Chemistry-
General
Easy
Question
Which of the following is not a fundamental particle
- Proton
- Neutron
- particle
- Electron
The correct answer is: particle
Related Questions to study
Chemistry-
The valency shell electron configuration of an atom is 4s2 4p5 The maximum no of electrons having parallel spin in this configuration are
The valency shell electron configuration of an atom is 4s2 4p5 The maximum no of electrons having parallel spin in this configuration are
Chemistry-General
Maths-
Let
Then f(x) has
Let
Then f(x) has
Maths-General
Physics-
In the figure shown there are two semicircles of radii
and
in which a current i is flowing. The magnetic induction at the centre O will be
![](data:image/png;base64,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)
In the figure shown there are two semicircles of radii
and
in which a current i is flowing. The magnetic induction at the centre O will be
![](data:image/png;base64,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)
Physics-General
Physics-
In the figure, shown the magnetic induction at the centre of there arc due to the current in portion AB will be
![](data:image/png;base64,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)
In the figure, shown the magnetic induction at the centre of there arc due to the current in portion AB will be
![](data:image/png;base64,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)
Physics-General
Physics-
The magnetic induction at the centre O in the figure shown is
![](data:image/png;base64,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)
The magnetic induction at the centre O in the figure shown is
![](data:image/png;base64,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)
Physics-General
Physics-
A current i ampere flows in a circular arc of wire whose radius is R, which subtend an angle
radian at its centre. The magnetic induction B at the centre is
![](data:image/png;base64,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)
A current i ampere flows in a circular arc of wire whose radius is R, which subtend an angle
radian at its centre. The magnetic induction B at the centre is
![](data:image/png;base64,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)
Physics-General
Physics-
An infinitely long straight conductor is bent into the shape as shown in the figure. It carries a current of i ampere and the radius of the circular loop is r metre. Then the magnetic induction at its centre will be
![](data:image/png;base64,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)
An infinitely long straight conductor is bent into the shape as shown in the figure. It carries a current of i ampere and the radius of the circular loop is r metre. Then the magnetic induction at its centre will be
