Physics-
General
Easy
Question
A heavy but uniform rope of length L is suspended from a ceiling Find the velocity of transverse wave travelling on the string as a funcition of the distance(x) from the lower end
![](data:image/png;base64,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)
The correct answer is: ![L square root of fraction numerator g over denominator x end fraction end root](data:image/png;base64,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)
Related Questions to study
physics-
A detector is moving in a circular path of radius r in anti-clock wise direction with a constant angular velocity w as shown in the figure. At time t=0, it starts from the location shown at A, assuming source at rest. The time interval between minimum and maximum frequency as received by the detector
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)
A detector is moving in a circular path of radius r in anti-clock wise direction with a constant angular velocity w as shown in the figure. At time t=0, it starts from the location shown at A, assuming source at rest. The time interval between minimum and maximum frequency as received by the detector
![](data:image/png;base64,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)
physics-General
physics-
A detector is moving in a circular path of radius r in anticlock wise direction with a constant angular velocity w as shown in the figure. At time t=0, it starts from the location shown at A, assuming source at rest. The time at which the detector will hear the maximum frequency for the 1st time
![](data:image/png;base64,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)
A detector is moving in a circular path of radius r in anticlock wise direction with a constant angular velocity w as shown in the figure. At time t=0, it starts from the location shown at A, assuming source at rest. The time at which the detector will hear the maximum frequency for the 1st time
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAW0AAACtCAYAAAB7ni4iAAAgAElEQVR4nOx9eXhV1dX+e+cx92YiEOZBCRAIgQgICKLggBCw1rHt15bfU+epDm2torUOVSvWOrQO/fTTz6HWoUgRRRCZRFRmCAIBmcOUkOTmzvPvj3zvzjoncaY1wfM+Dw+Q3HPuGfZee+13vWstUzabzcKAAQMGDHQImL/rCzBgwIABA18d1n/XibPZrPoDACaTSf2RiMViSCaTcDqdsFgsSKfTMJvNMJvNrY4l1q5di5dffhnRaLTV+b7qdZ1//vk4/fTTNb/LZDLq+zKZDDKZDMzm5nUtGo3CYrHA6XRqvpPXKI9t6z4NGDBg4FjgmBvtbDbbyvgBgMViUb9Pp9PIZrOwWq3IZDJIJpOw2+2azyeTSezfvx/BYFBjBLPZLNasWYMPP/zwGxvtTCaD3r17Iz8/X3PebDYLp9OJ7t27w+l0qmvJZrNIpVLKQPPfFotFHZ/JZDT3xPun0TdgwICBYwHTsea0U6kU4vE4rFYrbDYb0uk0ACgDl8lk0NTUhGw2C7/fDwDKiJtMJlgsFmQyGRw8eBCzZs3Cxx9/3HyhwjgPHToUF110EVwu1ze6RpPJhH/+859YtmyZ5ufZbBZ9+/bFzTffjLKyMpjNZuVx0wBbLBY0NTUhmUzC5/PBZrOp+6bRTqVSSCQScDgc6vcGDBgwcCzwb6FHSG8ALR4o0OJtWywWDa3Q1NSEjz76CAcPHlSGPhqNwmq1orS0VH0uk8nAYrGgtLQUgwcPht/v/9pGMZVKIZlMorq6GrW1ta12Am63G0uXLsX69ethsViQSqXg8/lw8skno0uXLrBYLGphMZlMynPn4sTFx2w2GxSJAQMGjjmOuactT5fNZhGPxxU3bLVaNQbbZDIhHA5jx44duOWWW7BkyRJlhLt164aHH34YZ5xxBoAW7tvlciGVSqGpqQk5OTnIycn5WtcXiUTQ2NgIj8cDp9OJWCwGs9msuOrNmzfjhhtuwKpVqwA0G/n+/fvjgQcewJgxY+Dz+VrRP6lUCul0GiaTCQ6HQ0OJGIbbgAEDxxLH3GjTI45Go4hGo/B4PLDZbIoDZrBx06ZNePXVV9HU1ASbzYYuXbrA5XIhmUwCAHw+HyZNmoQePXqoIKDFYkE8Hkc2m4XZbIbdbofdbv9a10fqIpVKAQAcDgcAIJFIwOl0oqmpCQsXLsSBAweQzWZht9uRSqVw8OBBxGIxFcQ85ZRT1AKUSqVgMpmQTqcRDodhs9ng8Xg0Ow4DBgwYOBb4t9Aj2WwWiUQCsVgMLpdLBRKPHDmC2tpaAMD69euxfPlyxONx9OjRAxdeeCEqKioQDocVt+1yuZBOpxGPx+F2u2G1WtXvaRS/7prD84ZCISQSCbjdbvUdNpsNeXl5mDZtGpLJJDKZDDweD/bt24dZs2Zh/fr1iEQi6Nu3L/Lz8wEAeXl5KC4uhslkUnx+NpuF2+3+2tdmwIABA1+Gfws9QoVIMplEKpVS9MPzzz+PZ555Bjk5ORgwYAAmTZqE/Px8eL1e9OrVC16vF8lkUgX8zGYz0uk0YrGY8qpJRWQyGRXs/DrgdZF3ZuAwHo+rwCHPn06nYbVakUwmsXv3bjQ2NiIej2PRokVYu3YtmpqaMGXKFPzmN79R9I3NZoPVaoXVajWkfwYMGDjm+LdI/hiUs1qtyGazOHToEDZu3Iiamhr069cPPp8PgwcPxujRo5VHSsmfzWZTAT56rXa7XalPbDYbzGazWgy+rlGUKhCrtfn2LRYLHA4H0uk0UqkUbDabWjRMJhPsdjt69+6tPltbW4umpiYEAgEEg0G8+uqrGDJkCHr16qWMdTqd1kgCDRgwYOBY4N8m+SPvbLPZsHz5cvzmN79BZWUlrr76ajidTjgcDlgsFgQCAYRCIeTm5ioqJZvNIplMIhAIwGKxIDc3V2MA5SV/E522/lj+rLGxEbFYDD6fTwUUSfU0NjbCbrcjLy9Pacuj0Shee+013HPPPbjvvvtw8cUXK1olm80akj8DBgwcc/xbApHpdBrvvvsu5s2bB5vNBp/Phy5duqCiogLDhg1T3ijQnESTSCQUVcHAYiaTQSKRUIqMeDyuMifpwX8T+oH0DZUfDHK6XC7E43Gk02mNZ59IJJBMJlUglYFLoHmB2rZtG1auXImDBw+ivr4eqVQKY8aMwYUXXqiCpwYMGDBwrHDM6ZFwOIyamhqsW7cOK1asgMViwZgxY3DZZZcpnTPQ4t3abDbY7XbEYjFN6jh5YRpZqj7sdrvSRn8TekQeS48+k8nA4XDA4XC0ypCkHpuSQClXtFqtGDhwIPr374/7778fy5cvV+caOnQounXrpgKWBgwYMHAscMw97Y8++ggPPPAAhgwZgrPPPhsmkwk5OTno3r073G63ogtIIdBbpsFm8I+fI89MuoVGn4b360rq5MJA7lmmoJPnZhIOuW0aeZk8w88lEgns378f9fX1yGaz+PDDD/Hmm28qSsiAAQMGjhW+1NOWdTdIGZhMJsTjcQCA3W6H2WxGLBbDypUrsW7dOhQVFWHo0KEYM2YMgBbDKz1j+TclfvRkpfcsf0+DSu/3m9Aj8jga43Q6rZJjJPh7PcUhv5ced79+/VBSUgKgORGoqqoKVVVVMJvNGD16NPLz8xU/zuAqn69cNL6trltfpIsLIe+BBbn4LA0YMNCx8KWedjabRTgcRjqdhsPhUIaloaEB2WwWubm5sFqtqKurw9VXX41QKIQ///nP6NOnjzIMXxT8+9wL+4Kg478rEHmsro/B2Ouvvx5bt27FX//6V5SVlSGbzaKxsRGpVAq5ublKBUND7vF4vjUHLgt2mc1mxONxlTgENGeEOhyOb1y3xYABA98tvtBo81fkfS0WC2KxGGKxmOKiHQ4H3n//fbz99tvIz8/HwIEDccYZZ6hiUN9XZDIZLFiwAGvXrkVDQwNGjRqF8847D4lEQgVVbTYb3G63MrKUO37dhYip9HLnwHfHvyXtw90MywoYMGCg4+AL9+LUXFPVwRR0lkSNx+Oorq7GJ598gtWrV6OiogKVlZVfux7I8QiTyYTTTz8dZ555Jnbt2oWVK1di8+bNCAaDKh2fnLnNZlOp/jTgXwd8T/pjyd1TA0/NObM3v8l3GTBg4LvFF3ralOPRYAPNnGgikUA0GsWaNWvw5JNPorS0FJWVlejbty8KCgqMTEC0cMvBYBC7du3CwoULMXfuXFxxxRWYNGkS3G437Ha78oCZqamXFX4V8J1wAZBeNt8DKRiHw6GCsceCQzdgwMB/Fl8YjWKwjoEybr/NZjNWr16NtWvXoqCgAGVlZRg5cqQK6BlBrmZkMhm43W6UlZWhrq4OVVVVqK6uht1ux4QJE+ByudSzlcHVrwsGavXlcNmQQSpkaNylVt6AAQMdB1/KaXOiU3VgsVgQDAZxyy23oLGxEffeey/69Omj+O5sNguXy/W99+Cy2SxisRjS6TRcLhey2SwikQhmzpyJXbt24f7778eJJ56oaQBBJc63Ca4Cza3R+B4oXaQyh80ZGIg0DLcBAx0LX0k9Qg86m81i8eLFePfdd9G1a1cMHDgQY8eOhd/vV5pnAIYXBy3PzCShVCqFFStWYMOGDThw4AAqKiowffp0tRh+21oliUQCiUQCADRUCRcFVjO02+2GesSAgQ6KL3SHZbcY8p9r167Fc889h169emHy5MnweDya7i9UQHzfQXUGk4S4No4fPx4jRozAO++8g2XLlmmaQ/B5f13I7jmygiEpF1l5kAuq1HMbMGCg4+ALyWfZ65CTnQHJZDKpZGtM4vi+UyKfBxpilnllUFAucjKY+HUDkTTYZrMZbrdbvSM2ZyDkufl5Y4E1YKBj4SsHImtqarBq1SokEglceOGF6N27tyqfamTYfT5kfXFqqYuKilBZWQmLxYJXXnkFI0aMQK9evQB8c46ZFAhjC5lMRlPmVl8u1/CyDRjomPhC19hqtcLpdCKbzWLTpk247bbbVMbjySefDJPJhEAggEgkYhiBL0EsFkNjYyOy2SwGDhyI3/3ud+jUqROuvvpqLF++XGWcfptSrjT4jY2NaGxsVIsuF1eWzDUaDxsw0HHxpYHIaDSKv//97/j0009RVFSE0aNH45RTTlFdaVjXgo0D9LVFvq+QWmnW304mk4q/ttls2LBhAxYvXowjR46gqKgIl1xyCYqLi7/Rd9GTDwaDeP3115FKpXDJJZcgNzdX9cNkffPv+7sxYKAjw8zgF3W8+j/JZBLvvfce1q9fjx/84AcYO3as4lABwOPxqJKmxrZbC/k87HY7cnJyVJp5JpPB0KFDceWVV+LgwYN488030dDQoJ6t/j3ozynfGYOemUwGgUAAy5Ytw5IlSxAKhTSJNDabrdW7but6g8Egtm/fjtraWs01yOOkoohp9PrrbGts6b9LVnEMBAKorq5GfX19q+P0enP9oij17vy3AQPHI8zJZFL1N5Q1K6SSweFwwOl0Ko8xlUrBarUqY81Jy4lsoBk0NHw2AFTKuuyh6XA44Ha7YTKZVEccGjJ9ejqlg/Tc23resVgM4XBYKUnYJYj9NtnUoS1ks1ls2LABv/rVrzBv3jzNffD7MpkMIpGI0oPHYjGEQiHl0QMtRbNisZjS+be1SMhjV61ahRtvvBGLFi1S98dzJhIJRCIRdS75jPkd/F7WyjFg4HiEFWhNZdBj2bp1K9asWYOuXbuitLQUbrcb/DypEE6OtsqqGmgJEPJZSQUOn93IkSPh9/uxbNkyNDY2oqysDPF4XMn1KAdkvRCZ+UjPncaNvDi7AfE4u92OdDqNSCQCp9PZZr3ybDYLm82Go0eP4qOPPsKwYcNaVTFMJBKaolORSETdFw2qxWLR3De/R9ZWkR48qx3W1NRg+fLlmDRpkmYcyaqF8uc06rx3+XxljXa5S6AmXl4XdyoGDHQEmG02m5ro+j6MCxcuxC233IKSkhJcdtllyM/PV4ZEr0owuNK2QYNAWZ+kM2hALrroIpx55pl48sknMXv2bDidTkQiEQSDQXUeGlwW66IBI4XFYLDX64XP50NOTg5sNhuSySSampqUlxyJRJQHzvOGw2EEg0GEQqE2PXcaQpvNhkgkgvr6epU2z+Cq2+1GPB5HKBRStdbZDYiLDuWOrHQYj8dVpcNUKoVoNKo8Zu5I+NysVquq18JFLx6Pq0UjmUwiGAyqhUcmE0WjUXWPkUhELTr00pPJ5L97GBgwcMxg5eSNRqOIRCLNP/y/CUKjbLfb4Xa7lbaX6dCsb0Fjb+i0tZDGlc+Z1ASr7VksFpWhKBdBj8ejtNzsl8lO9HzO8Xgcr732GjZs2ACTyYSJEydizJgxiMViyojLphV79uzBO++8g/r6eiSTSZjNZpSUlGDatGnweDwIBAJ44YUXsGDBAqTTaSxduhR2ux2TJ0/GgAED1HWGw2G8/vrr2LFjB4LBIEwmE/Lz8zF9+nT069dP03zBbDZj8+bNeOONNxCNRhW9Ul5ejvPPPx+JRAKHDx/GokWLMH/+fKRSKcyZMweJRAIXXHABunbtimg0CpfLhSNHjuC1117Dnj17ADQvOMXFxTj//PPRrVs3lQi2Z88evPHGGyguLsbUqVOxaNEi1NbW4vTTT0dxcbHGOeEzNWCgo8DKiZ1KpRAOhwE0bzMPHz4MABgwYAC8Xm+rgkZ64/NtCh4dr9B3uKGGOp1OK2+QFIbD4UDfvn1ht9tRXV2N4uJi+Hw+DS1CL5NBu5qaGnz44YdYsWIF7HY7/H4/OnXqhKNHjyrqgR7xvn37sGnTJmzcuBG7d+9GXV0dzGYzjhw5grKyMvTp0wcAsHbtWqxZswbpdBq7du3CkiVLMGzYMJxwwgmw2+0Ih8PYv38/Vq5ciY0bNyruOjc3FyUlJcjLy1N9MWOxGI4ePYp169bh/fffV9w1veqTTjoJOTk56jPV1dUAgC1btsDtdmPixIkoLi5GMplEIBDA1q1b8d5776G6ulo9u379+mHw4MHweDwoKipCJpPBoUOH8NJLL6FPnz4YMGAANmzYgEAggPHjx7fSqRs7RAMdDaZwOJy12+0aRcjGjRvx6KOPomfPnpg8eTIKCwtRWFgIv9+vtvrhcBjZbFZ5hNzC0mv5vk8EqW5gUo3FYlFdgDwej+KjA4EAGhoacOTIESxbtgyLFy/GzTffjFNPPRXBYFBRCAywmUwmvPvuu5g7dy7GjRuHPn36IJ1OY8WKFVi4cCH279+P4cOH4+GHH0b37t1RX1+Phx56CLW1tbjwwgvh9XoVRbF7926sWLECU6ZMwbRp07Bx40a89dZbeOqpp1BZWYkZM2bgxBNPRGFhISwWC5577jnMnTsX48ePR9++feFyuWCxWBAIBPD222+je/fuuP7665GTk4MDBw7goYceQiKRwJQpU2C1WhU18dlnn+GDDz7A+eefj7Fjx+Kzzz7D22+/jWeeeQb/9V//hYsuukg5DIlEAk899RQ++eQTTJ48Gd26dVOB1QMHDuDtt99GWVkZrrvuOlgsFqxfvx5XXXUVjhw5gtLSUkyfPh3jx49Hr169YDabEQ6H4XQ6Ybfblaf9fR+vBjoOrOQVAahATSgUwoYNG9CtWzeMHj1acYVyYMuyn4C296IBbTsy7kT4fOV2nB54Xl4eevTogU8++QQrV67EoUOHVKCRtV+kimPnzp1YsWIFzj33XIwfPx6pVApNTU3YtGkTamtrNQG4WCyGbdu2IRKJoFevXujTpw9sNpvilVevXo3S0lI4nU4MHjwYu3fvhtVqRc+ePTFq1CjNYrxr1y6sW7cOF110EcaOHQu32w2r1Yr9+/fj2WefRSQSQTweh9vtRiQSQXV1NQoLCzFy5EhVpyadTsPr9WLnzp3w+/3Iy8tDWVmZ8rT79OmD4cOHq+Cg3W7Hzp07sWXLFlxzzTUYOXIkgOYd4bp167B9+3a4XC41/sxmMxwOB3w+Hzp37owBAwZg4MCBimbi7kPKVI1xa6CjwBqPx5U309TUBLvdjlQqBbfbDZfLBavVitzc3FY6W4fDoeplsLONgdZg0DGZTKoKe/otOvXbNODksQHA5