Physics-
General
Easy
Question
A hollow sphere of inner radius R and outer radius 2R is made of a material of thermal conductivity K. It is surrounded by another hollow sphere of inner radius 2R and outer radius 3R made of same material of thermal conductivity K. The inside of smaller sphere is maintained at 0°C and the outside of bigger sphere at 100°C. The system is in steady state. The temperature of the interface will be :
- 50°C
- 70°C
- 75°C
- 45°C
The correct answer is: 75°C
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physics-
A metallic rod of cross-sectional area 9.0 cm2 and length 0.54 m, with the surface insulated to prevent heat loss, has one end immersed in boiling water and the other in ice-water mixture. The heat conducted through the rod melts the ice at the rate of 1 gm for every 33 sec. The thermal conductivity of the rod is
A metallic rod of cross-sectional area 9.0 cm2 and length 0.54 m, with the surface insulated to prevent heat loss, has one end immersed in boiling water and the other in ice-water mixture. The heat conducted through the rod melts the ice at the rate of 1 gm for every 33 sec. The thermal conductivity of the rod is
physics-General
physics-
Six identical conducting rods are joined as shown in figure. Points A and D are maintained at temperature of 200°C and 20°C respectively. The temperature of junction B will be:
![](data:image/png;base64,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)
Six identical conducting rods are joined as shown in figure. Points A and D are maintained at temperature of 200°C and 20°C respectively. The temperature of junction B will be:
![](data:image/png;base64,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)
physics-General
physics-
Twelve conducting rods form the riders of a uniform cube of side 'l'. If in steady state, B and H ends of the rod are at 100°C and 0°C. Find the temperature of the junction 'A'.
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)
Twelve conducting rods form the riders of a uniform cube of side 'l'. If in steady state, B and H ends of the rod are at 100°C and 0°C. Find the temperature of the junction 'A'.
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)
physics-General
physics-
Three rods made of the same material and having same cross-sectional area but different lengths 10cm, 20 cm and 30 cm are joined as shown. The temperature of the joint is:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAASsAAAElCAYAAAC8rsTEAAAgAElEQVR4nO3dd1QU19sH8O/SlCagCCo2VIgF7EGJRlExaowVbMQSoyYqxh6JJdYYNcZowBKiEXtXFFtEbGBDiUbF3sWKGgUEgWXnef/gt/Oy7i4s7FIGns85nINz79y5u8KXmdk798qIiMAYY0WcUWF3gDHGdMFhxRiTBA4rxpgkcFgxxiSBw4oxJgkcVowxSeCwYoxJAocVY0wSOKwYY5LAYcUYkwQOK8aYJHBYMcYkgcOKMSYJHFaMMUngsGKMSQKHFWNMEjisGGOSwGHFGJMEDivGmCRwWDHGJIHDijEmCRxWjDFJ4LBijEmCSWF3gDGp+u+//3Dy5EkkJyfDzMwMnp6eqFSpUo77KRQKhIeHQy6Xo0WLFihXrly29e/evYtjx47ByMgIn332GSpXrqxT/+7fv4+oqCikpqbC3NwcXl5eqFKlilgeExODpk2b6tRWUSDjRU4Zy73g4GCMHz8eKSkp4jYTExMEBARg+vTpMDMz07jf2bNn8d1334GI0LBhQxw8eBCdO3dGUFAQSpUqpVb/119/xcyZM/Hll19CJpMhLCwMM2fOxDfffKOxfSJCaGgogoODER4ejgYNGsDb2xtGRka4ePEiypYtiwYNGiA5ORmxsbHYs2ePYd6QgkCMsVyJiIggAOTq6koTJ06k8ePHU9WqVQkAAaD+/fuTIAhq+4WGhpKxsTENHTqUEhMTiYjozp07ZGdnR/7+/mr1L1++TObm5nTixAlx29WrV8nJyYkOHjyoVv/9+/fk4+NDAKht27Z0+PBhtX5ERkZStWrVCAA1a9ZM37eiQHFYMZYLCoWCqlevTrNmzaKMjAxx+7t372jYsGFiYGUNGCKilJQUqlixIjk6OqrsR0QUFBREAGjdunUq23v27EkrVqxQ68OxY8eobt26KtsEQaA+ffoQAGrSpAmlp6drfQ3R0dHk4uJCNWrU0Pl1FwUcVozlQmxsrMazICKitLQ0qlu3LgGgMWPGqJQFBgYSAOrbt6/afo8fPyYAVL58eXr//r24vXHjxnT37l21+oIgkLm5ucq2ZcuWEQAyMzOjq1ev5vg6rly5QlZWVjnWK0r400DGcsHa2hpz587VWGZmZobhw4cDAK5cuaJSdvz4cQDAJ598orafk5MTnJ2d8fLlS+zatUvcXq5cOZw5c0at/p07d1RuyhMRpk2bBgDw9fVF3bp1c3wdbm5uaNiwId6/f59j3aKCw4qxXKhatSpsbGy0lstkMgBA586dVbbHxMQAACwtLTXup/xU7uLFi+K2gIAAzJgxA9evXxe3/ffff+jTpw9mzpwpbrt48SLevHkDQHMYavPLL79AoVDoXL+w8dAFxgzon3/+AQD4+PiI2169eoVHjx4BAIyMNJ8f1KlTB0DmMAWldu3aYezYsWjfvj3at2+PjIwMREVFYc6cORgwYIBYb+PGjeL3jRo10rmvnp6eOtctCjisWLGWkpKCJ0+eQKFQwMjICIIgwMrKCpUqVdIaHHlFRDh79iw6dOiAatWqidvj4uLE711cXDTua2pqCgB4+vSpyvZRo0bB19cXJ06cgJGREZYsWaI2Livr2Zgul4BSxWHFipVLly5h586diIqKwo0bN/D8+XOxrHHjxrhw4QKAzPtLNWvWhLu7Ozp27AgfHx+UKVNGr2OvX78ejx8/znbskrm5ebZtvHz5Um1bhQoV0KdPH637pKWlid+bmBTfX+ni+8pYiSKXyzFy5Ej89ddfIB3GOaenp+P69eu4fv06tm3bhsmTJyMkJASdOnXK0/Fv3LiByZMn4+DBg3B1ddVar3Tp0lr7n1dZR7Tr8tqlisOKSd7ly5cxbtw4HD16FEDmTe42bdqgWbNmcHNzQ61atWBsbCxeBiYkJCA2NhaxsbE4dOgQHj16hBcvXqBr165YuXIlvvrqq1wd//Xr1+jevTtWrlyJli1bqpVnHc2enp6usY2HDx8CyLyBn1tZL/1u376Nxo0b57oNSSjckROM6a9fv37iYMzBgwfTgwcPdN5XoVDQ4cOHqXLlygSAnJyccnXs1NRUat26NQUHB2utk5KSQkZGRgSA9uzZo7FO8+bNCQDNmjUrV8cnItq9e7f4+hcvXpzr/aWChy6wAvPs2bN8uUx5/PgxKleujK5duyI4OFjl5nZOjIyM4O3tjcDAQDRr1gxpaWlISkrSaV8iwnfffYdBgwZpfVYPyLxPpTzjunHjhlq5IAiIjY0FAPTv31/nvit5e3uL98IiIiJ03o+INN4jK6o4rFiBEAQBvr6+CA4ONnjbdnZ2ePz4McLCwtCyZUv89ttviI+P12nfU6dOYdSoURg8eDCio6ORnp4Oa2vrHPcjIsyfPx+9e/fG4MGDNdZJTEwUv//yyy8BQAylrG7evIl3796Jg0Nzy9LSEqNGjQIA7N+/H0eOHNFpv8DAQJWhEkUd37NiBWLJkiU4ffo0rly5gs8//zxP92a0yXqD+dy5czh37hwmTpwIZ2dn1KlTBzVq1ICxsTFsbW3x9u1bJCYm4saNG7h69SoSEhJU2mrSpEmOx1MGVZs2bdC8eXO18rS0NISGhoKI0K9fPwCAn58ffv75Z0RHR0MQBJVhEzt37gQATJ8+XRxUmlszZszA2bNnERUVhf79++Pvv/9GgwYNtNZfunQpAGjsf5FVmNegrGS4desWmZubi/dVPvvsM4O27+/vTwCofv365O7uLh7nw6/GjRtr3G5qakqurq4EgHx8fLI9liAINHHiRLKxsSFXV1eNX2XLliVHR0dKTU1V2feff/4hKysrmjx5MqWlpRFR5kPFpqamNHToUI0zNeRGUlISDRs2jIyMjMjExIR69uxJJ0+eFB+cjo+PpzNnztC3335LP/zwg97HK2gcVixfKRQKatmypVpArFq1ymDHUIaVp6cnERHdvHmTVq5cSWPHjqVu3bqRh4cHNWnShHx9falJkybUqlUrGjBgAM2aNYvCwsIoMTGRevfurVNYBQQEaA3DrF8zZszQuP/p06epefPmVLZsWWrVqhW5uLjQypUrSaFQGOz9uHLlCn311VdkZmZGAKh06dJUpkwZsrCwoH79+tGxY8cMdqyCxGHF8tWSJUs0/jLb2NjQ48ePDXKMD8MqL3QNK7lcrtNXTuHz4sULOnPmjNrZlyHJ5XKKi4ujmJgYiomJoXfv3uXbsQoC37Ni+ebu3buYMmWKxrKEhAR888032L9/fwH3Sj+GGiHu4OAABwcHg7SljYmJCSpXrqzzNMhFHX8ayPIFEeHrr79Wmfb3QwcOHMC6desKsFdMyjisWL64efMmIiMjc6z3559/FkBvWHHAYcXyBek4+FPXeoxxWLEC0a5dO/H74nIPhRUsDiuW79zd3eHn5yf+e8OGDQafS4oVf/wTw/KVhYUFtmzZojLzQOvWrbV+SsiYNhxWLF8tWbJE4+yVM2fOzNV84YxxWLF807t3bwwbNkxjmbGxMTZt2gQ7O7sC7hWTKg4rli/s7e1zHJZQrVo1LF68uIB6xKSOR7CzfFG+fHmd6mlbQIGxD/GZFWNMEjisGGOSwGHFGJMEDivGmCRwWDHGJIHDijEmCRxWjDFJ4LBijEkChxVjTBI4rBhjksBhxRiTBA4rxpgkcFgxxiSBw4oxJgkcVowxSeCwYoxJAocVY0wSOKwYY5LAYcUYkwQOK8aYJHBYMcYkgcOKMSYJHFaMMUngsGKMSQIvcloIiAgXLlzAtWvXQESoWLEiWrVqhVKlSuW475MnTxAREYFatWrh448/hpmZWQH0mLHCx2dWBey///6Dl5cXmjZtioEDB2LQoEH47LPP4OLigvPnz0OhUGjcLz09HT///DNq166NU6dOYcGCBahatSrCwsIK+BUwVjj4zKoAERH69++P06dPo3fv3qhTpw7u3r2LzZs3Iy4uDt7e3ti6dSs6duyosp9CoUC3bt0QHR2NLVu2oHPnzgCA+fPno1evXjh58iQ+/vjjwnhJjBUYPrMqQLt27UJsbCyuXLmCrVu3YubMmVi/fj3OnTsHZ2dnJCYm4ocfflDbb/Pmzfj7778xduxYMagAICAgAC4uLvDx8cHLly8L8qUwVuA4rArQ0aNHER4ejtq1a6tsb9y4MZYtWwYAuHTpEu7fv69SPmfOHABA27ZtVbbLZDJ0794dcXFxWLhwYT72nLHCx2FVgPz9/dWCSqlTp06oUaMGAODatWvi9ufPn+PWrVswNjaGh4eH2n4tW7YEAKxcuVLr/S7GigMOqwJUt27dbMuJCBYWFvDy8hK3xcTEAABMTEw0fvKnvFf19u1bPHr0SK380KFD6N69O2rVqgVra2t8/fXXavVevXqFOXPmwNHRETt37kRSUhKCgoLg6ekJExMTjB49GqmpqQAyb/QHBwejSpUqsLCwQN++fZGQkJC7N4KxPOCwKiL+++8/3L9/H59//jksLS3F7RcuXAAAGBlp/q8qV64c7O3tAQB3794Vt2dkZCAgIACDBg3Cd999h9u3b2PDhg1Yu3YtatWqhb179wIAwsPD4e7ujunTpyM+Ph5JSUno378/goOD4eDgACJCUFAQRowYAUEQ0LNnT2zZsgUeHh5QKBQaPxBgLF8QKxIOHDhAAOjQoUMq24cOHUoAqH79+lr3rVixIgGgNWvWiNsCAgIIAO3YsUOlbufOnQkAubq6itvi4uIIAAGgVq1a0cGDB8WyP/74QywbMmQI7dq1Syw7fPgwmZiYEAC6efNmtq9v/fr1YjuG5u/vTwDI09Mzz2307t2bAJCPj48Be8YMic+sioCMjAxMnToVfn5+aN++vcY6ZcqUyfGe1KtXrwAAaWlpCAoKQoMGDdCzZ0+VOn5+fjAzM0PNmjXFbZUrVxYvUYcOHapypvTtt9+K99Lq16+PHj16iGXe3t5o2LAhACA6OlrXl8tYnnBYFQEBAQGoVKkSVq9eDZlMprGOsbExjI2NNZalp6cDgLhvWFgYUlJS8PHHH6u15+fnh6SkJBw4cEBlu/J+mIWFhVr7VatWBQCVy1MlZZDFx8drfX2MGQIPCi1kq1evRmRkJCIjIzU+bqMMEWUgfejdu3d4/fo1gP8PlcuXLwPQfp+LH9FhUsRhVYiOHTuGJUuW4NChQzA3N9dYx8XFBQDw8OFDjeW3b98GAJiamorDGJTu3btnwN4yVrj4MrCQ3Lp1C3PmzEF4eDgqVqyotd5nn30GAHj69CkSExPVypVnUe3atUOFChUA/P+lXEREBGJjYzW2q1AocOPGDb1eA2MFicOqEDx8+BBLly5FWFiYGDBZpaenIzk5GUDm2KxGjRoBAK5evapW99y5cwCAVq1aidt69eolfh8YGKixDwcOHICzs3PeXwRjBYzDqoA9fPgQgYGB+PXXX2FlZaVW/vz5c3z77bcwNTUVt02dOhUAcPbsWZW6aWlp2Lt3LxwdHTF8+HBxe61ateDu7g4AWLVqFaZPn44nT54AyBzPdeTIETx8+FCnKWkYKyr4nlUBun//Ptq0aQNBELB79261ciLC/fv3MXv2bJWb4D4+Ppg4cSJmz54NT09PNG/eHAAwYsQIvHnzBocOHYKdnZ1KWyEhIWjVqhVSUlIwZ84czJkzB05OTnj69ClcXFzw77//inUzMjLw/Plzrf3Wdr8MUB2Iyli+KuyBXiVFXFwcVa1aVRwYqe3LzMyMXrx4oba/IAg0d+5ccnR0pHr16lGNGjWoX79+dOnSJa3HPHv2LLVv357MzMzE9tu3b08PHjxQqTNs2DAyNTUlU1NTcnZ2pu+//56IiP7991/6/vvvxbIaNWrQ6NGjSS6X0/Xr16lXr15UqlQpMjU1JUdHRxo5ciS9fftWY194UCjTF4eVxCgUCrpx4wbdvXtX531SUlLo9OnTdOPGDRIEIR97px2HFdMXXwZKjJGRET766KNc7WNubg5PT8986hFjBYNvsDPGJIHDijEmCRxWjDFJ4LBijEkChxVjTBI4rBhjksBhxRiTBA4rxpgkcFgxxiSBw4oxJgkcVowxSeCwYoxJAocVY0wSOKwYY5LAYcUYkwQOK8aYJHBYMcYkgcOKMSYJHFaMMUngsGKMSQKHFWNMEjisGGOSwGHFGJMEDivGmCRwWDHGJIHDijEmCRxWjDFJ4LBijEkChxVjWTx79qywu8C04LBiLIvY2FgIglDY3WAacFgxlkViYiLWrVtX2N1gGnBYMfaB6dOnIzU1tbC7wT7AYcXyRWpqqk6XU+/fvy+A3ujO3NwccXFxCAoKKuyusA9wWLF88eTJE/z+++/Z1klPT8fkyZMLqEe6qVevHgBg3rx5ePPmTSH3hmXFYcXyTUBAAC5cuKC1fNq0aTh//nwB9ihnVatWRf369fHmzRvMmzevsLvDsuCwYvlGLpejb9++ePfunVpZeHg4Fi5cWAi9yp5MJhNDKigoCHFxcYXcI6bEYcXy1e3btzF69GiVbfHx8Rg4cGAh9Shnn3/+Oby8vJCamorp06cXdnfY/3BYsXwXEhKCM2fOiP8eNGgQXrx4UYg9ytmCBQsAAOvWrUNsbGwh94YBHFasgKxevVr8/u+//y7EnujGw8MDvr6+EAQBP/zwQ2F3h4HDihUQKY5b+vnnn2FsbIz9+/cjMjKysLtT4nFYsXzh6OgIJyenHOs1bdq0AHqTNy4uLvjmm28AABMmTCjk3jAOK5YvrKysEBwcnG2datWqYe7cuXod5+3btzh37pxebWRnxowZsLCwQExMDJYuXZpvx2E5MynsDrDiq3PnzhgwYADWr1+vsXzVqlWwsrLKU9tv3rzB4sWLERgYiISEBHF7RkYGoqKiEBUVhRs3buDu3bt48uQJFAoF6tati2vXrsHKygrOzs5wcXGBu7s7OnbsqPU4jo6OmDhxImbPno0xY8agZs2a6NSpU576zPREjOWj169fk6OjIwFQ+Ro6dGie25s6dSqVKVNGbMvOzo4AUK1atTQeS/nVuHFjrWUVKlQgAOTj46N2zMTERHJwcCAA1KFDB1IoFPq+LSwPZEREBZqOrMQJDQ1Fz549xX87OTnh6tWrsLGx0bmN169fY9GiRVi6dCmSkpIAZD4a8+OPPyIyMhLLly9XqW9paQk3Nze4ubnBxcUFxsbGsLS0RHJyMhISEhAbG4vY2FjcuXNHZb/PP/8c+/fvVzt+UFAQRo8ejQoVKuDOnTuwtLTMzVvADKGw05KVDL179xbPYvbv36/zfi9fvqSAgACysrIS93dzc6Nt27aRIAhERPT111+LZQ0bNqS1a9dScnKyTu3fvHmTpkyZQqampgSAnJ2dNdZLT0+nmjVrEgCaPXu2zv1nhsNhxQpEfHw82dvb08CBA3Wu//3335OlpaUYRPXr16cdO3aIIaXk7e1N1tbW1Lx5c3rz5k2e+rdu3TpydnYmGxsbevfuncY6mzdvJgBkbW1N8fHxeToOyzsOK1Zg9u3bR69fv862zvPnz2nChAlkYWEhhlSDBg1o586daiGltHDhQrHu+PHj6cKFCzr3KSUlhXbs2EENGjQgAGRvb6/1OIIgUJMmTQgAfffddzofIzuCIFBoaCgFBAToVP/t27c0ZcoU6tmzJ82fP59u3bplkH5IAYdVFsnJybR3717avn07nTp1ijIyMnTaLzExkQ4fPkyPHj3K5x4WX8+ePaNx48aRubm5GDyNGjWi0NBQreGhlJycTM2aNVO5Ye7m5kZDhgyhRYsW0a5du2jPnj104MAB2rNnD61fv56mTp1K3bt3J1tbW3EfmUxGf/75Z7bHioiIIABkZmZGd+/ezfPrVSgUtGvXLjEkPTw8ctxnx44dVL58efL29qaoqCiaNm0amZub065du/LcDynhsPqfI0eOUPXq1VV+4Fu0aJHtmYAgCLR69WoqX748de7cmRo2bEhubm507ty5Auy5tD19+pTGjh2rElKNGzemPXv25Kqd9PR0Wrp0qUo7H365ublpLWvWrBldunRJp2N99tlnBID69u2bl5dMRET+/v40YMAA8TI3p7Dav38/yWQyGjdunMof0YkTJ5KlpSVdvXo1z32RihIfVoIgUEREBFWuXJmmTp1KmzZtotGjR4s/xJ07d9Z4hqVQKMjPz4/Mzc1p9erV4vZRo0aRjY0N3blzpyBfhuQ8efKERo8eTaVLlxbf66ZNm9LevXv1ajcuLo5WrFhBfn5+1KBBA7K2tlYLJplMRpUrVyYvLy8aO3YsHThwgNLT03U+xsWLF0kmk5FMJqOYmBi9+vv999/nGFYKhYLc3d0JAD19+lSlLDExkczMzMjV1ZVSU1P16ktRV+LDKi4ujoYMGUIJCQkq2zdt2iT+cGs6zd6xYwcBoB9//FFle3p6OlWtWpUaNGig8ydSJcnjx49p1KhRVKpUKfH99fDwyNUnhLpQKBS0fv16+uijj9TCasyYMXq3/+WXXxIAateunV7tbNy4McewUl56urq6aiz38vIiALRu3Tq9+lLUlfiwio6OprS0NI1lQ4YMIQC0Y8cOtTLlJUVkZKRamfLMbN68eQbvr1Q9evSIRo4cqRJSzZs3p4MHDxr0OAqFgjZs2KASUra2tjRr1izxD1CpUqXo4cOHeh3n/v37ZGZmRgDo0KFDeW5H2afswmr+/PkEgHx9fTWWT5kyhQBQx44dtbaRkJBAp06doosXL2q9B5iWlkYRERHioFdBEOjq1at05swZtX3kcjkdPXqULl68WGCDZEt8WGVn5syZZGtrS2/fvlXZ/vTpUwJApqamGk+9t2/fTgCoSpUqOd4cLu4ePnxIw4cPF3+xAdAnn3yi1y+4JsqQql27tkpIzZw5U+X/r0WLFgRA5yEU2RkzZow4tiuv/8+6hJWvry8BoN69e2ss37lzJwGg6tWrq5Xdv3+f2rZtS82aNSMvLy8yMzOjDh060OnTp8U6b9++pQULFlClSpUIACUnJ9PWrVupbt264nvZv39/8Y96WFiYyvvcqlUrSkxMzNPrzw0OKy0UCgU1bNiQVq1apVa2d+9ecbyNJg8fPhT/I58/f65WfuHCBfL39ycPDw+qXbs2/fjjj2pje1JTU2n16tXUuHFj2rdvH6WmptLu3bvJ19eXqlWrRgsWLBDvpQmCQPv27aPmzZuTi4sLTZgwodDvXzx48IC++eYblZBq2bIlHT582KDHUSgUtHHjxhxDSunkyZMEgIyMjOjy5ct6Hfvly5fiYz8bNmzIUxu6hFWtWrUIAH311Vcay6OjowkAGRsbq5zlREREkK2tLQUEBIjblbcvTE1NKSoqioiIFi1aRC4uLuL7t2bNGvLw8KBff/2VfvjhB3H75MmT6ejRo9SmTRv666+/aN68eeL/r7a+GRKHlRa///47LVu2TONfzJkzZxIAKlOmjMZ9BUEQR1yfPHlSZXtQUBDZ2tpSSEgIvXz5kpYuXUoAyMbGhk6dOkVERIcPH6aKFSuKPyRr166lr7/+msqWLavyfNukSZOIiGjw4MHk4uJCHh4eYtkXX3yRD+9Kzu7du0dDhw4VR4Qr//IeOXLEoMfRFFI2NjY0Y8aMHAeGdu3a1WDv0U8//SSe1Wi7nZAdXcKqfPny2d5WOHfunPgePHv2jIgyB9Xa2tqSq6uryocHgiCQjY0NAaCRI0eK20NDQ8U25s2bJ/7cC4IgXoaWLVuWxowZo/KHUHnPzcHBIdevPbc4rLIQBIHi4uKob9++4sA/TaOZBw0aJJ7+a1OuXDkCQFu3bhW3/frrrwSAQkJCVOq2a9eOAFC9evXEfly7dk384Wnfvj0FBweLZ1LKsARAAQEBKqG6adMmkslkBIDu37+v93uiq7t379LXX39NJiYmYt9at25Nx44dM+hxFAoFbdq0ierUqZPrkFKKjY0lIyMjrfcccyM5OVm8fFq8eHGu989NWP38888ay7OGlXKQaEhICAGgZcuWqdVfuXIlde3aVeVS/MGDB2IbcrlcpX5cXJxY9uHI/aSkJDI2NiYAFBcXp/PrzgsOqyx++uknatq0qfiDDGSOtfrwenzgwIHiJ0Ha7lUowyooKIiIiDIyMsS/dB8OhVi6dCnJZDJq1KiRuE0QBPHU/I8//lBrv3Llylr/2ioHGm7ZsiXX70Fu3b59m7766iuVkGrTpg0dP37coMcxREhl9dVXXxEA8vT01LtvwcHBBIDKlSun9qlyTnITVr/99pvG8iNHjojvifKDA+UfQF0/Zc166+LDsEpISBDLXr58qbav8kOT27dv63SsvOLJ97KYOnUqzp8/j+vXr6NLly4AgFOnTuVpgriMjAwAEFclDg8Px9u3b9GiRQsYGxur1PX398