![](data:image/png;base64,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)
Physics-General
Physics-
In the following circuit,
resistor develops
due to current flowing through it. The power developed across
resistance is
![](data:image/png;base64,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)
In the following circuit,
resistor develops
due to current flowing through it. The power developed across
resistance is
![](data:image/png;base64,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)
Physics-General
Physics-
A solid sphere of mass 2 kg is resting inside a cube as shown in the figure. The cube is moving with a velocity
. Here t is the time in second. All surface are smooth. The sphere is at rest with respect to the cube. What is the total force exerted by the sphere on the cube. (Take g = 10 m/s2)
![](data:image/png;base64,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)
A solid sphere of mass 2 kg is resting inside a cube as shown in the figure. The cube is moving with a velocity
. Here t is the time in second. All surface are smooth. The sphere is at rest with respect to the cube. What is the total force exerted by the sphere on the cube. (Take g = 10 m/s2)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJIAAACBCAYAAAArOeO7AAALj0lEQVR4nO3de0xbZR8H8C+0BVrWcV3ZaF2Aya5koriV6TqmEpLNxTHjLZtLTLyFOaJRtzDjbcviNeEPiVk0MTEx0wR3Q8kUW+NAmGyAQ6ArdpuhlIG0lQ2kpe2hfd4/fNOE9BV4t4dzTsfvk5x/TjkPX5ovz7k2jWOMMRByk+KlDkBuDVQkwgUViXBBRSJcUJEIF1QkwgUViXDBvUgjIyOYmJjgPSyROa5F8nq9OHz4MBobG0HXOecXJa+BGGP4+eefYTabcenSJRQUFMBgMPAanshc1IzU0tICj8cDABAEAXa7HX19fTMOdP36dVgsFtjtdlgsFnR1dSEUCvFPTGQpqkivvPIKmpqaAAAejwcffvghWlpaph0kHA6js7MTDocD2dnZKCgowGeffQafzzc3qYnsRO3acnNzcfXqVTDGYLfb0d/fj82bN087yOjoKBwOB7Zu3QqFQoGysjI4HA788ssvKCsrm7PwRD6iZqTCwkI4nU4IgoBvvvkGGzduhF6vn3YQQRCQk5ODHTt2IC0tDTqdDpWVlRAEYc6CE3mJKtKKFSvQ2tqKrq4uNDU14dlnn51xkLS0NKxbtw6pqamRdZmZmSgpKeGblshW1K4tOzsbPT092L9/P/bs2YPFixfPOIhKpYJKpYpav2DBAj4piexFzUhFRUVgjEGr1WL37t1SZCIxKGpG+vbbbxEfH4+6ujop8pAYNWVGcrlcOHjwID755BOp8pAYNaVIp0+fxtatW7Ft2zap8pAYNWXX9tRTT0mVg8Q4eoyEcEFFIlxQkQgXVCTCBRWJcEFFIlxQkQgXVCTCBbdntv9fNpsNHR0d2LRpE5YuXSpVDNkYHx9HS0sLnE5nZN19992H3NxcxMfL//9dkoQ+nw9HjhzBvn370NDQIEUE2RkaGsJHH32EtrY2XL16FbW1tfjqq6/g9XqljjYrksxIjY2NGBoaQlFREXp7e6WIIDterxehUAgHDhxATk4Ojhw5gs7OTvj9fmi1WqnjzUj0IvX39+Po0aMoKyuDz+fDsWPHxI4gO5OTk+jr64NOp4Ner8fw8DDOnTuH9evXx8zDgaLv2s6cOYOFCxfi/vvvh9FoxO+//y52BNkJBoNobW1FfX097rzzTphMJiQkJGDLli1ISkqSOt6siFokm80Gs9mM4uJi5OXlQa/XIxQKweFwiBlDdkKhEPx+P2pqanD27FmYzWZ4PB40NDQgEAhIHW9WRCuSz+dDfX09Tpw4gcrKSqSmpqKgoAB///03Wltb/