/OpwBt3ROFwGIFAALW1tYhGowCat/lTpkzBSSedhOuuu04F6Cip4/c1NTUhGo3CbrfD6XSqUrsMcHo8Hni9XuWF6jM0qcjIyclBXl6eRjXE8RKJRNQ4ysnJgd/vV+VgM5kM4vE4KioqcNJJJ6nvcblccDgcCIfDiMfjSoUiszq5ywCgOHl+hnVVSAl5vV6Ul5fj1ltvRW5uruYYXrfUxBu8toGOAisNBpM/JOcYiUQQDodVwSh9sgcN0rctKXo8g8+F2Yg0QISU7+lTzanbZoCNyp2cnBxNBxoaM6vVqgxuLBZTP3M4HLDb7di2bRuefvpp1Yw5nU5j586dCIfDmuvgGOC5uTAwWNrY2Ijnn38eS5cuVXK7YDCITz/9FMOHD4fL5VK0STgcVgsFjTqrDgItumouWl6vV9Vjj0ajMJvN6lxms1mpYOj96z1m3kckEoHJZEJhYaHireUCxKCow+EwDLaBDgUrtdcAVFf1QCCAvLw8eDweVRBKLzPT187WJ0583424/nnIprukPWiYSXkkEgl4PB706tUL8Xgchw4dgt/vVx42vXCXy6V2NnIh5bnku6Kk02q1oqmpCWvWrFGLAaVu3bt3R35+vgou67XllPCxPnc0GsWqVatQVVWlzmEyNTdxKCoqgtPpVN/J7u+Sj6cUMR6Pq8WBBpULDA00qQ5SRLI7Eq+RBl0+cwZ82YUeaGluTPUT9evf97FqoGNBZRSEQiEcPnwY77zzDg4ePIhLL70UQ4YMgdfrVfpZr9er1AvsUuPxeAC0lPo0vBYtpCdsNpuVMfF4PIr2YAak0+nEGWecgS5duuCjjz7C3r17cemllyI/P18Fz2SyDQBNhUWpk5Z6a76v3r1748Ybb0R+fj5SqZSG283Pz8fRo0fh8/ngdDpRWFiosmDJRdMDz8vLw5VXXomRI0e2yjwsKChQxpXgQiMTWHg+UjAcN01NTYjH44rioNYagKoHToqIiyC9c45BfqfekAMtsRePx6NJzPm65XANGPiuYNXTHVu2bEFjYyMuueQS9O/fXwWs6H3pPbHPy1wzoC0FIINkeu8YaKFPevXqBb/fj7fffhuHDh1CMBhEfn6+ogPk89a/A9nDE4Amg5I8dEVFhdI0A8Dhw4exceNGxW/LnZT++ujtu91uDB48GKeccoo6fyQSwapVq1BfX4/u3btrYhz6XRoA7N27FytWrMDw4cNRWlqqfi/rhnBRk7VOZECX1yZrsJCnptHWS1FJx9jtdtjtdrUgGDDQUWAGmr1kt9uNoqIihEIhHDlyRNUbAZq5TNbG4KRwuVzweDyaLaqkTQy0GG1pYPjcAKhn5XQ64Xa7ldfM3o6hUAihUAgAkJubq4pz6RNCaOTsdjs8Hg+cTifMZrMmAaotWiuRSGDt2rWYOXMmli1bhoKCArVI19XVIRqNwmKxKB6ZGY6kMkhxJJNJ1NbW4rHHHsMzzzyjAp/y+qTBBZr14Lfccgvef/99TTBQ6v55rQx6U5lCT5m7lVAohGg0qjx8yZHr1U3xeBwNDQ2tygQYMNBRYKXB1Rte6b1wUMusx7a0re1h8EvvFtB6o3JH8Z/gMWUsQH89EvL58m/eg9PphMlkUooPGsxTTjkFN954IzZs2IDVq1er42KxGNavX48ePXoo4+5yufCjH/0IW7duxfPPP6/4bBqtCy64AKNGjQIARa243W4sWbIEAHDuuediwIABMJvNOOOMM+D1evHJJ59g6dKliMViSrkxcuRI9O/fX3HweXl5+PnPf47q6mrcd999mnt0Op248cYbMXr0aADaZK158+YhGo3ihz/8Ifr06QOTyYRzzz0XxcXFePfddzF//ny1MJnNZkyePBkVFRXq2VqtVuTk5Ci1Cg03F0UukB2pew/ligDULoYUE+9LjjMuXlywuUjpA69MjpJjy0D7hpV1G/SUhozG67fkn0d//KeNtvTcZOBM711JZcR/ymDLxa4tyN/pKSbeEw0u6QcGIlOpFMrLy9G7d2/cc889WLhwoTqe761z587qWIfDgalTp6JTp06YNWsW9u7di1gsBqfTiVNOOQX/7//9P3Tt2lUZAZfLhRNPPBH79+/H/PnzMW7cOOXFjho1Cr1798Yf/vAHLF++HLFYDGazGT169MDvf/97DB8+XCVe5ebm4rzzzsM777yDe++9V/08m81i2rRp+O1vfwun06mcBI/Ho753yZIlmDhxono2kyZNQvfu3XHrrbeiqqpKecj9+/fHTTfdhLKyMuVkuN1u9OjRA506dVKLtQyC6gtudQSjDUDx73a7Xd0TjbZ+TpKv5zhkwJjBZABq4WIMwTDaHQOmYDCY3b9/v9LTXnnllaipqcFf//pXlJSUtOsBza05ByaDVFIip4fkV9sjMpkMQqEQrr/+etTU1OCxxx5Djx49EIlE4PV6kc1mUV9fryiV7du3o66uTh1Ljyw/Px9Dhw5VNWR4XHV1teJxmdTDeiFUZRw9ehRbtmxBNBqFzWbDsGHDkJ+fj1AopMrxbtmyBQ0NDWqhdDgcGDRoELxeL4LBoJL9ZTIZ1NbWYvv27YpmSSQS6Nq1K4YOHap2d9lsFocPH8b27duVp9+/f3/k5uaqhTYQCGDDhg0IhULKm/d4PJpSCxaLBY2NjVi5ciUKCgpw8sknt+LI5bOWBbzaMyS1Jbl+vnPy+ABU1qksAifLJpOO4i6OQen2/gwMNMMKNPObu3btwoEDB9ClSxeVnsxJ3F4hqQ8aYelF6AOnPKa9w2q1oqysDHa7HcuWLUNZWRkGDRrUaktvtVpRWlqquU8AGm03J3Mmk0Fubi5GjhzZKjDIet8Mhnbu3Bl+v189N2rC6c1ZrVYMHjxYbcvpKdM4MIEIaH4PnTt3RufOndX1cZsvaYtsNotOnTqhU6dObe7kGDysqKhoc4EGWjJ6fT4fysvLWyV88R6l8e4IMRguLnx++t0Y0GKopZSUC6J0YqT+nolI9LCN+kEdA5a77rrrTr/fj4ULF+IPf/gDzj33XFxyySWqNkZ73jLx+uhRUC3AwSgNtb7aXnsemBaLBV26dEEymcQjjzyCbDaLs846C0DzPTMARw8JaOm8Tlkc0KxVBlqCjplMRhOUpJFlwJF0Cp8reU4aCCbXsAmGNMw0CPycNAT08mgw2UGHyTMWi0VTkhWAxgABUEFIatR5HBcySX3oOW0A6l4lbaU3cu0VrHnOeAPvRb9gcTGTCW8shcv3zs8CaKVIkqowA+0XVr60WCyG2tpa2O125OXlaTSv7RWyKBPQ4rHp21Jxkkv+u70ilUopeqNLly7qfjgBM5kMXC4XAKj75CSlQeW9MylFbv/lBCVd0ZbXLbfXNMbMZKSB5s+lLFAqNmTGorw/Xp/T6VTno7HW8/tccGX3HdmOTQbSASh5KtPog8EgvF6vonWkikYuYu0ZXIhkjEYG1vl7+f75THkcfyZlndyBSZrIMNrtH1agZSXnJKQH096NNtBSRU/qdOWkBKACeED7NthAs6FKJpNwuVyqZofsXEPKSkrqOBn5HhlYJmcp66DLLbCkF7hLYaYgAOXN8hhOdAZGuZjwDyWi9Jr1RpvXn0wmlWcvA95ygZKeMQ0QS9syjsFrl00mSA2x3kssFoPb7dZ4pNK48X7aO/gM9Iua3MEkEgkVcNQnGeljP/Ic3KV1hOdgALCyjnYmk4HP50MqlUIkElGyqPYMGhL2VYxEIvD5fPB6vZoFiMaoI6QsU5JmMrX0i2TGJPXK4XBYNSSQ74geVzweVwsW+zTKWh8s3kQVAg0gDT4AVb2PxlivyqExkIbEbDarnYL8jLw+Lg4E+ztKT1FeW1sKJtnVBoBSR8TjcVVrhQY5NzdXw23Lei0dBaxJw+X1kvIAACAASURBVIxYqfqIxWKw2Wzw+XxIJBKIxWIqg/XIkSPIyclR84GGnzsVye1Lb95A+4ZV73l1pO2RNDL0pjdv3oyamhpN77+BAweib9++ANq/p81FZu3atVi+fDmCwSB27NiBuXPnYtiwYSguLlYTzGKxKAMteX3y0PrtNNBaGikDVvx+noOLHb9LL7EE0Or/fOY01vTuaXylZ8zP66+Px+n1xLJuiz77k+fhtbJgFotN8X7ldcjva8/Q0zr8Ge8jm22upVJdXY1t27apXUsikcCgQYPQv39/DQVFikkGLNu7g2agBVYA8Hq9MJlMaGpqUmnKMpuvvSIWi4GlZd1uN/x+P5588kn85S9/AdDiEd5xxx048cQTv+Or/epIJpN48cUX8eqrryISieDDDz9EdXU1Zs6cialTp8Lr9Sqj2tTUhEQiAZ/PpwKApB2o/NAXlwKgApAmk0m9f757GlF6eG63Wy0KkpahUaexpGqEmbKSimBxJmZ80liyuJS8Pv6RnqAscMX/S8215G9plCQVkE6nVSIQDXlHAbNQSf3QWLvdbtWbMxqNYsmSJXjppZdw+PBhWK1WdOvWDRdeeCEKCgpQWFioxgFpJBm4lby2gfYNKyciPSSu5h1h9SXdEYvFsGnTJixevBgffPCBpnmr1WrF22+/jUwmg7PPPls1AGivg3PFihV48803sXz5cjQ0NABo2R7/4x//QCAQwHnnnYeioiKlJGEXFrlbIjfOUqhAi1dMaoABWhkLkN4rjYP0fvUeueRHZY9RqUyQn5PSwM+7PnrEQIsnLNPNJaXDVH35HXpvn172F+n32zP0WnLSUKSEtm7digULFmD58uXYvXs3IpEIzObm0raLFy+GyWTClClT0K9fPwAtlTnlDofvnzsVA+0XVgYp+MK4ne0IDU/ZM7GhoQGbNm3CE088gcbGRsXbAc0T+IMPPkBtbS0GDhyo0rvbK9asWYM///nPrXjXZDKJBQsWIBaLYcKECSgoKIDZbAZL6+q9VBptAG0aXnrh0oDJY3nc540DvVSOSTNMtJGBLS4E8vr4eb36Q3ry0vOTZVXlOWRiiTQ20uvWqyPk4tOR6EB9AS12o9+yZQuee+45HDp0SGU3mkwmHD16FKtWrUIymcSoUaNwwgknAGhZVCXkezfQvmHNZDIqsxBo+4W2V0j9sN1uRyKRUEE7grI2FhTqKCU4pTGTWW9cXGVgkT+jkeSCJTvFcMJL2kBvwLhNJn/MmiLSsPHzVCNwy202m1XGplSN0BBImRr5VF4fW4DJXZ6+ABmvgd/L+5VGXEoQ6Y3G43FFL8jdI2MBrG7YnqFXjFAdxJK0Ho9HlfxlshP7iobDYdTU1KhGFjyffG4A1Jho746agf8rzUoOUAamOor3wesFoDw9Dkr+Pp1Oo7GxEcuXL8fRo0fb9b2tX79ekxAiQUXAggULsHnzZpjNZmV85ISjIZe6ZmlEaRT1RpuqBC4Qn7eA02gDaJV1yN9LD1x63dJoUwMuYycycaet2jI0WPrrkjsTfh/pA6ouJGKxmDLa7d1QcbEhJcJnxHG/evVq1anHZrOpe5MeuVTNyGct54/c5RCSUvsiiaSUDsp3I8eWHJfyHDLfoq0dkH4etLUjlHOeaM/z/NvACrROhe0oNys9N3Z+4ZZe8qupVAqHDh3CQw891O67b0ej0S/cpm7duhV33HEH3G43nE4nIpGI0kXLglJtnUMGnT6v0BDxnxwH8ruO9fd+3vn0nHl7BpOQwuGwplMQ0LKAhsNhuFwuOJ1OFbQNhUKa1m/c1XAOsCuV2+1WweK2dh7cxXABbGuhlhmu3HFxbnKcyQqS+nGnz62QzmNbRpv0Gp+PXoff3hfibwNrNptVtbNls96OkGATDodVtbqysjLcdNNNWLBgAVavXq0Jqk6ePBljx47VHNteJyulWm+++SY2bNiggoEejwfnnHMOSktLAbTItujVMKjHTECZ4gy0BJr0C1Z7fQ4GWqDn5IHWkksAKhDPeIXFYsFZZ52FqVOnomfPnpq6IxaLRROIlvQZvWH5XZIqo8dPz56GksaciiLueGhDZIcl1qjhv1kyVi9NpTPGxK1QKKRyGWQAW/YOzWQyqqgYs4ePJ1gBqDoTNHR8Ie19QkejUeVNlJaWomfPnojH49i/fz9cLpfi8yZMmIAbb7xRw7G2Z8RiMdTX1+Pw4cNobGxEbm4u+vbti0suuQRnnXUWLJbmhrmhUAg+n081LpD6Y6BlW82JJiekVA0ZaN+IRqNIJpNwu92apCN9YNVsNmPHjh1K/mixWDBlyhT8/Oc/V7QKQcNO0EjL4LVc6ElZMeuW8kkpA5W7OFn/BICKu/B+AKg4FA24XlLK+coEIgBqR+H1etV5uRMgdUavP5vNKmN/PI1zK7ctkUhEbW/I87X3G+Wg44Dy+Xw499xzMWTIEOTk5GDFihV47LHHNEEqfWp1e4TdbsdPfvITdOrUCU8++SROPvlkXH755ejRoweamppUH0cOclbAC4VCqj2ZzWZDU1MTHA6HSuNm4I5bYaNrS8cAKQkaTdn+j9mf4XAYkydPRnl5OYBmbzcUCqGsrEyTWCO17kCL0ZPUBMHFwuPxqOPl/KEnTXpScuScX1QISUWX1Mkzp0CWYQBa0vbtdjt8Pp8y+AUFBWrch8NhpNPNPUJ5TaRj/H6/4tH1zkxHh5UPX1+DQHbEaK/gFlBmt5WUlKBfv35wOByor69XL7i9JwoRnDilpaU4evQoXC4XunfvjnHjxiEajSKdTiMUCsHpdMLpdCKRSODw4cOoqqqC3+9Hr169NIuSrJ73eRyhgfYNGbhLpVJKCSXpgXQ6jX79+mHIkCHKsHOcyPiFVPGQmtD/XE/BMJBJOoP12PXGm06BjJlIflnGoGjA6WFTdkxIVZHdblc8PYUG8vpk9jOvx+FwaNRHxxOsAFoFFyiR4zarvYKlQ02m5gp4kUhEeZbcdslEDX2woj2Cg5NxBk4GZjZGIhEcPnwYXq8XRUVFsNvt2LlzJ26//XZUVlZi5syZarJ4PB4Eg0HU1dUhNzdXZSIyWNvRanB8nyGllrFYTMn9aAgdDocmuYgxKspgaRypMqKiitSE1+tVBp7gbi4QCKh4SSAQQDgcRm5urjLGPC/jMawnw+Qv6aUnEgk0NTUpo+73+2Gz2RAKhWCz2ZCTkwOgZafAawuHwwgGg4jH4/D5fCgqKoLH41FUjc1mU7uO4x1WckYnnXQSfvvb32Lbtm149tlncc4556BLly7f9fV9IbglozGWA1dKorg9khKh9gqqP958801s3rwZF198McaMGQOgpYh/bm6umkxvvfUWtm7disrKSmQyGdx33334wQ9+gAEDBmgaEjDQw2fQ0erMfJ8hszlJFzADlk4JO/nonS1p1KRGPZlMqiqQ9JRJU0gKjQXGaHhphElxSB09AOVgyEUGgHI4GFTk9/K6ZJleAKrcAa+ZQVB61eyOxLGdTjc3fmZwVVY17Ag77K8DazabRSwWw7BhwzB8+HBcfvnlWLp0KU499dR27WUDLU1JuVVkNToOPpn2yy0YB0t7NVbcNbz99tvYu3cv/vSnP2HgwIEaXj43NxepVApHjhzB7Nmz0djYiMcffxxvvPGG+vyAAQPUllbWHuHfbellDbRP0DAzmUnfI1Lqs2XFRJm+D0At2tSvkyumIZRUBqs1ZjLNLd34ObfbrYKA+p0sj5dtzCi9ZbA8mUwq71pSMczslYuALN1LOpD2KhQKwWKxKJaA1TDlTuJ4Hd+qYJTValWdTgCtmL69Qh9xlkGWjv6yONn0XhO3wvR2SJvog4pms1l5X1SW8I9MWjHQ/qGX39LwyrZyUgEGtCirHA6HMpI01haLRWmpKZPTOzEcT9yRxWIxhMNhRctI8Lr0QU4uJoyZsRAdAFUzRiZ6kfrhPdP4c/GRiVg+n08tAgxE0mvn2Jc68fbqpH0TWIEW8TwjvR2lrq4sOqQ30jLDU2ZPAW1nfrUX6DMGaYj1herle9J7VCyGLyvcyW40kiZpz8/CQAs+LytQSjq3bduG6upqZQDD4TAqKipQVlamiV/QK1+1ahXq6uqUYfV6vSgvL0d+fr6iHaPRKNauXQubzYaSkhI158xmM/bs2YP169ejrKwMffr0gdlsxt69e1FVVYXy8nLk5uZi9erV8Pl8qudpKBTC6tWr0djYqHa8+fn5qKioUHXkJT777DOsX79ezeFkMomSkhIMHz5c0yiauxAZpGzPsatvAyvQLFgHoKK15Jfau7caDocRDodRUFCg0Zwyek69KIAvzQBsL+AgZGCFWz02cdCnHJMiIl+YzWbVVjEnJ0fT8UXK/Nr7czDQAhpcWZ2P85PecDwex+uvv44nnnhCcb2ZTAa//vWvUVZWpjxOZiPu378fjz32GFasWKH47BNOOAGzZs1CRUUFgsEgnE4n9u/fj1mzZqF3796YNWsWAChK8qOPPsKtt96KO++8E3379lU/+9WvfoX7778fw4cPxx//+Ef0798fd999tzLqDzzwALZs2QKHw4F4PI4hQ4bgT3/6E0pLSzWUrMlkwuLFi3HbbbepuZBIJDBjxgwMHTpUNR8nj88dgKSN2jNT8E1hNZvNmu0OpTZtZdW1N1BdIQMiMmgjPVFZn6M97yJkUIiehb7mQzqdxooVK/Dee+9h0KBBmDp1Krp06YLTTz8dNpsNu3btwquvvoqzzz4bnTp1UnSKrNnQnnl9A1pI+oE7LFlvY9u2bZg7dy4A4Nprr1U7NIvFgrq6Ojz00EOorKxEv379kM1m8c477+DDDz9ERUUFTjrpJI3s77333sO+fftw2mmnKeoxEAigoaEBkUhEsyCEw2EcPnxY1XRnyYimpia8/vrr2LlzJ8aPH49BgwYhnU5j9uzZ+PTTTzFhwgRMmjRJxZlSqRReeeUVjBgxAlOmTAEA7Nu3D3PnzkVtbS2uvfZaTYGweDyOe+65Bz/4wQ9QVlamUZDx2ehb8h1PsHL1BZoNdm5uLgKBAA4dOoROnTqhsLBQc4A+G4vH8Wf/SQ/O7XarSnHc/nOx4W5BX4TmP+1hSiPJ727rGRKhUAiHDh2CzWZDXl6eJpouqZ6VK1fi8ccfx1NPPYWLLroIANClSxcMGTIEN9xwA9auXYvy8nKViCMlfuQSgeMrU+x4BpUTgJbjTqVS2L59O55++mlcddVVuOGGG9R4s9lsuP/++zF79myMGjUKJ554ItLpNBYtWoR//etfePrpp3HKKaeohgg7d+7ENddcgx07duD000/XLA70aKVqhOOJKhN+3mazYdWqVchms7jvvvtw4oknIhQK4Z133sGWLVvw5JNPory8XM2DdevWYebMmUin0zjrrLNgMpmwb98+/O1vf8P48ePx0EMPKefMbDbjkUcewcyZM9G/f3+UlZXB4XBo+Prj3SGxSoG62WzGjBkzsGbNGjz11FM4/fTTcdlll2kO4Moogx7snOHxeL6T0qfSEMuaB+SHZZ2F/zTYg9Nms8Hj8QDQltfUF99ZsmQJnn32WYwZMwajRo1CcXGxpk0U04H1tZXlrojeuZRq8bNsqtvelUEGWsCFlu9Sxmc43mVwUgalp02bhoqKCpSUlGiOkeNCJtYwyUXKZwGoPpRA83xnn07OLe562SHoZz/7GS6++GKV7EXVC3d8/F4AOOGEEzBz5kx4vV4kEgk1binzi8ViGvkfr5+Gmkl2dGxkmj2DmccTrDTWQLM3V1ZWhsbGRjz44IPo1q1bq2pospaAvk7AdwGpD+Xf8lpk7YTvCvKZyb8l+LM9e/Zg8eLFmDZtGoYPH64GIQtB1dbWYvPmzaiurobNZsPGjRsVtwc0d4/Zu3cvIpEIVqxYAZPJpLLk6IFxYkmO3ED7htyp0Yhzx1RcXIyJEycikUjgX//6l2ZRLykpwamnnqop0ysLi8m4j9wRSmqRc0g2FZZ0nT6jMp1OY9CgQRgzZoz6TrkIyHMCzRLWsWPHquuRc3jv3r1YuHChJjV+06ZNmucir0Ffzvd4jN1Y4/G44qkY1JAruZ7/lNwS5TeUnR2PD+jbwmq1qiwvQNvqS7/QSfqCg7yurg4ejwcFBQUwmUzYvn07br/9duzbtw8ulwv/+Mc/8Oqrr6o4RCqVQjAYhNlsxgMPPIBIJIIhQ4ZokhzC4TAikQj8fv9xWQXteIN+Xkl6wmKxoKysDHfffTcee+wxXHvttZpxddtttynNPosqWa1WVQKBAW7OZ5keT9qRYLIWxy7pSF6L3nGSclPuwPWVBqUBlxnOPHblypXYs2cPAoGA0nyzfDG9cem5MwApPfPjDVZZvxaAehiFhYXK2ITDYbUiS3E/5T9c0Y53LumbQNIXHKhSl8r6DyaTqZXkiUWwstksGhsbVfJQIBBAaWkppkyZotL16Xnxz65duzB//nwEg0EA0HDYnHQGRdIxIOkPjiEqI5iy3rlzZ5x22mmKtgCajWxTUxOefvppnHnmmejcuTMikYhSGnE+cyxSKkopHY14Tk4OnE4n4vG4cs7oIMgEGR4rA97kmRmklMWhYrGYojZkYSfqrz0eD0pLS3Haaae1si02mw3l5eXKu5YLEh1QXg8Xg+MFitOWWmaXy4U+ffrA7XbjwIEDahXlC5aNcWW6qKRQvu/GW1Ih3CKyyDx3Kiz+wzhBIBBAOp1G9+7dVcDH7/cjFAohEAggGAwiHA6jqKgIp512Gq6++mpNcIpb1kwmg2XLlmHr1q1Ip9M4cOAAcnNz4XQ61faYJSsNtH/IlHBZxpQLcSwWQ0NDA4YPH44xY8Zo6l4/8MADeOaZZzBo0CB07txZ1QaRvDQ9almtT5Z8YKyKRldei8wwpmPCf9MLB1pUXfSqKU3l9x86dAgulwtFRUXq3C6XC+Xl5ZgxYwby8vLg8XiUaiUYDCI3N1fF4oCWrkcy85Pc9vFktM3yBbMiXNeuXVFZWYna2lr88pe/xLZt21BQUAC/39+qBi/TS202m1rtjlepzdcFV3oWkHe73a2CO36/H/n5+airq8M999yDuro6PPLII6ioqFBp6y6XC263Gy+88ALmzJmDGTNmoLKyUjNxOdCB5m1i//79cfPNNyObzeLWW2/Fxo0bkUqlEAqF1Hs20DFAY2i321VNbdbaSKVSWLduHW666Sa89957SknBgCQ72LCGSGFhoeKzAagxAbRIaGViVyaTQWNjIyKRiKb4E40zFxA6dax1nUwmEYlEVNq7rH3CoKrf74fdbseePXvwwAMP4NVXX1WLEksLZzIZFBQUqIzthoYGzJ07F9dddx0WL16MSCSi2AG32414PI7GxkZ1T/zu4wlWKSXjSpWXl4cRI0ZgzZo1WLhwIS644AIlrZPQe9jHYxnEbwtSR/Qu5A5EppZHo1F88MEHmDRpEiZOnKg8Exp9u92Oqqoq1NTU4Prrr0dJSUmrQIssiVlQUIAJEyZgw4YNeO+99zB16lQMGTJEXZOBjoXPC6pxTNlsNuzYsQPz5s1DPB5XdJvVasW4cePg9/uVsRw8eDDq6uqwbds21NfXKwMfCoUwYMAAlJSUKC220+lUWu5FixZpvOiqqqpWwXXaEqBF5UFHhTK/zZs34+DBg8pe1NbWqoQdLgZ5eXkYM2YM3G43Fi5cqOxTU1MTPvvsMw0FBLQ0cYhEIprU/ONxrLdJarpcLvTs2VOj0eZDI+/En0lhflu9477PkCu85LQlJSVbhvFz5OYod5K/Z1BHDnBODJbh5P+5M0okEggGg0gkEsjJyTEUIx0MUr5Kx4l8dDabxdChQzFr1iw8+uijuPLKKxVv7HQ6cdVVV+Hqq6+GzWZTHWOmT5+OIUOG4K677sKGDRvg8XgQjUbRuXNn3HLLLTjllFNgt9sRi8Xg9/tx4403Yt68efj1r3+NUCikAuVsnEI6RdbxttvtyMnJ0RQ6u+SSS1BaWoqHH34YVVVVKrA4ePBg3HHHHRg8eLA6T/fu3XH77bfjxRdfxBVXXKGke5FIBD/60Y/wyCOPtMlVU4rMXpnhcFg1ATleYGXKtNQyM0g1btw43HTTTdi6dSv+93//F+eccw7y8vKUoWYpSJZHPF5Xtm8DcoCM1MtEF/5uzpw52LhxIy666CKMGDFCU0KAxjgcDqOyshLJZBKFhYUagy8ntPTsM5kMxo0bB7vdjqFDh6qgj1yAj9cI+/EEKWvjvxk0pDfbqVMnlcUoG3+Ul5erMcd37XQ60bt3b/zwhz/EyJEj1VjJz8/H0KFDkZ+fr85LPnj48OH46U9/qrx4qQYpLy9Xgc2Kigr87ne/U+elaslqtcLr9aJv376YPn06Ro0apTjvrl27ol+/fvB6vRpJos/nw+jRo3HppZdqVGvDhg1TlQeBllKzlCPyWTH2djwZbAAwNTU1ZWX7H0CbsRcKhXDFFVegtrYWTzzxBHr37q10muyiQj4JaAlCfheZh+qm/m9g//3vf8fll1+OO++8EzfeeON//HqkZjQWiyESicDr9ar6v9RMX3nlldi5cyeeeOIJDBgwQHM/TCNubGzUKHoYOKKnwbojQEv2pJRryvfCycJIu4H2DTkWOC+DwaCqH82GGRxzVGOwVGs2m1X8sZSV0sgxQaWtnTI/x5iXlOdxjrOjkqyJLcswcHcYi8WUwycVHlL+R36a45pxMu4wnE4notEogsEg/H4/LBYLIpGIcjSlEksucseTM2mVwQFOdCodpBieD02K6M1ms6Y/G7dfhva3GZTzuVwuTREubl9ptOXzlanBAFTnDk6SWCym1DyyyQODU4yuA81BmGg0inA4rNFkswCV4WV3HHBXy8VWljmQSgwaMQBq3AEtlf0CgQA8Hg/cbrcm0A2gVYCaxpL0Ap0NuVOjV8zAqPX/OqXT+9W3SmODYrmTlFJVPV1Ij1k6JXwerETodruVEyMljPSy5Vw5HqACkUCLdygDjtzy7NixAytXrkQ8HlcFYKTW11CMfD5kRpkM0uzatQvr169HQUEBunTpAq/X2yqbk4un1+tViwDQdoacDAzLiaD3MqSu3kD7Bw2UfJcya5FjgtppmSQjvV7peMnAOFUmdAZkzobcLXJsSWkfz9fW/NdTdW3twOUYpXGVziMhjyNfr9erA1D3TFrmeLRLVtnVRO/hURT/i1/8AsuXL8fdd9+NadOmYdCgQRpROx8MOVPDGDSDyTCytrf0PN5//33cfffdmDlzJs477zz4fD41yK1Wq5JNUerFRVKeg4ZdJj/l5OSo73U6nepYqbeXWnsD7Ruy7RedJOqt6V273W40NTUhGo0qTb402Cy7XFhYqEm00o+BturaAFAURltxEHrfctftcDgU781rIAXD+5EeNH9HAy673nAB4iLFz8r7M5vNmjojMsvzeINVvjRZo0Ma39zcXAwePBg/+clPUF9fj/vuuw9nn302Bg4cqPG0pSCfgRJ90aJMJqO6U1AX2tFAbk5fVIe1rbmVpOGUnm0qlcK+ffswf/581NbW4he/+AVGjBiB/Px8ANoaL4yCcxLJ9mlSWsV3JTW2eh5bz/kbBrvjgO9TBqhJcclywzRucrcFtFAM0iljPINBcpk0R8PJc0tDLfMBGKSUc1j2bZXH85zSs+Z30qnhOfWxGV6nbBfI7+S/Odc4V6Qt4m5E5pBIKaI+K1zOFXrsvE86SbwPqWfXZz3z3HwevDdmnzIewfcpnxuP5XdIqKfNm2cQQL/F7tWrF6655hq4XC48+OCDKllDL8Qnr0r5GVdhudWKx+OIx+Otft5eob9Oejn8v7xHZptJD1sW1Emn09i1axeefPJJNDQ04NZbb8WQIUM0z5qwWCxwuVzKq5Ap8EDLO6OHrecCZWlNeQ0GOhb0VAf/SC+SXDBrbnD8SQMMQJU9ALQGDdBSEKT09DtnBi7JWUunhAaNAVBJb+jpOn6X3nbIAD6NGmlFBtBldqU8v/y5vHcem0gkEI/HVe9L+V1tzT+gJUFOgguAvEd+J5+JZC7YkIWf4y6C1yHjiPp7a2un8IXSgbY8RW7VmZnFYANXXbkVY+NQpmvzJbBEqdlsVjek98jbE2iMuQVjb0bK8WKxmJJVeb1e9XlZ20FWWJPPT885ylXagAGCk13uwOgtsvwv6wLJNHQae33QkV6dDGLT++P30VjLok+yMmQymUQgEFDfyx2mvgFBMplENBrVeMl0KGi45Dyh0yOLPkl6RIom+EeyBAx4yoQbJgrJ3Si/i4sir1nuRBnIlQsXdzMyhV4mEvEaY7GYihXIXbKU3srgL98da7J8XgD1K3ETcoXs27cvTj31VBw+fBirV69WtTNkQ079jRP6lag9e9dfBLmK6rNA9bSEyWRSXkkmk8GmTZuwbds2DB06FIMGDdIYbQMG2gLnCrX+3DJTwkdKAoBmt8VjOd9kMJxVIQG08qZ5jN5zbUuyJ6+vrbEvA6BtjXMpP9RTHpQaRqNRZdx5fv15+DnZSzWTyagFgFSMXHD4LHldMnlJyhVlolsoFNIEbPncpKcsnyOfrz6Qymvh99NA87rD4bBa6PT4Qk9b8rD0AsePH49evXrhwQcfxAcffIA//vGPMJvNCIVCyM/PVzIj3qDH41GytXg8jnA4rAIoubm5mlKP7RVms7YlWygUUl08nE6nCsBw20Nv2mRqboEUCATUDuPFF1/E5s2bcfPNN2PYsGEAPv/lGjBAkFY0mUyaLuX63p8ANHpr0gKSPiNNIPldSb3RYAEtclKOY+6W6XXrPVR61Sz3TGmg1+tVdkQaLHrl0lBLxy8SiaCxsVHNQeYp8J4YcGxsbER9fT2KioqQk5MDq9WKaDSqaqbIHpOkdyyW5q70PJ/kqPk57ogBoKmpCQ0NDSguLlaSSRruSCSiOHe3262ej76vK58vnwvPzXnPhfjIkSOw2Wzo2rVrK2/7C422XAVIe7jdbvTp0weVlZWoFBb0swAAIABJREFUrq7Gyy+/jGHDhuHkk0/WBCW5VeLA4WrHrQEAtZK1xZ21J0i+DGgZ5LJTBjk96qmlBM/j8WDjxo344IMPkJ+fjwsuuAADBw6Ez+dTW099kMaAAQlprOkMUGvPn1utVgQCAcydOxcOhwOVlZXqZ++++y727t0LABg/fjxGjBihMSA0vJLnlcEzs9msHBGOTxp3mX8AtNTc5/inIad3Ljl1OVckRcgFKZ1OK6dIypMZGOT1OJ1O+P1+pRenkZZ8OKkiUhT6eUpPmZSF/Ew2m4XT6UReXp6m2imfgwwAk54hVWQ2m9VuweVyobq6GvPmzUMymURBQQEmTpyI7t27a8QNfr//cx24LzXacisgueqLL74YH374Ie644w4kk0kMHz5cw0mTz6W8h9l79FhZS1pupdqrlymDIFK6BLRsszioZGYat0yJRAJVVVV44YUXcNddd+G8887TbHe5kLX3gKyB7wacGy6XS40PeoI5OTnK2wyHw9i9ezdmz56NgoICnHnmmUgkEti7dy9mz56NTz75BNlsFoWFhTj11FMVZSeDZJJ2oEGkc5WTk6PRi8s5LI2xNKjcgYZCIWV8JV0jjT2vhdw25a5+v1+jhgFaVCZ0BhlnCgQCaoGgkeccpVEl98w5qNeH08BL2WA2m4Xb7YbH49HQOLwXyRYEg0HFJvD+4vG4Kq28fv16vPDCCwiHw+jevTsKCgqU6MBkMsHr9SI/P/9zHbgvpUcAKKkMXX2eqKSkBLfffjtWrVqF2267DVOmTEFFRQWKioo00eG2VlOuTnpJUXuEDNZwUMtsLwYr9DzXkSNHsGXLFsybNw9+vx8PPfQQBg8eDABq8HAQswZMe34OBr476DMiGTwzm81K4fDWW29h2bJlOOecc1BeXg6Px4M33ngDixcvxpQpU1TtkGHDhmkUJTw/A2Ycg+FwWNXd5q6ZzgW9UWZLSsPNno6kKAAgPz9f45HTS5eUID1jziOfz6c8bmlU6SBFIhFlTIFmXlnmM3DRkNcspYh0KBln83g8ai5Tmkchhs1mU7QKDTfPZ7FYlKCCOwW/36/oITZiAIAXXngBoVAId911F0wmExobG/H+++9j9+7d+MUvfqHsTFsxQeILLcQXSWEymQx8Ph9OPvlk9OnTB9FoFBs2bMDatWsRDAZbrd76c/DBS1lae4a8Xr1h1UuwGJWuqqrCJ598gsbGRhQXF2PChAkoKir63BK2HTk4a+A/C9KPcixu2bIFH374Ifr164dhw4Yhk8lg8+bN+Pjjj3HiiSeisrISU6dORd++fQG0lFGlU6YPlkljyvkpA4z8HGVtPIeedpFepDRI+gCmDCYy61Fy5oQ+aCp38zTK0pvnvfBnMo9B2h7pYOq/kxQpA6L6a5GSYNkGjXaQevRPPvkEBw4cwOmnn45zzjkHI0aMwM6dO7Fx40Z1vfTM9an7xBd62lR78MFRHsP+cjzx6NGjMWDAADz++OPYs2cPevfurQJvTLKhp65PqOkoPC4fnl7rTMkfBwCfTUNDAxYuXIidO3fimmuuwQknnNAqkEN5DxNo5HMyYECCnLJ+rsjtPvuDknYLhUJoampCOBxWXrRM1qJzEQ6HlZfJGIvL5VI/a8vr4xxm0bhEIoH8/Hy1G5fUn74aH38mE1AsluaaKXV1dSgqKtIE6Bgnkjt2ACoYKFPwSUmyCBazkiXNK+/B6XSqXQSPZx0X1guiwQag2VXIc0sHVMr5stmsRmbJAnsAlD0EoCp5snphMBiExWJRSXcSljvvvPPOLxsw8sFwJeMFUZvMoFosFsPmzZthtVrVik7pDb0Dymfq6uqQzWaPeVlXnqeqqgpvvfUWJkyYgNGjR3/r80YiEdTW1mrug6nm5PAtFgvWrVuHF198EVarFeXl5Rg9ejQKCws19Ak17TTUUqNtUCQG9CBnHY/HAWjrx7B0ciqVwvjx4zFq1Cg0NDRgzpw5WLp0Kfbs2aOcjt69e2Pp0qV45513UFRUhJqaGjz33HNwuVzo1asXstksPv30Uzz//PNYsmQJVqxYgTVr1iAQCKC4uLiVBjqdTmPhwoWYPXs2Vq5ciaamJpxwwglYsGABVqxYgW7dusHj8SCZTGL+/Pn4+OOP0aNHD/h8PjVPa2pq8Morr+DIkSPo37+/MmomkwmbNm3C66+/jiVLlmDx4sVYtmwZ4vE4TjjhBOXRJxIJbNq0Ce+++y5yc3MRiUTwxhtvYNGiRfjoo4/g9XpV+r4McO7evRtz5szBokWLsGTJEixbtgz79+9Hz549VVGreDyOLVu24OWXX0YikUDfvn0VRw4Ay5Ytw9y5c1FUVIROnTopioi/J421ePFivPjii1i1ahUaGhpQW1sLp9OJ7t27q4X0448/Vr0MeP/MYZH4Qk9bitN5sD5KTM85nU7jrLPOgsvlwqxZs+B0OjFkyBCNDplBOqB51a2trUVhYSF8Pt+3H9X/ZphMzVUMDx8+rEkQYsCRBeGz2SzWrVuH1157DTfffDPOPfdc+P1+FdiQmZRcsRnMYTKSAQMS9PTC4bDiXjl2AODTTz/Fgw8+iOuuuw7XX389zGYzlixZgvnz5+Ozzz5DMBjE/Pnz4Xa7ceqpp2LhwoX45z//iW7duiEQCODll19Gt27dMHr0aITDYaxbtw5PPfWUShDz+/2YOHEievbsCZ/PB4/HA6/Xi1gshqNHj2L58uV48803kUgkUFlZibKyMsyZMwdbtmxBRUUFCgsLkUqlsGDBAmzevBknn3wyunXrpu7twIEDeOKJJzB27Fice+65yvtPJBJYtWoVXnjhBdTX16taJI2NjSgvL1fzJZPJYP369fjv//5v1b5vzpw52LFjBywWC/Ly8lBUVKSug5Ld9evX45VXXsHu3btVc4cxY8Zg8ODBKrEnFoth06ZN+NOf/oRLL70Up512GhoaGhRF8v777+Oll15SHX+AFpkl6R2TyYSPP/4YL730ktJeP/PMM+jSpQtGjRqFn/70p3j11Vdx2WWXIS8vD2PHjoXb7Va7Jcocia9kIWhouU2hEkRyNplMcwnHk046Cb///e+xcuVKXHHFFTCbzRg2bBhmzJih6nFQy9ijRw9VGKk9ZwJy0lDuyG0qqYzc3Fw8++yzeP/995FOpzFgwAA8/PDDKCkpURmSrO/AnYqUQMp6wQYM6EHONicnR3G03H5z3NDxCQaDcLvdKCkpwS9/+Us899xzWLlyJS699FKcccYZSlsdDAbx5z//GRUVFfjjH/+I8vJy1NbW4qmnnkI4HMa9996rPMB0Oo3q6mr89re/xYwZM3D22WcjFAph+fLlePnllzFixAg89thjyGQyqK6uxvXXX4/t27ejoKBAXSMdPpmUJksscE5EIhHYbDbU1NTgqaeegtPpxA033KChWT799FNce+21uOqqqzBu3Dhl4Hbv3o3HH38cZWVl+MlPfgK/349kMomVK1di9+7d+PGPf4xu3brBarXipZdewp49e/CjH/0Iubm5KrB44MABPPzwwzj77LNxwQUXaBQjLM3h8Xg0AU0prgBasjclXz59+nTk5+fjb3/7GzweD6644gqMGDFCY/OkVp4xAr3BBr6i0ZYdLIAWDgpo6bLMLX+3bt3QtWtXHD58GB988AFsNhtqa2uxevVqDBgwAD179lQ3xW7KsmCM1CwDWkE6v1fSB7JmgT4bU0bImcmlD2K0VahGUjUyK4zNeXlcKpXCoUOH8Nlnn6Gmpkbx98XFxTj77LPVfUgdrD4Kzog5n6EBA22BWmSO8Wg0qihHvXLD6XSiqKgI48aNw+LFi7FhwwaMGDECQ4cO1QTZUqkUunTpgilTpsDlcmHbtm1YsWIFunbtismTJysKIxQKoba2FosXL8ZZZ52lWpfV1NTgvffew6RJkzB16lRks1ksXLgQS5cubTWn6eRxrhKyvAPvwW63IxgMYunSpRgxYgROPfVU1Y0dAHbv3o158+Zh2rRpag5lMhkEg0FEo1H4fD6MGzcOPXv2RDgcxpw5c3Dw4EFMnz5dzcmqqirU19fjyiuvRElJiYq/rV27Fhs3blTz0WKxKBGByWTC0qVLcdJJJ8FisaCqqgoWiwUTJkxAfn6+WohkAJfzv6SkBE6nE3PmzEFubi7OOecc5ObmAtAKEKTt0it8iC812vSKeRHyb3lh/CypkDPPPBMjRoyA3W7H+vXr8Ze//AVnnnkmfvazn6kMJf3KImsQANo60TSIsh4BP8Oi/7xOoKWKmdSFy6wxHsuaIoz2AtB8hl6wPrOJ2Y9LlizBo48+iquvvhqXX345EomE8q75AqV+XUbhCY/H0yp6b8AA0ZbCigkrTMKQqd5AS81pAGqXR3kge4X+8pe/xMSJE9XngJZGuTJJzGq1KkqQc8Dr9bbqsp7JZDB69GgMGjQIM2fOxObNmxUtCLTsGGTWI8UM/JxMoOG9s0Hxl8HhcGDGjBm48MILlcSQ12U2m+Hz+VQDY1numPPeZrOhvLwc9957r5IyptNpDBw4EPfccw+ee+453HvvvfjDH/6AdDqNW265BdOnT8d9992nerGyATrZCC6kstT15zEKUvHidDoVzaKvyfSVjPaX0RbyIdMjzsnJgc/nQzKZRL9+/TB9+nTU1dXh4Ycfht1ux4ABAzB16lSlf6S32dTUBKfTqfSKHDRyK6WvZ8BBoQ9mSj0pg5/cikmhPY+TD002yTWbzSrY6HK5MH/+fKxevVpd90UXXYTBgwcjPz9fnU9f3e+rPj8DBvTgeOc4paKCnisrS7JZBueILFAmnSv2X+zUqRP8fr/m3C6XC9u3b8eDDz6ojotEIti4caPSRQPNxjYajSIWi6m/pSjB4/G0ShaT0jspz6PahLkbci4y65ocNwCsXbtWUR+hUEhdJ++LXDfnldRr05njAsJWi7LfphQNAM2LARUtoVBIqVMOHjyITCajkfFyB05FCb1lOnpc4Eiz0CDzPWWzzV2IZFEpPf4tUS+ubBaLBeFwGF27dsUVV1yBRx99FLNmzQIAjBs3DmVlZXA4HIjH4+jevbtaBWlMpZ5ZVs+SWVx8qPydNNyU1JE6YSCDnoXFYlEGX/JSVMc0NTUhNzcXJpMJBw8eBNBcW/zdd9/F66+/DgD48Y9/jDvvvBOBQECtqHLQGTDwbSEzBelESW5a1nfnLk82GqBGmo4OaT4Aql4GjYnD4cCuXbvwxBNPqLpBNFRut1s5V2xjR4NNB0Z+j5yvQIuSgobNZDKp+hxMTmEWNef+zp07MXv2bOzfv18FAH0+H/r27asSbMiX0xjH4/FW5SSkFpvVSblzZ1xNUqnS6JO+kKVvgRaWQcb49AXx5HXJ3BVZM4bvlBmvDADLXYrEMTfaXPFkBBVoNqBnnnkm+vbti3Q6jX379uGee+5BPB5HQUEBrrjiCpSVlSmlBQDVBkl635Qa2u12xevl5OQokT9Xbv0qT50rXxy3idyGhMNh9R0AVIDR4XDgwIED+J//+R9UV///9s48uMq7+v/vu+QuuSS5SSCQTUIIgSSQhE4pS6WlFFAExtFWOlZF2zrSOlqdwaUzLiiIhbajMqUddRzb0RnbUatY6NSOuCANNGDD2mILSAohBVK4We6+fv/I7/3JuQ+h/bG0cOG8Zph27vLk3uc+z/mcz1ne501kMhncdNNNePzxx2G321FdXW1qQjlDT9aWKsqlwp0uQ4Sp1NDcUbfbjYKCApSWlmbVA/MeodATSwVpINnuzSRhPB7HwMAA+vv70djYiGXLlqGwsNBc0/xXV1dnhOCYGJWhk2g0iv7+fgAwXj8/M3cCtA+RSMSEKKyhS95DLGLgrpnvKS0tRV1dnek85OLAPgi+nuEXKVdrRWql8HzLMCZFnOLxOM6ePYtgMAin04nS0lIUFBSY8C2/B+0XwyvMPTidTsRiMXg8HrMg0tBzWLHNZjOJTxl2zvq8l+WqEliD6nJaeH19PRobG5FIJLBz507s3LnTrIwdHR04ffq0WWG9Xi+mTJkCv99vvpgskpehjPPVeNOD4A9qTYbImk0eKxwOY//+/QgEAuZH6+3tRV9fn6k3b2howMKFC03Gm/FyXqCKcjmx5pKkAJscWmJ9DzsDpTwpa3+5A5UhPG7hq6qqsHjx4qySupMnT+K///2vcY7ksGnZ3HPs2DF0dHSgq6sLwLkdg7I72upYyb4Fvreqqgpz5swxzl8kEkF3dzdOnDhhPFF65lajKUOow3Vly+o3lvf19PSgs7MTFRUVqK2tzfK2x44di6lTp6KzsxMulwvTp0/H+PHjTTiKHrP0wNlkJEujZUiXTihfK3s4aOusXHajLXv8GbawVm6kUik0NjZi3bp1SCaT6Onpwfr167Fjxw5zEisqKvDwww9jzpw5KCoqQl9fH4LBoFlZOVRBCrjIrQQNtty25OXlmRWeNZS9vb2mksVut6OzsxOPPvooOjo6Bk+Q04m6ujp8/etfR0NDA+x2O3w+n/HqZZOD3GXILZqiXCosD6XHJr25ZDKJQCBgaoCH21JLnRsaGOvOkoaY4RMa/XA4jB07dmD9+vW477778IlPfAJA9lguvm7nzp34yU9+gq6uLtTU1Ji/zXv27NmzpnCAMV3en6zPtqrn0Zvlsf74xz/isccew8MPP4zFixcjGAya+1sabRpHmSi1LhLs0rTb7ejp6cHWrVvxy1/+EnfeeSe+8pWvmEUuHA5jwYIFaGpqwiOPPIJUKoWvfe1rmDhxYtboMrlIMRLAHhfrwsrnmdCVSF1wK++L0ebkBSmyRONNAz5ixAhT8ufz+TB37lxUV1dnfch///vfeOWVV+BwOBAMBhGLxeD3+9HY2IhbbrnFxIlkETtHAPFilCV9MqbX1taGjo4Oo9VbWFho2vYnT55sDDQTDfX19aisrDRbHnoFALLieHw+EolklUkqysXC643VVsybSE+McWx6a8BQEQFjpTJ0x+QdDRn7ED7+8Y/j9OnT+PnPf24eZxhl/vz5qK+vN63tTU1NWLFiBU6dOoV169aZv7l06VJs2rQpayJ6IpHAvHnzUFZWhra2NuzYscP87bffftuEObkwVVZW4rOf/SwCgQDWrl2bdT4SiQTuvvtu1NbWmvCM9GJ5LmiUeZ4YBvF4PPjkJz+J119/Hc8++6x5fGBgAJlMBrfffjuam5sBwEy9cTqdKCkpMbXkqVQKlZWVJucldzA04lwo+dsxLs5qOe4UuGiUl5fD5XIhHA6bBOZwEYT3xWizWUbWKMusMTO2/NFGjBiBpUuXGs2DTCaD48eP4xvf+AZefvllo9ORTCbh8/mwYMECTJ482WRai4qKzErGSTqcTs2LLhAIZI1r2rp1K5599lkEg0EAMAnR2tpaPPbYY6bwnQkDuQViDI0KZlycuEXjVud8wlCKciHIRCS337wfKJ9QUlKCRCKBU6dOGblWm22wy5ZC+owrFxcXo7y83CTgeM96vV4sXboUL730EtatW2cMXjwex+LFi7Fy5UozuCSdTqOlpQVTpkzBd7/7XTzzzDMoKCjAXXfdhZUrV6K7uxu7du0yi0ssFsPixYsxceJErFmzBnv37kUoFDLfYdSoURgzZoyJy3/oQx/CF7/4RTz99NNYvXp1lvH60pe+hB/96EcAhgZgFxQUYMSIESacwzg2S3CBoUHibrcbn/70p/Gvf/0LK1aswPHjx80OZe7cufjxj3+MiooK44ACgwUIsuyQSUnuRvibMDHKnYosTAAG1Q7Z1k+j/PbbbyORSGDSpEkoLCw0kQBZXCGxZS5ziYOMzfAHY5yGsSfWLFpjTbJ+MxgMYvv27XjnnXdMUT09jmPHjpkLgiuTrC91Op2IRqM4efIk3nzzTdTU1JjuSy4kU6dOxaRJk0xMj5UuHo8Hs2bNwqhRo8znl8pksuyQngRXS67o/D5y26QoF8tw8WB6lW63G11dXdi+fTv27NmDvr4+LF++HJMnT0YqlcKRI0fQ09ODxsZGU8q2b98+dHd3Y+rUqSgqKjLzJdmrcPToUbS3txtBI5vNhoqKCjQ2Nprwgux/eP3113H8+HHk5eWhuroaTU1N+OpXv4pdu3bhySefRGtrq6mU6O/vx65duzAwMJCVQEyn06itrUVra2tWjunQoUPo6OjImiFbW1trJDK40zhw4AB2796NWbNmYdy4ceYYiUQC+/fvRzweR3Nzs6kM8/l86O3txe7du00pYyqVQmlpKZqamlBQUGAqXRhmtdvt6O7uxvLly2Gz2fCLX/wCBQUFiEajRuiJoVHGqpkozmQyCAaD2LdvH5xOJ1paWuDxeHDq1Ck88cQTCAaDuPnmmzFx4kSjfULH1hruuuwWhdsxZm5lqR5/cKsHymyt9MydTqcReZI63olEAm1tbdi+fbvxNqTR5t8Jh8NGfY8KWiSTyWDChAlYtGhRVl2oHDLKUiiGOKzJExkfk0kerqByPJmiXCryHpKJunQ6jdGjR2PhwoV49dVXsWXLFtxxxx1mZztp0iSzK+V7GhoaMGHCBONIsSSWhqmmpgbFxcWmQoXv47ZelvTZ7Xa0trYaKVjuCmSzmPzMfr8fs2bNygprMOQADGn3M3ZfX1+PsWPHZqno8ZiSuro6VFRUmL4POmI+nw8zZswwO2E5Zm306NH46Ec/akSwaLhlB7McdiKrW/haaQfo9fNY8ntzt37TTTdlVbgNDAygvb0dfr8fM2bMMDk77hhYBil539xAJhZ4IciyG9nqKUt9pJ4uMNThyA4mrrYzZsxAfX09zpw5g3A4jNLS0qyuLh5r06ZNWLlyJZYsWYLPf/7z6Ovrg8PhMKIy3OaxUYDz4LgIcAGSCVUW+PNHA4YSJqweyWQy53weRblYZDMK7xsabDomDIlwZyjL2+hxyuoKJjABmPg2k3nMEdHwB4NBOBwOU1orDZUcLiw1tVkfTm86Ho+bOC/nRXI4AJONVAn1er0mrEDjyxmMcuiChI5db2+vKQLIz883oRG5o7Z2VUej0Sx5WllcAAw2EvX39xtHjAsoPz/PHxud8vLyTKMM/244HEYoFDJTagCYgehcEBjikTFyjniUvC8xbW4paLikoZYxGul5W0MKspuRxporvcPhQHV1NUpKSrKSnjJrzPlr7DQaOXIkRo4caS4m6mDL4aRcZWUSARjK5FpLDHnyZUiEF5ucaqEolwKvLVnCCgx5dnzNrbfeCofDgVdffRWRSATz5883W3ZpCHgND7cI8P6SchJy2ILM3cj3y8YUeY9zYZC6KUD2lBpZeidnyAJD8XxpqOX3Z/EA7zUuFHKHzMVEdhnKx7gz5nP8/DwnR44cwcaNG03RQ3NzM2pra7Mm67A23FqQwBp1Fl8wBp5IJLB161a0t7dj9uzZmDRpkvlcPDeswLPyviUiqVfA7ZR1+IGM09EzYCKSF1cgEIDNZkNxcbHxDPil2P3l9XoRDofNxSa3T/QsWLxeXFxsFhKW+rAjy+VymVWawzsBmM4pXjS8IKylOKz3pjC6VPVTlMuFNcRIwxSPxzFv3jxMnjwZ3/rWt3Ds2DHMnTvXvFZezzL8ID1WVj/I1zPEQGOWSCTMll02o9BIMmRJbRLeh/RSZY5IapJwViMLEejo0cDRuMqwA0MrVi9ewoWIDiEXCfmYHEoidyk8/ltvvYXf/e53OHPmDCorK7Fq1SrMnTsXbrcboVAIoVDIeNTyd+L3YsybuTnuKNra2vDPf/4Ta9euxY033mgkY+Wic1GCUReK7AbkDzNsBvT/eQ3Sc7Aeh/WZsrmAWsI8Hj16GUPj32VYxuPxwO/3Z5XfyUnJvAgYw5MXBzB0UcrjW+EJ5ve2joJSlIuFxpUhDjlwlvcQr/fi4mIsX748S2jJGo6U949EOk3DweuaXuD5jkE9no985COoq6s7RzDNaoh4D8tkP+893lPy3pNVFfSu3+0zc8GQx7A+BmSPG+PjDocDLS0teOSRRxCLxZCfn48pU6aYRYv2gueVIRg6jNy1WCtPfD4fPvWpT2H27Nmm1psyrO/l7L0vRtt6IobjfBeOPI41LkwP23ocehvyMSlOIxODNMbyYuaqSINrTbQM972syO8p36colwtelzJeLYXJgMEwxMyZM819Yb3H3s0Y0PgPB4/zXtVQ/Bytra3nPY71Mw13b/E157uX3ut5+TrrdxruMXlM62OVlZVmaIMV2cwDZJ9fuQOR8PHm5mZTD25977tx3dWjMXYtV3ypzEXjz23Tuy0sivJBwG27zLHQGEhNEXrf52vKUK4NrjujDQwN8JSlPdZ4GYBzMvaKciWwJgtleSu9VBkulDoYyrXHdWe0uT2jkAtlFZnAoLci5SPlVkxRPmholKWzwXCeHM4BDFVOAf//220lt7jujDarW2Smmp6M1C2RpVRWwStF+SBhoxi79FheRmSif7hEn3JtcV3+uix5Gq4EUVaMAEN1p4pypbB24ALISpqzPE5ewxrSu3a57ow2K1Bk8lE+xxIj+ZiiXEnYlcu6ZdYls3EGGBrswb4IlpXp7vDa47oz2izvk62qjGHT+5ZzJflfzcgrVwo6DqFQCOl02jgdUg+DipMsf9V49rXLdWe0ZccmDbGcSZdMJnHmzBlTVsWGG70JlCtFLBbDwMAAenp64HK5MHbsWNNVV1hYCGBQn8fr9apQ2XXAdWe0GR7h3LzCwkLTxp5KpfDWW2/hV7/6Fbq6ulBUVIQ77rgDs2fPvtIfW7mO2bRpE/7whz8gnU5j2rRpuP/++7O6HWVtdiaTMRrQ7DJUri2uO6NN5KSP06dP4+jRo0gmkzh69Cg2b96MY8eOwe/3o7CwEPn5+WhqaoLf77/SH1u5Djl48CD+8pe/GBW7+vp6FBUVmcRkSUkJxo8fn6VRr8b62uW6M9oUnfL5fBgxYgQikQi2bduGtWvXGpnJ48ePIx6Po7e3F7/97W/x2muvYc2aNee4H7j+AAANa0lEQVRtzVWU9xOXywWv14tIJIL//Oc/eOihh7ImQ82fPx+rV682oRJqcajhvjbJeaNNaUSK51C4SZZJyS7HN998Ey+++KKJYUejUezevRuHDh0y281YLIb6+nrcdtttcLvdRgZWyUZ6dVLwnqjRuDzceOONeOCBB4xM6JYtW8xQD6fTiZ07d+Lxxx9HYWGhUcOsqanBrbfeisLCQqPXw4opJtxjsZgRgZLKefq7Xd3ktNGm0eDgBDYVyJpVYDCz3tvbCwBob2/H2rVr0dfXlzVBh1rdpKGhAffffz9KS0uNCDmPoQzCc0xlM6lFPJyyo3JxTJkyBZMmTYLX68WWLVvQ1taGgYEBozJ3+PBhrFq1yijwRaNRzJ07F1VVVaiqqjLdvlIf2+FwIBKJmK5KuQDr73Z1k/NGGwB8Pl/WJOZwOJwlRbl582YcOnQI8XgcnZ2dpnQKGCrnc7lciMfjpgV47969WLdu3TkzIq93ZF07MKR/wRpi4NxFE3hvVUfl/PAcu1wunDhxAv39/eY5OT6L2Gw2HDp0CE888QQAmBLW6dOn49577zX625QVlbolytVPThttlupRv5YGNhQK4ciRIzh48CDS6TT279+PAwcOIBKJnCO7SplEq0Hp6urCSy+9hGAwaLLxanSGFkre4KxccDgcZvADp3NYZ4Hq+bs4OLCAC2M0GjVCUbJBTM5nPHnyJP72t78hFAohEokglUrh1KlTqKurQ0NDg5nGrqWsucdln8b+QTIwMIBIJJIlyp6Xl4cTJ07gBz/4Af7+97/j9OnTxjDLoaRyKoRU/JNt7B6PB7FYzHSdKYMwDgoMenrcbkejUaNVLsdS5fAldtUgxf+lHnwikchyRIAhLRIae7vdjmg0ivz8fJSVleHb3/427rnnHjMthtOWrPNblauTnPa0ZfeXTKC43W5MmzYNgUAA27ZtM0JQQHaXI8Mp9fX1mDNnjhlHJJOa0viopzgEvbxwOIz8/HyzwHGEE5XotJP00pHOBCtGONs0lUrh8OHD+Mc//oFgMGjEzTgImwN0bTYbqqurMW/ePNTV1Zn7Rg79UGOdG+S00fZ4PCbzDQwa4kgkAp/Ph2XLlqG4uBj79u1DKBTKmnFHj5AedkNDA775zW/C5/OZ7LvL5TIz7jSrng1jotFoFOFw2MwD5I4kLy8P8XgcyWTynEGtyoUjK6BisRj6+vqM2h8AvPjii9izZ48J/zmdThQUFGDMmDHo7e1Fb28vnE4nZs6ciVWrViE/Px/pdNpMtpFjy5Srn5w22sBgaIOZdJY80QNPp9MIhUL42Mc+hgULFsBut2PHjh146qmnjFdos9mwb98+rF692iQi8/LycPPNN+Mzn/mMubB1iz8IdxwcoUSvziq6z/NPQ64G4dKJx+M4cOAA/vSnP6Gnp8fojZw4cQI9PT3mXNtsNjQ2NuKee+4xoQ+73Y4xY8aYnSN/M6nBo+QGOW206X0wfMGYHAATo06n02hubsbSpUvhcDhQVlaGo0ePGq8kk8mgr68Pzz//PAYGBhCPx+FyuXD27FmUl5fD7XajqKgIEydONM0L1zMyEclwEoCsGZt8XtZuawngxdPZ2YnOzk5Eo1F0dHTg+eefR3d3NwYGBpDJZDBy5Ei0tLSYhZROx8KFC1FcXGwej8ViZtfJ2ahS8lUaceXqJaeNNmNxhYWFWdOpmaCx2+0m3kqPefr06Vi/fr3xAsPhMDZv3oxHH33UlEbFYjFs27YNBw8eRF5eHhobG7Fy5UpMmTLlSn7dqwKZsGKlSDQaNTsUTqZmokxzAZfO5s2bsWHDBtjtdoTDYfT09JiB1clkEq2trVi9ejVKSkrMfeDz+eD3+7MGIlB3h4/JCU2yrFCN9tVNThtt61YvnU6bEAez5jK7zsTYyJEj4fV64XQ6EY/HEYvFEIlEEIvFTMLyjTfewMsvv4wPf/jDmDlzJoqKiq7kV72qkMkrVijw/zOZDMLhsDHcarAvnUAggM7OTgDAuHHjsGzZMqPmZ7fb0djYiJqaGvj9fhMalOPJpBYJvW46NdSQt9bfK1cvOW206S1TZpVlZ+FwGKWlpbDb7YhEIkgkEiZ5Fg6HEQwGTQzc4/Fg1qxZmDVrFsLhMGKxGOx2OzZu3Ig33ngDd955Jz73uc+Zm+F6h9tqNiHRO+P5CYVCOHPmDNxuNzwejzEKqjh38Xi9XpSUlCCZTOKGG27A97//ffj9fqRSKXi9XiSTSfT29pr6bVm2Zx2aQO/cmiSmcVcv++onp422LNGj8fb5fOZitBpZDkHlbMhwOGwy8NRk4LSPadOm4Tvf+Q5mzJhh/o4anUEymYxJgsmtdigUQkdHBzZu3IhAIGCabWbOnIn77rtPtZ4vknnz5qGsrAx5eXmorq5GcXFxVvjJ6XSanSBL/oChsXpcMLnY2mw2szvl65hI1mv86ienjTYvMnrSAIw2tnWmHgATbwVg9EoIS6D4fG1tLUaNGoURI0booFQL1vNKI753717s2bMHZ8+exZkzZxAMBpFOp1FUVIRt27ahoaEBVVVVWXFuOYOTW3ots8ymqakJ9fX1pu0cGDLOPGf0oK1dqNIQM3YtQ1oysaznOjfIeWsky88ksnphuIy42+3OSrpYt+9M2GiN8bk4HA4jQkQCgQCeeuopOBwOrFixAvn5+UgkEgiHw2hra8NDDz2EBx54AF/4wheyYt2JRMIkgJ1OJ7xeLxKJhNm+64I51L37XrNLpfcNnCsbYG1CI2qsc4ucvyNke698TD43XAWD9aIf7nmN751LIpFAKpUyISN26IVCIXR1dcHv96OsrAyjRo0y8p+vvfYajhw5gkAgYMa7yfNNKV2eb3qOakwGGe46PN+5ebdzNtx9oOc491CrpFwQ7CiVsgCcAk4NmFgsZmKn7FoFhhZClloGAgEzqJblZxQA005KRRmenPe0lQ8Wl8uVpThHXZeysjI8+OCDcLlcKCgoMEkvGd6QKnS7du3Cb37zG9x1111obW3Fr3/9a3g8HixatAjl5eUoLi6+gt9SUa5e1GgrF4Rse06lUqbe1+/347bbbgMAE/6IRCL43//+h3feeQfTp09HVVWVOcbx48fx5z//GUVFRYhGozhy5AhGjx6dpcSoKMq5qNFWLohEIoFEIgGPx2MkBFh1wyoe1gqfOnUKP/vZz5CXl4e1a9di7Nix5rUejwculwvPPfccDh48iC9/+cuYNm0aSkpKTDhFUZRzUaOtXBCMS3M0m9vtzlKKAwarFNra2tDe3o6ysjI0NDRg4sSJ8Hq9WUm1dDqNCRMmYM6cOWhubkZ5ebmREk0mkyZGrijKEGq0lQuCGi79/f2w2WwoKioyhtblcgEYVKN74YUX8MILL+CnP/0pbrnlFpNolBNvUqkUlixZggcffBBOp9OUCFLbhP8URRlCjbZyQYTDYUSjUdNdGovFjHHt7+9HR0cHnnvuOVRWVmLNmjVoamoCMKR1QTmBdDptKktYW8zuPQBqsBXlPGjJn3JBUOVPVpAAg8nHffv2ob29HYcOHcK4ceOwZMkSjB492rRJ22w2hMNh7N27F2fPnsXMmTNRXl5uulcp96piU4pyftTTVi6I/Px8uN1uI+lJwxoIBPD0008jmUzie9/7HsaPH28UFymRa7fbceLECWzYsAFerxc//OEPUVpaimAwCJ/PZ7r+4vE4MpmM1moryjCo0VYuCpb+2e12vPLKK9i1axfKy8sxYcIEtLS0ID8/33SqMtSRSqUQDofR3d2NiooK1NTUGJ0YmaCk2Jd62opyLjlvtOXAU6laxv/Kf4C27V4q9LBZ1ud0OvHXv/4VzzzzDDZs2IDbb78dAIyGs2ydjsfjWTKhiUQC+fn5RjtGThpXCQFFGZ6cN9rA0AQbabRjsZgpS5OVC2q0Lw0pOhSPx9Hf3w9g0Jg/+eST+P3vfw9gKIwSDAZxww034N57781S73M6nXC5XCYxyaoU/Y0U5d3JeaMt59xxm82mDxpz6Wkrl4Y1xpxMJlFdXY2WlhaEQiEcPnwY6XQahYWF8Hq96O/vR0VFhdEr93q9qKurw+jRo42mM73386nQKYoyRM4bbWBI04JVDXl5eXC73VlCRSrwfvlxu90oKSnBokWLMG3aNJOgjEaj8Hq98Hg8SCQSRpPc4XCgsrISd999d9bcTmAwdGK323VQgqK8BzlttGWpGI2yFIanVyjjqhrbvjS4o+EACZvNZqRY3W63CXcwbs3Xp1Ip2Gw25Ofno76+3uyIWJ8tS/xkuEt/J0XJ5poy2sNVHKghuLzQCFPYibFpOYiC49xkfTbf63A4UFxcbAw/jbbUG5FDgxVFySanjbaMY8vBB4xpu1wulJeXw+v1Gp1m5dKQnYtyVJWcPygNOJtvWC1C3e3hYtdUDZTjsBRFycaW0QydoihKzqDFsIqiKDmEGm1FUZQcQo22oihKDqFGW1EUJYdQo60oipJDqNFWFEXJIdRoK4qi5BBqtBVFUXIINdqKoig5hBptRVGUHEKNtqIoSg6hRltRFCWHUKOtKIqSQ6jRVhRFySHUaCuKouQQarQVRVFyCDXaiqIoOcT/AZM/Ind+kGnMAAAAAElFTkSuQmCC)
physics-General
physics-
A detector is moving in a circular path of radius r in anticlock wise direction with a constant angular velocity w as shown in the figure. At time t=0, it starts from the location shown at A, assuming source at rest. The frequency as received by the detector when it rotates by an angle ![fraction numerator pi over denominator 2 end fraction](data:image/png;base64,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)
![](data:image/png;base64,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)
A detector is moving in a circular path of radius r in anticlock wise direction with a constant angular velocity w as shown in the figure. At time t=0, it starts from the location shown at A, assuming source at rest. The frequency as received by the detector when it rotates by an angle ![fraction numerator pi over denominator 2 end fraction](data:image/png;base64,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)
![](data:image/png;base64,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)
physics-General
physics-
Two speakers
driven by the same amplifiers are placed at y=1m and y=-1m. The speakers vibrate in phase at 600 Hz. A man stands at a point on x-axis at a very large distance from the origin and starts moving parallel to y-axis. The speed of sound in air is 330 m/s. If he continuous to walk along the same line how many more maxima can he hear
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)
Two speakers
driven by the same amplifiers are placed at y=1m and y=-1m. The speakers vibrate in phase at 600 Hz. A man stands at a point on x-axis at a very large distance from the origin and starts moving parallel to y-axis. The speed of sound in air is 330 m/s. If he continuous to walk along the same line how many more maxima can he hear
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GRFZBKpcTOTgKi6zpeeukl7Ny5E4ZhIB6PY8mSJfjhD3+IaDSK4uJiVFRUeFqcy0JAyAubohEU5qTb6G+QLQR2Mk48WBRuEHJHYTK5s7P0gCHrwXEcJBIJuK6LSCQCx3FEPj/9bjqdhuu60DQNV65cgWmaIpNw79692LZtGwDgsccew7PPPiteS0VFBcrLy+H3+0V04auGDUda8CwGExMWhRsE5ePLOyslAAUCAWFmU34/WQyUZETefLp/f38/ent7xTn+008/xYkTJ8TuXFdXh+9+97vw+XxobGwUyUOyBaCqKsLh8DXt0BhmJFgUbhDyDAJamLTzk2UgWwt0O3DVL0B5A1euXIGiKDh8+DC++OILkRY8bdo0LFu2TPQXmD59OqZOnSrMdzqykD+Ajh2yo5BhxgKLwg0ie2qRHLKjBUuiQIlFfX196OzsFLv40aNH0dLSAsdxUFtbi1WrVgmH3rRp01BeXi4elwRHPu/L38uvg60EZjywKNxgaPFRPYHc5NRxHCSTSQwODkLTNHzyySfYsmULgKuLeM6cOXjggQfgui5qa2tRV1fn6WdI+QemacIwDNGHIDtiQVYJ1TfQ92wxMGOBReEGIZcFy5ZCZ2cn+vr6UFJSAsuysG3bNrz77rtIp9NYs2YNnnvuOei6DsdxUFFRgUgkIo4IANDf3w9FURCPx4UlQI5D6nok+zKyB64qiiLyDlgUmLHAovAVyO43IDcwpSgE/b9582a88sorYrdftmwZnn32WQSDQVRWVqKsrOyaECGVKKdSKcRiMTHvgCoYyVoAINqW0euRcxqoLoGzDW89uXxku6tEQR5USl/Lu67cxIMWODnt6EO2bRu6rotGoqqqYnBwEAMDA7BtG6Zp4vDhw/jwww+h6zrmzZuHf/mXfxHViPF4HGVlZcLRmJ3gRBcSNSahYakyqqoKMbje7wPwZCoyNw8ScSoey2QywuFrmqanBX0ucNeJAp3vaaGk02mR2SffLosACQTNPTAMA4ODg+jt7YWu6zh58iSOHDkC0zThui7Kysqwbt06qKqKSZMmoba2FpqmIRgMehqFEMMtWnmwynC3Xy/xiLn1UC4JAM/061Qq5clRyRXuGlGQU4/JGsieeCQnDhmGIcRCURQkEglcvHgR6XQag4ODSCaT2L9/PxKJhKguJMdeWVkZamtrRcRBbmjCTDzkHJSenh6Ew2Hk5+cLSzPXuGtEgZBDdeSECwQCQgzkD7i1tVV0Ljp37hwOHjwo2pFVVFRg5cqV8Pv9iMfjqKqqEolIADypyMC1Y9WYiYOu63BdF2fOnMGGDRswefJkrFq1CoWFhTAMQ4ywyxXuqqvUNE1RUkze+Ly8PCEGhmEgkUjAMAxcunQJ//Zv/wZd16GqKhoaGrBkyRLRsmzGjBmoqqoCcHWnoGiBruvIZDIoKCgQpmP2cYGZWGiahmQyibfffhtvvvkmJk+ejJKSEixfvtxjlebKNXDXiAJ1CKZqQtlSIMth//79+O///m+cPHkSdXV1+OlPf4pUKoWCggIoioLt27fjxRdfxJw5c/Af//EfwtFIZcbUDo0KnYCh7EU5mYmZWNi2Dcdx0NnZiUuXLsFxHHR3d0NVVUSj0ZwrGpvwokBWgG3byGQyyGQyotCoq6sLzz//vFjAs2bNwo9+9CMUFhbCtm0UFxejqKgIqVQKn332GQ4ePIiXXnoJbW1teP755/HXf/3XKCsr8zRKpeehmYrU+ESuUmQmDhR5+MlPfoKPPvoIpmni8uXL+Md//EcUFhZi1apVIpKUK9wWUZAdfLJZlX0GlxU2+77ZLcyHew46Epw7dw6GYYhIwTvvvINkMolZs2bh7//+70Wpcl5eHsrKykQBE9UdxGIxAFc9y5WVlTAMA93d3Z4W5OQz8Pv9YoQapSPnkunIDA/5mrL7X7iui76+Ppw5cwa9vb0AIIShra0N6XQa0Wj0dr3sr8QtFQVaaMDQos0WCELXdeEApNsNw4BlWQiFQiIWTDUAlmWJuYOpVAptbW1IJBJIJpP47LPPhLXQ29srjgS1tbUi56C6ulok+VDWoK7rokbhwoUL6OrqwqFDh9DZ2SmsC4owyBmFJAQcNpw4kD8KGGo2Y1kWDMPAL3/5Sxw8eNAzRs80TbzxxhtobGzEkiVLcio0ectEgRp/0iIiU5uEgHZ+WTjovvLi6u3tRWlpKfx+v5gx6DgOTp48id7eXkQiEfT29mL//v3o6+tDKBTCihUrxILXdR26rmNgYAAHDhzAuXPnUF5ejkWLFqGyshKTJ09GKBSC67rCYjh8+DB2796NgYEBbNq0Cd3d3eL1Ucuy7GIkZuJAG5Y8eZuu25MnT6K5uRlXrlwBMDRfAwBOnTqFffv2YcaMGV9rLsat5pZaCtmtvMjhlz3th87icjEQ7cRFRUXCajh9+jTS6TQSiQS2bt2KVCoFAIjH41i2bBmKi4uhKArq6+sBDAkTicM999wD27bR3d2NzZs3Ix6P48EHH8TMmTNF1ySyLkpLS/Enf/In0DQNBw8eRH9/vydTjYVg4kKdseg6JKcyALz//vs4fPgwgsGguC5pU0un03jnnXewcOFCFBcX58w1cstEQe79BwxlgQ2XYiyH+Mi6cF0XPT094vGuXLmC119/HSdOnEBJSQl+8IMfoKKiQkQAqD05pRdnMhmRRARA+A9c14Wu66ivr0dLSws++eQTaJqGOXPmwDAM8RqKioowe/ZsHDlyBMeOHcM//dM/iagE5TLw0NOJCSW2kRDIrfWok3VRUREuXbqErq4uKIqC4uJiBINBpNNp0WYvV7ht0QfZp5DJZERlIDnrDMMQ3YfC4TB6e3vxwgsv4OjRo6K0+O/+7u8wa9YsBINBMR5d13WEw2FPgxPLskQHIgofZjIZhMNhUeJMFYqZTAZvv/02nn/+eYTDYfEagsEggsEgbNvG5cuXkZeXB9M0Pc/FTExoCjbltwSDQeE/eOaZZ/C3f/u3yGQyeO655/D222+juroazz33HB555BHk5eUhGAzmVDj6ljsa6RhAxwN5kpFt2+jq6kJfXx80TcNbb72F9vZ2WJaFvLw8/OhHP0JlZSVs20YoFEJFRQU0TRMJRpqmiSnG6XQamqbBsixRcyBbHbTAyX8AXLUeyMGo6zpSqRQikQhqamrwu9/9ThxXpk6dKiwfXdfF4ww3+5DJfcivRT0xKC9B13UUFBTAdV2EQiHk5eXB5/MJX1cwGEQoFMopQQBusSjQeYyq/BzHwdGjR0XqcCaTwd69e9HW1ob8/HysXLkSsVhM7NI1NTXIz89HIpFAKBQSfQSAoTM9Of+oRblchCR3QpYFiqyJgYEBDAwMoKysTIQWVVXF/fffD9d18atf/QplZWV4+umnxfPTB55rHzwzduTBOPIRguZ2yh23LcvyjNWjay1X/AnAbTg+UJfiQ4cOYWBgAOfOnUNvby9s20ZeXh7mzp2Lb3zjG9A0DZMmTRJRAypLlbPEKD9AnkcAQAiBHNGQ05uBodHthmHANE0RjbAsC9/85jeFc0lVVcRiMdx3333iiFFVVeWZokRkx7Ll/gijHS/kuguqyqSwJqdJe2dfyE1s5Pd7OLGXIwf03pIPSB5yMxJyKJI2GzkyJpfb0+vIrrHJJW65peDz+ZBIJPDRRx8hGAzi4YcfxqRJk0Ty0IwZM1BbW+tJRQaG0oXJNAOGHEBkMdD95YuFnpPMPnodJEi2bSOdTqOnpwc9PT1YsGABpk+f7nF8uq6LoqIixONxcWFQKJSci9k5F8CQ4zE78Wo4ssu6ycNNls3XadOe69CiJmgjkKHPS76NrEZavCSudG3RY8uDb4Yjuw+m/DP5Nno8+pern9ktFQXyHbiui1gshlAohLNnz+LSpUtwXVeMNu/o6BDJS9mNUClhJBaLYfLkySgqKoKmaSJfIDuUSY1UdF3H0aNHkUql4Lourly5go8//ljcp6KiAo8++ihqampEeCmTyQjLgtKY5XZrsjOTLkp5zgJZKrI4XQ/5sWVxoNeXaybozYB2Z3liFR1HSUjp7E8Ln66H/Px8T8s84FrrbDRGSkbLznak++ealQDchuODoigoKCjAX/3VX2HJkiWiyYmmaeju7sYvfvELvPzyyygoKEAymRQOG3Ls0Dk+Fovhz/7szzB9+nQRdqRFmMlkxAdoGAYKCwvhOA5eeOEFdHV1we/3o76+Hk8//TRc10VxcbHwN1DVpOu6nvRUMuflkWq0WOWLgVKcU6mUaIWWndyUjbwTUis38mfI49zudmQfEr2fcs0J5QnQe0YOZRJoy7JExIg+Q35vr+WWZjSSE8bv9yMSiaCgoADRaFR47aPRKH784x8DAJLJpFgYVJNOH6Cqqmhvb8eLL76Iw4cPAxhyBsmOv2g0Cl3XEY1G8ZOf/AQvvPCC5/xHF1hPT48QK/JXUNiSHousFvJj0DGFRIFEIpPJIBQKIT8/X/zduq4DwJiKosh5RRe6nEV3tyK3qidLka4Nul1Rrs7GpMiRPHELGKqSJR+V/N6yKHi5pclLZE7Rh2mapjgy0GLNZDIIBoOIx+NisYVCIY+PgZyQFB+WP1hyIJJlEQgEoOs6Xn75ZY9PgV4TMJRiXV1djfvvv18MYCURyDYDyfM8ZcoUj9lvGIaY8kT+DjJV5V0um2wHGf1srGbtREc+CgIQdQTZGw1w7TxPcirKJexfxRF8N3FLjw+k0PICl6MEiqJ4dlO5NiJ72AkATJkyxdOrgHZqShaRTcq/+Zu/ERYHMOQQovOn3+9Ha2srtm3bJtKl5QuJnJy048RiMTQ2NkLTNI+jE4DotEw/Ly0tRWNj44jvi8/nQzqdFtWV9H+2yXw3QiJLCW7UPFeevek4Di5fvowTJ07g2LFj6Ovrw549e1BXV4eamhpPViuFrOXP7W63xmRuuU9BPstRiFHeFcl0lyc109fyrilXnckOOTpDAkMdmYPBoBisIkcUyEdAXxcWFmLSpEnCaUi7j1wJSb/b3d2Nffv2icckE5buT88PAGVlZejs7BzxfXFdF4lEArW1tZg5c6bYBQF4nGHy3zxS6fhEhT4bSkS7cOECTp8+Lfojnj17FqdOnYJhGNizZw8uXLiAtrY2mKaJ8vJyNDU1AfCW7zNebnlIErh2x8tuRU7muBxHpn9yuEfOT5BjyHLCiPxYtNvTfShiAVwVnuLiYpSUlAC46vAjgSGvNR0HLMtCIpFAXV2dCJHS7k4ZlOT1dl0Xx48fx5YtW4RYXO+9sSwLFy9eRG9vr1jscl9HEjDaMadMmYLy8nLP8Uu2pmRrbCRPuBwylf8f7rOSH/d631+PseRqkFUmfy//nATS7/fj0qVLaG5uxtGjR6HrOmpra/Hoo48iFovhypUrePTRR9HW1obf/OY3cBwHNTU1iMVimDp1queauxHCOtx7QJZqrll4tyUkKWcY0geSfWaXL+LsD022LOSdU36M7N+n2+WiJdkRJV8krut6HH6ylUKPEYvFUFBQ4Hk98kKSd6Jp06Zh9erVI/oUSFA2b96MN99885oiMeCqE5KGzEQiETQ1NWHWrFmexUL/yKRWVRX19fViwtT1nl8Oq8p/Q3bOB92fvPvy918V2aciPzeFGLND0q57NQGuubkZhmHgqaeeQiQSgc/nQygUEg13q6urMWvWLKxcuRKWZaG5uRlbt27FI488gqqqKs9n+nUXrizA9FjyxpJL3NZ2bCN9EGO5Tb7PcHHj0b4ey/2vd/t4FkEgEEBeXt51b6cF4Loufv/3fx+rV68WFZjyghsYGBDp1z09PXj//ffx4x//WFgONHzEcRyEw2HRdObJJ5/EjBkzrvv8sjDG43EAVyNBcuyfBEMWD3ofvu55nJy0ch6LZVlIJpPIz8/3RBls28aVK1fw+eefo6urC48//jiKioqgKAry8vLEGD0KMUejUeTl5cFxHKxevRqbN2/GRx99hN/7vd/DtGnThNh9nboV+XhHIWsSh1zMapzwPRpzBWoTXo2193wAABP/SURBVFRUhKKiIk8eBC0KunBd92qL+e9///t46qmnRBUfOVkDgQAGBweFU+1f//Vf8Ytf/GLEC9NxHMRiMaxfvx6TJk0CMNTvgha9pmno7+9HJBJBJBJBcXExysrKxhRqla2nbKhGRY4wqKqKwsJCERqmNPdkMoldu3bhwIED+Mu//EsUFBQIUZSjDrLVQ6JWWFiItWvX4u2338Zvf/tbBAIBlJeXf+12aSQI06dPx6JFi1BQUCCiarlYQcuicAegKAqi0ainnRf5KbKPO5SYJftLqDQ8HA57wr4+nw+GYeAv/uIvRK7E9XAcBwMDA9i6dSv2798vulzLr1HTNJGxGYvF0NDQgHg8Pqql4PP50NTUdF3xoN2aRJD+LjK9I5GIyFf54osv8Jvf/AbPPPOMaIQTjUZFBir5HuQjEb0Geg/XrFmDDz74AJs2bcL3vve9r50tSsK5bt06PPTQQwiFQigsLMzZZr0sCncItLPJ9RTA0IKRU3zljD3ZvyLXS8gJPSQWI0HmeklJidhxs3dbXdfFUJNLly5h7969OHjw4DV1CNn4fD50dHRct6ux7FOg8G00GhVHIXKwUuISAEydOtVT2CS/P/LxRhYaMunJmdzR0SEe4+tA7215eTmKi4s9kSP6+3LJWmBRuIOQd1z5gqbQqny7bIrLERm6+OQEH9n5db1oAu12paWl4oxN+QFkmVAKsd/vR3l5OaZMmSKStUYSHcMwsHHjRpEhOhz0GiKRCNrb26FpmmdBU2boqVOncP78eezcuROzZs0SjXGAIeGSI0zykGA5dFxdXY3+/n6cPHkS99577xg/oeGRo2B0lCMfj5w8lSuwKNxByE62bI84WQjUA5ByPIChaszswiDqYCUnYI0EJXHJERe5eCgcDovEn0gk4qnPGM1fUVJSInb562HbNr788kts3LhRjPOjzt2O4+DixYtoa2vD9OnT8fHHH6Onp0ckqtHr1HUdx48fRzKZRHNzM6LRKKqqqtDQ0CASoFzXxX333Ycvv/wSv/3tbzF//nxRTXk9gZPDvNk/U5ShBDzZKZt9/1yBReEOgS5IunDlMKhsJtPClPP2s2dgyOPqaJGPJAh04UajUSQSCU/dxnAp3rQDj3X3U1VVWCDXe366rbKyEitWrPBM+6bozObNm/H666/jpz/9KVpbW/HKK68gmUyKx6EjREdHBxznaodvAJg9ezbWrFkjrARd12GaJs6cOSNGANB7VV1djfLycpE5mW2BydEEen/IdyNHHUhkyK8wXM4FfXbZG8BwIVI5/Cu//2PJQcl+j+VQ83CwKNxh0IxLYGgnym4Imx0+y54pkL2IR4OqTAGI8N5oIeHxDsv9unkMNAWcfBqLFi1CU1OTp18CWVkbNmxAe3s7nnjiCRQVFWH37t14+eWXhdVEdTHt7e1QVRX/9V//Jeonli5dinnz5iEUCnkK2bJFW9M0lJSUCAEh64CsIfJz0PGKXiP1eKB2gBQ2poVNIjScWNDxx7IsUfPj9/tFTs313juyPCnRjqy+630mLAp3ION1St0IJ9ZIPofbDfkDiouLMW3aNJw7d0700ZAHApFFEYlEEA6HEYlEkJeXhzVr1mDFihUAIBZie3s7NmzYgHg8jvXr14vIyq9//Wu89tprSKVS4mhCPgv5eTRNw9y5c1FfXz9qnwxN0zB9+nSRMEXl9YODg6IvKDl36bFI7Og5ZeuRBMw0zVE7iNN7Qo2NHccRVhCLApOzkCNv9uzZuHTpEt566y3ce++9ngzC7IpW+X/afWkxW5aFnTt3IpFI4IknnhCWgKqqePTRR7Fy5UqxKLOHv5Dprus69u/fj507d46awKWqKlpbW8XYAblFvJzSHQqFsGDBApG4Rv4b+pqspGzH8mh+C9nRSpGckSJGLArMHQ9d1JqmoaCgAKlU6poOSiMhn+MpIYt6LpCzlMSF2u6R3yC7zydZUplMBuXl5UgkEp7j13DPres6du7cif3794uFLGeKkiD5/X50dHSIcQSyEAFDJeSUITtz5kxUVlZ6ivGG+7vl7FMSIarkHQ4WBeaOh3ZnAJg8eTKmTp2K3bt3Y8GCBWK690jQwiNhaGlpgW3buPfee0WbNmqkQ5B4yN2/gaG6nEgkAr/fj8LCwlGzFi3LwiOPPILly5d7Zp8CQ/4g27YxMDCAHTt2oLOzU/QCye7uRQltfr8fFy5c8DSbud57F4lEsHjxYlEfMlq0iEWBueOhXTsYDKK2thYPPfQQduzYgUgkInpajGQtyKHaCxcuYOfOnZg8eTJWr14tTH95OjidwwGIszhFd+j+pmmKKtuRjg8kKLFYTDhxAQhfRTAYFJW3AwMDWL9+vbAuyIEJDDUpJl9CR0cHPvzwQ5w9e3ZUx3AoFEI6nfZMNCsoKMBDDz007P1ZFJg7HjpXUyJTQ0MD/H4/Pv30UyiKgsbGRs8MBhk5W7K9vR3/93//h7q6OqxZswY+n09kacqp0cCQU1E2zckEJ48+CclITjv5GEDWB1kHcmm+z+dDYWGhJ3uVfh+AxwdgGAYKCgowa9asMeVBdHd348UXX0R/f78QlcrKShYFJrch77ymaSgsLMSMGTOQSqWwb98+dHZ2IhwOo7S0FFOnToWu66I1XmtrK06dOgXbttHa2ori4mKsXLlSmN20ME3TxOnTp3HmzBnPeV/TNNTW1opZH7QIqWeGnDh1PaglII1FlHtIZjf+lY8CJFQkRmQtRCIRj1UzWp/JiooK/PM//7PI9KT383qwKDA5hdwoZ8GCBTBNE1u2bMHg4CBKS0sxbdo0fPHFFxgcHMTmzZvR3d2NM2fOwLIsLF68GGvXrvUcCeSEopaWFvznf/4nXNcVsz9UVcWMGTOwZs0a1NbWimQk2unHUhpNYUi6j1woNZw/IDvdnbhe+HE0nwqVkI81u5JFgckJ6IKWw42BQAALFy5EQ0MDHMfBuXPnsGfPHnR3dyOTyeD8+fOYNWsWHn/8cRFpoEY18uPS90uWLMEnn3yC8vJyPPHEEyJp6o033sDevXtRXV0NwLvLjrXY6XrJZbeK0fwOMiwKTE4gFzhR+rCiKMjPzxdt+SsqKtDQ0ICNGzeis7MT3/72t0W/B2rRL0ch6HFpkcdiMdErorKyEoqiIJVKwTRN9Pf3Q9d1z44/nlTvXIJFgbnjkcNx8gBXCuUBEEJRXFyM/Px8DA4OIh6PIxaLidvp7E+t6ij3gBY2VVjS0BjbtnH06FHE43Hcc889nrkj5GzMtbLoscCiwNzxUARBnsxFUDhQ7qotL3Q565EGwMhJT3KB0cmTJ5Gfny96Zdq2jba2NsyfPx+LFi1CNBr19ImUjzQTCRYF5o4nO42ZHHUUkZCLnIAhh5w8YJby/cmDL4c56X47duxAXV0dXNfFli1bkJ+fjwcffBBLlizxDK7NHmw80WBRYHKG7Jkd9DMy4SlvQDbrqfyZwoGBQEAcQeTSZcdxkEgkEIvF8Nhjj+Gxxx7zVC9S5iQ9rtxrYqIxMf8qZsIhFydRCTCl+8o+B+rTSEcNqiPInhECeFOMjxw5Ap/Ph5qaGkQiEWFtyCXH9Pty+3+2FBjmNpAdTiOzXfYXyNYCHTXkPH+5RwV1jlYURTSD/dnPfgbbtrF8+XKRB0HJRXLbdnoM+bVNNFgUmJxjuJi7LAzD3Za9kOl7qnOora29pg2enME4EUOP14NFgbmrCQQCWLBgAWbNmoVUKiWiGbI1cTcJAsCiwNzlUC8EanIiN5fNrku4W2BRYBgM+Smoh0H2uLzRehBMJFgUmLseWvj0j34mVyjeLYIAAHfXYYlhhkHuuUD9E6gLE+U53E3cUEtBfvOoFbU8fl6+TZ7kI2er3W1OHebOgI4PcvNXSk66267JG358kMtSgaG+82SWyXFf+p7E4W4y0Zg7B3nRywVOX2dWRS5z0ySQTDDKOJM7y2Z3miEhuVs/BObOgTemGywKlEdOBSqUg04daEmRDcOArutCDMhMG216McMwN58bKgpyk0m5qozyx+kfCUUmkxEz+Oj3GIa5vdxQnwIdBaj2HYCnGq2vrw9bt27Frl270NbWht27dyMYDGLt2rWiQy/DMLeXm+JopCMEzeDTNA2Dg4PYsGEDXn/9dRw5cgTNzc2io257ezt+8IMfoKmpaUJ2smGYXOKGi0J2sQkA9Pf347333sPrr7+OEydOIJPJiMm5ALBx40a4rosf/vCHaGxsFDPzGIa59YxLFOSx3wA8TSrkfvL0fSAQgGma+OCDD/Dqq6/i2LFjSKfTQiwoMeTy5cv46KOPoGka/vzP/xyNjY2ewZv0P4ctGebmM25HI7WuouiCaZqikw2Z/pZlwTAMUa/+8ccf4/jx46IBBkHhSdu20d3djY8//hhnz54VDkk5fHm3ZZUxzO1iXJYCOQ9N04Trukin0xgcHITf7xf5CKFQCJqmid55iUQCyWRy1HRRx3FgGAYGBwdhmqanFRb7GRjm1jFmUaChlzRkM51OY9euXfj0008RCoWwYsUKnDlzBtOnT8fSpUvFYt60aRNaW1tHDTe6rouBgQFs3boVDzzwACoqKjy3sSgwzK1hzMcHeTKPZVnYvn07Wlpa0NDQgEmTJmHHjh144403cOLECQAQbbE+++wzdHR0eJptDofrukgkEjhw4AAGBwc9I7jltlsMw9xcxuVToLHbruvi+PHjUBQF3/nOd7B27Vr09PRg/vz5IqxIwzTWrVuHadOmjVrspKoq4vE4Hn74YRQXFwtRIYvjbm14wTC3mnH5FBRFEeFE0zTR3NyMuXPn4t5778W6detQUlKC6upq4SSkWX9VVVU4cuTIqIs6HA5j4cKFiMViwrJgC4Fhbi3jFgXqcrty5UrE43EcOnQImqZh3rx5yM/PF1WRgUAAPp8PoVAIBQUFYnT3cDs+lanm5eUhGo2K1tuyk5FToJmxkMlkMDAwgEQigXQ6LbomZTNRpzvdCHzPP//882O9My1Q0zQxadIkzJ49G67rYu/evYhEIigrKxOiIS9sTdPQ3t6O7u7ua+bv0ZGkqqoKa9euxUMPPYTS0tJhu92w1cAMh9w1ad++fXjllVdw/PhxxONx1NfXe6pv5ftSTg3A4iAzLp+CZVno6enB5s2b8fnnn8N1XcybNw+9vb04ffo0enp6RPhRLodevXo1vv/972Px4sUoKioSw0FJQKqqqvD444/je9/7Hurq6oQvge5DEQ/+4Jjr4TgOBgYGsG/fPnz66afYv38/mpub0dvbKyxUau5D32f3/mCuMi5LwbIsvP/++/jZz36GgoICzJ8/Hz6fDzt27EAgEMDp06fR3d2NWCwm8hUymQx8Ph+mTZuG0tJSnD9/Hl1dXQCGnItPPvkk/vRP/xT19fViMg/DjBVa7IcOHcLPf/5znD59Go7jIJPJIB6Po6GhQcyfpMxY2mTYUriWcfkUXNfFqVOnMGPGDKRSKTz33HNQFAUzZsxAU1MT2trasH//fmiahmXLlsHn88Hv94sah0WLFuGZZ55BR0cHFEVBMplENBrF4sWLUVZWdlP+QObuwLIsnD17FgcPHhQ+rba2Nhw+fBh/8Ad/gHQ6LRr/kPVJ/q27rd3aaIzb0fj444+LFOcLFy7ANE3MnTsXRUVFmDRpErq6upBKpYTvIRAIIBQKiWzHJUuWiIxFOtPReC/+cJjxQo7tffv24bXXXoNhGCJ1Pp1OY+vWrZg+fTqeeuopYQ1QeT9Ht4ZnXKLg9/tRU1MD4Gr4cP78+Z42a+l0Go2NjSgvLxfHABIA+iBUVRU+BU3TxPANLnZivgokCtSfwzAM4by2LAunTp3Cnj178Md//MeIx+Oewj1KxWe8jOsdoSm+0WgUgUDAE2EAgL6+PjFyS27Qmk6nRTWl7DxMJpPiceWe+wwzVhzHwf79+/GrX/1KWJ60SQFXr61Tp05h06ZNSCQSYl4kObnlHqHMVcbtU6CjgJxroCgKWltbsW3bNgQCAcTjcU+LNVVVhUDQByBPBaYW7wwzXhzHwblz53Dy5EmUlpYimUwikUiI0v1YLIZkMokTJ06I44I8NJYEhJsGD6G441iN8l2zvz5//jyOHz+OSCSCGTNmoKSkRJztaPED3j6Mw43k4iMEMx5s28axY8ewb98+WJaFnTt34t1334WiKFi2bBn+6I/+CPn5+aipqcHChQvFsVYWCNqgmKuM29E43NcAUFNTI/wNMtlvdvb3fKZjvg4+nw8zZ85EQ0OD6MPxwQcfAABmz56N9evXo7CwcNhEOPl/ZghekUzOo6oqDMNAT0+PyI8Jh8MIBoOwLAvpdPp2v8ScgtsnMxOCQCCAwsJCLFq0CN/97nfR39+Phx9+GOFwWMyFZMYGiwKT89Cxwefzobq6GgsXLsSFCxdQW1srIgzM2GFRYHIeSlsGIELimqZdEzJnxgaLApPzyMVyhmGISlzmq8F2FZPzyCnLhPw1C8T4YEuByXmyqx3JcvD5fFxy/xVgS4HJebJFYaR8GmZ0WBQYhvHAosAwjAcWBYZhPLAoMAzjgUWBYRgPLAoMw3hgUWAYxgOLAsMwHlgUGIbxwKLAMIwHFgWGYTywKDAM44FFgWEYDywKDMN4YFFgGMYDiwLDMB5YFBiG8cCiwDCMBxYFhmE8sCgwDOOBRYFhGA8sCgzDeGBRYBjGA4sCwzAeWBQYhvHAosAwjAcWBYZhPLAoMAzjgUWBmVDQgNnsQbPM2OFR9MyEo6ysDKqqIhAIsDB8BRTXdd3b/SIY5kbhOA6SySRs20ZeXh58Ph8LwzhhUWAYxgP7FBiG8cCiwDCMBxYFhmE8sCgwDOOBRYFhGA//D6sLoqBdeiXJAAAAAElFTkSuQmCC)
physics-General
physics-
Two speakers
driven by the same amplifiers are placed at y=1m and y=-1m. The speakers vibrate in phase at 600 Hz. A man stands at a point on x-axis at a very large distance from the origin and starts moving parallel to y - axis. The speed of sound in air is 330 m/s. The angle q at which he will hear maximum intensity for first time?