ejR48QExMjbpPJZOKT/eXKlVNrv1atWgCA8uXLq5XVrl0bAPD48eNc91tXd+7cwaBBg1C7dm2sWbMGGRkZaNeuHSIjI3H06FG0bt3aIMcRBAFbtmyBu7s7/Pz8cP36ddjY2GD69Ol48OABZs6cCVtb21y3O3v2bJQuXRpnzpzB7t279erjkCFD8NFHH+H169fiQhOGpHx9iYmJGsvv3r0LIHM16cqVKwPIXEEIAKgYTarCYaWBq6srwsLC0KNHDwDA4sWLVda+MzHJnLNQEATIZDK1/ZOSksQJ4ZQ/PMrVXUxNTTUes3LlyjAyKvr/Hbdu3cLAgQNRu3ZtrFu3DgqFAu3bt8fJkycRERGBTz/91CDHyRpS/fr1w7Vr11RCatasWXkKKaUqVarA398fADBlyhQoFIo8t2VsbCyuNbhkyRI8ffo0z21p4u7uDgC4d++exvLr168DAHx9fdV+hqKiogzal8JU9H87CtG6desAZC5znpaWJm6vWbMmAGhdAPPWrVsAMn+ImzVrplJm6B/kgnLjxg30798fdevWxfr166FQKNChQwecPn0a4eHhaNGihUGOIwgCtm7divr164shVaZMGfz444+4f/++3iGV1ZQpU6H2yy4AAB+FSURBVGBjY4Pr169j7dq1erXVo0cPeHp6IiUlBTNnzjRI/5S6desGALh27ZrG8n///RcA8MUXX4jblH8kV6xYoXGRWSDzqkGfkC5oHFbZsLKyQp06dVClShWVS7E2bdoAAO7fv68SYkpXrlwBAHh7e4uLJpiZmQEADh48qPUvJBGJp/RFxfXr1+Hn54d69eph48aNUCgU6NSpE86cOYO///4bnp6eBjkOEYkh1bdvX1y9elUMqQcPHmD27Nmws7MzyLGUypYti4CAAACZc63ruwKP8hJw9erVuHHjht79U+rZsyfKlCmDq1evqoVLeno6YmJiYGFhIf5cAsCAAQMAZF46fjgxIQCkpaXh0aNHarckijIOqxyYmZnBy8tLZVuzZs1Qo0YNKBQK3Lx5U22ff/75BwBUzjaUfx0VCoXGHx4AOHLkCBwdHQ3Vdb1cvXoVffv2hZubGzZv3gxBEPD5558jOjoaBw4cQPPmzQ1yHCLCtm3b4O7uXmAhldXYsWNRqVIlPH78GEFBQXq19emnn6JLly5QKBSYPHmygXqY+Udz/vz5eP/+PSIiIlTKVq9ejaSkJMycOVPl/mWHDh1gb28PAAgICMCgQYMQFhaGCxcuYNWqVRgwYIBKuElCvt6+l7iwsDAqXbo0xcbGqpUtW7aMAKg8xEyU+RiCs7Mz2draqn3Mq5xp0sTEhIKDgyklJUUsu3nzptpH3w0bNiQAtH37drXjK58H0zRotU+fPgSAfv3111y9XiKiK1euUK9evcThD/jfeCRDzyQhCAJt3bpVZSaEMmXK0LRp0+i///4z6LFyovw0z87OLs+T9ynFxsaKH+Urx81lZ/z48QSAPvroI0pISMh2Lq3Ro0dTuXLlKCQkhF6/fk2hoaFkampK48aN07jf8ePHVR4Uz/q1du1albrKwaIA6MmTJypl4eHhYtmHn/idP39eLMs6pjA/lPiwCgkJoS5dulBwcLA4HUxGRgbNnz+fbGxsaPPmzRr3EwSB+vTpQ1WqVFF5zmzcuHFkZmZGBw4cUNsnIiJC/EEGQObm5tSsWTOysrKiSpUqqfyiKBQKqlKlitawUj77pimslI+U5CasLl26RD4+Pioh1bVrV71nFfiQIAi0bdu2IhFSSnK5XHw/dZ0ELzuDBw8WR+xrc/bsWfr555+pT58+1KtXL/Fr/vz5WvcRBIG2bNlCXbt2pSpVqlCnTp3o33//zbYvt2/fpgkTJlCTJk3I0tKSPD091YaVbNiwgQYNGkTdunUTv5Q/c9u3b6eRI0eqlCmDbuvWrSrbu3XrRoGBgbq+TblW4sPK399fJTyqV69ONWvWpC+//DLHWRjT0tJo2LBhZGVlRZ06daKWLVtS27Ztsx1jtHfvXpVR1wDI3d1d5Yfu8uXL4sOpyvJffvmFiDLPwLLOjFm/fn366aefSC6X071798jf318c81S9enWaOXMmJSUlae3PxYsXqUePHmJIyWQy6t69e65m29SFppCytramqVOn5jh7aEFQnlmYm5vT48eP9WorLi5OnFcrt/NyMe1KfFgpFAp68eIFHThwgCIjI+nFixe5fij17du3FB4eTpGRkTrv+/DhQ9q2bRtFRESozaWUnJxML168UPsiypyGV1OZIAj0/v17jWWa5uO6cOECdevWTSWkevbsmeNf6twSBIG2b98uzsdU1EIqK+Vso3ldJiyrSZMmEQCqW7euzjPOsuyV+LAqaWJiYqhLly5icMhkMvL19dX7od4PaQupKVOmFLmQUjp27BgBmQ8EX79+Xa+23rx5Q2XLltV6qc5yj8OqhDh37hx17txZDA4jIyPq3bs3XblyxaDHEQSBduzYQfXr15dMSGXVsWNHAkA9evTQuy3l5bqTk5PKhyksbzisirno6Gjq1KmTSkj17dvX4HN2Sz2klP7991/x0vjMmTN6tZWamkpVq1bV+gwnyx0Oq2LqzJkz4lmCMqT8/Pzo2rVrBj2OIAi0c+dO8eFpZUhNnjyZXr16ZdBjFRTllMWtW7fWu601a9aID11LKbSLIg6rYubUqVPi6ivK+y/9+/enGzduGPQ4mkLKyspK0iGllHXKYn3nhs+62MP48eMN1MOSicOqmIiKiiJvb2+VkBo4cCDdvHnToMcRBIF27dolDlhVhtQPP/wg+ZDKSjmPfv369fWeY3zfvn0EZM79/uDBAwP1sOThsJK4EydOUNu2bVVCatCgQQafW6ikhJRSfHy8uIyXIVaNad26NQGgAQMGGKB3JROHlUQdO3ZMfORG+QjP4MGD82W9wtDQ0BITUlnNmjVLHFyblymLs1LOk25kZGTwsWwlBYeVxBw9elT8Kw1kTvw/ZMgQvZYy1yY0NJQaNWqkElIBAQEaZ4ssjpKSksjR0ZEA0JIlS/Ruz8fHh4Dsl8xi2nFYSURERAR9+umnKiE1bNiwfJlnfffu3SU6pLJSLuhhb2+f6ymLP3Tz5k3xUShDL6BREnBYFXHh4eHig8kAyMzMjL799tt8uVG7e/duldVzLC0tadKkSSUypJTS09PF2TI+XH07L4YPH04AqGnTpiV+Tcnc4rAqov7++2/y9PRUCakRI0bQo0ePDH6sPXv2cEhlY/PmzeL7omkdyNx49uwZWVpaElAwC3oUJxxWRcyBAwfEB2qVH3f7+/vnyzJHHFK6EQRBfJ+yrrWXVz/++CMBoJo1a6o9xM6047AqIvbt26eySGnp0qXpu+++03u6Ek3CwsKoSZMmKiH1/fffq00WyP7foUOHxHuF+g4LSUxMFJfXUi7VxnLGYVXIwsLCqGnTpiohNWbMGLXZGg11LA6pvFOuxdenTx+92woMDCQgcyXjD9elZJpxWBWSD29mm5ub07hx48Tlvw1p7969KoFoYWFBEydO5JDKpfPnz5NMJiOZTEb//POPXm2lp6dTjRo1CABNnz7dQD0s3jisCpCmUeAWFhY0fvx4vW/caqItpJQT+bHc6927NwEgb29vvdtSrsZsZWWVL///xQ2HVQFQTp+S9aHf/AyOffv20ccff6xyrAkTJnBIGcDt27fFsVKHDx/Wqy1BEMTL8hEjRhioh8UXh1U+0jRbpvITt/y4BOOQKhgjRowgANSkSRO9x0pFRESIj0vlNOd/ScdhlQ8UCoXaMlPK5+nyY1jA/v37VT5J5JDKX4YeK9W+fXsCQL169TJA74ovDisDUigUtHnzZqpbt67abJn58dCvppDKr/tfTNXUqVMJANWqVUvvsVIXLlwQZyeNjo42UA+LHw4rA1AoFLRx40aqU6eOGBzKtfDyY3bIDweOmpubc0gVsISEBLK3tycAtGzZMr3b8/PzIwDk5eVlgN4VTxxWesjIyKD169eLC2Qqp6+dPn16vizYqSmkxo0bxyFVSH777TcCQI6OjvTu3Tu92rp3757BZictrjis8iAjI4PWrl1Lrq6uYnDY2trSjBkz9F5+XJODBw9S8+bNOaSKmNTUVKpWrRoBoNmzZ+vd3pgxYwjIXNRW39lJiyMOq1yQy+UUEhJCtWrVEoPDzs6OZs2aRW/fvjX48Tikir61a9eK9yb1/fDk5cuXVKZMGQJAa9asMVAPiw8OKx3I5XL666+/xKlCAFDZsmVpzpw5es9xpMmHMy6Ym5vT2LFj82V0O9NP1gUhxo4dq3d7P/30EwGgqlWrUmpqqgF6WHxwWGUjPT2dVq5cSc7OzmJwlCtXjubOnZsvz3NxSEmTckEIMzMzvSdDTE5OpooVKxIAWrhwoYF6WDxwWGmQnp5OwcHBVL16dTE47O3tad68eZSUlGTw4x06dIg++eQTtYeZnz59avBjsfzRqlUrgy0I8ccff4hn7/lxD1SqOKyySEtLoxUrVoir6AKg8uXL04IFCzikWLbOnDkjLghx6dIlvdqSy+XiJ8yTJk0yUA+lj8OKMkNq+fLlVKVKFTE4HBwcaOHChXp/JK3Jh1MVly5dmkaPHs0hJXHdu3cnAPT555/r3dbOnTvFn438mHhRikp0WKWmptLSpUupcuXKYnA4OjrSokWLKDk52eDH45Aq3q5fv07GxsYEgE6cOKF3e8pPggcPHmyA3klfiQyr9+/fU2BgIDk5OYnBUaFCBVq8eDGlpKQY/HiHDx+mli1bckiVAEOGDCEA1Lx5c73bioyMJCBz4drY2FgD9E7aSlRYpaSk0JIlS8RPWwBQpUqV6Pfff6f3798b/HiaQuq7777Ll1lAWdHw+PFjMjc3JwC0a9cuvdv74osvCAB98cUXBuidtJWIsEpJSaHffvuNKlSoIAaHk5MTBQYG5ktIfbjGH4dUyTJp0iQCQLVr16aMjAy92oqNjRUvLSMjIw3UQ2kq1mGVnJxMv/76q7iqLgCqXLkyLV26NF8G3H0YUqVKlaJRo0ZxSJUwb968ITs7OwJAK1eu1Lu9wYMHG+zSUsqKZVi9e/eOfvnlF3JwcBCDo0qVKrR8+XJKS0sz+PGOHDkijrPJGlL5sTINk4YFCxaIZ/D63geNi4uj0qVLEwDauXOngXooPcUqrJKSkmj+/PniMkcAqFq1avTHH39wSLEC9f79e/FT5vnz5+vdnvLS0tXVleRyuQF6KD3FIqwSExPp559/FucXAkDVq1enP//8M18WkTx69Ci1bt1aJaT8/f05pJiKVatWiTNy6DtlUNZLyz/++MNAPZQWSYdVYmIizZ07l8qVKycGh7OzM61atSpfQurYsWMcUkxnGRkZ4oSM33//vd7t/fLLL+Iwm/wYrFzUSTKs3r59S9OnT6eyZcuKwVGzZk1avXp1vpwiHz9+XC2kRo4cySOLWY5CQ0MNNhL9/fv34lMWc+bMMVAPpUNSYfXy5Utq1aqVOF+18gFjDilWlCln0hgyZIjebYWEhIjTZufH4iNFmWTCav/+/WRqakq2trZieCi/mjdvbtBljE6cOEFeXl4cUswgso5Ev3btml5tKRQKcdWk0aNHG6iH0iCZsNq9e7cYHr/99hstX76cateurfLgsb4/CB+GlJmZGY0YMYJDiumtc+fOBIC6d++ud1tZ58+6d++eAXonDZIJK+UzV61btxa3yeVyWrp0qfh4Q6VKlfI0+VlkZCS1adNGLaQePXpkyJfASrDLly+TkZERAaDTp0/r3Z7y9kS/fv0M0DtpkExYDR06lABQo0aN1MoiIiKoatWq1KBBA/Lz89O5TU0hNXz4cA4pli8GDhxIAOjTTz/Vu62zZ88SAJLJZPTPP/8YoHdFn2TCavHixQRkLrOtaUSwcv4fIyMjioiIyLatqKgoatu2LYcUK1APHjygUqVKEQDat2+f3u35+PgQAPL29jZA74o+yYRVeHi4GC5HjhzRWKdRo0bZ/udpCqlvv/2WHj58mJ9dZ0w0btw4Agyz3NbNmzfJxMSEAFB4eLiBelh0SSasEhMTxTnRe/furbHO2LFjxeexsjp58iS1a9eOQ4oVulevXonLba1du1bv9oYPHy7eHhEEwQA9LLokE1ZEmau/AKAWLVpoXLJ78+bNYiDFx8dzSLEiSbncVrVq1fSe/ePZs2dkaWlJAGjjxo0G6mHRJKmwIiIaNmyYOGZlx44dKmVHjhwRgynrMuumpqb0zTffcEixIiE5OVmcW+23337Tu71p06aJj5rlxwP7RYXkwur169fiyh8AyMPDg9atW0fv3r0TT4mVI3yVIfXgwYPC7jZjKpYvX05A5jqU+i6Um5iYKM40smTJEgP1sOiRXFgREd27d09l4VHll3K6llKlStGwYcM4pFiRJZfLycXFhQDQ1KlT9W7v999/Fx8/y49VwosCSYYVUebKNB/OAmppaUkdOnSgU6dOFXb3GMvR1q1bCQBZWFjovep2Wloa1ahRw2DhVxTJiIggcXfu3MH9+/fx8ccfw9bWtrC7w5hOiAgeHh6IiYnB8OHDsWLFCp33VSgUOHz4MA4ePIgLFy7gwYMHSEpKQkJCAszMzHDv3j04OTnlY+8LXrEIK8ak6ujRo2jXrh1MTExw7do1uLi4ZFs/PT0dy5cvx+LFi/Ho0SOt9Tw8PBAdHW3o7hYqDivGClmHDh0QHh6OXr16Ydu2bRrryOVyrF+/HgsWLMCtW7fE7ZaWlujcuTPq1asHuVyOkydP4tWrV0hNTcW1a9dgampaUC8j/xXiJShjjIguXLhAMpmMZDIZnT9/Xq387Nmz5OrqqvIh0kcffUSBgYGUmJioUnf27NkEgFxcXAqq+wXGRFuIXb9+HUuWLMGbN29ga2uLAQMG4NNPP80x/M6fP481a9bAwcEB7dq1Q4sWLSCTyTTWTU5OxqJFixAbGwtra2uMHDkSTZo0yfEYjx8/xvr163Hp0iUIgoBy5cqhT58+8PLyAgA8evQIt27dgre3d45tMVbYGjVqhD59+mDLli344YcfEBERIZaFhIRg+PDhSE9PBwBUqFABt27d0ni5eO3aNcydOxcA4ODgUDCdL0iaEiwoKIjMzMzUhgasWrVKa+olJSXR0KFDydTUlBYtWkS///47ubi4UL9+/TQu9BgXF0c1a9akVq1a0cGDB2nlypXk4OBAixYt0nqMy5cvU5cuXcjY2JiqVKlCixYtosOHD9P+/ftpxIgR5ObmRm3btiUXFxeaN29eHrKbscJx584dMjU1JQB06NAhIiKaMWOG+LtXvnx5+vvvv7Xuf/fuXXHKYzs7uzxNlVTUqYSVQqGgDRs2kLe3N504cYLS0tLo9u3b1Lx5c3FowIULF9QaEQSB2rRpQ3Z2dirTVVy8eJEsLS1pypQpavuMGjWKfHx8VKYjjouLo3LlytHZs2fV6u/bt49Kly5N1tbWtHPnTo3TGF+5ckUcfzV+/PjcvROMFTJ/f3/xOb8tW7aoBFV2k+ydP39eDKrSpUsX24eaVcLqxYsXNGPGDLWnwZOSkqhevXoEgMaOHavWiHIWz+HDh6uVjRw5kgDQ/v37xW2pqalka2urcfDa2rVrqW/fvirbrl27RhYWFgSAQkJCsn1BN2/epI8++ogGDBiQbT3GipoXL16QlZWV+AQG/jcDrrbJ+tLS0mjKlCnizAulSpWigwcPFnCvC45KWMXHx2u8ZCMi2rZtGwGg33//Xa2sRYsWBIC2bNmiVrZ3714CQE2aNBGfCk9ISFCbGUHp+PHj1KFDB/Hf79+/F4OyY8eOOj1ZHhoaqtIGY1Ixffp08YyqSpUqGp/CuH37Ni1atIi6dOki1q1Vq5bWqZOKC50/DVy3bh3Z2dmpLdYol8vFaYVv3ryptt/r16/FN/Tq1atElHm56eTkRFFRUWr1J0yYQBMnThT/feLECXH/7du369RXuVxOXbt21fWlMVZkJCYmimdKI0eOFLdnZGTQnj176LPPPhNXd6pfvz7Z2NjQwoULi/UDzEo6hZUgCNS8eXPatWuXWtmlS5fEMLl7967G/ZX3kbKGzfbt28nZ2Vm8x5WamkqBgYHk6upKr1+/FuuNHz9ebD83syY8efJE57qMFSU1a9akatWqUevWralVq1bk6ekpXhYqv4yNjembb76hFy9eFHZ3C4zWoQtK7969w/jx4zFu3Dj06NFDrfzixYvi96VLl9bYRvXq1XH//n08ePBA3Obr64uMjAz06NEDpqamSEhIgK+vL86fP48yZcqI9Xbt2gUAsLe3R5UqVXLqrqhSpUo612WsKFmxYgU6duyIhw8fqpVZWlrCz88PY8eORd26dQuhd4VHa1jFxsbi1KlTCA4OxsWLF7Fjxw6YmpqqBdbr168BANbW1qhYsaLGtpTjrJ48eaKyvW/fvujVqxdev34NCwsLWFlZqZTL5XIx4KpWrap1vBZjxUn79u1x5swZbNq0CSkpKTA1NUX16tXRuHFjtGzZEqVKlSrsLhYKrWGVmpoKhUKBihUr4uLFi3jz5g18fX