Physics
General
Easy
Question
Given figure shows a graph at acceleration
time for a rectilinear motion. Find average acceleration in first 10 seconds
![](data:image/png;base64,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)
- 10ms-2
- 15ms-2
- 7.5ms-2
- 30ms-2
The correct answer is: 7.5ms-2
Related Questions to study
physics
The motion of a particle along a straight line is described by the function .X=(3T-2)2 Calculate the acceleration after 10 s.
The motion of a particle along a straight line is described by the function .X=(3T-2)2 Calculate the acceleration after 10 s.
physicsGeneral
physics-
A long insulated copper wire is closely wound as a spiral of N turns. The spiral has inner radius a and outer radius b. The spiral lies in the
plane and a steady current
flows through the wire. The Z-component of the magnetic field at the centre of the spiral is
![](data:image/png;base64,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)
900553 |
A long insulated copper wire is closely wound as a spiral of N turns. The spiral has inner radius a and outer radius b. The spiral lies in the
plane and a steady current
flows through the wire. The Z-component of the magnetic field at the centre of the spiral is
![](data:image/png;base64,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)
900553 |
physics-General
biology
In angiosperms, female gametophyte is represented by
In angiosperms, female gametophyte is represented by
biologyGeneral
physics
A particle is projected vertically upwards with velocity .30 ms-1 Find the ratio of average speed and instantaneous velocity after 6s.[g=10 ms-1 ]
A particle is projected vertically upwards with velocity .30 ms-1 Find the ratio of average speed and instantaneous velocity after 6s.[g=10 ms-1 ]
physicsGeneral
Maths-
Maths-General
physics
A particle moves 4 m in the south direction. Then it moves 3 m in the west direction. The time taken by the particle is 2 second. What is the ratio between average speed and average velocity
A particle moves 4 m in the south direction. Then it moves 3 m in the west direction. The time taken by the particle is 2 second. What is the ratio between average speed and average velocity
physicsGeneral
physics-
In the adjacent figure is shown a closed path
A long straight conductor carrying a current
passes through
and perpendicular to the plane of the paper. Then which of the following holds good?
![](data:image/png;base64,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)
In the adjacent figure is shown a closed path
A long straight conductor carrying a current
passes through
and perpendicular to the plane of the paper. Then which of the following holds good?
![](data:image/png;base64,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)
physics-General
physics-
A current I enters a circular coil of radius R, branches into two parts and then recombines as shown in the circuit diagram
![](data:image/png;base64,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)
The resultant magnetic field at the centre of the coil is
A current I enters a circular coil of radius R, branches into two parts and then recombines as shown in the circuit diagram
![](data:image/png;base64,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)
The resultant magnetic field at the centre of the coil is
physics-General
physics-
The figure shows the cross-section of a long cylindrical conductor of radius a carrying a uniformly distributed current i. The magnetic field due to current at P is
![](data:image/png;base64,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)
The figure shows the cross-section of a long cylindrical conductor of radius a carrying a uniformly distributed current i. The magnetic field due to current at P is
![](data:image/png;base64,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)
physics-General
physics
Rohit completes a semi circular path of radius R in 10 seconds. Calculate average speed and average velocity in ms-1.
Rohit completes a semi circular path of radius R in 10 seconds. Calculate average speed and average velocity in ms-1.
physicsGeneral
physics-
If Young’s modulus of elasticity Y for a material is one and half times its rigidity coefficient
the Poisson’s ratio
will be
If Young’s modulus of elasticity Y for a material is one and half times its rigidity coefficient
the Poisson’s ratio
will be
physics-General
physics-
Four wires of the same material are stretched by the same load. Which one of them will elongate most if their dimensions are as follows
Four wires of the same material are stretched by the same load. Which one of them will elongate most if their dimensions are as follows
physics-General
physics-
A current
is flowing through the loop. The direction of the current and the shape of the loop are as shown in the figure.
The magnetic field at the centre of the loop is
times.
![left parenthesis M A equals R comma blank M B equals 2 R comma blank angle D M A equals 90 degree](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOwAAAARCAYAAADe30DTAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAOJ5y/mQAABOZJREFUeNrtW29kllEUf7xek8noQyYzY15JH2ZMZmYSM0mSMXklSUymD/sQfUgyGdOnScbkNZOMyUwmMUmSiUySzEj6kNmXSSavvKxz6vfY3XHvfZ/nPn/qqefHYbvP3X3P+d1zzz3nPO88by9GSCa8HDly/PXoIFnJaciRIE7mFIQCX6DbJN/w8x68IunU/FGVpL/Owvy8RlKwzBlNyUjWd4fkC8lrkickByOs5Wp7FeOfST6SPCY5FKOdvSSPsJk/SN6SnE+Rm7C4SzJn0McXds55krYM++FxkpfQ9zv2qF0zr4lkCvvAMo0xFby3rfj7b+qDThxYiRKIvGdRcD+c8p1lzjk4VTFhskpwXBXjJHcc13K1XafHbZKZGG19QVKGDoyj2MNyCtyEQRMCw7o4iFKfAgLaVXA6mEE/HCB5T3IM9vDnXCZZI2kWc5+RnFF+P40xFduwvU0e2DsgSuIsSN2wKDmNOXOG5wdA4jLWSxK8/kPNJs04ruVqu06PQc1Y3GizOGyc3AQF3w4f4IgHAujjYwgOWsiYH74x3KZDIjAOIeOQmBQBd5jkK7gYVic+JenTLHCL5DoiRLchBWESxjDPRCQrcbFOhIwDrO81MTbmmAZFsf2WZmw2pRqumgI3QVP2TZKKIUXV6SNvl2MZ88OaYZztX1V+f4TbWOIEntUFn+AGzfg8otE4REUj0pxOZZ5ED8kSfm5GLWfDTgCxYV6kGU2GdCQIotjujxUwp2I5GFFtlny/SoGberiAwHEtxF55mpSxP2N+yOt2GTKf78rvW4bz1oAg5xwZmIgWRLU1TRPBJ28N81QUkSK0KmMcZY4keLusow4q4jZbRfrhupar7euikZLGzboPzYveFLixYQLOeSbgXpnwSWmIZcUPh6D3cQTrAmrTVdTO9c6bJ+aFOrAFERU2FCN7UVwXNfNsKQ8TO5KQwxZghxoF+yKs5Wp7AYfUj5h8S/DrssMJHlauzxYNaVbc3NiaPovgqisAv9uW543KTZM1P+TD+hwZRhW3fknoVnMoaeqmxN34YLUGuK6kIF2GeR4IXTUY8zihlFjq0ROhAxrF9m5Nt++8RZeoKXE7DkopJW50aEHD550X7NWVjiMVXGfez6gf2rIfH5uGlHhf0JR4WZNKlUUHsR8fOinqiLKm0/jSYmhSbXWdHsue/p1e2LXC2F5GzSpruvsJ2HwE6zamyI3u8LGTPfF2XzEF4bdiec4HvyOjfugZmkm3RdNJVyYNBG066V7rcG0wLNIYvok/CEPlvGGQaQK33U8lQIrUw79JZmNYK6jt/tglMVbxzO9HXdGMdKuYMjcqziGFm3Tg95Lh2aRYL2t+qMO4qK0HDQF8Jqif6L44saAx6IGmPlHnHUJ0tEXayw4bHAQLhg3g1Ouo2Kgdz/4uzsV2dcyPngfRiHhrSIGiYClE4yRObnzcxNwRx71Sb5gG3C58S09l2A+f4TA2KKXCTUMDjtP3UQQdnn/D+/1lmMBYUdIQxhZy6npQ582jK1av3llP4MCa9O2BI4RxShfb1TE/7ari81oSsDdMfRUnN+q8oLJk4aiGlPoh9IljL/6UH/bjINaQBcyJMyUbhRVv9yuM0yFKil/4n778n2Y6lHOTIzFc8f79f6/j9P99ig2HnJscOSKgxUvm2z05NzkSx0+dofTiZqOX9wAAASh0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW8+KDwvbW8+PG1pPk08L21pPjxtaT5BPC9taT48bW8+PTwvbW8+PG1pPlI8L21pPjxtbz4sPC9tbz48bWk+JiN4QTA7PC9taT48bWk+TTwvbWk+PG1pPkI8L21pPjxtbz49PC9tbz48bW4+MjwvbW4+PG1pPlI8L21pPjxtbz4sPC9tbz48bWk+JiN4QTA7PC9taT48bWk+JiN4MjIyMDs8L21pPjxtaT5EPC9taT48bWk+TTwvbWk+PG1pPkE8L21pPjxtbz49PC9tbz48bW4+OTA8L21uPjxtbz4mI3hCMDs8L21vPjwvbWF0aD4PzqQSAAAAAElFTkSuQmCC)
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)
A current
is flowing through the loop. The direction of the current and the shape of the loop are as shown in the figure.
