Question
In a Δabc if b+c=3a then
has the value equal to –
- 4
- 3
- 2
- 1
Hint:
Semi perimeter of triangle = Sum of all sides, also
![c o t c over 2 space equals space space left parenthesis s right parenthesis open parentheses fraction numerator s minus c over denominator triangle end fraction close parentheses](data:image/png;base64,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)
The correct answer is: 2
Given :In a Δabc
b + c = 3a
Adding a on both sides
a + b + c = 4a
We know that Semi Perimeter of triangle(2S) = a +b + c
2s = 4a
s = 2a
![rightwards double arrow c o t b over 2 space cross times c o t c over 2 space equals space left parenthesis s right parenthesis open parentheses fraction numerator s minus b over denominator triangle end fraction close parentheses space cross times space left parenthesis s right parenthesis open parentheses fraction numerator s minus c over denominator triangle end fraction close parentheses
N o w comma space w e space k n o w space triangle squared space equals space s left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis
S u b s t i t u t i n g space t h i s space v a l u e space i n space a b o v e space e q u a t i o n
rightwards double arrow c o t b over 2 space cross times c o t c over 2 space equals space fraction numerator s squared left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis over denominator s left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis end fraction
rightwards double arrow c o t b over 2 space cross times c o t c over 2 space equals space fraction numerator s over denominator s minus a end fraction
s equals space 2 a comma space s u b s t i t u t i n g space t h i s space v a l u e
rightwards double arrow c o t b over 2 space cross times c o t c over 2 space equals space fraction numerator 2 a over denominator 2 a minus a end fraction space equals space space 2](data:image/png;base64,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Related Questions to study
In a
simplifies to
In a
simplifies to
In a triangle ABC, a: b: c = 4: 5: 6. Then 3A + B equals to :
In a triangle ABC, a: b: c = 4: 5: 6. Then 3A + B equals to :
A bullet of mass
is fired with a velocity of 50
at an angle
with the horizontal. At the highest point of its trajectory, it collides had on with a bob of massless string of length
m and gets embedded in the bob. After the collision, the string moves to an angle of 120
. What is the angle ![theta ?](data:image/png;base64,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)
![](data:image/png;base64,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)
A bullet of mass
is fired with a velocity of 50
at an angle
with the horizontal. At the highest point of its trajectory, it collides had on with a bob of massless string of length
m and gets embedded in the bob. After the collision, the string moves to an angle of 120
. What is the angle ![theta ?](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKYAAACkCAYAAAAdQFV8AAAgAElEQVR4nO2993Nc1333/9resMAugAUWvRCNBHsvoqxIohw7iaJkLNuZOIl/SzKT+G/If5HMJB4/mXHm+U7s+dpjayRHtiyFKiwSC0iA6J3odRfbd++9zw/Lc3B2uQBJFBKU8Z7ZIQHcvffce9/ncz79mAzDMNjHPvYYzC96APvYRyHsE3MfexL7xNzHnsQ+MfexJ7FPzH3sSVhf9AD2sXeg6zqGYWA2mzEMg2QySSwWw2QykclkWFlZIRwOY7VaCQQCBAIB7HY7hmFgMpkwmUw7NpZ9ibkPCcMwJDkNwyCdTpNMJjGZTFitVpxOJ7quE4lEiMViZDIZ+b2dJCXsS8x9kCUWgKZp8udEIsHy8jKhUAi73Y7b7SYajWIYhvxdIBDA5XLJ71kslh0b0z4x/8Ch6zq6rmM2mzGb1xfQRCLBwsIC8/PzuN1u7HY78XicaDSKpmnY7Xas1nX67EvMfewIxLKt63qOfphOpzGZTITDYRYXF0kkEgA8fPgQm81GJpMhGAxSXl6O0+mUy7hK6p3APjH/QGEYhlyCzWYzsViMqakppqamqKysxO12EwgEMJvNZDIZotEoRUVFLC4uSn3TarXKc+w09on5BwIhGQXUFIn5+Xl6e3vp7+9naWmJ8+fPc/78eRoaGtA0jWg0Snl5OVarlVu3bpHJZCQhTSYTuq7v+Hj3ifkHAk3TJDHFv4ZhEIvF+PDDD/nss8+oqanhzTff5OjRo3g8HiBr0Hg8HtxuN1arVbqOHA6HJKSw5HdSz9wn5h8IxLIrSKRpGul0muXlZZaWlvjWt77FK6+8Qnl5+WP6omrk1NXVsbKywtraGpqm4fP5gCw5d9IqN+2nvf1hYWVlhWvXrtHT00NraytvvfUWmqZhs9mw2+1PZcTcunWLW7du0dDQwJUrV9B1PYe8O4F9ifkHgnA4zBdffMEXX3xBKBSira2NtrY2HA4H8XgcgGQyid1uf6Lkq6ysxOFwsLi4yPLyMm63+zF303axT8yXHKpuJ3Q+k8kkjRtBlgcPHnDv3j0qKyt58803aWhooKysTEZ1rFYrqVSKp1lAKyoqqKmp4eHDh0xNTdHZ2flU33sW7C/lLznUECIgfYrJZJKZmRlGR0dpbm5G13WWl5fx+/0Eg0FcLpc8XpBb0zQsFssTjRhN0+jr66Orqwuv18u3v/3tHfdl7kvMlxz57ppUKsXKygqDg4PcvXsXm81GfX099fX1NDU15Ug24VgXRHxaPdFkMhEMBonH4zJevu9g30dBCGIsLCzQ1dXF4OAgmUyG48ePU1lZidlsziHwdlw7JpMJn89HW1sbkUiElZUVysvLt30PKvaJ+ZJD13XW1taIRCIUFRURDoeJRqM0NTVx8eJFKioqSKfTOUv9dqGmuS0uLjI3N8drr72GzWbb9rkF9om5hyEIkE8q4YfMZDIsLS0xNDREb28vR44c4fDhw7S1tWGxWKSUNJvNO+r8FuqDpmksLi5y69Ytjh49SkVFRcHxbgX7xNyjEPmQFotFJlxYLBYsFguaphGJRBgZGeE///M/iUajXLx4kUAggMPhwGazSVLspNNbQBg6Ho+HqqoqfD4fw8PDBAIBIGscbXcy7BNzD0N1/wgJKKTR0tIS77//PsFgkG9961s0NzfjdDp33AjZDFarFY/Hg8Vi4datWxw+fJiioqIdkc77xNyjEP5FISnT6TT9/f1MTU1RUVFBbW0t7777Ln6/n5KSEqnfZTIZdF3PkZo7DeGeMplMeDwe6urqGBkZyUns2O6194m5hyGW8+npaW7dusWdO3fw+/3U1tbi9Xrxer24XC4pRVXdbrdICUhjymw243K56OzsJBgM4na7c9xX+0v51wCFDAaTycTQ0BBXr14lmUzS3t5OW1sb9fX1MklX/Y5hGE/lIN8uhEohVAyfzyd9oJqm5RS0bXUs+8TcA1CTdgFWV1eZnp6mpqYGm81GRUUFlZWVtLW1EQgENnTLCP1yt4kpDCphlKXTaQYHB/F6vbS3t2O327d9jX1i7hEIS3tqaoqenh5CoRB/+qd/SnNzMw0NDdhstidaurtNyPzrCAmt6zoTExNomsaBAwdwOBz7OubXBSsrK/T09NDV1cXs7CzHjx/H7/dL6fO8SPc0yA9rOp1O6urq6OnpIZ1Oy2O2M+b9uvIXiFQqRSwWI5lM0tPTw2effYbZbOaHP/wh77zzDm63Wx67k5Gb7UKtPwdwOp20tbWRSCSIRCLSat9OycW+xNxlqK6V/MhNf38/MzMzNDY20tbWRmtrKz6fj6KiIjKZTM7L3W1L+1mQb6AJI8hqtZJIJHLcRlt18O8Tc5ehFoGJMOLi4iLvv/8+H374ISdPnqSyspKSkhLS6TSpVEq+7J1Ovt0p5E8Ss9mM1+vl3Xffpbi4WI57O2PfJ+ZzgFjyUqkUDx484Gc/+xmapvGDH/yA48ePU1FRwfT0NCMjI3i9Xvx+/44n3u4mTCYTNpsNTdMIh8N4vV6cTue+H3Mvw2Qy8fDhQ5aWligqKiIQCPDGG29QXl5OXV0dXq8Xm81GKpVidHQUs9nMwYMH8Xq9L3rozwRd17l//z4Oh4Njx47hdrv3/ZgvEmrURTiWxcuIxWJ0d3dz7do1AC5evMjRo0cpLS2VcW21k0U4HGZpaYmpqSkOHTqUk12kvuS9omuq0HWdWCxGOBwmk8lsWyfeJ+Y2IAijljZA9iUNDw/z5ZdfMjg4iNls5tChQ1RUVMisHMglmGj5Nzc3R1dXFwcOHJCuItUB/zwiO1uBMHRWV1dzmnNtdax7T7N+yaAW+wsdK5VKMT4+Tm9vL16vlytXrnDlyhWqqqpyLFYVKysr8nPv3j0WFhYAChJ/r8IwDFKplOyJtO8uekEQZBFZ5BMTE8zNzXHq1Cnq6ur4zne+Q21tLT6fTyZkFFridF0nHA4TDodJJpPMzc0xODhIVVWVPEZIyr0oLSE70UpKSkilUthstm072PeJuQ2Idinz8/Pcvn2bq1evYjKZ6OjooKWlBbPZTDqdzumoJnyTqislk8lI0jocDtLpNN3d3Zw5cwaHwyFdL3uVlJCdOE1NTZSXl+PxeLbt5ton5gbIJxM8vvwmk0lu3rzJRx99RCgU4vz587zxxhvSlwfIvEg1GpK/LKfTaUKhkDQcotEofX19LC4uUlVVtSd9mfkwm80Eg0GKiopkj6N9ibnD0DSNRCIhE3V1XcfpdD4WxRgbG+Pzzz/H4/Hwl3/5lzKzptBLEb6+/O69Qqo2NDRw8eJFAFpaWmhubsbn88lrqhNlL0pOTdMYHR3l008/5Zvf/CYNDQ3bOt8+MTeA1Wolk8kwOjpKOp2mo6NDNgkQSKfTVFVVUV9fT1tb24akVKFKYMgSzuVycezYMWnNl5WVSVVgL5JwI2QyGWKxmMzJ3E/i2AVYrVZisRgPHjzg7t27LC8vP3aM6sIRDU63ei2v14vD4SCVSuF0OiXJXybspPdgn5gFIBzeq6urjI2NMTQ0xOzs7GPHia1EhItkqwkLgoDJZJJMJvOYZH6ZsFPk3CdmARiGIZMtFhcXmZ2dZXx8XBIHkHqnUPSF1HxaKZff2iWTyZBMJrFYLJSUlMhjCn32GkQAwOPxEAwGdySDfZ+YBSC2E5mfnycajRKNRhkdHWVlZSWHTFarVRLyWSxn1doXutja2hqJRILi4mJKSkpyUuX2MilhPT8zEAhw4sQJiouLty0194lZABaLhVgsxvT0tFTmHz58yMOHD6U0ENJxqy9A7Y6m6zpzc3MkEgmqq6tlG+mXgZSwXmpsMpmoqKjA5XJt28W1T8wNMDc3x/j4OIuLi0QiEaanp+nr69vRRviiy0YymWR2dhZd16mrq8NkMj11r8q9ADFphKEYiUT2Q5K7gVQqRW9vL6urq7J22maz8eDBA+Lx+LYlQr7DfmFhgZmZGVwuFzU1NVJn242t8HYLmqbx4MED7Ha7rPvZDvaJWQBms5nDhw/T0NDAwMCArOkG5JIFuYX/z0pUNTTZ3d1NNBqlpaUFl8slexaJpljpdFrqs6LkQoxDxOALjUEQXHXs55dF7ASETj49Pc0rr7ySU6u0VewTcwM0NTWRTCYJhULE43E6Ozsf8y8WSkV7kpRTpaHVamVwcJD+/n5qa2tpa2vDarXKjsC3b9+mqKiI2tpa2Yp6dXWV4eFhxsbGsNvtnDlzhkAgIAMCY2Nj9PX1kUqlOHDggHTch8NhPv30U1ZXV2ltbaWzs5Pi4uIdeVZi49OZmZmcnNH9kOQOw2w243Q6gXWp4nA4ZB7ldiBcS4ZhsLq6ynvvvYfFYqG9vR2/3y/1ywcPHvCv//qvvPbaa5SWluJyuRgZGeGzzz5jbGwMr9fL1NQUY2NjvPvuu1RVVXHnzh0+//xzpqen0XWdnp4enE4nra2tDAwMsLa2JrOgysrKdoyYYpMqj8eTU1KxT8wdhlgSxXIr9sfZSaRSKT766CNWVlZ47bXXaGhoQNd1xsbG+OKLL+jp6WFsbEwWsCUSCfr7+5mcnKSlpYVDhw4xOTnJjRs3GB8fx+VyMTQ0hGEYvPLKK+i6Tn9/P1988QXV1dXMz8/L5lsmk0nuEbkTsFgslJWV8cd//Mc0NDRgt9vl89qqLv5SEDO/aRTk+gLFzzuF/DJbsfQWGtdGYxO/E24fUUZhGAaRSITbt2/T09PDqVOnOHr0KF6vl1QqxdraGktLSwQCAZqammSbP8MwKCkp4fjx45w4cYJgMEh9fT03btxgdXWVyclJ1tbWOHDgAFeuXCGVSuFyufjkk09YXFyktLSU2dlZ4vE45eXl0om/VeTH+5PJJPX19fj9/h3pybnniZmfwZ2/TUj+MYVqnrd63SdJSzVTWx2jOjZ1qzxN0wiFQvT09HD9+nXa2tq4ePGi3NbEZrMRDAZ58803KSkpYXV1VbqNHA4HR48eRdM03G438Xic0dFRlpaW5LFipzKx705NTQ3RaJTl5WWam5tJJpNyswDRZHU7z0YYfrFYjDt37uB2uwkGg38YxIT1lK/85gGqxFStU/F78bK3ek2VbIUInk9edYwCwrKORCIsLCwwMDBAV1cXtbW1vPXWWzmlularlUAgQCAQIBKJYDKZchKNRURlbW2Nvr4+/ud//ge/309jYyPT09NyPGLsoq9QOp3G5/Px+uuvb+lZFLpvtQnY2toad+7c4ejRo/K5F8o7fRa8FMQUMzCRSEjXibqRu2EYskJP7XK71ZkrHq5w0WzU7kT8TbhwBBHUJgdi6e7v7+fatWtMTk5y5swZ/vzP/1z2kxTZ6/n6mBp/F+dMJpN0d3fz3//93ySTSf7pn/6JYDAoI1TxeFyqH4CM5+80VMEgqjvVZXy7wYE9T0xVUqVSKb744gusViuHDh2iuroaTdNYWFjgN7/5DR988AHV1dW8++67nDhxYsvJBJlMRhJb6IaF9uUWhBFdfIEcv+Hq6irLy8t89NFHXLt2jaqqKv72b/+W48ePy/vaqMmpkPZWqzVHEnZ1dfHBBx9QWVnJ3//931NaWophGBQVFeF2u6WxZLFYiEQiJJPJnP6VOwkxUVZXV3E4HNTV1eXsR/m1tcpVn18ikeC3v/0tv/nNb2hpaaG2tpbq6mqWl5e5evUqd+7c4Y033pA/WywWTp8+vaUXotaIqxnk+RDkVaVjPB5neHiYO3fucOPGDUKhEIcPH+Yf//EfaWtrw+PxSF0vP5+z0BjUz5dffsn7779PJpPh7bffJplMyiYJLpcLt9vN3NwcQ0NDlJSUMDIygmEYeL3eHS3PUMck0v06OjqoqqqSz+NrX/NjGAahUIhf/epX9PT0kEqlKCoqktIwFArR29vLt7/9bY4fP04sFuN3v/sdS0tLrK2t4ff7n/maalRFqAyFliaHw8Hy8jJffvkln332mSzhTSQS+Hw+Tpw4wYEDB2hsbCQQCEjfaL6eDI9LF7PZLBts2e12NE1jZmaGyclJ4vE4P/7xj+XLP3nyJFeuXOHIkSP87//+L//2b/8GQFlZGd/97ncpLS3dUWKazWapLthsNlkKovbF3K6XZE8TU8w8q9VKa2srHR0dXLt2DYfDQSaTIZPJSPdKbW0t5eXlMi9QlMNuhZjqw90sx1LooTabjaKiIkpLSwkGg/h8PsrKymTjfpfLlaPvPs3Ls9vtvPrqq9jtdtxuNxaLhRMnTlBZWfmYh0Jcq7S0FF3Xqa2txTAMqqur6ezszNntYifcauK5iH2GpqamOHLkyI667PY0McVyYbfbOXr0KE6nk/7+flKplJyxiURC6lTiX7/fL9uU7Pb4fD4fZ86c4dixY3i9XkpKSnLKV7e6rFksFg4cOEAikZDnaGhooL6+Pud8qo6qaRrNzc3U1dUB4HK5sNvt8lns1J4/guSJRILJyUkGBwc5cuTIjpxbYE8TE9bbKTudTqmTiW2MIfsC1Z0bICtBgB1JJtgMIou9srKSjo4OOSZhEG2HDCaT6bG8zEKuL0FM8a/dbpfPQ42+7GRhmxAYi4uLTExMyFVjJ7Gr+ZiqLyuVSkmfXCHFXhyf7/8SD1RYviL5QRgMNptN7uAg3DXhcFi6lYCcl6Qq7epY1Ouq/6oWdz7E3zOZzGPRIVUN2A4h7HZ7Tv/1/I+QnmazWR6rGlMWi0V+fyeRTqeZnJxkenqapqamHd+BbdeIKRy7wrIeGxtjZmaGeDye45RWX2g6nZbkzU80FRGURCJBMpmUkkS8iNnZWaLRKPPz89y7d4/p6Wl5bjW0KM6r/pzJZOTEUV1DmqaRTCZJpVIb3mchp7/FYpFG03YJ8aRaIkFO4SEQx1utVmmM7LRKYzabiUajrKysYLPZaGho2LbfMh+7spSLlyvyDdfW1vjNb35DfX09Fy9ezNnEXXVGqw9QEFu8aJvNRjqdRtM07Ha7fAnl5eW0trby4YcfyqL7VCpFTU0NXq83hzTLy8s5UlqQJx6PEwqFcDgcBINBKX3zJetexWak3Q2IVUu05w4EAjt+rR0npiqdBObm5piYmKCurk6mRakOZjXRQfwr/GO6rkv3TSqVoqqqSh6jaZrspjY5OclPfvITkskkf/3Xf83Bgwel3iN6N3788cfcunWL2dlZ0uk0LS0tlJaWMjAwwMDAAJ2dnfzDP/wDTU1NO+b2+DoilUphsVjk/pXine+kE39XJKZwowhyTk1NUVxcTFVVlczQ1nWdaDTK+++/T19fH6WlpTI85/f75RbHHo9HSl+n08lbb72FyZTdwkNERlwuFz/60Y+kte50OnO2j9N1nVQqRVdXF/F4nO9973uYzWZu3rzJ3Nwcr776Kt/85jfp7e3lk08+obq6OsfnKO4pH3tZiu4mwuEwd+/exel0cu7cuR1RWfKx48RUJZ6YQQMDA9jtdoqKiqT/Syynfr9fxliFU1vojZAND66srDA/Py91KVWfE0t+MpnEMLLNBxKJBLquU1xcTE1NjWyYqmkaR44c4ciRI1itViYnJ0kmk5w/fx6bzUYoFJJ1PYLYbrebSCRSsI5FdGJT9eT8DKevA8Q9iX/v3r0rXUTqqraT2DUdU9XTFhYW5IacQjHXdR2Px8OJEyeora2V+mgqlcJsNhMIBLDb7SSTSaanpxkeHiaZTALrcWRd10kkElLJF9cT+2WLSaAaJMKKd7lcOBwOGbITbVri8bh8AcLqBwom1oqk272ug+4EhCH68OFDRkdH8Xq91NXV5TjvdxK75scUg11bWyMWi9HU1CSlkNAl4/E4Q0NDfP755xiGgcfjkUQ7dOgQbreb4uJiKisrZQN9QEpOkeomjKH8EJ/T6cTn80mSqmqEODadTpNIJHC5XDm6rpopJLwF+VAl49ddYorgxfDwMJCtiaqsrMw55qWI/AiLdnFxkUQiQSAQyOk9Lv4uWq4IK9tut0uiQdaZHgwGCQaDZDIZrFYr6XSaxcVFFhYW5DLS2NiYoxfmu3EgS2iRFpbvNlJ9lmpSRn5M+w8ZYtIeOHCA+vp6ueJsp2/TRti1pVwsb/Pz82iaht/vl8QRcLlcnD17llOnTkkpJUhjs9lwOBzSgBJJG7quMzo6yp07d5iampIP5fLlyxw+fDjHmZxPyvLychwOhzymrKwMt9uNx+PBbrdTWloqrX51e2Ph0N8Iqr/160ZgNYk5kUjQ0NCAw+GguLg4x/Oy591FkBtdiUQiBAIBiouLc16uiFQ4HA75HViPFqkJsuLvQme8d+8e9+/fJxgMUlJSQldXF++99x41NTWUlZUVJJHdbufcuXP4fD5KSkowm82cOnUKwzBkr6DDhw9TXl4u96gBHnN9qRDjy89g/7pBpPN1d3dTX19PaWmpTNsTtsFOY1eIqeqAVVVVvPXWW1RWVj52A+osE//PJ5W6pQhkiVJSUsKFCxc4ceIEDocDv9/P+++/n+NLUw0YyBoqhw8fzjm32nxf/FxVVSX9dLDehW2jRGE1pJp/T18HCD38q6++4r333uP73/++dO3tRvKxwK4RU/SO7Ozs3Pb5VKvX4XDw+uuvo+s6KysrdHV1ce/ePerr66UkVNtIbwdCSttstoJJCiaTCbvdLn2q4jtfJ3Lqus7y8jL//u//zp/92Z/JpXy3sSuxcmEtR6NRUqmUbGy6FYhSAbFkiF1exVbKv/zlL+nq6qK4uFhGiET20XYbqQp/qzDICh0n1BHhu/26LeWrq6t89tln1NXV8corr+xIi8Gnwa67i8SSvhUpoiZgiGVDJHO4XC65c+39+/dlh4qWlpac5X8r1xXfUQ2gjaTv19ViV8nn8Xh45513KC8v3/H0to2wqyFJ9YVu5+WpzvNQKMTs7Cwejyen389nn33G/Py87ASxnWuKa8G6D2+jDCOxR8/XYQlXDc1UKkU8HieRSHDq1CnZIx6ejx69axJzKx3QCkGQUiyVmqbR3d1NOp3m3LlzBAIBQqGQdPkICbad5UZ1Makd1wpBzT562YkJSL/y9PQ0vb29eDweXnvtted+b3s6gz2/LEHErj0eD729vfzud7/D6/WytLRETU0NwWBQEkmN7W712uqE2OneRXsVJpOJcDhMX18fQ0NDnD179oVMuD3fUVglp9AtT5w4wbFjx8hkMoyPj2O1Wjl79izl5eU7mkOpdvX4QyFmOp1mYGCAqakp6uvrOXbs2AsZx56WmALqjBVbw1VUVHD58mUSiYR02QCbZps/LdRUt82IqRo+agj0ZYOaOyAadJWWlsqk7hdxXy8FMVUICSpChfl74qj9GbcD1UG/WYa46DyRTqdz0vX2OtTAgBpQsNls0tgJBAI5uQPPEy8dMWFzq3CnSPm041CJ+zL5MIUbTrjDRCmuz+ejurr6sd05njf2vI65j92BMO5EPf7Pf/5zvvzyS6kaqYksLwL7xNwB5MfLXwaIBJTZ2Vn+4z/+g56eHg4ePChzGjYrKXke2JSYhWaMyKHMrxHfrPPu84A6DjUfcytQl2Y1JFrommo+6V7OLlKfiRhjKBTi+vXrDA8P88Ybb8hdM+DJ7XF2G8+sY6oDFWUL6gt5ESE6tZwikUiwsrKC2+2mpKRkW8ZIfj36Rn8XZSR72SJXJ4wqXMrKyvjGN77B+fPnKS4ultLyRYdaNyWmuqWcOli1tibflaC2JXneiEQi3Lt3j6GhIY4cObJtH5waltzo73tVQuZDvKdUKsX4+DgLCwtUVFRw/PhxALmDxV5xeW1KTJHRI4q+xM/io9Zti+ZWVqsVp9P5XIkplp2xsTFu3LjB2NgYwWBwR879onWtnYJ4R4ODg3z11VdkMhleffVVioqKcnJP94rk35SYgmhra2uMjY2xtLQkJabf76e1tRW73c7CwgKTk5MkEgmKioqorKwkGAwWTCTNf9Gqc/dJyJdgqrQyDIPl5WXZv1zUtW8nmVUd12aRn70qNVXpJyI6H3/8MclkkkuXLtHQ0EAqlZK+2L10H09cyg3DoK+vj1/84hcMDQ1JaXn27FkqKytxOp389re/paenR5bV1tfX884771BRUQHkZq3kE1GQXzyUfL+gWmoB2c3mY7GYzPEU5y4qKuL06dMcPnyYn/70p7In+XYg7keUdORDuFuEWrMXJI2AeDbiHUYiEXp7e6msrOTs2bO0trbKQj6hkoly5L2ADYlpGNmG+yZTtpFVbW0tly9f5syZM7Krr8/n4+7du/T19XHhwgXOnTvH2NgYd+/epbu7m9dff10STqSOCaJpmobFYpFNEMbHxzEMg/LycmkZJpNJpqamCIfDVFRUUFVVxfDwML/+9a9lhlE6ncbhcPDDH/6Q119/nUQisSMbhIrJI6I5hbKL1Oyj59GP82khxiMStufm5nC5XLz11lty9zL1+ezFaNWGxBR12SaTSW4gn0gkGBoawuFwUFFRgclkor+/n8rKStrb22Wd8cLCAqOjoySTyZz6n9HRUT799FOGhoYAZPVkaWkpw8PDhEIhjh8/zje/+U0sFgsffPABt2/fBrKZ1FeuXOHNN9/kBz/4AbFYLMf4EBsqqSHLncKTlri9tATC+qozMzPD+++/TygU4q/+6q+orq7OeS57kZACmy7lwg20urpKX18fo6OjOJ1OotEoJ0+e5Pvf/z6hUCin2lHc+OrqqpyxInE4nU6zvLxMcXExly9fJhwO86tf/Qqfz8d3v/tdJiYmGBsbY2xsjKKiIlZWVnj11Vc5e/Ys3d3dxONxzGYzFRUVkuzqMioavNbX11NWVrZj5HySJNwrklJgZWWF27dv8/HHH6NpGu+88w6lpaVy2c5kMlJg7FU80So3mUw0NzfjcrlkHXZvby83b97k2LFjOb2I1HobtQWz0BHj8bjMPD916hRTU1N4vV4aGhro7OzE4/GwsLBAJpPB5XJhtVq5efMm4XCYhoYGmpubKSsry0mWEHqSWjh24sQJPB7PlssA8t1fov0hIP2laoXki5KY4vQudMYAACAASURBVP0IXdJkyja4nZiYoKenh8bGRk6fPk1LS4vMvhLPaK9Npnw80fjRdZ3m5mYaGxvx+Xw4nU6Ki4vp6+tjcnISt9vN2toaqVRKxldF6pmmaTnp+BaLBZ/PR0VFBUVFRdhsNux2Oz6fT7ZoFqSuqKjgwoULWCwWJiYmmJmZoa2tTe4aK4iZb9FbrVZqa2u3vZyLPkmCkEJvi8fjOc3+xb0+j7S3/GtkMhlsNpvcVmVtbY2Kigp8Ph9nz56lqqoqp6nqi3aaPws2JaZwFY2MjOByuSgqKpJRDtEky+l0MjQ0RDgcJpPJEAqFWFpawuv1yopGIT1F5aLqglFrtoV0EvUmbrebK1eusLKywr1797hz5w61tbUEAoEcnVKFSEXbLhYWFpiZmWFkZIT5+XmZpFxdXY3D4cixxlXrfzfIqdbUw7q3JJPJMD8/z/379+nt7ZXbr7S3t9PQ0CC//7KQUcWmxBTumtu3b5NMJgmHw5SXl8uN2pubm8lkMty4cYP+/n4AxsfHWVxclM0IYP3BqK4e8bCTyaRUBZLJpCTq7OwsX331FbW1tbS3t9PS0sLc3NxzK3MIh8Ncv36d3t5ewuEwAwMDhMNhvve97+X4R5+HFFJbgqukXFxc5Pe//z2Dg4N4vV6ampqorq7e1UYEzwub3kE6naaoqIiOjg6++OILPv74Y9xuN6FQiPb2dmpqatB1nYMHD3Lv3j3u3r0LZDuBHTx4EFiXIEIPElt8CL9ZeXk5Xq8XQC7rJSUlUln/8MMP6erqIhaL0d7eTnt7uzx+t2AY2b6dmqaxsrJCKBTC6XTKrh8iKVgcu5s6phAOatWi8JjMzc0xOjrKxYsXOXXq1IbtcV5GPHFqmc1m/uiP/oiWlhaGh4eJRqNUVVVx5MgRuV3JW2+9RV1dHSMjIwQCAU6ePElJSUlOb0rDMGhra6OhoUFuWxwMBvmbv/kbGT5saGiguLhYErSmpobh4WFmZmZobGyU2S+7LaEymQx+v5+mpiYGBweJx+NUVVVx6NAhPB6PDN0JqKUX6lKuGkdCsm40dpXgaiIFZFeVpaUlhoaGuH//PpqmceXKFY4dO0ZHRwcej0fq98I4e9kJuikxxVLsdDppbW2ltbW14HElJSWcP3+ec+fOPVYHI2CxWOT+O4Ds6NbR0SH9nWLnXPE9v9/P6dOn5Xeel64ktqJrbm7G5/MxMDAgt2xWm0gJK1hIs/zN6TVNkzXnQt8WBqWAsKaFG8dkMsn2fiK48fvf/56bN28SjUZpbGzklVdeobW1VRqPAqpB+LLjiX7Mp4E4rpAhshGE20KVKvF4XHb9fZEQBprP5yMQCMgdzwKBQE5M2TAM2QxWzctUz5Pf8EEQ0G63S0tfeBDETsJjY2M8ePCApqYmTp8+TTAYlCHekpIS2Sspvy/l14GQAi9USxYvIpVKyfYje2EJElLM7/dTV1dHQ0MDVVVV+Hw+YD1cq2ka7e3tcj/LRCJBTU1Nzh7h+auHmlAcjUblCtPb28vVq1cZHR2luLhYXtPpdMpd18SEVc+ZTCZlKcTXCS+MmKlUipmZGW7fvk1nZ+djWyy/SAgp53K5qKmpoa2tjbq6OqnaZDJpQqEQNpuNyspKHA4Hc3NzrKysYDabqampkfH1RCKO1ZpdckUEbWBggMXFRWKxGMeOHeXEiZN4PG5aW1tpbGykurqayspKiouL5YauQg3I70m5E3kBexHPjZjqkhWNRhkdHaWrq4tIJMKlS5d2PO0q3/AQvyvUS0l1QKvlFGIXN5fLRSIR486dr0gkkni9RdjtNoq8XhwOJ2azQSoVJxwOMzKaYmxsBE3LEA6HiUQjBMoDtLS0YrGYmZubZnl5EZvNTDAYoKKiHK+3iNIyP5WVAWx2Ox53tiV4Op0bZQJyntPLEsXZCp4bMUX4LJlMMjk5yc2bNxkeHubQoUMUFxfvWmfajSB8gYlEglgsxtraGisrK6yurua0T1xYWGBlZQmb3cLDqXES8SS1tVW0tLZiMhtkMkkSiSiZTJJINMTs3BSzM7MsLi4SjUXRdR2v10t9bwN+v59QKIyuaZSWlj+SxDVYLGC1mnC5vFgsNjBA07J7YRqs661iYqkG5ouoFHgeeG7EFBbm9PQ03d3dTExMPGap77SzWnXRCFfK2toay8vLkoDhcFj6KldWVlhZWZFLp9vtlvuFezxOvMVFpD0ZTGYTsVgEXddkckoylSCdTmIyQXVNFS63U8bxs1sCrrAaWkHXQc9ozM3NsLyyzPDIMEVFHoqLi/GV+Ckp8eHz+fB6i7BYzJhNFnjBNVUvAs+FmEI6jY+Pc/PmTcbHxzGZTHi9XiorK3Mq8nZKXxKZTUIihkIhotEoMzMz9PX1MTU1lRMKLSsro66ujuPHj1NSUkJJSQk+nw+3243VasFqM2OxGKytrRGNRllYWGBubk7G1NPpNF5vMc3NzbS2tkpCiuwqXdOJxbPjWFhYZH5+jvHxCe7cuUMsFpUToby8nOamZpqamnE4PPj92dwAsUfSHwqeCzFNJhORSITu7m4GBwdJJBJyD57y8nJgPct9uwaQmATxeJz5+XkGBga4e/cuAwMDRCIRuXHSqVOnaG1tlZuhCn3N4XCwtrYmEySy50uRTmUwbGbcbjdut1tuFRMKhbIRMm8RVYEqKioqZNMAkRsgzuN0OvH7/dTW1uKwOzCZTaSSKdYia8zOzvLw4UMePnzItevX+NWvf0VkLUVHx0HOnDlDS0uLdF0Jq//rLDmfGCvPx9M+DLWk1mw243Q6OXbsGOl0mq6uLtbW1qiqqpJ7+oicyvzzq1EVcf2NljPDMGQLvVu3bnH//n1ZByRKVH2+7FJps9lIJBKk02m5v5DYdEpEtMQ5MxkrmpbCbFl/HpWVlXg8HkKhEJlMRpYLCwe62WyWW0qrkRyHw4GhZ6V5OpOWCTFFRUW0tbVJa351ZZX+/hG6u3v4+c9/zszMDMFgkEuXLnHp0iXa2tpkUs1m0ST1HbxMMBmbmML5NTNPCqupEEupiOjouk5PTw937twhHA5Lgly+fBmPx0MqlZJZO4XOlb+tijrGubk5+vr6uHfvHgMDAzgcDlpbW+ns7KS+vl66XfKzm8RLzS/sVxs5ZI/T0Y0MhpFbXqHWm6sZU0KfFZ6IjTYBVZspCHfZ+j2DCRvxeIpwOMTa2hoLCwuMj48zNTUFQEdHBydPnqShoUFmc4kxiZVD+D9fNum6q8QUmUAmk4m5uTmuXr1KOp3m8OHD1NbWAlBaWipntqjWU88hCvPFlnpCGsViMQYGBrh+/TqDg4NYLBbq6upobGykvr5e7i2U1RGtMsUun/iFpEl+RxEDHV3PJWa+JBe/E99X49aFiJ/fMeTxcZgxYQXM8vmkUimi0SihUIjFxUVmZmZYXFzEarVSX1/PoUOHaGxslEku6rlfNqNpV4ipnjKdThOLxfj9738v3UMXLlyQmz6pVXr5+qV4+YK0yWSSmZkZhoeHGR4eZnFxEbvdTnV1NXV1dVRWVlJeXi6TGoQ0VO8n/3YLScxnIaZ6nDiXGLMIU+Y/M7XyU3WU5xLdRCYN6118TBiGjrhcOp2S7q3Z2Vmmp6fJZDKUlZXR3NxMW1sblZVB7HbbS7mcb0rMJzUr3QjqKTOZDFNTU/ziF7+gqKiIS5cu5SSDiLKIQrqSml0zOjpKf38/Dx8+RNd1ioqKKC8vp66ujtraWrxerwxpZjKZnMwmMSaRfvek+8lPZSu0lAspln8uoU9uREzVWyD2WxffWf9kz5dO6xiGCQyyLiPZKZlHKkL23tbWssbTxMQEs7OzpFJpysvLOHjwIB0dHZSVlT8KkZpQb1WN+e810j5zEsfTLgeqTjgyMoLVaqW9vV2WPYiXqi75wvgQDyyVSsltiIeGhlhbW6OkpISDBw/S3t5OMBiUyQz5+xpuFHPfyGja9DiTGbNhQtdzv1soWiWkrVBh8pdyldD5CcDCXWYYOrpuoGkZ1NNnCZ49dzqjo2lmdMPA7rDQ2naAmpogM7MzTD2cYnFxkdu3bzI2NkzHwYM01Dfi95fl7Mmp+nj32lK/qcTcKsSLSafTjI2N8eGHHxIMBrlw4QLV1dU50kFIOJE4rOs68Xic1dVVxsfHuX37NrOzs1RUVHDs2DE6OzspKyt7Ypa2eo2nGWt+il6OSvGUS7m4Z/V3hQwuVZoK5IdD1ZS57PfIOtzNFsB4tCpo6Lr2aMxW7Hab1NOXl1e4e/cOAwMDFBV5qaysoaPjEM1NB/B6i+RkEM9fjHGvSM5dI6amaSwtLfHTn/6USCTC22+/zcGDB3O6buQntWqaRjQalVV+Q0NDWCwWTp8+zblz5+SOr0+TCLtXiFlItytUHpJPTFWaqseI41R1RVRA6vq6RW6xWHE4HESjUe7du8/Vq59TVlrB2bNnOXToEGVlZTmtYYQE3SuJNLvmYE+n00xOTrK0tERnZyc1NTUyU0Yk4grHszj+4cOHfPXVV9y5cwe73c7rr7/OpUuX5BZ9sH0H/PNGIV00Hxvdz2auMzVECbkTQHgyhEF1/PhxmppaufbFdX79619z//59rly5woEDB7BarY/tgLwXsCMSM/8hGYbB0tISH330EQ8fPuS73/0uVVVVctkQ7WFEIm0qleLTTz/lk08+wel0cvnyZU6ePClLMADpqAaeyv2xUxLTMIyCEhMoKDGFWpI/DhWFsvwLScz8TCjVR6r27RTkEknWiUSCSCQi8zSj0Sgej49UMs3w8AjXr18nFApx4cIFXnvtNSorK3OMz3w31osQBNsmpniYqpN4bW2Nrq4uPvzwQ958801Onz4tfYmCjOpy/1//9V/Mzc1x7tw5Tp8+TVVVFQ6H4zEXC2w9iUHc5kYVlvnLr+qqypJSA1Ou5Csk0R5zNW1gWAkDUP3kTyYRdhSkSafTJJPJnD5K6vIr/hXLvGwvqGmYTTa0THbMy8vL3Llzh56eHsrLy3nnnXdob2+X70jot0JNeBHJ2zsiMdXkVV3XGRkZkc7073znO5SWlsqHJepUlpeXuXXrFteuXcPn83HhwgWamppkuHA3UMgpXgiq9Mrem4bFAhZF8SkkCQtJ380gVo+NWoTnE0I1jJ40DmFpyz8ZFlZXwxhGtho1Ho8zMzPD1FTWgj969CgnTpzI8XSIMbwIg2hHdEyxfJnNZsLhMOPj40QiES5evIjf789eSLFOx8fH+fTTT+nr66Ozs5Pjx49TU1OT00R0LyEr4UxYLWYM1n1/W+05r5JefXb5lZeFxpGvYxcykh4/h+q2yuYteDwevF4vtbW1TE1NMTg4yODgIBcvXuTo0aN4PJ4X2lN/R4gpdMZkMsnExARTU1MEg0GZ/iVixvF4nL6+Pm7fvs3S0hJHjx7lG9/4hpSoexVZIunZpVx5TwZbe2kqMdWoV6GS4Hy1IF9iit9v9jOQUzME6x4Rv98vo0PDw8PcuHGDhYUFDh/upLa27oU1T9iRq4rZODc3x8jICKlUiiNHjsgabMMwZCuT7u5uMpkMp06dkg3pxUPaK1CXx3UXjU4mk0uI7RgGqmEjdG+hQhQiJKxLRzGJhe75pFXGZALd0LLOecNA09PrUbVUnEQiRlNTA4FAGXfv3uXWrS9ZXJznwsULtLS04nQ4MdDlpMx+d3ff17aJaRjZeHcqlWJycpKVlRWCwSD19fVSEV9ZWeGrr76S/XXOnj1Le3u7rJ+G3OrBF+0OUrOL1p3OBpget663CkEo1dMgri2scuHGUSWryFbKj62LZ6eOSx1fMhnDZNYxG2AyaVgsVsxmE4lEBkwaGS1JIODnzNmT3L9/n5mZh3z++VWSyRgd7QdxuhwYuo7JZMZsFrmgu/eetk1MMduXl5eZnp7G4XDQ0dFBIBBA0zQWFxe5evUqExMTnDhxghMnTuTskAAvtlxgI+Mh37ENJtihMWqaJlu9iPOrW1Crv8t3K6ljFMcWynLKJ22W2Lq8vq5rj6R1BrM5G0NPpZOUlfl59dVXmJycoLu7h//5nw9IJRMc6uzM+p6t1kfRp93Ftq1y0Ybv+vXr3Lt3j+bmZr7xjW9gsViYnZ3lJz/5CZFIhHfffZejR48C2aQMh8MhU9nkYJ4hrW4rKGSV58fZxTjyvgk87i7a6PzP+kgNw8jpwak+A9VIEn9TdU0Rscm/J/X3hXy6664wPUePjMfjMjdW13VpE/zJn/wpZ8+cw+l0YLM5sVi231FvM2xbYtrtdrq7u7l16xZ+v5+Ojg7sdjtDQ0P8+Mc/JpFI8M///M/U19dLB7vD4chxSbxIFLKuhaTaTSleiEwisVcYQmqCiiCn+OSPP/+e1EmYn1UlVCyx664gocjEF01vTSYThw8fxmQy8X/+z0/QMhkuXbqM01m0a89FYEvEVGOr4XCYsbExUqkUFRUVuFwurl27xq9//Wvcbjc/+tGPZGRBOJVFzY8oDYB1y/55L+liycx3sG8VhSRmIUOmUHRIXFeQTeytJD6q/i0ML7H8i7+L/+dH1/K3HRQTTyRQizGIySCuDdDS0sLbb7/Nz///n7Oyusobr3+TioqgHKtqvO0UnomYhfQaUdZQU1NDY2MjDx484JNPPsHv9/P2