3W7u+++G3FxcTG9rF+/ftr3ZmJiAh0dHcjJycHChQuh1+uhVqvhcrli5kOmohwjMcbQ29uLS5cuoa6uDqWlpZHXnnzyyVnt3tasWTOXEeeM1Wqd8WcuX76M4eFhhEIhWK1WNDY2wufzoby8HMnJySKkvHmiFEkQBDidThgMBhiNximvbd68ecq1k3/T09MzV/HmVFxc3Iw/Ex8fj7y8PLzzzjsAAK1Wi/3792Pt2rVzHY8bUYqUkJCA7du3Y/v27VGvPfPMM2JEkLXi4mJ8//33Use4KfK/ZEpiAhWJcEFFIlxQkQgXVCTCBRWJcEFFIlxQkQgXVCTCBRWJcEFFIlxQkQgXVCTCBRWJcEFFIlxQkQgXVCTCBRWJcEFFIlxQkQgXVCTCBRWJcEFFIlxQkQgXVCTCBRWJcEFFIlxQkQgXVCTCBRWJcEFFIlxQkQgXVCTCBRWJcEFFIlxQkQgXVCTChWRfs/X/Yozh1KlTsNlscLvd0Gq1WL58OUpLS7F48WKp4817MVOkPXv2YHx8HLfffjsMBgMCgQCam5tx5swZ7Nq1CyaTCUplzPw5t5yYeOc1Gg2Gh4fx4osvIiMjAxqNBsFgENeuXcOxY8fw7rvvYtWqVTQzSUj2x0hKpRL33nsv3njjDeTn52PJkiXIyMhAVlYWcnNz8fTTT2PlypV4//33pY46r8m+SAkJCXjwwQeRmpoKtVqN5ORkqNVqaDQaqNVqaLVamEwmnD9/Xuqo85rsd21+vx/5+flQqVRQKBSRJRwOQ6lUQqVSYenSpejr65M66rwm+xkpMTERHR0d8Pv9CAaDUUsgEEBnZyfuuOMOqaPOa7KfkYLBIOrq6pCXl4eNGzciFApBqVQiFAohEAjg4sWL+Omnn1BeXi511HlN9kUKhULo6upCdXU13G431q5di/T0dHi9Xtjtdpw6dQrt7e3Q6/U4ePCg1HHnLdkXCfjn+966u7tRXV2NVatWISkpCYIgYGBgAH19fRgfH0d1dbXUMec12ReppqYGY2NjAP75Ej2FQgHGGOLi4sAYQzgcBmNM4pTTS0lJkTrCnJN9kTZs2CB1BDILop+1WSwWFBcXIyUlJbLU1NSIHUOWRkZG8Nprr0Xel5UrV2JgYEDqWLMiepHsdjvuuece2Gw2jI6O4scff8SBAwfw8ccfix1FVgYGBvDSSy/B4XDg4sWLGB0dxWOPPQaLxYJwOCx1vBmJumubnJzEyMgIdDod0tLSAPzzdexvv/02jh8/jhdeeEHMOLIRCATw9ddfw+1249NPP4VerwcAHDp0SOJksyfqjPTnn3/i+vXryM3NhVqtjqxPTU0VM4bseL1eHD9+HKWlpbjtttukjnNDRC2Sx+PB5OQkFi1aNGV9d3c38vLyxIwiK9euXYPT6cTq1auljnLDRC9SOBxGVlZWZF1vby8aGhqwc+dOMaPIyl9//QWFQoEFCxZIHeWGiVYkQRDwxx9/IBAIIDMzEwBw9uxZvPrqq3jggQdgNBrFiiI7WVlZSElJwQ8//BBZV1tbiwsXLiAUCkmYbPZEO9j2+/0YGhrCd999hytXrkCpVCIYDKKyshIbNmxAcnKyWFFkJzs7G1VVVXjrrbfQ1tYGACgqKsK6desQHy/7++oARCySRqNBRUUFHnnkkcg6lUqFZcuWQaFQiBVDllQqFcrLy1FYWIjJyUkAwKJFi5CRkYG4uDiJ082OaEVSKBTQ6XTQ6XRi/cqYkpiYiBUrVkgd44bFxrxJZI+KRLigIhEuqEjzhNvtxrlz5+ZsfCrSPBEMBtHd3Y3Dhw+jpaWF+/hUpHlCr9dj27Zt8Hg8ePnll1FVVYX29nZu48cxzo8XVlRU4Pz581H304g8uFwuXLhwAWq1GqtXr8bevXvx+OOPT7mJfiO4X0cyGo3YsmULli1bxntowkFHRwf27t0LvV6PJ554AiaTCYmJiTc9LvcZSRAEKBSKmLm0P59YrVbs2rULO3fuxKOPPgqDwQClUsnl6jn3GUmlUvEeknAwODiI5uZm1NfXw2AwcB+f+4xE5Mnr9UKj0czZvbtZF8nv98Nms8HlckXWbdq06aYP0sitYVa7NpfLhdOnT6O5uTnykWmr1YqHH34YFRUV8/oREPJfbAYTExPs888/Zzt27GBms5kFg0HGGGOtra0sKSmJtbW1zTQEiTFHjx5lv/76K2OMsZ6eHvbFF1+w/v7+abeZ8dTK6XSiqakJZWVlKCkpiRxMG41GZGZmYnh4eM7LTsTV29uLDz74AIODg/jyyy9x+fJlJCQkTLvNjEUaHByE2+2GyWSKOiPzer1IT0+/udREdnbv3o2uri4cOnQIExMTeP7556c8Z/+/TFskQRAwODgIlUoVNZDFYkEwGERhYeHNJyeyotfrkZ+fD5vNhueeew5LliyZcZsZZyRBEBAfHx/1OOybb76J119/nc7abkEnTpzAlStXkJ6ejt9++21W20xbJJVKheXLl8PpdKK2thZjY2MYGxvDQw89BJ/Ph6qqKi7BiTyEQiFYLBbs27cPJ0+eRElJCcxm8+w+yTKbo/iTJ0+yNWvWRJb33nuP+f3+mz89ILJitVrZXXfdxTo7OxljjLW3t7OKiorIGdx06Mo24YLurBIuqEiECyoS4YKKRLigIhEuqEiECyoS4YKKRLigIhEu/gMg+Am+Ge7ZGwAAAABJRU5ErkJggg==)
