Maths-
General
Easy
Question
The value of
is
The correct answer is: ![sec squared invisible function application x](data:image/png;base64,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)
Let,![y equals fraction numerator tan squared invisible function application 2 x minus tan squared invisible function application x over denominator 1 minus tan squared invisible function application 2 x tan squared invisible function application x end fraction](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJ8AAAAqCAYAAACtHIkmAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAbSkFbcgAAAyNJREFUeNrtXNGHVGEU/4xkJJGVJImxkmRfs/YhkSRZvWStJIkeetp/YCWJ9DBPvSQ9JIkkyeolPawkkYy1D1l6Ti897MNaI2bPcc9w3b3XfNN835n7nfn9+HFn5t65zu+e+33nnPvd49xkoifsEr8Qpx0AbZTRIN4h/oAU0GZc2IYE0GYcOEtchQzQRhtHJK5pFb6fI74hbkrs0yFegzb28VfpPCeIKyJyEXy3LxL3y+dTciEWoY39bEvjrv5APDDEMceJa9DGfprfqxB6nvhNpsINmR7LLs5V4i8JlnkUO1bYj8U9GSj4vkV8WPL9ffnNojZaNtfq7n4pUyDjJnG95FgW95GMVP39VgdcSJ8RZVam3jJwOeJw7jOf87FxbbRsruXU0pC7vHjsOY/9hkVTRpW5it8vEtuyfZ74aQK00bK5tnFNz/PYUWKlg8R3xAsD9vsopQnOjKeGnEJ9R5u6aTOMzck737LEM/8qLlJogVvieD6PmJZkFJmZEG20bK6F8z2RmKWpdHdz0P2UuM9j335dsB25HFMXbTRtVkVXYpEiNhWnFg6kXxP3eI6O78VJuS74PeIUVAdttG1WRafiTvqZS+OPSlr/W7ZDC7ziWYo5JKWJvPCXiS8Ma6Ntsyo4I/tTIsqMpPddyTzPEO/JvqEF9kkE9hLfFi5wH68kG7SmzThsBgAAMIhnxIWKVPoB5AFi4obLHrvkwZnMRkUW879FUgDYhUtSWsjjrssKlwAQFTy6rRfSaV750Ixwrh448dyFrdx2W+K9URwIALzx2WWV65aMeg1IAmjhucsWJPK6sOuQA9DEkpRc1iAFoI0rEqvNQ4qRkylrb/tHt4ud7iv8Jwisvu0fzS5eqTALvwmKbdg1GKddtowICAerb/ubs4tfUuanKR0j9ljthGCyiwEvRLzt4hanrXZCQBeDgFlViv+dHxm0OyGgi0HNHcRqJwR0MTAw8qXcCQFdDAxNu6l1QkAXA0UHsfK2f6hOCOhikPjIl3InBHQxSNj5Uu+EgC4GCTif1U4I6GKQgPNZ7YSALgYBnC72MnyrnRCS7WKwA6QRYQJaPkTNAAABtHRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT55PC9taT48bW8+PTwvbW8+PG1mcmFjPjxtcm93Pjxtc3VwPjxtaT50YW48L21pPjxtbj4yPC9tbj48L21zdXA+PG1vPiYjeDIwNjE7PC9tbz48bW4+MjwvbW4+PG1pPng8L21pPjxtbz4mI3gyMjEyOzwvbW8+PG1zdXA+PG1pPnRhbjwvbWk+PG1uPjI8L21uPjwvbXN1cD48bW8+JiN4MjA2MTs8L21vPjxtaT54PC9taT48L21yb3c+PG1yb3c+PG1uPjE8L21uPjxtbz4mI3gyMjEyOzwvbW8+PG1zdXA+PG1pPnRhbjwvbWk+PG1uPjI8L21uPjwvbXN1cD48bW8+JiN4MjA2MTs8L21vPjxtbj4yPC9tbj48bWk+eDwvbWk+PG1zdXA+PG1pPnRhbjwvbWk+PG1uPjI8L21uPjwvbXN1cD48bW8+JiN4MjA2MTs8L21vPjxtaT54PC9taT48L21yb3c+PC9tZnJhYz48L21hdGg+d+BHDgAAAABJRU5ErkJggg==)
![table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell equals fraction numerator left parenthesis tan invisible function application 2 x minus tan invisible function application x right parenthesis over denominator left parenthesis 1 plus tan invisible function application 2 x tan invisible function application x right parenthesis end fraction times fraction numerator left parenthesis tan invisible function application 2 x plus tan invisible function application x right parenthesis over denominator left parenthesis 1 minus tan invisible function application 2 x tan invisible function application x right parenthesis end fraction end cell row cell equals tan invisible function application left parenthesis 2 x minus x right parenthesis tan invisible function application left parenthesis 2 x plus x right parenthesis end cell row cell equals tan invisible function application x tan invisible function application 3 x end cell end table](data:image/png;base64,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)
On differentiating w.r.t. X, we get
![table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell fraction numerator d over denominator d x end fraction left parenthesis y times cot invisible function application 3 x right parenthesis equals fraction numerator d over denominator d x end fraction left parenthesis tan invisible function application x tan invisible function application 3 x cot invisible function application 3 x right parenthesis end cell row cell equals fraction numerator d over denominator d x end fraction left parenthesis tan invisible function application x right parenthesis end cell row cell equals sec squared invisible function application x end cell end table](data:image/png;base64,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)
Related Questions to study
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The derivative of
with respect to log is
The derivative of
with respect to log is
maths-General
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The derivative of
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The derivative of
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The rate of change of
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at
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The rate of change of
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at
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If
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If
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If a1, a2, a3, ........., an are positive real numbers whose product is a fixed number c, then the minimum value of a1 + a2 + a3 + .... + an – 1 + 2an is