229TUVEhl/twOEx/fz/T09NUVlZy9OhR/H6/rOEWmxE8T3IWsqy3shzDxg78J95Tnj6bnzKXb5Wr4UpRTiE+4p7yw7aFxibSDEXiibi2KqUh25Hk8OHDRKIRenq6sVhsvHLpG1RVVUtHvqZtb0+lfDwzMWE9ZCeam46OjhKLxQiHw8RiMdmmura2Vn4nHo/z+eefs7q6SklJiWxgf/78+ZyH+ELisjt8zXy1YCOneP7xORlNj/TIfN3Q0HO3RBSEUj/imuryX2jCqC4r9drq/81ms8xCunD+Ai6ni5GREew2FxcuXJR7Oe00nnnNkv6vZJKhoSFmZ2dpb28nkUhy48YNQqshTp3MlsaKB2qz2ZicnKSvrw+bzcbhw4cpLi7h/v37jIyMSD1nL/kydwpqYsZGn40iLIIwOcnGeQbNM40l72fhetrsI9QA0Ymvra2NQHmAwcFBbty4weLiojzXTuKZJKaa5RIOh+nu7qa4uJjSUj+pVBJd13C5nMwvzFG3VoevpOSRK8LE6OgIhqFTURGgvLyMpaVF5hfmGBoa5NChg4BJJr0+f4LmvzIDUF68ycC0xSiPkFaFMow2HVGePzffgBHH5EMsq2qsW/iZ1QmguqhUmwHW9xAV5BcbhyWTCRwOB4cPH6avb4De3gfE4jEuXbxIfX0D688NMJkwbcPP+czENIxs67vZ2VmWlpbw+YoZGOyjpqaas2dPMTo6yvXrn2OxmLj86iuYzTY0LcPi4hyZTJL5+Wm67t1menqGSCRMLBYBNFKp9KOmAw4MY/OWKE8jLQo5mQvDAPJfeNbPJ3lpMsD8uDv5sWVWWVbzj8n3iz6NXpvvDjIMA4P18+VnXKneBDU4sP63dXVWLSsWe8+rESX1XtaJawY0ysr9HDt2hEwmRVfXbUCjqMiN3+9DNx4V2pksmMwWthohemZtNZPJMDs7y+3bt7FarUxOTlBaVsKpU8dpbmqmuroSTU/x2eefUF1TwbGjx9C0FLH4GlPTEywtz9Pf30s8EScSWcVT5AA0ND2FxeoEHlfSt0LMQt97HI9IadJQpaZBGt1QdUAwG+ZHL2Z9DIXIlC/tBTmeNN5CWe35xoRhGGS0DJqea+yohFSNufxsJItlPY1O7RQnJoCQqKrkFPdgsVhkUCASWcNsMXPq1HECgVLudt3F6bDy+huvP+p+Zwazgckw5TyzZ8EzGz/z8/Ncu3aN27dvEw6Hqa2t4rXXXqOpqQnd0KkMVnLx4gVmZ2d47733qKurw2634/UWcfLkSc6cOUtbaysDgwP87Gc/y3a9MOVW771oqOHR3UC+haxKKPWawpuR/11QJp2idwqICaM64VVjSfwrLGoMI2dDLwF1mVevLwIjGTI0NDZgtpj55S9/ic/n49TpU7JduW4YWLb4Xp+JzolEgvn5eSYmJh4t4z5+8IMf0NHege2Rsmyz2aisqOTs2XNMTEwwOjqK1WqlqamZjJaR2xAnU9ltVLL15aJib2s3sdMQEkIYADudkyiWzXzjJ38iiNxV8VE7eshjDSPH3STOLyJJosxCJWS++8lgPftIlECr9w+5JI1EIpLwyWSS6upq/uRP/oT/+//9X+7du0cinsZs3l73jydKTHU2i51cx8bG8Pv9/N3f/R31DfUAaJpORssq+m63h0MHD3Hu/Dk++eQTmpqaqKmp4datW3Tfvw+GQW9vL/F4HL/Pj6HvnVoTeHw5LrRsb+TaepKULeRgF+fL/znHWjeQSq7JbM4JChSS7kIi5ocs1WW6kNNe9Z2qUlVVEzRNk11N7HY7mUyGhoYGTp06xdWrVykrK6ehvhG73YnZasEwnt0lZ/mXf/mXf9noj+pMjsfj3L59m9/97nekUin+4i/+gqNHj2K1WTDQMMj1p4m2eh988AEdHR3U1dbhcrtIJBLMzc1hNps5d+4crW2tWG1ZSWAxWx/pJIVfeL5S/jS+z3zjI/d72QpIw1i3nNXoifryCkF15WyUAqdeT9UjRbMDIZELfU8lRzqzXlym592PSDIW/xf3LeLgJSUlOeqJWObVojWVyOpzEERcz4g3SCQSJBKJHI+DYRiUlZUxMTFBZG2N8vIAfn+296mu50a2ngZPlJhCPxkfH+f69essLS1x4cIFGUNNpVJYrbkEEd8JBCrwuD3MzMzQ3NzC4c7DVFdXZ31iNjv+Uv/6rr0m8yNdaQsNCTZAoe8Vkiy6kXVzPCsKnWsjSahKynxDR9UH1e+JfdsFMcT+7OpxIqaukk64eETdj1rIpxJOtF1Ux5bvjBfEUw04MQnF9opCWJSWltLe3k5PTw9F3ju43EVUBIIYhi5zbp9Wcj6V8ROLxejv75cbQZ05cwan0/noYo97q7IPB9wuF42NjUxNTRGLRqmsrMDtdqEpkmjdV/hU41XOv/WSBuU3ZK3yZz4VsLXQpSqxNjtX9pg0hgGalnmkL+bnYGZJG4/Hc76rVlkaRnZ3DEFy9fzqdTdeFZCri7CwbbYsbcREERNA13Xq6+sZHx+n98EDir1+zp4twu12ywnxtKUzT2wRYzabmZycZHx8nLKyMi5evEhtba2ccRaLASYdVeJkH54Jq8VOY1MTPQ96sk3y9XJ0A3RNR9N1LGYzFrMFi9mCyWTGZLKQZcnT90ZSx7oVZO/RkjP+Qq/o8US4R+UWOUcLPezxb5pMWb+oxQJms17QFfS4H3OdkJqWAUyyj+f6MZrc+VicRxgyIqE4FothGBs3LRPky/XDmh7dmxkDDQydrK1sPEoytsi9ilSpKvJx79y+y4MHPQQClXR2dj5zo9knNm4NhULcuHGD2dlZDh06RH19PbFYDOCR4pvCQEnD0rOkM2HGanXgcLhYXQkxMzOLy+V+tGQrDnBEaYBI188l5kbLo7p0wXpMNz8trFCMONdBrWcd6CrBTLkuHbPZDMbjGUGpdCpruKn3k/fwhYoiljOxjFqsj4wXw0DXDbJdNB6/T6n7KQkaFosF86N2MSaykiv1qKRX3RU426fIIBaNk0pl5N/S6cwjois+UEwYZP8GBmazBbM5W2WZldzrDb+sVgtWiwWT2YzZZMVkMUinUkSjcZLJNCUlfsrLAwwPj/Hll19SVVVFIBB4ptVlU2Lqus7AwACff/45uq6zurrKzZs3ZWuSrJ6RItv8KWs2CheE1ZrtlDszO0NoNcq1L75kaHAUq9WGxZJ1VqtWYfZ9Pi4tH19+ydn6TiQ6OJ1OgsEgq6urrK6uSqmi+gLN5myFoKr8Z5e93OZVVquFdDrzSBLxqHGA+dF9i2djkEol0XQdszJRUuk0IlMcwGa1YbXaMJlzo1mWRzHojJZBy2gkkkkyar242USxtxiL1QqPCJHVNTNSMjnsDhwOB/FEnPn5BQxDp6TE96hlY7bddrYZrvVRax5dLr355RuZTAan0ykno