Physics-General
Physics-
A string of negligible mass going over a clamped pulley of mass m supports a block of mass M as shown in the figure. The force on the pulley by the clamp is given by
![](data:image/png;base64,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)
A string of negligible mass going over a clamped pulley of mass m supports a block of mass M as shown in the figure. The force on the pulley by the clamp is given by
![](data:image/png;base64,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)
Physics-General
Physics-
The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle
should be
![](data:image/png;base64,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)
The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle
should be
![](data:image/png;base64,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)
Physics-General
Physics-
In the arrangement shown in figure the ends P and Q of an unstretchable string move downwards with uniform speed U. Pulleys A and B are fixed. Mass M moves upwards with a speed
![](data:image/png;base64,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)
In the arrangement shown in figure the ends P and Q of an unstretchable string move downwards with uniform speed U. Pulleys A and B are fixed. Mass M moves upwards with a speed
![](data:image/png;base64,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)
Physics-General
Physics-
A vessel containing water is given a constant acceleration a towards the right, along a straight horizontal path. Which of the following diagram represents the surface of the liquid
![](data:image/png;base64,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)
A vessel containing water is given a constant acceleration a towards the right, along a straight horizontal path. Which of the following diagram represents the surface of the liquid
![](data:image/png;base64,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)
Physics-General
Physics-
A rough vertical board has an acceleration ‘a’ so that a 2 kg block pressing against it does not fall. The coefficient of friction between the block and the board should be
![](data:image/png;base64,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)
A rough vertical board has an acceleration ‘a’ so that a 2 kg block pressing against it does not fall. The coefficient of friction between the block and the board should be
![](data:image/png;base64,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)
Physics-General
Physics-