The magnetic field at the centre of the loop is
times.
![left parenthesis M A equals R comma blank M B equals 2 R comma blank angle D M A equals 90 degree](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAL8AAAC/CAYAAACv6g0GAAAgAElEQVR4nOx9d5hV1bn+u8vpZ3qhD1UEggKiFBGsyVXhKsYoxmhMDGok18dovBHsYP/FxKBGrDGWRGPMVbElxoqRJlgQRAKIIFIGpp2+6/v748xas8/MAKMMzAycd579zCn77LL2t7719U8hSeSRx0EItaMvII88Ogp54s/joEWe+PM4aJEn/jwOWuSJP4+DFnniz+OgRZ748zhokSf+PA5a5Ik/j4MWeeLP46BFnvjzOGiRJ/48DlrkiT+PgxZ54s/joEWe+PM4aHHAEP+e0hJc14XruiAJx3Hgum6L35mmiUwmI79zHAckYVlWi2Pt7hq835Pc7ZZHx0Hp6sksgohUVZXvBXGTRCAQ2OVvHceBqqpQFGWP53EcB4ZhIBwOw7ZtuK4LTdNAUv53XRe6rgMAbNtGJpNBJBLZ7XHbcu489g30jr6AvYUgQgFFUaAoCnw+HxRFyeGygpPrug5VVeG6rtwHgCRkAcMw5ORxHEd+rus6bNtucV7btmHbNnRdh67rCIfD+/r289gLdHnOL2BZFjRNkyuA67ryteM4OYTqhSBi70QRvxPH9fl8LY6xq2NalgVFUeQKsKfhzXP+jkOXl/mFfC24OZAlaC+nzmQySKVSLX5r2zZISgIUE8A0TbmPz+cDAEnoiUQih/ANw4BlWfJ8Yv9MJtOu95lH+6PLiz1ClEmn0/D5fAgEAtB1Hel0GqqqIpFIYOHChVixYgU2bNiATz/9FBs2bEA8HkcikZDij4Df70fPnj1x2GGH4ZBDDkFFRQX69OmDIUOGYNSoUdB1XRK+4zhSLHJdV04KXddzJl8enRNdXuxpLn6YponXX38dd911F959910Eg0HJhcPhsFwBQqGQFE+Eguy6LgzDkMcS4o7f70cmk4Gu6xg1ahTOOeccHHPMMRgzZgyqq6tRWVkJoElEApr0hbzY03nR5YkfyBLdCy+8gHnz5mHp0qVIJpMAssRuGAZGjBiB6dOnY+rUqSgpKYHP58uZMILwhZwONFmC5s6di3Q6jQcffBAbN24EAESjUaRSKYwfPx4nn3wyzj33XAwYMCBHzxCKb574OzHYjjBNkySZSqVIko7j7NXxxHFIMp1OkyQNw6DrujRNk7fccgsBEAA1TSMAKorCX/7yl9yxY8denVvAdV1aliXfr1q1itdffz0PPfRQAqDP56OqqvT5fPzVr34l962rq5O/yWQyOce0bTvn/lzXpeM4dF1X7uM4Dg3DaJd7yKN1tBvx27YtH7x4uG0hfvGABZEJIq+trZX7eInnnXfe4XHHHUcALCwsJAAWFxfzpptuYn19fc6xxWTcW5im2YIQxb298cYbHDlypJyEuq7zggsu4KJFi+g4Ts4ENgxD3l9NTU3OsWzbziF+7zny2DfYa+JPp9OcP38+AbC0tJRbt24lSSYSiTYfo/lDbw1btmzhpEmTCIDhcJiHH344H3roIZJZLuvlos05bXvAdd1dXmddXR1d1+XDDz/MgQMHUlVVAmBJSQkXLFiQM3G8r8Xq4LoubdvOE/t+Rrtw/muvvZYAeNFFF5HMcn4vx9sTmu+7YcMGkmQ8HufatWt54oknUtd1AuCPf/xjNjQ0yH29BClWnF29/zbwEqtYncQ5veIQSVZXV5MkY7EYzz77bAYCAQJgQUEBn3jiCcZiMZLkmjVrWtzz7iZXHvsGe038juPw3Xff5dy5c7l69WqSTeJGWziw2Me27RxRYOPGjZw2bZoUJy688EI5KUhKEUmIEYJ7imOlUqkWxPlt4CXITCbDRCKR81k8Hm91MsZiMZqmyWOPPVZO3FNOOUWuiKZpysnQ/HxC/s9Phn2LdlV4ySzhJZPJb/w7QaiC2w8ZMoQAGIlEOHv27BwdYFeyvJCbLctqN3nfO4Gbc34x2byEKojXi9WrV7NHjx4EwDFjxuRM4uayvpjEeTFo36NdiH/SpEn86U9/SjJXFIjH4236vZgssViMP/vZz+j3+xkMBvnAAw/IfVzXpWEYtG2bmUxGEreXQJoTUntw/ubYnVLqnXDNJ2AymeSf/vQnaZH64Q9/yGQyyXg8zkwm02ICNLf+5NH+2Gvi/+STTwiAY8eOZSKRoG3bNE2zzfK2kKkNw+Cll15KAKysrJSc3nXdHOW5tVXFMIycz5tz6L2BsMS0Zo0R54rFYnKiOY4jJ4QYA+/1x+NxDh06lAAYCAS4c+dOxuPxdtFP8vhm+FaxPa7rSq/p5s2bAQBjxoyRwWWGYUDTNJimKeNk0um0/A0bHT+WZcHv9+OCCy5ARUUF5s2bhx/96EfYuHEjiouLZZCYNyy4tUhJv9+f87nw3LaHA0lVVWiaJoPfmkNRFBQUFEgHmaqq0tGlaRps20YkEpE5AX6/H5999hnWrl0LXddRWVmJc889V/6mtRgkMV4ihCKP9sEeiZ+NkY7eYDFVVaUbf8mSJQCA0aNHo7i4GED2AYv/fr8frusiFAohGAwCaApG8/l8ePbZZ/HEE0/AsiwsWbIETz31lCQ0r8e1q8Ib3+99P2jQIDz55JPo2bMn3n77bRxzzDEAmgLobNtGLBaDaZryt2Ii2raNeDy+v2/lwENblwivE4vMyrfJZJLnnnsuy8vLuWbNGpJNS7wQEYRYk0wmpYxLZuX7m266iQA4fPhwqQQKBXPnzp17s6J1OgirFJmrRFuWxZ/85CcsKytj9+7duWDBgpx9vfs11yny2Du0mfi9CphQyBKJBA877DBWVlbKByYcN177ePMJYZomZ82aRQCcNGmSNPkJl77w1B4ICl88Hs+x4JCUYyfur76+ntdffz3Ly8vZq1cvef/NJ4EI7RDI6wl7hz0Sv1chbY5MJsMhQ4ZwxIgR8qGkUik6jiO5lPeBJ5NJ3nvvvdJ2f9ZZZ+U8QK/jZ194aTsCu7o/oZR7FfV//vOfLCsro8/n46JFi6S/wjsJDMNo1dKVxzfHHmV+r/LWKCZJBWzDhg2wLAtHHXWUVGZDoZDUCerr66FpGlKpFN566y2cd955uPnmmwFkFdfTTjsNmqbBdV1YloVgMAjDMGDbNgKBgIzO7MrwRo8Gg0E5dkKnCYfDSKfTsCwL3/ve9zB79mwoioJZs2ZB0zSpKwnDgd/vl4q3N+Msj2+BbzpbBNcxDIN//OMfCYBz587Nsem/8cYbfP755zlnzhxqmibd/KFQiH369CEATp48Oee4rTl7WpN9uxpa486ZTIaWZbWI3BQrw9KlS1lQUMCxY8fmRKd6x8M0zQNCLOxItNmcIuLTBddxHAfr169HJBLB2LFjEY1GAQCff/45zjjjDGmN8Pl8GDZsGHr37o3a2lo0NDSAJIqKinKOL1YAx3FkgomwDnVl2LYNv98P27alGdSbDeb3+2VCjs/ng2EYOOqoo/DQQw/hhz/8IW6++WZcf/31KC8vz8kNoCf9Mo9viT3NDq/sbRhGDqcaPHgwA4GAfO+NYXddl9dccw179erF8vJy9unThyNGjOC4ceM4cOBAbty4sV1m74EGwc23b9/Oa665hgB43XXXkWzi/F6HWh7fHnsUGkUqnkjnEzb8L