In this question, we have to find that minimum value of a1 + a2 + a3 + …… + an-1 + 2an. Remember always the inequality of A.M and G.M. Always A.M ≥ G.M.
If a1, a2, a3, ........., an are positive real numbers whose product is a fixed number c, then the minimum value of a1 + a2 + a3 + .... + an – 1 + 2an is
Maths-General
In this question, we have to find that minimum value of a1 + a2 + a3 + …… + an-1 + 2an. Remember always the inequality of A.M and G.M. Always A.M ≥ G.M.
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The domain of the function
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The domain of the function
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Range of the function
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Range of the function
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The domain of the function
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Let
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,
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physics-
In the adjacent diagram,
represents a wavefront and
and
, the corresponding two rays. Find the condition on
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and reflected ray ![O P](data:image/png;base64,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)
![](data:image/png;base64,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)
In the adjacent diagram,
represents a wavefront and
and
, the corresponding two rays. Find the condition on
for constructive interference at P between the ray
and reflected ray ![O P](data:image/png;base64,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)
![](data:image/png;base64,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)
physics-General
chemistry-
Select the rate law that correspond to the data shown for the following reaction.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAUsAAACSCAYAAADM8ejNAAAgAElEQVR4nOydeXAcx3X/P3vf2AUW9w0QIEASIAmKh0RKFkVRoihSliVZ1uEokspHopQrqdhJnCpXKvkncSX1KzuHrcRlR4ot25JjXSZp6rAu0rxFiiBBkAJxn8SxuPbCnjO/P5AZLZa7i10CILH0fqtQ5M686X7d/abn9Xvd7ylcM36RDDLIIIMMEkJ5oxnIIIMMMkgHZCbLDDLIIIMkkJksM8gggwySQGayzCCDDDJIApnJMoMMMsggCWQmywwyyCCDJKCO/GHWa28UHxlkkEEG1wS3L3Bd6slolhlkkEEGSSAzWWaQQQYZJAH1/CTxEQwGOXv2LD6fD5VKtVg83TQQRRFBEBAEAaVSiVKpRKFQ3Gi2FgRRFAkGgwBoNJq0b89iQRrrcDic6Zd5IIoiarWasrIyioqKUCrTQ2db0GTp8Xj4wQ9+QG5uLjabLSMgURBFkenpacbGxsjOzsZms6FWL6jLbzhCoRBtbW0A1NbWotVm7NwwO9bj4+MMDg5SU1ODyWS60SwtW/h8PiYnJ9mxYwdf+MIX/jAmS4VCQWFhIX/8x3/MihUr5EaLoohCoZD/jYQoivKz0b8jn0t0LbKsZOtJhj7etch70fxE8hnNsyAI9PX1ceHCBWpqaqiqqkKr1SZVT7w2pEofzVc0z/H6NlZ5oiji9/vZt28fAPfffz8mkynmWMYqJ9a9yPZEty0S0fwu5rgvhF76LYoily9f5uTJk+zatYuCgoKr2pnsOEb3yWLQS/WnIgPXwkO8MiLfienpaT744IO0UxwWPFmqVCo0Gg1arTZtvhDXC4IgoNFo5D+tVotOp7vRbC0Ioiii0WgQRfGmaM9iIXKstVptzI9iBp/1Uzqa7TKzWwYZZJBBEshMlhlkkEEGSWDBk2W0bWm+e6IoXnU90u4TTRP9b6Lnkql7ofTRPKbCc6y2LzV9Ir5i8R6rnuiyEo15LMz33Hz9Ox//seqKVf5i0Sd6fj6er7We+ehjIdH4JiMDN4Ln5YwFW1gT2WVi3Ut0LfrfeNdSubfY9PHKSJYmFb7i9W0q9In4StQfqfA/H+Z75lrH+3qOezz6WM6tyH66XvIbC8u9L9MNmWV4BinjZhD8DDJIFUuyDF/osiezDF88+uu5DE9Uzs20DI+17I7X1uUiv4nkNlY7rgfP6YYlWYYvVFXPLMPj85Qq/VIsw6P36yXLbzxkluHXX35vJA/piswyPIMMMsggCWQmywwyyCCDJJCZLDNIGvPZHjPI4GbGdZ8sU3EkzPdcKmVGXkuWfr6y5nPwJFtWIiyU/lr7ezGRSvnxHBGR95J5Ptl7iylXicpbqroTIRV5vxHvXLrhup9kT8VoPt+1VOlTNU6nUn4iI3qy9cSCIAhMTk4yMTFBOBwmLy9Pjl4ULYhS2X6/H4fDgdPpRKvVkp+fj8lkks/uJ+tIisV7IgdPoudSoRVFEZ/Px9jYGF6vF4PBgN1ux2g0XlWvVLYgCExNTeFwOFAqlWRnZ2O1WtFoNAn5WCy5ih6Day3rWunnK0MQBPlaLEfjjXjn0g0Lnizn+/pEd1IsoZLoIv+Npo8sK3piildPvGuR5Ud6MxPRR9NFlxHZrlg00rPJ1iNdd7vdHDhwgIMHD+L1ennqqafYtWsXVquVQCCAw+FgYmICk8lEQUEBer0eh8PBz372M44cOUJ+fj5PP/00W7ZsQa/XX8VfMi96NP8L0XZj1RHdv6I4G8Hn5z//OZcvX2b16tU88sgjVFVVMTIygtfrRaFQYLFYyM/Px2w2MzMzw/vvv89rr72GSqVi165d7N69m/z8/Jj1JHMtGfp42th8dJH9EYtWEARCoRAKhQK1Wh2z36T4mQBqtfqqQDZSnR6Ph97eXvx+P9XV1WRlZc356MWTgWTeoVTo033CXNYneAKBABcvXuTIkSO4XC75Xm1tLdu2bSMvLw+VSpVyPYIgEAwGZUGMF5Q30daLZDTLWDSpfn2DwSA9PT309fVx//33s27dOgwGA6Io0t/fz89+9jOOHj1KTU0NzzzzDE1NTWRlZbFjxw4uX75Me3s7o6Oj8ksVq75UNb9UMd8zse5PTk7S1taG0Whk69atWK1Wfv/73/PKK6/Q3d2NUqlEr9ezcuVKHnvsMbZs2cLq1avp6Ojg6NGjdHV14fP55q1noSuQyEk+0bOhUIihoSFOnjyJXq/nzjvvJCsrKyatz+fj/PnzvP766xQVFfHkk0+SnZ1NOBxGqVSi0Wjw+/2cOXOG3/72t5SUlPDQQw9RVFR0lRwKgsDo6CivvvoqV65c4Wtf+xrr16+/apWRimYZCoUIhUIolco5k3RGs5wHS6lZSgLxwx/+kKmpKRQKBUqlkl27drFy5Uqys7PnDEa0dhevfI/Hw7/+678yMTHBV77yFerq6uTlWiK+oq9JWCrNMvIZo9HILbfcQnV1NWq1mkAgQGdnJ8ePH6e5uZmhoSGampqoq6vDarWybt06VqxYQXd3d0zbXzKaZaLxi4V42kMqmqUEQRBQKBSUl5ezbt069Ho9Y2NjDAwMUFhYyLZt22htbeW9996TJ83y8nIaGxtpbW2VI9Qn07/RfC1Us4wcZ+nfYDBIV1cXL7/8MtnZ2axduxaz2XxV/ysUCsLhMJOTk3z66ad4vV6mp6c5e/YsL774Ig888ACPPfYYoVCIiYkJ2traCAaD+Hy+uJq/z+djaGiIgYEBvF7vVfxFPhOpcUaWI02IoVCIjo4Ovvvd71JXV8ef//mfyzFNpf6OLEf6f0azZGk1S8l2pVKpePrpp3n66aexWq1otVr0ej1utxtRFLFYLCiVSlwuFwqFAoPBQCAQkJcp4+PjqFQq7HY7er2eyclJzp8/z9jYGH19fRQVFZGdnX3VMmY5aJaR91Qqlcyj2+3m0qVLhMNhNmzYgMPhoLOzk/HxcbKyslCpVHPoE/EXbwzj8R/rQ5BKOcncj6wrUvPXarVUV1ezZ88eqquraW1txeFw4PP5sNlsc9ocr73J1J0sfSzNMnqikBAMBnG5XPLHzu12yxr/5OQkgiCQn5+PTqfj1ltvpba2FgCVSkVnZyenT5+mtraWyclJDAYD27ZtY82aNbJsB4NBpqenGRkZQalUUlJSgsFgiNu3oigSCoVwuVyI4my6EI/HQ35+PgqFgvHxcaanpzGbzeTl5aHX65mZmWFwcJDTp0/LtnGFQoFOp8Pj8TAyMkIoFCI/P3+OzTjdJ0q4AQ6ea4FCocBoNJKTk4PNZkOpVNLV1cXf/u3fMjAwwPe//31MJhN/93d/R1lZGU8++SRvvvkm7e3thMNhLl26hN/v55FHHuHxxx/nu9/9Lr///e8JBAJ8/etf58knn+Sb3/wmhYWFN7qpCSEJuSAIjI+P09bWRk5ODuvXr+fUqVN0dnbS2dlJSUlJTMdGugpsJN+hUIjh4WGOHj3KuXPnCIVCrFmzBrvdfgM5TB6SPXJgYID/+q//4vjx45SVlXHixAn0ej0PPfQQTz31FCMjI/zHf/wH2dnZFBUV8T//8z9MT0/zH//xH5w6dYpvfvObCILAiy++SE1NDY8++ihHjx7lhRdeYGBgAICmpib+7u/+DpvNFpMXQRDo6OjgW9/6Fj6fD4VCQSgU4umnn+bSpUu89tprOJ1OTCYTDz/8MM899xzd3d0899xzDA8P09fXR1tbG3/2Z39GY2Mjzz//PO+//z6hUIiVK1fyne98h+3bt8u28nTHkizDF7rsiS7T5XKxf/9+Ojo6sNvt3H///WzcuJE77riD559/nv/5n/9Bp9MxPj7Ol7/8ZWw2GzMzM3zyySesW7eOL33pSxw7dow333yTuro67rnnHgYGBnC73ezevZsdO3ZgNpuTaseNWIZHP+/3++no6GB4eJiKigpuueUWXC4XR44coa2tjU2bNsne8ui/aKSyDJ/PwZOonMj6Yj2X7HLf6XTS0tLCoUOHUCqVlJaWYrfbCYfDcdMULPYyPJI+2WV4NJ0gCMzMzNDR0YFer+cLX/gCra2tHDp0iFWrVpGbmyvbXJuamujr6+O9996jqamJxx9/nPLyctrb2/H5fPh8PjweD4FAgD/6oz+itLSUEydOsH//fvbv388Xv/jFuDyGw2GcTieXLl3illtu4b777sNisZCVlcW3vvUtDAYD+/bt49ixY2zfvp2qqioeeeQRfvGLX1BUVMQTTzxBbm4uL7/8Mu3t7Xz729/GarXy4osv8qMf/Yi6ujoqKipuimR9y/5sOMwKltPpZHBwEL/fj8fjQalUcv/99/PBBx+wf/9++fctt9wCzApEbW0tX/nKV7jzzjv5yU9+wo9+9COGh4d58sknOXz4MOPj4zzyyCNs2rQJg8EQd4m1HJbhkfB4PDQ3N3PlyhUsFgstLS04HA7Gx8dpbW1lZGREtodJzweDQRwOBy6XS95aYzabEwrxjV6Gx0JWVhZ79+7lkUceYWRkhF/84he8+OKLFBQUcNddd82hFQQBt9vNxMQEwWAQi8WCzWabk33xei7DY6G8vJw/+ZM/YfPmzbzyyiscOHAAp9OJ1WpFEAS0Wi2NjY14PB6OHTvG1q1beeKJJ/D7/bS3t8uTXk5ODo8++igOh4OxsTEKCwvRaDRMT0/j9/uv+mBFy2tlZSX/9E//xOrVqwkGg9xyyy2MjY0xMjJCbm4ufX19eL1eSktLefjhhzlw4AB1dXX88R//MRcvXqSlpQWz2YzZbEav12O1WhkdHcXhcFBeXp72EyWkyTLcZrPxxS9+keeee26OU8dut1NWVsbJkycJhUKUlJRgNBqZmZlBoVCg1+vlwbNYLGi1WkKhEKIoyqlpY9m4lhNiaSRjY2NcuHCB8fFxWlpaaGtrIxQK4fV6uXjxIh0dHZSXl8svkrTse++99zh79ix6vZ7du3dz1113YbVakxZkiZdETp6lhlarpbCwkPXr1xMMBmlpaeHDDz+UbX6RcDqdfPrpp7z11luMjY2xdu1aHnvsMaqqqpbNy6vX67HZbBiNRgwGA0ql8irtPdJuG23DlcZ3ZGSEN954g7ffflt2+Ei2yFiIvK5SqcjOzqawsBCFQkFnZycvvPACp06dQqlUMjExMcf2Hc2LZCsdHR3lJz/5CXq9HqVSSW1t7ZyEdumOZe0NlyB5/rq7uxkfH8dsNpOVlcWJEydobm6mqamJoaEhjh49yvbt2yksLEQUZ1OTXrp0CZvNRltbG4FAQDagKxQKZmZmGBoawuFwUFBQcNV+tuWwDI+mCwaDtLe343A42L59Ow8//DD5+fk4nU7eeOMNDh8+THt7O1u2bJGf8fl8tLa20tnZSV1dHQ6Hg+bmZurr62UNNHpMEvGQKuZbhidbj0KhIBAI0NXVxbvvvsvU1BStra1UVlZSVVU1JwmWIAgMDg5y8uRJsrKyKCsro6WlhdOnT8vLQqmeVM0i0TISi+9UvL/xVhyR95VKJYIgMDExwdDQEDqdTq4rFArR1dXFhx9+iM1m46tf/Sp9fX388Ic/TMhjdJsUCgV+v5+WlhZOnjzJ5s2buffeezl48CCnTp2aw6soirhcLgYHBwkGg+Tm5pKVlcWzzz5LQ0MD4XAYhUJBWVlZUrKdDrju3vBkrkdONKIo4vF4+PDDD+nv70er1dLU1MTmzZt57bXXCIfDPPfcc5w+fZpXX32Vt99+mwceeIBwOMzAwAAvv/wyH374IW1tbRQXF7N+/XqysrIoLCzk7NmzvPzyy3g8Hh588MGrcp8nWobH4j36Q7AYy/BoBINBJiYmKCsrY+fOndx2221kZWURCARwOp1MTEwgCIK8RQRmt2A5nU70ej0bNmygu7ubvr4+nE4n4XBYzta4VLiWlyWaVq1Wk5eXR3FxMb29vbz00ktotVrKy8vZs2fPnL2DgLz9xuPx0NTURElJCZ2dnQwNDSVdd7LL8FRMEqlCoZjdC2yz2dBqtRw+fBi73c7OnTvn0Oh0OoxGI5OTkxw9epTe3l5CoVDSdUT+X6/Xo9Vq6enp4cMPP6S9vV0uS6FQYDabsdvtXLx4kf/+7/9mw4YN3Hrrrezfv5833niDCxcuEAqFsNvtlJeXz/kgpzOW5XFH6Zpkr3n88cdxu93yZJOVlYUoiqxevZrbb7+dbdu2UVNTg1arlb2iCoWC4uJiVq1ahVqtprS0lDvvvJP169djNBp55JFH5O1HRqMx7ub2hbZjMSA5daTTK1u2bGHNmjWUlZXJgqjT6bjttttkW1UgEGBqako2O4TDYXnCirWlaKmFOdXyI50Po6OjVFVVsXHjRvLy8uQDCgaDgeLiYoqKitBqtYyNjTE2NsbMzAzw2QmXyHYnsjUvpG3zfWw0Gg1lZWU88MADmEwmysvLufPOO6murqa8vByDwcDatWsJh8OsXbuW7Oxs9u7dS15eHtnZ2TQ2NvL1r3+dixcvotFosFgsGAwG7r//fvLy8mhoaECj0XDs2DGcTieNjY00NDRQXV1NSUkJ27dvZ2pqiuLi4jljn5OTw+c//3lUKhVmsxmj0cjGjRv58pe/THNzM6IosmPHDhQKBTU1Neh0OkpKSvj617/OkSNHMBgMVFZWsnHjRnJzc2ltbWV0dBSr1UpZWVlMX0C6YlnbLHU6HZs3b2b16tVzTqDodDrUajWNjY3o9Xp5W9E3vvENeVuNSqWioKCAL3zhCzQ0NMg0Uj7nrVu3UldXh8/nw2q1YrFYluWgSh8Ih8PBT3/6U7Kysrj77rvlI2uRyM/PJy8vjytXrvDLX/6S9957D1EUUavVmM1mAoEAw8PD8j49ycGTKi/JTA4LhWQLO3HiBDabjSeeeIKGhgZKSkquopVWH8eOHePXv/41w8PDrFq1CpPJhFqtZmxsTLZX5+XlLSnf8WRIo9GwYsUKnnnmGZRKpTzRB4NBmc/bbruNpqYm9Ho9KpWKyspKVCoVJpMJq9XK1772NSYmJjAYDPJ2oPLyclQqFQaDgaqqKm6//XZCoZB84ketVqPX68nLyyMcDs+JEaBSqcjPz+fZZ58FwGw2o1KpqKqq4qmnnmLv3r1oNBpMJhOhUAij0YhOp0On0/HFL36R7du3o1Qq5f3LlZWVTE5OEggE0Ov15OTk3DTbhmCZ2yylJYFer49p94o0HqvVanJycuQlaFZWFna7HbvdTmlpKVqtVn5WFEVZUBItD5Pd0rNYNstYMJvNPPjgg9TV1REIBKitrUWn08WkjXxm48aN2O12LBYLjY2NTExMcPHiRV577TWsViu7d++moKAAlUoVd8tPrP5ItHUo0XMSknlxFAoF9fX1/MVf/AVjY2MUFBSQl5cXt9+kVUhdXR1f/vKX5zgXhoeH+fDDD/H7/axatYoNGzbElL1Y5SY7VpHtS2Sz1Gg0WK1W+XfkVieFYvYwReQm8kiZBWRvc+Q1iQZmJ7/i4uKY/EdujYscb5VKhc1mm0OrVCplLTOW6Uh6L8vKyuZcMxqNGI3GOdcS9Vu6YVmf4Il3LV5ZkiG8oKCAr3/96/h8PoqLi+dsFYlXfiL+k617vufms1nGuq7T6Vi3bh1r1qwBSHiWXXrGYrGwbds2brvtNvmF8Hq9WK1WxsbGMBgMVFRUyDsLFmp+WMxnJNqCggJ27twpH3uMFUwi8rdWq2X16tWsXLlSbnMoFOKhhx5iw4YN+Hw+SktLKSsrm6NNp2pDjnctGXt1sm2Ph2RXAamYVhLxG+kwS4aXRPyl+0QJy3wZfi2QJpjKykr5a7actwbNB0loEwlurGcinTYKhQKTycTKlSvnHKFLtV8iX6ylXoZHtiHZF01qU6SGVFhYSF5enryauBk2R2dwY3DDsztG/o78N9a1ZOuRtCVpL2WyfCVTfjSPqfAcbwm7VPTSpCCKorynVK1Wy9ppLN4TlTffMny+chI9F6tt8foz0ThGXpdkQK1Wo9VqY06Usfi6VvmNbmv0Xzw+FyKPydInkttY7VgKHtIdN/wEz3zL12TKutbl/rXQJ7PMutZleLJLt1ToE5kc5luuJct/svwm81wq4309xz0efeQHSfod+ZcIN1J+byQP6YobrlnGol+oZrmU9OmkWc7HVzKaZTL8JMPvtWqWyfA/Hw+LTZ/o+fl4vtZ6FkofTxvOaJbJ44ZrlrHoM5plfJ5SpU/E17VqlvFslhnNcm4fpdqe69WOVPt7qXhON6Sv5yODDDLI4DoiM1lmkEEGGSSBzGSZQQYZZJAEMnnDF0A/n4NnIbwuFv1iOG6i6VI11qfyTDwHWuS9eL/jXVtq+kQ8LkXd19KX8927Ee9cumFZBtJI1nicKv31MPQvFq+LRX+t/b2YSKX8a+3zZOpaSrmKdPAsdd3J9udSOMuS4S9ZHtINizJZXqvGcbMjluZ5M/XRzdaexcDNOM5LgXTsnwVNlqIoymGwpDzCGXwGUZwNMxb5l2yMweUKqR3wWf7oDK4e61AodFNoU4sNUZzNKBkd1T4dsGDNcnx8nNdffz1mVJg/dIiiyMTEBFeuXOH8+fPk5ubGTaqVLpBSOUhtmy8C0h8KRFFkZGSE3t5eOX1s5n24GqIoynnMpWj+6YIFv7kmk4mGhgZKS0szmmUURFHkypUrmEwmSkpKKC0tnZOiNh3h9/vl4LsbNmyImZf6DxGiKNLb2wvA2rVrycnJyUyWMSCKIm63G0g/O+aCJkuFYjYGX319PTU1NZnJMgqCIGCz2RAEgRUrVlBdXZ32mpjP56OnpweAxsbGmyoh1UIgCAIGg4GpqSnWrFlDQUFBpl9iQBAEpqamGB4eTrv5YlGOO0Yf8cpgFpH9EpkRL50RfZQv3QR+qRAr+2K6j/VSIDoSWDphUSKlx5sspXvR12CuCi7RRf4r0UTfi1V+onuLTR/NYySf0TxHtzOSPl490m9BEOTr0S9fJH00bSQ9cNU9CYIgyIF1RfGz1MCxxiXyd3Q7EtHHei7e/ci2xPoAR/dPNG1ktsZ45UhOhWh+4rU7GTlJtLdwKeVX+p2snETSR9JJz0t9Ez2ZLfY7NN8Wq+WMmyJS+mLs+UqWPl4ZydLMV4/f72d0dJS+vj5cLhfZ2dlUVlZit9tl55BEL+XU6e/vx+12k5OTQ0VFBXa7XQ4W7PF4GBgYQKFQUFpaitFoJBAIcOXKFQYHB/F4PJjNZqqrq8nLy7sq1UEqiEc/XzmCIDA9PU13dzcOhwOtVktFRQUlJSVyziSpHEEQcDqddHd3Mzo6ikajobS0lPLycjQaDV6vl/7+foaGhhBFkdzcXCoqKrBYLIyPj9Pd3Y3P5wOQk2+VlJTEbHcychI5MUm/oyf5+cpKVR5hduxHR0fp7e3F7XaTnZ1NdXU1OTk58tjHoh8fH6eoqEjORRQMBunr66O3t5dgMEheXh41NTVx88kv5juXbrjurtlUvtbJaC2R96JPC8TTfBZLE5WQSLNMtv0wuxWns7OTt99+m87OTvx+P4IgsHXrVu6//34KCwvloL3BYJCOjg7eeusturq68Pv9KJVKbrvtNu677z7sdjuDg4OcOHGCQ4cOkZ2dzdNPP01NTQ19fX387ne/o7W1Vc4AuW3bNh5++GFKSkoWfZmUSLMURZHR0VE++OADTp06hc/nw+fzUVVVxUMPPcSqVavktCCiKOJwODh8+DBHjx7F4/EQCAQoKiqSaS9fvsxHH31Ed3c309PT6PV6du/ezbZt2zh9+jQvvPACarUaq9VKTk4Od999N/n5+TF3KaQiJ9H/jyXTi6GlwaycdHd3c+DAAS5fvizf27x5M5///OfJz8+fs/KYmJjg7NmzHD58mIGBAR599FE5ZcelS5f41a9+xdjYGArFbPqOO+64gz179sScMBfzHUo33DQneERRlLUyr9dLdnY2OTk5c7zPS6mJxtIs4/Eaj3+Xy8XHH39MT08P9957LzU1Nbz11lscO3aMqqqqOduzXC4Xp06dor+/n/vuu4/q6mreeustTpw4QUVFBevXr+fcuXO0tbUxPT0NzDpnpOVpVVUVDQ0NaLVa3nnnHY4cOUJ9fT1FRUVxJ8tIrSmVTcWJ+iMYDHLhwgVOnjxJQ0MDt99+O+3t7ezbt4+PPvqIkpISOb1xKBSira2NY8eOUVlZyY4dOxgaGuLVV1/ld7/7HYWFhRiNRm699Vbuv/9+ent7ee211zh58iQrV65kenoaURS555575MygBQUFc5J+JTNWsa5Ff+BTkelU6hEEAbfbzZkzZ2hra+P++++nrq6O999/n0OHDlFfX09OTo48+YdCIYaGhjhz5gxjY2NMT0/jdrsRRZGpqSnefvttxsfH+dM//VOMRiMHDx7krbfeora2lk2bNi0Kz/HupRvSe9Pf/0EURcbGxti3bx89PT14vV7MZjN33XUXmzZtmpPZbrlCFEWmp6cZHBykuLiYxsZGysrKmJiYoK2tjaGhIfx+P2q1Wl62DgwMUFpaKtOOjIzQ1dXFyMgICoWChoYG6urqOHjwIIODgwByqtPKykpg9mW6cuUKHR0d+P3+695mj8dDf38/Go2GpqYmqqqqsFqtnD9/nitXrjAxMYHdbkcURWZmZhgYGEAQBJqamlixYgX5+fm0tLTI+xvr6+vldnk8HiwWC3q9Xv5oSlkJJY1Vo9GklcMhUk4KCgrYuHEj+fn5TE1NcfbsWQYHBwkGg3KCN5VKRVFREXv27JG1UZg9XOBwOGhra+Nzn/scDQ0NAGzZsoXm5mZ6e3tjTpZ/yLhpJstgMIjFYmHTpk243W4OHz7MoUOHqKysxGg0LvsXQpo4XC4XpaWlGAwG1Go1drsdrVaL0+kkGAwCyNqFx+MhLy8Pg8GASqWS86K73W6USiUrVqzA5XKh0+nmfOElm5ZU5+DgIFlZWfLy7XrC5/MxPT2NVqslKysLjUaDxWLBZrPhcDhkLUiy5zqdTlQqFVlZWWi1WkwmE9nZ2bS3t+N0OnG73bS2ttLS0mhmoUEAACAASURBVEJ7ezt+v5+7776bnJwclEolfX19/Pu//ztvvvkma9asYceOHdTV1aXNYQFp7F0uF1arFbPZjFqtJisrC4PBwOTkpHzCCmY/jrm5uWRlZTE+Pi6PryAITE5O4nQ65+z/tVgs6HQ6JiYmboql82IiPSRkHigUCnJycvjc5z7H9PQ0fX196PV6pqam8Pl8KS0ZbxRE8bPjcpEeSUlDCIfDc46ISUfGIlPESpNgJG0i22kwGOSTTz7h0qVLNDU1sXLlyuv+UYlss0qlQqH4LMlYpFdb4jmSFma9t1IWSKkst9vN+Pi4PNmOjIwQCoXYvHkz3/nOd/D7/XR2dnL8+HEmJyf5oz/6IyorK5f9B1WCIAiEQqE52Sql/4dCoaTlXeqvyFTRUt9mjrFejUXZOpToXjwjdSLHy7VsvRgbG+PHP/4x7e3tGAwG+vr6WLFixZwJZjGM09E8RvIZi+fo8hLVI6W8lSZCyQ4riiI6nQ6VSiWXIWVoDAQCchsDgQAwm0Nbmngk+mgeQqEQFy9e5J133qGkpISdO3ditVoT9on0bLwxj7ctJJ6DRxRFuc3BYJBgMIggCPL/pWVyZLkqlYpwOCzThkIh/H4/KpUKnU6HxWLh1ltvZe3atYyMjPD+++9z/vx5Vq1axfr16ykvL0cURYaGhggEAly+fJn+/n4qKioSjnuiPok1xrFkerGcJVKWzkAgIH8Yg8Eg4XAYg8EQ04YayWukDKlUKmZmZmQZkiZQvV5PLGQcPAvAtTgz4l2LZQyez6AsaR+HDx+mvb2dr3zlK5SWlvLGG28wOjqaUlnz8ZWojGRp4tWjUCgwGo2yRuz1egmHw4yOjhIMBuXluKQ5GI1GtFotU1NTzMzMyDaoYDBIdnb2HKdFdJ3SRPnqq69itVp5+OGH5eOqiRxV8fiPR5/MdZ1Oh9FoxOv14nQ6Zc1wcnKSrKwsbDabvKxUqVQYjUZ5OR4KhXC73TgcDkwmEzk5OcDsEVyLxYLRaGTFihX09/fLzh1JIzWbzVgsFpRK5VVBHa7FsXe9tg4pFLOn5qSlstvtxmQyMT09jd/vJy8vT/7gRmrg0eWoVCrZntvX1ydrktPT04RCIYqKihaN53j30g03PLtj5O/oL18yZcHsssTlciGKIllZWYRCIYaHh69aSiRT1nz00TymwnM8rUy6ZrVaKS4upq+vj4sXL9LX18fJkycxGAxUVVWhUCh48803+elPf4rL5aK4uJienh4uXrxIV1cXn3zyCUajkaqqKlQqFX6/n5mZGYLBIKFQiJmZGWZmZujo6ODVV19FEAR27dpFQUEBPp9vjpYai99EWuV87Yt3z2QyUVZWhtfr5cyZMzgcDs6ePUtvby/V1dWYTCbOnDnDSy+9xKVLl8jPzycUCnHmzBlGRka4cOECly9fprq6GoPBwIkTJzh69Cjj4+OMjIzQ1tYmf4i6u7sZHBzE6/XS3t7OxYsXycvLo6ysLK4GNl8b4/2O9Rdv3FORR4VCgdVqpaSkhIGBAc6ePcuVK1c4ffo0arWakpISzp49yz/+4z/S09MjryK8Xq+8FS0QCOD3+7Hb7VRXV/PBBx/Q09PDyMgIx44dQ6/XU1dXd1X918pzvHvphhue3XE+jSyZstRqNTt27