Maths-
General
Easy
Question
- 0
![e to the power of x](data:image/png;base64,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)
- tan x
- 1
The correct answer is: 1
![Lt subscript x not stretchy rightwards arrow 0 end subscript fraction numerator e to the power of tan space x end exponent minus e to the power of x over denominator tan space x minus x end fraction](data:image/png;base64,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)
We first try substitution:
= ![Lt subscript x not stretchy rightwards arrow 0 end subscript fraction numerator e to the power of tan space 0 end exponent minus e to the power of 0 over denominator tan space 0 minus 0 end fraction space equals space 0 over 0](data:image/png;base64,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)
Since the limit is in the form 0 over 0, it is indeterminate—we don’t yet know what is it. We need to do some work to put it in a form where we can determine the limit.
=
=
![Lt subscript x not stretchy rightwards arrow 0 end subscript fraction numerator e to the power of tan space x end exponent minus e to the power of x over denominator tan space x minus x end fraction](data:image/png;base64,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)
![Lt subscript x not stretchy rightwards arrow 0 end subscript fraction numerator e to the power of tan space x end exponent minus e to the power of x over denominator tan space x minus x end fraction](data:image/png;base64,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)
Related Questions to study
maths-
If m and
are the mean and variance of the random variable X, whose distribution is given by: ![](data:image/png;base64,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)
If m and
are the mean and variance of the random variable X, whose distribution is given by: ![](data:image/png;base64,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)
maths-General
Maths-
A random variable X has the following Distribution
The value of ‘K’ and P(X<3) are respectively equal to
A random variable X has the following Distribution
The value of ‘K’ and P(X<3) are respectively equal to
Maths-General
Maths-
A random variable X has the following probability distribution
then the mean value of X is
A random variable X has the following probability distribution
then the mean value of X is
Maths-General
Maths-
If a random variable X has the following probability distribution
then the mean value of X is
If a random variable X has the following probability distribution
then the mean value of X is
Maths-General
Maths-
If X is a random variable with the following probability distribution
then the variance of X, V(x)=
If X is a random variable with the following probability distribution
then the variance of X, V(x)=
Maths-General
maths-
A random variable X has the probability distribution given below. Its variance is ![](data:image/png;base64,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)
A random variable X has the probability distribution given below. Its variance is ![](data:image/png;base64,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)
maths-General
Maths-
If the probability distribution of a random variable X is
then k =
If the probability distribution of a random variable X is
then k =
Maths-General
Maths-
If the probability distribution of a random variable X is
then second moment about 0 i.e.,![blank M subscript 2 end subscript superscript 1 end superscript left parenthesis 0 right parenthesis equals](data:image/png;base64,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)
If the probability distribution of a random variable X is
then second moment about 0 i.e.,![blank M subscript 2 end subscript superscript 1 end superscript left parenthesis 0 right parenthesis equals](data:image/png;base64,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)
Maths-General
maths-
X is a random variable with distribution given below Then the value of k and variance are ![](data:image/png;base64,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)