774AplMBgMHDsSOHTsAQNr54/E4FEXBtddei82bN2Pq1Kno2bMnSOKjjz7C2LFjUVVVdUDI9HsLUQNI2PIFKisrMXXqVJSXl+Phhx/Gq6++KldCXddhmmZe5t9LtCmN0ZubCjSVBdm2bRsKCwtluqBpmigoKJD1cEQ1hKqqKpk6GI/HcfPNN+Oiiy7apzfW1eBNgTRNUzKZ+fPn4yc/+QkGDBiAV155Bd26dZMiz+5KsuSxZ7SJdTiOA8dxYJomSMok7+7du8Pn88E0TQQCARQUFEjZVlEUxONxHHPMMXBdF+eccw40TUMsFoPP50MsFtunN9bV4OVB3vKIp512Gq666iosX74cjz32GIBsWZQ84bcD2iIbpdPpFoFiiURCWn682VNCHl27di0nTpzIgoICvvnmmyTJ2bNnU9d1acHIO2ma5HjTNKUML8ZQ+AJisRgnTJhARVH4/vvvk2SruQB5fDO0ifMHg0EpZ6ZSKaTTaWmdSKfTUBRF1q/RdR2ZTAaLFi3C6tWrcc011+CEE06Abds47rjjoKoqysvLAeQrFwBNcVA+n0/W+xTij6IoUFUVBQUFmDNnDkji5ptvBkkUFBR05GUfGGjrLGnO+VvLNBKc629/+xu7d+/O8vLynEwtkvzd735H27YPCBv+voAIoSabwrmFD2XevHkMBAK8/fbb5b55fHt8I+IncwdcEL/4rKGhga7r8le/+hUB8LXXXiPZtLSL0AfxcPOlObJIJBJ7DOcQ419RUcFwOMzNmzfnxca9RLsUrfJaJ1KpFA455BCMGjUKL774Yl4payew0cITi8UwYMAA9O/fHx988EHOPul0GqFQSFrnhDlU13UYhgGfzwdVVXNCJYCsAu0t5JXJZBAMBnNEsAMRe31nrutKD6ZpmpgzZw4KCgowe/bsPOG3E9iYTwFk43kmTpyIL774AmvXrgUAaX0LhUIwDEMSrN/vl8lFgUAAqqqCJPx+P3w+n8yrCAaDcj/xvTjXgYy9vjsxQJZlYf369bj77rvRr18/jB49eq8vLo+mUorecIgzzzwTtbW1uO666+RngpBFyXWReOTtPyCOJ/YThXwFNE1DJpM54IleoF04v8jUeuutt0AS06dPB4C8B7cdILK3BAH7/X6cffbZOP/88/HOO+/gmWeegaIo0jcgrG6WZcmUSCHCAJBRtuJ9NBqFaZowDCMndmtXrZcOJOy1zC/kfcuyUFFRAZ/Phw0bNkjzaB7tA69eBQDLly/HxIkTEQ6HsXnzZhkiLSaKl4hVVZX6gFgRNE3D+++/j2OOOQaapuHkk0/G/PnzATSt5kL2P1Cx15xfPJCXX34ZDQ0NuPjiixGNRg+apXNfg40N8bw8qq6uDsOHD8eoUaPQ0NCAmpoaBAKBnJwLoGlVFpGyAGRxgXQ6jd/+9rfo168fdF3HihUrZNSpWEW8IS0HJNrDZOQ4DsePH8+ioiJ++umnjMfjeTNmO8Ib9+84jjSLLl68mAByagB5/Sei8JXX1yLM03/9618ZDoc5ZcoUjh49mgBkuml7Vdnu7Nhr9iwUpEWLFqG0tBTDhw9HNBqVolAeewfDyEBVFfj9PpAuACIQ8CMej2Hs2DHQdQ1PP/00wuEQotEIHMdGY5YoFAVQVQW6rgEg0ukUFAWora3BX//6DDKZNMaMOQrHHjsJmqYik0kDIDRNBUCo6oHtgW8z8YuwWxGCKxAMBqW9efr06XLJjcfj7bJsirZDQFOvLW/PLLaisrAxBFuYXwWEuVC0Ke38yBI64AJwoShEVpp0UVAQAeDi/nn3QdOBdxe8DcBFIOiD7ZgAXKgqYFoZKCoBuNB9KgAXL738Il559SV0616BmbN+jTO+fzoc18W9981FxkjBtDIgHIhJ1NFoaGgA0HqfM9d1cwwrguG2JXByrzn/V199hcceeww+nw/jxo2TEYcitHlvIYpfAZAKnZhUjuPsspCUsJL4/X6k02kAkP9Fj9yuMgF2t11wwY9RXFyEF154HgChaxoMIwPbseDSgd/ng+tmCTkYCMB2LHzyycewbRtz5swGQJSUZPMwvvhiPYKBAKKRCADCZecokCXimFp71qqqyoJlhmFAURSYponCwsIcxtcq2iofecv2NZcFp0yZwhNPPDFn3/ZE8xo1uypCu6uc1l2VGez8cEnaJK3dbt26l7GktIDpTDznc8tOy9fxRB1tJ8P7591DKOCpk7/HjJEgaXHjpvVUVHDI0EF0XIOkxYZYTeO5O3acvCEczcvnkGxRycJxHJkfvSfsNeevq6vDpk2bMGDAgJzZ2J7QdR2WZcllz9v0TYC74OKCGwhnjlgimzt/uipMy8SUKVNQVxfHmjVrYNkWXDa2Z9V0+ToaiSKTyeCxxx5DMKjj97//PQL+rE+gvLwcY8ceCdM0W/gLOhreCnaic6bIKwGamgaqqootW7ZIk6+qqntsB9smKmWj3di7iZPfe++9WLFiBaqqqnJOlslk2kXhzWTSUokLBgMAiK1bt2DNms8bFbIm5S67KuaKBYGAH199tQmJRBymaSASCYN0YZpGq/u33Do3/D4/fv7znyMcztYAFY4q0zJhWiZURUUsnpV///73v+ODDz7C+eefj0MGHYJUOusEc10Xffv2xY4dO/DRRx+BIAL+gJw4HQuCdGHbFgDi17/+X/TtWyVLWmYV+uw9Dxw4AN/5zjAsWPAumvSl3R16DxChy7vapk6dylAoxOXLl5PMFVHaR/xxSTp0HIvJZJx//OMj7NGjGwFw/PixdF2bpJOzOY5F2zZpmhkmEjH27t2TANi7d0+mUgmSjvy++W9zt44WjfYs9lh2mnX1O1hcEuXlv/yF/FyIQKl0jKTFBe+9xfFHH0Uo4IknHcv/e/5ZPvnUY5xz8w386YXns7AoTCjgK6++yIyRoEuTnUHsSadTtG2T4pkMG5bt26CqYHl5qeRSkUiIfn+2CciQIYMZi9Xv8dr3mvhPOOEEHnrooTmdGNs31NZlIhGjuPlnn32G48ePZVVVb37/+1Np22aLCWDbJtPpJBOJGC+44Hw5WGeccTpJh4lEjJlMirsn/K5B/ILQ+w/ow3Hjj2RzWV9sPzz3LEIBNR2EAqpadoMChiN+QgH9AZX/9/yzdGmyrn4HHddk5xiD7PNIJuMMhQI87LDvcOnSxbRtk5ZlkHSYyaSYSMQ4efIpBMA777ydrrt75tumKs0CQuTxfldfX4/i4mJZcyYUCskAqb1HdmILbb6+vh5LlizB5s2bUVtbi4ULF7Yqtwuvpm3bWLhwIcaMORKBQAAnnngiACASiSAQCLTBGtU1RJ9gIIgjjzwyx7MLQIo1//f8/+H5558HANxzz1x89NEHeO65Z/Hee+/ihReew6pVq3Dffb9HKBTCokWLoEBBcVExVKWjvfSEYWRy4prSaQM9e/bEsGHDZLd7IKujRCIRnH766QgG/Vi4cCH29PzaRPxeoieJRCIBRVHgui62bduGSZMmyRKD4kLbMyYka3IjwpEQXvvHq7BsEyNHjUC//n2h6xoUBTDMDAAinUnB59MRiYRx9ITxKCouhOPaGHTIQPz4gvORMbKOnLr6WqiqAss2ARA7a3YAoHyfTGUV5Ewmk1NWRNyfsCOLWBnxX+wrzGxCORP6j9jPW4ffq7h7zyGUdNMyQc9DtOxcXcowDfTu3RvJZBKbvtoEvy8r62qaBtuxMX/+fBQUFOCOO27BjEtnYOjQoThj6hk46qijcPppp6Oqqgq/mPELRKNRPPDAA/K4qXSqBYNgow+lPSHKVbaGbDEEACD+/n/PwedXQbiAkiVs8dzFc+3dpxcyhomevXrsMU12j8Qv6sGLhynydR3HwWeffQafz4chQ4bIGSgGa3c39M1AuK4Dw8xg+/ZtUFUFfftWoU+f3ojFGrC9ehsc10bA70fGSCMUDAIgPvxoOVavXoOSkmJ89dUmrFz5GaLRCIKBABLJOEqKiyXBA0R5WRli8Qb4dB2mZSASDiOeiOUE6DmOI+9J2J69gWIAWsTFiNqawlIhCF2MoXdfIDvZxKopquD5fX4oUOQEkF3eHRu2YyPgD2DIkCFYt24dduzYAYJIZ9II+AOYO3cuHn/8z1BVFRdccEH23P4AYvEYfHr2vKlUChkjI2OBhIIsqnB40VqINBvrtzbf2uLnISlru5JEOp2WDMRxHPh8OgCCcLF48SL069cX3/nOMETCYbh0EPD7s88pEEA8EcOf//wUSkoKcMQRo7CnVbtN61pzcUfXdbiui82bNyOZTOLwww/P2RfIbWCxdyB8ug6fT8emTRuxbdtW9OnTG8OHfwc1NTvx9ttvIZ1OQThxBPe/7rprMXBgXwwdOgQ+n47jj5+IhoZ6AEQ0EoFhZlBeVgafriORjAMgCgsKYDsWNE2F49qNlqGmLjLCaSbuM5VKyfeCS4dCIfl9Op2WZRuFOU6IcF7nnaqqclIEg0F5jBzPpd1k6tXUpommaRpi8RjKysrQo0cP2cUmFAwhnUnj2muvBQD84Q9/QPdu3ZExsscoLCiESxeGaSAaiSIYCDYWBzZQXV2dvZZAUE5QLyF7CVxMkNY2kTyzuy0Wi+VMJpF0I6JRHdeW3H316s/Qv38/lJWVIp6Iyee5atVK/O+vr0JFRTn+9rdnMW/e/fjJTy5AuxC/16sqHpjP54Nt20gmkxgyZEjTAVVVhkC0h4dXmNsURcHKlSuxc2cDRo4ciWOOOQbbt9eCJKKRKBy3UexwbNxzzz147bU3MGPGDNTU1ODrr6sxfPhwFBcVwzANuHQR8Adw7333QlH9OOecczB5ymQoqh9XX321FOm8Mq+wJ5umKUUebyskbxy9N7OqoKAAhmHA7/cjk8nISWJZFkKhkPQ6i98nk0kpKgWDQdhOlgv6dB9CwRBMy5REGwqGoEBBYUEhqqqqUF1djS+++AKu6yKVTuHyyy+HYTg45phxOOWUU+R9uHRhO3Z2FW+09VfvqEZhYSGCQR0ff/wxkqnsxBOrnpf5eQl+T9jVxBBbUVGRHG+RdimIX1EUaKomrzGTyWDlypW4+eab0b17d3Tr1g2K6sekSZNw111zYVkuLr30Ukw7exp0rQ3h9N9U9/Y2SHjiiScIgK7r5nhd26+ToEvSokuDpMlrr/s1oYCrP19B0iQU8PobZjKdiZE0SZpMpRsYCuscO+4I1tZt55FHjWBJaZQLF71L0mTGiJM0+eRTf6Smg088+SinnjGZc++5i+8ueIN9+/XkxZf8lA2xnSQtOk5TpQmvFSuTyeTU2Wlu4dqTmbf5981/n23qZ5G0mUw10DCT9FpvDDNJlyaTqQZadpqfrV5BVQP/8vQTjWbK7D7Ciyu2mtrtJC3W1e+g1xTqNZsKL69ppZnJpFvc7zeBaNC3q635PXthGJnGazO54L03OfywQ9mzVwVP+u6xHDvuCJ5y6kn80Xlnc+CgKmo6GC0IcOy4I7ji0+XMPusEd2etahPxizaguRdm8De/+Q0BMB6PM5VK7YOQAZemlWIqXU/S4LRzziAUsKZ2K0mDvftU8pDBfRlP1JA0SBp84slHCAX8ZMUHJA2OGTuS/gC4bfsmuc8nKz7gwEF9+ORTj/L8H0/jm2+9xrn3/IannHoi//rsk7z9jtn8cuN/mB34pnvytkrydlgUqKmpkQ9QTBjvfl9//bUcI2+1hubdGw3DaPw+a+r0mi7rG3ayNXOn4xosKS3g//76CvmZ7WTk61Q6RstO5xzLS/je1/FEXePrJju/t6iWCHHxEu+uwl/2ZCrPZDI5Ydg7duzwjGGqcdIb/N9fX84hQwfwl1fMoMsMbSdF0mA8UUPHTZM0+M67rxMKOPjQftyx8+sWz6852mznb15aw7Is3nvvvaysrOTOnTtzOFfzleDbw6HtpElmSGY4cdIYlpSGGU/spGHGOOfma9mjZ6n8/vkXnmHvPhU84/unkswwFt/BQ4f047DvDOSWrRto2QmaVpyGGeOlMy7klP/+LjNGA9OZepIZWnaCjzz6B44bP4rP/PVxptINTKeznVPS6TRPP/10Dh48mCNGjOCRRx7Ju+66S16pYRi84oorOGHCBB5//PGcPHkyb7zxRpJN8fE/+tGP+LOf/YyvvfYab7rpJr777rs5nVlmzZrF4cOHs6ysjIcddhgvueRiJlNNRPnqa/N5+IhhPGRwfw4ZOoiTp/yXJPA1/1nF8UcfxXDEz6LiCEtKC1hSWsDSskJCASsqS1hYFGZJaQGhgKVlhXLfPlU9WFFZwqLiCH1+hVDAUNhH3aewb98qjhgxgmVlZSwtLWXPnj0ZCASo6zpVVWUwGKTf76emaVRVlaqqUtM02UsZe3Chi94NiqJQ13X6/X6edNJJfOONN5i175u07AT79utOKOD/XHYRXTbRBJmhYcbouCmaVpxnfP9UQgGff+EZxuI1jcdoHXsk/uZBZaLPLkm++OKLHDx4MDdt2tSi83j7OLqyYg9pMpGs48BBVTzs8CEUIk71jq9ZXBLh52s+peNm2L1HWY5YtOHLNQyFNZaVF9Aw4yQNGmacLjO85Oc/5dPPPC4/TyRr+eZbr/HjT5Zy5qwrOXTYQL6/8B2KwVu7di3D4TABsLi4mAB46KGHksxyvVWrVnHw4ME53xcUFPDLL78kSW7bto0FBQUEILuxB4NBOVbbtm1j3759Gx1yWSJSFDQ68GzGE/W89bY5hAIqatY5VVgU4Xv/foeJZAMnTjo6x4lVWlZEKKDuyxJzlqCzzqxoQUh+5vOr8rU4tjiGIFBxPwDkGIhNTILmRK2qKnVd3yPxezdN0+TrbIJOQj7/Q4cMYFFxmC/Of46kSdNK0qVB00pKeiBN3nDjLOo+8JVXX+Bec34ytyOIIPBkMikzid56662c/S3LasdugVkP3+2330oAvOiin0mPbkNDHfv06cW3336TlmUQAIcOPZTCI3jjjdcTCvij86bRpSm55Lr1n3Pc+CN5w43X8KKLf8r3F75Lw0zy1ttmc/PXX/KcH/6A110/k53BvZ/1Urpyy8rB2deOk72+yZNPJQBeddWv5PeWZeb87ttv+xat0UlJSQlnzJjRyEBdJpNx+nwadV2VoQ6OY1F4fcXzvv/++wiAxx9/LJPJ+B49vG3KMPdGaZJNtuZgMIhwOIyGhoacPrPtm7iuAFDgOEQ0GsWoUaPhuoCmqdB1P6qq+uGKK34lLUu3334ngKzpcMmSpQiF/OjXrx8UZC0H1TuqMXDAQNx5550499xzcd555+Hjjz/G5ZdfjjvuuAPTp0/HP/7xBuhaIIiOzmVSlGyRKVFXJxwOe56BhtNPPx2vvPIqJk2ahOnTL4LfL2qm+rpE9xZd12XEJpDNuRDJ9pqmwbIshMNRHHXUWDJvNcIAACAASURBVCxfvhz33vsH9OnTB36/Hzt37kQ4HMbixYuxaNEiLFmyBBUVFbjwwukIBEJQ9uSh/qazU7y2LItffPEFR44cyb///e8k2UIBao/ANiEvn3vuudQ0TYoRQgf51a9+JeXG5557Lue3o0aNZEFhmG+8+Q9pAfFuz/z1KfYf0IenT53MxUv+zYLCEL8z/FA2xcd0POffVU1Tcf8ffvgh77//fn711VckKas6k7vOe+hs8OYo27bNYDDIWbNmye+ffPLJHBHM5/MRAP1+f47YVFVVxUceeaTN5/3GnN87YwsLC6EoCjZs2AAg6wMQnF/YbvcWoVAIqVQKH330ESKRiOz+IjyCO3bsgGEYKCoqwgknnCB/l0gk8Mknn8AlcdRRR0GBgmQqiUg4glg8hsKCQkw7exomT56MESNG4Pbbb8cvfvEL3HTTTUgkE4hGont97e0BESayY8cOVFRUyLr8wkM8atQoDBo0SHqDHceRTrKuUH1BOLO8XT9N05TOwUQigeXLl6OoqAhjxoyBz+fD1q1bUVdXh4EDB8JxHEycOBGDBg3CmDFjcnxOeyy98k1nqVeRTafTPP7443nNNdfkzGKxX3v00hWcf9GiRdyyZQvJ3AK3pmnyP//5T06ja2FB+dvfnuX/+83t0tbdPNNJmA1f+8dL7NW7G//1xmv0mgjTmd3bifcH0ul0i4oML7/8shxnb1+E5kaGrpCtJlYn8T8ejxMAr7jiCjY0NJDM3pswM4t7EhKIt7exgKhqvSe98xsL5976mz6fDzt37sTChQulV1d8r2lau9TqFFxs4MCBqKiokAFhoj4oG9seBQIB+T4cDsO2bXz/+9+HqgKpdBKO6yAYCMKyLRnTUlRYBMPMuvN37tyJ0tJSANlAs3Ao3ClqjQrO1dDQgKKiIkydOhXvvfcezjzzTDz66KPSM+yNH8rGxPg6vbwPQNYJEpx/+/bt8Pv9mDBhAgoLC5FMJhGJRFBWVgYAsgaRuM9QKIRMJgO/3y+z9qLRqKxPuttzf9uLZqMy1a1bN2zfvl0WQxIE016Rf0J0qqioAJANKQiHw0ilUtB1XQaOJRIJ6LouJ4eIpWmINWQJWc1GOMq0uMawgYA/gLVr18IwHKxbty57jlA2bEFMko6Ed7KXlZXh5Zdfxplnnol77rkHQFM4hTfDThCSN3K0M8PLNGtraxGJRDB06FAA2fBzNga8WZaVU3FatK8VaYuiYXeb0dblqbVGFI7j8LTTTmNZWRk3b96cEwbQmgf020IcK5lMtlCivaEUYtlvaojdlAzidfML9z1pMZGsJ2nxg2WLct4nUw3sDAovmb2f2267jQA4aNAgudR7HWTN0R4i5/5AczH6n//8J3Vd58KFC5lIJHJEPiHGeBV68b03/KK5x3xXaDPnb76ECiXlv//7v1FTU4MNGzZIJcwbCNceEJGK4XC4hfLtDbsV3EMof16I4CgAOQFrkXAEhmngyNFHwnGblEXB/fc1vFWSm7cjBbIrWCQSwfjx4/HII49gwYIFshS5N7CuOTpLAvqeICQEwzAQDAbx6aefwrZtDB06FOFwOIeTCxO6CCf3+XzyexENCiBHed4d9jpVp2/fvgCAxYsXy6JWAKQM1hUgJoamZu3KIm7em0CyrxCNRqVlQ9f1nMkgQpYVRcGkSZNw8skno0ePHgCaOrd3dYiQcDb6LjZt2iTF532ts+w18Y8ZMwbBYBBvvPEGfD6fvBnXdbsE9xFZUdurtwNoLHXS6NraH+UW6+rqJCezLAvRaBTpdBqu6+K+++7DBx98IEN9e/XqJX93oLUiDQaDMAwDH374IRzHQTKZ3Ofjv9fEX1RUhKOPPhpbtmyBZVkyd7ar1Hf36T5c/svLMXDgQCxbvgyFBYUAsqmBIh1wX6KkpARAVvwRomIoFMLEiRNx5ZVXYuvWrYjH43AcR64Ktm3LPICuDnoyvlzXxdatWzF06FBpvduX2GviJ4kpU6bAdV0sWLBAWmGE27qzw3ZshMNh+Hw+lJSUgI1/mqbtl7o1ovy40FNE4d+FCxfiiCOOwNixY1FWViYdW0BT2cYDAcIZalkW0uk0UqkUvvvd76KkpETqX/sKe038iqJg6NChqK2txb/+9S8UFmY5Zzqd7hLNKXRNR21tLerrEygoKIACRcrS+6N6gbDHO46DeDyO448/HiQRCoWwePFidOvWLWdfwSXD4XA7VcjoeOi6Dp/Ph3g8jq1bt6JPnz77RZ9pl6c7YMAA+Hw+LFq0CEB2We5K5cl79OiBsrIibN26FTtrdkLX9LalwbUDvM5B13WxaNEivP3220gkEjKYLZ1OS+OB14hwIDQA8RaTFZO5qqoqR/HfV2iXJzx48GAMHjwYy5cvl/EUhYWFnaSV5e4tBgSxdes2KIqKAQMGoiBaID8HRQnEfQd6nFJFRUUwDAPHHXccUqkUwuFwC6OB0Assy8ppU9RVIe4nHo/DdV0UFRVh0qRJKCoq2uf0s9dHFhUGbrvtNtTV1WHmzJkwDGO3F25Z1n5SiJXGTd31RhUPPvAwdlTXoCBaBMOwYBgWFGhwXWJPk6ctELKsgODeZFa3mDZtGp5++mkAWSuOsHm3BiFKdoWgtbZAmDOj0Sjmz5+PeDyO7t27A2i/KIFdYa85fyQSgeu6OOqoo9CjRw+sWLEClmUhEAhg+/btOTKrABuLOImmyPsWuydeRVFy4kD8/oAsS7I7J1JbIWLTAeTU6RGTv0+fPtiyZQui0SimTJkizZ4AukQ8fntAhC18+umniEQisCwLiqLs8wneLpQn5LbHH38cS5Yswbx58wBAEr7jODmcXjgwOouTJhAIoL6+HkBTvZ09NjZoIwThb926VTpvxKp4yCGHYMuWLbjkkktw55135hB+MpnsMubivYG4R0VR8OWXX+Loo4/eT0wR3zykuTlEXI0IP/3Od77DMWPGyLgK0SzAsqxOGWJr2zb//e9/s2/fvrz77rtz4kGaYoS+PRKJRE5DOBGau2XLFpmAsX79+pzrqaur2+vzdhWIRBbHcahpGmfMmEFy/yTitIupE2jicLfccguWLl2KJ554AkDWIiHs/mys0tWZIPrWbtq0CcFgEJqmyR5QrcUIfVOIZVycS4TmlpSUwHEcrFy5Ujb2EOmKkUhEXsOBDkVR4PdnewuI5BwA+4VW2mVtEfI7SUydOhWHHXYYLrvsshbmKlVVW4hAHQ3btrFly5Yc+bqoqKjdTG0NDQ1yEqVSKWQyGWnaFGG4ALBlyxZpvUmn0ygqKjpgvLhtwYIFCxAOhzFhwgQAkOLhvkS7EL8oXVhbWwsAeO6555BMJnHppZeioaGhhWwvZnRnWAV0XUdZWZmUMYUlpj24PtAUkbp582ZUVFTIRmlCmRPn7dmzp+wsKByF+9rD2RkgchCefvppRKNRlJWVwTTNnBj/fYV2If5UKpWzpB9yyCEYPXo0nnrqKezcuTOHi4ouiUDr3fU6AocddhgGDRqEkSNHIhAISI7rLRT7baHrOuLxOGbOnIlUKoWzzz4bwWBQcjWxGgrzsJgsncUYsD9AEqtWrcKgQYNQWVkJv9+/f8I39lZp8NarJJuqDcRiMZ544olUFEVWXGiOztKl3atgCoU3k8l8IwW9eTdAobC5rsszzzyTAPizn/2MjuO0WvvzQIY3z9YwDJqmScMw5PP/4osvCIDnnHOO3K9LKLyyVnxjEJtYzgsKCvDDH/4QJPHUU08BgIxbF27szuKhFBUhgKb7aVvnlqZUQW8uqohVEQFbM2fOxMCB2VpB6XRaOrA6y8q3r+H1UovS9X6/H36/H6lUSjbEmDZtmtxPVMXep2ivWZTJZFpwsng8zqlTpxIAP//8c5K5qXe7S8Pb3xB1b8hd18ppDd60Sm8FBa+ZtLa2lvX19TnHbw8zaleDdyX1vu7evTt9Pl+LMdnXK+Nec36v11JwMlFrPRqN4qmnnkJhYSF+9KMfSa9pQ0NDYyWu/ZMquCd8/PHHOO200zBnzhxZFx9oPa2wOYQZU7QvEmOwYMECrFy5EgBQWFiIoqIiueIFg0FEo9FOZfXaV6CnTxg9Bg7TNOX4btu2DQMHDszx6Iostn2JdonnZ2NwljeHUjzYSCSCf/3rX1i+fDnOO+88AFlTYmeKTQkEAvjoo4/w0Ucf5fQea0tIdiAQQCKRQDAYRDAYhKqquPDCCzF58mTMmjULtp2tGLF161YEg8GcaNeOD/rbPxA04mWOgUAAuq7jjTfeAABMnjw5Z2z2Szh8eywfu1MMhVLz85//nAD44IMPtlN/3vZBLBZjOp3mgAEDeMUVV5DMiiWtFUNqDcJ7W11dTZK86KKL2KtXL0YiEa5evTpnH8dxpCInKhAcbPA2NyHJE044gZqmcenSpfIzb0nMfYl2k/mbNyUQME2TlmXRMAyeeOKJDAaDfPHFF0l2HmtPIpFgZWUlZ8yY0aIMyp7gfUCzZs0iAPbt25fLli1rsa+3vLuwCh1s8JZU+fDDD1lUVMTjjz9ejru31H2XkflFJB7QFKzExqVOFJeaN28eXNfFLbfcgrfffrvTWHs2btyIHTt2tAi2a4tM7i2UdcMNN2D69Ol4/vnnMXr0aKTT6RZtSH0+HxKJhLQKHQzw6k7inuvq6rBgwQJUVFRgypQpUBQFsVhMVmwWyTz7FPt0ajVCzPZMJsM///nPjEajBMAVK1ZI7u8tSCVEjv0lHnlt+5lMpsWKJEQUYQUyTVNeY/OVwjCMFt/lkYVY6YSVb/To0VQURY6vYRg5lra2ip7fFvuF+JuXLn/mmWfYv39/9u3bt8W+38TM2B7Y3fn2NPlc1+V9993Hzz77LKdCneu6OSLOwQwh8npFPNd1uWzZMpaUlPCUU05hPB6XYuD+1Af3OfGbpimbmXmJ4ZZbbqHf72e/fv2kh1VwXNM0WVtbu68vjWQTgYuQbC/S6bRssiYg7PXV1dWcOXMmAXDevHlMpVI0TVP2MMsjC8MwcsZP0MBPfvITAuDbb79Nsuk5iPFLp9P7fCLsF84vYFmWdGTU1dXx2WefJQAOGDCAL730EsmmJbGmpma/KYR1dXWcN28e161bl3PO1lYFUQL9sssuIwAOHjyYixYtkt8LBT+PLLxjYdu2zOsIhUIcNmxYznfe//uj1uh+JX6yZY/e3/3ud7LJ2cKFC+U++ws1NTV87rnnWFhYyFtvvTXH6+yVOS3Lklz/lVdeIQCWlZVxx44dch9xX3lxpwleri/GduXKlQTAv/zlLySzhC4myf4cu/0i9ohMHQEx+wWx3H777QyFQgTAK6+8cr9nMq1fv57RaJTXXXddq997QxPIrIj06quvyveu67K2tjYne43MTwIBIQ4K3HTTTSwpKZFirvjfvOXtvjZ17nfO3xxea8lNN91EACwpKWF1dfV+IZ54PM7q6moC4Jlnnkly11aG5p+n02nGYrFdrlT7W3nvrPCKPmvXruUhhxzCiy++WH7XvLn1/lpB94t/XSSDi9gWemzfwjfgOA5uvPFGbN++HXV1daisrMTs2bP3+bVFo1HZ+OKrr74C0JREIhoiAMCdd96Ja6+9Fjt27MiJZyooKICqZjsmkpSx+QC+WaOEAxTeEjamaWLx4sVYu3Ytzj33XLmP+J6NYTJsjAE6IOz8bYHXKvDVV19xxowZspnxb3/7W6koJxIJKTK15lX2LpvevlVe7iMsT94cBO/34lziWKNGjZKNkQ+m5PL2gFj9hLwPgJWVlR15SRIdTvyC6FzXzSHALVu28JVXXpG6wNChQ7l8+fJWzYjNzagkWzWVpdPpHIW2uTPLK3OK440dO1Y+sC+++ELuu2nTpm9zuwclhA/khRdeYFlZGW+88cZ27dzzbdHhxO8lUK/nVCCdTvP3v/+9bGXfq1cvaRtujraaGVubQNu2bSOZleu9q0wkEuHkyZO5bNkyycXa2u0vjyxs22Y6nea4ceMIQDKYjs5p6HDibw6xAohN4LHHHuNJJ50kGw4Hg0FecsklLTypok/TrpTQ5k4okXL46KOPSrOl+D4Wi7Gurq5FLR8xCfLEv2dkMhmm02n+z//8DzVN4/jx40nuX3P2rtApiN+yrN0SrDfvlSR/85vfsEePHvT5fNQ0jUOGDOHcuXNbmMmam868DczIJuvN559/TgCMRqP85z//2cK0adu2DFn2htvmTZltR9++fdmvXz9ZtCsv9jTCW7VLKLLeCm+C4LzLZHV1Ne+55x4CYCAQYDgcpqqqHD58OG+++WauW7dO7ltfX58z2F5ZX3D1MWPGsGfPnjz88MMZjUb5+uuv55ybbAq+83YDzGPPeOKJJ6hpGq+++uqczzt6AnQK4t8TvBYWESdE5hLmww8/zB49ekixSGwnn3wyTz31VM6dO1dyHQGxKsRiMR555JE8/PDDqes6R44cmROZaZpmCytSXuRpGzZv3syioiL27t2b9fX1Uv7vDOgUxC+sNUJhFZzfS+iCQ4t9xCogBtIrx99www1UFIWKoshJoCjZ/5qmcuzYMTzzzO9z9OgjePjhh7G0tITl5WWNplWFdXW1JF1aVhNnb64riGvMY/d4+OGHCYBz5syRnzUXYzsKCtkJyqbtJUS5RKApgSbrXFGwadNGzH/pRaxYsQJLly7FunXrkExm4PdrMM3G9kMqEI1GMGXKFDz44IMIhULQVA1N9f0PjhIj3waiGUk8Hs+pMm0YBgzDQFFREc444ww88MADqKyslCXbU6kUAoFAh/YWOyBSicQAOo4jE89JwnFc9OrdE//zi1+gvqEexUXFcOnCcRxs3rxZ9n569dVXcfXVV8M0DUQbK6YBhEsXqnJADNE+QzAYRCqVkoTvOA7S6TSi0Sguu+wy+Hw+nH322aisrATQ5D3vDE31unz5AFEoCshOApEmJwrBZjk4UFxUjLr6OqiKCp/uQ/9+/QFkG1AfffTRSKfTOdUUbMfeLw3pujocx0E4HJZ92DRNQzQaxYMPPoiHH34YV1xxBc4++2wAyCm86/f7O7x0ywHzdNPptKwIJ7Bjxw4AQMbIwHEdlBSXwDANOG5W3NE1Hal0dvndunUbTNOUTan3V0O6rg5RTVnTNDn+1dXVuPTSS+Hz+XDttddCVVUp5gBNtY46umlhlyd+URp99uzZ6N+/PxRFgaIo0DQt+17VEY0W4JRTTsGy5csQ8Aegqiqqd1QDAMKhMIqLiqEoQGlpaU4Cu2m1T3eWAx2xWAyKoqC0tBQApLhz/vnno7CwEIlEAn6/PydoDUCLZnv7G12e+IWC+/XXX6Ourg69evWSRbNSqewyq6oK/vWvt3H66afjy41fQoEiq8XZjo2dNTsRDofRt29fBANBZIwMXLoHTXWFvYFhGLLWaW1tLd58802sWLEC4XAYDz30kKxYIcbSdV34fD5Zlboj0eWJX3TuXr16NUaMGIElS5ZIxdeyTNC1kUqlMHPmVdiypRqXXHIJLNtCJBKB4zrQNV3KqqLERjAQhKIoeZm/DRAFfRsaGlBYWIjzzz8fW7duxSeffALHcXI6x3tLvpPM6SncEejyT9fv98M0TaxYsQIrVqxALBYDkK2erOs6TMuErum4/bbbMW3amViyZAmeeuopKFCkgqso2ZUgHo9Lmd9xHKkb5LF7OI6DoqIizJw5E1u3bsVJJ52EqqqqnLpMJBEOh6XoEwwGO775Rse4F9oPpmlyw4YNBMAJEybkeGKzTiqb8UQdSYtfbd7AgsIQoYDbtm8macmtrLyI3z/zNJIWLTtNw0yStEnmKzF4PewiNESMs