ODEiRN8+9vfljdw19fXx9SwlqNmCWCz2di+fTuDg4P8v//3/3A6ndTW1vLMM89QV1eHIAj09PTgcDjYunUrd911F0NDQ/zLv/wLbreb+vp6nnrqKWprawkGg/zwhz/klVdeYXJyEoBDhw6xc+dOqqurOXfuHJcuXeKVV15BoVCg1+v52te+xlNPPSVv1YnHfywTQ7w+nO+6Vqtl8+bNOBwOXn75ZX784x9jNpt55JFHuPfee9FoNIyNjdHR0UFBQQHr1q1jenqaX/ziF7z00kuYTCb27t3Lgw8+iNFoZGRkhJdffpmenh5UKhW1tbU8+eSTFBYWcuDAAV599VUCgQBarZZbb72Vxx9/nMrKymtegSTSLOfTpq5Vs7Rardxxxx309/fz3e9+l2AwSE1NDc8++yzl5eUcO3aMCxcuyNr3yZMn+ad/+icuX75MOBzm0KFDvPbaa/z1X/81jz/+ON///vd59NFHMRqN1NXV8Wd/9meUl5dnNMsoKFwzflnqzfrY+83iwel08t3vfpdnnnnmhgfSCIVCuFwuJiYmMBqNGI1G2Y51oyL9CIJAb28vFy5coKamJqlAGuFwmJmZGSYmJggEAthsNiwWi2y7izx9Iv2enJwkEAiQnZ2N2WyWab1er2zbk6DRaObYuyRIS2LJsx4PPp+P3/zmN4iiyN69exdlW5Zkc5ucnJTDm+Xk5Mh9JdnjJMePFIxhamoKg8GA3W6XPf7BYFBexisUCrKzszGZTLKm7XQ6mZqakpfter1etu8utA1tbW2cPHmS++67b8kDaUgrBckMY7fbsVgssk3X7/ej1WrRaDQEg0G8Xu9VRyOlXSJer5exsTEEQaCgoEDur6XgXxq79957D51Ox969exe8E8HtCywSd4lxU3jDYdaeZbPZZCdFun7JlEolJpMJo9EIXP1ljrwuiiJmsxmTyRST1mw2X6UBSvdihVZLRhtaCiiVSrRaLfn5+eTn51/FS/SmcZVKRV5eHrm5uTFpc3JyyM7Olukj+85gMFBQUDDnejrKikqlijn28NkOAem6NGlGQ3omKysLi8Uy51o69slSY1G84VJQhlj3ojs9GY9ZPM/yfM9FInrLyXz01+KtlBCPZ6lfIvsoHA4nVXd0O6LtYrHoI72w0XxG9kUij+58NknJ+yq1KVZ7Yj0nIRlaqe+in4nFt9Q30WMcq/5Yz1/LuMe6FjnGke9DPN6vtZ5k5DEV+uh3bin6Jt47kW5YcFoJv99PX18foihetQxPNEjxhH6xJsvrKZyJJsuhoSGuXLmCRqNBEIQ5e9oWylcszDdZxqovFk28sv1+P8PDwwB0dnbKmu58z0lIdrKM9UwsvhfSN/NdS4Y+ks/e3l5GR0fp6urC6XTG7PNrrWc++kTtvVYZWAqeRVHE6XQyPj5OcXHxvG1YTljwZDk4OMjzzz+fCQIbA6L42akck8kk24LSGdJZY4CTJ0+mzcmXpYY0CUxOTvLxxx+j1+sz70MMiKIon0T74he/eIO5SQ0Lnix1Oh3FxcXYbLaMcERBFGfP8Y6Ojsp2tHSfLCMdRitWrEj7yO+LBVGcjYik0Wiorq7O5OCJA2l1Mjk5KUfQShcsaLJUKpUUFhby2GOPyfsAM/gMoijS39/PxYsXqa6uprKyMm6Em3SB3+/nt7/9LQC7du2SHQx/6BBFkY6ODk6dOsXOnTtvyDn7dICkQBw+fDimSWo5Y8E5eNRqtRz44EafrU3WlnO9IEUHMpvN8mmUdNfEfD6f7GW32WxpEdHpekAQBCwWC2azGZvNRnZ29rKSxeUCaVWSjonuluQET6J7kZ7LaLrIf2Ndi1d+pDcyHA7HrCPZsuajj64zFZ5T5Wsx6BPxFYv3WPVEl5Xq0mm+5+br3/n4j1VXrPIXiz7R8/PxfK31LJQ+kdzGasf14DndkPZnwyWMjY3x5ptv0tTUxLp162Iud5MtKxF9vDKSpZmvHmnCj9xALAWbiC5XFD+LtCOKn+XRkc54S/ek7UfSpu7IFUAoFJoTySdR/pV4/M+HZJ6R+JA0DylYRGSdkjdVoouklfhOtIVNOgceq29j8ZuMnESOhfQ7muf5yroWeYwlJ9FjmEhOpFUhzLVDx5K3xeI53ZEeMamSwOTkJB9++CHt7e0Eg8G0/JJJToKf/exn7N27l4aGBr70pS/xzjvv4PV6r9JgxsbGePHFF9mzZw8NDQ088cQTvPvuu3g8HtxuN7/+9a956KGHWLNmDffeey8/+clPGBoakl8wr9fLyy+/zEMPPcT3vvc9RkdHk+q3xRZ8j8fDRx99xDPPPENDQwPbtm3jBz/4ASMjI1dNfjMzMxw/fpznnnuOxsZGtmzZwj//8z8zNDTEyMgIzz//PDt37mTjxo3ccsst3HLLLXz+85/npZdeoqurix/96Eds27aN1atX89RTT/H+++/LEeTTBYIgMDY2xksvvcSuXbtobGzksccek8c+cgzD4TBDQ0M8//zzbN++XZapt99+G6fTyejoKN/73vdoamqirq6OZ599llOnTske6ww+w5KEaJO+dLFsiJFf4Hj0kTTzlSXdk8J1SUe7pDh9UriyZPhKZk9ZNI+RfMbiObq8RH3i8Xg4fPgwJ0+e5Mknn6S2tpb9+/fzxhtvkJOTw+bNm2UPohTg+PTp03z5y1+mqqqKgwcPsn//fnJycrBarXR3d7N3717+9E//VM7FU1RUxD333INWq+XChQscP36c3t5e+XhldFsjxyrZ5XS89kXfk8atpaWFffv2sXr1av7yL/+SlpYW3nnnHaxWK1/60pdku6h0pHD//v2UlJTw05/+lO7ubt544w1MJhNPPPEEO3fupLa2Vg4i0traSmdnJ8FgkHfeeYdDhw7xN3/zN5SWlrJv3z5+85vfYLPZuOWWW+ZkiExWfpMxVSQjv8nKI4DX6+X48eN89NFHPPnkkzQ2NvLWW2/xyiuvUFRUxLp162Q5CQQCnD17liNHjvDMM8/Q2NjIG2+8wb59+8jNzeX8+fMcP36cf/u3f8NqtfKrX/2KH//4x9jtdlauXHnd94YuZ9zwQBqx6FNdhkvLnnA4TH9/PwcOHGB6eprKyko2bdokJ/pazstwQRCYmJigq6uL0tJStm7dSmVlJTMzM7zyyiv09vaybt06DAYDojibP6Wjo4OysjK2bdtGRUUFMzMzvPnmm/T19bFnzx7+6q/+CoVCQSgUIjs7m1dffRWXy0UgEGB6eppTp05htVpZt25dzP2SqS7D491L9IzH46GjowO1Ws3dd99NY2MjRUVF9PX10d3dzfj4uDxZ+nw+uru7CQaD3Hfffaxbt47Kykp6e3vp6elhenqauro66uvrEUWRgYEB+cxzXl4ex48fZ9WqVdxzzz1oNBqcTifvvvsu3d3dNDQ0XJU9c6HL8FgyEevZVOQxHA4zMTFBZ2cnhYWF7Ny5k6KiIgKBAC+88AI9PT2sWrVK3ucpnZU3mUzU19dTU1NDTU0Nzc3NcrSinTt3cscdd8jRu1588UU+/fRTVq5cuSg8x7uXbripHDxer5djx47xySef0NbWxksvvcR7770nxzJcDON0IkP5fDzH08qk6263m+np6TnBM6SEWlNTU3JwX0mopVS5ZrMZrVZLbm6unIIiFAqh0WhQqVRyKgKlUklWVhaCIHD+/HnGx8dZvXp10kEfEmmVyTwX61kpGIRGo8Fms8m7K7Kzs+UYl9JzUtAQhWI28o5Go8FsNpObm4vf72d6elq22Uofzr6+PjnUm9PppKCgQA42IgXSiOxbid/If6PbkqhP4rV1sZwlojh70MHpdGK1WuVUHDabDaPRyPj4+JwAKTqdjoqKCvR6Pe+99x6/+93v6Orqor6+HrVazfT0NNXV1ajVavlcvUajweFwZBw8UbgpHDzSV1xKevW1r32NYDDICy+8QGdnJw6Hg6ysrKs0h1T5SsTPQjVLURTluJORkc6lqDjRUYL8fj+hUAidTie3S4qmLkXpkZa5IyMjtLa2kpWVRVlZGWNjY7S1tVFYWMiqVau4ePFiTLNBLD6lv1SEP5GMBINBORGbVquVnVA6nU6Ogi49HwqF8Pl8qFSqObR6vV6O0wjImvelS5cIh8PU19cTDocJhUJyJHGFQiGXESsCUzy+U9Es5+uDa9HSpKV1IBCQPxhSIBK1Wj3H/iq9E+Xl5dTX1/P666/zzjvvsHr1au6++265zyJzVEmONSm61WLwHO9euuGmcfDAbOa+mpoabDYbNptN1jgiw+YvZ0imAimtBCBHRo/OQihNprFoJY+3tLQ/fPgwDoeD2267jfz8fC5cuEB/fz9qtZqRkREcDgejo6MMDAxc5SC4Hm2WNMHICT4yJJvEj+TtjdwiJoV3k2hhdgLu6+ujt7eXiooKKisr5RBukQGhpQkyeofAckes9COSZzxyo7cozmbE7OzsZGhoiLvvvpsnnngCk8nERx99JB9blRyiUn9K8pbBXNxUB3sjNR5JgCKTfy1nKBSz8SS1Wi0ej0d2tkxNTSEIAjabTd4OpVDMphbQarW4XC45T4/L5UIQBFmLdjqdvP/++7S2trJ582Y2bdokHzWbnJzkzJkzALS2tqJUKjlx4gTFxcXX9Zy/VqtFp9MxMzOD2+0mHA7j9Xrl8/QWi0XmRaPRYDAYCAQCeDweBEFgZmaG6elp9Ho9WVlZwGyc1dbWVmZmZli9ejU2m43x8XF5yS1NmFJ9Vqs1bU5WSXKi0+mYnp7G6/ViMplwu90EAgE58DUgfyw//vhjAoEAX/3qVykqKuL999/n5z//OTqdDqVSyfDwsPzh8Hg8hEIhcnNzbwptcDFxU02WbrdbNuILgkB3dzclJSVYrdZlfyZbssPl5eXR1tZGW1sb4XCYM2fOoFKpKC0tRaFQcOTIETweD6Wlpdjtdjo7O7l8+TKhUIhz587JqQVmZmY4cOAAJ0+eZMOGDaxatYpAIIBSqeRzn/sc9fX18sTpcrlQKpU0NDRc9zP+RqORoqIimpubaWlpITc3V04itm7dOrKysmhra2NgYID8/HxycnIIhUK0tLTIjqCOjg5WrFhBQUGBvFWmvb2d/Px8amtr5QDBBQUFXLp0idbWVrKzs2lpaSEYDMqaZzpAqVRitVrJz8/nxIkTtLa2Ultby/nz5wEoKiqis7OT8+fPy04bn8+H2+2W/6QEbwUFBZSUlHDs2DG2bNmCTqfjk08+QavVUltbe4Nbuvxw02R3VCqV6PV6pqen+f73v4/H48Fut7Nx40bsdru8lWK+suKVH7m0ibbZJeI5urxE9dhsNjZv3kx3dzf/+Z//CcxOJvfccw8rV65EEASOHTvGxMQETz75JJs2baKnp4fnn38emM35fPfdd1NTU8PAwAC//e1vuXDhAu3t7Rw8eBCTycQdd9zBgw8+KHs6R0dHaW1tRaVSsXr1aqxWa9zJMpGjJhHibR2StKS1a9fS1dXFgQMH2L9/P4Ig0NjYyO23345araa9vZ2TJ0+yZcsWqqurWbNmDR988AHvvPMOALW1tezYsQOLxYLX66WzsxOXy8XGjRspKChAqVSSl5fHHXfcQV9fH//wD/+ATqfDbDZzzz33yM6O6PFIRk4SbR1KRX5TkUer1cqGDRu4dOkS//7v/45er8doNHLXXXdRVlZGc3Mzr732GrW1tdTW1rJu3TpaWlr4+7//e3k3xZo1a9i6dSs1NTX893//N9/61rfQ6/VYLBb27t1LZWVl3LFc6DuUrrgp0kqI4mx6hZ6eHhQKBZOTk/j9fgoKCigtLcVkMt0Q3lJNKyHZmIaHhxkcHJSTSpWVlWGz2QAYHBwkFApRWFgIwJUrV7hy5QqBQIDc3FxKSkqw2Wx4vV76+vpwuVyyw0GlUmG32ykqKpL5CAQCDA8Po1AoZM97osnS7/fz5ptvAixKWgnJsTU+Ps7AwACTk5OYTCbKy8vJz89HqVQyPT2Ny+XCYrHIXu2BgQHGx8cxGAyUl5fLvEtba1wuF3a7fc7k7/V6GRoakvswPz+f0tJSrFbrVZktU8X1TCsRKScDAwPy2JeVlWE2m3G5XIyMjFBaWorZbMbtdtPf38/o6CihUAibzUZxcTF2u51wOExfX598WKGkpEQuZynemT/otBKRX9JkNI5kv9bJfLUi7+n1eurr6wFkI3XkCzAfb6l++WJpS7HaEb21KDKCeyxImRwrKioQBOEqm2t5efkc+hUrVlBVVSXXLf1ZLBbWrFmTULuHWZthWVnZVe2I1+ZE2R8TIVH/ajQaCgsLyc/Pl9scSWu327Hb7XIZer2evLy8mDZplUo1Jz1FJIxGo/zRkuQjmXbP147oMY63dShVmU5WTiRaqT3R/WWxWFi9erW8/1TqX0njq6+vZ+XKlYiiOOeYYyJZTbU9sZ5PNyyKzTL6JUqGfr5rye7jindPEoRUBuVaBzDyucj/R6ZfSPWjAiQ87xyNyBf+Wvsy2ckicuJf6LhHI/IUTaznIv8fr3+SqSfaGZgK4vVddN8k+kglw2uyfEVObonKiNzSFC0nkZNnvP5Ohr9klJI/2LQSLpeLU6dOMTAwkPY2icWGdIa3p6eHiYkJ+vv7035LRiAQ4OLFi8Bsoqt0DLW1FBDF2dilbW1t8qb6zPtwNURxdlN9T09P3NzkyxULmiwlj/PBgwfTYnvO9YYoivJm6MgoOukMyT4siiK/+MUvMuP+fxBFkVAoRCgU4te//nWmXxJAFEUKCwuprKxMKw1zwcF/q6urefbZZykqKkr7iWCxIYoiIyMjdHV1UVJSQnFxcdprlsFgkMOHDwOwbds29Hr9DeZoeUDSLFtaWti6deucVLwZfAZRnD3We+HCBfmgQLpgwWklzGYzDQ0NN9QbvlwhecPVajUrVqyY1xu+3CF5w6WTHxs3bsxESv8/CIIgn2dvampaUm94OkPyhk9NTaXdfLEoZ8Mjg85GIpHncLH3WS50z9e10Ef2QTyeJc9jpAdysfiKhVgeeYmvePXFoklUtkSX7OmoWDsH5qsj2d0GC/UwL1ROJD4jxzdyzBernvnoE7X3WmVgqXhe6DatG4UlPcETr0NSuZ6oU1PtcIk+2edSKT+WwEU/P1+7400K8ehT8VTGKjN6UlpqLOa2kmhPdqwJLLruZCeaVOQkXh+mKjup0CX6GMS7H+taoj5cKK/R9Ok4OUbjuh93TGYgF2PSvNZBXUj5CxU2UZzdbNzR0cH58+eZmJigsLCQDRs2UF5eLgdJkITb6/XS3t5OS0sLk5OTFBcXs379ennfZFdXF+fOnWNkZASbzcbatWupra3FZDIhirObwdva2mhtbaWiooLGxsYlORc+X3nBYJArV65w9uxZenp6MBgMNDU1sWbNmqvybweDQUZHR2lubqarqwutVktjYyNr165Fp9MxNTXFxYsX+fTTTwkGg1RUVLBhwwZyc3Pp6+vj448/xuPxAGA2m1mzZg319fVJnw2PN+7zTfBLpQhITkQpNmVfXx9Go5H169fT2Nh4lV1QGneHw8GFCxfQaDTceuutMW3PS/3OpRtuqrPhEHu/ZTpAEuILFy6wb98+ZmZm0Ol0nD17lq6uLh599NE56YYDgcAcWq1Wy7lz5+jp6eGhhx5CpVLx+uuvMzAwgFqtZnx8nHPnzvHYY4/R1NQkRxzav38/Bw4c4L777qO8vByj0ZhQA47U0Bar3QMDAxw4cIDLly+TnZ3N2NgYLS0tPProo/KZZQnDw8McPHiQlpYWbDYb09PTnDlzhkceeYRNmzbR2trKiRMn8Hg8TE1Ncfz4cUZGRti9ezctLS28/PLLWK1WcnNzycnJkc+TLxaut7wJgsDw8DCvv/46n376KXa7XW73V77yFW677bY5K5GZmRmam5t56623OHv2LLW1taxfvz6zBSwJ3DSTpbTZ1e12MzAwgN/vp7CwELvdnvAI33KBKM7mUz537hyBQIA9e/ZQVVXFe++9x4kTJ2hvb6esrAyNRoMoijidTpqbmwmHwzzwwANUVFTw7rvv0tzcTEdHBxs2bGD37t1yvMfTp0/z4Ycf0tnZSX19PSqVio8//pjh4WGMRiMzMzOLOmkk22a/38/Fixfp7Oxk69at3HrrrfT19fHrX/+aU6dOUV9fT15eHgrFbNTv9vZ2Ll++zMaNG7njjjsYHR3llVde4ejRo9TX11NXV0dJSQk6nY6enh5effVV2tvb2bJlCzMzMxgMBvbu3cuGDRvQarVpFXEoFvx+P21tbXR2drJt2za2bdvGlStX+NGPfsTBgwdpamrCaDQCnwWNHh4epri4mIGBgbhxKzO4GjfNZCkIAoODg/z85z/n9OnTKBQKysvLeeyxx+QXY7nD6XQyPDxMfn4+NTU1lJSU0NjYyOnTpxkZGcHv98uT5fT0tEy7YsUKSktLWbNmDS0tLYyNjaHX61m3bh0KxWwMx7GxMXn5HQ6H6e3t5dKlS5SWluL3+2+YZ1I6r61Sqaivr6ekpASj0UhJSQmjo6OMj4+Tm5sLzEZVHxoaIhwOs3LlSkpLS7HZbFRVVdHe3s7U1BQNDQ2ytuhwOORo6tJyXqfTUVhYSEVFRVzHZDrB7/fT19eHRqNhzZo1lJaWykddz549i8vlkgMeK5VKsrOzufPOO+Xz9VNTUze6CWmDm2ayDAQCHDt2jE8//ZRnnnmG2tpaHA5H2pykEARBzsooacNKpVJOteB0OuWMe5IG7fF45KAYCoVCTkXhdrsJhUJyu71eL729vXIuGr/fz9mzZ1EoFKxfv56xsbEb1kczMzM4nU45CpBSqcRoNGK1WhkeHpbtizA7MbhcLnkCVKlU6PV6bDYbwWAQp9PJ5OQkH3/8sayNW61WPv/5z2O321GpVHz66ad84xvfIDc3l82bN/Poo4+ybt26OUFz0wmBQIDJyUm0Wq0cMEar1ZKfn4/L5WJmZkamVShmI6dnZ2cjiuKCA1j8oeGGZ3eMt+Um0bVY9fj9fs6cOUNxcTGbNm0iNzeX2traOVs4FmPbQ7ytLYl4jiwvUZ9E34/cqiPdk/4i80VLiGynVGYgEODy5ct88sknrFy5ktraWrq6uujp6ZE1ueh82onGKrLsaMTzqsbbOhRZXuT16DbHqjuyn6X/S22IjKLe1dXFhQsXqKur484772T16tUEg0Gam5vZt28fP//5z7FYLHMyGV6L/MZqUzSWYhuOtFKILF/qk+gxjbXrYr5dBanyHK+MZLc7LWfc8OyO0S9JMtdi3RPF2YRlubm5cqKu6GdT4StVfpKliVePQjGb9F6twHMNdwAAFyVJREFUVstJ7xUKhRwF3WAwyMclI3OuBAIBOYCCRCvl7QmFQvT29vLGG29gNpvZuXMnWq2W5uZmhoeHsdlsuFwuurq6UCqVnD9/HovFQk5OTkxe4/GfqA/nu65Wq9FoNHJeGcnRFQgE5CjqEq10ZFRKeQyz3nGfz4dGo8FoNGK329m9eze7du1ifHyc/fv309zcTENDA5s3byYvLw9RFCktLcXlcnH27FkGBwfnBLu9FvmNnCgi/xJhMeRRpVLJ+Yqk9BDhcJiZmRmMRqO86oh+V6J5XAgP10qfbrhpsjtKEaRdLhdOpxOfzycvQ6TJJJmyEvEVi8dUeI6ncUjCazKZMJlMTExMyCkD+vv7CYfDc7I8Tk1NodPpMBgMOBwOpqamZNtfOBwmNzcXpVJJV1cXv/zlL1EqlTzwwAOUl5fLS3spkPD+/fu5fPkybW1tnDhxYk5Wv2T5T9SHsfoqElLA2ZmZGRwOBz6fj/HxcRwOBzk5OWRnZzMzM8Pk5CThcBiz2UwgEGBsbIyZmRkmJiYYHh4mKyuLnJwcPB4PXq8XQRDQarVkZ2ejVqvxer1ykjdRFOX8NVJu+VjtSEZOotsVSy7mK2sh8ihlqfR4PIyNjckZMDs7OykrK5P7dmxsDLfbLU+mUlI7KXZBZC6nVHm4Vvp0w02T3VGr1bJ+/Xpef/113n77baqqqpiammLlypU0NDTM8YgvR80SIDs7m8rKSg4dOsQHH3xAWVkZR48eJScnh+rqagRB4De/+Q3T09PceeedVFZWcuTIET744ANKSko4ceIEOTk5VFVVMTExwY9//GO6urq499575Zw7eXl5PPjggzz22GMAjIyM8IMf/ACVSsVXv/pVysrKrorzGM1/LBNDvD6c77rJZKK6uppPPvmEjz76CK/XS0dHB6Ojo9x3330YDAbOnDnDhQsXWL16tWyjPXz4MIFAgKGhIfr7+9m+fTt6vZ7jx4/jcDgoKCjA5XLx8ccfYzKZyMrKoqWlRc5Z093dzaVLl6isrKSioiJlmYv+HUuzTLashcijXq+ntraW48eP8+677+J2u7ly5Qr9/f088cQTaDQaWlpaePfdd9m6dSu33XYb/f39tLe309/fj9Pp5MyZM1RXV1NdXT3H2ZXRLOfiprHwarVatm3bxsjICKdPn+bjjz+msrKSVatWpc3xKrPZzLZt2+RtQSdPnqS4uJhdu3bJeyyldpjNZm6//XZcLhfnzp3j1KlTlJaWsnPnTiorK+nt7UWj0aBWq/noo484dOgQJpOJrVu3smfPHkwmEzAbRLa+vh6lUnlDIsprNBrWrl0rJ1f75S9/iV6v58477+T2229Hp9PJmpp0xt7v9/O73/2O//3f/0Wn03Hrrbeyc+dOea9gc3MzY2NjABQXF3PvvfdSUlLCkSNHOHz4MKFQCKVSSX19Pbt376a4uDgt5CMWtFot9fX13Hfffbz99tv86le/Qq/Xs2fPHrZv3z7nw6dQKHC73fz+97/n8OHDuN1uFAoFr7zyCnfccQfV1dU3uDXLGzdFWgkJoijKSbgEQcBqtc7JiXy9kWpaCfisDVNTUwSDQaxW65xJTLJLSpqy3+9nenqaUChEVlYWRqMRlUolZ0mUMhlKk4FWq5VtmhKPPp8PhUIhZ/tLBJ/Px29+8xtEUVyUtBJSm8PhsJw+wmQyybsAAHmZKNkspf2CTqcTg8EgL7Wl9ng8HpxOJwqFQu4ThWJ2C5XT6cTtdmMwGLDZbLIXfKGT5fVMKxENyazgcrlwuVwYjUZycnLksZSW3Wq1GpVKhc/nk+UIkMde2mK0lPiDTiuxnCANupSfRrqWTlAoZtMmFBQUzLkmIfpYmsFgmHNNolWr1Vgslrh1SJC26qSCxbY/SY6enJwccnJy5lyHWe0zMrSdZHeV8hJF0qpUKiwWy5y2R5YjpVyIvJ7uUCg+2xIkhYaLbJvkOJRgMBhinti5WfpjqbCoOXgir0Ui2q4TeT3VFy9yQGOVF6/MeDxF30tUfqqYb+tLIt4i2xG9VSQWbXR9iQQ/UbvmG6tYzoxUy0mGj2TuJ6prvv6NR5+KnCRyYC5WvyTTjsh78cpPBpFlXM++TBcsOK2E0+nk6NGjdHV1Zb5MUZDSSvT19TE8PExnZ2faB/8NBAJyjmpp6ZbBZ2fc29ra5I3ymffhaojibFqJjo4OVq1adaPZSQkLniylKDDhcDgjHFEQRZGJiQkcDgcKhYJwOJz2pyZCoRCTk5MADA0NpXUw48WEKM5GxZ+cnOTKlSuy8ySDuRBFUT61lW7a5YLTSlitVnbs2EFVVdUNd/AsNwiCQH9/P59++ilVVVVUVlamxRn1RPD7/fKEf++99yaMUvSHBEEQ6Ozs5PTp09x9991y8I8M5kIQBJxOJ7///e/TTnFY8GSp0Wiw2WzY7fZlN1lG2vpuBKQz3BaLBZvNRk5OTtprYj6fD4vFgiiK5OTkZNJK/B8EQcDhcGA2m8nOzsZut2cmyxgQBAGVSpWyU3E5YElO8My3yz+ek2C+0zCxTk/Eq0c6Fxt5KmExTh/Ec9gkc2ojnuF/KekT8ZWob2Ndn895MV85iZ6L1bZYfZyo/fF4WEr6RH0Uqw2p1LOY9InkNlY7loKHdMdNczY8Gg6Hg3PnzpGfn09dXd2ciNHL9QSPZNcMBAL4/X7C4bAcWUeKQhRJLwgCgUAAn88n20MNBsOciOqCIOD3+4H/3975xTR5vQ/8Q0tbrFKoQIHyn/JfTCa6zIHLZJmCzuiyxGTJsmV3u9nVEu+2m90tu3LXZlEvdsGibk6JGnHqdLoNZ1QcpajAoCh/7B8KLS0t7/eCvOfXspYWxT/4O5+EAO3p6TnnPe/zPuc5z3meBbcjjUaDoiz4cs7Ozgr/RaPRiE6nW/IER/TplHiTP5EmlUzDUm3fs7OzhEIhNBoNGRkZIqxa9PiogTJUX8G0tDTWrFkjNHb1jHn0QzL6LH04HBZHYHU6nRjbRNcjWV8W7/xGj1Gyfj/NfFTniXrt1b5EX8N48yQcDgtfWzXcXygUEmOi1+tj4hCsZJtXO6vLaLAMRkdHOXnyJJs2baKsrGxVLH8VReHx48dcvXqVq1evMjY2RlFREe3t7WzevJl169bF3ACTk5Oi7Pj4OKWlpezcuZOmpiaMRiMzMzMMDAxw6dIl0tPT2b17N8XFxbhcLq5du8bly5dxOp3k5+ezZ88e3njjDTIzM1MSbivJzMwMd+7coaurC4fDIU7wvPvuu+Tl5QkHelgI6Wa32zl//jy9vb0iLUJ7e7s4BnnlyhV8Ph+KsuCsnZ2dzTvvvENjYyPd3d1cvHgRn89HRUUFbW1tNDU1/Sd9xcvM/Pw8LpeL33//ncuXLzM5OUlRURE7d+6MmSeqtjgxMcHFixf57bffmJqaoqSkhJ07d7Jp0yYCgQDnzp3j0qVLzM7OUl1dzd69e2loaJBpjhfxygTSUG8Mv9+Pz+cTT9HVsgxXlIWoSdevX+fs2bNYLBba2trwer38+OOP9PX1iXBb8/Pzouy5c+ewWCzs2LEDl8vF8ePHcTgcBAIBuru7OXLkCCdOnKC7uxuPx0MkEhGbTgUFBTQ3NzM+Ps7hw4e5e/du3PFK1v5kJFqKqtfMbrdz4sQJfD4fe/bsoby8nNOnT3PhwgUCgYD4bCQS4cGDB5w4cYJHjx6xY8cOampqOHPmDKdPnyYUCmGxWKirq6OxsZHq6mp0Oh2Dg4OMjo7S1dXF8ePHqampob29XYyX3W6PiRK/nHmSzFSR6vxN9j3Rdfv9frq7u/nll19Yv349bW1tzMzM8MMPPzA4OBhzDYPBILdu3eKnn34iPz+f9vZ2JicnxZw6c+YMx48fp7m5mb179/Lw4UMOHTrEyMiIXIYv4pUIpAELobocDge3b9/G7/czPT2Nx+OJmTgv8zJ8fn4et9uNw+EgPz+f9957j6qqKnJycujo6GBgYEAk8FIUBbfbTV9fH4WFhezdu5fKykrMZjMnT55kYGCAkpISwuEwO3bsYP369bhcLhRFQavViiRd6jKsuLiYjo4OHj16JAzwicbkSViqnkAgQH9/P6FQiA8++IAtW7YwPj7OoUOHsNvttLS0iHPswWCQ+/fv4/P52LVrFy0tLXg8HgKBAL29vbS2trJ161aam5sBcDqd/PzzzwwPD5OTk8Nff/1FZWUln3zyCTqdDpPJRFdXF/39/dTW1ord2ZVahqda13LmYyQSwePx4HA4yMrKYv/+/RQXF2OxWDh69Cj379+nurpamFvm5ubweDxkZGTw1ltv0djYiNfr5ebNm4yMjHDt2jVaWlr48MMPURSFrKwsDh8+jN1ux2azrUibE7232njuy3BFST0X8+LX4g24+rR1Op0cPnyY8fFx8vPzcTqdIrzZ4jpSaUMq5VWib5hE5VPpx/T0NF6vl9zcXHFu2Wq1kpGRgdvtJhgMCmGpno0uKCjAZDKh1+vJz88nIyMDr9eLXq+ntbUVn89Hf38/LpdLtFU1SSjKgs/bzMwM69atw2QyPZNJHe96qvj9flwuFwaDgZycHHQ6nUgoNjw8jNfrFWM2OzuLy+UiPT2dvLw8DAYDJpMJi8WC0+nE7XZjs9lIS1vI1zM8PMzQ0BA2mw2TycTU1BSNjY2YTCYikQgWiwWj0SjGdvEO7XLmSby/n6SuZOXVeeLxeMTxUL1eT25uLkajkcnJScLhsLDRGwwGEampq6uL4eFhhoeHaWhoQKvV4na7qa2tFXbb3NxcDAYD4+PjT9S+5dxDq43n7uuT6tN6Kc1tMfPz89y5c4d79+6xf/9+Dhw4wL59+0QQ28V1rMRTMZ4RP5Wn6FKTLxgMEgqFMBgMwsC+Zs0aEfxAjQCuKIrYDMnIyBAakfq3usGhBp5YanyHhoa4e/cu5eXl2Gy2Jd2/Ut24SPS5eKgbO+np6SKQh7oBEQ6HYxJqqWXVMhqNBp1Ox5o1a2I2sgC8Xi+9vb2EQiHq6+sxGAzMzc0JgagKEq1WKzbT4rV7ua8l6meqdSUrH705p27maTQaDAYDOp0uJvFcWtqCa5/NZqOuro5ff/2V7777jn///Zf6+nr0ej3BYJDMzEyRi0g9hx+djuJp+iM1y6dgpTVL9b2RkREyMzOpqKjAbDZjs9mwWq0xjq/PUrOMbvOTPJEBEUouOhWAOvHT09NjQs2pf6sCNFHZRHYkNYXq+fPniUQitLa2UlhYuOSkTmR7TEY8LTx6LKLTWqj9iEQiaDSamOunCt3FqSPUslqtViw9h4aGhDmirKyM0dFRNBpNjFBUv08dr3