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)
Two speakers
driven by the same amplifiers are placed at y=1m and y=-1m. The speakers vibrate in phase at 600 Hz. A man stands at a point on x-axis at a very large distance from the origin and starts moving parallel to y - axis. The speed of sound in air is 330 m/s. The angle q at which he will hear maximum intensity for first time?
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)
physics-General
physics-
Two speakers
driven by the same amplifiers are placed at y=1m and y=-1m. The speakers vibrate in phase at 600 Hz. A man stands at a point on x-axis at a very large distance from the origin and starts moving parallel to y-axis. The speed of sound in air is 330 m/s. The angle q at which intensity of sound drop to a minimum for the first time
![](data:image/png;base64,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)
Two speakers
driven by the same amplifiers are placed at y=1m and y=-1m. The speakers vibrate in phase at 600 Hz. A man stands at a point on x-axis at a very large distance from the origin and starts moving parallel to y-axis. The speed of sound in air is 330 m/s. The angle q at which intensity of sound drop to a minimum for the first time
![](data:image/png;base64,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)
physics-General
physics-
When a composite wire is made by joining two wires as shown in figure and possible frequencies of this wire is asked (both ends fixed) then the lowest frequency is that at which individual lowest frequencies of the two wires are equal. The lowest frequency such that the junction is an antinode is
![](data:image/png;base64,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)
In the figure given : ![l subscript 1 end subscript equals l subscript 2 end subscript equals l comma mu subscript 1 end subscript equals fraction numerator mu subscript 2 end subscript over denominator 9 end fraction equals mu](data:image/png;base64,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)
When a composite wire is made by joining two wires as shown in figure and possible frequencies of this wire is asked (both ends fixed) then the lowest frequency is that at which individual lowest frequencies of the two wires are equal. The lowest frequency such that the junction is an antinode is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJwAAAA/CAYAAAAVMKENAAAMm0lEQVR4nO2c2VMbxxaHv5nRhmRkIST2vcRmYnBlIy+JXZW85T9MnlPxX5ByqlKp2HkwiWMSjMAIBEhgARaYRRaLNNt98O2+AuneQkbIXJivSmUXFj3T3b8+5/Tp01Zs27ZxcKgT6od+AYebhSM4h7riCM6hrjiCc6grjuAc6oojOIe64gjOoa44gnOoK47gHOqKIziHuuIIzqGuOIJzqCuusz+wbZtisYiiKKiqSrFYRFVV3G43qqqiKMqHeE+HD4Cu61iWhcvlwjRNDMNAVVVs28a2bSzLoqGhAdu2cbnKpFSRMgtnWRYApmlKsdm2jWEY1LqwxClUqYyYTMuyPtgY2baNoihomibnH5AGx7IsNE3DsixU9fyOsuybtm2zv7/P/v4+lmWRy+U4ODiQgqvVAIhBdUR3GjHGpmnKz4cYI+HhLMvCMAxyuRwbGxsAHBwckEql3svjldlB0zRZXV3F6/XicrmIx+N4PB5GRkbI5XK0tLScepBYCdVgWRbFYpF8Pk9jYyNer1cO6k132aZpykUOEAgEaGpqQtM0FEWR433Z41T6nGKxyOLiItvb20SjUVKpFOl0mv7+finK81q5sm9pmkZvby+hUIhkMkkmk6G1tZWZmRl++OEHdF2/8IorFAosLCzw008/sbu7i2VZH2wlXwVE/y3LYmdnhydPnvDw4UN+/PFHfv31V7LZLLquYxhGzT3N/8I0TXRdZ3t7mydPntDV1cXq6iqJRILR0VGy2Sz5fL6qNssEp6oqjY2NHB8fMzs7SywWo1gs8ujRI2ZmZi7cYdu22d3d5fHjx/z111/kcjkMw6iJkP9fEf03TZNUKkUul2N4eJixsTH29vZYWlqS4y4symUj3Lpt2+TzebLZLACzs7N0d3cTCASYnp4mk8lgmua5263oUt+8ecPs7CzDw8M0NTUxPz9POBxmZ2fnwqZcURTW1tbQNA2fzyc7dpNdqXBHuq7T3NzMZ599RjAYRNd13rx5w8HBAaZp4vF4UBRF7hbr4VZVVUVVVQ4ODkgmkwQCAdrb20kmkxiGQTgcruo9yiycruusr6+jaRp9fX28evWKQqHA4OAgbre7Jp1sbW0lFovR0NAgg1Oxcm+ilRNjqqoqHR0d9PX1EQ6HuX37toxvhYWrh3UTaJom329ra4vNzU1GRkbIZrOsrKxw9+5dmpqaqpqzijFcJBJhaGiIjY0NNjY26O/v5+joqGZur7Ozk7a2Nlwul1yp9RzIq4ht22iahtvtlvHc0dERJycn+P1+XC6XDOLFBuIyEYZAzHcwGCQWi1EoFEin09IAHR4eVtVumeBcLhednZ0AzM/P097ejtvtJpFIUCgUamaBPB6PXEEiJrypiWUxsSIFIdIhqVQK27bp6OiQghPfr4fgSjMRkUiEtrY2Xr58STgcpr+/n/n5eV6/fl1VuxXzcAcHBywvLxMKhejs7JQxVy1XVmlyE5Bb/puISEGIMRFx7traGv39/XR2dspY9zIS8P8L8V75fJ5UKgXAwMAAqVSKo6MjvF5vVe1VPGnIZrMYhsH4+Dibm5sUi0XGxsZk46XKfx9KhSu2+qXtXkWEFb6slISwKIqicHBwwPT0NH6/n9HRUXw+nww7DMOoW/hR2t+9vT02NzcZHR1lb2+PdDrN8PAwHR0d0lOdh4rZOq/XSywWY39/n62tLXp6emQnRWBfGuBXOwGapqGqKh6P59xncB+K0r6W/r30Z7X4CFd6eHjIs2fPWF5eJhgM8vbtW/L5/ClB1vrZlT5n51fTNFpbW/F6vayurtLS0kIkEqFYLFY1nmWzrWkaXV1dpFIpkskkbW1t+P1+FhcXpSUyDOPUOVu1lsm2bdxuN9FoFL/fL7f74t+uEkIMYrINw8DtdkvXVwurLPpsGAbb29s8e/aMk5MTpqenWVxcZHJyklgsJgsoSg/QL4tS0SmKQmtrK729vcTjcQKBAGNjY8zNzRGLxQgEAudut6KFOzw8ZHV1lVu3btHb20s6neb4+Fg+/Ky1ex+CwSCjo6M0NDRUZZLrTaWJrfVkn41jh4eH6e3tPRV6lKaPxDtcJmcXmmmabGxskM/nuXPnDplMhkwmU/VYlFk4wzBk9nhiYoJ0Os3JyQmffPIJP//8szSvqqpiGMZ7bSQsy6KxsZGhoSFZ3gJXO4YTVkWkLYCaWLjSDYOmafT09NDe3k6xWJQL0efzSW+iqqpMlF/WmWqpgIQny2azrK2tcf/+fXK5HHNzc9y7d09mNM5LxXq4QCAgg8NkMsnHH39MJpPB4/HILXvpSqt2tYmBa2hoOBXDXTV3Cu/eqVAokMvlpJsR4qulZTZNk0KhgMfjkXWIXq8XVVU5Ojri+PhYjrt49mUKzrZtedy2t7eHZVkMDAwQjUb55ZdfaGtrY2Bg4OLVIiIPl8lkmJqaYnBwEEVRePr0qQwQxamAy+WSL1fV8ca/f7/UlVzVtIiiKMTjcR4+fIjL5aJQKOD1euXCqxWqqlIoFGQyXNf1U/GaGLN6eQHxnGKxyOHhIW63m76+Pp4/f04oFOLu3bv8888/dHR0EIvFzt1umeBUVeX4+JipqSna29sZHBzk8ePHp1ZT6eAIU18NQqAi+Ss2I+/TVj1IJBJ8//33aJomq6FrLTiPx1MWI4vD89JEr/jzsqtrVFWVBsXlcnH//n2WlpZ4/fo13377LTs7O7x8+ZLu7u6qFkGZ4CzLYnl5mUAgwPj4OOl0GkVRGBsb4++//+a7776TInnfnaoYKOEWRHlOPeq83od4PE53d7dMvor4tVabB1VVZfUsnA4tzsa3wuLVUuz/DTE/wq2urKzwzTffkM/nefr0KZOTk7S3t19McAAdHR1Eo1EZHD548ID19XU8Hg8DAwM1i11EHCg69T4plnrQ1dXF119/LQUmxFFLwQFlCd3S9EephbvslAj8R+iiHu73339nYmKCaDTKo0ePGB0dlZu+akrMywSnKApNTU1ks1mmpqa4c+cOqqry22+/EQgE+PTTT2XerDTuuopCuSyuarxZK84mo1dWVkgkErS0tPDixQtaWlro6+sjHo/T1tZGX1/fuY1QRcGdnJzwxx9/EIvF6Onp4c8//5SVDOFwWO6eSn/H4fogduPFYhHbfne27vV6WVtbY39/ny+++ILd3V0WFhbo6em5mIUTina73QwMDLC5uUmhUJDlSpqmnSoruqpu0OFiiB2xaZq43W52dnZYXl5mcnKSQqHAzMwMo6OjBINBTNM89xFlxW9Fo1GCwSC5XI5EIsH4+Djr6+s17ZDD1UacbOi6DoDf7ycWixEOh3n+/DldXV10dXXJ47bzUvFOQzQaxev1Mj09TWtrK36/n7m5uWsdtziUU1os4PP56OjoYH19nYaGBnp7e9na2mJ7e7sqXVSU5vHxMS9evCAYDNLX18fCwgKFQqHMdToCvDnous7m5ia7u7vEYjHevn0rvd6F7jRYlkUmkyGfzzM2Nsbbt2/Z3d2lp6fnVMOO2K43Z+c6l8uxsrJCW1sbiqKwtLREc3MzwWCwqnb/az3c2NgYuq6TTCaJxWKEQqFTtWDFYvHGXnq5CZTm+kTuMRKJ0NzcTDKZpLGxUVa0VJOELhOcoih0d3cTiUSIx+P4fD66u7vJZDJlhYg3/QLzdUdUGGuaRigUYnh4mGw2S7FYZGhoiL29Pfk/BJyXitUiJycnJBIJLMtiZGSE1dVVtra2TiX3xNmfw/VFGBZ4F8Pt7u6yv7/P4OAg+/v7vHr1imAweLEYDmBra4tUKsXnn3/O0dERy8vLDA0N4Xa75YuIHUw1W2KH/y9KryQeHh6SSCRob2/H6/WyvLxMY2MjkUikqjYr3trSdZ2JiQm8Xi/pdJqhoSG6urpO3Y2sdMDscP0QRRWqquL3++nv72djYwO/38+9e/fw+XxV3UupmIcbGRlhZGQEXdfxer1MTEzQ2NiIz+eTl3TFSzgx3PVF0zR5bh6NRvnqq69wuVwcHx/z5Zdfcvv2bdxu98VKzBVFweVy4XK5aGlpIRQK4fP5CIfDfPTRRwCnjjJK6+wdrheiuvnWrVtMTEwQDodpaGjgwYMHwDsdiFK181o5xT4jT5HyEBlmXdcJBAKcnJxweHhIKBSSRXnC3IrYzuH6IKpFhDzy+Tw+n+/UnQ7DMORd5fNqoKIsS62Xx+MB3uXmPB6PVP1VvdbnUBtE+ktowe/3y0LR0iOvag7uoYKFc3C4TJzgy6GuOIJzqCuO4BzqiiM4h7riCM6hrjiCc6grjuAc6oojOIe64gjOoa44gnOoK47gHOqKIziHuvIvHND0DKVnsRYAAAAASUVORK5CYII=)
In the figure given : ![l subscript 1 end subscript equals l subscript 2 end subscript equals l comma mu subscript 1 end subscript equals fraction numerator mu subscript 2 end subscript over denominator 9 end fraction equals mu](data:image/png;base64,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)
physics-General
physics-
When a composite wire is made by joining two wires as shown in figure and possible frequencies of this wire is asked (both ends fixed) then the lowest frequency is that at which individual lowest frequencies of the two wires are equal. The lowest frequency such that the junction is a node is
![](data:image/png;base64,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)
In the figure given : ![l subscript 1 end subscript equals l subscript 2 end subscript equals l comma mu subscript 1 end subscript equals fraction numerator mu subscript 2 end subscript over denominator 9 end fraction equals mu](data:image/png;base64,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)
When a composite wire is made by joining two wires as shown in figure and possible frequencies of this wire is asked (both ends fixed) then the lowest frequency is that at which individual lowest frequencies of the two wires are equal. The lowest frequency such that the junction is a node is
![](data:image/png;base64,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)
In the figure given : ![l subscript 1 end subscript equals l subscript 2 end subscript equals l comma mu subscript 1 end subscript equals fraction numerator mu subscript 2 end subscript over denominator 9 end fraction equals mu](data:image/png;base64,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)
physics-General
physics-
Figure shows the shape of a string, the pairs of points which are in opposite phase is
![](data:image/png;base64,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)
Figure shows the shape of a string, the pairs of points which are in opposite phase is
![](data:image/png;base64,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)
physics-General
physics-
In the circuit shown L1, L2, L3, and L4 are identical light bulbs. There are six voltmeters connected to the circuit as shown. Assume that the voltmeters are ideal. If L3 were to burn out, opening the circuit, which voltmeter(s) would read zero volts?