3D0/e1vf6OiKBw7dixJ7jIX2rZt+duOrnLR5Tm/z+fDqlWr4Pf7MWzYMLnEOo4j5cxoJNtiqLi4GIcddhgqKkrgui5cNsmcyWRSrhq61vE26M4C27ZRXFwMwzBg2zZ0XUc6nUYgEEAmk4Gu63AcB3fffTeCwSBeeOEFAEA4HJYdeYRTC4AUg1zX7fDuM12e+GOxGN588024roshQ4bIzwXxpjNZpdeli2AwCL/fjx076lBTUyPTKg3TQCZjIxaLgWhMoVO1nMlxsEIwENFR01uWUuC2227DBx98gLvvvhvdu3eXNv9oNArLsvD000/j0ksvxQcffCBLuXeGco1dnviFKa2wsBADBgyAbdvIZDJSERZyp6qosh4kkG0FGg419QcIhbJN9TraAtHZIBiEaZr4xz/+gTfffBPBYBANDQ0IBoO45pprcMMNN6Bfv36YPn06EokEDMOQ4SY+nw/3338/nnjiCSSTSSiKklO7tCNxQNjy6urqkMlk0K1bN8mhAEDTVKgqkDHSCAaC2LZtG7Zs2YLS0kJUVlaCoDS9lZeXy4kiOL6St/YgEAjANE2oqoqFCxfikUcewccff4zKykosW7YMDz30EEaNGoWFCxcCaOpimUgkEA6HYVkWJkyYAJIYOnRojm1/fzSg2B26PPE3NDRg/fr1SKVS0t4sllXXdaGoihzwjz/+GNu27cTIkcNzvIs+3YeSkhLZXYaNjhj1IOmZtTsI2TwUCmHYsGHYunUrHn30UYwbNw7Tpk1DTU0Nnn76aQSDQSQSCUSjUTiOIydBIBDAHXfcgdraWpSWlsI0Tfj9/pwOOB2FLk/87733HlavXo3KykpUVFTkKLqqqgDIcvH6hno8++yzKCqK4Nxzz812UVFU2E5TIz1h5z9YOqa0BZqmIRQKYefOnbjvvvsAADfeeKNsL/Xiiy/iu9/9rmxD1dDQIBtoC+dWQ0OD9P4KnYFkh5eo7/JPOR6Po6ioCMceeyzKy8ulI6Wp55OCuvp6/OlPj+OJJ/6CPn2qcNFFF0NVNKQzGaiNocuuS1iWDRJQoEKBiq4f7L33EB0ly8vL0dDQgKFDh2Lw4MHo06cPTjvtNJx22mkAsv4W8SxM08yGhWsaHn/8cVRVVeGqq64CSdln2MtsOgqdnvjZCgWysTiUbdt499130dDQINtYCq6dbXOZBqDgg6XLccUvr4JP17Hw/cUoLipFOm0gFIw0hiyrcGyiqLAEmuqD4xCA2ijzHxyij2EYOaKg8L6mUin4fD48+OCD2LhxIzZt2oR4PI5NmzbhpZdeQiAQwNtvv41YLCbDmnVdz4qcioI1a9YgEAjgyiuvlAqubdtIJpMdbu3p8mLPypUrYZom3nvvPRQXF8uYnbVr12L16tW44447AGStQmeddRb8/gAABaFQGIZhyL6wyWQK0WgGjuPCth0oiirjUg50iAZxQJbovfJ4NBpFKpXC448/jv79+8Pv9yOZTKK0tBTr1q1DIpHAlClToGkaZs+ejSuuuEJ2VgmFQvj0008Ri8Xg9/slsYdCoVaZ2v5Glyf+TZs2gSTmzp2Le++9FyRzMoUikQhGjRqFW2+9FePHj4fP55PyqNfy4I0GFRaIg0H2b54FJ8aEpHRmCUbSu3dvlJWVYfny5ZK7//jHP0b37t0RDoelVUeYOjVNw7Zt29C3b1+Ul5cDgMzksixLKtIdhS5P/EcffbTkMPF4HKZpolu3bgiHwzj66KNx2WWXQdM0OfhA1gIhlmDHcaCqKuLxeIu+wMKjeSBDTHAxHmLim6Ypx2P69OlIp9NYu3YtVq5cieLiYvz5z3/GiSeeiFgsJmudCm4uVo0PPvgAa9aswX/9138ByO1x1tHKLnAAEP8zzzwDoImjiEhCYVLzQjTBVlUVlmXlZIGJ9wL09I09kOFNRgEgRUGxAlx33XVYtmwZSkpK5Ao6ZswYOW4VFRVwXReZTAaKokhOThLLli1DPB7HqaeeCiA70bycvqOZS5cnfuEoEVxHPES/3w/DMGCaplTEwuEw0uk0FEVpYWPWdT1HzBEi0MEAy7JyRECfz4dUKoX77rsPt956K6qqqnD55ZfjyiuvBJC1sGmahnA4LLm5d9UUDGjVqlVQVRXjxo3LRsk6Tg5D6uhVtdNXb2iNA5PMaWfvOI58eK7rwrZtmSPaXG73Hk+EP2iahuLiYpSVlWHt2rUAmmThA13uZ2N3dBFqrCgKEokEHn74YVx//fVwXRdr165Fr169QBKpVEqaK1OpFEKhUE4LWu94lZaWory8HP/5z38AZEUpYeIUq01HToAu/2S94QxiyRYPQ1EUOdBionh7BAtbNJDVAwSxCwvQgU74QHaMVFWFYRhy3B588EFcf/31SCaT+Prrr9GrVy8AkHZ60W8hEAjAtu0mj3jjcZLJJAzDQCwWy5HzdV2Hoijw+Xw52V0dhU4v9rQmdzcXSbwEDEBaL0QDbC/Evt7jxuNx1NbWYuzYsVJXEOERB8IEME1TWrHEimbbNmzbhqJkwz90XUcymcSwYcOwadMmFBUVSc4u4PWhAMixjImxCgQCCAQCmDlzJiKRCI499tgcr69YNVRVlTV/Ogpd/8m2AwoKCtCvXz9UVlbKB9ta6G5XhOu6UrSLxWLw+Xyor6+HrusIBoM5zOHYY4/Fpk2bUFJSglWrVrXJDGlZVs6q4TgOamtr8eWXXyIWi2Hy5MkoKioC0CTjC8tSRyewd3rOv68hOFZhYWHOAxQeyq4O0zRlRbVQKIR4PI7i4mLpYRVRmyNGjIDf78e4cePw1ltvtTn0oLkTUNM0lJaW4gc/+AH69OmD733vewByfQi2bUPTtA4f306v8O4P2LaNIUOGYPDgwXj55ZdzlL8DAdu2bUP37t0BNOlFoqgX0CRGvvTSSzjllFO+1TlE9KfwFovwCEHwwhQNQIqWHW3qzIs9aOL0dXV18rMDhfBN00T37t2lH0Mo9q7r4oUXXpAmyrvuuksSfiwWa3P4gW3b0lEoykQKxiHSFYXOIeBtQNeROOjFHiDLnSoqKqSiC7Q023VV+P1+yXWFlaa2thbDhg3D9u3bAQDr16/HgAEDpGhUWFgobfV7gld88fpPRDExYTkT+zTP8upIdP2n204oLCzMIfYDKZ1RxNL4/X5skR4gwQAACkFJREFU3LgRQ4cOxfbt23H88cfDdV0MGDBARmVqmob6+nrpJd8TvCuk8JA3Fxm9r72m6I5GnvgbIcJsBQ4Erg9A9gf2+Xz4wx/+gH79+qG6uhoXXngh3nrrLekLEdxeURQUFxe38MbuCl7FuDknF5On+T7inHmxp4MhlvdDDjkEixYtkvE/zV3+HQmvPdzrkW1tH3E/wp4vQpBHjBiB9evXo6ysDEuXLkWfPn3kb72VrQXaGtrRmsIqOLsYv9b26WgHF5Dn/DmueW81gc6yNAO5q5BlWTkimeCuwWAQ6XRaEq3gwvfffz/Kysqwfv16VFVVYePGjejbt2+Hy9udAR0//ToYiqLIrDDTNCXRd6agNhEUJiwqqqpKsUGIJg0NDTJpXIgvIvygoKAATz75JMaPH49IJIKamhqUlZUdUObcb4M8529sYUQyx6vbmYjfW95brAK6rstqx5lMBkVFRdA0DYZh4Oqrr5YhDNOmTUN9fT3OOuss9O7dG4lEAmVlZdi+fXuHy9wdjYOe8wNZObp5XHtngRBxRKaZgMitFXJ1fX09fvGLX2D+/PlIJBIoKSnBunXrUFJSAkVRpC4j7q9bt245jqeDEQc95weyhCW4a2dQxLwQ3lggVy8JhULw+XywLAsfffQRTj75ZPzlL39BIpHAjBkzsH37dpSWlsKyLMRiMenMEmbPhoaGg5rwgTznB5AlMBH8JXSAzrQCCHEsnU7LxJyGhgaYponDDz9cOqtuuukm3HjjjTm/FUk9Qr6vrq5GZWUlioqKZJGpgxV54gdkjLkg+M4mC4vQbEH4a9aswdVXX40XX3wRAHDooYfi448/RjAYlJ5pYeq0LAsFBQWyYYe3HejBTPjAAUL8IkPIq7wKW7dIoBDwhi2I167rYtWqVUgkEjnVDNoCr8VEyOfe47tuU3uj5iETza0tXnt+LBZDYWFhTvDXli1bMGnSJKxfvx6RSASapuHVV1/F6NGjJeELNA8h8K5kB7u4I9DlZX7htlcURRZU9ZYeEVWBRa14VVVhmibq6urka13X0bt3b/Tp0weapiGTybQ5vEFwVAEhl3sDvgSaO6YE4YtrE/UuLctCYWGhjMD8/PPPMWvWLIwcORLr169H9+7d8Yc//AG2bWP06NEoKysD0JTeKa6royuidXZ0ec7v8/mko8ebiCJs4CJ2XCzxgrv6/X7JXQGgpqZGcmavN3VPdnCvguyNVhTpkM2rSDQP400mk/LaRARkNBpFOp3Gr3/9azz66KOyf23v3r0xf/58TJgwQda+FIQvztuatzaP1tHliR9omU4nZHgAOfm9Pp8PwWBQcnZB+LZtY+fOnUilUojFYjIVr63w1rxpzt39fr90OrVmTRJpfaIKxeLFizFnzhwsWbIEmqbBcRyMHj0ac+fOxciRIxGJRGTNfG8+shD18mg7DgixRzx0UYdHEFgmk8HChQvxgx/8AFOmTMHrr78OIEuQ4XBYrhi6riMSiaB///4oLCyUhN8W76dYLcQ12LYt614Kcci7gohAM/FbAJg/fz5OOOEEaJqGyZMnY8mSJSgrK8Ntt90Gknj99dcxYcIERCIRJJNJuTKJYwqO781EEzkKeewGe9HPq9PAMAxu375dvn/44YdZWVlJAFQUhdFolABYWVnJBx54gDU1NSTJdDpNMtskbfTo0Zw4cSLr6+tlMzXHcb7RdTiOw0wmk/M70bCt+et///vfPOecc6hpGgsLCwmAAHjMMcdww4YNrR6bJBOJBEnmNN7zNnazbZu2bX+j6z5Y0eWJ3/vgY7EYb775ZmqaRl3XefHFF/P666/n+++/z5dffplHHHEEAfDII4/kunXrSDYR5A9+8ANedtll3/j8XoIWnQoF6urq5ARLJpO8/fbbWVBQICelIPgzzzyT77zzDkkyHo+TbJqY4v68xC7em6ZJkjnEnif8tqPLE79AMpnkLbfcQgAMh8P8y1/+Ir8ThJNOp3nPPfcQAC+66CL5vWmaPPTQQ/m9732PqVRKElxbOH8mk6HrurQsK4dAV69ezccff5wnnHACA4EAAdDv91PXdQ4fPpyPPPJIzvHr6+vltZBNRG8YBl3XzZnkorWn+Mw7Ab3H9LYQzaMlDhji//vf/04A1HWdsVhMEoQgSPG/oaGBU6ZMIQC++OKLJLMEdtJJJ3HEiBFcu3YtySyBCUIUcF2XjuPQcRxJePX19fz973/P4cOHU9M0yc293L1Hjx686qqruH79+pxjeYk2j/2PA8LaE4/H8cILL0BVVZx33nkoKCiQFhChvHqV2PHjx6O0tBQjR44EkFWAe/fujTVr1uCPf/wjevToge3btyOVSiGZTELTNCSTSWzcuBGff/65DCcQ1hgvdF3HEUccgZ///Oe44IILoKqqLJculGJveHIeHYcuX7okHo/jww8/xHHHHYfS0lK89NJLOProo3McPqLjooBpmojFYrJseSqVwuWXX45HHnlE7iPs9N7mdgJVVVWYOHEiRo4cif79+6Nnz54YPHiwtLkLq1NrpsfOUrMmjwOA+AHgueeew1lnnYVp06bJkuUCXkJs3nXEW6jWa4tPp9MIBoPSa9w8l1WEUHiTsYV5UcThiKZrwhQq3ovfiWvLZ1R1HLq8nT/+/9s7f1XFoSCMfxJFTRQbsbWIoNZpxcewFay19QnslYC9tbXtrXyQgIiilfEmRhFOttA59+Tiwu7CbjZmfpX/Iik+zxnPfDPz+YmPjw8AgGmaACAzogAihrV8Pv+c1XUBANmolmwRahMnEjUJn+wKQHRXIAuBpmmRohP6HnWVV5NSdG9MfCRe/OVyWVYy1et1CCGkcUsdOOH7vhQ5eduPxyOALwNa+BzFo9obiGw2GwljKItMP4L7/S5DGnXaye12k/4fei+TycjXmfhIvPh934cQAq7rIgiCSPsR1eZgGIa0GpzPZwBArVYD8DCUaZom25kTvyJOCnPUltsUAmmaJnee79ElhVtMfCRe/Lquo9lsAngISrXrkhjVPvGz2QydTgfT6RTAQ6i0O+RyObkrhIpJ7DvhcxQqFZmQ2IlXU11onq16PRMviRe/EAL7/R4AMB6P4TiODEPofcMwZChi2zY2mw0sy5KhiBp7q633fgaJW/XKv+pFqT6m3YGu52PO+Em8+DVNQ6/XQ6PRgOd5WC6XUpie58k/p5fLBcPhEIfDAa1WC91ul1fftPMvM2p/A0rnr1YrmVkdDAah67ryM9vtNqxWqyGA0DTNcLfbxXW7zH/EW5zzA48jz8lkAtu2cb1eUSqVIISQx5q6rqPdbmO9XqNYLEamrzPpJPHiV+tegyCA4ziYz+dYLBZS+JZlYTQaod/vy+teJa+YdJF48auQoF3XRaFQeDkV5HQ6oVKpyNpeXvnTS+KPHNSCcZo5RQPQyM5AJzHUo5KK1t+lDTnzZ7zVyq+26VZ9N+SvocQTPY97JhQTL28lfob5HXjfZ1ILi59JLSx+JrWw+JnUwuJnUguLn0ktPwA2xR8QiVzvsAAAAABJRU5ErkJggg==)
physics-General
physics-
A part of a long wire carrying a current
is bent into a circle of radius r as shown in figure. The net magnetic field at the centre O of the circular loop is
![](data:image/png;base64,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)
A part of a long wire carrying a current
is bent into a circle of radius r as shown in figure. The net magnetic field at the centre O of the circular loop is
![](data:image/png;base64,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)
physics-General
physics-
A wire shown in figure carries a current of 40 A. If
, the magnetic field at point
will be
![](data:image/png;base64,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)
A wire shown in figure carries a current of 40 A. If
, the magnetic field at point
will be
![](data:image/png;base64,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)
physics-General