jtftk0S0AItkgkEmPHVhQlZjdcjSg1MDAgbLwmk4mBgQGuXLkiQrKpAZHVzyhK8vw8/x81y+cuLJdjB0r2mop6A6uTSL2pFt8AK61ZJvr/STQGVdPR6/XMzMwI7XBqaor5+XlMJpOwMQJCq5ienhbpGHw+H+FwWCQui7fJoP6MjY3R2dnJyMgI27dvZ+PGjc8saddS2paaOiIYDOL3+4lEIgSDQaanpzEajSJ6kCoIjEZjjPvP7OysSHhmMpkA8Pl82O12/H4/zc3N5OTk4Ha7MRgMIpydupydm5sT45VKu5fS+JL1NdVxWaq8Ok8MBoPICLB27VoxZ8xms3hoqLvmf/75J4FAgI8//hir1cqFCxfo6OgQgnViYkIIyUAgwNzc3H9WZU8zNsn6ulp4uY7cPCFpaWlYrVYeP37MgwcPmJiYoLe3l8HBQRHP8WUnLW0hO6PZbBb2VpfLRU9PDwDFxcVotVr+/vtvrl+/LlxinE4nIyMjTExM0NfXh0ajwWq1otPpRMoA9ffc3Bxzc3OMjY1x6tQp+vr62LZtG5s3bxbll9Ian3QZvhRr167FYrHg9/t58OABfr+fgYEBRkdHsVqtmEwmBgcHuX79Og8fPiQrK4tQKMS9e/fw+XwMDw8zODiI1WolPz9faMwOh4OcnByqq6vJyMjAbDazfv16HA4HQ0NDeDwe+vv7CQaDlJaWrho3GY1GI1JoPHr0iMHBQbxeLw6Hg0gkQkFBAU6nk87OTsbGxkTWS9W/UvWp1Wq1mM1mLBYLf/zxBy6XC7fbjd1uR6PRUFVV9aK7+tLxwrM7xisfb0m7VF1arZampibOnj3LwYMHycvLEy4n0drlSizDF7cxup3x2ry4vqW+x2w209TURE9PD99++y06nY7Z2Vna2tqora0lHA7T2dnJxMQEn376KZs3b+aff/7hm2++Qa/Xi93vmpoawuEwx44d4+zZs9jtdgKBAENDQ7S2tmIymTh16hQjIyP09PRw5MgR9Ho9+/btY9euXWRlZcUdk2TL8ETaVaJlOCxELtq4cSO3b9/m+++/59ixY3i9Xmw2Gy0tLaSnp3Pz5k2uXbvGtm3bqKiooLS0lI6ODjo7O/H5fBQWFop+qbvrLpeLt99+m4KCArRaLRaLhTfffJNDhw7xxRdfYDKZCIVCtLW10djYGOPLuZx5kugax5vTyzXzJHotKyuL1157jRs3bvD111+TnZ1NIBCgtbWVoqIibty4wdGjR/nqq6+ora2loaGBq1evcuDAAXJychgbGxPja7PZOHjwIJ999pnYBHv//fcTRk1fSVPWauOFn+CJVz7ekjZZXUVFRXz55Zf09PQQiUQoKytDURSys7OF68lKLMMT1ZFqmaW+R02RUFpaSl9fH9PT02LjRV1ifvTRR8zNzVFUVER6ejplZWX09fXh9/spLy+nsrISk8mEoihs3bqVkpISsfGh0+nEDnBdXZ2IjJOWtpA5sbS0NCbkWqrtX2oMk72u1Wqpqqri888/p6+vTzjJNzQ0iCC9qsuLGvC3qKiI7du3MzQ0hNlsZsOGDVgsFmF7fP3116mpqaGgoIC1a9eSlrawUbZ9+3aqq6u5e/cuoVAIm81GVVVVjLP/Utcv0ZjA83MdgoWNvC1btmC1WsU8sdlsVFZWYjQaMZlMVFZWUl1dTWZmJrt372bDhg309/cTCAQoKSmhurqa7Oxs6uvrqaqq4tatWwA0NDRQWVmZ0El/JU1Zq40XrlkupZGl+mSGBSN9UVERhYWF4v3oC7Wcupbqx7PULGEh7UN5eTmlpaXMz8/H2GEVRaG8vBz4vxzhFRUV4sGQlpYWU1a9gRaPc1paGmVlZf/57sXCMN61WmqZ/iSaJSA0v9zcXNGe6Lbk5uaSm5srPp+Tk0N2djZbtmyJsVGrP1arFavVKsZJrTMjIwObzfafMYzX7+XO3+j3F4/TSmuWsPBgjXftAfLy8sR4qZHw6+vrqaurEymWozcLq6qqqKqqEvWoWvZKtllqljybjZHlPuWjfyc725xqu5bbnpXQLKPfixaS0eWil4vRZeO1IZ7AVt9L9Hqy/5PVG49kN4n6fqJrl0jAJiqb7Lonc7p/kvkbT7NM1oeVmI+pjJlaJtosFf2+uiH0pG140vKrjacWlpFIhKmpKVwu10sXou1FoygKXq+X6elppqamcLvdr0Q8y5mZGRRl4RRRKPR8kkW97CjKQtaAmZkZPB7PM/MsWO2o90QgEFgV8RqieWphqdFouH79Or29vSvRnlcK9QaamJhgbGyM3t7euJrhaiISiXDv3j2hiax24b+SPH78GKfTycWLF4WdXPJfZmdnmZycjEksuBp4qlS4oVBIuB28CjaJlWY5S9XVxOJ+vQp9elqi7dGvio3uWaCOi9FopLa2luLi4qdekT6vVLhPJSwlEonkRfO8hKU0MkokEkkKSGEpkUgkKSCFpUQikaSAFJYSiUSSAlJYSiQSSQpIYSmRSCQpEOOU/ry24CUSiWS1ITVLiUQiSQEpLCUSiSQFpLCUSCSSFJDCUiKRSFJACkuJRCJJASksJRKJJAWksJRIJJIUkMJSIpFIUkAKS4lEIkmB/wF1s8DqtFEmgwAAAABJRU5ErkJggg==)
Select the rate law that correspond to the data shown for the following reaction.
![](data:image/png;base64,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)
chemistry-General
chemistry-
Select the rate law that corresponds to the data shown for the following reaction.
![](data:image/png;base64,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)
Select the rate law that corresponds to the data shown for the following reaction.
![](data:image/png;base64,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)
chemistry-General
maths-
is relation on
given by
Which of the following belongs to
?
is relation on
given by
Which of the following belongs to
?
maths-General
physics-
Two magnets A and B are identical and these are arranged as shown in the figure. Their length is negligible in comparison with the separation between them. A magnetic needle is placed between the magnets at point P which gets deflected through an angle
under the influence of magnets. The ratio of distances d1 and d2 will be
![](data:image/png;base64,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)
Two magnets A and B are identical and these are arranged as shown in the figure. Their length is negligible in comparison with the separation between them. A magnetic needle is placed between the magnets at point P which gets deflected through an angle
under the influence of magnets. The ratio of distances d1 and d2 will be
![](data:image/png;base64,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)
physics-General
physics-
Two small magnets X and Y of dipole moments M1 and M2 are fixed perpendicular to each other with their north poles in contact. This arrangement is placed on a floating body so as to move freeely in earth's magnetic field as shown in figure then the ratio of magnetic moment is
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)
Two small magnets X and Y of dipole moments M1 and M2 are fixed perpendicular to each other with their north poles in contact. This arrangement is placed on a floating body so as to move freeely in earth's magnetic field as shown in figure then the ratio of magnetic moment is
![](data:image/png;base64,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)
physics-General