybNkyxo8fj6Ojo1Y8ecXFxezevZu0tDQmTZqEj48PpqamSCQSzM3NWbRoERs3bkQulxMYGFjveaqrq8nOzn6u76Cvr0/Pnj3p2rUrr732GmfPnmXJkiXMnj2bcePGNcfX0yA4OJiKigpkMhk7duygvLxcNYuoXcfA09H4z383hFwuJzU1laNHj2JlZcXixYvx8PDA1NS03XhnW8ydM23aNA4cOICLiwtBQUHo6urWeVFiYmK4desWEydOBJ7uJrBkyRLy8/OxtLSkU6dOiMViLC0tsbS0RC6X87e//Y2qqioMDAxUjorWoqKigu3bt3PhwgWmTZvGrFmzMDc31/CM9enTh2XLlrFu3TrS0tKYPXs23bp10zhf7ZP7RUZRExMTTExMeOutt/Dz82PLli2Eh4ezaNGi5w6KbIzatZxCocDX15fIyEjGjRuHRCKhqqpKpf+9e/fo169fo9+nsrKSjRs3kpqaymeffcbYsWMxNDTU2mziRWkxA9LV1WX58uVMnz6dqVOn1nthqqur8fHx4ZNPPqG8vJw9e/awf/9+FAoFnTt3VnnpxGIx3bp1QyQSYWRk1KrvRGpf4t26dYvVq1djYGDA999/T9euXeuVEYlEODg48Pnnn7N7924++OAD3N3d8fT0pGvXrnTq1Im7d++Snp7+TFVMG8LAwABXV1e+/fZbTpw4wT//+U/GjBnD5MmTMTMzQywWU11dzfHjx5k8efJz9/XFF18wZswYPD09kclkXL16FVtbW+zs7Dhx4gQpKSlYWlpy+PBhunfvjqenZ53nqb2Op06dYu/evQQFBbFmzZoGr2Nbp0VfKHh7exMSEsLmzZt577336qzUKZFIsLa2RiQSYWxsjKurK/fv31crW1v7gz948KDVRxypVEp6ejonTpygoKCAhQsX4uvr+8w6WFhYsGTJEt544w2io6NJTU0lMjKSiooKHBwccHJywsXFpVm+k5GRESEhIQwYMIDQ0FB+/PFHRowYoZoW5eXlcf36ddzd3Z/rvNOmTWPNmjUUFhYiEol45ZVXWLFiBQCvv/46O3fuZNOmTQAcPHhQ47solUrKy8tJTU3l1KlTiEQifv31V7y9vZv8nbVNi6d05+bmMnbsWFasWFFndMMvv/xCcnIya9asQSwWc/LkSa5cuYKRkRHV1dUsWLAAKysrHjx4wDvvvMOWLVuazTXcEDKZjOzsbFJSUkhISKBHjx6MGzcOGxubZjXgZ/XCvQgXL17k119/xdnZmfHjx5OcnExMTAxff/11izoc/kxFRQW3b9/m8uXLZGZmEhwczOzZs9vNGqcxWqUmwq5duzh9+jRLlizRiDy4fv06H330ETNnzkRXV5eUlBS8vLxwdnZm27ZtDBgwAEtLSyIjI+nTpw/vvvtuS6tLfn4+MTExJCUl0aVLF1Ud6MZqXb8IBQUFrFixgs2bNzf7uWvPf/78eVJSUnjy5AlxcXHMnz+fmTNntqiXS6FQcPfuXZKTk7l58yaurq7Mnj0bOzu7DmM80ErF5QMDAzl37hxxcXGMHTtW7X/u7u58+OGHJCUlATB48GDGjRuHoaEhM2fO5MqVKxQXF+Pg4MCiRYtaVM+SkhKuXr1KSkoKMpmMYcOG4e3t/ULhRmFhYTx+/BgLCwsmTJhQb9yWUqmktLS0RRbPtTsc9OzZk9zcXM6cOUNRURHHjh3D1dW1xaoB5efnc/HiRW7duoWdnR2LFi3C09OzQ24i1ioGZGJiwvTp09m/fz/9+/fXeKs8evToOkPJfX198fX1bXZ9lEolVVVVKBQKpFIpZWVlXL9+nfj4eJ48ecLQoUPx8fHBxsbmuc9du+t2bTjKjRs36NatG6+++mqdx0skEoyNjVvkqaxQKCguLiYnJweZTMbw4cMpLS2lpqaGBw8eNPvOeAqFgujoaM6dO0evXr2YOnUq3t7eDe6O0d5ptbJW+fn5/PDDD+jp6fHGG29odRiXSqVcvXqVtLQ0EhMTKSwsJC8vj0ePHvHhhx/y5ptvvnDA5nfffUfv3r0ZO3Ysenp6nD9/noyMDN555506j6+qquLGjRsNbt3yolRXVyOVSlUPC7lcjlwup7q6GiMjIywtLZst5yg1NZVDhw5hYGCAv78/fn5+z7z5cnum1cJ6a3fw3r9/P+np6c8UG9VS6Ovr4+joSHx8PNeuXePRo0fIZDK8vb2ZMGECenp6L3Te2jJgI0eOxNjYGIVCgUKhUHtP8t8YGBjU6/ZtKrU5Vy1Jbm4uv/32G7du3cLf35/x48fTvXv3lyYZsNUMSCKR4OXlRUREBOfOnaNHjx5amRPX1NSQlJTE/v37SUlJoVOnTnTv3p2srCyWLFmicqm/CGfPnuXkyZMcO3ZMdQ5TU1OWLFlS7zmlUikJCQktMlVtSaRSKTExMfznP//BxcWFr776ip49e74UCZJ/plUTS0xNTQkMDOTXX38lPT29RaYtDVFaWqqKUatNFVi4cCEHDhzA09MTd3f3F17Mp6Wloa+vz/79+1UxYAUFBbz11lv4+PjUa0BPnjxh7dq1HDhw4IW/V2tTWFjIt99+S3Z2NmvWrHmurNCORqtnZvn4+HD+/HliY2NxcnJq8fcRCoWC8vJyLl26xPfff49CoaBHjx68/fbbDB06FKVSib29Pd7e3k3S5f79+1hYWGBubq4ywu3btzNq1CiNIhZ/pjZurK2HsCgUCsrKyjhy5Ahnz54lODiYuXPnvlAlm46EVmpUTZgwgTVr1nD79m08PT1b5OapdQ8nJiZy9OhRRCIR06ZNQyaTMXfuXNX0MTc3l5EjRzY5nKSiooLy8nJqfTJJSUlcvny50fc7Ojo6L+Ttay1qamooLCzkypUrREREYGlpyaZNm1Q1A192tGJA/fr149VXX+Xs2bP07du32ettP3nyhFu3bnH9+nUyMjLw8fEhICCgzqelhYVFsyy2e/XqxeXLl/n999+xtrbmyJEjrF27tlEXrrm5OYsXL26TI1BJSYkqebGgoIA5c+aoagkIPEVruzPk5uaybNkyAgIC6t2A60XIzMzk1KlTZGVl4eHhgb+/P7a2tq1ygx44cIDk5GQA/vGPf7RI5EJrIJVKSUtLIz4+nuzsbAYPHkxISMhLP12rC61ub3LmzBlWrVrFDz/88ELp3X8mOzubmJgYMjMzEYvFDB8+nIEDB7b5pKyysjJOnTpFSEiItlVRZQ7/8ccfqrSEkSNH4uLi8sKu/Y6OVg1IKpXy/vvvY21tzf/7f//vhc4hk8mIiorit99+w9bWFh8fH1UhjvZAXl4eixcvJiwsTKt6yOVyjh49yu+//46Xlxf+/v64ublhZmamVb3aOlotdG1gYMBnn31GYGAg/v7+z5X/XpvNePDgQaqrq5kyZQr9+vXD2tq63U2dpFKpViMzYmNj2bFjB/b29ixcuJBXXnkFKysrrenTntB6pXh7e3vmzZvHL7/8wrp1655JpqioiLCwMM6fP09AQACjRo1qtJhjW0UikdClSxetGFBWVhZ79+4lKyuLGTNmMGbMGDp37tzuHkDapE1s8ahQKAgKCmLmzJkEBATUe5xcLicyMpLt27fj6OjI//zP/+Dk5NSuf3ClUolcLm/VNUZFRQWnTp1iz549DBs2jKVLl2JlZdWur6O2aBOPbB0dHRYtWsRPP/2En5+fWohP7Q2Wl5fHDz/8QHZ2Nu+++y5Dhw5t8w6CZ0EkErXa95DJZGRmZrJ+/Xqqqqr48ccf8fT07FD5Oa1NmxiB4Gkp3K+++gobGxtmz56NRCJBJpNx9+5dzp8/T0REBD4+Prz55ptN9ti9bEilUnJzczly5AiJiYm8/vrrTJ06tdWyUjsybcaAampqiIyMZOPGjbz//vuYmppy6dIlwsPDsbS0ZP78+Tg6OmpbzXZFdXU19+/fJzo6mvj4eJycnJgzZ06zV+x5mWkzBgRPgxR//vlnrl+/jp2dHU+ePGHYsGGMGDHipQmPby5yc3OJjY0lNTUVuVzO9OnTX+qgz5aiTayB4KkjISsri9u3bxMdHc3MmTN5//33teahaq+UlpYSHx/PlStXKC0t5bXXXmPChAkaBS0Fmoc2YUA3b95k3759VFZW4unpiZWVFQYGBg3uiiegTnV1NTdv3uTUqVMUFhYyePBghg0bhqOjY7t077cXtHplKysrOXDgAGFhYXh4eBAUFISHhwe3b99mw4YN3Lhxg6FDhwojUCNIpVJ27NjBhQsXGD16NDNmzKBnz57takOu9opW1kAymYzffvuN0NBQ+vfvz9ixY3F2dlZFRsvlcrZv305mZiZvv/12g/k0LzunT59m06ZNeHl5MW3aNPr169fs0e0C9dPqBpSTk8OmTZuIjY1l/vz5TJw4sc5i4vn5+SxYsEBVUF54yadOWloaP/30E3l5eSxdupRhw4a1y9rS7Z1WmcLV7gMaFhbG8ePHGTx4MLt27aqz2Hot1tbWzJ07lyNHjuDr64uFhUVrqNqmUSqVFBUVcfDgQcLCwpg6dSr//ve/X7o6BG2JFh2BampqKC0t5ebNm/zyyy9UVlaycOFCvL29nzl0Zd68eXh7ezNnzpyWUrPNo1QqefLkCcnJyfz888+YmZmxYsUKevfuLawPtUyLGVBZWRkpKSmcOHGC69evM336dKZMmbFbPMoAAAijSURBVPLcT8uLFy/y+eef869//atNpz63FKWlpdy6dYsTJ06Qk5NDcHAwo0ePFtzSbYRmN6DKykrS09OJi4vj0qVL9OjRg3nz5jWpIPznn39OQUEBq1atemnm+HK5nLS0NMLDw7l79y7u7u4EBQUJ0RhtjGYzoNpsxnPnznHjxg1MTU0ZP348Xl5eTZ5m3Lt3j9mzZ/Pll192iC0xGuPOnTuEh4dz584dOnXqRHBwMF5eXtpWS6AOmmxAtQ6CmJgYzp8/j46ODn5+fvj4+GBubt5sc/SwsDB27tzJ5s2bO6xDobCwkMjISOLj49HV1SUgIIDhw4cL6dRtmOc2IJlMRllZmeqTlJTE6dOn0dfXZ8KECQwaNIhu3bo1+9vvsrIyFi9ejJ+fH7NmzWrWc2ubqqoqEhISOHr0KNXV1fj7++Pt7a2xGbNA2+O57vKcnByuXr1KZGQkUVFRlJeXU1JSQnV1NcuWLWtSXenGMDY2ZsmSJaxcuRJfX1+cnZ1bpJ/Wpri4mE2bNpGQkKAK+LS1tRVGnXbCcz3erK2tGTJkCFZWVjx69Ijr16/z8OFD3NzcmD17dov/6L1792bAgAEcPny4RftpLfbv309wcDAAa9euZfr06Tg6OgrG0454rincnTt3+Pjjjzl37hyOjo74+fmxc+dOzp4922qL3OTkZNavX8/bb7/N4MGDW6XP5iYhIYFvvvmGiooKvvnmmwZrZwu0bRodgRQKBZmZmXzyySdMmDCBa9eusXjxYo4ePUppaSkff/xxq3qInJyccHd35/Tp00il0lbrt6nI5XLu3LnD6tWrWb58OZMnTyY8PJwhQ4YIxtOOqXcNVJvNeOPGDQ4cOEBqair+/v4sXLgQd3d3qqqqqKqq4r333mtNfTExMWH06NFs27aN8+fPM2rUqDa90K6uriYvL49Lly4RGhqKs7Mze/fu1dilT6B9UucUrri4mLi4OPbv34++vj7BwcF069YNe3t7VR79nTt3yM/Px8fHp9WVlslkbNmyhezsbN577702G6FQUFBAQkIC586do6qqiqCgIF599dUOuVfoy4qaAdW6pWNjY0lPT2fgwIEEBwfXuXOBVCrVahDjnTt32LRpE76+vqrtFNsKMpmMK1eucObMGcrLy/Hy8mL06NFt1tAFXhyRUqlU1mYznjhxgocPH+Lg4MDYsWOfq1KoNti3bx+xsbH87W9/azNTotTUVI4cOUJhYSFOTk6MGzeuzV9HgRdH9PDhQ+Xp06e5ePEizs7O+Pn54e7uTqdOnbStW6MUFhby9ddfM2jQIEJCQrRaeOThw4ecOHGC5ORkbG1tGTNmDJ6enkIxlA6OaO7cuUpra2vGjh2Lp6cnFhYW7corFBkZydq1a9m8ebNWMlcrKio4f/48Bw8exMLCgokTJ+Lh4dFhw40E1BEdOnRIOXToUCwsLNpl8Ymqqiq++OILjI2NWb58eav2nZOTw+rVq8nMzOTdd9/l1VdfxcLCQsiefYkQKRQKZXv/wXNychgyZAinT59utaKBmzdv5pdffmHGjBnMnTtXqC39ktKmCis2hX//+99ERkayY8eOOkdShUKBVCpFIpG8kBtZqVQik8mIjY1lzZo1mJqa8umnn7b6TuMCbYsOY0AAI0aMYOnSpQQFBanaZDKZKk0gLCyMrl27snbt2ucq+VRRUcHNmzc5dOgQ8fHxzJ8/v03sKCegfTqUAZ09e5bNmzezceNGTE1NefDgAVeuXCEqKgqAwMBAfvjhB9566y1mzpzZ6Plqi9tfuHCBkydP8sorr7Bo0SLBQSCgokMZkEKh4NNPP0VHRwc3NzcSExMRiUT4+fkxatQojIyMiI6OZuPGjXz99df06tWrzvMolUrVnqtxcXEYGxszefJkBg4c2KZe2Aponw5lQEqlkkuXLrF48WI8PDwIDAzEz89Pbat5uVzOpk2buHfvHp999pnGFh9SqZRz584RHh6OkZERvr6+DB06VNhSRaBOJF988cUX2laiuRCJRJiZmVFSUoJUKmXBggUa0y2xWIyVlRURERGIRCJcXV1V/7t48SLr16/n7t27DBw4kNdffx0fHx8hdk2gXjqUAQHo6elhYWHB1atXMTExwdnZGZFIpPYxMTFBX1+fiIgIHB0dKS8v5+eff+bs2bO4uroyffp0RowYIYw6Ao3SoaZwtVRVVREWFkZKSgp//etf6wziLCoq4ujRo1y7do379+/Tp08fQkJCcHZ2bhdhTAJtg/YXevAM6Onp4e3tzZUrV7h8+TKTJk1S+79SqeTRo0ecOHGC0tJSVqxYwaBBgzA0NGxXYUwC2qftZqI1kd69ezNkyBCio6PJysoCnhpOZWUlq1atYtasWYwcOZJ9+/bh5+eHkZGRYDwCz02HHIFqGT58OBEREVy6dAkjIyMuXLjAtm3b6N69O7t378bFxUXbKgq0czrkGujPnDp1in379qGjo0NxcTELFixg7Nix2lZLoIPQoUcggGHDhpGUlISlpSWzZs0SXNICzUqHH4EEBFqSDutEEBBoDQQDEhBoAoIBCQg0gQ5rQAUFBXz88cf06NFD9Vm/fr221RLoYHRYA8rLy+PJkyf8+OOPZGRksHHjRv7xj38QFxenbdUEOhAd1oAeP36Mqakpjo6O6OjoYGpqiq6uboM7gwsIPC8d8j1Q7XaTaWlpZGVloVAo2LhxIzNmzKB79+7aVk+gA9EhR6DKykru379PRkYG27ZtIzg4mF69evH9999rWzWBDkaHNKDy8nLKysr4y1/+wpEjR5g/fz5JSUnI5XJtqybQweiQBlRcXEx+fj4ODg7A02o9WVlZFBQUaFkzgY5GhzSggoIC7t+/r3IYeHh4UFNTo0prEBBoLjpkLFxxcTGZmZn07dsXY2NjAOLi4ujduzeWlpZa1k6gI9EhDUhAoLXokFM4AYHWQjAgAYEm8P8BuTkRtGjHZrQAAAAASUVORK5CYII=)
PQR is a right angled prism with other angles as 60o and 30o. Refractive index of prism is 1.5. PQ has a thin layer of liquid. Light falls normally on the face PR. For total internal reflection, maximum refractive index of liquid is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANAAAACKCAYAAADbscTlAAAgAElEQVR4nO2daVRUV9awn6pillEEQUBEHBAQxSBIJCqKMyoS1Bg1+sYY/TpqupMVTWKnk3QGfeMQE1vTxmicX5R2No4YAijggIwqCiIqIiCTMlVRBfX9cFEr1cWgMhTgfdaqHxzuvmfXrbvvOWffvfcRKZVKJQICAi+EWNsKCAi0ZwQDEhBoAoIBCQg0AcGABASagGBAAgJNQDAgAYEmIBiQgEATEAxIQKAJCAYkINAEBAMSEGgCggEJCDQBHW0r8KwolUq2bt3KsWPH1NoNDQ1ZtWoVPXr0aFD+5MmTbNu2jaqqKlWbrq4ub775JsHBwQ3KJicns23bNu7cuaNqE4lEuLm58c033zSqe3Z2Nlu3buXq1atq7SYmJuzevbtB2b1797Jv3z61NgMDAz766CO8vLzqlbty5Qpbt24lJydH1SYWi/H29uaTTz6pU2bXrl385z//0ejr73//O/3796+3r7i4OLZu3Up+fr5aX6+99hoffPBBvXJFRUVs3bqV8+fPq7UbGxuze/duRCJRvbJtBVFzBZNmZWWxbt06YmJi1NrNzc0JDw/XOD48PJx169apXXSJRMKkSZP4+9//Xmcf9+/fVzu+VqZv374YGho2qN+jR4/Izs6mpqZG1SYWi7G1tcXGxqZB2dLSUrKzs6moqFBrNzExoU+fPg3KAkilUrKzs3n8+LFau46ODgMGDGhQNicnh4cPH6q1icVievbsiZmZWb1yjx8/Jjs7G6lUqmoTiUSYmZnh7Oxcp8yDBw/Izc1Va5NIJDg7O2NiYlJvXyUlJWRnZyOTydT6srCwwMnJqV45uVzO/fv3KS4uVmt/luvSVmg2A1IoFJSVlaldRHj6Y1tZWWkcL5VKKSsro7q6Wq3d0NAQU1PT5lBJQKDFaTYDEhB4GRGcCAICTUAwIAGBJtCsXriioiISExMpKChQazczM2Ps2LEax9+5c4fExETkcrmqTSKR4OLigpubW739PH78mMTERPLy8tTajYyMCAwMbFDHlJQUbty4odamo6ODn58f1tbWDcpmZWWRlJSkts4Ti8X06dMHDw+PBmUB8vLySExMVHMmiEQiunbtyrBhw+qVk8vlJCYmqnkBAfT09Bg/fjz6+vr1yt6+fZvExES1taZEIsHNzQ0XFxeN42UyGYmJidy9e1ejr8DAQHR06r9l0tPTSUpKUnPUSCQSPDw86N27d71yhYWFJCUladw35ubmjBkzpl65tkCzGlBZWRnXrl3T+KFtbGzqNKC8vDwuXbqkdkNKJBI6derUoAFVVFRw/fp10tPT1drNzMwaNaB79+4RFxen1qanp4eHh0ejBvTo0SMuX76s5o2TSCTo6+s/kwGVlJSQlJSk5ukSiUT06dOnQQNSKBTcvn2bS5cuqbUbGBgQEBDQoAHVXuM/P6R0dHQwNzev04DkcjkZGRnEx8ertRsaGjJhwoQGv19ubi5xcXFqBqSjo4OVlVWDBlRWVkZqaipZWVlq7ba2tm3egAQngoBAExDWQAICTUAwIAGBJiAYkJYpKyvTCNURaD8IBqRlHj9+zI8//qhtNQRekFYxoM8//xxra2u1z/Dhw7l165bGsWlpaUyfPl3j+BkzZjTYx7/+9S8NGS8vL86cOdOgXExMDKNGjVKTs7GxYd68eY1+r/z8fBYuXKjRb2BgIAqFolH51atXM2DAAC5fvqyS9fX1JTY2tkG5c+fOMXToULU+u3fvzueff16vjEKh4JNPPtHQddSoUdy7d69euVOnTuHt7a0m4+TkxMqVKxvUMS8vr95r89/hW39mz549ODs7q8m4ubmxY8eOBvvTFoIXTsvk5eWxePFiwsLCtK2KwAsgGJCWkcvl3Lt3r94IaYG2jWBAAgJNQHAiaJnS0lK2b9+ubTUEXpBmHYEyMzPZt28fGRkZau12dnb885//1Dg+Ojqa0NBQtaQvHR0dJkyYwJQpU+rtJzs7m9DQUI2YNnNzc9auXdugjgcOHODEiRNqbfr6+ixdurTO0JY/ExMTQ2hoKOXl5ao2iUTC6NGjmTZtWoOyANeuXWPfvn08ePBA1VZRUcGDBw+IioqqV66iooJ9+/ZpZG4aGhqycuXKBpPd/vjjD0JDQzVCeaZMmVJnaE5paSmhoaEa4U5GRkasWbOmwbCh8PBw9u3bpxbKo6urS0hICAEBAfXKZWZmEhoayu3bt9Xa7e3t+fLLL+uVaws0ayycpaUlo0aN4pVXXlFrNzY2rvP4nj178vrrr6t5rMRicYNZjPDUUPz9/TXizwwMDBrV0cPDQ+OG09HRaTQODqBHjx5MnTpV7WYUi8V07969UVl4GhM4btw4ysrKVG2FhYWNurH19PTw9vbGzs5OrV1XV7fBGxqgV69eTJs2Tc3zJRaL611z6evrM2TIEBwdHTX6aiiQFKBPnz5Mnz6dPz+TJRJJg3Fw8PS+CQgI0EhRb+jB0FYQ1kBa5tGjRyxfvpxt27ZpWxWBF0AwIC2jVCqRSqWN1nQQaJsIToQ2gK6urrZVEHhBBAPSMqWlpWzZskXbagi8IK1SFy4jI0MjXMTY2Bg3Nzc6deqk1l5eXk56ejpFRUVq7ZaWlg2WOrp3756G98/Q0JDevXvTpUuXeuVKSkpIT0+ntLRU1SYSiejSpUuDtdAAqqqqSE9P18iMNTMzY9CgQY3WNbtz5w6XL19mw4YN9O3bF3jq7XJxccHc3LxeucLCQjIyMjS8gXZ2dvTq1atOGaVSSXp6OtnZ2WrtJiYm9O/fv14HTEFBAenp6VRWVqr15eDgQM+ePevVsb5rY25ujqenZ73XJicnh4yMDDXHkp6eHk5OThpOlLZAqxjQ5cuXOXXqlFqbvb099vb2GgZUXFzM2bNnSU1NVWvv379/gwaUmpqqEdXcpUsX5syZ06AB5ebmcuzYMbUUZpFIxKBBgxo1oMrKSqKiojRcvr1792bgwIFIJJIG5ZOSkggLC+PRo0eqWC8bGxvefvvtBg3owYMHHDp0SK1enJ6eHiNHjqzXgGpqarh48aJGjb7u3bvTo0ePeg3o3r17HDx4UK0en76+PmPGjGnQgCoqKhq8NvUZUHp6Ov/3f/+nZrCmpqYEBwe3SQMSnAhapri4mPXr17f59x0CdSMYkJaprq6mqKiozuKTAm0fwYAEBJqA4IXTMgUFBSxevFjbagi8IM1qQAkJCUyZMoVu3bqpffz9/es8fu/evfTp00ft2B49erBmzZoG+7lx4wYzZszQ6Oe/Q4jqYuXKlRpyvXv35sKFC43KhoWF4ebmpibr6OjI119/3agsQGRkJP7+/mrybm5uGrs2/DdPnjzhgw8+0NDbxcWFwsLCBmV37txJz5491eScnJzYsGFDnccXFhayZMkSjb769eunUVz/v9m6dSsODg4afW3durVBuatXrzJ58mSNPkeNGtWgXFtAmMJpmQcPHhASEtJoFqpA20SYwmkZAwMDhgwZom01BF4QYQQSEGgC9b5ILSwsJCIiQvV3165dGTBggLB3TzOjUCh4+PAhDg4O2lblpSI+Pp67d+9SU1ODWCzGxcUFV1fX5z5PvSPQoUOHWLZsGRMnTqSsrIzi4mJmzpzJlClThODHZqSoqIjvvvuOVatWaVuVl4KysjL++OMPDh8+jJ6eHnp6ehQXF1NWVsbKlSufacfBP1PvCJSQkMDUqVP57rvvKC4u5ttvv+XixYuMGzdOMKBmpLKyksjISG2r8dIQExPDnj17mDhxIsHBwRgZGZGXl8cbb7zBb7/99twGVK8TITY2VpXxWV1dTVVVFZ06dXqmrE8BgbbIo0ePOH78OG5ubgQFBWFkZASAhYUFgwcP1th/91mo04Dy8/O5evUqAwcORC6XExUVxbVr1xgyZEijab0Cz05ZWRl79uyhc+fOGsG2As1P7abLXl5eGmUGZDIZlpaWz33OOq0hJyeHyspKAgMDkUgkdO/eneXLlzNixIg6T5KamkpQUNBzd/6yU1NTQ1FREQqFgitXrrSLGgBtES8vL0JDQxs9rqSkBLFYrFH/QqFQcPLkyXpfLjdEnQZ09epVhg8fzqFDh4CnRSh0dHQQi+ue8VlYWDB27FjMzMwYOXJko53euHGDCxcuMHHiRGxtbZ9b6fbM3bt32b59O48fP+Yvf/mLKv2grKyMw4cPExERwaxZs3jttddemrVmVVUV27dvx83NjaFDhz6TTHR0NL/++ivjxo3j008/fSaZmpoalEqlxn28YcMGHB0dGT169HPrXqcBnT9/nhEjRjzzesfOzo6pU6fy008/MWDAgEbzNoyMjBCLxejq6r4Ua6rq6mry8/M5d+4cCQkJjBgxgjFjxqCvr09RURGrV69m5cqVvPPOO/j6+rJ582bi4+N58803sbe3b7TyTnvHwMAAAwMDqqur0dPTq/NBrVQqUSgUZGZmcvz4ccrLy9m1axfDhw9/5n7s7OzIz8/nwIEDWFpaYmhoyJ49e/jqq6+4ePFivQNEQ9RpQHp6eg1usVgX7u7uuLq6kpycjI2NTYNrpdo6cBKJpNGszfZMdXU1JSUlpKSkEB0djbW1NX/961+xt7dX/VhKpZLi4mLVdXB3d2fDhg2cOXOGb7/9lpEjR+Lv74+FhYVq0dseePLkCfn5+RgbG9OlS5dG184WFhaUlJQglUo1kizlcjkPHz4kPj6elJQUJk6cyIIFC567EIuLiwsfffQRa9euZdKkSQAsWrSIYcOGMXfuXI4dO/bcM6JmjUT4/fff2b17N/7+/vTq1atO46ipqeHAgQMoFAoCAwM77Lz/8ePHpKamkpKSQklJCSNHjmTQoEEaN1JBQQFffvllnfPv3NxcIiIiSEtLw8XFBT8/P2xtbbXiyElISFBliVpYWNCvXz/g6Xusu3fvqv5Xm4m7d+9eLl26hIODA9OnT683U7aW1NRUzp49y+jRo3F1dUUsFlNTU0NeXh43b94kISEBR0dH3nnnHXr16vVCo0V9yOVyfvrpJ0xNTZ9pV44/I/niiy++aC5FzM3NuXXrFnl5eXTv3h09PT1EIpHaJzc3l5iYGFxdXXF2dkYsFmsc054/FRUVXLt2jejoaK5fv06vXr0ICQnB2dlZNeL+90cikdC3b1+N9tp6BZaWlqSlpZGWlsbjx4/p3LkzRkZGrfad7ty5w969e8nJySEzM5OTJ08yePBglEolR44c4cKFC+Tm5hIVFUVJSQl9+/YlNDSUDz/8kIqKCuRyOc7Ozg320blzZ7KyskhMTMTY2BhdXV2SkpK4cOECCoWCadOmMWfOHGxtbZt91iKRSPDx8WHgwIHPLdvssXDx8fGsWbOGkSNH0r9/f7UnRXFxMcePH6empoZJkybRuXPn5z5/VVUVycnJXL16lf79+zNo0KA2sUaorq4mIyODuLg4kpKS6NevH+PHj8fe3r5Zzl9RUcHFixdJSkpCX18fT09PBg4c2CpryGvXrqGrq0uvXr2orKzko48+YuLEiVhZWXH48GFCQkIYNGgQN2/eZP78+fz8888cPXoUsViMkZERAQEBjZZNhqfhY8ePH+f27dtIJBKcnJzw9fVlxIgRbbIeArRAURF3d3cGDBhAUlISffr0oVOnTtTU1HDv3j0iIiKorKxk/PjxGoU+/pxTM2TIEAICAkhISOCPP/6gvLwcsVjM4sWLKSkpITo6GlNTUxISElQ5J9qkpKSEqKgokpOTcXBwwM7ODh0dnWcq+SuXy7l7926jUxxjY2P8/f1xdXUlPj5eZagBAQGNls5tKn8urlJaWopSqcTGxoaHDx9iamqKo6MjYrGYfv360blzZzIyMpg2bRrXr1/HwcGB3r17P9OUq6ysjNLSUvT09BgxYgTjx49XTRXbKs1uQPr6+sybN4+lS5dy7do1zMzMiI2NJTk5mSFDhjB+/HhsbGzULuiSJUtwd3dX/VDdunUjPT2dnTt3MmzYMGxtbQkPD+d///d/mT17NjKZjJEjR3L27FkqKiqadT78PMhkMi5evEhUVBTW1taMHz+ePn36UF5ezrp16wgPD2fMmDENnqO8vJydO3c+U1KeWCzGzs4OKysr+vfvT2xsLFu2bMHT05OJEyc2WMmnqWzcuJG0tDTkcjnDhw+nf//+qhJZurq6qt/A0dERuVxO3759VaW6GqO4uJioqCjS0tLw8PBg3LhxuLu7t4mZRWO0yGrUxsaGoKAgvvrqK7p164aHhwfvvvsujo6OGm+Az5w5g4mJCXPmzFHzvuzatQsHBwdGjBhBly5d6Nu3LzNnzmTMmDHo6uqybNkyxo8fj6Ojo1Y8ecXFxezevZu0tDQmTZqEj48PpqamSCQSzM3NWbRoERs3bkQulxMYGFjveaqrq8nOzn6u76Cvr0/Pnj3p2rUrr732GmfPnmXJkiXMnj2bcePGNcfX0yA4OJiKigpkMhk7duygvLxcNYuoXcfA09H4z383hFwuJzU1laNHj2JlZcXixYvx8PDA1NS03XhnW8ydM23aNA4cOICLiwtBQUHo6urWeVFiYmK4desWEydOBJ7uJrBkyRLy8/OxtLSkU6dOiMViLC0tsbS0RC6X87e//Y2qqioMDAxUjorWoqKigu3bt3PhwgWmTZvGrFmzMDc31/CM9enTh2XLlrFu3TrS0tKYPXs23bp10zhf7ZP7RUZRExMTTExMeOutt/Dz82PLli2Eh4ezaNGi5w6KbIzatZxCocDX15fIyEjGjRuHRCKhqqpKpf+9e/fo169fo9+nsrKSjRs3kpqaymeffcbYsWMxNDTU2mziRWkxA9LV1WX58uVMnz6dqVOn1nthqqur8fHx4ZNPPqG8vJw9e/awf/9+FAoFnTt3VnnpxGIx3bp1QyQSYWRk1KrvRGpf4t26dYvVq1djYGDA999/T9euXeuVEYlEODg48Pnnn7N7924++OAD3N3d8fT0pGvXrnTq1Im7d++Snp7+TFVMG8LAwABXV1e+/fZbTpw4wT//+U/GjBnD5MmTMTMzQywWU11dzfHjx5k8efJz9/XFF18wZswYPD09kclkXL16FVtbW+zs7Dhx4gQpKSlYWlpy+PBhunfvjqenZ53nqb2Op06dYu/evQQFBbFmzZoGr2Nbp0VfKHh7exMSEsLmzZt577336qzUKZFIsLa2RiQSYWxsjKurK/fv31crW1v7gz948KDVRxypVEp6ejonTpygoKCAhQsX4uvr+8w6WFhYsGTJEt544w2io6NJTU0lMjKSiooKHBwccHJywsXFpVm+k5GRESEhIQwYMIDQ0FB+/PFHRowYoZoW5eXlcf36ddzd3Z/rvNOmTWPNmjUUFhYiEol45ZVXWLFiBQCvv/46O3fuZNOmTQAcPHhQ47solUrKy8tJTU3l1KlTiEQifv31V7y9vZv8nbVNi6d05+bmMnbsWFasWFFndMMvv/xCcnIya9asQSwWc/LkSa5cuYKRkRHV1dUsWLAAKysrHjx4wDvvvMOWLVuazTXcEDKZjOzsbFJSUkhISKBHjx6MGzcOGxubZjXgZ/XCvQgXL17k119/xdnZmfHjx5OcnExMTAxff/11izoc/kxFRQW3b9/m8uXLZGZmEhwczOzZs9vNGqcxWqUmwq5duzh9+jRLlizRiDy4fv06H330ETNnzkRXV5eUlBS8vLxwdnZm27ZtDBgwAEtLSyIjI+nTpw/vvvtuS6tLfn4+MTExJCUl0aVLF1Ud6MZqXb8IBQUFrFixgs2bNzf7uWvPf/78eVJSUnjy5AlxcXHMnz+fmTNntqiXS6FQcPfuXZKTk7l58yaurq7Mnj0bOzu7DmM80ErF5QMDAzl37hxxcXGMHTtW7X/u7u58+OGHJCUlATB48GDGjRuHoaEhM2fO5MqVKxQXF+Pg4MCiRYtaVM+SkhKuXr1KSkoKMpmMYcOG4e3t/ULhRmFhYTx+/BgLCwsmTJhQb9yWUqmktLS0RRbPtTsc9OzZk9zcXM6cOUNRURHHjh3D1dW1xaoB5efnc/HiRW7duoWdnR2LFi3C09OzQ24i1ioGZGJiwvTp09m/fz/9+/fXeKs8evToOkPJfX198fX1bXZ9lEolVVVVKBQKpFIpZWVlXL9+nfj4eJ48ecLQoUPx8fHBxsbmuc9du+t2bTjKjRs36NatG6+++mqdx0skEoyNjVvkqaxQKCguLiYnJweZTMbw4cMpLS2lpqaGBw8eNPvOeAqFgujoaM6dO0evXr2YOnUq3t7eDe6O0d5ptbJW+fn5/PDDD+jp6fHGG29odRiXSqVcvXqVtLQ0EhMTKSwsJC8vj0ePHvHhhx/y5ptvvnDA5nfffUfv3r0ZO3Ysenp6nD9/noyMDN555506j6+qquLGjRsNbt3yolRXVyOVSlUPC7lcjlwup7q6GiMjIywtLZst5yg1NZVDhw5hYGCAv78/fn5+z7z5cnum1cJ6a3fw3r9/P+np6c8UG9VS6Ovr4+joSHx8PNeuXePRo0fIZDK8vb2ZMGECenp6L3Te2jJgI0eOxNjYGIVCgUKhUHtP8t8YGBjU6/ZtKrU5Vy1Jbm4uv/32G7du3cLf35/x48fTvXv3lyYZsNUMSCKR4OXlRUREBOfOnaNHjx5amRPX1NSQlJTE/v37SUlJoVOnTnTv3p2srCyWLFmicqm/CGfPnuXkyZMcO3ZMdQ5TU1OWLFlS7zmlUikJCQktMlVtSaRSKTExMfznP//BxcWFr776ip49e74UCZJ/plUTS0xNTQkMDOTXX38lPT29RaYtDVFaWqqKUatNFVi4cCEHDhzA09MTd3f3F17Mp6Wloa+vz/79+1UxYAUFBbz11lv4+PjUa0BPnjxh7dq1HDhw4IW/V2tTWFjIt99+S3Z2NmvWrHmurNCORqtnZvn4+HD+/HliY2NxcnJq8fcRCoWC8vJyLl26xPfff49CoaBHjx68/fbbDB06FKVSib29Pd7e3k3S5f79+1hYWGBubq4ywu3btzNq1CiNIhZ/pjZurK2HsCgUCsrKyjhy5Ahnz54lODiYuXPnvlAlm46EVmpUTZgwgTVr1nD79m08PT1b5OapdQ8nJiZy9OhRRCIR06ZNQyaTMXfuXNX0MTc3l5EjRzY5nKSiooLy8nJqfTJJSUlcvny50fc7Ojo6L+Ttay1qamooLCzkypUrREREYGlpyaZNm1Q1A192tGJA/fr149VXX+Xs2bP07du32ettP3nyhFu3bnH9+nUyMjLw8fEhICCgzqelhYVFsyy2e/XqxeXLl/n999+xtrbmyJEjrF27tlEXrrm5OYsXL26TI1BJSYkqebGgoIA5c+aoagkIPEVruzPk5uaybNkyAgIC6t2A60XIzMzk1KlTZGVl4eHhgb+/P7a2tq1ygx44cIDk5GQA/vGPf7RI5EJrIJVKSUtLIz4+nuzsbAYPHkxISMhLP12rC61ub3LmzBlWrVrFDz/88ELp3X8mOzubmJgYMjMzEYvFDB8+nIEDB7b5pKyysjJOnTpFSEiItlVRZQ7/8ccfqrSEkSNH4uLi8sKu/Y6OVg1IKpXy/vvvY21tzf/7f//vhc4hk8mIiorit99+w9bWFh8fH1UhjvZAXl4eixcvJiwsTKt6yOVyjh49yu+//46Xlxf+/v64ublhZmamVb3aOlotdG1gYMBnn31GYGAg/v7+z5X/XpvNePDgQaqrq5kyZQr9+vXD2tq63U2dpFKpViMzYmNj2bFjB/b29ixcuJBXXnkFKysrrenTntB6pXh7e3vmzZvHL7/8wrp1655JpqioiLCwMM6fP09AQACjRo1qtJhjW0UikdClSxetGFBWVhZ79+4lKyuLGTNmMGbMGDp37tzuHkDapE1s8ahQKAgKCmLmzJkEBATUe5xcLicyMpLt27fj6OjI//zP/+Dk5NSuf3ClUolcLm/VNUZFRQWnTp1iz549DBs2jKVLl2JlZdWur6O2aBOPbB0dHRYtWsRPP/2En5+fWohP7Q2Wl5fHDz/8QHZ2Nu+++y5Dhw5t8w6CZ0EkErXa95DJZGRmZrJ+/Xqqqqr48ccf8fT07FD5Oa1NmxiB4Gkp3K+++gobGxtmz56NRCJBJpNx9+5dzp8/T0REBD4+Prz55ptN9ti9bEilUnJzczly5AiJiYm8/vrrTJ06tdWyUjsybcaAampqiIyMZOPGjbz//vuYmppy6dIlwsPDsbS0ZP78+Tg6OmpbzXZFdXU19+/fJzo6mvj4eJycnJgzZ06zV+x5mWkzBgRPgxR//vlnrl+/jp2dHU+ePGHYsGGMGDHipQmPby5yc3OJjY0lNTUVuVzO9OnTX+qgz5aiTayB4KkjISsri9u3bxMdHc3MmTN5//33teahaq+UlpYSHx/PlStXKC0t5bXXXmPChAkaBS0Fmoc2YUA3b95k3759VFZW4unpiZWVFQYGBg3uiiegTnV1NTdv3uTUqVMUFhYyePBghg0bhqOjY7t077cXtHplKysrOXDgAGFhYXh4eBAUFISHhwe3b99mw4YN3Lhxg6FDhwojUCNIpVJ27NjBhQsXGD16NDNmzKBnz57takOu9opW1kAymYzffvuN0NBQ+vfvz9ixY3F2dlZFRsvlcrZv305mZiZvv/12g/k0LzunT59m06ZNeHl5MW3aNPr169fs0e0C9dPqBpSTk8OmTZuIjY1l/vz5TJw4sc5i4vn5+SxYsEBVUF54yadOWloaP/30E3l5eSxdupRhw4a1y9rS7Z1WmcLV7gMaFhbG8ePHGTx4MLt27aqz2Hot1tbWzJ07lyNHjuDr64uFhUVrqNqmUSqVFBUVcfDgQcLCwpg6dSr//ve/X7o6BG2JFh2BampqKC0t5ebNm/zyyy9UVlaycOFCvL29nzl0Zd68eXh7ezNnzpyWUrPNo1QqefLkCcnJyfz888+YmZmxYsUKevfuLawPtUyLGVBZWRkpKSmcOHGC69evM336dKZMmbFbPMoAAAijSURBVPLcT8uLFy/y+eef869//atNpz63FKWlpdy6dYsTJ06Qk5NDcHAwo0ePFtzSbYRmN6DKykrS09OJi4vj0qVL9OjRg3nz5jWpIPznn39OQUEBq1atemnm+HK5nLS0NMLDw7l79y7u7u4EBQUJ0RhtjGYzoNpsxnPnznHjxg1MTU0ZP348Xl5eTZ5m3Lt3j9mzZ/Pll192iC0xGuPOnTuEh4dz584dOnXqRHBwMF5eXtpWS6AOmmxAtQ6CmJgYzp8/j46ODn5+fvj4+GBubt5sc/SwsDB27tzJ5s2bO6xDobCwkMjISOLj49HV1SUgIIDhw4cL6dRtmOc2IJlMRllZmeqTlJTE6dOn0dfXZ8KECQwaNIhu3bo1+9vvsrIyFi9ejJ+fH7NmzWrWc2ubqqoqEhISOHr0KNXV1fj7++Pt7a2xGbNA2+O57vKcnByuXr1KZGQkUVFRlJeXU1JSQnV1NcuWLWtSXenGMDY2ZsmSJaxcuRJfX1+cnZ1bpJ/Wpri4mE2bNpGQkKAK+LS1tRVGnXbCcz3erK2tGTJkCFZWVjx69Ijr16/z8OFD3NzcmD17dov/6L1792bAgAEcPny4RftpLfbv309wcDAAa9euZfr06Tg6OgrG0454rincnTt3+Pjjjzl37hyOjo74+fmxc+dOzp4922qL3OTkZNavX8/bb7/N4MGDW6XP5iYhIYFvvvmGiooKvvnmmwZrZwu0bRodgRQKBZmZmXzyySdMmDCBa9eusXjxYo4ePUppaSkff/xxq3qInJyccHd35/Tp00il0lbrt6nI5XLu3LnD6tWrWb58OZMnTyY8PJwhQ4YIxtOOqXcNVJvNeOPGDQ4cOEBqair+/v4sXLgQd3d3qqqqqKqq4r333mtNfTExMWH06NFs27aN8+fPM2rUqDa90K6uriYvL49Lly4RGhqKs7Mze/fu1dilT6B9UucUrri4mLi4OPbv34++vj7BwcF069YNe3t7VR79nTt3yM/Px8fHp9WVlslkbNmyhezsbN577702G6FQUFBAQkIC586do6qqiqCgIF599dUOuVfoy4qaAdW6pWNjY0lPT2fgwIEEBwfXuXOBVCrVahDjnTt32LRpE76+vqrtFNsKMpmMK1eucObMGcrLy/Hy8mL06NFt1tAFXhyRUqlU1mYznjhxgocPH+Lg4MDYsWOfq1KoNti3bx+xsbH87W9/azNTotTUVI4cOUJhYSFOTk6MGzeuzV9HgRdH9PDhQ+Xp06e5ePEizs7O+Pn54e7uTqdOnbStW6MUFhby9ddfM2jQIEJCQrRaeOThw4ecOHGC5ORkbG1tGTNmDJ6enkIxlA6OaO7cuUpra2vGjh2Lp6cnFhYW7corFBkZydq1a9m8ebNWMlcrKio4f/48Bw8exMLCgokTJ+Lh4dFhw40E1BEdOnRIOXToUCwsLNpl8Ymqqiq++OILjI2NWb58eav2nZOTw+rVq8nMzOTdd9/l1VdfxcLCQsiefYkQKRQKZXv/wXNychgyZAinT59utaKBmzdv5pdffmHGjBnMnTtXqC39ktKmCis2hX//+99ERkayY8eOOkdShUKBVCpFIpG8kBtZqVQik8mIjY1lzZo1mJqa8umnn7b6TuMCbYsOY0AAI0aMYOnSpQQFBanaZDKZKk0gLCyMrl27snbt2ucq+VRRUcHNmzc5dOgQ8fHxzJ8/v03sKCegfTqUAZ09e5bNmzezceNGTE1NefDgAVeuXCEqKgqAwMBAfvjhB9566y1mzpzZ6Plqi9tfuHCBkydP8sorr7Bo0SLBQSCgokMZkEKh4NNPP0VHRwc3NzcSExMRiUT4+fkxatQojIyMiI6OZuPGjXz99df06tWrzvMolUrVnqtxcXEYGxszefJkBg4c2KZe2Aponw5lQEqlkkuXLrF48WI8PDwIDAzEz89Pbat5uVzOpk2buHfvHp999pnGFh9SqZRz584RHh6OkZERvr6+DB06VNhSRaBOJF988cUX2laiuRCJRJiZmVFSUoJUKmXBggUa0y2xWIyVlRURERGIRCJcXV1V/7t48SLr16/n7t27DBw4kNdffx0fHx8hdk2gXjqUAQHo6elhYWHB1atXMTExwdnZGZFIpPYxMTFBX1+fiIgIHB0dKS8v5+eff+bs2bO4uroyffp0RowYIYw6Ao3SoaZwtVRVVREWFkZKSgp//etf6wziLCoq4ujRo1y7do379+/Tp08fQkJCcHZ2bhdhTAJtg/YXevAM6Onp4e3tzZUrV7h8+TKTJk1S+79SqeTRo0ecOHGC0tJSVqxYwaBBgzA0NGxXYUwC2qftZqI1kd69ezNkyBCio6PJysoCnhpOZWUlq1atYtasWYwcOZJ9+/bh5+eHkZGRYDwCz02HHIFqGT58OBEREVy6dAkjIyMuXLjAtm3b6N69O7t378bFxUXbKgq0czrkGujPnDp1in379qGjo0NxcTELFixg7Nix2lZLoIPQoUcggGHDhpGUlISlpSWzZs0SXNICzUqHH4EEBFqSDutEEBBoDQQDEhBoAoIBCQg0gQ5rQAUFBXz88cf06NFD9Vm/fr221RLoYHRYA8rLy+PJkyf8+OOPZGRksHHjRv7xj38QFxenbdUEOhAd1oAeP36Mqakpjo6O6OjoYGpqiq6uboM7gwsIPC8d8j1Q7XaTaWlpZGVloVAo2LhxIzNmzKB79+7aVk+gA9EhR6DKykru379PRkYG27ZtIzg4mF69evH9999rWzWBDkaHNKDy8nLKysr4y1/+wpEjR5g/fz5JSUnI5XJtqybQweiQBlRcXEx+fj4ODg7A02o9WVlZFBQUaFkzgY5GhzSggoIC7t+/r3IYeHh4UFNTo0prEBBoLjpkLFxxcTGZmZn07dsXY2NjAOLi4ujduzeWlpZa1k6gI9EhDUhAoLXokFM4AYHWQjAgAYEm8P8BuTkRtGjHZrQAAAAASUVORK5CYII=)
Physics-General
Physics-
A convergent beam of light is incident on a convex mirror so as to converge to a distance 12 cm from the pole of the mirror. An inverted image of the same size is formed coincident with the virtual object. What is the focal length of the mirror
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)
A convergent beam of light is incident on a convex mirror so as to converge to a distance 12 cm from the pole of the mirror. An inverted image of the same size is formed coincident with the virtual object. What is the focal length of the mirror
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)
Physics-General
Physics-
A point source of light S is placed at the bottom of a vessel containing a liquid of refractive index 5/3. A person is viewing the source from above the surface. There is an opaque disc D of radius 1 cm floating on the surface of the liquid. The centre of the disc lies vertically above the source S. The liquid from the vessel is gradually drained out through a tap. The maximum height of the liquid for which the source cannot be seen at all from above is
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)
A point source of light S is placed at the bottom of a vessel containing a liquid of refractive index 5/3. A person is viewing the source from above the surface. There is an opaque disc D of radius 1 cm floating on the surface of the liquid. The centre of the disc lies vertically above the source S. The liquid from the vessel is gradually drained out through a tap. The maximum height of the liquid for which the source cannot be seen at all from above is