9VqeyTVDRKJpBw3JrA/cinpuuor1R51Z86WbESjMVZWVrl37x4tLS1cvnz5saTkzbDpURaLhaqqKjo7O+nv7+fmzZtEIhFJTMMwsNnsys5cxqPlKkuArDVoxel0MTAwSH//QNY/ZrFitqy7JOTLMD1enmqxWGRvHgGRJqdGP/x+PzU1NYRCIbk5lN1uzyG12Zzd/VeQXbSqyU8gyeaNZkn/yJGC0+nE7V5PkM0uoRkyj150ofrw7IQxcLksWBCrQtbtmNF1NM1A18AwTLicbsyuAj2OUuuZ64lEkrW1Nbn3pnB2u91u0unsBF1biwBIvTM76c3Y7TZ5X1kLm0dVBFqO+8fQDdKZtGyukEqlSCQSOeMSz9Rms+Nw2LFYrFgsuVExq9VKcXGJ3JVkXWA9HTE3La2IRqM4HA6SyaQMR+W3TVZdFPnId++I458VhUKShaA2TX2WRqVPO6Zc/QxyEj22eP6ciZm/WhTQdlULWhCkkP6mnlcYQhu5s1RPwWPtcTa5v6d5bsJ1KGLy6qasm35vM2KKZTA/X1IdkBpjVQeTTwzR1kT1uT2tzvEkHVMszUKHEop4oQcn/HFqZs3jRsc6scVLK+SHK1SjU8hRnv87QQLV/1loHBvdt/j/Rl6BQu9IjXurz0ZNSlYrMdVzbPaexPMp9LxV1UW1BZ4GT1zKxck2mh3iJRf6vXpj4iU/rfTLP9dmP6tj3Ewy5y+zhcaz0bGFVoZ8Czd/dSh0LvXY/Mm82Rjyx7LRtQp9N3+FUye2eg71/vK/o0KdEE+6h/xxPy02lZgq47eLjW5gp5bC/BvfSCKr97TReVXpop77acbxNATLfxZPQ658POmd5F8jP0VOPe5Z3+9GpNzq8ymEXWncuo99bBdfv1qGfXwtsE/MfexJ7BNzYZUjBgAAADFJREFUH3sS+8Tcx57EPjH3sSexT8x97EnsE3MfexL7xNzHnsQ+MfexJ7FPzH3sSfw/eJU5ZRPPxkIAAAAASUVORK5CYII=)
A spherical hollow is made in a lead sphere of radius
such that its surface touches the outside surface of lead sphere and passes through the centre. What is the shift in the centre of lead sphere as a result of this hollowing?
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)
A spherical hollow is made in a lead sphere of radius
such that its surface touches the outside surface of lead sphere and passes through the centre. What is the shift in the centre of lead sphere as a result of this hollowing?
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)
On heating a mixture of
ans
, we get –
On heating a mixture of
ans
, we get –
Three identical blocks
and
are placed on horizontal frictionless surface. The blocks
and
are at rest. But
is approaching towards
with a speed 10
. The coefficient of restitution for all collisions is 0.5. The speed of the block
just after collision is
![](data:image/png;base64,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)
Three identical blocks
and
are placed on horizontal frictionless surface. The blocks
and
are at rest. But
is approaching towards
with a speed 10
. The coefficient of restitution for all collisions is 0.5. The speed of the block
just after collision is
![](data:image/png;base64,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)
Two identical masses
and
are hanging stationary by a light pulley (shown in the figure). A shell
moving upwards with velocity
collides with the block
and gets stick to it. Then
![](data:image/png;base64,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)
Two identical masses
and
are hanging stationary by a light pulley (shown in the figure). A shell
moving upwards with velocity
collides with the block
and gets stick to it. Then
![](data:image/png;base64,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)
In the given figure four identical spheres of equal mass are suspended by wires of equal length
, so that all spheres are almost touching to each other. If the sphere 1 is released from the horizontal position and all collisions are elastic, the velocity of sphere 4 just after collision is
In the given figure four identical spheres of equal mass are suspended by wires of equal length
, so that all spheres are almost touching to each other. If the sphere 1 is released from the horizontal position and all collisions are elastic, the velocity of sphere 4 just after collision is