Block A weighing 100 kg rests on a block B and is tied with a horizontal string to the wall at C. Block B weighs 200 kg. The coefficient of friction between A and B is 0.25 and between B and the surface is 1/3. The horizontal force P necessary to move the block B should be ![left parenthesis g equals 10 m divided by s to the power of 2 end exponent right parenthesis](data:image/png;base64,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)
![](data:image/png;base64,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)
Block A weighing 100 kg rests on a block B and is tied with a horizontal string to the wall at C. Block B weighs 200 kg. The coefficient of friction between A and B is 0.25 and between B and the surface is 1/3. The horizontal force P necessary to move the block B should be ![left parenthesis g equals 10 m divided by s to the power of 2 end exponent right parenthesis](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGYAAAATCAYAAABiMHgQAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAtNJREFUeNrtWE1kHVEUHlFPRYSIireoElFvERUqoiqixBMVT4WIqK5KRUVFNlFRWYXIoioiREQWXZSKripKRVU8ESoiiy66iS4qojxVEfEMyTl8ieu+c2fu3HmTyWI+Pt47c+/Muefc83Ov52W4KpyBVWKZ2JGZ5HqhgfiSuBtlEk+Yy2wXiC7s+Lg4VX7PwfYi7hG3M7uHYoX4NOY7+ojfNVkZPqhBGbshbdwlviHuBYxpJi4Rd8BlyJLGLeIB0pEr8rB1uya/T9xKKjzrgffEFyiUJmwSS8r/QciSxjQ2TZxN9xnOkbAFB11injh+DbsYCcPEBUH+jjiacNE+QNS4RspGSGS/0mv8F2KvYXAjHPcXBWuduEicSskx/P2iIH+EZypmoGcbnHlEPCQ+xvMW4ltihfif+DpAH3b6qkVE/Sb60F+1ETulEDL/gR75rFROGHgDRWoKv5mT+PCTkH49iHEcUzHomoPhVXyEc37AsKz/Hez8PNY2AvltbLw22zQjOGXFoJtnaYccfHEJ3/AyzqezgvxXQJ5MOmL8gDlVQc9NRIaKPzCiJM87tsj8vL8O667aLJbDvlXItccp1hjf8mzAep4gFXsR5K4t8jAOjaV6OkZKZWL7RughfrO4ekgqlR0Z0sVNLZWZ9Iwqj9Ii52Ezfk+Tg1NqUtlX4kNt0BBaV6kIrqUYMVzgBwR5USv+Jj2jyqO2yLxB9onPHNZcU/yldplD8oPhnPE8RccMIbXoWNPa5QWch3REkbu2yKuOtwPj8EVgcWtGauhSxqyjQPal6BgPqWIC3VQOu1q/4viktMWucpsWWUc38adQm20gdn7bwl1NCX15FS1nEeeZhoQdElaTWmCwUxTsZSGnV5BWvBjysBb5Av+gp49NU3BYt6mmW11idhrSW4b4MF5iMsaUKwH2+pLS13djciGzYd0xb6h7IppQEI+RLjYQMRmuAOdQXcnAFedchQAAAKd0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW8+KDwvbW8+PG1pPmc8L21pPjxtbz49PC9tbz48bW4+MTA8L21uPjxtaT5tPC9taT48bW8+LzwvbW8+PG1zdXA+PG1pPnM8L21pPjxtbj4yPC9tbj48L21zdXA+PG1vPik8L21vPjwvbWF0aD67BSBBAAAAAElFTkSuQmCC)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALkAAACTCAYAAADSmrgMAAAYhUlEQVR4nO2de1BU5/nHvwsiLgsZLlLBaBJDNEatpoCaNkblMhFXXMWampui1KRabSYzMZ3SJqmgqZ2EyTDGGDRJzR+pEyaYVLxSVEiwNChYUyAgWVaQCstFdiUI7rK75/cHv7OePXtuC3vf9zPDnHPey3nfXb777PM+zzlnZRRFUSAQ/JggT0+AQHA1ROQEv4eInOD3EJET/J4Jnp4ATXd3N86ePYuRkRFr2VNPPYVHH33Ug7Mi+ANeIfLu7m68++67aGxsRHh4ODQaDRobG3HgwAEicsK48bjItVot8vPzodfrsX79evT29iI4OBjBwcGenhrBT/CoT97V1YU///nPGBoawsqVK9Hf34/q6mqkp6cjKSnJk1Mj+BEeE7lWq8Xu3bthMpnw9NNPQ6fT4eTJk8jKykJqairCwsI8NTWCn+ERkXd3dyM/Px8GgwFpaWnQ6XQoKirC1q1bkZaWhtDQUE9Mi+CnuNUnpygK3d3dKCgogF6vx8qVK9HX14eioiK88cYbWLZsmTunQwgQ3CZyiqLQ2dmJQ4cO4ebNm0hPT4dWq8XJkyeRm5tLBE5wGW4ROS3wTz75BC0tLUhNTUVvby+qq6uxefNmInCCS3GLyLu7u3Ho0CG0tLQgJSUFvb29qK+vh0qlwrJly0i4kOBSXC5y2ge/efOm1YI3NjYiNTUVy5YtI4tMgstxqciZiZ709HSrBU9NTcXy5ctJmJDgFlwWQhRK9KSkpEChULhqaALBBpeInCR6CN6E00VOEj0Eb8NpPjlJ9BC8FaeInCR6CN7MuEVOEj0Eb2fcIieJHoK3My6Rk0QPwRcYs8hJoofgK4wphEgSPQRfwmGRk0QPwddwSOQk0UPwRST55CTRQ/BlREVOEj0EX0dQ5CTRQ/AHBEVOEj0Ef4BX5CTRQ/AXOEVOEj0Ef8IuhEgSPQR/w86S5+fn4+jRo4iOjkZNTQ0iIiKwfft24qIQfBY7kV+/fh0ffvghZsyYgaGhIezcuRNpaWlkkUnwWTh98tjYWMTHx2NwcBAAiMAJPg35ORWC30NETvB7iMgJfg8ROcHvISIn+D1E5AS/x+O//uYPGAwGnDhxAvv370d/f7+np2NDXl4efvnLX3p6Gh6FiHycjIyMoLy8HJ999hl27tyJxMREAIBMJrNpxzxm1zlSJqW+v78f+/fvx5EjR6DT6URfg79DRD4OTCYTvv76axw4cAA5OTlYunSpoJjdIXS9Xo+jR4+iubkZ6enpkl6Hv0N88jEyMjKCyspKFBQUIDs7G0uXLrVrQ1EU7zG7zpEyvnq9Xo/Dhw+jqqoKv/nNbzB16lTR1xEIEEs+BgwGA8rLy/H+++8jOzsby5cvB0VRkMlk1i2N0DG7TqgM4LfqFEWhv7/fRuDTpk1zymv1B1wm8paWFtTX18NoNCI4OBjJycl4+OGHXTWc27h79y5KS0tx9OhRbNmyxcaCu1LoQuXd3d04ePAg6urqsG3bNiJwFi4R+cWLF1FcXIy4uDjI5XLodDpcvnwZ7777riuGcxvDw8P48ssvcebMGbzwwgt48sknAXCLlm19hY65LDWf9WYLvaurC++//z7UajW2bdtGXBQOnC7ypqYmfPbZZ5gzZw62bNmCiIgI6PV6VFdXO3sotzI8PIySkhJUVlZizZo1eOKJJ+yEymWducTtDPdFJpOhs7MT+/fvR3d3NzZt2mQVOJ/FD1ScuvC8e/cuysrKEBISgjVr1iAiIgIAEBkZCaVS6cyh3Mrdu3fx5ZdfoqKiAhkZGUhOTraxwOwtvc+30HTGgpQW+K1bt5CVlYX4+HjRPoGKU0Xe19eHH374AQkJCZg8ebIzT+0xDAYDSktLcebMGWRkZCApKQkTJtz7AhQSOvvYWULv6enBgQMHoNVqkZmZialTp/L68AQnuyuDg4PQ6XT4yU9+4jf3gtbW1uKtt95CaGgobt68OaYbSPhcB0dcCmZbrVaLyZMnY9OmTYiPjyeuiQhOFblMJkNQUBBMJhMsFguCgoJgNpthNBohl8udOZTbGBwcxNSpU/HSSy9Zy2hRsbfsfbG2XO3Ezjc4OIhz584hMjLSZpFJ/HB+nCry6dOnIzk5GadOnUJ8fDwefPBBtLS04NKlS8jPz3fmUG4lJiYGiYmJkMlkdgIUOxbajmVfr9fj2rVrMBgMdvMkQufGqSIPCwvDiy++CJPJhE8//RTA6P2ihYWFzhzGYzgSFqSPmZEXpo/MF4kR22fOxZEYeyDj9BDi5MmTsWvXLmef1uOIxb/pMjGhM/uIhRzFhM5XToRuC7l2RSK05aT/LBYLb2SF2Y6rnK8NV4SF6zxcc5NSFqgQkUtAqmj5tkIC5jsP374jQieM4tMi7+joQEVFBW7duuWW8cZjncWELlbGVS8Uayfcw6dFLpfLcfr0aRQVFUGv17tlTLbbwixjt2Ees/uyy7nassvY+3zHROy2+LTIY2Ji8Mc//hFNTU04duwYTCaTS8ZxxMdm92Ees8/Jdy6uPkLiJT65MG67npyiKBgMBslCNBqNuHv3LgYGBjBhwgTI5XLOREtUVBRycnLwt7/9DZmZmU5POg0NDQGANbnFjpawoyHMuTk78sKsZ8MXZSG4UeS3b9/Ghx9+iPLyckntb926hdDQUBQVFSE2NhalpaXWC77YLFq0CK+99hpSUlIQFOTcL6fBwUEkJSUB4I57s8UMgLcNn/D5PixCwuez3iR0aI/bRB4ZGYnc3Fzk5uZKav/ee+/hsccew9atW5Geno6bN29i9uzZnG2NRiMUCgW++eYb3g/CWCkrK8Phw4dFxcks52ojZQvYx+Ppc9F1TPisNxG6LT7hkycmJqKsrIy3vqGhAQkJCS57+i57sUnHyPl8Zj7/XaPR4B//+Ac6OjocWnyK+fZk8SmMT4hcpVLhq6++wo0bN+zq6J9bzMjIwMSJE106D7bY+aIsXH8DAwM4ceIE9uzZg4sXL8JkMglGafgiMlzzYbYn2OMTNzIvXrwY69atQ15eHtauXYuFCxciNDQUTU1NKC0thcViwdKlS22u83Y2UhaVfD62yWTC1atXoVarMWfOHGi1WgwPDyM8PNzhBSnXfLjGJNzDJ0QeEhKCLVu2oLKyEuXl5Th69ChGRkYQExOD5ORkpKSkYMqUKS4bn7aYUqIpXELv7+9HeXk5FixYAIPBAK1Wix9//BHh4eGSFqRsoYstOolfbotPiBwAIiIisHLlSiQlJWFoaAgWiwVyuRzR0dEICwtz+T+VT9xMuMRpNptx5coVdHZ2YteuXaipqYFWq8XQ0JBDC1OusbnCi3yWP5DxGZEDwIQJEzx6Nzpf5IQLum54eBiffvopnn/+eYSHhyMqKgpGo9Eaf3c08iIWYSFW3B6fErmnoCMqdDKIiVgY8aOPPkJzczPy8vKQl5cHihpNiimVSsmuCpeQpVh0Ys1HISJ3ACExc9X19fXh2LFjKC4uRkJCAmQyGQYHB7F79250dnbCYDAgNDRU8FpytmDZURu+hJHBYIDBYEBXVxcaGxvtXkt4eDgefPBBZ79FXgkRuQAURcFoNFr32Yi5KxcuXMCzzz5rfXIYRVEIDw/H/PnzERwcDLPZzBlZYZ6by5KbzWaYzWZre7YVNxqNuHr1KgYGBlBRUYHKykprfU9PDxoaGrBixQqcPXt2zO+NL0FEzgNFUejs7MSFCxcEkytC/vn69es5w4KbNm2y9qXr2OfjGoNuO2HCBGucnf2NMjIygu+++w7Nzc3YuHEj0tPTrT8y3NnZicLCwoBzY3wiGeQJ+vr6cPjwYdTW1gLgv26cL6HDzIryteFK5nBtxWLk9LHZbMbVq1fR0NCAzMxMG4F3dHRg3759+N///ofnn3/e+W+YF0NEzoFOp8O+ffvQ39+PzMxMAPw3RIgJl+uYRuhDwN6y2zDr6f3a2lrU1tZi3bp1NgJvb2/HX/7yF9y5cwebN292aU7BGyEiZ9Hf348//OEPMBgM2Lx5M6ZPn24nMi4rDQhfZ+6I0IX6M8dh7n/77beoqKhATk4OUlNTMXHiRFAUhfb2duzbtw8ymQzPPfec3zzZzBGIyBnQAg8JCcH27dsRFxdnUy/FZXFE6FI+HFxjs/n3v/+NsrIy/OlPf8KTTz6JkJAQAKMuyl//+lfIZDKsWbMG0dHRTnmffA2y8Px/dDodcnNzERISgt/97ncIDw+3qeda5LFFyIyjS4lTS0n+sNuy/2pqavDPf/4TBQUFmDdvnrVvZ2cn3nnnHRgMBjz77LOIiYkJ2CRRwFtyiqLQ29uLPXv2IDg4GNu2bYNCobATsMVi4V1M0m0tFou1vSP+OXsr9rgLYHSRefnyZVRVVWHPnj2YO3eu9YPQ1dWFwsJC3Lp1Cxs2bEBMTIzdmIFEQFtyihoNEx4+fNjqg0dGRtrU8/nCgONXI3K15erHNQazzmKxoL6+HmFhYXj11Vfxs5/9zEbgRUVFuHHjBrKzswPSB2cT0CKnH4H8n//8ByqVCj09Pejp6QFwL4at0WjQ29uLmpoaaxlzy1XGt2W6C1zHzC3fOe7cuQO1Wo22tjZs2LABcrkc9fX1AEat+4kTJ9Dc3ByQURQ+Alrk33//PU6ePIn58+ejrq4OdXV1dn7r8PAw5HI5Tp06JemcY/F7xfqw64OCgrB48WLodDqUlpZay3t7e1FfX4833njDbtEcyAS0yI1GIx544AH8+te/thMSn0Vm10utExKyUH+hvuzyb7/9Frdv30ZcXJydaxTIBLTIgdEn8d5///3WYzG3g92Or42UfbE6sfbsY7VabQ0fMmFGbAKRgI+uAOI3EUtNyIjFydn9hNpxjSPWX+w1BmJkBSAityKU6KHLmFuuPsxyoX0xMYsJmUusYvVS6vyVgBc5n5iZ+1KtutAHQOzDINSHq72YZSZCv0fAixwQvvLPUVGPx60R6sMeh6+e7zyBjFcuPOmbAvjuanEW7e3tALjFICXFzm7PhKsv1zm59oX6C9UD97KuXO2YDA4OuvS99SRRUVE29wJ7ncjNZjNaWlqg1+tx6dIlnD9/3mVj6XQ6zJw5E4DttSlSMo9cN0PwZTj52tJlYu1ppNTTdzIx4fqQNDU1YceOHQ6+Y+JoNBoMDQ0hISHBrb/4R1Gj2d4ffvgBW7duxUcffWSt8yqR0wL/6quvMHPmTOzatQtRUVEuG+/rr7/GsWPHeK200AVUXOJkn4PPYrPbcrVxxIoz60JDQzn7MNtSFIWf/vSn+Pvf/+7YGyaBU6dOobS0FPPmzUNiYiISExPdIva2tjYcPHjQ7psM8CKRUxSF1tZWlJSUYPr06VCpVC4VOHts5lV+dMrdEZ9WqL3QdStcZXxWne+Yb1ytVou6ujr09/fblN++fRvt7e147733JL8+R2hra8OZM2cwc+ZMKJVKrFmzBo888ohLxqLHKygogNlshlKpxPDwsE2914i8vb0dR44cwezZs90qcEDY35YiXiEXBhi9Rob5M49xcXF45plncP/994u6OY64MOx5hoSEIDIyEkFBQTZ9goKCEBoaivj4eEfeJkkYjUZMmTIFzc3N1jlMmjTJ6ePQaDQa7N27FwqFAiqVCleuXLFr4xUip+8/fOqpp6BSqXDfffe5bWxmlIPPJxfyv8WsMkVR+O677/D999/jtddew9DQEEpKSjBt2jSsXr3azr2Q4rbwuTDMfZlMhujoaPziF7+wm1t7ezva29vx3HPPjfPds8VoNOL06dOQy+V4/fXXsXTpUsyYMcPpj9OmaW1tRX5+PmJjY6FUKtHc3IyGhgb8/ve/t2nncZHfuHEDubm5WL16NVQqFcLCwtw+ByluBp9PzW7LFqrZbEZfXx8WLlyIJUuWgKIoVFRUQK/XWx9JwfcNIGbJ+SInQnWuCisajUY0NjZi0qRJeP311xEfHw+FQuGSsYBRC56fn4+4uDisWrUKLS0tOH78ON5++22kp6fbtPWoyDs6OpCbm4usrCysXbvWpU+lFUKqhQYct+pmsxmtra1YsGABAOBf//oX7ty5g6SkJOvXuKMhRiELz2XRuV6vs5k4cSLmz58PiqIQHBwseK3M1q1bcfHiRQCj7sxvf/tbbN++XfJYbW1t2Lt3L2JjY7Fq1Sqo1WoUFhaiuLgYaWlpds+p94iqKOreDbarV6/2uMCF/ul80Ra6L1d7uk4mG31sc1lZGb744gu8+eabMJvNyM3Nxbx582zaMfeluCl8vrlQH1cj5UcQNBoNenp6UFpailmzZuHatWvYuHEjHn/8cfz85z8X7EvrpqCgAAqFAkqlEi0tLSgsLMSxY8eQmprK2c/tyqIt25EjR6w+uKcETuNIyJCJkJtBl9+5cwehoaE4f/48oqOjcfXqVXzwwQdISEjA4sWLOccXGkNoPK7XJRSK9AR9fX2YNWuW1ZWZMmUKYmNjRT8gFosFbW1tKCoqgtlshkqlQnNzM44fP47i4mJegQNuFjkdBy8pKbFGUTzhg3Ph6Fe4VKteW1uL6OhoREVFgaJGn3JrNpvtbnqmzyHVP5f67SJk8T1BS0sLwsPDrc+EOXfuHCiKEnxaMUVRaGtrw8cff4yBgQGri1JdXY23334baWlpgmO6TeTMRA8dB3dnFEUIrpChVGvO7Mc+FzB691FwcDC++OILAEBjYyMWLlyIhx9+WJJ7ItU/Z7pdXML2FqG3traio6MDJ06cwKRJk3D8+HHk5ORg2rRpvH3a29tRVFSEgYEBKJVKaDQaNDQ04JVXXsGKFStEvwXcInKK8lyiRwypizUadtKIr55mwYIFCAkJQVdXF2QyGR5//HEsWbIEkZGRoi4Q33n59tmvi+t8nnRXBgYG0NPTA4VCAZ1OBwDYvn07li1bxtuHmehZtWoVNBoNmpqakJ2dDaVSKSkG7xaRezLRIwVHLDYNn8vALlu+fDlSUlKs4uJzR7jOz9VuLGJnCttkMuHatWse+R90dHQAADZu3IiFCxeKtmcnetRqNRoaGpCdnY3MzEzJrq7LL7WlEz1z585FVlaW1wmchrbOXH90PXsrpT1fW2Y53/nZ/bnK+fb5jquqqtDU1ITNmzeP/c0aI319fYiIiJCUHGptbUVeXh6io6ORlZWF69evo7q6Gjk5OVi9erVDMXiXWnJvSPSIQVGjDw6SyWR2FlmKHy7kVvCV8fnbjlh1KW4I24pfuHABVVVV2L17N+bMmcP7ulxFcnIyZs+eLWrohBI9K1ascPgyAZeJ3FsSPVIR+9ofS3iRS5TMsdht6X1mOzGXhCl2roUnXVZZWYmysjIcPHgQDz30kEd8c4VCIWqBHU30SMHpyqMo70n0SIFpyeljLqsOSL/SUMo3Ad+HgLmoFQsVCsXK6XKLxYKqqipUVVXh4MGDmDFjxpjfK1dC68bRRI8UnKo+b0z0SEWKkGmcYdXFXBN6TmILULbFZp7XYDDg0qVLaGhowO7du/HQQw9JfTvcyngSPVJwmgK9OdEjhlRRO4KYsPn8bL4PgdA3BZfQh4eHUVdXB7VajZdffhlz5szxeLaTC4oaX6JHCk4RuTcnesRgRyIAexGxfWquNmNdrI7VpRFieHgYtbW16OjowIYNG5CYmDgmX9YdjDfRI4Vxi5yivDfRIxV2uI32h2m4hMgl/LEiVbxS2hsMBtTW1uLGjRtYu3YtFi1a5LUuozMSPVIYd5ycTvQ88MADPvtrBlwxarE/qe24+rD7Mp9HzjcfrvHY7S0WC7RaLdRqNdatW4cnnniC87Fx3gAdJpTJZFCpVGhra0NDQwNefPFFhxI9UhjXR9yTd/Q4i5qaGuzatYuzjs9SO1o+1j5S6pnt9Ho9FAoFNm7ciMTERK+14Fx39FRXV+OVV16BUql0+lpuzO+CLyR6xEhOTkZxcbGnp+FU5HI5pk6d6rU+uLMTPVIYk8h9LdHDh0KhwKxZszw9jYDBFYkeKTikTl9L9BC8A1cmeqQgWaG+nOgheA5XJ3qkIEmlvpzoIXgOdyR6pCAqcl9O9BA8izsSPVIQFblOp/PpRA/BM7gr0SMFGcVKm2VkZEAmk+G+++6DyWRCaWkpYmNjsWDBAiJwgmS6uroQFRUFpVIJtVqN//73v9Y7elz50CEuOC35kiVLrD8WpVKpHL44iRDYUBSFHTt24NChQy5P9EiBU+TJycnW53YTCI5CUaNP0dJoNDh+/Dj27t2LjIwMt7ooTEgMkOAyCgsL8fnnnyM9Pd2jGVg7kYeFheFXv/qVJ+ZC8COCgoJQUlLitjChEHYLTwLB3yC//kbwe4jICX4PETnB7yEiJ/g9ROQEv4eInOD3EJET/B4icoLfQ0RO8HuIyAl+DxE5we8hIif4PUTkBL+HiJzg9xCRE/weInKC30NETvB7/g+Vp9E8M+iGcgAAAABJRU5ErkJggg==)
Physics-General