Maths-
General
Easy
Question
Statement - I :
attain its maximum value ![text at end text x equals fraction numerator pi over denominator 3 end fraction](data:image/png;base64,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)
Statement - 2:
increasing function in ![open square brackets fraction numerator pi over denominator 6 end fraction comma fraction numerator pi over denominator 3 end fraction close square brackets text . end text](data:image/png;base64,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)
- Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
- Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
- Statement-1 is True, Statement-2 is False
- Statement-1 is False, Statement-2 is True
The correct answer is: Statement-1 is True, Statement-2 is False
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maths-
denotes the greatest integer function, is continuous and differentiable in (4, 6) then.
denotes the greatest integer function, is continuous and differentiable in (4, 6) then.
maths-General
maths-
denotes greatest integer function)
denotes greatest integer function)
maths-General
maths-
If graph of the function y= f(x) is continuous and passes through point (3, 1) then ![stack l i m with x rightwards arrow 3 below blank fraction numerator l n left parenthesis 3 f left parenthesis x right parenthesis minus 2 right parenthesis over denominator 2 left parenthesis 1 minus f left parenthesis x right parenthesis right parenthesis end fraction text is equal end text](data:image/png;base64,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)
If graph of the function y= f(x) is continuous and passes through point (3, 1) then ![stack l i m with x rightwards arrow 3 below blank fraction numerator l n left parenthesis 3 f left parenthesis x right parenthesis minus 2 right parenthesis over denominator 2 left parenthesis 1 minus f left parenthesis x right parenthesis right parenthesis end fraction text is equal end text](data:image/png;base64,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)
maths-General
maths-
A function f from integers to integers is defined as
then the sum of digits k is
A function f from integers to integers is defined as
then the sum of digits k is
maths-General
maths-
Let f(x)
a prime number. The number of points at which f(x) is non-differentiable is ( [.] G.I.F )
Let f(x)
a prime number. The number of points at which f(x) is non-differentiable is ( [.] G.I.F )
maths-General
maths-
If graph of the function y= f(x) is continuous and passes through point (3, 1) then
is equal
If graph of the function y= f(x) is continuous and passes through point (3, 1) then
is equal
maths-General
maths-
Let f be twice differentiable real valued function satisfying
where
and
then
Statement -1:![vertical line f left parenthesis x right parenthesis vertical line less or equal than 5 for all x greater than 0](data:image/png;base64,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)
Statement -2:
is decreasing ![for all x greater than 0.](data:image/png;base64,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)
Let f be twice differentiable real valued function satisfying
where
and
then
Statement -1:![vertical line f left parenthesis x right parenthesis vertical line less or equal than 5 for all x greater than 0](data:image/png;base64,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)
Statement -2:
is decreasing ![for all x greater than 0.](data:image/png;base64,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)