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1kZmbSRPDX+sZwOBzQ6/U0DLenxY47G41HsNlsaG1tZQR4BU4c9BY8Ho+6/MfExCAjIwPz58/HunXr8O233+LTTz/F008/jRUrVuDJJ5+k0Zoc/6TLxuF2u9HU1ISTJ0/i/fffh0KhwMKFC7Fhw4ZeS27j9XphNptRX18Pg8EQEpPeHyCG5HA4cPnyZWi1WsjlctqtJAuCvUWgy/3tt9+O22+/HZs2bcJf//pXPProo8jLy8ODDz6IvLw8ThHm/9Np4yBGUVhYiH379kEsFuPVV19FXFwctFotQ4k7MjISqampHc4sud1ulJWVwWq10jKFQhH2KXbq1Cn4/X5ERUWhqampXxpFOMhsXVVVFfR6PTIyMlgfJh6PB7W1tSFCakRoLfimNZvNqKurg8VioWU8Hg9paWmIj49nrUtjYyNqa2sBALNmzUJBQQF++eUXvPPOO0hOTsa8efMwduzYIT893CnjsNvt+Pnnn7F37164XC6sWrUKEyZMgEQiwc6dO2l/lFBQUICVK1ciKSmp3eNevnwZq1evRkREBORyOdxuNxoaGrBx40ZMnDgxZP/XX38dPp8PS5YsQUxMTBf+zf4DWb0ni3zB2Gw2fPnllzhy5Aij/I477sADDzwQIqNz+fJlbNu2DRUVFbSMx+Nh9erVmD17NmsdioqK8Le//Y1RNmLECDz11FO4cOEC3n33XRQUFGDOnDkYNWpUd//VAU+HA/Jly5bhq6++wuHDhzFmzBjMnz8fycnJPfLjP/zwA95//3288cYbSExMhN1ux7p163D8+HF8/PHHrNOPHo8HR44cgUgk6vH4796AdKXS09P7bTq506dPY/v27dDpdHj66aeRlpY2JAfkHSav+fbbb/H1119j/vz5ePDBB3vMMACgqqoKo0ePpu4QMpkM9913H/x+f9iEOT6fj441+vtKeDB8Ph8ejwfNzc0wm819XZ2wXH/99Xj11Vcxbdo0/OUvf8Hx48f7ukp9Qrvdqrq6Onz33XdYtWoVZsyY0eMKhMXFxRg5ciSjq0A0n8Lh9/upP5XZbIZCoaAaTf0xhwTR17JarTAYDFRB5WokhXoDsViMlStXQiqVYtOmTZg1a1anpn0HE+22HEVFRRg1ahRuvvnmHjcMorGbnZ1NF8o8Hg9KS0uhVCoxYsSIdr/v8XhgNBqh0+lQVVWFqqoqNDc3w+fzUUfC3o4N5/F4EIlEkEgk4PP5sFqtqKmpQUVFBerq6tDa2gqLxTJguoMikQgLFixATk4O9u/f39fV6XXC3vGnTp2CVCrFsmXL0NTUhLVr1+LAgQOMfX7729/i+eefZ/3+3//+d6xduxYNDQ0AgJqaGsbfa2tr6aozmYExm8148803sXDhwk7PlBBxN+DKxEFgd8vv90MqlSI6OhpOpxNarRZ+vx8KhQI8Ho+mThCLxWFvWOLaTsTb1Go1nYXz+/0Mz2CSCYn8jYi9sVFYWIhXXnmFMcsnkUiwbt06LFmyhPU777zzDv77v/+bUTZx4kS8/PLLGDNmDKPcZDJh7dq1+OSTTxjlK1euxIsvvsh6fo8ePYq1a9eitLSUUaeJEyeitbWVtU6DmbAD8vXr16OgoADvvPMOAGZAEP1yO4t8wfsHT0Hu2bMH3377LZ577jlkZWUBuNKU33bbbdi7d2/Y4zqdTnzwwQdd+Bf7JzfeeCPrwLYr57Q39rdarfjd736HCxcu4P777x9SA/KwLcd1112HoqIi2Gw26gbelQFwR/s7HA78/PPPDP+iffv2MRzvBjPdiQjs6WvQmf1bWlpQVlaGCRMmdPo4g4WwV2fcuHGQSqV44403YDQae/yH77//fhQXF+Py5ct0GyqGMVBobm7Gb3/7W4wYMQLDhw/v6+r0Ou0+uubMmYOjR49iy5YtDLVzjsFPdXU1XnvtNajVatx///19XZ0+od0pqPj4eDzzzDP4+OOPYTabcffdd2PEiBGMmavjx4/j559/ZnwvIyMD06ZNQ1RUVI9W9s0334TH4xnUgsp2ux2HDx/GxYsXGeU33HADJk+eHDJrWF9fj8OHD6OxsZGW8Xg8Vpd+QnFxMY4cOcIYXyQnJ2PatGmIjY1FUVERPvvsM7S1teH5558f1Oe7PdptOXg8HkaNGoWHH34YPp8P7777Lj799FPGzEWgvmygzuy1gBx/oGci6kiCtCvnNFjjtzPXgG1/n8+H2tpabN68GR9++CFSUlLw/PPPh/XPGgq06z4iEAgwb948AIDBYMCxY8fwyy+/QC6XY86cOZg5c2avh616vV4UFxfjzJkzVDFkIMHj8aDRaDB+/PgOfc96C4PBgIMHD+Lw4cOQSCSYNGkSxo0bRx9CRqMRhw8fBjC03Ec6vbIXGRmJWbNmIT8/H0VFRdiyZQs+++wz3HnnnZg7d26vpSATCATIz89HfHw8zpw5g8uXL/fK7/YESqUSubm5yMzM7NXYjnA4HA588sknOHDgAKRSKW6++Wbk5eVR6aChTpeWvSUSCVJSUqDRaDB9+nQcOXIE7733HjZs2IAHHngACxYs6JWnoUQiQWpqKjQaDVpbW3H58mVUVVXBaDResy5ddxGJRDRPIomR7+tEoBUVFfjss8/w+eefIzc3F/Pnz0deXh6XTTaIdrtVfr8fp06dCll0W7x4MdasWYO4uDj4/X4UFRVh27ZtOH36NCZPnowHHngA06ZN6/V4AKvVCq1WC4PBAK1WSzOt9hZ8Pp/K5cTFxSE+Ph7x8fH94ilsNBpx4MABfPDBB7hw4QIVowiOew/33YHUrVq4cCG++OILCIVCLFy4EFu2bOmWX1inxxydoaWlBQcPHsQ333wDp9OJG2+8EVOnTsXEiRMZySzPnDmDtWvX4uTJk4zvr127FitXrgw57u7du7F27Vro9XpalpGRgd///veYPn16yP5utxt/+MMfsG3bNshkMiQkJEClUmHSpEmYOHEiPB4P/H4/FWgjogusJ+j/+0vx+XyacFMikaCxsRFFRUXQ6XTQarWwWq3QaDRYs2YNpkyZEnKcV199Fe+++y6jbN68efj3f/93Ro5E4IqrzR/+8Ad8++23jPJnn30Wzz77LGs99+3bh7Vr10Kr1dKEnFFRUVi4cCGsVivOnDmDtLQ0zJ07FzNmzIBEIsFf/vIXfPTRR4zjzJkzB0899RRjID6QjKO4uBiPPfYYDhw4cNW6BT1qHIFUVlbixIkT+OWXX9Dc3IyRI0di5MiRyM3NRVJSEtVtioiI6BdP1oGI3++H0+mkqZiNRiOqq6tx8eJFlJaWQqvVIjU1FRMmTMBNN92EuLi4bv3OQDEOj8eDV155BTqdDk8++SRGjRrVraxfhGvWwczMzERmZiaWLl2KxsZGnD17FqWlpThx4gSVvSTx1LGxsYiOjkZMTAzVsOL6vkyIIRBFyLa2NrS0tKCpqQk6nY5uYrEYOTk5mD9/PnJycgZsxGR3ILrJFosFd955J37/+99jwYIF3X4o9ModSIzg1ltvhcvlQn19Paqrq1FbW0sDaYjMpVwuh0KhQFRUFM2rLRKJkJaWhpiYmEEf+O/z+eB0OtHW1ga9Xo/W1la0trbSvO0kFoTcCHK5HMOGDcO0adOQnp4OjUYz6M9ROJRKJTZs2AAA+I//+A+8/fbb8Hq9WL16dbeO12njaGpqwoEDBxiqgQAwe/bskHjviooKHDx4EM3NzbRMIpFg7ty5yM/PR3p6OtLT0wFcuRna2trQ3NwMnU5HJXZaWlpQUlICr9cLvV5PFTFIC0NaGbVaTTWilEolVCpVv705yDiH5FonGxFiI0ZgNpsZWlgCgQBCoRAKhQKJiYmIjY2lg32VSkXP98GDB+lvSaVSzJs3L8SVnXD48GEcOnSIUZadnY3Zs2cjNjb2mp6H3uCll14Cn8/HqVOn4HQ6u7XK32njkMlkyM3NDWmm2eK81Wo1xowZwwgFFQqFrE08UUSPjY3FyJEjAVxZ6LNarbQvTcSWyabX6+nA0+VyMVItOxwOOpZRq9VUb5eolUskEppGIDAVcnBaZKFQSLV7g9M1k98MTvFMysg4gOjaBm5Op5P+hlgspvWRSqWQy+WIj49HRkYGbUFVKhXdwolkk/MdqEAiEonaHZAmJSWhoKCAURYfHz8otIiBK///2LFjYbVauz2m7bRxREREYPz48Z3aNy4urtv9PABUUZxNaDkwPwe5KUnAE7l5SfoCYkwtLS2wWq2w2+00lwfJ58H2St6TzySlM3mCd/RK0j8rFAoolUokJCQgKysLSqUScrmcGh4xPmIsEokEEomkywuqpBXpCtnZ2cjOzu7SdwYSVqsVe/fuxcKFC7s9fh1wo15yA7VHoL8QieAL9jlikwUN9z4wzoHtfUdZnYI3jmvD0aNH8Zvf/Aatra2QSqV46qmnMGfOnG4fb8AZR2fgbsKhydSpU/GPf/yjx47XoXH4fD4YjcaQlWalUomIiIiQPrDL5YLRaAxxCiRZidiwWCwwmUwM1w+xWAy1Wh3igev3+2E0GhkqiQCoeDObUbDVicfjQa1WhxVWI7q7BJFIBLVazdpqGY1GRn8fAORyedg1HKKI7nQ6GeVqtZrVq8But8NoNDLi0YVCISOe/WrqRMQqghVRyERHT+NwOGA0GqFUKqFQKKDX6+FwOJCYmNjjv3U1dGgcVqsV//d//xeSe4Io8AVfnEuXLuGDDz5AWVkZo/yxxx4LG+l36NAhbN26lXEz5ubm4uGHH0ZOTg5jX4/Hg127doWoYcyaNQvLly9nHadUVFRg69atDFVAPp+Pxx9/HLfeemvI/seOHcPWrVtpzkAASEtLwyOPPMIaI7Fnzx7s3buXUTZlyhSsXLmSdeantraWunEE8sgjj+COO+4I2b+oqAhbt25lCDgkJCTg0Ucfxbhx40L29/v92L17N7766itG+fTp07FixQqo1Wq0tLTQMVFjYyO2bt2K4uJixv7Lly/HokWLQo5/Nfj9fvzwww947bXX8Oyzz2LBggU0Rr2wsLBHf+tquWYr5Bz9D6/Xi7q6Oly8eBF6vR4TJ07sVPhrT66QWywWvP322zhx4gTWrVsHmUyGJUuW4P7776euMSSlRXFxMatbT1xcHGbOnNntOnSWQTnm4GBCjOLEiRP46aefIBQK8fjjj/dJXLhOp0NxcTFyc3ORmpqKvXv3wmq1Mlpwv9+PlpYWFBcXswr8paenhxjHV199FZIpi417770XKSkpnaorZxwDFIPBgP3794eE07Lh9Xqh1Wrx66+/wmQyYfz48SEOh+1BNL+AKzNCnZ02Xrp0KcaNG0fHOB6PB+fPn0d1dTXuuusuCAQCHDlyBFlZWSG6wUT5ks042LTASE7JjuiKGgtnHAMUiUSCnJycTgdNlZWVoaSkBC0tLRg1alTIAmB7EHkm4Mr6SGeTcSYkJDBuRovFgh9//BECgQCxsbH44osvcOLECdx666349NNP8cgjjwC4cgMnJiZiypQprIbANo4jOUd6km4bx/79+7FlyxbGoHX48OFYvXo166DVbrdj8+bNIaqJc+fOxcqVK0NmjcrLy7F582aGIiBwZWA/f/581jp9/fXX2Lx5M2NWKisrC6tWrQrJ+eHz+bB582bs27ePUT5z5kysXLkyZHWZxFcHD1offPBB3HPPPaz1+f7777F582aGp0BKSgpWr16NsWPHhuy/bdu2kHQOkydPxkMPPRSSR1EmkyEqKgqff/45Tp8+zfjbI488goULFzLKpk6dCqVSiU2bNuHAgQM4ceIEgCv998cee6xdXSqj0Uifylcz5jCbzThy5AgqKyvx9ttvY/LkyXSAHnhN+Xw+0tLSkJaW1q3f6Sm6PSC32+2wWCyM6VehUAilUskqgOD3+2GxWBjGBFy5yEqlMqS5I96Vwc0qWWUOV6dg9XKSwZatySUynoFIpVIolUo0NzczXGM8Hg8sFkvIFHV79XE4HDCbzYxzJBAIoFKpWM+RxWIJmTKXSCRQKpWsU8JdrRNxa/H5fPjoo8KGnfYAABQYSURBVI8wZswYXH/99dStJhw9MSD3+Xw4dOgQPv/8c7z88svUi8But8Pn8yE6OrrfeWJ3uzYymaxLvvI8Ho/6CHUGkUjUobSPTqeDw+FAcnIy+Hx+p+pUUVGBtLQ0iESisPWxWCx45JFHsG/fPrpuQvKjh8NqtaK1tZXRdyYBXmyQhJYej4c6SyqVyi5FT3ZUp2ACvQueeeaZTn+vJ3C5XHjjjTcwduxYRivY06nySAZhANRLobsM6GVkr9eLDRs24J577sGXX34JnU4XNqKP8MUXX2Dt2rUMj+FA/H4/du7cifLycqxbt67DOvh8Ppw/fx5r1qwJ6XKxHdtms6GyshLvv/8+Fi5ciKNHjw4Y1fWr4eLFizCZTNdU1dLtdmPHjh3Izs5GWloa5s+fH7JY3BX6VzvWReLi4uh04JkzZzBv3jzcddddGDFiBGJjY1m7LlarFdu3b8epU6ewcePGkNzfDQ0N+Oqrr2Cz2bBjxw6sXr06bN50r9eLc+fO4eWXX0ZtbW27g1yLxYLq6mocP34c33//PU6cOAGlUom4uLh+1524FowdO5Z2za4VNTU1OHLkCIqKilBRUYFly5Zh37593VZsHNAth1AoRHJyMhITE5GYmIi4uDicPXsWZ86cCRlLECwWCwQCAWpqavDGG2+guLiYNsNerxfffPMNoqKiIBaLMXbsWLz55pthj3Po0CH8+c9/RmVlJY1LCUdDQwOKioqoMqFUKkV2dna/kOgZLKhUKvzpT39CbGwsXC4Xhg0bdlWD+g4fWQ6HA4WFhYycDQCQl5eH8ePHhwx0GxsbUVhYGKKtO23aNNYssSUlJSgsLGT4GUVFRWHKlCkhwgPAlRv42LFjdBarrKwMQqEQUVFRsFqteOKJJxhTfS0tLSgsLKTz9EVFRfD7/YiIiMCMGTNw4sQJCIVCZGZm0kCjSZMm4cSJE0hPT8ff//53JCcnIyYmBpMnT0ZycjLsdjtKS0tx9uxZTJs2DaWlpTAYDDh+/DhtrbKysjBx4kQ6hkhNTcXy5ctRVFQErVaL5ORkGI1G7N69m8a5TJkyhXWmr7y8HIWFhYzBekREBKZMmcJ68YuKikLEK9LT0zFx4kTWMYper0dhYSHNMEuYMGEC66xaf4VMoGzevBkfffQRoqKiMGnSpG4fr0PjIOobwQNLkUjEuqBCVDqC9w83MBIIBJBIJIxjkcxI4QisT1JSEkaPHo0ZM2agtLQUmzdvxksvvRS2PpGRkViyZAl++OEHZGdnY8KECbBYLODxeLBYLHTlVSQSITc3F1lZWTAYDEhMTKR14vF4iI2NxQMPPIDi4mJkZGTguuuuowl/gCuOk4H/k1gsRmVlJb777jvcdNNNyM7ORktLCzQaDe1WdXSOAscm7WWuEgqFnb5e5P/pyjXr70ilUmg0Gpw9exYHDx4Mm1W3Iwa8b5XBYMDp06cxYsQI8Pl8/Nu//RtuuukmPPbYYyH7ms1mfP3111iwYAG2bduGuro6/PGPf6R/t9lsEAqFEIvFKCgowMmTJ+Hz+WC328POqpB1joKCAhw7dgzz589nHevo9Xq89957iIqKwtKlS1FeXg6JRIKRI0f2e/f6gaI+Esi5c+ewcuVK3HDDDdi4cWO3VEj691XpBGq1GiNHjkRERATi4+Pxn//5n9i/fz9rBlQej4fp06dDIpHg7rvvRklJCUMLSy6Xh9zYfD4/rGGUlJSgqakJM2bMQHR0NCZPnhx25mnHjh3wer249957oVKpkJmZifT09H5vGAOVtLQ02iXsrvD4gL8yPB4PcXFx9MmQmpqK//mf/8Frr70Wkq5ZoVBQdY7o6GiMHDkS33zzTbd/e9++fZg2bRo1Ko1Gw7qYtnPnTvz0009YvXo17fNHRET0+Bw/xz/RarUoKirC1KlTu9097LZx+Hw+GmcduIXTqmXbv73UyGQxJ/g7bE9mPp8Pv99P90lNTcWKFSuwZs0axjx3YEirQCDA0qVL8c0333SqTsH1MRqNOHbsGGOaMDhtmM/nQ0lJCd5++2288soriIqKoueIrf8f7hyxndOunJ/A73Tlmg00tm7dShOgTpo0Cb/5zW+wYsWKbh+v2xPsX375JTZt2sSYQcnOzsbTTz/N2id966238PHHHzPKZs+ejSeffJLVy7OkpASbNm0K8Rt69tlnsXjx4pD9v/32W2zcuJHRTeLz+Vi/fj1efPHFEHcKn8+HAwcO4PTp0xg7dixdKb/99tvx5JNPhhy/uroamzZtool69Ho9xGIxfvrpJyozFMz27dvx5ptvQigUYtWqVQCuzBo988wzuOmmm0L2f//99/Hhhx8yym655Rb8y7/8S4hAd2NjIzZu3BiydvDwww/j0UcfZa3Pjz/+iI0bN0Kn09EyjUaD5557DlOnTmX9zkDioYcewkMPPdRjxxvwA/L2qK6uxnvvvYf8/HwsWrQopMtjt9uxe/duNDU14ZlnnmEsxpEBORtOpxMvv/wyZs6ciTlz5rC2AgaDARs3bkRUVBSeeOKJAb3QNxAH5D3BgB9ztEdqaioWLFiAixcv4uTJkyFOjFKpFDk5OaipqaH50jtDWVkZXC4XRo8ezWoYZrMZX331FSQSCRYvXjygDWMoM6iNg8/nY9y4cSgoKMDBgwdDFrl4PB7S09ORlpaGX375pVPH9Hg8OHbsGG688UbWuAKXy4XDhw+jsrISixYtYhW94xgYDGrjAK5M4918882IiYnB7t27GfkMASAmJgbp6emorKwMUQNhg6QcGDVqVMiimdfrxZkzZ3Dq1Cm6et2VyDOO/kWn2vuWlhbs2rULp06dYpQvWLAAd911V8j+586dw65du6jLBnDFxX3ZsmUhurqEL7/8Env27GGU5eXlYcmSJUhOTmaUm0wm7Nq1K2QtY86cOVi0aBGrS8vFixdx/Phx/Prrr5DL5eDz+VixYgWmTZuGnJwcVFRUoLS0FPn5+fR7Dz/8MOM4OTk5iIyMRHx8PJKTk+mN73Q6sXPnThw6dAhNTU3Q6/W4cOECtFot7rnnHtbYipKSEuzatQs1NTW0TCQSYfny5az5PQ4dOoSdO3cyYjfS09Nx3333hSi0AFcWNHft2oWjR48yymfOnIm77747xLCrqqqwa9culJeXM8qXLVvGqnAyFOiUcURERGD+/PmYNm0aozxcLHF6ejpWrFjB0EESCATtpkQbP358yKyPSqVi1deVy+W47bbbQqLXwnm4Jicn44UXXoBer8e6deswa9YsTJgwgdYnMzMTCoUCJSUlDOMIThTD4/Gwa9cu5OXlMWJNRCIRCgoKcOrUKSQkJGDx4sUQiUSIiYkJG0SUkpKCBx54gOEgyefzw56j/Px8xMXFMaZqZTJZWK0niUSC2bNnh3gKx8TEsC6KJSQk4N577w1x8e4vST37gk4Zh1gsDgmAbw+lUtllHdau6L0KhUKkpKR0WkVCoVAgMzMTfr8fL730EtasWYN58+bRUFiFQoERI0agtLQUDQ0N9IYLdgL8xz/+QQW1A28wn88HrVYLn8+Hxx57rFPdKYVCgaysrE7VHwCio6O7lKlIIBAgOTk5pNUNh1wuDxsbbjQaO/27gwnWMcdg7SfzeDxMmDABzz33HFatWsUIjMrOzoZWq0VlZSXrd/1+Py5cuAA+nx/iLXz+/Hn87//+L1atWoX09PRBe/6GGqzGQWQ+/X4/Y1FtsHDHHXdgzJgx+Nd//VfarUlPT0dycjJqa2tZY0GI4YwcOZLR1autrcV7772H5cuX47rrruu1/6G3IPKrQPthv4MR1m5VYmIiamtr4fV6UVFRgTFjxrB6NdbX1zMGlMAVw0pPT2f1G3K5XKiurg6ZMUpOTkZKSkrIE9doNKKmpobRD+bz+Rg+fDhrF6yxsRE1NTWMfrlSqURaWlqITOgf//hH/O53v8Pf/vY3XH/99QCuTNMePHgQGRkZDDcSv9+P2tpaNDc3w+12MyYCtm3bRtdT2GhsbER1dTXDRUOpVCI9PT0kft3n86GmpoYGRBHi4+ORmpoaViSiuro6RBc3IyODdRpZp9Ohurqa8f/J5XKkp6eHBF7x+XwYjUY6Ba5UKodUcBarcZCpzcbGRuh0Oly4cAFpaWmIjIxkDHhLSkpCNGIzMzOxcOFCVuOw2+0oLCzEr7/+yiifNWsWhg0bFmIcTU1N2L9/P2PWSyQSYfHixazGUVFRgT179jC6SykpKVi0aFGIcQgEAjzxxBN49tlnsX37dowdOxYCgQBarRY//vgjY1rXbrfj0qVLEIvFuHTpEo4ePQqLxYKioiJcf/31YWfggCsLhnv27GEYbHp6OhYuXMhqHCdPnsRPP/3EKJ8wYQI0Gg2rcTQ3N4es4fB4PCxZsoTVOKqqqrBnzx7GZEliYiIWLVpEb3yBQACv14umpiZUVlaira0NYrGYBn0NFVjdR4ArrcLx48eh0+nA4/GgVCqRmpoKjUZDp0IHOh6PB0ePHsW+ffuwcuVKXH/99di5cyeqqqqwbds2Gv1IhJ+nT5+OW265BR6PB59//jl++eUXvPDCC2FjzAcaQqEQPB4PRqMR9fX1KCsrg8fjoZGSN9xwQ5fUTgY6gv/6r//6L7Y/qFQqREVFwW63w2AwMHLZuVwumo1oIA8+Sco1g8GAn376CampqcjJyYFUKsWBAweoA6Lf74darUZeXh6kUikOHz6Mw4cPY+nSpcjKyhrw54DkWTcYDKipqUFVVRXq6urg9XohEAgwatQo5OfndyiVNNgI23IQ9Ho9qqqqUF5eTgfnYrEYCoUCkZGR0Gg0iImJgUgkGrASMzqdDtu2bYNCocDSpUuhUqnw3XffsWYFKi0txbZt2zBp0iTMnj2724E0fY1IJIJAIIDdbqfpmg0GAywWC+2WJiUlYcSIEUhJSQkrXDeY6dA4gCt6QG1tbaioqEBVVRUd/AkEAprLLi4uDvHx8YiOjoZIJAobh9Af8fv9uHz5Mt59912MHTsWd9xxB8RicUjXsaGhAR9++CGGDx+OuXPndkmAra8hAmcikQhWqxXNzc1obGyEXq+H0+mE2+2mD7e4uDiqiUuy+A5FOmUcwD+DaywWC6qqqnDx4kWG1CVJNSYUChEdHU1TAkdGRtJ0yRs2bMBnn33GOO6SJUvw9NNPhwxOz58/j/Xr14cIpb300ktYunQpax137dqF9evXM1wsRo0ahRdffDHEzdrn82H9+vXYsWMH/f9sNhsKCgqwfv16fP/99/jggw+gUCjw+OOPIy8vD3/605/w/fff0y4lcEU5MNjNhLBv3z6sX7+esYg2fPhwvPTSS6yD+L/+9a/YsmULo2zWrFl47rnnWJVYysrKsGHDBhpjQnjhhRdokI9QKKTTsc3NzdBqtbBYLDRfIrl+AoEAGo0Go0aNQnJycrsCDkOFThsHG3V1dSgvL0dVVRU90cGHEwgESEhIQEJCAk19LBAI4HK54PP5+mV/fffu3Xj99ddRV1cHHo+HrKwsGr/RHwk870KhEA6HAxaLBXq9nrYOwV1ePp8PHo8HuVxOM8t2ZQV+KHBVxkFwuVzQarXQarVoamqC1WoNG3ZKNGElEgliYmIQGxsLhUJBpym9Xi+9cOSV0FvdtBUrVuDQoUP0hhKJRLjnnnuwfv36Xvn9YAIz35KMuCSk1u12w263o6GhAW63GyaTKSS3H+lSkTTQarUaycnJSEpKojH1HKH0SBSOWCzG8OHDMXz4cLhcLuj1ejQ3N6OlpQUGg4HmDCd5w00mEwAw9GolEgkVdpbJZJBIJPQ1UC+KdN9IGuPAuO2eMp5g9XiPxxNWQfFqCb7hg9NEe71euN1ueg6dTifsdjtsNhtj8BwI0eoim1wuR1RUFGJjYxEXF4fIyMh+2WL3N3o8RI2ocJAFKKfTCYPBQKeBzWYzbDYbHA4HnE5nyNbS0sI4Hp/Ph0QigVQqhUQigVgspn1+MuMSaCTkc3AOcIFAEJIznBD8fsyYMTh37hyNj4+MjERWVhZrHvP23gff7MF50cnNT1pYksmIbMQY3G43q+HzeDwIhUKqnk7OE8msGxERAbVajYiICC4asRtc8zMmkUgYxkJE0qxWK2w2G30KEoMJNhqXywW73d7hk5sYAOk6CAQC+plMFAR204INIrB83LhxOHv2LE6fPg2hUIi8vDxkZ2ejrKyM0cXpaCOGQF6JEQRunWnt+Hw+fTgEPihkMhnkcjl9lcvlUCgUQ8r/6VrSI2OOnoA8JUn3i2xOp5O1lXE4HPQJ25HMT3fQarWora2FQCBASkrKNcmRHTi9SpQWA40guMUkr2STSCRci3AN6TfGEY5gfabgrgjpopDBKRnXkPfks8vlorpOgVtwX5/tMwBGFy1w7ENu8MAysolEItoFJN3AwC4h6RYGdgVJqxf4GjwxwdE79Hvj6CzhZnQCX4PHBoHfbe+VENwl68xr8Mxb4PiImyXq3wwa4+Dg6Gm4RxcHRxg44+DgCANnHBwcYeCMg4MjDNwkeTu89dZbaGtrg1QqxcSJE1nF1jgGL1zLEYYtW7bgwIED0Gg0cDgc+Pjjj0NcWzgGN9xUbhjy8/PxxBNP4IknnoDJZEJVVRVycnKGZETcUIUzjjDcdddd+PXXX0OkhziGDly3KgwfffQRsrKykJCQgDVr1vR1dTj6AK7l6IDLly9j+vTpeP3111kV5TkGL1zLEYTNZoNOp6NevjweD1OnTg1RH+cY/HBTuUFcunQJ7777LmbOnAm5XI6ioiK4XK6Q9Ascgx+uW8XCW2+9hdOnT8Pn80GlUuH555/vdLoDjsEDZxwcHGHgxhwcHGHgjIODIwyccXBwhIEzDg6OMHDGwcERBs44ODjCwBkHB0cY/h+Aqw5jexMljwAAAABJRU5ErkJggg==)
Physics-General
Physics-
A slab of glass, of thickness 6 cm and refractive index 1.5, is placed in front of a concave mirror, the faces of the slab being perpendicular to the principal axis of the mirror. If the radius of curvature of the mirror is 40 cm and the reflected image coincides with the object, then the distance of the object from the mirror is
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)
A slab of glass, of thickness 6 cm and refractive index 1.5, is placed in front of a concave mirror, the faces of the slab being perpendicular to the principal axis of the mirror. If the radius of curvature of the mirror is 40 cm and the reflected image coincides with the object, then the distance of the object from the mirror is
![](data:image/png;base64,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)
Physics-General
Physics-
A ray of light strikes a plane mirror M at an angle of 45° as shown in the figure. After reflection, the ray passes through a prism of refractive index 1.5 whose apex angle is 4°. The total angle through which the ray is deviated is
![](data:image/png;base64,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)
A ray of light strikes a plane mirror M at an angle of 45° as shown in the figure. After reflection, the ray passes through a prism of refractive index 1.5 whose apex angle is 4°. The total angle through which the ray is deviated is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJYAAACsCAYAAACZ4FUpAAAfF0lEQVR4nO2deVzU1f7/nzPDJojsiwgyLBLuCiooYiKpydVcrsvjXlOzUitzq6y0WzdL61bcmxsutzK9aeWSuVG4FbihlSkKKCCLrA77rjDMzO+PvvDTGGUbmIXP88/PnDnnPfLyfc7nfd7vc0QqlUqFgICGEWvbAAHDRBCWQLsgCEugXRCEJdAuCMISaBc6tbDq6uq0bYLB0mmFVVFRQVZWFpWVldo2xSAx0rYB2qC8vJzbt29TUlJCRUUFHh4eWFpaatssg6LTeax6UZWWlqJSqSgpKSEtLY3y8nJtm2ZQdCphVVZWNohKqVQ2PC8rKyM9PV0QlwbpVMJKSkoiMjKSwsLCB56rVCqdFldaWho//vgjd+/e1bYpzaZTCcve3p7ExET279/fSED14srIyNC5Bf3WrVtJSkpCn7Z1RZ1tEzo1NZUVK1ZgZ2fH9OnT6dq1a6M2tra2eHp6YmFhoQUL/0ClUpGZmYlCocDJyQlTU1OMjPTnXatTeSwALy8vwsPDyc/P59ChQ2q9U3FxMenp6VRVVWnNS1RUVHDs2DH27t3LvXv39EpU0Ak9Vj1JSUm88sorODk5MWXKFKysrBq1sbe3RyqVdqjnUqlU5ObmIpPJcHV1BcDR0bHDxtcUnc5j1fPYY4/x6aefUlBQwL59+yguLm7UprCwsMFzdRS1tbVERUVx/PhxrK2t9VJU0Ik9Vj2pqam88847KJVK/vrXv+Lg4NCoja2tLR4eHmrXY5okMzOT69evY29vj4uLC25ubu06XnvSaT1WPV5eXrz77rtYWlpy4MABCgoKGrWpX3NVVFS0qy3btm0jOzubgIAAvRYVCB4LAKVSSXJyMps2baKoqIgZM2Zgb2//QBuRSISNjQ1SqVTj2z/p6ekolUoKCgrw9PTU2+nvfjq9xwIQi8X4+PiwdOlSrK2t+e677xqtueq3fzIyMjTquUpLSwkPDyc2NpahQ4cahKhA8FgPoFQqSU1NZc2aNYjFYmbMmEG3bt0eaFPvuTQR5yorK0MsFpOeno5UKm00lj4jCEsNaWlpLF++HHt7e2bMmIG5uXmjNnZ2dnh6eqr9rDnk5eXxySef4Ovry9y5czEzM2ur2TqFIKyHcOvWLZYtW4arqytTpkxRKyB7e3s8PDxaJC6VSkVlZSV37twhLy8Pb29vXFxcNGm6TiAI6xHUi+tRQVQHBwekUmmzxVVWVsZXX32FtbU1Tz/9tKZN1hmExfsj8Pb2ZsOGDRQWFnLgwAGKiooatSkoKCA9PZ3q6uom+5PJZMhkMiwtLQkODm4Pk3UGQVhNUC8ukUjEwYMH1ca5CgsLSUtLe2SEvqamhvXr15Ofn8+8efNwd3dvT7O1jiCsZuDh4cFbb72FpaUl33//vVpxFRUVkZ6ernZTWyaToVKpcHFxQSqVdoTJWkdYYzUTpVJJUlISERERlJaWMnXqVLVBVFtbW6RSacP2T1xcHNu3b+fll1/Gw8ODLl26aMP8DkfwWM2kPoj68ssv07VrVw4fPvzIIGq957KysmLIkCG4uLh0GlGB4LFaTH0Q9b333kMikTB9+vRGWzwikYi6ujpOnz7NlClTGDhwICYmJlqyWDvolLCqq6sxMjLC2NgYkUikbXMeSUZGBkuWLMHR0ZGZM2eqDXDK5XIGDhyoNmPC0NGpqfDevXt8++23/PzzzxQVFel0pbJUKmXDhg3cuXOHgwcPqi10MDY2prCwUK+KIDSFTnks+CNF5aWXXkIsFjNz5kyGDBmCk5MTxsbG2jZNLWlpaSxZsgRnZ2cmT56sNojq6OiIVCrtXGusrKws1ZUrV3SqMqW4uJhVq1ZRW1vL1KlTGT16tE5v0Kanp/Phhx8ybdo0Jk+ejJ2dXaM2Dg4Oneqt0Ki0tJT4+HhKSkq0bUsDFRUVSCQSxGIx169fp1u3bmo9QVs4evQogwcPpkePHm1ez9XU1DBv3jx2796NSCRi4sSJjdZV9bEvd3d3rVb/dBRG/fr1o1+/ftq2o4Hy8nL++9//4u3tzaRJkwgMDCQwMFDjHquoqIhZs2bxxBNPIBa3fqmZkJBAZGQk8+fPZ8+ePXTt2pWjR48yceLERrlVhYWFqFSqDi/Q0AY6tXivqanh6NGjdOvWjfDwcJYvX864cePaZRp0dHRs+EO3hRs3bqBUKrGwsMDa2prFixdjZWVFZGRkowi9SqWiuLiYjIyMDi3Q0AY6VaymUCgIDg7Gxsam3U9/cXBwaJOwEhMTSUxMZMCAAYwZMwZjY+OGIOqLL77Ipk2bOHbsGFOmTMHGxqbhe0qlkuLiYkQikUFPizrlsbp06ULPnj075Eghb29vEhMTUSgULf5ubW0tP/zwA6Wlpbi4uGBra9vwmUQi4bHHHuOVV15BpVJx5MiRRi9GSqWSwsJCbt++bbChCJ0LN3QUJSUlhISEcP78+RZ5jZycHPLy8ujfvz+mpqYNz+VyOb6+vqSmpjY8y8zMZPHixTg5OTFr1iy10XdHR0c8PDwMLoNUpzxWR2JjY0NgYCCHDh1q9nfKyso4evSoWi+kjp49e7J582Zyc3PZv3+/Wu+Un59PRkYG9+7da5H9uk6nFRbAk08+ycGDB6mtrW2ybU5ODtevX2fOnDm89tpramNV6nB3d2fr1q3k5OSwf/9+ysrKGrWRyWRkZGRQU1PT4t+gq3RqYQUHB5OZmcn58+ebbPvTTz9x/PhxjIyMWvyWWi+uiooKDh8+rDYTVSaTkZaWZjBrLoNcY508eZLExER69+7NuHHjHtn22LFjfP7553z++eeN8qsA4uPjycnJwdvbm27duj10Q1ndGuvPZGRk8MEHH1BXV0dYWJjavhwdHXF3d2919Y+uoDfCKigo4PDhwygUCmbMmIGtrS2vvvrqA23GjBlDr1692LlzJxYWFpw7d449e/Y88Nb2Z+rq6nj++ecZMWIECxcufOCzmpoa1q1bh1Qq5dlnn32kfc0RlkqlIjk5mYiICCorK5kwYUKjIKpIJMLBwYGePXvqdShCb6bCn376iW3btvHTTz81rFPWr1+Pvb09AQEBDecd3L59G2traxYsWEBBQYHaNc39GBkZsWLFCn7++WfOnj3b8PzGjRukpKQQFhbG1KlTNfIbRCIR3t7evPjii3Tr1o2oqCi1x1YWFhaSmZmp10FUvRBWcnIyCQkJ+Pn5YW1t/cBnTzzxBDNnzmTmzJkMGDCAoUOHEhcXx8SJEwkKCmpWzV7fvn2ZPn06X3zxBVevXqWwsJAvv/ySpKQk/Pz8HghwthWJRIKPjw8vvPACZmZmDfGw+6mPc2VmZjar+kcX0fmpsLS0lK1bt1JXV4e3tzdnz55l5cqVeHh4IBKJcHZ2xsTEhCFDhrB27Vp69+5NQUEBd+/excrKqtmb1+Xl5Xz55ZdER0fz5ptvYmtri729PdbW1s3apG7OVHg/SqWStLQ01q5di5GREdOmTWs09YnFYhwcHHB3d9e7rAid91jJycmcOHGC2bNnNwowKhQKcnJy+OWXX+jevTsffPABeXl5DWuUlmREdOvWjZCQEIqLi4mKisLd3R0bG5t2y2QVi8V4e3uzdu1aZDIZBw8ebLQLoFQqkclk3L59W+9CETotrLKyMrZt28aECRMwNTWluLiYqqoqZDIZCoUCsViMWCzGycmJcePGce/ePWQyWYvHUalUVFRUYG9vz5YtW1i8eHGH5ai7urqydetWcnNz+eabb9QGSuvjXM2Jt+kKOrUJ/WdUKhUFBQUkJiZy8OBBiouLKS8v59q1a+zevRtnZ2fs7Oyora2lqKgIW1vbZgcu7+fevXv85z//wdnZmUWLFrXDL3k0rq6ufPbZZyxcuJD9+/czefLkRrGyO3fuAH/UOOpDYYbOr7Hu57vvvuP06dOsXLmSK1eucP78eUaMGEFRURHR0dGEhYW1+DyE1NRUlEolFy9eZNy4cTg5ObXKtpausdSRk5PDypUrMTc3JywsTO1/EmdnZ9zd3XV+b1Gnp8I/4+3tTUhISMN6SKFQcPbsWRITE5kwYUKLRVVZWclHH31Eeno6c+bMabWoNEWPHj1Yt24dxsbG/PDDD2orru/cudPoLVIX0SuPpUkyMjKwtLTk8OHDPPXUU2qj7i1BEx4L/pj+U1JS2LJlC1VVVYwfP/6BCH1LT7fRFnrlsTRFcnIy27Zt486dO8yfP7/NotIkIpEILy8vFi1ahKWlJcePH28IotYXZOi6qKATCqu2tpauXbsyYcIEunfvrpOFsfVB1EWLFmFqakpUVBQmJiZ6VUKm02+FmiY5OZldu3YRGhrKqFGjkEgk2jbpoUgkEnr16sWKFSv4/fff9WL6u59OJSy5XE5QUBBDhgzRi7tpxGIxXl5eeHp66qRnfRS6/6+rAQoLC9m1axf+/v6EhYVp25wWo2+igk6wxioqKqKkpASFQsGgQYO0bU6nwaCFlZ2dzfr167Gzs+P1119vlBkh0H4YtLBkMhm1tbVtqnQWaB0Gvcby9/enV69eOn2giKFi8P+VBVFpB4MXloB2EIQl0C4IwhJoFwRhCbQLgrAE2gVBWALtgiAsgXZBEJZAuyAIS6Bd0HthKRQKvSgu6GzovbDy8vKYOHEi3333nd6ec2CI6L2w6urqSE5OZv369Tz11FPExMQgl8u1bVanR++FBeDi4sLbb7/NmDFjeOWVV3juueeIi4sTPJgWMZi0mS5dujBq1Cj8/Pw4e/Yszz//PKNHj2bu3Lm4urpq9CgigaYxGGHV061bNyZNmsTw4cM5c+YMS5cuJTQ0lNDQUHr16qVTNYSGjMEJqx4HBwemT5/OyJEjuXDhAhs3bmTgwIEEBAQwePBgIU25nTFYYdXj4uLCtGnTyMrK4vfff+ebb77h3LlzjBgxgqCgIJ0/XENfMXhhwR/Fn56envTo0aPhvPa9e/dy8uRJwsLCGDVqlLZNNDgM4q2wuZiZmdGrVy/CwsKYNGkSFhYWbN26lWXLlvHrr79q2zyDolN4rD/TpUsXPDw86NGjB0FBQZw7d441a9bg6+vLc889R+/evbVtot7TqTzWnzEzM6N79+5MmzaNN998E5FIxIsvvsiaNWvIycnRtnl6TacWVj1GRkY4ODiwcOFC3nnnHbKysnj66afZsmULRUVF1NXVadtEvaNTToWPomfPnqxatYqEhAT27dvHyZMnmTp1KmPGjMHe3l54i2wmgrAeQv/+/RkwYAC//PILhw4dIjo6mpCQEAIDA3F1ddWbc6q0hSCsJggICCAwMJCYmBhiY2O5fPkyAwcOZMSIEXpzgrE2EITVTEaPHs2wYcO4dOkS8fHxxMXF0a9fP0JCQvDw8NC2eTqHIKwWYGFhQWhoKH5+fsTFxZGQkMD58+cZPnw4EyZMEAR2H4KwWoGtrS0hISEMGDCApKQkLl26xN69ezEzM6OoqKhVlxgYGkK4oZXU3ys4cuRInn32We7evUtJSQmzZs1i3759VFRUaNtErSIIq42IRCLs7OzIzc0lJyeH5cuX89VXXzFt2jROnz6td5craQphKtQAiYmJWFtbM2zYMIYPH46fnx/R0dGsWrUKLy8v3njjDXr37o2JiYlenifaGgRhaYDz588zZswY5s2bB/yxVTRhwgSCgoKIjIxk0aJFjBo1ijlz5jRcd2foAhOmwjaiUCi4cOECw4cPb3RvtJWVFbNnz2b37t04OTmxYsUKIiIiuHjxotqb7A0JQVhtpKCggIyMDPr27cvw4cPVtnF0dGThwoVs2rQJY2Njtm/fzo4dO4iOjjbYmkhhKmwj8fHxDbn0oaGhj2zr5ubGwoULuXXrFjExMRw8eJDY2FgCAgIYMWKEQe1DCh6rjVy+fJkhQ4agUCjYsGFDk+2NjIzw9fXlmWeeYfbs2Zibm3PkyBHWrl1LTExMB1jcMQjCagO1tbXEx8czbNgwxGIxEydObPZ3zczM6N+/P7Nnz2bOnDl0796d//3vfyxfvpxLly61o9UdgzAVtoHU1FSsra1xc3MDoHv37i3uw8LCgj59+uDh4UFoaCinTp0iPDwcd3d35s+fT9++fTVtdocgeKw28Ouvv+Lk5ISZmRlKpZJ169a1ui9zc3OkUinz5s3jX//6Fw4ODqxYsYJ//vOfZGdna9DqjkEQVitRqVTEx8c3lJCJxeKGOFZbMDExwdXVlRUrVrB582YqKiqYPXs2GzdupKysDKVSqQHr2x9BWK0kOzub4uJiHBwckEgkiEQiBg8erNExpFIpH330EeHh4SQkJDB37lx2797NnTt3uHfvnkbH0jSCsFrJrVu38PDwaDgTQqFQ8Oqrr7bLWIMHDyYiIoIVK1Zw5swZVq9ezYEDB0hNTeXu3bvtMmZbERbvrSQ9PR03NzesrKyAPy6tnDNnTruOOXLkSIKDgzlx4gTHjx/n4sWLDB06lMDAQKRSKaampu06fksQPFYruHv3LoWFhTg4ODyQ+95R9/aMGzeOl156ibt37xIbG8tnn33G119/za1bt3RmDSYIqxXk5eWhVCpxdnZuuFdaqVSyadOmNvddXV3NmjVreO+997h69araNkqlkpycHEQiEUuXLiUkJIScnBzCw8PZsWMHubm5bbajrQjCagXZ2dmYmZk9cCSSRCJhzZo1Le4rJSWF1157jY0bN1JXV0dkZCRyuZyuXbvy448/qj087t69e8TFxeHt7Y2vry9hYWE899xzzJgxg6ysLBYvXsyXX35Jfn5+m35nWxCE1UIUCgWpqamYmZnh4ODQ8FylUpGSktLi/nbu3ElsbCyJiYmoVCoyMzPx9fVl0KBBlJSUqD32sqamhvT0dPz8/BqeOTs7ExISwksvvcTKlSuJj49n/vz57N27l7Kystb92DYgLN5bSFFREcXFxfj4+DywaaxUKtm5cycLFy5sdl+nT5/G2NiYgIAAFAoFADNnzsTf3x9fX19Wr16tdt1WV1dHUVFRo0i/SCTC0dERBwcH+vbty/Xr19m8eTO7du1i2bJlPP744x220S0Iq4WUlpYiEolwdXV94LlEImnWJnQ9aWlpHDx4kPHjx5Odnd3g7dzc3MjPz29IBFSXEKhQKCgpKXnAY96PSCTCysqKkSNHMnToUE6ePMnq1auRSqW8++679OvXr90TDYWpsIXk5uZSUVHRSFgqlYobN240qw+5XM6pU6fo0qULQUFBLbZBoVBQXl7e5KmEtbW15OfnU1paipWVFQ4ODhgbG7d4vNYgeKwWUFtbS0FBAdbW1jg6Oj7wmVKpZN++fcydO7fJfpKSkjh79iz+/v4kJSWRnp7OnTt3uHDhAqNHj27y+xKJBEtLS8rKytR6LYVCwe3bt7l8+TJRUVFIJBLef/99hgwZ0mGxLkFYLaC0tJTc3Fwee+yxRp+JxWJefvnlZvVjYmKCjY0NcXFxxMXFkZKSQkVFBZ9//nmzhWVjY9MQS6un/gXi8uXLXL58mcrKSmbNmkVQUBBdu3Zt/g/VAIKwWkC9sCZPnqz286ysrGb14+Pjw8aNGxGJRIhEIiIiIkhJSSE8PLxZ3zcyMsLOzo7s7OyGQ+Ju3brFuXPnuHHjBtXV1YwfP56RI0dq7RhyQVjNRKlUIpPJMDExwcXFRe3nkZGRLFiwoMV9BwcH079//4Zga1OYmpri5eXFlStX6N27NydOnODmzZuYmpoyatQoAgMDtX7suCCsZlJbW0taWhoeHh5q1ykSiYR33nmnVX0PGDCgRW9pZmZm9OvXj1WrVpGWloazszOhoaEMGjQIZ2dnnSgtE4TVTGpqakhNTX1o+rFSqeT7779/IGjZXhw4cIDdu3djZGTEsGHDmDRpEnZ2dhgZ6c6fU3cs0UGqq6upqKige/fuyOVysrKy8PT0VNtWpVJx4sQJ3n///XazJyoqig0bNuDg4MDSpUvx9/ena9euOlndIwjrEZibm7N+/XpWr17N+fPnMTY2fmhQ0sjIiNjYWI3boFKpiI2N5d///jfl5eW89tpr/OUvf9H4OJpGEFYTWFlZsX//fg4dOkSPHj24ffs2KSkp9OrV6wHvpVAo+PDDD1u9zrofpVJJdXU1SUlJfPvtt9y+fZtp06Yxa9YsnfRO6hCE1QQ9e/Zk9erVWFhY4OjoyN69exk7dmyjQ9ZUKhVxcXFtHq+4uJjU1FROnTrFrVu3CAwM5K233sLJyanNfXckgrCaoHfv3lRXV1NVVcXNmzeZPHky/fv3b9ROIpGwZMmSVo9TXFxMUlIS586dIysrC19fX9asWYOXl1dbzNcagrCaoGfPnpibm2NsbMwzzzzD6NGj1e63KZVKYmJimhU5v5/S0lKuXbvGhQsXKC4uxtPTk2XLlultPWE9grCawNTUFDMzMyZOnMjUqVMfuYnbkvq/qqoqrly5QkxMDHfv3sXX15epU6cyaNAgTZitdQRhNUFeXh5yuZwXXngBc3Pzh7YTi8UsXry4yf7kcjnXrl0jMjKSsrIyAgMD8ff3p3fv3h2WedARCMJqgps3b9K3b1+12zj3o1Ao+PTTT9m1a9dD29y6dYs9e/aQkpLCpEmTCA4Oxs3N7ZGC1VcEYTVBTEwMYWFhzWr7sMvNc3Nz2bVrF0eOHGHBggUsW7YMe3t7g77dQkj0a4KEhAQef/zxJtsZGRmxd+/eB54VFxcTERHB2LFjUSqVXLx4keXLl+Pm5mbQogLBYz2SlJQULCwsGmWLqqOuro7Zs2fz9ddfU1RUxJkzZ/j666/p27cv0dHReHl56cTmcEchCOsRXLt2rdmZBwqFgvz8fCIjIzl16hSmpqZ88skn+Pn5dcr7dgRhPQSFQsHVq1cJDg5usl1mZiZXrlyhT58+nDt3jvnz5xMUFISFhUUHWat7CMJ6CPn5+WRnZyOVStV6LJVKRUZGBr/88gvp6elUVFSQkZHByZMnG85z6MwIwnoIqampODo6qs3EzMvLIzo6moyMDMzNzRkzZgyBgYF88skngqj+D0FYDyE1NRVPT88HsgnKy8uJiooiISGB7t27M378ePz9/Rs2iMeNG6ctc3UOQVhqqK2tJSUlhdGjRzekIR8+fJiff/4ZqVTKjBkzGDRoEPb29g1Zm3V1dYSHhzN27Fhtmq4zCMJSQ05ODiYmJri5uRETE8POnTtxd3dn0aJFDB06FEtLy0ZpwCKRyGD2+TSBICw13Lx5k4KCAv7xj39gY2PD6tWrGTt2LGKx+KGhB4lEwqpVqzrYUt1FENb/oVKpqK6u5rfffmPHjh1IJBKWLl3KzJkzm5W1KZfLCQgIICkpqQOs1X0EYQFlZWXk5ORw8uRJzpw5g5+fH2+//TY+Pj7N7kMsFjd7T7Ez0KmFVVpaSmZmJpcvXyY7O5uqqioCAgJYunRpi0QFfwhr9uzZ7WSp/tEphVVeXk5KSgrXrl2jsrISHx8fRowYwalTpwgKCqJfv34t7lOhUPDGG29w+vTpdrBY/+hUwqqqqiI5OZnff/8dpVJJnz59CAoKwtfXl/Xr12NnZ8eTTz7ZqsJPkUjEU0891Q5W6yedQlh1dXUkJSVx/vx55HI5w4cPZ+jQofTp0wcTExMOHTrEjRs3WL16Nba2tq0aQyQS6W3hQ3tg8MJKT08nKiqK/Px8Jk6cSHBwMFKptCFrUyaTERERweuvv463t3erx1EqlXz88cctugHMkDFYYeXl5XHs2DEuXbrEs88+y/Tp07Gzs3sgDbiyspKVK1fyxBNPMHr06Gaf9qIOsVjMokWLNGG6QWBwwiopKeH48eMcPXqUv/3tb1y4cAFzc3O1ojl06BBVVVW89tprbRIVCFPhnzEIYSmVSoqKivjtt984fvw4/v7+REdH07Nnz4emvCQkJLBjxw4+/vjjNosK/ljHzZ8/v9nnkBo6BiEsmUzGF198gY2NDREREfj5+TV6s1MoFNTV1WFqakp+fj4bNmxg2rRpGtvfE6bCB9F7YXXp0oXQ0FCeeeYZgoOD1RYpKJVKsrKyKC0txcfHh6NHj+Lm5sbf//53jZ0pJRaLGTBggEb6MgREKpVKpW0j2oJSqaSqqgpLS8uHtqmurubEiRPI5XIsLCw4duwYzz//PIMHD9ZYgYNcLsff359r165ppD99R+89llgsfqSo4I8/enJyMikpKZSWlhIUFISPj49Gq2YkEgkrV67UWH/6TqeoK6ypqeHq1ascOXIEmUyGUqnkyJEjxMbGavQatqqqKo31pe90CmHJ5XIyMzPJz88nJSWFmzdv4ujo+NBCidagUCjYvn27RvoyBPR+KmwO1dXVJCQk4O/vz/Llyxk1ahTOzs4arfczMjJiy5YtGutP39H7xXtTyOVy1q1bx7lz59i+fTtSqVQjcSt1qFSqTlXt/CgM3mPFx8cTHR3N5s2b2z0yLojq/2PQa6zi4mLee+89FixY0KocK4HWY7DCqqqqIjw8HHd3d6ZOnaptczodBjkV1t+tfPPmTTZu3GiQB5vpOgbpseLi4jh27BhLlixp1hFEAprH4IQlk8nYs2cPISEhrbq9VEAzGJSw5HI5hw4dwszMjPHjx3fKc6l0BYMS1rVr18jIyGDy5Mk4Oztr25xOjUEFSBUKBRUVFXTp0qXD7j4WUI9BCUtAdzCoqVBAdxCEJdAuCMISaBf+H+y67xRGNnB2AAAAAElFTkSuQmCC)