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)
In the circuit shown L1, L2, L3, and L4 are identical light bulbs. There are six voltmeters connected to the circuit as shown. Assume that the voltmeters are ideal. If L3 were to burn out, opening the circuit, which voltmeter(s) would read zero volts?
![](data:image/png;base64,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)
physics-General
physics-
The potentiometer circuit shown is used to find the internal resistance of the cell E. At balance, the galvanometer pointer does not deflect, and NO current flows through
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)
a) the potentiometer wire PQ
b) the resistor R
c) the galvanometer G
The potentiometer circuit shown is used to find the internal resistance of the cell E. At balance, the galvanometer pointer does not deflect, and NO current flows through
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)
a) the potentiometer wire PQ
b) the resistor R
c) the galvanometer G
physics-General
physics-
In the above circuit, C denotes the balance position on the potentiometer wire AB. Which of the following procedures can shift C towards the end B?
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIEAAABXCAYAAAAjxyZiAAAQ+klEQVR4nO1dS2xU1R/+7nNu25l2YPqCDoXyElqx0toSqwQUMAVsgopbUWPcuHGhO3duXbgyxmgCUVAwMRBFYsw/4RGJREBopSCtPKzFPuh0ZjrtzH3Mvf+F+R3OTFtpO73Th/dLms60M3PPnPOd3/m9r+A4jgMP/2mIcz0AD3MPjwQePBJ48EjgAR4JPMAjgQd4JPAAQM7nxRzHgSAI456Tq4L/31wgezwAxj3PN/IxJ3kjgeM4sG0bwD9fTBAEpNNp9iXT6TRkWWYTLkmSa2OYiIg0BlEU4TgOe61t2zBNE6IostfTYzdgWRYkSYIgCLBtGz6fD6qqunY9IM+SgGCaJlt0URRhGAYkSUI6nWZEEUVx1ncBkc+yLHYNuqbjOJBlGclkEoIgQJZljI2N4ciRI/j111/ZeGlx3ABtAMdxkE6nEQwG8c4772DFihWuXI+QVxLQZPPPAUCWZfbczUkGHuxk2u10PVmW2W8ihmmasG0b+/fvx9q1a9lr3JRS9DuVSuHw4cNIp9Ozfq1s5JUEgiDAMAyMjIxAEAQEAgEYhoFkMgnbthEMBiFJkiuTTLBtG5ZlQVEUpNNpWJaFVCrFCCgIAgoLCwGAieVQKISKigpomsaOgtmWUjQuSZJg2zZGRkbg9/tdPXoIedUJTNPE8PAwzpw5g1gshra2NrS3t+P27dt49NFH8dhjjyEQCLgqCWRZhiRJ0HUdABCJRHDq1CnE43EUFBSgrq4O9fX1KCwshCiKkGUZsixDVVVIkgTDMKCqqiuLQ0cVEcGyrLwopXkzEUnJ8vv9bDJt24amaYhEIgiHw/D5fBnKolvjSKfTbJeLoohoNIpwOIxNmzbhwoULGBgYYOOlHzo+VFV1ZXykh8iyDMuymJKcD+sgbyQQRRGiKMLn8+Hpp59GIpFAe3s7bt26hZdffhnhcJiZY2598exzFwDGxsYwNjaGNWvWQFVVFBUVQVGUDCuAl0xu7UxBENhRqGmaq0diNvJGAn7yFEXBpk2bcP78eTQ3N6Ompga2bWN4eBimaboqAokAZKFYloWuri588cUXOHXqFJqamlBWVsaUQNu2IYoiTNMEANcVNdJL8om8kYCYbts2+vv7cfPmTcTjcWiaxhb9gw8+wN27d11ThogAZOrpuo6hoSHs2LEDr7zyCioqKlBeXs4shLGxMaRSKQCAqqpMTM+1U2u2kTcSWJaF+/fv49KlS7h48SK2bNmC8vJy/Pbbb4hGo3AcB8lkEul0GoZhuDIGQRCYqJdlGf39/fjhhx9QVVWFUCiEyspKXL58GcPDw4jH47h37x7TBXRdRyqVcl1SzQXyqhh2dXXhxIkTEAQBNTU1EEURV65cQW9vb4YYJKWId57MBujzyda/c+cOkskk+vv7EQwGUVlZiUuXLiGZTCKVSuHo0aOIx+NIJpMYHh5GLBaDruuLjgRTNhGzXa50Vk5VdCuKgubmZjQ2NkJRFEiShHfffReGYUBRFJimCUmS2FlMZy959SRJytmLyCuGALBt2zZs376dfY+mpiY0NjZCFEWMjo5i8+bNOHLkCFasWIGenh7U1dWhvLw8Yy7Iu7eQj4kpkYD/0rxThX/8MIiiCE3TMv5Giw48MN1IGbtx4waqqqpQUlICURQZ6XJFMpnEX3/9hbt377JYATDe+WNZFgzDwO3bt3H06FHs2bMHmqahp6cHPp8PmzZtQjAYZO/LlznnBqYsCUiE8iKaFi6XxaGdRD+0848fP47XX3+dBVDS6XTOE00Oq/Pnz6OrqwulpaUZdn/2Z+u6jn379kHTNFiWhd7eXjiOg9u3b6O0tJT5PNyIc+QTUyIBOTIAMA1f13X09fUxr9pMQcEcWmQy2wYHB9Hb24t4PI7CwkKm1ecqDYaHhzEyMoJdu3ahvr4egUBgUlc1kZx0FHr++eefI5VKQRTFjI2xUDGt1SNXJgDE43EcPnwYfX19CAQCMx4AHSuSJGFgYIDFF7q7u/HZZ5+hoqIClmUxnSHXHZdIJBCJRFBbW8tcwROZfrximkwm4fP5MjYD+Q7IhfyfOA4cx4FlWex8tiwLBQUFeOONN1BRUTHjAfBx+/fffx+O46CgoAA7duxAW1sb/H4/+z+J3lyuFY/H8eOPP+LPP/+Ez+eDoihMmmUvIh9m5v93//59AGDm5kLHtCSBoigQBAGmaUIQBBQVFaGsrAzhcHjGA6BwLSVQkGv5tddeQ0lJCRRFyXh9rjpBLBbD+vXrcenSJQwNDbH4wWQKLh9y5rOMioqKMv6Wj2ifW5gyCbInYbbAZ9LQ50uShFAoNOsuVJImLS0taGlpYXrAdBW7VCoFn883Lqaw6I+DbMzWF1YUBZZljUsvc8OHTlIGAFPoJrMMJoPjOEwiujnWfGJO0st40ATKsgyfzwdN05hzyI1rkQma7Y2cjjjnlVnSGRbycTBvRi4IAl566SWEQiFXJ5QcVCR9sr2IUwEdWbx562YijNuYc0kgiiLLpm1oaGC2t1vilaRBdnLIVK/Hi346Fqbz/vmIOScBP3lup1bz18xl0RbDwvOYN8eBh7mDRwIPHgk8zAOdIF94mPa/WM73mWDRkoDPKJ7oOQWAyBpx0yKZ71i0JKAF5+sMASAajeLs2bO4cuUK1q9fD1VVsXXrVpSXl+c1zXs+YdHqBLwZR0GvWCyG9vZ22LaN3bt3IxaLQZIk+P3+/6wUABaxJKAYP+UqOo6D8+fPAwC2bt0Kv9+PwsJCSJKEgoKC/zQJFq0koFQyClMDQFdXFwuBA0BNTQ1qamrmcpjzAhNKAl6BisViUFWVVeouRFDQSFEUluxKCSHk958P+gCvvBqGwWIoFOOgusl4PM7+HggEUFZWlpMkG0cCSqKIRqMQBAG9vb04ffo03nrrrQUlMul7UFqabdvYsWMH2tvbEY1GoaoqLl68iKVLl6K5uXmuh8tK41KpFAupU/Kt4ziMFBcuXMDBgwdZKDwUCuHDDz/MybqZVBJomoaOjg58+eWXrItI9kX41LD5BrIIaIfbto3Vq1cjlUrh008/hWmaaGpqwsaNG2Ga5pynilFug6qqbD5poSmtT5IkVFRUoLa2Fq+++irOnTvHinlmXRJQHV5HRwfq6upYhVA2KPs2H900pgsiKOVEEqqrq3HgwAGIosh6EFCLmrmUdDTe7LJ0vsjHsizcuHED169fx0cffYRVq1bhzTffzJm8E5IgFovhypUr6OzsxLp161htYHZ62cjICK5du4ZIJJLTINwAnzVkmiYSiQQMw4CmaRnJqwDmhbOIT24RBAHxeBxVVVUoKiqCruvQNI11dGltbUV9fT2+/fZb7Nq1K+dxjyMB6QEff/wxWltb0dPTw3LssxGNRnH9+nX09fXlNAg3QAvsOA56e3tx4sQJJJNJPPfcc9iwYQMTr261n5ku+K5tgiDA5/Ohra0NgUCAJcFEIhGYpoktW7agsrKSZU/nmoSTQQLbtjE0NITjx49j//79eOaZZ3D69Gn873//w8DAAEpLSzO06OXLl6O1tRVVVVU5DWK2QUea4zgYHh7GyZMnsXv3bvj9fvj9fjQ0NGDNmjUsv9Hn880L64AHNasA/mmk4TgOOjs70dnZidLSUvT09ECSJAQCAdaDaaaY8DhYvXo1DMNAMBiEqqpoaWlh5yYP6uxRXFw84wG4Ad706+vrQygUQkFBAdLpNJqamgCAlZBRcex8zRGkBabS+LVr17Iineeffx6BQCDnsQtOllZBZWCUVWtZVkYyKPDPGTswMIATJ06gra0N1dXVOQ3CDViWxUTo0NAQuru7EYvFsGfPHvj9fqbMUhXSXOsEk4H6NdDxxVtp1ESLT3ObCSakEOXhLeQsWpq0JUuWIBwOo6CggH0XUr58Ph8sy5qXJi6Bd2TxpXFUr0HJrrlg3ArTruercv6tQmc+I9sTyJNAUZRxldbzFXyrH75Qh9YlVxJPaB2Q2KHfsyENsjuPZBOK73cATK8OYCLQ8UXVzHRdqmzmK55mYze5BbIMaNFp7OT/mI1K7QlJQBehQQC5t4zhI3r8DqWFz4765XrOZU8a/72yS+nnm2XAQxAEpvlnj3O2xp23UDLPXuDB4pOiQ/rHQtVBFjLymk+QTqcxOjqK/v5+mKaJ6upq9PX1Qdd1LF26FCUlJVBVNaemFx6mj7w2szQMA5FIBN988w0OHTqEgYEBfP/99/jqq69w7do11sKO+g57yA9c23IT6RCqqqKyshIbN27E4OAgBgcHsWTJEuzcuRMrV65klcnzMSC1mOEKCXhLAHiQ7ElWwSOPPIKrV68ikUigsbERNTU10DSNKW+5KoUepgdXSMArfbwtS6YYdQMrLCzEhg0bWEjXw9zANUkAPLD9yfQjC6GrqwvV1dXYv38/iouLPQLMMVwhAXnhyBxMJBL4448/sGzZMkiShF9++QWjo6MwDGPee+v+C3BNMaQoHmXudHZ2ori4GIFAAE1NTUgkElMOfxJRDMNgloOmaVPSHTySPRyuKobk57YsC8lkEsA/Xb+2bds2zjOZDd4fTp3Fu7u7ce3aNYiiiMcffxwrV67M8AoS+Me8LuJG463FgJxIQIudPbEkAcgvT/EI4EHollcaJ1oYMhMty8LAwACOHTuGQCCAcDgMXddx8uRJFBcXY+/evQgGg8zBRNVGRC4Ki1OvYs/8HA9XNDI+skU7nlKq4/E4dF3PuC3dZKDU9zNnzqCxsRGNjY3QdR2JRIIt9sGDBzE0NMTek31bPVJKF0MPYreQMwl4acCnoJNPgLcMTNPEuXPncO/evQxpwfsReIVS13VEIhHE43GsXLkSuq5jZGSEZQrfvXsXd+7cweDgIPM28l1I+aINWZaZL8JDJmZdJ+BDwZT4QH+XJAlXr15FdXU1u+vnv+kEg4ODOHbsGA4cOICOjg6kUim0tbVBkiT8/fffSCQS2LdvH86ePYtQKIQlS5aw+x3yPYgpcWS22uUvNsyIBBSr7+/vx6FDh8blGNJOptIvumNIc3MzhoaG8PXXX+P06dP/egs8x3HQ19eHnp4elJaW4rvvvsPbb7+NwsJCRKNRSJKE7du3o7i4GFevXmV3L+HzIehzKY9g+/btrJmlhweYNglokouLi/HCCy8gEomMi2vzSSNUx9DR0QHbtqEoCmpra1FVVZXRVjYbjuOwdvd0F1MyKW/duoWTJ0+iuroazz77LIqKirB582YEg0Em/vmcBcrKXbt2rUeCCTCt3sYEOpMbGhomfC1PAtu2ce/ePQwODkKWZSxbtgxPPPEEamtrM1rFZ7/fNE3cv38fo6Oj6OjoQH19Pbq7u7Fs2TLYto2amho0NTXh5s2bePLJJ9HS0oKysjL2fsox9PBw5DWULAgC9u7di+XLl2d0D5kIFEhqbm7G5cuX8eKLLyIajeK9997DJ598gqqqKixduhS3bt1CQ0MDSkpKximDHqaGvGZviKKIcDgMTdMy8gknA8UVVq1ahYsXL0LTNLS2tsKyLIyOjuKnn37Chg0bWCtcIhYfsfTwcLiaTzCZF49P8pxsoUiTDwQC2LlzJ37++Wf8/vvvuHHjBlRVRV1dHdatW4eGhgbWCdUwDHaHEg9Th6uh5GxHEJ8rwOsM2Wc372EkZfKpp57C5s2bmbhXFIXd15je4y3+zOBqKJkeO46DoqIitmhTUdh4zZ4+h7+l7kSLzusYHiGmjnFlaLMBCtqQm3ZsbAwjIyMoKSnJqATyMD/gCgl4VzAfKfR25/yEKyQgeBr6woCrctkjwMKAdzh78EjgwSOBB3gk8ACPBB7gkcADgP8D/8ADXPfgf8YAAAAASUVORK5CYII=)
a) replacing the driving cell X by one with a smaller EMF
b) adding a resistance in series with the galvanometer G
c) increasing the resistance of the rheostat R
In the above circuit, C denotes the balance position on the potentiometer wire AB. Which of the following procedures can shift C towards the end B?
![](data:image/png;base64,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)
a) replacing the driving cell X by one with a smaller EMF
b) adding a resistance in series with the galvanometer G
c) increasing the resistance of the rheostat R
physics-General
chemistry-
Identify Z in the following series ![](data:image/png;base64,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)
Identify Z in the following series ![](data:image/png;base64,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)
chemistry-General
chemistry-
Which does not give iodoform reaction?
Which does not give iodoform reaction?
chemistry-General
chemistry-
Which one of the following compounds when heated with KOH and a primary amine gives carbylamine test?
Which one of the following compounds when heated with KOH and a primary amine gives carbylamine test?
chemistry-General