maths-General
maths-
Let
Then which one of the following is true ?
Let
Then which one of the following is true ?
maths-General
maths-
andE..
then-
andE..
then-
maths-General
maths-
If for a non-zero x, af
where
then
f(x)dx=
If for a non-zero x, af
where
then
f(x)dx=
maths-General
chemistry-
Which of the following is correct?
Which of the following is correct?
chemistry-General
chemistry-
In the thermal power stations, electricity is produced by producing heat energy from the burning of coal. This is an example of ..
In the thermal power stations, electricity is produced by producing heat energy from the burning of coal. This is an example of ..
chemistry-General
chemistry-
Burning of a candle is an example of ..
Burning of a candle is an example of ..
chemistry-General
physics-
A bob attached to a string is held horizontal and released. The tension and vertical distance from point of suspension can be represented by.
![](data:image/png;base64,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)
A bob attached to a string is held horizontal and released. The tension and vertical distance from point of suspension can be represented by.
![](data:image/png;base64,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)
physics-General
physics-
A ball whose size is slightly smaller than width of the tube of radius 2.5 m is projected from bottommost point of a smooth tube fixed in a vertical plane with velocity of 10 m/s. If N1 and N2 are the normal reactions exerted by inner side and outer side of the tube on the ball
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qKiYmhli1bcp/bu+++y4tfLMuSWq2mmzdvUs+ePbnPw9zcnObNm2f0HBLLsrR7924Si8UEgIKCgujhw4dG9amxU+9CUVBQQEOGDOGara5bt66+TdSK8vJyOnXqFHXt2pVLUDo7O9PMmTMpIyPDID7k5+fTmDFjCAD5+fk99bVZWVn06quvcovkPvnkE173KCkoKKAPP/yQWrRoweUG3N3dac+ePVRYWMib3WfBsiy9/fbbXI3F/PnzhdXERqRehUKpVNLKlSu5DPvkyZMpPz+/Pk3UiuLiYlq1ahW5uLhwd+mBAwfSoUOHDJrAq41QEBHduHGD/Pz8uKHKoUOHeI/IwsLCKDg4uFrPy7fffpsePHjAq92noVQq6bXXXiOGYUgmk9H69euNPnxtrNSbUOh0Ovr111/JycmJ6ylx69Ytow05kpKS6NVXX+V2EZPL5bRq1SpKTU01+I+ttkKh1Wppx44dZGZmRgzD0IgRIyg9PZ1XH1mWpdzcXPrhhx/I0dGRy9/07NmTbty4wavtp3H9+nXq3LkzASBbW1v6/fffjeZLY6behOLevXvcNKNYLKYjR47U16lrhU6no9DQUHJzc+OGGm5ubkbd+q62QkFUNXWrF11bW1s6e/Ysz17+jwcPHpCvry83FJFKpbR7926jTaPu2rWLbGxsuM9PKMYyPPUiFCqViiZOnMjduT/66KP6OG2tKS8vpy1btlCzZs04X8aMGUM3btwwajK1LkKh0+m4btYAaPPmzQaNhLKysmju3LncBWphYUHLly/nZR3Ls6ioqKB33nmHGIYhsVhM8+bNo9LSUoP70ZipF6HYsWMH1zF70qRJRkk65eTk0KJFi7hFZ/b29vTFF1/wHrLXhLoIBRHR8OHDOaH44IMPDH5HLygooO3bt5OrqyuXnA4ODqbk5GSD+kFU9f0OHjyYK6c/evSowX1ozDy3UCQmJnJ38I4dOxplPKtfK6DPkLds2ZJCQkIaTHv/ugrFwoULjSoURFVbB8bFxXF5ArFYTB06dKBr164Z3JekpCROtNq1ayfsWG9Anqv/mFqtxtdff43MzEyYmZlh2rRpaNeu3fOcstbEx8dj+vTpOHz4MDQaDTw8PLBp0yYMGjSowa2UrC2ZmZncYycnJ6NUtEqlUvj4+GDv3r3o0aMHiAg3b97E+PHjcfbs2cf2yOALV1dXrFixAjKZDH/99Re++OILXpsECfyNuioMy7J06tQpLmk4ZMgQysnJqUcNezZhYWHcnQ4AtWnThk6cOGH04q5/UtcchT45rFAo6I8//uDZy2dz7do16t+/f7W+F3v37jXo552WlkYjRowgkUhEDg4OFBERYTDbjZk6C0VRURGNHz+eRCIRWVlZUVRUVH369UwuXbrElfkCoB49elBkZKRBfagpdZ310O+H4e3tTTExMTx7WTNu375NI0aM4D53Z2dnOnz4sMHs629Qjo6OJBaLadKkScL+pgagzkJx8OBBbkn2pk2bDHpXuXfvHr3yyitc6XFAQADdunXLYPZrS12EYu/evVwNyBtvvEFFRUU8e1lz8vPzacKECZxYNG/e3KB3do1GQ0uWLOESm4YoSGvs1Eko8vPzyc3NjRiGocGDBxt0KXB+fj7NmDGDE4l27drRlStXDGa/LtRWKLKysmjYsGHccnBj1aQ8jYcPH9Lw4cO59Rg9e/aku3fvGuyCVSqV5OvrSwCob9++QlTBM7UWCo1GQ2+//Ta3su/06dMG+3GoVCpasWIFF8l4e3tTaGioQWw/D7URiuzsbFq2bBmZmpqSXC6nlStXNtg1Drdu3aK+fftysyETJ0406AUbGhpKjo6OJBKJaMOGDQaz2xiptVBcunSJmjRpQhKJhP71r38ZrFOSTqejL7/8kmtR5+Pj88IksrKysqhXr15PFQqtVkvHjx+nAQMGkIWFBTk4ONDWrVupuLjYwN7Wjjt37lCPHj24Are33nrLYNO4fy/EcnZ2ppSUFIPYbYzUSigqKipo9uzZXMY5PDycL78e4fDhw2Rra0sAyM3Njc6ePfvCjEvv3r3LrZ9wcXGhjRs30tGjRykhIYGOHz9On3zyCfXr14/Mzc2JYRjy9fWlkJAQ0mg0xna9RqSkpFRrY2fIFcNnz57laivmzZtnMLuNjRp3uCIihIWFYdq0aUhKSsLYsWPx66+/GmQruNu3b2PmzJm4fPky7OzssH79ekycOLFBb0PHsiwuXLiA8PBwhIeHIyMj47GvYxgGMpkMXl5eCAwMhJ+fHzp16vRCdXQiIoSHh2PWrFlISEiAk5MTdu/ejT59+vD+HZWUlGD27NnYv38/mjVrhoMHD6Jbt2682myU1FRRVCoVvfXWW8QwDJmYmFB0dDRf4lUNpVJJM2bM4ErEG/KY/Z8UFhZSRkbGM4/i4uIXJjp6EhqNhrZv305mZmYkEomoX79+lJiYaBDbhw4dInNzc5JKpbRgwQJhHQgP1Fgorl27xq2jmDhxosEWKH399ddcXmLs2LENfszemCkrK+MS3TKZjObPn2+QfIVSqeQ6iLVo0aLBz4K9iNRIKFiWpT59+hAAMjExMVjNQlhYGDcN6uPjQ5mZmQaxK1B3dDodd9ECoP379xvEbkhICGdz/vz5QoObeqZGQnHo0CGut0NwcLBB7uqpqalc+zpnZ2f67bffhC//BeHWrVvk7e1NAMjS0pLi4uJ4t8myLAUFBXFL4mNjY3m32Zh4ZqapsLAQGzZsAADY2dlh1KhRvG9PX1lZiV27diEuLg5SqRRTpkzBoEGDGnTyUuB/tGnTBkuWLIG9vT1KSkqwatUqlJaW8mqTYRgsWrQIJiYmKC0txbJly7htIAWen2deedHR0bh79y4AoH379ujZsyfvqxjj4+Oxe/dulJeXo1WrVli4cCHMzc15tSlQf0ilUowdOxb9+/cHwzA4deoUTp06xbtdf39/dO/eHQBw+vRp7ncr8Pw8VShYlkV4eDhyc3MhlUrRu3dvODs78+oQy7L46aefcPv2bchkMnz//fdwcnLi1aZA/WNpaYmPPvoIFhYWyM3NxS+//FJt2TwfODo6on///hCLxdBoNDh06BCv9hoTTxWKjIwMREVFQavVwszMDCNHjuTdocjISOzYsQNSqRSLFi1Cjx49eLcpwA9t2rTBV199BYVCgTNnzuD48eO82pNIJOjevTuaN28OoCqqKCoq4tVmY+GpQpGUlISYmBgAQEBAANq2bcurM8XFxZg3bx7KysoQEBCAOXPm8GpPgH+mTp2KsWPHQqVSYfXq1cjOzubVXufOndGmTRsA1X+/As/HU4XiwoUL3J6Z8+fPh1gs5tWZXbt24ebNm7Czs8PMmTPh6urKqz0B/pFKpXjnnXfg6emJ+/fv48svv+TVnrW1NQYOHAiRSITMzExERkYKXbDqgScKBcuyOHz4MIgIHh4eGDx4MK+OpKWl4ZdffgERoW3bthgwYIAwy/GS4O3tjSFDhkAkEmH79u2IjY3l1d6YMWOgUCig0WgQERGB3NxcXu01Bp54Jd64cQM3b94EUBU+8jnTodVqceTIEcTHx4NhGIwaNUpIYL5EmJqaYuDAgXB0dIRarcbGjRtRUVHBm70WLVpg+PDhAKpm7VJSUniz1Vh4olBs2LABOp0Ojo6OvEcTmZmZ2L9/P0pLS2FnZ4fg4GBe7QkYnp49e8LX1xcsy+L06dO4evUqr/aWLFkCkUiEnJwchIaG8mqrMfBYodBqtdzUUseOHdGsWTNenbh16xauXLkCABg3bpwQTbyEWFlZYejQoQCA5ORknD9/Hmq1mjd7Xbp0gZeXF4gIZ86c4c1OY+GxQnH16lWUlJSAYRj4+fnBzs6ONwe0Wi3Wrl0LjUYDCwsLvPfee7zZEjAukydPhq2tLXQ6Hfbt24f09HTebIlEIgwZMgQAEBERgfLyct5sNQYeKxQXL14EUFU04+3tzev+GJGRkQgPDwcAjB49Gi4uLrzZEjAudnZ2WLBgAQDgzp07OH/+PK/2AgMDIRaLoVQqce7cOV5tvew8IhREhOvXrwOo+mJbtGjBqwN79uwBy7IQi8UYNmwYr7YEjM+kSZMgk8lARLxXTrZo0YKLhgWheD4eEYqcnBw8ePAAAODg4ABPT0/ejJeUlODXX38FUFXFx3dBl4Dxad68OYKCggAAISEhyMnJ4c2WnZ0dvLy8AAAnTpzgzU5j4BGhiI+P56rnvLy8eE0s/vHHHygrK4NIJEJAQIBQYNUIkEgkGD16NCQSCXQ6HTZv3sybLXt7e3h7ewMAUlJSkJCQwJutl53HCoW+QCUoKIi3+ony8nKEhIRArVbD0tISQUFBvC9fFzA+IpEI/v7+cHNzAwAcOHAAhYWFvNgyNzeHj48PFAoFtFotIiIieLHTGKgmFBUVFbhz5w6XIe7Zsydvhu/evYubN2+CiNCkSRP07t2bN1sCDQsvLy/4+fkBAFJTU3lLajIMAx8fH9jY2ECn0+Hy5cu82GkMVBOKrKwsnDt3DkSEfv36wcfHhxejOp0OoaGhuH37NoCqdSTCsKPxYG1tjSlTpsDBwQGlpaXYt28fb5WavXr1gqurK1iWxdWrVxEfH8+LnZedakJRWlrKJTL5nIFQKpW4ceMGiAgikYj3yk+BhkeXLl1gY2MDoCp/kJqayosdExMTdOzYEQCQl5fHa+3Gy0w1ocjOzoZSqQQAXvdGKCsrw7Vr1wBU/WCEaKLxYW9vz/3GHj58iOTkZN5s6WfTSktLUVBQwJudl5lqQpGYmAiWZcEwDKfCfHD//n0uAz1p0iRIJBLebAk0TEQiEcaOHQug6gYVGxsLnU7Hiy19f4qSkhKubYJA7agmFGlpaQAAW1tbmJmZ8Wb08uXL0Ol0kEql6NOnD292BBo2PXr0gFwuBxEhNjaWt7Uf+mpfnU6H/Px8aLVaXuy8zFQTCn1yUT/3zAdEhL179wKoaobasmVL3mwJNGwcHR0xYsQIAFWVk2VlZbzY8fDwgKmpKYCqfIhKpeLFzstMNaHQJzL1c9x8UFBQgLi4OABVdRpSqZQ3WwINH30f1tTUVN6a70qlUnh4eAComtnjc9Xqy8pjhcLd3Z03g3fv3oVGowFQlWQS8hONG39/f4hEIuh0Oi6i5QNfX18AVUJRWVnJm52XFU4oMjIyuNCPT6HQRxNWVlZwcHDgfY8QgYaNpaUlmjRpAgC8tsjTC0VmZqYQUdQBTiju3LkDoCpM07c75wP9XcPBwYGbRxdovEilUm6oq7+J8IFeKHJycoTeFHWAEwp9xZqNjQ0sLS15M6j/MQhCIQBUCYU+guVTKPS1FJWVlcjIyODNzssKJxRZWVkAqhbSyOVyXoxpNBokJiYCqCq4sba2rvU5SkpKsHLlSq65joBxKCwsxObNm9GtWzc0b94c7u7ueP3113Hr1i3uNTdu3OD2rX0SMpmM63mSmJjI27DA0dGRG+YKXblrD5dJ1O+opFAoeJuJSEtLQ2VlJRiGgaOjI6ysrGp9jgcPHmDLli0oKipC9+7dhVkTA6LT6RAfH49t27bhyJEjEIvF6NatGxYtWgQLCwtkZWXhgw8+QEVFBSQSCe7fv49+/fo99Zz6oYdIJALLskhISOCGCfWJSCSCqakplEoliouL6/38LzuPCIWJiQlvF19OTg60Wi1EIhHs7Ozq1GJv586dKCwsxKFDh7B06VLeO3AJVKFfyPfee+/h+vXrmD17NoKDg9G1a9dqEejEiRNx5MgRrF27FgkJCc+syWEYBjY2NjAxMYFSqURqaiovQsEwDMzNzaFUKlFSUlLv53/Z4YYehogoKioquLZ3JiYmtX5/bm4ufvrpJwBVQ6Xvv/++vl0UeAKJiYlYsWIFYmJi0L9/f3z55ZcICgp6ZJiqUCgwbtw4fP3112jTpg03pH0aMpmMu2mUlpby4j9QNawGIEQUdeARoeAzoqisrOTWkigUilq/f8eOHVCr1VzxzPr163lreiLwP4gIn332GaKjo2FpaYkNG4XOn3IAACAASURBVDY8Nb8kFovRp08fzJo1q0Z7jUokEq6eRr8osb7RRxQAhIiiDhhcKPRLy2ubMM3Ly8POnTsxYcIELF68GKampqioqMD27dtBRLz4K1DF7du3sWfPHgDArFmzOKF+FmPHjoVarX7m3p9/Fwq+pi7/LhRCRFF7OKHQ35n5HHroIwqRSFTriCIkJASFhYVYsmQJ+vTpw60IPHjwIG+lvwJVHDx4kBP4Xr161XhPWFdXV6xcufKZq0INHVEIQlF7REBVokr/BZmYmPBWVl3XiKKkpAQhISEYOnQo2rRpAy8vL/Tt2xdisRj37t3D2bNnefFXAFCpVNi2bRuAqint2u4aN2vWrGf+noSIouEjAqpUXCqVQi6Xw9zcnLeIQqvVQiqVQqFQ1CqZGRsbi9jYWLz99ttgGAZisRiTJ0+Gubk5ioqK8Oeff3JDJ4H65c6dO1wPBzc3t1oX40ml0meW6UulUpiYmEAul/O2spNhGFhaWkIul/O6QfLLChdRuLq6chum8LX+QiaTwdXVFa6urjUeemi1Wly4cAG+vr7V1qD4+vpyS5QvXLjAlaAL1C95eXlcDkihUPASbcpkMjRt2hQtWrTgtQ+Kra1ttU2BBGqOCKjalj4xMRHx8fFIS0vjrbGHVqtFYmIiEhISapx5ViqV+PPPPzFs2DAudASq7hDvv/8+zM3NkZaWhmPHjvHic2PH0tKS94V7FRUVePDgAeLj43lb2UlESEtLQ3x8vDD0qAMSAJDL5VzOoKKiglsGXt/I5XKuAq+mP4jQ0FDk5uaCiB4p2yYidO7cGWFhYfjhhx/w4Ycf8lZ+3ljx8vLihKImMxh1QavVcjcnviIKIuJWR9elIrixw8WR1tbWyM7O5l0oGIYBy7I1GotqNBp89dVXKCwsxOrVq5/4GlNTU2RnZ2Pjxo1YvHhxfbvdqLG1tYWrqyvu3buH+/fvIz8/v97bEPxdKPSdqOobQSieD26eS//hqVSqBhNRRERE4ObNm9i+fTtu3br12OPChQsYMGAAAODbb78VFvzwgP7zzcvL42VfDI1Gw3tEAUAQiueAEwr9ku+KigrechS1iSh0Oh22bNkCHx8f9OnTByKR6LGHg4MDAgMDIZfLkZaWhsOHD/Pie2Nm5syZEIvFAICjR4/W6r1ZWVm4fv36U18jRBQNH04o9CW5fEYUMpkMDMOAiJ4ZUdy6dQuRkZFYsGDBU388YrEYAQEBaNasGYgIv/76K6/rBRojHTt25FrrHzhwoMaJ4/LycsyePRvOzs5PfZ2hhYLPfisvK48IBZ85Cmtra0gkEmi1WhQVFT0xMabRaHDx4kWIxWK8/vrrzzxvx44duVWkycnJuH79ulDWXY/oZ5i6d+8OhmEwffp0nDx5EkVFRY/9nIkIqampWL58ORYuXMi1unsSZWVlXITp5OTEy98gRBTPB5fM1A89+IwoXFxcuH0ccnJyUFpa+tgvLTY2Frt370azZs1qVPxlYmKCpk2bAqjadWrnzp1o3759nRrjCDweHx8ffPvtt9i4cSN+++03TJ06FYMGDcLgwYPRpUsXWFhYoLKyEmlpaUhLS0NkZCT8/f3xyiuvPPW8Wq0W6enpUKvVYBgGrVq14sV/lmW56mMhoqg9nFDY2toCqAoX+RIKfSPVlJQU5ObmorCwsJpQZGdnY/369Th16hTi4uJgYWGBSZMmYfTo0Rg2bNhjpz4jIiKwe/duhIaGAqjKbfz2229ISUnBq6++irlz5wqdvusBkUiEbt26Yf369XjzzTexbds2HDx4EMePH4eTkxNkMhl0Oh1kMhleffVVjBs3Dp07d37muhC1Wo2kpCQAVV2o9L/D+qasrIwb3ggtGGsPdwXpVwQWFBTwujDH29sbkZGRyM3NfaTs2srKCm+99Rbeeuutav//aStavb29sWzZMixbtuyR50QiEZeEE6gf7OzsMHDgQAwYMAAZGRlISEjAw4cPUV5eDnd3d/Tt27dWC/40Gg0ePnwIoCpq4au46969e9xjYa/b2sMJhb4TUUVFRY2ajdQVfZNTfUTxdxQKRa07VtnY2Ah3CCPAMAyaNWtW60Vi/+TvQqH/bfCBfisAe3v7ahW+AjWDiwvd3d250F4fCvKB/sdQWFiI/Px83uwIvBiUl5cjNTUVAHhpgafnr7/+AgA0adJEqN6tA5xQKBQKbj8P/Y5hfKAXCo1Gg/v37/O2g7XAi8Hdu3e51Zx8RhR6oWjatKkgFHWgWqZJn6fgM6JwdXXldpcODw/nLXEq8GLw+++/A6gaQvI140FE3MZTTZo0qVNT58aOwYUCAIYOHQoAuHz5srCSrxFTWVnJFW/5+/vXqeFyTcjJyeHyYcLQo25UEwpPT08A/9t/gy/0QpGfn48LFy7wZkegYXP16lWkpKQAALp3716nhss1Qb/plEgkgrOzs7AXTB14bERRWVnJfbh80L59e66sV9+0VaDxoR92WFhYoH379rxdwPrfsqmpKezs7Grc81Pgf1T7xJo3b86N3561kOd5sLS0ROfOnQEAp06dEtqnN0JUKhVOnz4NAGjRogWvGznpV7xaWloK3a3qSDWhsLS05HaWru0qwdpgbm6OLl26gGEYqFQqnDx5kjdbAg2TmJgYbs8Pd3d37ndX31RWViI6OhpAVfXxs9adCDyeakJhbW3NzWWfOnWKtwpNmUyGdu3aceXbBw4c4G1pu0DDg4hw/vx5FBQUQCqVom3btryty3nw4AGXB2nevDlatmzJi52XnWpCYWNjg3bt2oFhGBQXF+PatWu8GW7fvj2XE7l+/To3fSXw8pOVlYVLly6hsrISZmZmGDBgAG95g9jYWBQUFEAsFqNDhw6wsLDgxc7LTrVvRyKRwNvbmyuJDgsL482wp6cnunTpApFIhKysLISFhfHSj1Gg4REfH8/lwDw8PBAYGMiLHZ1Oh7i4OBQWFkIikSAoKIgXO42BR2S8TZs2XE+AyMhI3vZZEIvFGDlyJORyOZRKJcLDw4V9RBsBOp0OFy9e5NYTzZw5k7cCqMLCQty+fRs6nQ6mpqbo1q0bL3YaA48IRatWrbjeDikpKdyCHT7o3bs3t5IvIiICycnJvNkSaBhotVpui0I7OztMmDCBN1u5ubnckLZbt25wcHDgzdbLziNCYWpqii5dugCo6g9x9+5d3oybmppi1qxZAIDU1FSEh4fzZkugYRAVFYWbN28CAMaPH89rc6HMzEwkJCQAAMaMGcP7/iQvM4/NIPXu3RtAVeXk3bt3eV24NWXKFG5u+5dffuG1IlTAuGg0Gnz++ecAqqbIJ06cyKu9S5cuQaPRQCaTYdiwYbzaetl5rFD4+/vDzMwMWq0WMTExvO7raW9vj5kzZwIAbty4gePHj/NmS8C4REZGchtKDxo0iNuRni/09Tnt27d/7r4ZjZ3HCoWtrS23r2dYWBgyMzN5dWLixInw8vICy7L44IMPhJqKlxCWZbFt2zbodDrY29vj9ddf53XY8ddff+Hq1asAgNGjR/Nmp7HwxMnrBQsWQCQSITs7G6dOneLViVatWuG1116DWCzGnTt3EBISwqs9AcNz/fp1XL58GQDg5+fHa+0EEeGbb76BWq2GlZUVBg0axIudxsQTvyl/f3+uPd6uXbt47Rshl8sxatQoeHh4gIiwe/dulJeX82ZPwLBoNBr8+eefSE9Ph1wux4wZM3htX5iZmYnffvsNANCjRw9uFk+g7jxRKBiGwWuvvQagKozje0aiU6dO3PLzqKgoREVF8WpPwHCkp6cjJCQEKpUKvXr14r5nvjhy5AjKysoglUrRo0cP2Nvb82qvMfDU2K9v376wsbEBy7L49ttveXVEJpNh4cKFMDExQUpKCnbt2sVrElXAcBw4cABXrlyBVCrFunXreNsNDACUSiWOHz8OlmXh6OiI7t27C/0n6oGnCoW7uzs6deoEAAgNDeW1RwVQ1SZvzZo1EIlE2LNnD86fP8+rPQH+SUhIwOeffw6dTod58+bx2kAXqMqF6JeVu7m5wc/Pj1d7jYWnCoWzszO6desGiUQClUplkA2A33rrLfTu3RsqlQorVqzgVv4JvHjk5uZi+vTpKCkpQdu2bTF79mxe7Wm1Wly+fJnr6t23b1/eNhRqbDxVKGQyGQIDA2FnZweNRoNz584hJyeHV4ekUikWLlwIJycn3LlzB8uWLROKsF5AtFotNm/ejMuXL8PMzAyTJ0/mWi3yRX5+Ps6cOcNtTzhu3Dhe7TUmnjk/FRQUxO0Ufu3aNURGRvLuVK9evTBixAgwDIOjR4/iv//9L+82BeqXiIgI7Nq1CyzLom3btpg0aRLv3a9jY2O54Wr37t3Rrl07Xu01KqgG/PTTTyQSiQgAzZgxg0pLS2vytuciIiKCWrZsSQCoY8eOFBMTQyzL8m5X4PnJyMig0aNHEwCSyWT022+/8W5To9HQ0KFDCQCZmppSZGQk7zYbEzUSivLycurZsycBIEdHR4qJieHbL9JqtbRmzRoSiUQkFovpjTfeoMLCQt7tCjwfWq2Wli9fTlKplBiGoTlz5pBGo+HdbmhoKEmlUgJAU6dOJZ1Ox7vNxkSNhIKo6g5vampKAGjmzJl8+sRRWlpKkydPJgCkUCjo008/NYhdgbrz448/krm5OQGg/v37U25uLu821Wo19enThwCQi4sLhYaG8m6zsVFjoaioqKApU6YQABKJRHT//n0+/eIoKiqijh07EgACQCdPnjSI3edFrVbTunXrqGvXruTg4PDYw9HRkVq1akXTp0+n1atXU3x8/As9vIqKiiIbGxsCQK6urhQREWEQuyEhIWRhYUEMw9CsWbNIqVQaxG5josZCQUR05swZatq0KQGgadOmGSSkZFmWTpw4QS4uLgSAPDw86Pr16y/MBaXVamnjxo1kYmJCAMja2pree+892rlzJ/3xxx/0888/05w5c8jT05PEYjH17NmTDh069MINs5KSkmjgwIHEMAyZm5vTunXrSK1W8263rKyMJk+eTCKRiJo1ayZEEzxRK6EoKiqi6dOnk1gspiZNmlBUVBRfflVDqVTS559/TiYmJiQWi2nIkCEUHx9vENv1QXp6OnXu3JkAUGBg4CPPV1ZW0qVLl7hknI2NDW3YsMEgF1p9UFhYSDNmzCCFQkEAaMqUKZSfn28Q2xcvXuSS3rNmzaLKykqD2G1s1EooiIjOnz9PdnZ2JJFIaPHixQb7YgoLC2nUqFEEgKRSKQ0fPpxKSkoMYvt5ycnJoUGDBj1RKPSkpaWRt7c3F7obanj3PGg0Gpo2bRonEp07d6asrCyD2FapVPTee++RWCwmCwsLSkpKMojdxkithYKI6M033yQA5OnpabBxKFFVmNm5c2diGIYA0ODBg6msrMxg9utKbm4uDR48+JlCQUT07rvvcvmYdevWGcjDulFRUUFz584lAMQwDHl6ehr0Yr1z5w7Z2dkRwzD0+eefG8xuY6RODQE+++wzNGvWDImJidi2bRsqKirqcppaY2Zmht27d6Nz585gGAYnT57E3LlzkZGRYRD7huDvncjVarURPXk6xcXFWLVqFXbu3Amgal3FunXruGbJfFNWVoZFixYhPz8fXbp0wZw5cwxit9FSV4XZunUrSSQSMjMzo19//bU+xeupaLVaCgkJIU9PTwJAJiYmNGfOHMrOzjaYD7WlphGFSqXixtsmJiYUFhZmQC9rjlarpS+//JLs7OwIAJmZmdHWrVupoqLCYD6sX7+eRCIRWVlZ0Y8//khardZgthsjdRaK7Oxsbtzt7OxssHEpUdW4+Oeffya5XE4ASC6X0+TJkxtskU1NhEKtVtPSpUu5Ctjx48c3yBwMy7L03nvvkZmZGTdE+vjjj0mlUhnMh+vXr3OCOmzYsAZ9k3hZqLNQsCxL+/fv5+bNZ86cafCM82effcYV9wCgESNGGKTAp7b8XSicnJxo/fr1dPDgQTp48CB9//33NG/ePOrbty/JZDKSSqU0efJkSk1NNbbbj1BSUkKLFy/mPm8TExODFd/pKSsro9mzZ5NYLCZra2s6fPiwQe03VuosFEREeXl59Prrr5NIJCInJyf6/fffDVrfwLIsbdmyhbu7MAxDY8aMaXCFS38XCmtrawoODuaOIUOGkJeXFzdrYGlpST///DNlZ2c3qL8hJyeHFi1axEUSdnZ29P7771NxcbHBfGBZlv744w9q0qQJAaDg4GBhOtRAPJdQEBGFhYWRhYUFiUQievXVVyk9Pb0+/KoxKpWKfv/9d25aUSaT0fDhwykxMdGgfjyNvwtF165dqby8nDuysrLoypUrtGPHDvL29iaGYcje3p4mTJhg8M/ySSiVSpo5cyYXvVlaWtL27dupqKjI4H7oS7WbNm36Qkwfvyw8t1DodDp65513uPqGb775pj78qrUPt2/fJnd3d67E3MvLyyCL12pCTXIUOp2O0tLSuLyPSCSiHj16GL3oKjExkfz8/EgsFnNDpytXrhikKvefrFixgsvhbNu2zeD2GzPPLRREVYu32rRpQwDI3NycLly4YJSwuaCggIYNG8aVS5ubm9PGjRuNXg5dmzqKjIwMTvAA0JYtWwzkZXUqKiro8OHD5OXlRQBIIpGQv78/Xb161eC+aDQa2rNnDyeg/fr1ExKYBqZehIKI6Pjx49x6DFdXV4qOjq6vU9eK9PR0evfdd7mpO0tLS5o9e7ZRS75rIxQqlYoWLlzICcWsWbMM5OX/yMrKog8//JCcnZ05kZgyZQrdvHnT4DcAlmXp/Pnz3HR4y5Yt6eTJkw12hutlpd6EoqKigtasWUMWFhYEgIYMGUIPHz6sr9PXiuLiYjp48CC5ublxQ6IuXbrQ0aNHjRLp1EYo1Go1ffrpp5xQLFq0yEBeVl2UkZGRNHDgQG7q2dHRkbZt22a02aTk5GQaOHAgicVikkqltGHDBoNOxQpUUW9CQVSVbBozZgwBILFYTO+++65Bi3D+SXZ2Npf80k/nLVu2zKCZeqLaCUVJSQkNHz6cC7Nv3rxpEB81Gg3t2LGDHB0duc/Lx8eHIiIijDr7smDBAq5kf+rUqQ1qJqgxUa9CQVR1B2jbti0BICsrK9q7d299m6gVWVlZtHDhQi6MFolE1KdPHwoNDTXYOpHMzEwKCAh4qlAolUqKi4ujDz74gEQiEZmbm9NHH33Eu28qlYpiYmJo/PjxXMLS2tqaxo4dS3fu3OHd/pPQaDS0fft2EolEJBKJaMCAAUa96TR26l0oiIiuXr3KjSnd3NwMunDscSiVSjpy5AiNGTOmWh3A4sWLKS4ujtfxbkVFBZ08eZJsbW25z2Pt2rX0/fff07FjxygkJIT27dtHixcv5gTW2dmZPvjgA94rMzMyMmj16tXk4eHBTS337t2bfvzxR4NPff4dlmXp8OHDZGVlxa1IbSgzWI0VhojoedaKPIk9e/Zg/vz5KCwsRNu2bbF3716jd0XOycnBqVOn8PnnnyMhIQEymQxeXl4YNWoU5s2bV697VGq1Whw5cgRhYWFIT09HcnIyiAgMw0Amk0Eul8PU1BQMw0Cn08HCwgLOzs5wc3NDnz590KpVK5ibm9ebP38nLy8Pu3btwt69e3H79m0olUpYW1tjxYoVeP311+Hi4sLbBsI1ISIiAnPnzsWtW7fg5OSEb775BmPHjoVEIjGaT40evhSovLycli5dyjU8feWVV+jBgwd8masV+fn5NHv2bFIoFNz4VywW05w5c+jOnTsvZbWfWq2m9PR0+uijj7gZIYZhSC6X04gRIygtLc3YLhJRVacs/TBNJBLRsmXLhLxEA4A3oSCqGpuPHTuWuxDfeOONBlNtSFTVhGf8+PFc/gL/313qzTffpCNHjlBCQsILnWHXarWUnJxMJ0+epPnz55OTkxP3d1paWtLgwYNp3759DWbsn5ycTEOGDOGmZCdNmkTl5eXGdkuAeBYKIqIHDx5wMw9SqZQmTZpk9AKov1NYWEjHjh2jyZMnc2Ni/P/eEAEBAbRw4UI6duyYQfYyqS/Ky8vp/PnztHLlSurXrx+XH8H/z/wMHz6c9uzZQxkZGcZ2lSMpKYleffVVLpIYN26cwdrpCTwb3oWCqEosOnTowN0pgoODG1xnquLiYjp//jwNHDiQJBIJd2FJJBKys7OjDh060JdfftlgQvTHUVpaStu2baOePXuSk5MTN+zTH+3ataMDBw40uBW2WVlZ9MYbb3CzLkFBQRQXF2dstwT+hkGEgmVZOnPmDFcAJZPJaMmSJQ3yLq3RaOiPP/6gwYMHk4ODA1d4pD/kcjn179+ftmzZQvHx8VRQUGCUnIZaraaioiJ6+PAh7d27l1577TVu3xX9IZVKydbWloKCguiHH35okMOo0tJSWrx4MSfOLVq0oLNnzxrbLYF/wNusxz/RaDT45ZdfsGzZMhQWFsLa2hpLly7FwoULYWJiYggXagXLsoiNjcXx48cRHh6Ov/76C+np6WBZlnuNlZUVOnfujMDAQHTo0AFNmzaFvb097O3tYW1tXW8zB0SE0tJS5OXlIS8vD1lZWYiLi0NERASioqKqbRzNMAzs7e3h6+uL7t27Y+jQofDz84NCoagXX+qToqIirF+/HmvWrEFlZSVsbW2xYcMGBAcHG9s1gX9gMKEAgIqKCmzcuBHLly8Hy7KwtrbGtGnT8Nlnn8HMzMxQbtQKIkJOTg5u376NqKgohIeH4/Lly8jPz6/2OgsLCzg5OcHOzg52dnZwdHSEm5sbPDw80KRJE8jlcigUCsjl8mqPGYZBZWUlKisroVKpqj3Oy8vDgwcP8PDhQ2RlZSE/Px/5+fnIyclBUVFRNdGysLCAn58fAgMDuQ16XVxcwDCMoT+yGpGVlYWPP/4YP//8MyorK2Fubo5169Zh+vTpEIvFxnZP4B8YVCiAqoaxn376KVatWgWWZSGRSDBhwgRs2rQJlpaWhnSl1mi1WqhUKqhUKkRFReHIkSM4duwYMjMzH3ktwzCQSCSQSqUQi8VgGIY7RCIR9xioEqPHHTqdDhqNBlqttpoo6DE3N8fQoUMxcuRI9OrVC5aWllAoFJBKpQ1WIICqepZFixZh//790Gg0UCgUWLlyJZYsWdIgIx8BIwgFUBVZrF+/Hl9//TUKCgoglUoxadIkfPrpp2jWrJmh3XkudDodrl+/jrCwMNy+fRvx8fHIy8tDRUUFVCoVKioqoFarwbIsWJaFTqfDkz5yvYiIxWKIRCJIpVIoFAqYmJhAoVDAysoKrVq1gre3NwICAhAUFASpVGrgv/j5yMzMxNKlS7Fnzx4QEezs7LB48WK88847DXIIKlCFUYQCAJRKJf773//is88+Q1paGqRSKcaNG4dVq1YZrOU7XxQVFSE9PZ078vPzqw0r1Go1NBoN1Go1iAgymQxSqZSr2NQPTaytrdG0aVM0a9YMzZo1g729fYOOFJ7FzZs3sWLFCpw4cQIA0Lp1a7z33nsIDg5+4QSv0WHQ1Ok/UKvVFBoaSr6+vlxRVlBQEMXGxhrTLd5hWZbUajVVVFRQeXk5qdXql7q/AsuyFBERQYGBgdyMTGBgoNEaHAnUHqMKhZ7ExMRqPyJfX1+jdFIS4IerV6+Sj48PVy7fs2dPunfvnrHdEqgFDUIoiIgSEhJo9OjR3Hy6u7s77d69u0HWWgjUjKKiItq7dy9XOm5qakpjxoxpUBWhRFWRbUpKSo