X is a random variable with distribution given below Then the value of k and variance are ![](data:image/png;base64,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)
maths-General
maths-
maths-General
Maths-
Maths-General
Maths-
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 0 over 0 or
Maths-General
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 0 over 0 or
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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Rgbm4OUqn0WKkH5IuSyWSoqKhAUVERDg4OsLq6CofDERI840W0SePz+SAUCtHS0gKTyYSvv/4ajx8/Rm5uLs6dO4f6+nrodDpGvYO9dA+XSVAUBZlMhnPnzqGpqSlsHSl4+R/JP7/fj8zMTHz00Uf48MMPw76P1J74fH7MzIaiKGRnZ+OTTz7B9evXX9oe8V2j0eDSpUvo6OiIuOwm4403gJEAlZ+fD5PJhH/4h3+I6m+sZ5JkoIWFhcjLy4tYjyNjj2WPoigIhUKUlJSgoKAg7L0iAe7p06fo7+9PmnjAxMQEvvzySywtLaGzsxOVlZV47733kJKSkhT7x42IYVYgEDBprVKphM1mw/Pnz2G326FQKJCWlgYAePbsGex2O1QqFTQaDbRaLbKyslBQUMBQCyQSCRM80tPTkZ6ejqysLBiNxmM/R0h+0cnyNSUlhaE6JBPsB1gsFiM/Px8ff/wxSkpK8ODBAzx+/Bhutxvt7e3Q6XTMTm+sYjR5cMVicdTPjqdILhAImF/wSEikBV6y7QHff1/x0AESAcnso/mbyGZDsu0B0e8nybKS9dySDbqJiQk8ePAAh4eHePLkCYaHh9HW1nakFcqrQNgAxuPxoNPpkJWVBYlEgosXL6K5uRkHBwe4c+cOfD4fqqqqkJ2djS+//BKbm5uoqKiAXq/H7OwsdnZ2sLy8jM8//xw0TWNzcxMqlQpWqxUymYxZjp7k+UGyFDupg9cSiQQmk4mhm3R3d+P+/ft48uQJrl27hurq6rhrfaRW8bJINpXhuKgRxyVN9LqPP5o9EjCT9XlOpxOTk5MYHR2F1WoFRVHwer2Ynp7G0NAQLly4cGwk82QiYgA7e/Ys/vVf/xVjY2PQ6/UoKiqC0WhEVlYWFhcXUV1djcrKSmg0GiwsLKCoqAhyuRxOpxMulwsHBwfY2dmBy+WCz+fD3t4eFhcXodfr8dOf/hStra1vrIoDyRBomoZKpUJ9fT1TD5qYmMDnn3+O5eVlNDY2wmQyATi+ScuBQzhYrVZ0d3dDJBLhRz/6Eb7++ms0NjYiNzcXw8PDaGpqikiNep0QMYCVl5cjIyMDGo0GGxsb2NjYQFFRES5duoTZ2VmmeNne3o6cnBzI5XJQFIWysjIsLi5Co9GgsrISh4eHcLlcmJ+fx8rKCoxGI8xmM7Kzs09FivqyINlTYWEh1Go10tLS8PXXX+P+/ftwOp1obm6G0WhkSILJ+IUNJicG85SOkjkEE5SDcVS74Wg4bKrHUbMctq/R+GSJ2os2/mTaO65u9jRNMwmFzWZDQ0MDiouLMTAwgLa2NlRXV2NychL7+/uQy+WvfRCLWgPT6XS4evUq1tfXIZPJmFpSUVERU5sRCoUoLCxkHrj3338ffX19kMvlyM7OxtraGnQ6Hfb29rC5uYnKykqYTKZTLykdCWyyJPsBFIlEyMjIwKVLl5Cbm4u7d++it7cXKysruHLlCoqLi5mNhVj1n2gPNlkKuN1uZtkZvDsmFosTrgN6PB7mCAo7KJL/kxpjIrtXPp8PHo8npLMTGR+pnya6k0k2mYi/wQGc1NnIEZlE7QEIGX8i9sh35PF4wtojNCOJRHIstVqHw4Hd3V00NzejtLQUDoeDUVduaWlBdnY2NjY2mF4Wr/M8jXi3yURMS0tjtu9JgTF4UITkRtM09Ho9mpqamBuSnp4OqVQKn88Hr9fLyNi8zjflqGAzuclEZ4PHe6HUUV5eDo1Gg5GREQwMDOCPf/wjWlpaGG6TUCiMuBMV7v8ERJetp6cHjx49wvLyckBApCgKarUaLS0tOH/+PLKysuLiDlEUhYmJCdy/fx8zMzMBQYE0cKmtrUV7ezvTIyFaNkJsLi0t4cGDB+jv72dOTBBQFIXi4mJ0dHSgrq4u7qNZfD4fLpcLQ0ND6OzsxNzcXMC98vv9kMlkaGpqQmtrKyOqGck2n8+HzWbD8PAwY48dpIi9lpYWtLa2Ij8/Py57g4OD6OzsZM4Js+2pVCo0Nzejra0NJpMpqeUFEmxzc3MhlUqh0Wjw/Plz5vWUlBQUFhbCarVCqVS+9vM06s8F2fWQy+Uhf4/0fh6Ph/T0dOZvr+P5qeMAj8fD4eEhhoeHsbu7y5w+YEOj0aC8vBylpaWoqqpCamoqeDweurq68Pe//x0rKyvIzc2F3W6H0+kMeHAJibO0tJQ5lxY8SdiZi1QqDUsVkUqlTO0x3onBztzkcnkACZRQPcRiMZN1xrsxIRAIAgjNwfeLZCCJLiMJX4/cAzY3jvibSFZHfCWdtYIJyWT8wRlkLHtSqZThULLtxcvHOwp4PB6kUimys7MDlunkNcKHOy3tD3n0cSy031BQFAWr1Yqenh5MTk4yMtnA91++0+nE+Pg4Dg4OAq7l8V4c47h06RLa29uhVquZY1ZPnjzBrVu3MDk5Ca/Xi83NTaSkpECtVgc8ZHl5ebh48SJaW1uRkpISNgCxNxAiZXEkWMRbgySfT7K1cJkl2248gYFN6I0UoNjL8USXkLHOS5JVQDz3gD3+aH4mYi+af+z7ySYo8/l8TExMoLe3N+AMsd/vh0gkwocffoiqqqqElvF+vx9zc3P49NNP8Ytf/AK/+tWv4r72dcDpoNueAlAUBa1Wi/r6ely8eDFkUpLUXavVQiqVMkRWhUKBsrIyqNVq9PX14cGDBxCJRKivr0dtbS10Oh3z605SfqlUGjF7IvWoSJOe+JVIkZhk4oSLFs5uIgesiQ1SR03W4Wq27WTeA/aJkmhF93jtHcd39LaCC2BJhEQiQWZmJtLT05njU2wEP5TkQVUoFCgoKIBWq4XJZEJPTw8WFxdB0zQ+/vhjFBYWQiaTwefzxfVQH2XSx8Jx2CRZTTI4bsFIpr/sgJIsHMf9fBvBBbAkgxyqDbfciBR4yE6WTqdDfX19QHenP//5z2htbUVjYyPXPJcDhyBwAewYcFT+EingNjQ0ID09Hd999x3u3LnD7NCZzWau+xEHDixwAewYEOsAb7CSBRskGzMajfjkk09QXV2Nzs5OfP3111hYWEBHRweMRiOzexXPMiRWcT2aP8FgF5jDgR28Ewng7EJ4JLtHOVcZjxDkq8JxjPltAxfAkggyab1eb4DkDhtkZymSbj5ZelIUBalUioKCAni9XvT29mJsbAxTU1N4//33cebMGaSlpQUw7sOBcNLCFZnZB4SjKZUG+0eWyeGCFHtsiexykmV3uHvG9jGR7JOMO3g5zx73q5KNIWMO5x/xkX0vX3c+1qsCF8CSBPLAeTwejI6OYnx8HJubmwG/8BRFQaVSoaKiAmfOnEFGRkZA8OHz+bDb7YwqwNraGoRCIfx+P9Ob8+DgAOvr61hbW8PFixdRVFQUcYufz+fDarUy9oIFAimKQkpKCsxmM8xmMzIyMqJmJHw+HwcHB5iamsLQ0BB2d3cDJhZFUUhNTUV1dTXMZjPS09NjFujJPXv69ClGRkbw7NmzgHHQ9Asxv8rKSpjNZuTm5kYN2OS7oGkay8vLGBkZwdTUFLxebwAlgaIodHR0hN0xPm4Q/xYXFzEyMhJCDgZe3Jfi4mLU1taiuLiYC2ARwAWwJIL8slssFiwtLTE7iWzWukajQVpaGjweT1h1AYqiYLFYsLi4iMXFRaZjEwDmyJZQKMTY2BgoioLL5UJ2djYUCkXIxCYT1WKxYGFhAcvLywEZh8/nY+SP2AJ/0cZHURRzMH9tbS2ERa7X62EwGBJq9kvY6cvLy5ieng64ZyQT1Wq1KCkpSWgiO51OrK+vY3p6OkDAkYy9urqaGddJBzAAcDgcWFtbw8zMTECAJURXmUyGkpISLgOLAo7ImgCiEVlpmobBYEBdXR0jnxzuOBFhn5NOMsEPpt/vZ84ysq8nwZE0Wrh79y4eP34MrVaLjz76CFVVVYyGE/sziT2iChIMoqoazzlGHo8Hv98Pt9vNnLUMNz6JRBL3uUBy78hZQ6/XG3Y5RXxMhKFO7qPb7Q5rUyaThZwyiYVwwe4oAZCUGtxuN3MWNNimWCxmxkyW5ByRNRBcBpZEkMxBLpdHbYIQrWhOAhzJqMLB5/Ph3XffRVpaGnp7e/G73/0Ozc3NuHDhAgoKCphfbPZxHSL7HMmfeBVT+Xx+SPOHo9ojICRddju/cJ+daEFbLBZDKpWGzXRJME7ET/KdBR8OPwpIUI7VBo0r4kcHF8CSCPayJ9Kxk3gQT/MLk8kEpVIJqVSK+/fvY2JiAm63G83NzaiuroZMJmPqT8nebTtOUutx2HwZuzweDz6fDxaLBX19ffB6vbh27RrEYjE8Hg8mJycxMjKC8+fPw2QyJZT9HMeY3zZwAewUggRGrVaLjo4O5OXl4dtvv8Xc3BwsFgtcLhfKy8uh1WoTOmDNIRQ8Hg9utxuzs7O4efMmBAIB3nvvPUgkEuzv7+Phw4e4efMm8vLykJWVdWqaYbwp4O72K0CsA8+xAg65niy9CgsLkZGRgaGhIXz77bf4wx/+gI6ODrS1tTFyRpHssP8N5wf733gQbWyJ2jsu/8i/8QR2Ho8Hu92OiYkJZGZmorKykukXsbCwALvdjubmZphMJuY+B/udCMeO/W/wa/EelH+bwAWwV4BoD3Q8BWHyOkVRzK4k+xjSw4cP8c0332BychIffvghzpw5A5lMFrLsixUAEilOB1MfXhbx2guuSSXLLgGfz4fD4cDMzAz0ej1KSkogFArhdruxtLQEu92OiooKpKSkMMRiIueTaICN5ht7h5LD9+AC2AmCCA5OT08zvKxgyoBWq0VdXR3KysqQmpoa8MCSyTQ+Po7x8XGsr68DCPzllkqlyMjIgMfjwcbGBu7cuYOtrS20tbUhMzMzgC6xvr6OsbExTE5OwuFwBGQMAFBcXIz6+nqYTKawh9MJSGawurqK0dFRTE1Nwe12M6+T68rKylBfXw+j0RjTHk3TWFlZwcjICJ4+fQqPxxNgj8d7IXteV1fHdLeKJ2vd3t7G1NQURkdHUV1djQsXLgT4GHyNy+XC1tYWtre3UVxcDJPJBB7vhfbb7OwsHA4HqqurmU0NoVCIzc1N3Lx5EysrKzCZTGhsbEReXh5kMlnEz/F6vVhaWsLQ0BDm5+dD+kxKpVJmh5ELYt+DC2AnCEKDODg4wNLSEp4/fx5CBNXr9SgoKGB4VMG8LpqmGZ7Zs2fPQnbE9Ho9qqqq0NDQgIWFBfT396Onpwc+nw+1tbXIyspiDou73W5sbW1hfn4eNpstxBe5XI7y8vKAz442No/Hg83NTczPz8PpdAb4BbxQ+6yoqIhpj+x2ulwuxp7L5Qqxp9FoAj4nFkig2N3dxdzcHLKyskKCdvD79/f3sbS0BJlMBqPRCJ1OB5fLhY2NDezu7kKlUjFy4CQj9vv9eP78Oebm5gAA5eXlTNCN9DkAYLfbsba2hrm5uZDGtlKpFHq9nmlnyOEFOB5YAoiHB1ZfX4+0tLSIGQZFUSH66mwQJVF2t20CEgAJtynS9UTRk6IozM7O4vbt2xgbG0N+fj4++ugjFBYWQqlUwu/3w+VyheVJAWD4avGql/p8PrhcrrC8JuAFrUEmk8UtKR6PPalUGrM3JRuEx+ZyuRjqRjiQkxWTk5O4desWfD4frl69ivr6emxvb+PevXsYHBxEeXk5rl+/zlBAyK6lzWaD1+tl7mE8vS7Z4w3nj0wmw9zcHAYHBzke2P+By8BOGKTlfCSeF6mPRVJbJQ9ytOvJtaQBy8cff4zMzEx0d3fjv//7v/GDH/wAFy9ehMFggEgkglqtjuhHIjuYIpGIkZYOh0QOjbPtRSpeH4WGIBAIoFQqmT4P0eggAoEABwcHmJmZQVZWFsRiMaxWKx49eoS//vWv0Gg08Pl8+Oyzz9DS0sLozAsEAmi1WuYHJ97NAhKQIwU6Ho/3xrYiPCq4APYK8LL8n3ivJw03ioqKmInV2dmJvr4+hjPGbmrxssl4tOD7MvaSjXh4djRN4/DwEJubm1hfX8fGxgYoikJWVha2t7exsrKCtT9Ze2YAACAASURBVLU1AEBBQUFIkD3K9xvteyUZIbdgCgQXwN5wkAmRmZmJq1evoqioCA8fPsTo6CjTWqukpARqtTpiN6S3DaSONT8/j83NTZSXl2N/fx9ra2twuVwoKirC+fPnsbq6itTUVJw9e5bp7ckFmJMFF8COAUQGJVqROhaVIpoUTaJLO3KOTqPRoLa2FgaDAd3d3RgYGMAXX3yBlpYWpsBPdO+j+UZsRvPvKDr2sThkiWZk8diM5CdRFdnb28PPfvYzqFQquN1uCIVCyOVypqelRCKBWq2OuMP4sv5xJOTo4AJYEkEeNNIAI1LdxufzhT3oDYDhdUVqdhHr+nD2SKNUUn9TqVRIS0tDXl4e7t27hz/96U+YnZ3Fhx9+iOrq6pjHb6L5R45RES2ueEG0uSJ16iY2E1ma8fl8CIXCiJsGHo8nrI8+nw9ra2tYW1sDRVEwGAzIyspi7jm572z6y1GCDPEvUtGdjDncZg2HF+ACWJJAAoXH40FfXx8mJyexsbER8GATPbDy8nLU1tYiPT09YGudyMo8efIEIyMjWF9fD9HvksvlqKmpQVVVFTIzM6NOHKLf9fTpUwwPD2Nra4sJEAKBABaLBcvLy3A6nZicnARN09ja2sKZM2eg0WhCznPy+XxYLBZGXyycHphGo0FVVRVqamqQlpYWlx6Y1+vF1NQURkZG8Pz58xBCp1gsRnl5OcxmM8PDikXpoGkaCwsLGB0dxZMnTwLkagjOnz+Pjo4OxndyrcPhwMTEBLxeL/Lz8yEUCpngmYxsiBT3Z2ZmMDo6itnZ2bB6YEVFRaipqUFRUVHc4pBvG7gAlkSQ2sn6+jqGh4exsLAQoItFURTTJi2cSB3hUm1sbGB4eBhzc3MhelspKSlISUlBfn5+VA4T297a2hoGBwextLTELFnI8iktLQ2XL1+Gy+XC2toabt++DafTiaqqKuh0OqauQ65zu91YWVnB4OAgVldXmc8hWZLBYIBKpUpIu4sEzomJCYyOjoaQe2UyGYRCIfLy8hL6PiwWC2ZmZtDd3Q23280s60mWG0kckbDpCwoKYDabmTZ2yVrKkc/c29vD06dP0dvby+jDkfshFArh8XiQk5PDXHPcOI1LVY4HlgDi4YGdOXOG6V4djr9EOp0rFAqm3kRAOEROpxM2my0sH4jP50OpVEIul4dcHw5+vx8Oh4PhJQWD1HT8fj+mp6dx7949rK6uory8HOfPn0dJSQlD2SAaZ8S/aPYUCkXcW/40TcPhcMButwcQVtn3RS6XQ6lURpUpCobL5YLdbofD4Qj5Hng8HtM8OBgURTHXJMozSwROp5Ppwh5uGspkMkZx5Dj1wGZnZ/GjH/0Iv/zlL/Fv//ZvSRnbSYHLwJIIwiBXq9URD1ADkeV2yC+vWq1GampqVJ5XvBmBUCiERqNheEmR/CaZjkwmQ09PD8bHx7Gzs4MLFy6gqamJIXyKRCJIJJKI9hL1D3gRTFQqFdRqdVQOWaJLOBL0ItmMVOsj3yFwtA2JeEF01aKN+bgbj5BsVCaTxfWD+LqBC2BJBJnQRAX1KMktWYolSycqEXsqlQq1tbVITU1FSkoKxsbGcOvWLWxsbKCtrQ0FBQUBfS+TidetGe9J6HS96q5IwItnVqvV4le/+hVqampeqS9HARfAODAg9brc3FykpaXBaDSis7MTjx8/htPpRENDA/Ly8gKyEw6nH2q1Gj/+8Y9PZb9RLoC9AsTSdYrF/XnZ62PZIvWh8+fPIy8vD7dv30Zvby+mp6dx5coVZpdSIBCEZBCxfDsqPyxZ9uKxeVS+2cvai2YnFmfsqCA70jKZLKl2TwpcAHsFiGfSxZoQ0WwksvsXbWIJhULk5OTggw8+QHp6Orq7u/HFF19gdXUV77zzDoxGY8g1Lzu2ROyR3bxEJ3Wss6aJ+BjvOceX8YvY4I4ShYILYCcI0vfx6dOnGB0dxebmJoBAQqRarUZ9fT3Kysqg0WgCHmgiMUP0wDY3N8PysJqamlBcXMwcWI7ky8bGBsOTcjqdAbQMmqZRVFSEhoYGmEwmdHR0QKVSYXh4GGNjY7DZbGhsbERlZSXTJZzogT19+hQulyuE5lFcXIyGhgYYjcaYulY83gt9sZGREUxPT8Pj8YT4R/TAiJRzrMnN5/Oxu7uLyclJjI2NwWq1BhTQCQ2kqakJ+fn5Mdn1fD4fOzs7mJiYwPj4eFhJouzs7AA9sHABiuw+Ly0thaXf0DQNkUiE6upqZocxFhcuHEgTEzbn7bQ3zuUC2AmC8LIIT2x+fj7gdb/fj6ysLKSnpyM3NxcajSbs9aurqxgeHsbs7GzABKRpGhkZGcjOzobJZEJKSgrz92A7AHB4eIj5+Xk8fvwYh4eHAXZomobb7UZ+fj6ysrKQmZmJK1euID8/n5Hn2dragtVqRXV1NdLT02G32zE7O4tHjx7B4XAE2ANeMNwLCwuRmZkZVYCQTE6r1crwuIL1xcgYCgoKkJmZGde9JyTV58+fo6+vD1tbWwFHvnw+H8rKylBQUACj0Qi5XB7VRx7vhdz04uIi+vr6sLOzE3Kgu7q6Gnl5ecjOzo66PCT9NqempjA4OBgQsIEXlAqpVAqj0XikLMzv92NzcxOrq6vY29sDTdNQq9UwGo3IyMiIKffzuoLjgSWAZOiB+f1+eDweOJ3OsLQAoVDI6EeF4/Ow+zKG42GRekasvozkSBLRxgqXGUgkkhAtK8Ir6+rqwt///nfs7u7inXfewblz55CZmcnYDLe0Cmcvmn+kb6LL5QobhEmvyEQmn9frhcfjgcvlCrvTKBKJIJPJIBKJ4ipqx7JHJHKiyQwBCODYeb3ekO+DfK9zc3MYGhpKiAfmdDqxsrKCzs5OPHz4EM+ePYPdbodGo8GlS5fwwQcfoLi4OKqUz+sKLgM7YQiFQojFYmg0mqgaV5E4TwKBACkpKWHP95HMhUyAWEs0iUQCuVzO2GK/n5wqCKZMiMViiMViNDc3Qy6X4+HDh3j06BE2Nzdx+fJl1NTUICMjg7EVfJQq3jOSPN4LeWyFQhExkBDfEinkk16MOp0u7JjZPsbz205EGl/WHhGyjMRbI7YTIfIS7Ozs4G9/+xuWl5dhNpvxwQcfYG1tDd999x06OzshEolgMBiichdfV3AB7ITBDlCRAlgskAO+0Yip8YDUQyIdFo6UQQKATqdDY2Mj9Ho9+vv7MT09jS+//BLLy8tobm5GWlpayC5losn+UfyL12Y0nlcidkkmG8leIraIWm+k75U0DUkUCoUClZWVKC8vR1FREbKysrC2tobNzU309PRgfX2d4S1yGRiHuPGyq/dkrf6PSrglmvkZGRnQarUYGBhAV1cXtre3cfbsWRQWFkKhULz0OcLjqHIk22Yy7YWz9TKBRa1Wo7W1ldnJ9Pl8sNvtEAqFKC4uhtlsDukQ7na7MTIywmwoSCQSZGdnQ6vVwmKxYHt7m9mYWFtbw87ODuRyOaqrqyGXyzEwMID9/X1otVqUlJQwdbZkgwtgHI4EtqSMXq/H9evXUVBQgM8//xx/+MMfsLa2ho8++ggVFRWnkiD5JoHUz0gNl2yMrK6uoqmpCdevX0dKSkpAAHM4HPj1r3+NGzduwO12QyKR4Ic//CGampowPj6O27dv48c//jFMJhPu37+P3t5eqNVq/Pu//zsqKirwX//1XxgdHUVFRQV++ctf4oMPPoi7t0Ii4AJYEkEK16RQHy7zYMvZRNL7IkucSFvu5Np4JFaID5HsETuJ2mPrkZFfdqPRiI8++ggGgwFjY2P4wx/+gPb2drS1tTEt4sJxmdhn/sItxYh9IhQZL9i0gXBZDbEXL40gmj22j4nai7T8ZH/PLzvxiUDjzZs3cffuXXg8HpSUlDAt6YDvn70nT57gP//zP+HxePAf//EfyMrKwsjICAoKCtDc3AytVouRkREsLy8zGwHV1dX461//it/85je4fPky/vmf/xktLS1YXV3F1tZW2A2nZIALYEkESc+npqYwPT2Nra2tgAedpmkoFAqUlJSgqqoKer2e+Tu5nlARxsfHsbW1FfDgkiJuVVUVKioqkJ6eHrUmQuzNzMxgfHw8rH6XUqlERUUFKioqkJaWFtOezWbD9PQ0xsfHYbFYQl6Xy+VIS0tDXV0dFhcX0dnZie3tbZw5cwb5+flhe13SNI25uTlMTExgZWUl5J4R+aHKykpkZ2cH3LNwIAXv9fV1TExMYGZmJmzNMScnB2azGXl5eXH1qVxdXcXExERI30YyDra9aLw0Ym95eRmTk5OYn58P8U8gECA3NxfV1dUB0klHAaltyeVy5Ofno7GxERaLBVarlQlMBQUFEAqF2Nrawt27d/H06VP85Cc/wU9/+lNkZmairq4OIpEIRqMRBwcHEIvF8Pl8MBqNaG5uxuLiIr777jtYrVakpaXh4sWLkMvl8Hq9x7q7yQWwJIHwgkiavrq6ipWVFaZXIMnOUlJSoNVqw0rlAC9+lQ8ODrCysoKVlZUQoqVCoYDBYGCuj0Vo9Pl8ODg4wPLyMjY2NkLsqdVqZGZmRvQneIw+n48RQtze3mb+DnzfmJdwxtbX1/H//t//w1dffYXh4WHU1NTAaDQiNTUVEokEIpEIKSkpkMlksFgsWF9fx+LiInPPgO+DtkajCSu1Ew1OpxPb29tYXFyEz+cLyTCFQiEKCgqYCR6rjuV0OrG1tYXFxcUQgUSieltYWBgXM59I9mxubuLZs2cB9uj/UyWRSqVM05WXAVGcKCkpQUFBAa5fv465uTn86U9/wsjICJRKJf7xH/8RCoUCY2NjGBoaQnt7Oy5fvsxw9srKypj7dHh4CJfLhbKyMjQ2NiI9PR1PnjxBSkoKGhoacOXKFSgUCuzv74OiKKaR8XGAC2BJAlmmCYVC1NbWoqKiIkSRgjCqCT2APVGB78X7zpw5g9LS0rBBhdQz5HJ5zB0pkvE1NDSgvLw8on4XkdGJZY9kbGfPnkVlZWXI7iAZn1wuZzKxw8NDTE1N4d69e+jt7YVcLkdVVRVyc3ORkZGBjIwM5ObmoqioCEVFRWEb1ZLsIV7defKenJwc6HQ6XL58OSTDITQShUIRk8VPXjOZTNDr9Xj33Xcj8tIUCkXMIz/kPufn5yMjIwNXrlwJa4/0rSQ/fi+TxfB4L1qyEZ5bfn4+Wltb8c0332BychJOpxMSiQRra2vY29vDtWvXGDVaEgD9fj/29vawtbUFtVqNlpYW5OTkwGq1YmNjA3l5eWhtbYXBYIDNZsP29jZ4PB4KCgqOLQvjAlgSQepTKpUqKl8nWq9Acr1arY74hcfba5AEFMI7O4o/0ezF8o/P56OwsBBnzpzB8+fPGYlsmUyGqqoqlJSUQC6XIzU1FWq1GhKJ5KXHzEa0/plkPInYJfpi8diLBRKUk2UvUYjFYqSmpkIulzOZLUW96BpvtVqRnp4eolVG2Pzr6+tISUmBRqOBUCiE1WrF8vIy02dBJBLB7XZjYWEBSqUSeXl5R+KvxQMugB0DjiK+xwbJ5pIBMjlfRa9Gmqah0+nQ2tqKqakpAC8C9PLyMnp6eqBWq9Hc3MxMhGRrcCXzPp4Ge5GwsbGBrq4uSCQSVFRUwGQyYX9/HwMDA7DZbKipqYFMJgOfz2eIyoTbdnh4iMXFRTx58gQ1NTWw2+3wer3Izc2FUqkE8GJpvbOzg9zcXKjVatA0jYODA3g8HqhUqmPllnEBjMOxgaZpKJVKlJWVoaqqiunCY7FYMD8/j9u3b0MoFKKpqYnpEs6dbEs+7HY7Jicnsbu7i5mZGRQXF2NzcxMTExPIyspCS0sLFAoFaJpGdnY2jEYjurq6sLOzA4FAgM3NTRweHqKkpAT7+/s4PDxEUVERk9VbrVbs7OygsrISGo0Gbrcb8/PzsNls2N3dxcrKCoqKio6lqzgXwE4YpNgf61xcrN3AaPIqibSzj+QLKTQnKg0dbI/P50On06GpqYk5X2g2m3H//n08ePAAf/zjH7G9vY0LFy4gPz8/gPhKbCVzicX2MdLRn5cd81HtRRtvPM9NJOj1erz33nu4d+8eHj16hC+++AIKhQJVVVW4cuUKKioqIJFIQFEUzGYzlpeX8fnnn+PmzZvIyspCc3MzPvnkExgMBiwuLjKbHyTbcjqdUKlUyMvLg0KhgMPhwOHhIfh8PtbX1zE4OAiDwRC1LHJUcAHshEGWluTf4AebzUuK1HeRcLCClx/shzweXlcwDyl4MifCa2KPiW2PnKksLS3F7u4utre3UVtbi+LiYuTl5aGnpwe9vb3Y3d3FpUuXUF9fz+xYURQFr9cb0T9yhjMRnlQwl+tlxpxMeyQYR+IPCgQCCASCuPuBsqFQKFBdXQ29Xo+LFy/CZrNBIpFAr9fDYDAwy0cejweDwYAPPvgAZrMZDocDCoUCer0eubm5EAgEaGpqQmVlJbRaLdMn4cyZMzCZTNDpdBCJRFAqlbh48SKz0UPOWXJF/FMOgUAAm82G8fFx9Pb2BrQlA15MhrS0NJw7dw5msxk6nS5ED8zpdGJgYABDQ0NYWVkJ2cXUarW4cOECk84DkeV0NjY20NfXh5GREdjt9gDqAk3TqKiowLlz51BYWMj8QocDmagrKyvo6+vD6OhogL4YgcvlQl5eHlPYTUlJQXl5OVZXVxn9/aWlJbS3t8NoNGJlZQWPHj3C2NhYwI4sGU9NTQ1aWlqQm5sbc/lJfNze3sbw8DD6+/uxv78fUqTOzc1Fe3s7SkpKoFQqo46Zx+Nha2sLQ0NDGBgYwMHBQYicTmFhIdra2lBcXMxkl8Eg/USJtNH09HQAz4xQSerr66FQKCKOMRIEAgGUSiWz0xvtHkkkEuTm5iI3NzfkdZqmw4pYZmZmMpJGZKPHZDLBZDIl7Gui4ALYCYNwqUirs+AAJJVKGbpDOLWJeK4n9AayhAkG2SGkKAputxt2uz3AFgkETqczhOoRbVw0TTOtzMLRIfR6PdMP0+VyQafToaOjAx6PBwaDAQ8fPsTjx4+xu7uLpqYmSKVSuN1uOByOAA4Y279ENhTIez0eD2w2G2w2W0gAs9vtcXfCJmMOdw+B79uzRTq4H2zL7/fD5XLBZrOFEGU9Hg/cbjeT9cTDW0s24n0OThKcHlgCSIYeGAkaDocj7EQhfSMlEknYYzMURcHlcsHlckXUA4t2PRter5exFUkPjGiLxfNger1eOJ3OiPpdhKBJ9PRJQCaBb2ZmBnfv3kVPTw+Ki4vR0dGBoqIiRq892KZUKk2oHRiPxwsYcyQ9MNJzM556k8/ng8vlYoJ9MIjcTix7NP1CBsnhcITtJ0pOOczPzyesB/Ym4+0Z6WsC8iDK5fKoxelIvyt8Ph8KhYLZwg53LfvfaCCcrnDNXWP5Ec1eJM4ZqRWxGefEvlQqRWlpKdRqNfLz89HV1YUbN26gtbUV7777LlJTU0MCQKL+kQCqUqkYtdpI74vXbix78doiy7dIXDgS7I9jJw8Ak2mfdAb1suAC2CtAIkEm0vXJSpyTaSsee2wJ5+DrpFIpI4Wt0+nQ39+P4eFhrK6uoqOjA2VlZVHrUsny8VXZi/ZcHHUHMp7P3N3dxe9//3u0tLTg3LlzSf+M4wQXwDicKGIdseHxeEhLS8M777yDzMxM3LhxA4ODg7Bardjd3UVdXR10Ot2Rxf04BIKiKGxvb+M3v/kN+Hw+F8A4gCFsRkI0blAwTynR61+1PTbzP5GshE01IAXt4uJi/NM//RNKS0tx69Yt3LhxA7u7u2hubg44IBzpc9g0hnAgfsYbCJNtLxpd5ij2jgoejweFQnFsx32OE1wASyLI5PV4PIwuffDDRzSoRCJR2AeXyE2ztePJBCWTWygUMrygWCC8sWB7JPgQf4RCYVxLlGD/gnlPxL947RF/PB5PiDSzQCCAVCpFVVUVBAIBRkZG0NfXh93dXabAH+38JBk3KXiz7yOxT+5lvJsU7H4FwfbY447HnsfjYe5lOP/Y3/Nx1qYS5dK9TuACWJJAHgK3242enh709fVhZWUlYAvd7/dDo9Ggrq4Ora2tMBqNAdvhfD6f0Wh69OgRnj9/HhCk/H4/VCoVmpub0dTUBJPJFLX+IhAIsLu7i+HhYXR1dWFtbS2ENpCamoqmpiY0NTXBaDRG/bUXCATY29vD0NAQ08iDjB14ESzT0tLQ2NiI5uZmGAyGmGf9CAdqZGQE3d3dmJ6eDnidcKCqqqpgNpthtVoxOTmJP/7xj2hubsa5c+dgMBiYzyf+0DTN8KqGhobg8XhCWtCVlZWhra0NFRUVUZUuCB1ldnYWPT09GBkZCbHH4/FQXl6O1tZWVFZWRtUX4/P58Pv9mJ6exuPHjzE2NhZWX6yqqgrnzp1DZWXlqQwuJwEugCURJAMhWQ9hVbMDGPnVZWdBwTYIA93j8QQsRdnXxwPyGWx77IDo8/kCmO7xjtHv9zP22DtXbP8SmXAk4BB/2PeG7FoKhUKUlpYiNTUVUqkU9+/fx/3793FwcICWlhamES17LMQmyYjZAYfck0jfQzQfw9kj/Lx47bH983q9IXpgbNb9cRTv3xRwPLAEEC8PTK/XB8j0BuNVkBDfFJDTCE+ePMGf//xnzMzM4Pz587h69SpKS0vfWP19kuFPTEygt7c3aTwwv9+Pubk5fPrpp/jFL36BX/3qV8fh/rGBy8CSCPZS8KhFfHJ9soruybYX76ZAojIxifhIOGP/8i//gpGREYyOjuIvf/kLGhsb0dTUBJVKxZBvk1kkP45NgWj1Lfb5Ug7hwQWwJIK9lDrKoVuCZO88JdMee5cxmUh04isUClRUVECr1UKlUmFsbAx3797Fs2fPGGULUtdKprZacKPfl7UX77ElDuHBBTAOpw7sjYuMjAy89957SE9Px927dzE0NASLxYKWlhbU1tYiPT09RNqbw5sDLoC9IkQ6thEPS59cF42HlYgfybJF7BzliFSi/rHtSKVSnDlzBunp6Xjw4AG+/fZbHBwcgKIo1NfXQy6XBxzBiTXmYPtH9ZHYSZat03jU57jBBbBXgHAcIvL34L8dx/WxbIU7iJ2orUj2Ep2A7GVlNHsSiQQmkwnXrl1DXl4e7t69i6+++gpPnz7Fhx9+GKD4Gs4m226iPsb6PhKxGen7iPTdvO3gAtgJgvC8JiYm0NfXh/X19YAHkqZfaMg3Nzejuro6rB6Y3W7H0NAQhoaGGD0xAh6Ph9TUVJw/fx4VFRXQaDQRd0EBYHV1Ff39/RgbG4Pdbg95X1lZGVpaWlBQUBBTDwwAowc2Pj4eVk6nsrKS0e+KxpMiWFpaQm9vLyYnJ0NaqvF4PFRVVaGlpQUmk4lRe9Xr9WhsbIRSqURfXx/m5+fx29/+Fh0dHWhqaoLb7cbo6Cj6+/txcHAQ8pnZ2dk4f/48ioqKoFKpYuqBbWxsYGhoCMPDw7BarSFjIp16ioqKIuqBEZWM+fl59Pb2YmZmJqA2RtM05HI5ampqmC5FHF6AC2AnCEKfcLvdsFqtTN88NudJKBRGlLdhS89YrVbs7e2F/LITMm2sgjjhLTkcDlgslgBKCIHNZou7fhRsz+FwMK+RDCJerS0yTiIvY7FYAgIi4UaRBhPsvwMvugc1NDQwnY4ePXqEu3fvwul0wmAwwOVy4fDwEPv7+wGfS9Mv+naGk7OJBL/fD6fTCYvFEtLol/wgxbLH5pjZbDbs7+/D6/UGZF0ejwcOh+PY+iueVnA8sASQDD0wspNFjhoFg0imEGnpcNcHHw0Kdz3p5xdrPMRWOF8TPRpDdl8jbf2zj1AlYi9S0CP+heN+EQKvxWLB6Ogobt++DYvFgubmZpw/fx5arZahWrB9JQ1q4z2+E+seJnJcKdp4iV/T09Po7+/neGD/By4DO2GQABPpDF8smgKP90I3KpLGeCI0h1hnIBM9lC0UCiOe8TxpeyRL02g0aGhogNFoxIMHDzAyMoK5uTlcv34dlZWVUKlUAL7PghL1kc/nM99FpO8jXntCoTCieCT7/CaH78EFsFeAl+Umva6crtfNHjuIkWbDcrkcw8PD+P3vf4/6+npcvnwZ2dnZEAgER/6cZI430nNBSLTcgikQXADj8EaDzWYnzVjT09PxzTffYHh4GA6HAy0tLaioqIBCoeCY76cMXABLItjb37H0z6Pxg8hyJNqxmkS5RbH4WYlkEfGML9GsJNk+hrPJ5/Oh1+vR1taGzMxMPHjwAFNTU0x/AtKJSCgURty9jYfnFu93k2x7byO4AJZEBHOAIj14sR7Io5ApT9IeEH3ZdJTPieVjMmwSn6VSKcrKypCRkYHx8XF8++23+J//+R+0t7fj8uXLyMzMPDLJNRE/j2PMbxu4AJYkkKzE4/Ggp6eH0XJnP4QURUGlUqGmpgZNTU0wGAwhO2CHh4cYGxtj+kYG64HJ5XI0Njaivr4eWVlZUR9yPp8Pi8WCsbEx9PT0YGNjI0SeJyUlBQ0NDaivr0dmZmbUwMTn87G/v4/R0VH09vZie3s7YKKTvpR1dXVoaGhAenp6XHpgPp8PY2Nj6O/vx/z8fABxk6IoSCQSmM1mNDY2Ij8/H0Dskwo0TWNhYQF9fX2M3hapIRHbxcXFKCsrw6VLlzA4OIiuri4sLi7iypUrqK6uhlKpZKSBaJrG7Ows+vv7MTExwdhjo7i4GM3NzSgrK4uYxRH/KIrCzMwM+vv7MTU1FWCP1O7Kyspw9uxZlJeXcwz8COACWBJB6i02mw2bm5tYXV0NEKrz+/3QarUwmUxMo9bgbXzCBdra2sLS0lJAwPH5fFCr1bBYLIwWF/ncSCD2Njc3sbKyEqIHptPpGHuxQAiXVqsVGxsbWFtbC5hYfr8fbrcbBwcHYVu+RYLf74fD4cD29jaWl5dDAphUKkV2djbTBzLeyex0OrG/v4/V1VW43e6AhiKE81VbW4va2lpkZWXhs88+w+zsLHg8HhwO0Xi6jgAAHdtJREFUB2pra5GWlsYcNHc6ndjd3Q2wx743qampAb00owUwmqYZeysrK2H1wNLS0hh73O5jeHA8sAQQiweWmZmJuro6qFQqhutFJhy5zQKBgOm3GI6vQ0QBnU5nAJmRfAaRWZZIJHG12CJBhd1Hkh34ErVHBP2cTmeIMCNNv2hbRmge8fKRKIqCx+OBy+UKCaQkGyE2EyFyEpuE2Bt8NIf0bBSJRPD7/VhfX2e6dvN4PNTV1eHs2bPQ6XSQyWRwu91wOp0hQpXB9uLto0m+F7fbHTYws8dMZHw4PbBAcBlYEkGWkUqlElKpNOL7iF5WJPKoWCxGSkpKxEng9/sT5hap1eqk2CMctkj2SLE9US6VXC6HSqWKunGR6A6hVCqFXC6PyiMjNoVCIXJycpCSkoLs7Gw8fPgQ9+/fx/z8PN555x0UFRVBqVRGtUfGHe9mg0wmg0KhSJq9txFcADsGkOwLSLwQSybV66xhlUx7BMcxUROxSTI9oi+mUqnQ29uL3t5e/Pa3v8XFixdx6dIlZGdnw+12M9eclH8cwoMLYMcIbnV+ukB2jkUiEcrKyqBSqSASifDgwQP09fWBx+Ohvr4eubm5jLIFh1cLLoC9ArwszytZPLHXndd0XDypWGcxyf0zGAz44Q9/iMLCQty+fRsPHjzA6uoqrl27BqPRyCwnk+VjtPGSv3G7kYHgAtgJg3TDcbvdIcswUosRi8XMgeJw15OuOJEO/Uql0qhnCAlIZ6HgojQBqXfFczCcpr/v2BOpKH0Ue263O6IihlgsZu5VvCDqEWTMwZ/J9lEgEEAul6O6uhrp6el4/PgxhoeH8bvf/Q5tbW2or6+HTqcDTdPMRkHwuMmmRqw+mTRNM89F8MFwstkikUgS2t19G8AFsBMEn8+Hw+FgeFSrq6sBv7iEZtHa2oqamhpotdqASSYQCOB2uzEwMICBgYGQ6wkP68KFC6isrIRGo4lYY+Hz+dje3kZvby9GRkZgt9sDtvFpmkZ5eTna2tpQUFAAsVgc9YC5QCDA2toaenp6MDo6CpfLFbBLR9M0qqqq0NbWxuiBxepBuby8jJ6eHoyPj8PtdofYM5vNaGtrg8lkisq7Yo95Z2cHw8PD6O3thcViCaGVmEwmdHR0MKx8mn6hxVVYWMhsrvT09OD27dtYW1tDZWUlbDYbBgcHYbFYQvpu5ufno729HSUlJZDJZBEVRPx+PxYWFtDT04OnT5+G8MJEIhEaGhqgVCqZa7glLBfAThSEwOjz+eByuUJE/yiKglwujyiVQ95Drnc4HCE0C6lUGiDVE+5BZwdMr9cLp9MZYIsEiHDZQDSwKSDB+l0AEu5pSew5HA6mcB5sL17/SKAnGTAZc3DAcblcIbudpNhuMpmQmpoKjUaDO3fuYHR0FIuLixAIBHA4HMzYyP2jKIq5h9GCNfmOCOUlHIVGLBYH9BTlgtcLcDywBJAMPTBCWSBBJnipQJYukXSu2PpT4YIB4SORlvSRQCYYu5ls8OsikShubSxijzRpDQdiK94lJFsfK9y9TMQeAdtmuKAiEAgCeFfh/PJ4PNjY2MC9e/cwODgIiUSCjo4OlJWVQavVQiQSMf6wNcuiLSFJkCSNhsM9FyKRCE+fPsXAwEDAd8/xwDicGMhkk8vlEXlUJMiFA5/Ph0wmi1iIZnObYm0EkPpMMnhIxB6Z/OF8S4TLRXTTomltHYUbFsvHWPeP3P+cnBxcv34d+fn56Orqwp07d7C1tYVLly4hLy+P4QESH2PdQz6fz5CKowW6eEmybwu4AHbCYC8voh0YjgbCwzrq9ez3so86vYwt8v5ok/Uo9pLpXzJ8JN8f4YzV19dDpVKhu7sb4+PjWFxcxDvvvIOzZ88iJSUloQAba7x8Pp/jjQWBC2CvEC+7ek/W6j/ZVYTX3V6ybFIUBbVajdraWqSkpKCzsxNjY2O4f/8+Dg8PUVdXh6ysrITFEsP5xmVd4cEFsGNANL0s8nDGKupGWjaxlzbJ4FMdl71EA0Q83LZEfIzHZrJ4aUKhEGVlZTAajSguLsaNGzdw48YN7O3tob29HVlZWYyEOPuzjovn9jaBC2BJBFkaOp1OpgNP8MNHGltIpdKwxXGyM0j4T8EgRWbCLYoGHo8XwM0Kt5xJxB4ApugfyR6pMYnF4riLyWTHMxLni8/nMz4mwvlyu90BPDcCcs8J5ysezhzbHuG5se0RKonZbEZaWhq6urowMDCAhYUFXLx4ETU1NdBoNAHUCDLm4K5FxD9yH7m6V2RwASxJIFmX1+vFyMgIBgcHsb6+HrBbRNMvJFzMZjOam5uRlZXF/B14MVFtNhuj37W2thbwGYSTdPbsWdTX18NoNMYs1NvtdoyOjuLx48fY2toKsUf0wBoaGmAwGGLqgdlsNoyMjKCnpwc7Ozsh9ogeWGNjIzIyMuLSA/N6vZiamkJvby8WFhZCfGDrgRUWFgbcs0jjpmkaS0tL6Ovrw+joaEhticfjobCwEC0tLSgrK4NUKo1ok9h79uwZ+vr6MDExEUJzEAgEKCkpQVtbG8P5kkgkGB8fx5dffont7W20trYiJyeH+aEjemVED4wNoVCI0tJSNDU1oaKiggtgEcAFsCSBPPxk90ypVEKlUoVshyuVSmYXMRxItqFUKkMUKQjPi0jVxENmJFI0SqUygFzK9odkg/GA7R9bk+yo9oDvqR8KhQJqtToggNE0zcjUJEIPAF4EAblczhTTg4OAXC6PO/sKthccEMnuJBlPfn4+FAoFDAYD+vr6MDg4iP39fZw9exalpaVQKBQQi8UB/rFBTgEkknG+jeACWBJBGtOazWaYzeawSyw+n89weoJfI+J9ZrMZFRUVEXlepO9jrMIwydhqa2tRWVkZwDsjk4/4E489iqKgVCrR0NCAmpqasGcuCS+LaGzFAtmNLSkpQUFBQcQekGTM8dSDyHuys7ORkZGBy5cvM0d82OMny3m20GE0ezk5OTAYDHj33XdDXiM0EnYfzfT0dJw/fx45OTm4c+cOpqamsLe3B5vNhtLSUmRlZcFoNDJLyHC1NfKchHudAxfAkgqyjBSJRAyRNRILPhJIhkPIkMG1kUQeZLLdnyx7yfaPfR0hzRK/w9lMtJhNAkq4648SDNgBJZY98ppUKkVJSQmys7PR3d2Nv/71r/jNb36DK1eu4N1332UK/OHGzSE2uAB2zDjqgxhJfeBNtRfNRqTPStTey/oWbCceeyQ4p6amor6+HjweD/39/ejr68PBwQFaW1tRXV3NLRWPCC6AceBwzCBL7YyMDFy4cAFpaWm4f/8+FhcX4XA4YLPZUF5eDp1O99o0rz0tS1YugHHgcAIgJwDEYjGqq6uRk5OD7u5uDA4O4tatW1hZWcGZM2eQl5cHuVwekf+VjKBCqDrBZ0jJ5/n9fhweHjK9El7nQBbf9gsHDhySBrFYDL1ej3feeQfXr1+HWq3GzZs38dVXX2F2dpbpvsRGskit5LjS5uYmLBZLAFeRvGaxWDA+Po69vb3XIhuMBi4DO2GQQn8kgTvyEIXbwSRFeaI0EY7FTRQm4lFlJTtn4Qi1hKsUr/498S2SPeB7JYh4j9UEj/Vl7QHf7z5GUrAg9y9e2R9yD/9/e+f21NZ1xeHvICShu4QECMxFMWAsg5JwseNxnJL60umkk3Q66aT1dKaTPHb62k7/j/alTZ9av7TpZdpOmzZx3Lh2QuJ0KARjLkKIe8ASIHSXAJ3TB885ETcbHCc28v5mNH7wnO1j6Zy19157rd9vN/UK9Tvcfo/q7+JwOOjo6MBoNOJ2uxkcHOQ3v/kN586d49y5c1RWVm4JLul0eous0G73st97zuVyDAwM0NbWhslk0speJicn+eSTT3A4HPsa61EjAtgDsNdMeL8ZUhU0nJ6eZnx8XJvh1AdPlmXsdjt+vx+fz7ejjkyn05HL5QiFQoRCIa2QVL1ercMKBAI0NjZqgny7IUkSy8vLTExMEA6Hd9XbamhowO/34/V676sBrwokBoNBpqamttijqdf5fD78fj/V1dX7KolYWloiGAwyPT29pStB/c58Ph/Hjx/f93iqMW84HCYYDJJOp7e89LIsU1VVRUdHB0eOHLlncSvc/Q5jsRiTk5OEQqFdx/N6vbS3t2unjcXjbW5uYjQaOX78OA6HA5fLxX//+1/eeecdwuEwdrtdC4IA6XSabDaLJEnY7Xatx7K8vByr1bqvgwA14JpMJubn51laWsLtdpNMJpmYmEBRFObm5vjud797TyerxwURwA5I8aqlOPhI0udiefcKGvl8nunpaS2JWzxGoVCgtrYWvV5PdXW19gAXX7+xscHk5CTXrl0jFAptWYXJskxNTQ1Wq5Xq6mpsNhuws2pdvSYejzM0NMT169dJJpNbAqGiKJw8eRK32011dfU9yxjU8WKxGIODg3zwwQdkMhnt79UX8MyZM3g8Htxu9z0Dovpvra6u8r///Y++vj5yudyW8SRJ4vnnn8fj8eDxePb4tXbeYyqVYmxsjPfee49IJLJDkbWtrQ2Xy4XH48FkMt3zHtXOhJGREd5//31WVla2vPCFQoGOjg5cLhdVVVW7BkRFuav1VV9fz3e+8x28Xi+///3v+eMf/0gsFqO8vJwjR45oApZerxe/34/FYtGeQYPBgNfrxWKx7CvgqNZ/NTU19PX1MTk5SSQS4f3332dxcVHLxZlMpsc+gAlBwwOgKHfdlIeHhxkYGGBxcXHLS+90Ojl27BjNzc07Vk/weQBKpVLE4/Ed2vHqw+h0OnedUdXexkQiQSKR2FFZD2hH9lar9b6V66qLdjKZ3FWf32q14nQ679k5UEwul9PG223LZLPZtPH282Jks1ni8TipVGrX8ex2Ow6HY9/jqRNIMpkkHo/vKJpVFAWTyYTL5cJsNt+3m0AdT/09dhvPbDbjdDoxm833XCWq95/NZpmZmeHatWtcuXIFt9vNG2+8wdzcHHNzc8iyvMU8V5ZlPB4PPT09+P3+fa+aNjY2iEQivPnmm/zqV79idXUVi8XCuXPn+PGPf8yZM2ce+wQ+iBXYgdHpdFq7THEVtjq7z8zM4HQ6d3WmVpS7Kqdut5uqqqo9H469jGYV5XPLeXVVdJDrt1NRUbGnsar6cuxHjE/FZDJhtVrvKZB4EH0s1ez2YRm/KoqiuaLX1tbuWox6kP+zOl5NTY3W11rM9vH2U+1vtVo5duwYNpuNlpYW0uk0er0es9lMVVXVjvxmRUUFNTU1NDU1YbVa9x1w9Ho9Xq9XU9FIJBK4XC4CgQB+v//QNJCLAHYA1O2jzWbb1Xl7Y2OD5eVlQqEQuVyOmpoaXC7XlhUWsO/E+F48LGNZ9cDgYfG4j6eO+bgZ/RanIdTDEJfLRXNzM7Ozs0xMTJBOp3eIYEqShMvl4ujRo7jd7gP1n8LdreSpU6d47bXX+MUvfkFnZyfnz5/H4XDsuz/0USMC2AHR6XQ4HA7cbjcmk2nLNlAtQpydnSUWi7G2tkZTUxMmk0nr5VNPq+7nJygofdRco6rRr0oVZTIZIpEI8/PzrK6uannV7TVbdrudp556SjPavd+zpCgKqVSKhYUFotEo2WxWa0pXV7LT09Ok02ltu+tyuThy5Agej+ex7BYQObAHYH19nampKfr7+5ment5VlUGSJEwmkxbs7Ha7pkSh9v0dxIxCUHooirLFISmVShGLxVhZWdGcmPaSmNbr9bS3t9PZ2YnX68VgMGhj7oUsy0xNTfG3v/2N//znP0SjUe1ke2lpCYvFgsvl0lIfsizzzDPP8O1vf5uzZ89isVi+nC/iCyAC2AOgJvNDoRAff/wxd+7c2VOjXjUkVRugi1dhYgX2ZFNca1csFKma5O5GoVDAZDJx4sQJOjo6aGho0FZGu+UEt5+U53I5wuEwi4uLWw6BdjtlVhQFj8eDz+ejtrb2wHJGXwUigD0giqKQSCQYHh7m1q1bLC8v7zpbFhciFv8pEBRTHEh2m9TUQGS322lqaqKrqwuv17vF/WhsbIzR0VEWFxe1Cnv1eVNLNQKBAE1NTQcqen2cJ9vHL6QeEtSHqaOjg0KhwPj4ONFoVCvgfBDlAoGgmOJT7oqKCux2Oy0tLbS3t1NTU7MlaV8oFJiamuLy5cu89957OBwO7HY75eXlmtlwV1cXP/jBD/D5fI9lPutBEAHsCyBJElarlaeffhq73c74+Dhzc3OaY/T2bYAIYoJ7sX11rhZMm0wmGhsbaW1tpa6uDpvNtqO9Sj1RvH37NoODg7z++uu88MILWCwWYrEYt27d0vwsD8sJ434QAewLotPpcDqdtLa24nA4OHLkCPPz83z22Wckk8lDI0siePQUPyfl5eVUVlZSU1OD1+ulvr6e6urqPYtLJemuWbIqy93V1cULL7ygeQ4EAgEKhQJ2u10EMMFOzGYz9fX1eDweamtriUajxGIxkskkyWRyy6nSxsbGgRqGBaWJ2kZkNBo1rwO1uNjtdmsfl8ulNVzvNRkqikI0GmV1dVVrr5JlmWAwyNLSEoFAQNt2ltKEKgLYQ0JV3lSNHxobG8nn86ysrLCyskIsFtPUBPL5PLlc7kBV6YLSRK/XY7FYsNls2Gw2rFYrLpeLmpoazXBETaLfC1mWmZubY2lpCUVR+Oyzz5AkiRs3bhCLxWhqasLj8ZTU6gtEAHvoqHItqrRMRUUFXq93SzvJw9J2Ehx+1FO+4s+9JIT2Qi2gDofDDA8P89Of/hRJuuuOdFiUJR4EEcC+JNSHRU3ECgT75UECjSzLTExMoNPpeOONN2hoaCASiaDX62lra9u19a0UEAHsK6AUZz7B44W6hTQYDLz66qucOHGCZDLJ2toaLpeLioqKknwORQATCA45siyTz+dZXV2lrKxMO600Go2YzWZNPshut2sWbqVCaWX0BIInkHw+z9TUFIlEAovFokkaKYrCyMgIf/jDHxgaGiKdTpdc3lUEMIHgkJNMJgmFQthsNnw+H+Xl5eRyOVZXV7l27Ro3btzQDpRKbRsptpACwSFFVbMIBoP8/e9/JxwOk8vl+PnPf45Op2N1dZXBwUFNubZU2oeKEQFM8NDZrnIq+PJYX18nmUySz+eprKwkn89z/fp1TWjR6XRy9uzZkqwBA6FGIXjIqMYmhUKBsrKyQ6GrfpiRZZlMJkMymdyiXqu+1jqdTpPmLrUqfBAB7ECoxadqk/ZuXoBPMoqisLy8zCeffEIwGMTv93PhwoXHUkeqlFCLpPdbtV9KiLfvgGSzWaampohEIiV3ovNFUKWRw+Ewf/7zn3n77beZmJgQ/Z5fAalUaovP6JOECGAHQJZllpeX+de//sXg4OCOJbu6fYpEIpqW+ZOCLMssLCwwPDxMNpvV+kJ3o3glu1t71b0+6vXF15UysiyTzWaJRCI77OVUFhYWeOuttxgdHX3oJiiPO2JtfwBkWWZtbY2PPvqIjY0Nent7MRgMKIrC+vo6mUyGtbU1ZmZmqKqqorm5uSRPfrajrr7GxsaYnp7m1KlTDA8P7/qyqcllVaED7uZpKioq0Ol0FAoFNjY2MBgMlJeXk8/nWV9fR6/Xa4oMqVSK9fV1DAYDZrMZo9FYslt5RVFIJpPcvn0bt9tNQ0PDFl9ISZKIRqNcvXqV5uZmTp48+ahv+StFBLADUigUSKfTrK+va3rm+Xye4eFh/v3vfzM3N8e3vvUtvF7vExG84G4h5ejoKPPz83i9XmprawmHwztswNTgFY1GefPNN/nHP/6BJEnYbDYuXrxIY2Mjs7Oz9Pf3c/78eaqrq7l58yaDg4P4fD5ee+01qqur+eUvf8nw8DCdnZ288sorPPfcc4fCRfpBKCsrw2w2A/CnP/0Jg8FAb28vXV1dGAwGdDqdZpasqgE/SYgAdgC2b2GSySSDg4MMDQ1x69YtEokE7e3t+Hw+zGazZpVVSmxXSlAUhbW1Nfr6+lAUhaeffprl5WU2NjY0u65iP8zV1VXeeustBgYG8Hq9mM1mFhcXyWaz2onlp59+SkVFBYFAgM3NTUwmEx988AH5fJ6vfe1r2vZ0ZmaG8fFxOjs7tRYZVQu+lCgrK9OMNW7evEkoFGJ4eJj29nZaW1t3bK+fJEQAOwDF3o8TExP885//5MqVK9y4cYNMJsPJkyfx+XwsLCywuLj4qG/3oVMoFKiqqsLv92vO5KlUipGREaLRKF1dXfh8PmZmZsjn85oaaCaTwWQykc1muXnzJr/+9a+5cOECP/rRj7DZbPT391NZWYnP58PtdvOXv/yFeDyOxWLhlVdeIZ1O87Of/Yzr16/T1tbG9773Pbq7uxkYGNiyEp6fnyccDpekCm6hUMBqtZJKpXj33Xe5evUqp0+f5qWXXtJ2BE/aCSSIAHZg1FzLRx99xMzMDLOzsywvLyNJEmNjY/z2t7/FaDTu2+7+sKBWfXd1dfGTn/wEo9FIoVBgcnKSv/71r1RWVmK1WgkGg4TDYZaXl5mdnaWvr49MJkN3dzehUIh33nmHQCDAxYsXaWpqQqfTadLHkiSRTqdJpVL4/X6eeeYZmpqauH37NhUVFbS2tnL+/HncbjcDAwPodDqqqqooLy9HlmX6+vq4fPlyyfptqqe86+vrRCIR+vr6yGazSJJEJpN5ImWbRAA7IOqW6MyZM7z44ou8++67pFIpMpkMx48f5/XXX8dkMpXkUr5QKFBXV6dpS2WzWaanp+nv7ycej/Phhx+yvr5ONBolkUgwNjbGp59+ysWLF3n22WcZHx9nYmKC73//+wQCAW0cp9Op1ZBFIhHsdjvPP/88gUCAtbU1FhcXaWtr4/Tp07S3t3Pnzh0ikYimfKu6Uvf09GC1Wnfk3koB1cbv6tWr2ha9ubmZ3t5e8vk8IyMjJZeu2A8igB0ANfel0+lob2/nm9/8Js3NzXR3d3P79m02Nze5c+cOL7/8MrW1tSX3EsHdHJi6wikvL+epp57i1Vdf1Vye19bWmJiYYHFxkZqaGnp7e3nuuedwu91EIhGi0Sitra243W6ALfmxSCTCwsICHo+Ho0ePYjKZCIfDhEIhmpubCQQCGI1GcrkcoVCIY8eO0dLSouW/Wlpa8Pl8JTd5qHnGq1evYjQa+frXv05rayunTp2ip6eH0dFRfve73z0RZSXbEQHsAZAkiY2NDUwmE6dOneLZZ58lGAxy5coVRkZGNNNRo9FY0sv6iooK2tvbOXbsmDb7Ly0t8fbbb/Phhx9y9uxZfvjDH2I2mykvL9cMTdRteD6fJxaLEYvFqKurIxaLsba2Rl1dnSYJk0gkmJmZ4eTJk1RXV2tlBUtLS/j9fu2ETq1CL7Wqf1mWSafTzM/PEwqFcLlcvPzyy5w+fRqHw4HBYCAYDD62xrNfNqX1a38FFBdRFht5nDhxgoaGBuLxOCsrKywsLFBfX1+yx/vwedDQ6/Xa7K/mY+LxOIlEAkArJ1HdcmZmZrBYLAAMDQ0xOjrKpUuXSCQSZDIZWlpacDqdAFqwslgsOJ1Ocrkci4uL2m+QyWS0IFZqqPWF0WiUeDzON77xDerr63G73Vgslh0lKk/a6gtEADsQ6ink9lICSZIwGAxUVlbidDqprKxEp9NpxYZPCqqw3scff0w4HKaqqopgMEggEMBkMtHT08PCwgKXL19Gr9fjcDhoa2vjpZdeorq6msHBQRKJBEePHsXlclEoFIjH46TTaerq6nA4HCSTSRYWFojH4/T399PR0cGFCxcwm80l912rE2RVVRVms1n77GZqq27rS+07uB8igB0A1Ym7o6Njh8Ox+vCUlZXhcrke4V0+OiRJwuPx0NvbS2dnJ/X19dpKS5Ik/H4/iqJgsVhIpVI4HA66u7vp7u6mrKyM1tZWADo6OrDZbEiSREtLC5cuXeL48ePo9XqMRiMnTpzg0qVL6PV6nE5nSb+0Op1Os1zbC6fTSU9PD7W1tSXbkbAXQo3iAMiyTCKRYHR0lMrKSpqbm0su5/JFUCvt1R5QNdGvbjXVeq3iHlG9Xq/lCdW/V68BNANgdRsqSRKFQoHNzU3Nwk79DUo5kN2LSCTC0NAQzc3NNDY2lnTedTsigB2A4oZtdXn/pM14gsePzc1NrV+0VGvg9kIEMIFAcGgRyweBQHBoEQFMIBAcWkQAEwgEhxYRwAQCwaFFBDCBQHBoEQFMIBAcWkQAEwgEhxYRwAQCwaFFBDCBQHBoEQFMIBAcWkQAEwgEh5b/A67hVsVv8PjFAAAAAElFTkSuQmCC)
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,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)
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
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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
physics-
Which of the following ray diagram show physically possible refraction
![](data:image/png;base64,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)
Which of the following ray diagram show physically possible refraction
![](data:image/png;base64,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)
physics-General