Physics-General
Physics-
When the rectangular metal tank is filled to the top with an unknown liquid, as observer with eyes level with the top of the tank can just see the corner E; a ray that refracts towards the observer at the top surface of the liquid is shown. The refractive index of the liquid will be
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)
When the rectangular metal tank is filled to the top with an unknown liquid, as observer with eyes level with the top of the tank can just see the corner E; a ray that refracts towards the observer at the top surface of the liquid is shown. The refractive index of the liquid will be
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMMAAACLCAYAAADcdC2rAAAgAElEQVR4nO2dd1yT5/r/PwkJIxBE9hRRhihLRKyryBK0Kg5wj7q1WrV65Nt12nNaj62lnirV6nFUrVoXguJeiGJZWkU0rAhEiIRNWGEF8vsDyc/HJwmoSCA879fL16u984zrCc+V+76u+xo0iUQiAQUFBejKFoCCortAKQMFxUsoZaCgeAmlDBQUL6GUgYLiJSqpDFevXsX69euVLQZFD4OhbAHeB8OGDYOVlZWyxaDoYajkzFBYWIjHjx8rWwyKHoZKKoNIJEJJSYmyxaDoYajkMsnKygpqamrKFoOih6GSM8Pz589x584dZYtB0cNQSWUwNDSEg4ODssWg6GGopDKwWCwYGRkpWwyKHsY7K0N5eTmePXvWGbJ0GqmpqTh27JiyxaDoYbyRMjQ3N0MkEiEuLg7/+te/4OrqCgMDA4wePRr79+9/XzK+Mc7Ozpg3b56yxaDoYbTrTZJIJGhsbERhYSGePn2KgwcP4tq1axCJRAAANTU1iEQi3L9/H8uXL3/vAncEsVgslY+CoqMoVAaJRAI+n4/Y2FhERkYiNjYWIpEIRkZGGDx4MFpaWmBnZwdzc3OMGjWqq2Rul+fPnyMuLg4+Pj7KFoWiByFXGRobG5GQkICTJ08iMjISTU1NGDBgAIyNjWFsbAwLCwu0tLTgxx9/7Ep5O4StrS00NTWVLQZFD0OmMjQ0NODUqVP49ddf8eLFC7i5uYHJZILFYsHa2hqampqg0+kwMTHpank7RGlpKdLT0zFixAhli0LRgyApQ3FxMX777Tf88ccf0NHRwUcffYSqqioYGRnB1dUVdnZ2MDMzg5mZGQoKCpCRkQEAKCsrQ1VVFUaMGAF9ff0uf5BXaWlpQUtLi1JloOh5EJShuLgY3333He7du4cFCxagtrYWHA4HM2fOxKhRo2BlZYXS0lJUVFRAU1MT//vf/+Dg4ID8/HzQ6XSkpKSgb9+++OCDD5T1PAAACwsLKhyD4o2RKkNVVRW2bduG3Nxc7NixA3fu3EF2dja++eYbuLm5oaqqCk+fPsWtW7fQt29fFBQUICkpCRwOB5mZmWhpaQGdTgePx4OnpyfodOXt5z19+hQ3b96Ei4uL0mSg6HkwgFZj+eTJk5BIJAgPD8eAAQNQVFSEdevWgcFg4P79+3jy5AkSEhKQlZUFLpcLT09PTJs2DUOGDAGdTseFCxfw8OFDREVFwdXVFY6Oju8sXG1tLW7duoVRo0bB0NCww+dZWFhQ9gLFG8MAWneRBw4ciIkTJ8LS0hIAMHXqVKirq+PZs2fYsWMHqqqqUFlZiVmzZmHhwoUwNjaWXiQzMxM5OTkQiUSIj48Hn89/a2UQi8UQCoW4cuUKIiIiEBoa+kY2iFgsRt++feHg4IC6ujoAgIaGhlJnqndFlUtbtdl3EokENBoNAMBkMpUiCwMATE1NYWpqSvhg165dmDJlCm7duoXi4mJMmTIF8+fPh7m5OekiIpEIqampaGxsRE1NDWpqaqSfFRYWoqioqEPCNDc3g8PhYN++fcjMzMSmTZugoaGBJ0+edOj8lpYWcDgc3LlzBxwOB+7u7lBTU8Ps2bPh7OwMBkPxHmNnv3SdacR3lmwSiaRTn/Ndr8Xn88HlclFZWQk2mw11dXVMmjSJdFx1dTUKCgpQX18v8zo6OjowNzeHlpbWW8si8+3g8Xg4fPgwsrOzIRAI8NNPPyncVGtubkZlZaX0v5ubm6WfxcTE4MSJEx0WqLq6GllZWaisrMTZs2cRFxcn/cVoj5aWFvD5fOkXlpCQACsrK+zatQt+fn7w9PRESUkJnj9/TjjPxMQEdnZ2hL2J+vp6cLlckiL3798ftra2Mu9fWFgILpeLhoYG6ZiWlhbs7e0VBg6KRCJwuVxSQtKAAQMwYMAAhc+cm5uL7OxswpiBgQHs7e2hra0t97yysjJkZWWhtrZWOsZkMmFvbw8zMzOZ57S0tIDL5SI/P58wbm5uDjs7O7m/6CUlJcjKypLO1EDrbG1vb4/S0lJSVqIsZcjKysLBgweRn5+PpqYm3Lt3D97e3tLPXV1dsXTpUtjY2Mh95vaQqQw//PAD1NXVwWKxsHPnTvTr10/hReh0OvT19cFkMlFQUEBYksydOxdz587tsECFhYU4e/Ys7t27BycnJyxbtqzD+xmNjY34448/8OLFC+mYq6srqqurce3aNfz999/Q1taGQCAgnOfs7Ix+/foRlKGhoQFPnjwhzUoffvihXGUoKipCXFwcqqurpWP6+vrQ19dXqAx1dXVISUmRuqlfpT1lyMnJwa1btwhj9vb2sLCwUKgMpaWlSEhIICiglpYWdHV15SqDRCJBRkYGEhMTCePu7u6wtraWqwzFxcX466+/UFFRIR1js9nQ09Pr8PJ12LBhGDZsGAAgMTERQUFB2Lp1K5ydnTt0fkegvV5rNSsrC/7+/vD390dISAg0NTUhFotBo9HAZrOhq6sLXV1d6OvrQ0NDAwDA4XAQGhoKGo2GR48e4eDBgwgMDHwnwXg8Hu7du4f+/ftj6NChCv+wbchTBhcXF+Tn5+PkyZOoq6tDQEAARo0a1e6yieL9w+FwkJCQQBj79ttv5R7f0NCARYsW4fTp05g/fz7++OOPTpOF9DZcvHgRNTU1aG5uxt27dyEWi5GXlwegVZtZLBYqKyvR3NwMPT09ODk5obi4GObm5qivr4eXl1en7Ez3798f/fv3R2FhYae8tLa2tli3bh0SExNx/fp1PHv2DJMnT6byHnoYd+/elS6rMjMzERcXh7Fjx3bKtUlzVFBQEObNm4fm5mZ8/PHHCAoKApvNRp8+fQAAI0eOhImJCerq6pCVlYXo6GhER0fj9u3bePz4Mby9vWFnZ9cpwgGtxn3bDPSu6OrqwtfXF8HBweDxeNixY0e3y8WgkE99fT2ioqLw1VdfgU6n48svv8S1a9c67fqkZRIACIVC3L9/H/7+/hCLxeByuSgvLweDwYCpqSn09PQQHR0NX19fxMTEwMXFBZmZmfDw8IChoSHYbHanCfgmKFomvapQLS0tKCwsxMWLF5GWloY5c+bAw8OD2rVWAm+yTEpISEBjYyOGDx+OPn36oKamBunp6WAwGHBycnpnWWQqAwDpjjJAdp/RaDQ0NzdDTU0NLS0toNFokEgkSvfld1QZ2mhubkZMTAwOHDiAyZMnIyQkpNNmIYqO8SbKUF1dDU1NTTCZTDCZTDQ1NUldxZ3x7sldjL96cVmuzbZf0bbjOur+VAbR0dEIDw+Xun+BVi9NaGgo/P39YWZmhh9++AHnzp3Dw4cPwWKxpM/l5uaGzZs3k7wWVVVVCAsLw/nz5wnjs2bNwqZNm9oNIT948CB27txJGBsxYgQ2b94Me3t7mec8ffoUYWFhePToEWE8NDQU8+fPV3i/mpoahIWFISoqijA+c+ZMbNq0Sa5//vLlywgLC0NZWZl0zMrKCqGhofDy8pJ5TllZGcLCwnD58mXC+IIFC7Bx48a3noFlrThoNFqnvXtyZ4aeyJvODK8iFAqxb98+8Hg8LF68GEOGDAGLxXrfIvd63tSb1EbbzNCZ9NwYhU5GT08PoaGhCAgIwJ49exAREYHCwkJli0XRhVDK8BpBQUH49NNPkZOTg1OnToHD4XT6LxBF94RSBhm4ublh1apV6Nu3L06ePIkrV64QdpUpVJNesQWbnJyMS5cuESpmmJiYYPr06TKja8+dO4fbt2+juroaHA4HsbGxSE5Oxtq1a0kBjUBrSERkZKR0cxJodTBMnz5d4YbQhQsXcOPGDcKYq6srpk6dCgMDA7nnPX78GFFRUSgvL5eO6enpYfr06XBzc5N7HgAIBAJERUWRQj/Cw8MVnvc25OXlISoqihQ7NW3aNEJcUXehVyiDjY0NgoODIRaLpWNaWlpyY3Dc3d0JnzU2NiI2NhY7d+7EkiVLSJuKRkZGCAwMJETr0mg09O/fX6Fcrq6upB1wfX196OjoKDzPysoKQUFBhIBAdXX1dmPIAKBPnz7w9vaGu7t7u8e+KwYGBvDz8yPlllhbW7/3e78NvUIZjIyMpHkaHcHa2prwB5NIJHBzc0N0dDTWrFmDTZs2ISAgQPo5m81+q02ffv36degFfp224L+3gcVidUriVUfQ1tbGkCFDuuRenQFlM3QAGo0GXV1dzJ07F1u3bsXPP/9M2iNQVZYuXYqzZ89CLBajrq4O06dPJ0WtqgqUMrwBdDodHh4euHDhAgoLC/HZZ58hPT2dsPxSJR4+fAhDQ0N4enqCwWAgMTERbDZb6QUf3he9Ypkki4aGBggEApKXqF+/ftKgxDaqq6shEAgIa/Tg4GDExsbixx9/xLx58zBq1CjCWr+wsJCUrKOvrw8TExO5Ubg1NTUQCASEbC46nQ5ra2uFdoRAIEBpaSlhzNDQEMbGxgp3e4VCIQQCAcRiscy8gPT0dFhZWUl3fuPj4/Hhhx+SjsvNzQWbzYaBgYHc3eCKigoIBAJC4peWlhYh4UfZ9FplqKiowLlz50jJO6tWrcLw4cMJY8+fP8epU6dQUFAgHdPV1cWiRYswdOhQ3L59GyUlJfDy8oKZmRnU1NSQkJCAixcvEq7j5eWFoKAgkrK1wefzcerUKYJXSlNTE5988onCtXdcXBwpetPf3x+TJk1SqERZWVk4deoUhEIhDh48SPispqYGHA5HquRCoRC3bt3CoUOHSNeJioqCk5MT/Pz85CpDeno6Tp48Sciss7GxkSbsdAeocIxOgMvl4vz586iurkZgYCA8PT17fATso0ePcPz4ccyfPx/29vYIDw/H06dP8d1334HFYsl0Mb8NVDiGimFnZ4f58+fD0tIS586dQ3R0dI+3I3g8HlJTU3H48GGEh4cjOTkZFRUVuHPnDmGpo0r02mVSZ2Nqaop58+aBw+FI8yQWLFjwVq5TZdNmR3z88cdgsVjQ0tJCQEAA8vLy4ODgAAsLC2WL+F6glKETYbFYGD58OExNTREZGYkvv/wSa9aswciRI5Ut2huRkpKCwsJCrFq1ipDkP3ToUCVK9f7pFcpw+fJl7N27F1VVVdKx/v37Y8OGDTIr74WHh5PK2/j7+2PdunUyK/s9fvwY4eHhSEtLk4615YMfOnQI+fn50qJsr7Jnzx5SQvu4ceOwbt06ubvjAKS74a9G1RobG2PDhg3thjnk5ORg586dSE5OJoy3rdsrKipQWFgIGxubdy7mlZGRgZ07dyIlJYUwvn79esyePfudrv0+6BUGtLOzM5hMJiFjj0ajgU6ny/R+yKriTafT5WZTSSQSaVW418/Jzc3Fzz//DGNjY6xevZpgeL7pfRTdT9HzdETWV929bdmL75o0o+h7aXtGyoDuYmg0GtTU1MBgMKT/1NTU5P6x6XQ64VgGg6HwBZV1/bZzBg4ciH/+85+QSCTYunUrOByO1Lh+0/u87fN0RNbXn78zsscUfS/dke4plYphbm6O//u//8OoUaNw4MAB3LhxA0KhUNli9Wg8PDw6/Zq9wmboDmhra2P27NmwtrbGiRMnkJ6ejqCgIAwcOFDZovVIXl9adQa9VhkqKyuRmJgIPp9PGPf29iaVdOTz+UhKSiL8mmtpacHb21uuofv333+TDMdBgwZh6NChMDU1xYkTJ3DkyBGMHz8eHh4e0NTUhEAgQFJSEiH5nslkwtfXV6E7Mzk5mbST7uTkBDc3N4WbjTk5OUhKSiLkefTt2xdjx46VW1ytvr4eSUlJpHpTI0aMwODBg+UugbhcLpKSkgghLUZGRtDT05MrX1fTa5VBIpGgubmZZITJ8idIJBKIxWLCsQwGQ2GVbVnXbrMVbGxssGHDBsTExODKlStIT0/H5MmT0dLSgqampg7J1N69mpub2z1P1v3ayq+86f3aqzj+tvfqSnqFN+l9h2O8LS0tLXj06BEuXboEoLXMjIODg5Kl6lre1pv0PqAMaCVCp9Ph5uYmLaX++++/IzY2lrCUoGit/xsYGIgxY8Zg5cqVhP2izoRSBiWjpqYGc3NzBAcHY/z48Th48CAOHz5MWMf3ZgoKCiAQCLBu3TocP34cKSkpOHfu3Hu5F6UM3QAajQYtLS34+vrim2++QXJyMr777rseH+zXGZibm2PZsmWYOHEirK2tMWLECEKIe1xcHNTU1KCmpobffvsNALB27VocOXIEampqYLPZ+OKLL6T/7+zsjAcPHsi8V68woC9evIjdu3cTplcbGxts3LhRZtzQL7/8guPHjxPGAgICsGHDBplelpSUFPzyyy/gcDjSMQaDgU2bNiEkJESuXLt27cLhw4cJY97e3vj6669x7NgxBAQE4LPPPsPw4cOhoaEBBoMBJpOJe/fuYceOHYSmK8bGxti0aRN8fX0VfhfZ2dn473//i6SkJML4mjVrsHjxYrnnHTlyBL/++ithzMPDAxs3bpRZDjMvLw+//PIL4uLiCOMrVqzAihUrFMr4OvX19aisrERRURHu37+PXbt2AWi1N9atW4fk5GTo6uoiLS0NBQUFyMnJwenTpyEWixETE4MJEyZg5cqV4PF4WLt2LSnpqg3KgO6m1NXVYerUqeBwONDR0YGvr6+0i6qbm5vSKp13Nh0xoG/fvi2NxfLx8cHChQthb2+PL7/8Ejo6Ovj666+lx/J4PAQFBSE8PBxjx47F5cuXsW3bNvz5559obm7G5s2bsXLlSvj5+ZFkoZZJ3RQtLS2sWbMGLBYLGhoaEAgEMDExga2tba+rAevt7Y1z584hMTERTU1N+OqrryCRSJCamkqa2Z89ewZra2u4ublBIpGAy+XC3d0dVlZWKCkpgampqdyaVL1imdRTGT9+PEaOHAkWi4WamhocP34cLS0t8PHxkZs6qmoUFxejoKAAtra20NHRga2tLZ4+fQqgdfYUiURoamrCixcvwGKxkJOTg0GDBkn3gfLy8uDp6QmgdfNUQ0MDurq6Mu9FKUM3RlNTE4sXLwaHw4GPjw9Onz6N6OholJWVYerUqW/UKL6nUlNTg7Nnz6KkpAQ6OjrIzs7GqlWrQKPR4O3tjb179+LGjRuwt7fHzJkzkZGRARsbGzAYDDQ3NyM+Ph5z5swB0KoMenp6cmtO9VplKCwsREREBMHoBVrrBL0eBMbhcEhVudlsNpYuXSp3kyw6OhpXrlwhjI0ZMwaTJk2S+6uemZmJiIgIQoiIWCzGkCFD4OjoiLVr1yI7OxtJSUnYtWsXpk+fDmdnZ0RGRuLmzZuEa/n4+GDixIkKG0M+ePAAERERhL4VZmZmWLhwodxqgDU1NYiIiCAZ4MHBwfD29pYbjpGYmIgzZ84QXMZtyxlFWFhYYNq0adLwjwkTJmDs2LGg0+lYvHgxBg0aBKA11MXY2Bjz5s2DkZGRNGT/n//8p/Rv5OvrK62BJYtea0DX19eDz+cTXgSgtYlJ3759CWNVVVXIz88nlHBhMpmwsbGRa8i2+cdfxdDQEObm5nKTZqqrq8Hn8wkvDI1GQ58+fQgBfWVlZbh+/TrOnDmDRYsWYdiwYaR+1SYmJjA1NVXYHLKiokLaV7kNLS0tWFtby1UisVgMPp9PiJ8CAEtLSxgbG8sN/S4rKwOfzye4i7W1tVFdXU3qA62sHeheqww9CYlEQnrJ2vpU79ixAy4uLli3bl273YK6I1Q4BsUbIevXVkNDAx4eHjh27BiEQiGWLl2KzMxMJUinOlDKoAJ8++238Pf3x7fffotr166hrq6uW0WDvg/eNT9bFr3CgC4rK0NJSQlhvaqpqQkrKyuZxhSfzyetwfX19WFpaSnzj1BTUwM+n0+oFkej0WBlZaWw6fqLFy9IrbL69u0LS0tLUvGAVxEKhcjPz0djY6N0zNnZGYaGhoiJiUFBQQH8/Pxgbm5OKmZWV1cHPp9PCnazsLBQWBissLCQsPwEWp0IlpaWMvc9GhoakJ+fT7LJzM3NFRY7UCa9Qhm4XC6io6MJhqmpqSlCQkIwePBg0vGJiYm4desWYczDwwMzZsyQmYxSVFSEc+fO4fnz59IxOp2OmTNnyu2ICQD3798nlYV0c3NDcHCwwmYlubm5iIiIIDUrCQkJwYoVK3Dq1CkcPHgQEydOhLu7O8GIrqiokOZQvEpQUBACAwPl3vPx48ekADl7e3sEBwfLVIbKykpcv36dlHT00UcfYdKkSXLvo0woA1oFKS4uxsWLF5GTkwNPT0/4+fl1211rqjoGxXvF2NgYc+fOxcSJE/Ho0SNs376d1EqKggylDCqKpqYmRo0ahYULF0JHRwfbt28nRZBSEOkVNkNvxsbGBkuWLEFycjIiIyPB4/EwdepUlYl67UyomaEX0NbUcNWqVUhJScGWLVsICTIUrfRaZcjOzsbChQulTQbb/l24cIF0bGxsLHx8fAjHDR06FPHx8XKvHxYWRrr2559/juLiYrnnxMfHIzAwkHCOo6Mj7t69q/BZtmzZQrrXv//9b1RUVEiPYTAYcHBwwBdffAE9PT1s2bIFYWFh8PDwIJzn5+dHKnHzKuXl5diwYQPpfgcOHFCYmRcREQEXFxfCOZMnT5ZGoHYHKG9SL6SpqQmXLl3ClStXMHHiRHh7e8sNXnvfdCdvEmUz9EKYTCamTp0KCwsL7N69G9nZ2QgJCYGVlZWyRVMqvXaZRAEMHz4cW7ZsQVNTE/bu3YukpCTCLnpvg1KGXo6lpSX+8Y9/wNPTE2fPnsXRo0cJjRx7E71imZSSkoLbt28T2qwaGRkhMDAQtra2pOOvXr1KWsc6OzsjICBApksyLy8PV69eJdgqdDodEyZMkKYcyuLmzZsk37+joyMCAwMV1iBNS0vD1atXCXE/urq6mDBhgszwklcpLi7G1atXSZtwvr6+CAkJwcWLF3H06FFMmTIFjo6O0s/v3buHGzduEM6xsbFBYGCgzJimsrIyXL16FVlZWYTxcePGtdtQRVn0CmUwMjKCh4cHweDS0dGR+8JZW1uToj7NzMzkRkqy2Ww4OTkR1tw0Gq3djphWVlakBuMmJibtGvv6+vpwd3cnKLempqbcdMZX0dLSgqOjIymA0MLCAjY2NjA3N0dcXBz+/PNPjBkzBmPHjgWLxYK5uTlJVgMDA7lhHpqamhg0aBBJJktLy3ZlVBaUN4mChEgkQkJCAk6cOAFXV1csWrTovXmbupM3ibIZKEiwWCx4eXkhNDQUfD4fW7duJYViqyKUMlDIhMFgwN7eHtu2bYO1tTVmzpyJpKQklU4a6hU2gyyampogFAoJSf6A7HVwfX09KioqCDusdDodBgYGcvOOKysrSQk02tra6NOnDynh5tX7CIVCwvRPo9FgaGioML9ZKBSiurqaMMZms6Grq6uwf5pIJIJQKCQ0OWcymdDX1yckF61evRr29vb44osvsGDBAgQEBJAao+vp6SmMd6qtrYVQKCT0cVBXVyckKCmbXqsMxcXFOHToEB4+fEgY37RpE0aPHk0YS09Px6FDhwglXPr06YNNmzbByclJ5vUvXbqEiIgIwtj48eMxa9YsUvWNNp49e4ZDhw4hNzdXOqalpYXQ0FC4urrKfZbz58/j/PnzhLHJkycjODhY4Qv68OFDHD58mJAk1K9fP6xZswZ2dnaEY319fTFw4EDs2bMHJ06cQHFxMSwsLKS22OLFizFx4kS5ip6cnIzDhw8TlNbW1hYffvihXPm6GsqApngjqqurcerUKWRmZsLLywtjx459p+p+lAFN0WNhs9mYM2cOvL29kZSUhMjISLx48UIlbAlKGSjeGG1tbfj7+2Pu3LmoqanBgQMH8ODBg3b7unV3eq3NQPFuMJlMODo6wsDAADdu3MD+/fuRl5eHGTNmKFu0t6ZXKMPNmzdx5MgRgvHWr18/rFixAsOGDSMdv3//fkRGRhLGxo0bh2XLlsmsWsHhcLB//35CES8Gg4GVK1cqrARx6NAhnD59mjA2evRoLF++HCYmJnLP++uvv7B//35CORtDQ0OsXLkSY8aMkXseADx//hz79u0jOQ4WL16MmTNnyj3vzJkz+P333wljrq6uWLFiBaZNmwYHBwccPXoUGRkZWL16NfT19cHlcrFv3z5SzkLbOd2NXmFAOzg4kNqsqqmpQVtbW2Z9otraWkKoA9BawU5bW1umq7KpqQm1tbWk5BYdHR2FLlFZ91FXV4e2trZcrwzQWpOotraWsCyh0+nQ1tZu11EgFotRW1tLMj5ZLJbCChoikYjUZ47JZEJbW1ta/r2mpga7d+/Gw4cP8dVXX8HJyQk1NTWk70VbWxtaWloAupcB3StmBkU1+WWhra2tsHr16zCZzLdq7v2m92lDQ0Pjrb1jDAbjrbw/7SkLnU6Hrq4uNm/ejKioKHz//fdYunQpAgMDFe51dCd6hTJQdB0MBgMzZsyAnZ0djhw5gtzcXAQFBcHMzEzhbNcRxGIx1NTUCLVnm5ubIRaLO8V13jNUlqJH0dbfev369SgqKsKePXuQkpLyzt1LCwoK8OzZM+nud1NTE548eYK0tLTOELv3zgzV1dVITU0l1VT19PQkhRkXFRUhNTWVYIBraGjA09NTbi3VtLQ0ZGRkEMZsbGzg6Ogo144oKSlBamoqISiOwWDggw8+gLGxsdxnEYvFSE1NBY/HI4wPHjwYdnZ2Cn+Rc3Nz8eTJE8KLamhoCDc3N5lLy7ZS+K9X13BxccHAgQMJv9r9+/fH+vXrcenSJalx3WYrAK05GK/3j5DX3wFoDfnYtWsXxo4dC4lEgpiYGMTGxuLTTz+Ve86boHLK8PqXKc8/0NjYiBcvXiAnJ4cw/mpCSxu1tbXg8XiEBh0sFktuKAYAlJaWkhJbWCwWKczhVUQiEZ4/f06ooKGurg5nZ2e55wBAS0sLioqKSPczNTVtdzOssrISXC6XYIzW1dXJ/B6A1mWJQCAg3cvKykpmHwkDAwPMmzcPBgYGiIyMxK1bt7B06VIwGAwwGAxSaBw0+ywAAAbpSURBVIq8UBWgVXmcnJzw/fffo6WlBf/5z3+wfPlymJubK3zGjqJS3qSmpiacP3+e0Jpq4MCB8PT0fCtDlaJzyc7Oxq1bt7BkyRI0NDTgwYMH4HK5hGPGjh0LHx8fudcQiUQICQnBlStX4O/vj+PHj3dabzuVshnodDpp2VJQUICCggJSlCVF1zNw4EB8/PHHEIlEePjwIaFqOdA6k7U3C7JYLGzevBk0Gg3Lli3r1CaPKjUzSCQS5OTk4MSJE4SXn8ViwdLSEiNHjnwvTS4oOkZzczN4PB5SUlJQXV1NsFM0NDQwYcIEODk5ybRx4uPjsX37duTm5qKxsRFpaWmws7OTzvienp7YuHEj7O3t31o+lVIGoNUwvnr1KsnDQKfTwWKxYG1tDVNTU+jp6YHFYkFdXV2h0Ubx9rS0tKCurg4VFRUoKipCTk6OzM1JABg5ciTGjBkjdy+jsbERtbW1cmf4VzcA3xaVUwagtcvMhQsXIBAIVCKaUpVpc8OOGzdO6cWQVVIZJBIJeDwebt++TdkL3ZS2HWsXFxd4eHiAzWZDLBYjPz9fOnMwGAwYGBh0WelLlVSGNgQCAZKSkqS9xSilUD5qamrQ0dGBkZERRowYQahbxeVyMWXKFKmrtG/fvliyZAkmTpzYJbKptDIA/7/RHpfLRVlZGaqrqyESiSAWi9HU1EQpyHuGwWBAU1MTWlpa0NLSgrGxMWxsbGBlZUVaFp05cwbnz5/H0aNHlWLHqdym2+toaGjA1tYWtra2EAqFKC8vR1VVFRoaGtDY2AixWEzZFe8RJpMJHR0d6OjogM1mw8TERO6LzuFwYG9vrzSHhsorw6vo6em9VXQpRdeQmpqK8vJyFBQUQEtLC3PmzFFYnrOz6VXKQNF9EQqF4PP5WL16NYyMjMBkMmFhYdGlMlDKQNEtyM7OBovFwvjx47tcCdpQqXAMip6LQCCAi4sLIaq1q6GUgaJbkJGRgbNnz8LKygra2toYMGAABAJBl8qgUq5ViUSCyspKykjuoVRWVoLNZistTVSlZgaRSISwsDBli/HW5OXlITY2FoWFhb3S3fvrr78SOpR2NSqlDI2Njbh48SJhTCwWg8/nkyo7dDfKy8tx6NAhzJgxAzdv3nznFMnuTF1dHfLz80njV69eVWpPOZX1JjU3NyM3NxeJiYnQ09NTGBHZHUhMTERpaSmprZZIJML27dsBtDYkDAwMRHx8PBgMBu7du4fa2lo4OTlhxIgROHjwIPT09ODv749BgwYp4zE6RFNTExITE5GUlISRI0cqzXv0Oio1MwCtYcP5+fnYu3cvvv76a2RkZMDR0VFpfY47QkFBAR49egRnZ2dS+9nPPvsMZWVl0NDQQEZGBgQCAS5duiRNcFFTU8PmzZvx888/Q0dHBzdv3my3ibqy0dHRwaBBg/DXX3/h888/x8mTJ1FaWqpssVRvZsjLy8OSJUvw9OlTVFRUwM7ODg8ePHjnMiXvAxaLhWPHjiEuLg61tbWYM2cOrl+/Lv08KioKWVlZOH36NNhstnQ9nZubCxcXFyxZsgTl5eXYtm0b3N3dMWHCBPB4PFKvho8++qhLn6sjiMVi8Hg88Hg8xMXFwcvLi1TQoKtROWUwNTXF5s2bsX37diQmJmLu3LmYMGFCt1QGNTU1lJSUIDk5GbNnzyYlw585cwYLFy6UprKamZkhLS0N9fX1CA4Ohq6uLu7evQtbW1sEBwejrKwMOjo6pGXHjz/+2GXP1FHq6+sRFRWFXbt2wcHBATNmzEBqaqpSZVI5ZdDU1ISfnx9Gjx6N+Ph47Nq1Cx988AG8vLy6ZWU3DoeD3bt348CBA6DRaBCJRLhy5Qqqqqrw+PFjhISEEI4vLS2VduWk0Wjgcrnw8fGBpqYmSktLIRQKSXnB7eUVdzVisRiXL1/Go0ePcOTIEYwbNw66urr46aeflCqXSikDjUYDk8mU1h319/eHv78/EhISUFxc3G4rWmUwZMgQaSutiooKLF++HFOnTsWsWbMQExOD7OxslJeX4/HjxwCAnJwc0Gg06U7t9evX8cknnwAAqqqqoK6ujn79+innYToIj8cDnU7H2bNnCU4NJpOp1BTc7vdT+Q6wWCx88803pPGRI0d2S0V4HTqdDgsLC/Tp0wc0Gg1fffUVfv/9d4wZMwYRERHw9vYGjUbD4MGDpRuLL168gI2NDYDWpQeLxYKZmZkyH6NdbG1tMWnSJJJ3LzQ0tEO9rN8XKrUDTUHxLqjUzEBB8S5QykBB8RJKGSgoXkIpAwXFSyhloKB4CaUMFBQvoZSBguIllDJQULyEUgYKipdQykBB8RJKGSgoXkIpAwXFSyhloKB4CaUMFBQv+X/W0Xd3adsDlgAAAABJRU5ErkJggg==)
Physics-General
Physics-
Following figure shows the multiple reflections of a light ray along a glass corridor where the walls are either parallel or perpendicular to one another. If the angle of incidence at point P is 30°, what are the angles of reflection of the light ray at points Q, R, S and T respectively
![](data:image/png;base64,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)
Following figure shows the multiple reflections of a light ray along a glass corridor where the walls are either parallel or perpendicular to one another. If the angle of incidence at point P is 30°, what are the angles of reflection of the light ray at points Q, R, S and T respectively
![](data:image/png;base64,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)
Physics-General