3rTFiWpZKSEkpKSqLMzMwXYm1QWVkZrVu3rs4bizeY5XheXl7YtGkTPD09sWPHDiQlJWHu3LmIiorC/Pnz4eXlZWwXeYWIUFJSgtzcXIjFYtjZ2cHCwuKFzUkkJSXhu+++w9atW6FSqeDs7Iw5c+ZgyZIlvK2KrS0ajQY3b97E77//jri4OKxatQqtW7d+5vuuXLmCvXv3IicnBzKZDM2bN8eoUaPQpUuXBju1m5eXh0uXLmHw4MF1O0H96tbzU15eTvv27avW1PWVV16hsLCwl3Icf+/ePVqwYAENGjSI/Pz8qF27dtSrVy/y8/OjwYMH05IlS164cua4uDgaMGAAt1eJm5sb7du3j5RKpbFd43j48CEtWLCAvLy8SCKRkJubG924ceOp76msrKQvvviCPD09adSoUXTx4kWKioqiqVOnUufOnY3WJ7Ym7N69m2bNmlXnBYANTij03Lx5kzp16sS1Z7ezs6NDhw69NHtMVlZW0vbt20kmk1Uru5ZIJNVWswIgFxcXOnjwoNFb9z8LrVZLFy5c4Jaxi0Qi8vDwMGqnrMeRkpJCvXv3puDgYG5Y9CyhYFmWNm7cSGZmZjRixIhqw5SkpCTq0qUL9e3bt0GWyRMRjR49mnbt2lXn9zdYoSCq6jU5e/ZscnBw4GZFFi1aRPfu3XuhBSMtLY2mTJnC3XFNTU2pdevWFBgYSKNGjaJJkyZRQEAAtW7dutr+qnPnzm1wC7qIqi4ifbcs/SZB1tbWNH36dCooKDC2e0+EZVl65513SCwWP1MoUlJSqF+/fgSA/vzzz2rPaTQaWr16NUmlUpo9e7ZR9jx5Gvfv3ydPT09KSUmp8zkaTI7icdjb2+Pbb79F9+7d8dVXX+HOnTvYsGEDrl69irfeegvjxo17Ibsebdq0CXv27IFGo4G9vT1WrlyJgIAAuLi4wNHRESzLIicnB+np6QgNDcXmzZuRkpKCLVu2wMrKCp988glkMpmx/wwAVbmVkydPYuvWrTh37hzKysrg7OyMd999F5MnT4aNjc1znT85ORknT55EeXn5Y5+3t7fHoEGD4OjoWOtzMwyDNm3a1KiG4+bNm4iKioK1tTUCAgKqPSeRSODr6wt7e3v8+OOPmDlzJrp27Vprf/hi9+7dCAwMRPPmzet+kvrTLf5Qq9UUExPDTaEyDEO2trY0YcKEBr3s+3GcPXuW69tpb29PoaGhT70DVVZW0s6dO7kQuVmznJo/qAAAD5JJREFUZnT8+HEDevxk0tPTac6cOeTg4MBNfXp6etLFixfrLQQvLS2lrVu3UrNmzcjExOSRw8rKigYMGFDn2psff/yRTExMnhpRaLVaWr16NQGgHj16PPY1sbGx1K5dOwJAy5Ytq5UP+lmXf9qMj49/bE6BZVm6f/8+ZWVlPfPcSqWS2rVrR6GhoY88p9PpKDU1leLj47n8X3l5+WP7xbwQQqFHp9PR2rVrydnZmetd4OrqSgcOHGhQibInUVhYSM2bN+dEoqYXPMuytGnTJq6/xKhRo2r0I+ELpVJJJ06cIB8fH064HRwcaNGiRbw1BL5w4QK5u7tX6xXy90Mul9P69eupqKioVkVcNRGKyspKmjRpEgGgPn36PPY1JSUlXIOm4cOHP9MHlmWpuLiYzp49S3369CFbW1vS6XSUlZVFa9euJXd3d2IYhnr16sVtvKTVaik6OppGjRpFYrGYFAoFzZo166k3y9OnT1PXrl0fmQgoLi6mpUuXkr29PTk4OJC/vz/NmjWLevToQd9///0j53mhhIKoSiyio6Np6tSpXNLMwsKCZs+eTdHR0Q06dxEWFkZyuZwYhqHp06fXan8RlUpFfn5+BIBatWpllJmQyspKioyMpDlz5lTrZv7666/TuXPneB+bZ2Rk0Jw5c8je3v6xYiGTyWjEiBF0+vTpGv8OaiIU5eXl1KlTJwJAgwYNeuK5Jk6cSAAoICDgmd9tQUEBffzxx2RjY8O1JkxISKB///vf1L9/fxoxYgRZWlpy4vTgwQM6ffo0DR48mEaNGkWDBw8mExMTrtfr49BqtbRixQpatWpVtf/Psix9/fXX5O/vT/v376esrCz6888/afjw4SSTyR4rFC/cAF8kEsHPzw/ffPMNxowZg82bN+Ps2bP4/vvvER4ejnHjxiE4OBienp5G7ST9OFJTU8GyLBQKBTp06FCr1bJyuRxjxozB1atXkZubC6VSCQCorKzEpUuXkJSUxJfbAIDi4mLEx8cjLCwMd+/ehUgkQtOmTdGlSxd069YNDx48wIMHD3j1Aaiqt+natSvCw8NRWlpa7Tm1Wo2jR4/ir7/+wtixY/H222/XyyJDlmWRmpoKAGjVqtUTX6df+VpRUYGioqKnfr+mpqaYOHEi0tPT8f3330OtVuO7777DwIEDsXTpUlhaWmLv3r34+OOPcfHiRaxduxYymQyfffYZWrduDZVKhW+//RZr167Fnj178OWXX8LW1raajaysLCQkJGDlypXV/v/9+/exdu1aTJgwASNHjoRMJsOAAQPg6uqKN9988/EOP1X2XgDy8vLou+++4+4yMpmMmjdvTkuXLqW8vDxju1eNVatWkUQiIUdHRzp8+HCt33/u3Dku1D99+jQRVd2Z3nzzTTI1NeX1UCgU3FS1/pBIJLzbfdxhYmLyiC//PCQSCXXs2JHOnDnz1PqbmkQUpaWlZG1tTQBozZo1TzzXjBkzCAB5e3vTrVu3avSdhoaGEgBSKBSP7O2qVCpp3LhxBIC6dOlCBQUF1Z6/c+cOt3/OP2di9OeeMmXKI9fB0aNHCQC9+eab1fIRLMvSf/7zn5cjovgndnZ2+Pe//42BAwdi+fLlCA8PR0ZGBv7zn/9g69atmD9/PiZOnAh3d3eYmpoa1VeGYdCuXTvY29vDycmp1u/39PREhw4dAFTdtfSIxeJ6W31JRFzfjb/3wGAYBnK5HDKZzOjVoizLQq1WP/U1IpEICoWi3n19ml2dTgfgf/1FaoI+6pDJZPD19a3mr0wmg4+PD/e6f84gWVtbw8PDA4mJibh16xYGDBhQzZdr167B29sbVlZW1d7n4+MDiUSC8+fP448//kC/fv3g5OQEiUSCadOmcdHq33nhhUJP69atcejQIYSEhGDPnj04deoU8vLysHr1auzZswcjR47E0KFD4e/vD2tra6P4SES4desW7OzskJ2dXev3379/Hzdv3uQuAgAwMzPDtGnT0Ldv3+f2r7CwEBEREbhx4wZSU1M5MXJyckL//v3Rvn17ODg4GLVMubCwECdOnEBERATKysoeeZ5hGHh6emLChAl466236m1TJ/3f/CRB1mq1XNczmUxWbx3bniV0T3pepVIhJiYG06ZNe6SEoGXLlhg5ciSOHTuG6dP/r707i2nq2eMA/m2PbRGolLYELNDInkbECj4okAgu0aAYUlzwQTBXxQf3+OD2oDHRBzTRKDyJmhgTtxhcEjTGiIJoVIwBgq3SsoiUClSsYmlte373wcvJHwEL1/V655NMQjg9zHBof5yZ+Z2Zf0Gv16OoqAhLly6FVquFSqUa9vP+mkABfLlog8Ggrq4OJ0+exI0bN9De3o7jx4/jypUrSEtLQ05ODgwGA8LCwn5p+wZ34Pr48aPQ5x2PR48eAfiyVudgsJNKpZgzZ853taujowPXrl3D7du38fz5c9hsNhARgoODkZeXh7Vr12LGjBnD/jP9al1dXdizZw/q6upGDBJSqRSLFy/Gtm3bkJ6e/sNybMRiMSIiImC329HZ2Tnia/r6+vDu3TsAX3I7Jk+e/EPq/m+1tLSgr69v1N35jh49itTUVJSVleHZs2cwGo2oqKjAli1bkJeXN/yEMXWk/ke5XC66ffs2paSkCPP8IpGIJBIJBQcH0/r166m+vv6XPUMyOOsBgIqLi8f1ZCzP85SWlibMenzvmh08z9Pz589p9erVpFAohk076vV6unv37h/zZOT9+/cpIiJi1LEJiURCJ06cIKfT+VOmR1etWkUAaP78+SO+pr6+Xtg79vDhw2Ou/9mzZ8Ksx9fvQ4/HQ/v37x91Wrarq4sWLVpEAOjIkSNDju3atYt27979zWvh9Xqpo6OD8vPzhc+GVCqlgwcPDnvtXx0oBjkcDjp27Bjp9XpSqVRD3mwymYyys7Pp9OnT1NTUNO55+PHo7u4WBp8iIyPp6tWrY6prYGCATp8+TRKJhMRiMeXl5VFXV9e46+/r66OGhgYqKyuj9PT0IddBLBZTWFgYzZo1i8rLy/+Y50ocDgeVlpZSdHQ0BQUFDSsqlYqWLFnyUxOufD4fnTp1iiQSCWk0mhH/ZpWVlRQZGUkikWhcGyr/jEDR399PcXFxVFNTM2KdDodjWFLVvXv3aPr06SQWi0kul1NjY+OQ439V12M0kyZNwtatW7F8+XJhFe1Hjx6hvr4eLpcLVVVVqKqqQnx8PDIzM5GSkgKdTgedTofIyMgfdgsbFhaG0tJSFBQUoLOzEzt27IDX64XBYBi1r+l2u3Hx4kXs27cPHo8HkZGRKC4uHtNgqM/nQ2dnJ5qamvDixQvU19fjwYMHaG9vFwYq5XI5UlJSMHv2bMyePRvp6ekIDw//7QOWgz58+AC5XI49e/aMeFypVCI7O/undiPFYjFmzJiBhIQEmEwmWK3WIdOuPM+jpaUF7969Q2pqKnQ63U9ry1jcuXNHWJV9JI8fP0ZTUxO2bdsmfC8zMxMlJSVYt24duru7UVNTg+TkZOH4/0WgGKTRaLBixQrk5ubCarWiubkZ169fR0VFBWw2G8xmM8xmMwICAqBSqaBWqxEbG4uMjAzMmTMH06ZNg0wm+642LFiwAFu3bsWBAwdgsViwceNGNDU1obCwEFqtVsj9ICK0tbWhvLwcZ86cEVb6Lioqwty5c0f9IHs8HhiNRlRVVaG6uhoWiwU9PT3o7e0dMmKv0WiwfPly5OTkICEhARqN5rt/t58hKioKhYWFv7sZ0Ol0yM/Px+HDh3Hp0iVs375dONbb24tbt25BIpGgrKzst64kTkS4cOECioqKRm3HwMAALl++jDVr1ghjXRzHISsrC9HR0SMPtI/5Hukv5nK56MKFC5SZmUkymYw4jhPGNP5ZwsPDqbCwkCoqKqi9vZ3cbjd5PB7yer3k8/nG3GWx2WxkMBiENHT8p3+o1Wpp6dKltGzZMpo8efKQNnAcR4sXLyaXy0U+n4+8Xi95PB5yu91CZt2mTZuE3dj+WUQiEXEcRxMnTqR58+aNucvzN+N5nnw+H+3bt48kEglptVqqq6v75nhVf38/5eTkkFKppMrKSnK5XPT582c6dOgQTZo0ic6ePTvuNpw7d07oerjdbqF+nufJ6XRSQUEBAaCsrCzyer3C343neTKZTMK6LSUlJeT1eqm5uZmSk5O/ub/vtWvXSCaT0YYNG8hqtQrvpStXrlB4eDilpKRQd3f3kHN+2yrcfyKfzweLxYKHDx+itrYWJpMJNpsNNptt2Ci7SCSCQqHAlClTEBMTIxStVguFQgG5XA6ZTAaJRDJi+fTpk3C3YLFYhHl3juOgVCrR09MzpJ7c3FysXLkSnZ2daG1tFUpbWxt6enqG7fsRFBSEiIgIaDQa6HQ6ZGRkICMjAzExMX9cxurv0NjYCKPRiPPnz8NkMkEikUCv1yMzMxMGgwFqtXrE8z5+/Ii9e/fi6dOnUCqV8Hg8CAwMxLp16zB//vwx3004HA7U1tbizJkzMBqNAICZM2fCYDBg4cKFsFqtqKurQ2lpKex2OziOQ15eHnJzczFz5kxUV1fj0qVLqKmpgc/ng1wux8qVK8FxHF6+fInS0tJR67558yZ27twJjuMgk8mg0+ngdDrx+vVrZGdnY/PmzcNmbVigGAURobe3F83NzWhubobRaERDQwMaGhpgtVpHTajhOA6hoaFQqVQICgpCQECAsCvY4NeDRSqV4smTJ3j8+LHwQReJRJBKpXC73QC+9I+VSiU4joPdbofX6x21zSqVCtOnT4der8fUqVORmJiIxMREqNVqFhy+0t7eLgTjryUmJn4z/drn86GtrQ2tra0gIqSlpQ1Ln/ZnYGAAZrNZSNIaFBgYiNjYWLx//x5v3rwZdp5arUZUVBRaW1vhcDiGHJswYQKcTidCQkK+uaSf1WqF3W6HVCpFf38/Xr9+DZ7nkZCQAJ1ON2KuCAsUY+R2u+FwOOBwONDV1QWLxQKLxQKz2QyLxSLMW/+KyymXyxETE4PY2FjEx8cjLi4OcXFxiI6OhkKhQEhICNtMh/mhWKD4QYgIdrsdr169gslkgtlsxtu3b/H+/Xv09fUJxel0gojA87yQ6ju4xaBYLIZMJkNoaChCQ0OhUCgQGhoKtVqNuLg4JCUlISkpCREREX/sIq7M34kFil/M4/Ggv79fKDzPQy6XIygoCMHBwX/kzAPDsEDBMIxfbISLYRi/WKBgGMYvFigYhvGLBQqGYfxigYJhGL9YoGAYxi8WKBiG8YsFCoZh/GKBgmEYv1igYBjGLxYoGIbxiwUKhmH8YoGCYRi/WKBgGMYvFigYhvGLBQqGYfz6NylPJgf+2B8+AAAAAElFTkSuQmCC)
A ball whose size is slightly smaller than width of the tube of radius 2.5 m is projected from bottommost point of a smooth tube fixed in a vertical plane with velocity of 10 m/s. If N1 and N2 are the normal reactions exerted by inner side and outer side of the tube on the ball
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)
physics-General