2xe/dudOnSRa1+6dKlIZfLYWZmpvVgCQkJatuMjY21DmCTyWSQyWQgIg4qVqJ4eHjAw8OjsLtRpBhpK2jatClGjhyJ/fv34/jx43BwcIAgCBg1ahTev3+vVl8mk2kNquTkZADI9XNKJiYmqFatGgAgIyMjV/syVhIpR7rrgoigUCh0rp+amoqUlJRc90kulyM5ORmpqalqZbnpr9awyqp169bYsWMHjI2N8ejRI5w8eVIss7a2BpB5b4u0PBN97949AMjxiXJN6tWrByDzUYK8vFGMlQSRkZFo164dRowYkWNdhUKBNWvWoHr16qhevTratGmDrVu3aq3/7Nkz9OjRAxUqVEC1atXg6emJ2NjYbI8hl8sRGhqKDh06wNLSEs7OznB1dUWLFi2wadMm3Lt3D/fu3UP//v11f5G5uRvv4eFBACg6OlrcdurUKfETiufPn6vt8+rVK7H81q1buf4EQPlgJgA6evRorvdnrDg7fvy4ykK9X3/9dbb1ExISqE2bNmRvb0+hoaGkUCho3759ZGRkpHFK5IyMDKpZsyb5+PhQYmIiCYJAa9asIXt7e62Lqx4/fpwqV65MJiYm1KtXLzp9+rQ4PvLVq1c0bdo08dGiqlWr6vxacxVWQ4cOpVKlSqmsyCGXy8X5n48fP662z9GjRwkAubm55eZQoqtXr4r/EaNHj9Z5vytXrmgMT8aKizdv3tCKFSto165d5ODgoFNYDRo0iACoPTY3b948MjExocjISJXtwcHB9Omnn6o93rZ+/Xpq3Lix2iDtiIgIMjMzI2NjY7W2PtzfysqKzM3NdV5CLFdh1aVLF+revbvaduVYqMDAQLWyuXPnEgCaMGFCbg6lQvkGGxsb07lz53Ks/+zZMxo5cqTW0fiMFTfKpemzC6sbN26QkZEROTs7q5XFx8eTTCYjJycnlQGmvXr1orCwMLX6giBQpUqVVKZjfvLkiXjiMmPGjGz7KwgCHTt2jABQUlKSLi9RNawEQdA4yEwQBFq8eDFZW1trHKX+5MkTcnBwoM6dO6ukZHJyMtWuXZscHBwoPj5epw5p8u7dO/Ly8iIA5OjoSAcPHtSaxo8fP6b27dvzWRUrUSZPnpxjWCnXKxw8eLDGcnd3dwJAGzZsELf17duXNm3apFZXEARydHRU+b3u3r27+JhQenq6Tv329PTM9iHtrFRusC9duhSVKlVCkyZNsGTJEpw/fx5RUVHo1asXgoKCcPjwYbi6uqrd96pUqRJCQ0Nx/PhxTJw4EXFxcXj16hW+/fZbxMfH49ChQyhfvrzuN9I+YGlpiQMHDmDu3LlITk5Gp06d4ObmhhUrViA6Ohrnzp3DypUrMWnSJPTr1w8rVqyAo6Njno/HWHF04cIFANA6N3uzZs0AAEeOHBG39ejRAwsXLkRaWppK3aCgINStW1f8vZbL5Th27BgAoF27djp/8j9mzBhxtECOsibXP//8Q97e3lSuXDkqW7YseXh40KBBg2jVqlU6PXt08eJFGjBgADk5OVH58uVp6tSpBn8c4PXr17RgwQJq0aIFOTs7k7W1NTk6OlKvXr3owIEDGqeOYay40+XMqmrVqgSApk2bprF82bJl4ornSoIgUL9+/ahhw4a0b98+ioiIoGHDhtEnn3yi8khbaGioeG9Z0+0gQ1AZFNq4cWMcPnxYt5TToGHDhli3bl2e99dF2bJlMWnSJEyaNClfj8NYcZKcnCwuMKHtqsPGxgZA5ky8SjKZDBs3bsTOnTuxatUqZGRkoEOHDli+fDlMTP4/Po4fPy5+37hx4/x4CdpHsDPGig+5XC5+X7169WzrPn36VOXfMpkMvr6+8PX11brPy5cvxe+zPttrSDoNCmWMFR+aRpIDEAd1Zw02XSnPyvIThxVjJUDWZ2u1zY7y4sULAICdnV2u269Tp474/Zs3b3K9vy44rBgrAcqUKSPOaqIMpQ/duXMHQOa959xyc3MTv4+MjMxDD3PGYcVYCSCTycRZHG7fvq2xjvJ5v6+++irX7Tdr1gwWFhYAgBMnTuSxl9njsGKshOjduzcA4OrVq2plgiDg33//BQC0atUq121bWFjAz88PQOYng1euXNFpvwcPHiAkJESnuhxWjJUQfn5+sLGxwaVLl9TKYmJi8O7dO3h7e+f4aaE2c+fOhZOTEzIyMjBgwAAkJiZmW//58+f48ccf0a9fP53a57BirBj4cIS5JtbW1lizZg3i4uJUpoRJS0vDuHHjYG9vjxUrVuS5Dw4ODjh+/Dhq1aqFS5cuoWnTplizZo3Gvl25cgUDBw7E7Nmztd7w/5CMSMskVIyxIu/58+d49eoVunXrhnv37qF27dqYMmUKWrVqJU5c+aE//vgD48ePR8+ePdGmTRvs2rULz58/x5o1a+Du7q53n9LS0rB8+XIsXLgQz549Q4UKFeDt7Q1ra2s8f/4ct2/fRr169bBw4cJcravAYcWYhMXExIgj07NydHREixYttO737Nkz7N69G9evX4eXlxd69Ohh8KnD09PTcfDgQdy5cwfPnj1DRkYG6tati549e8Le3j7X7XFYMcYkge9ZMcYkgcOKMSYJHFaMMUngsGKMSQKHFWNMEjisGGOSwGHFGJMEDivGmCRwWDHGJIHDijEmCRxWjDFJ4LBijEkChxVjTBI4rBhjksBhxRiTBA4rxpgkcFgxxiSBw4oxJgkcVowxSeCwYoxJAocVY0wSOKwYY5LAYcUYkwQOK8aYJHBYMcYkgcOKMSYJHFaMMUngsGKMSQKHFWNMEjisGGOSwGHFGJMEDivGmCRwWDHGJIHDijEmCRxWjDFJ4LBijEkChxVjTBI4rBhjksBhxRiTBA4rxpgkcFgxxiTh/wDm8vsS/1MzxwAAAABJRU5ErkJggg==)
Three rods made of the same material and having same cross-sectional area but different lengths 10cm, 20 cm and 30 cm are joined as shown. The temperature of the joint is:
![](data:image/png;base64,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)
physics-General
physics-
A ring consisting of two parts ADB and ACB of same conductivity k carries an amount of heat H. The ADB part is now replaced with another metal keeping the temperatures T1 and T2 constant. The heat carried increases to 2H. What should be the conductivity of the new ADB part? Given
= 3:
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)
A ring consisting of two parts ADB and ACB of same conductivity k carries an amount of heat H. The ADB part is now replaced with another metal keeping the temperatures T1 and T2 constant. The heat carried increases to 2H. What should be the conductivity of the new ADB part? Given
= 3:
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lpcfiuKLsKvrGxERkZGejYsSOio6MhFovtORyDi8NisRAeHo6oqCjU1taioKAAFovFoTbYVfC3b99GRUUFkpKSGLEzAABEIhFiY2PBYrGQk5Pj8OZNdhM8IQTl5eVQKpVISkpimqAyAPjFy8fHx0MsFuPixYsOX3W1m+C1Wi1u3rwJo9GI5ORkphEqg42IiAiEhIQgMzMTRqPRobU1dhO8UqlEYWEhfHx8EB8f32aPSGFofXx9fdG9e3cUFRWhurraoXG83QRfVVWFyspK9O7dGyKRiGmsxGDDx8cHvXr1AiEEZ8+ehUajcdjYdlNhVlYWLBYLBg4cyCw2MdwBm82GTCaDQqHApUuXHLr9z26Cz8vLs62uMTD8FhaLBQ8PD0RERKCqqgotLS0OG7vVBU8IgcViQVlZGcRiMfz8/BgPz/AHRCIRQkJC0NTUhObmZoeNaxfBt7S0oLGxEV5eXvDx8WntIRjaAQKBAHK5HM3NzW3bw1MUhaqqKhgMBkilUvj4+DAenuEP8Pl8REREQKVSobm52WElBq0ueIvFgqqqKhBCEBAQwKQjGe4Kn89HZGQkaJpGdXW1wzZ3283Dc7lcBAUFMd6d4a5wuVzI5XIIBAJUVlY6LDVpF8FXVFSAz+cjKCiotd+eoZ3A4XDg5eWFwMBA1NbWQqvVOmRcu0xam5ubwePxmHJghvvCYrEQGBgIg8HgsCIyuwheq9WCw+Ew9TMMD8TDwwNms9lhXcnsIni9Xg82m820wGa4L9aTvU0mk8PqaewieJ1OBw6Hwwie4YGIxWKYzea2LXi9Xg+hUMj0fGe4LywWC2Kx2HZ0qSOwm4dnBP//WCwWnDt3Dlu3bnW2KS6HRCJxqOBbvZuptZbGw8ODKQn+Fa1Wi9TUVKSnp6OsrAyvvvoq0zn5V8RiMQQCgcMaM9lFkWaz2akNM10FQghMJhOuXbuG4uJiNDQ0YMOGDS515pGzIYQ4tAtZq3t4a1xmMBhcogG+M7Ee7/PPf/4TFRUV8PLywrx585hTT36DVqsFi8VyWAq71T08I/j/R6fT4ZtvvoG/vz9mzJgBhUKBbdu2IScnx2Eri66Mdb4HwGGb/O3i4UUiERobG91W8CaTCfX19aitrcXf/vY3BAUFQS6X4+bNm1i0aBEuX76MhIQEZ5vpEuh0Ooeu2dgtpFEqlU7rEOtMCCGorKzE2rVrodFosGrVKlvFaIcOHbB69WrExMSgubkZGo0GAQEBbj2512q14PF4DjsNxm4hDU3Tbid4a3rtvffew759+xAREXFHalYoFCIxMRG3b9/G7NmzMXfuXGg0Goe3m3MVrCENj8dzWArbboKnKMphuVVXgqIoREZGYvr06ZgyZcod3pvFYoHH4yEsLAzdunVDXl4eFi1ahObmZqeee+RMNBqNQwXf6s8RNpsNqVQKk8nkVuk3pVKJtLQ0SKVSTJo0CTKZ7J698L29vTFlyhQYjUbcvn3b4f0VXQWaplFVVYXOnTu33SwNh8NBaGgoTCaTU8/ycSRarRbp6en46KOPsGXLFojF4gce/BAdHY1FixZh2bJlMBgMyMvLc5nTqh0BTdNQqVSora1FQECAww65s4vgO3ToAIvFgpqamtZ+e5fk0qVL+Oyzz6DT6bB48WKEhIT8qb8Ti8WQyWR488038eKLL+LQoUNuE9qYTCaUlZWBoiiEhoY6bOXZboLncrmor6+35VnbIzRNo7a2FgqFwubdw8PD/1LGQSAQ4NVXX4Wvry9WrVqF9PR0t5jsm0wmlJaWgsvlIjAw0GFpSbsIPjg4GAKBAI2NjWhpaWmXXkuv16O8vBxvvfUWUlNT0b17d/Tu3Rt8Pv8v7eNls9lITEzE/Pnz0bFjR1tb8fZ4zX6LVfDWVi6OSs22+ihsNhs+Pj6QSqVoaWlxaJMdR9LQ0IC1a9fi5MmTsFgsMJvND3XTWCwWBAIBhg8fjlWrVqFLly44ceIEKioqHN473ZEYjUZUVFTAx8fHoaUWdvlasVgsREZGQq/Xo6mpqV16q7q6Oly5cgWTJk3CpEmT4O/v/0jvJxAIwOVyceDAATz33HNYtmwZamtrW8la18NgMKCqqqp9CB4AunbtCovFgvz8fHsN4XCsCyXfffcdysvLsW7dOsyfPx9SqbRV3l8ikWDEiBGYNWsWTp06hTVr1rTbkFCtVuPmzZsICwtzaHc6uwk+KSkJPB4PJ0+ebBc3zFrGunv3bmzYsAHHjh1DWFhYqzab4nA48PHxwYwZMzB27Fh07doVXC4XZrO5Xa3GWr17dXU1evbsCU9PT4eNbbcChsDAQMjlcly6dAlqtRpeXl5tumaEEAKlUon169fD19cX48ePt0tXNS6Xi8jISLz33nvQarU4f/48VCoVhgwZAm9v73bR2Eqj0SArK8t2qp8jz/+ymwL9/f1tRVK5ubltOtVGURT0ej18fHzw97//He+//z4GDRpk1zH5fD7Kysrw0UcfYe7cucjMzGw3m2oaGhqQlZUFhUKB4OBgh7ZjtJvgBQIBoqKi4OHhgYsXL7bZuhpCCLKysjBz5kx8+OGHGDp0KOLi4hwydlxcHD744AMEBgbi448/xtmzZx0yrr0pKSlBbW0tevfuDR6P59Cx7SZ4NpuN8PBwSKVSXLp0yWHNMlsTQghKSkqwbt065ObmIi4uDr6+vg7zSCKRCF26dMH777+P559/HuHh4VCr1W16TkQIQX5+PvR6PZKTkx3ebNeuQXVoaCgiIyNx+fLlNlcGS9M0DAYD1Go1zGYznn76aTz99NMO76YmFosxatQoTJ06FfX19fj0009RWFjYZp+YarUaN27cAJvNRteuXduPhwd+Oa1tyJAhKCwsRGFhYZtZSLGmHzMzMxEUFIS1a9fi7bffdtrEm8ViwWw24+zZs9i0aROWLVuG+vr6NuVAgF+ua1lZGYqKihAYGIjOnTu3L8F7eHigf//+kMlk2LVrF+rq6uw5XKvR3NyM1NRUTJkyBWvXroVOp3PYjpx7IRAIMGHCBMyZMwcHDx7E/v3721x1JSEE586dg0ajwfDhw8Hj8RyedbLrXbTmlfv374+cnBwUFRVBLpfbc8hWITc3F1u3bkWnTp0wfvx4eHp6Oj0dyGaz4e/vj+nTpyMwMBD9+/dHXV0d9Ho9goODnWrbn8HasmTv3r0Qi8UYPHiwU66p3Z/PIpEIKSkpUKlUuHLlisumJ60NpG7fvg02m42nnnoKb7/9NhQKhUPzxPeDx+MhICAA06ZNA5/Px7p16/DVV1+hvr7e5VOWJpMJBQUFyMvLQ3x8PMLCwpxih90FLxQKMWDAANA0jezsbDQ1Ndl7yIfCYrGgtLQUb7zxBm7duoU5c+ZgyJAhLiP230MIQVNTE7Zu3YodO3a4/CRWq9UiLS0NNE0jMTHxgRtk7IXdBc/j8RAbG4uYmBgUFBSgqKjI3kP+ZQghqKurw5w5c5Cdnf3QlY+OJCQkBK+//jpGjhyJqqoqmM1ml05XajQapKenIzg4GHFxcU4LEe1+V60bl5977jlQFIUtW7a41M0hhIAQApVKBT6fj9mzZ2P48OHONuuBWEsQ3n33Xfz973/HoUOHkJqa6pKJAa1Wi7y8PGRlZaFv375QKBROs8VhqYfBgwfj8OHDOHfuHHJyctC5c2eX6B9fXV2NgoIC+Pj44L333kNsbCy8vLycbdafQiwWQywWw2QyIT09HSUlJWhoaMALL7wAsVjsMk+puro6/Pe//4VYLMaUKVOcehSSw65IWFgYRowYAZqmkZqa6rBT2+4FTdPQ6XT44Ycf8M4772D//v1ITk5ukwVaPB4Ps2fPhre3N7799luUlJTAYrG4xFOUoihkZmbi+vXrGDduHMLDwx3WVu+uEAdSUlJCJk2aRORyOSktLSUURTly+DvQ6XRkz549pFOnTuSZZ54hpaWlhKZpp9nzqJhMJpKfn0/2799PjEYj0Wq1xGw2O9ssolQqySuvvEJiYmLI1atXidFodKo9nMWLFy921JdLKBQiMDAQu3btgre3N2JiYhzWnuG3GI1GqFQqSKVSSKVSPPvss1AoFE5fXHoUOBwOPD09IZPJcOLECSxcuBBCoRBhYWFODR3Pnj2LPXv2YNCgQZgwYYJTFpt+i0ODPJFIhLi4OAwbNgz79u3DzZs3Hb48rtfrcfXqVbzxxhsoLy/H888/j8TERJeYTzwqAoEAEokEQUFBqKmpwZo1a5CZmemU0IaiKGg0GnzzzTcQiUSYNm0ahEKh0+cVDh/d29sb06ZNQ11dHY4ePerwWL6iogJr167FqVOnUFVVBZqm27Rn/z0SiQQJCQlYvHgxfH19cfnyZej1eofvmjIajThz5gyuXLmCvn37IioqymFj3xdHx1A0TROTyURmzpxJBgwYQI4ePerQ8detW0eGDBlC1qxZQ3Q6XZuO2++H2WwmBoOB1NfXk/T0dJKXl0f0er1DxqZpmlRWVpIRI0aQoUOHksuXL7vMdXa4h2exWOByuZgxYwYkEgm++OIL1NfX27WXvLWt29atW9GjRw+sXr0azz77LAQCQZvLyPxZuFyurTfQxo0bMXPmTJw/f94hpR2NjY3Yv38/rl27hldeeQUKhcJlrrNTAioWi4WYmBj0798fpaWlOHDggN02iJBfV1HXr1+Pzz//HEVFRYiPj3ebvuwymQxjx46FUqlEamoqWlpa7DoeRVHIz8/Hf//7X/Tu3Rs9e/Z0qQPcnBa8enh44Mknn8TFixfx1VdfoV+/fggPD2/1HTCEEGRnZ2Pbtm2IjIxE586dXcbbOAI/Pz+MHj0aBoMBnp6eUKlUMBqNCA4OBofDafVr0dzcjJ9++gk1NTVYuHAh/Pz8XOt6OzOeMhgMZM+ePcTb25u88847pLKyslXfn6IoYjAYSG5uLnn11VdJZWUlsVgsrTpGW4GmaaJSqcgXX3xBhg0bZpdrQdM0+eGHH0hiYiKZNGmSS6wD/B6nPtN5PB4SEhLw7LPPIjU1FceOHWu15qtmsxkZGRlYsGABrly5gnfffddtwpi7YT17y8vLC7dv38abb76JW7dutdr7G41GXLp0CZ9//jn8/f3x2muvueTB1E69+2w2GwEBAZg1axZ8fHzw7bff4vLly4+cPjMYDCgqKsLy5ctRVFQELy8vyGQycLlc13q8Ohgul4shQ4bghRdeAIvFgl6vb5USBIvFAqVSiTVr1kCr1WLcuHFOrYi8H053d9ad+QsWLEBTUxPWrFmDioqKh87aWI/aKSgogFqtxqRJk9C/f/9WtrrtEhwcjPnz5+Pdd9+F0WhEWloalErlQ4ueEGLbEnn48GGMHj0ao0aNcqmJ6h04OaSyYTQayVtvvUUUCgVZtGgRUavVD/U+DQ0N5OrVq0SlUpHi4uI/5J5pmnaZnHBrYv1c93r9/ndNJhOZOHEiiY+PJ1999dVDx9tms5ns2bOHxMbGklGjRpHCwsLW+Dh2w6G1NPeDzWYjIiICt2/fxq5duxAZGYmQkJC/1BajqakJq1atwsqVKyGVSpGQkACRSAQWiwVCCCiKwoULF8Dj8Rzaz9De0DSN3NxcFBYW4ubNmygtLUVFRQVqa2tBURRomgaHwwGbzQaLxQKLxQKbzUZ0dDQKCgpw+PBhPPbYYwgICPhLq86EEFy+fBmffPIJWlpasHLlSkRHRzu8E8FfwWUEbz39LygoCNnZ2Th9+jQ6dOiAoKCgP1VOStM0jh07hu3bt0Mul2Py5Mm2uB34JdQpKCjAZ599Bi6Xi65du7pkjPmwaLVa7NmzB9u2bUNlZSX8/PxgsVhw4cIF7NmzBzk5OfD394e3t7ctHenl5YWIiAj4+/uje/fu0Ol04PP5f0qwJpMJOTk5+Oijj1BTU4M5c+Zg2LBhEAqFLn1dXUbwwC9ZGy8vL4SFhWH//v3IyclBYGAgQkND73myBvm1q29dXR0aGhogFosxdepUdO7c+Y4sgdFoxMGDB7Fz504YDAYMGjTI5v3bOiwWC76+vlyBBH8AABb8SURBVKipqUF6ejr69++PF154AV26dEFoaCiUSiX+85//wGg0IjEx0RZf83g8hIaGIiEhAefPn8e3336L0NBQyGSy+2ZY9Ho9KioqsGTJEuTl5WHMmDGYOnUqPD09XT4L5nLW+fj4ICUlBYsXL4ZSqcRHH32EU6dOwWQy3XViZTKZkJ+fj+XLl6Njx45488030b179zt+x/qlOHnyJIRCIQoLC3Ht2jW7ljM4A5FIdEdFIpvNRmhoKCZPnoy4uDikp6cjKyvrjr+xNnmqq6vDgQMH8MUXX0CpVN5zDIqiUF5ejg8++ADp6ekYPXo0Xn75ZchkMpcXO+CCggd+KXN94okn8NZbb8FoNOL1119HWlraHyoraZrGhQsXMH/+fBw9ehRms/muHlun0yEnJwfBwcGYOXMmAGD37t1ucT4qTdM2QQO460q2RCLBc889h9mzZ9t6t9+LkpISfPzxxzh8+DAmTpyIGTNmQCaT2c3+1sYl62JZLBY8PDwwcuRIaLVarFmzBkuWLIHZbMbgwYPh6+sLmqZBCEFpaSkEAgHeeOMNhISE3FXwzc3NOHz4MMaMGQOZTIacnBykpaWhrKwMkZGR7aIW3orJZEJFRQUKCwvB5XJRXV2N8+fPQ61W4/nnn8djjz32h7/hcDjw8vLC5MmTMXLkSJhMJnz99dd46qmn4OvrCzabDYqiUFhYiJUrV+LcuXMYMmQI5s2bh5CQkPvG/MXFxaiurobFYgGbzba1W+RwOOBwODCZTPDw8EBMTAz8/Pzsdl2sPLTgVSoV9Hq9beZvDQ+sjzWapm0bEh521u7v748xY8bAaDTik08+wYoVK0DTNPr374+GhgZYLBY89thjWLRoEbp3737XCRNFUairq4NGo0FMTAx4PB569+6Nw4cP4+DBg5g2bVq7EjwhBDdu3EBaWhooisL169dx/fp1SKVSDB48+L4JgJCQEEilUluhncViwdixYyGRSFBVVYXly5fjwoULUCgUeOONNxAZGfnAe5uZmYnz58+jU6dO4PF4OH78OBobGzFw4EBIpVKUlJSgvr4er776qmsLPj09Hfn5+bbYrbKyEsAvJ3+wWCwolUqEhYVh9OjRj/RBgoOD8dJLL4GiKKxZswaffPIJGhoacOTIETQ1NeF///d/77uwpNfrUVhYCE9PTxQVFUEgEIDH4yEoKAgHDx7EqFGj4Ovr2y4mrwBsJwLOnDkTYrEYRUVF+OGHH7B582asXLkSb7zxBgYMGHDPz8vn8zFy5Ej8+OOP+OqrrxAUFITo6GgsX74chw4dwtChQ/H6668jMTHxT9mj0+kwdepUJCUlgaIoXL58GdXV1RgxYgQSEhJgMBiwYcMGNDY2tuZluCcPJXiKolBaWoqePXuiT58+MJvNePHFF0EIwWeffYagoCAUFBTgyJEjaGxsfGRBSSQS/OMf/4C/vz9WrFiBN998ExRF4eOPP0bnzp3v+7e3bt3CiRMnEBsbi7KyMrDZbBgMBvTu3RsbN25EUVERIiIiHN4G2xFwOBwoFArMmTMHvr6+WL16NdatW4fHHnvsnt0Z2Gw25HI5vvzySxw+fBhcLhfvvPMOTp06hWeeeQavvfYaIiIi/rQNiYmJiI6Ovuv/sVgsCIVCpKSkOKyTwUMLvmfPnoiKioJEIoHJZILFYgFN0xAKhZBIJIiOjoZWq22VmTubzYZEIkG/fv2g1+uxbt06FBQUgM/nw2g0ghByz5TllStXEBAQgIkTJ9pqaWiaRnJyMn766Sfs3r0bXbp0QWRk5CPb6WpYm2B5enoiLi4OQqEQWq32gdkpPp+PiIgIdOnSBZ9//jmuXbuGoUOHYsGCBZDL5X+phLtr16731YB1b8TdMnD24KEEz+Fw0KNHj/t6bS8vL/To0QMmk+mRwwWz2YzKykps2rQJkZGR+Pe//41FixZhw4YNMJvNGDVqFEJCQmzzCeCXOUR9fT1ycnKQkpKCwMDAO96TxWKhf//+uHTpErKzsxEaGurSK4QPgvzaDNZkMsFsNsNgMIDP58NisaC5uRk3b94En89H586d79sv02KxoKWlBZcuXcKyZctQVVUFHo+HlpYWiESiv1wB+Weuqcuf8cThcCAUCu872bOunD7qGZzW7Xlr1qxBamoqbt68iaSkJKxYsQIeHh5YtWoVVqxYgeLiYhgMBtA0bWuydPz4cSiVSnh6et7h1awZnvDwcOh0OqSlpaG+vt4lGhc9LHq9HpWVlaBpGtXV1bh8+TJyc3ORlZWF7777Dt988w0GDBiA559//p4Lbtb05Y4dOzB37lzU1NRg8uTJeOmll1BdXY38/HzodDq7r1+QX9sf2gOXTEv+FpPJhKysLOzZswdjxozB7NmzERwcjICAAMTHx2PFihX48ccfcfLkSXzxxRdISEgAj8ez3ZwePXrg1q1biIiIQGBgoC2Gv3btGoKCgjB37lxwuVycOnUKo0ePbpOrrxRFYf/+/eBwOHjxxRfBZrNRVlaG8vJyCAQCJCYmYty4cQgMDLxnrGxN8S5btgyHDh1CbGwsVq5ciaioKLBYLLz00kuwWCwoLi5GWFjYI588fr/PYrFYwOFw7NJNwqUFX1lZidLSUigUCqxfvx4xMTHw9/e35XADAgLw2muvoWvXrti4cSPmz5+PZ555BhMmTECnTp0QFRUFQgi4XO4dQubz+ejVqxcSEhJsnoTL5bp8Hci9YLPZGDly5F17xLPZbPD5fAiFwrtu6aMoCk1NTTh06BC+/fZbNDc3Y/r06Zg4cSIUCoXtC8Ln87F3716sX78eAwcOxLx581q1lMBkMqG2thbbt29HYWEhAgMD8cQTT6Bnz56tGmo6TPAqlQo1NTWgKAqdOnW67+9SFAWlUolvvvkGly9fxiuvvIKUlJQ/xI88Hg9hYWEYP348QkJCsGrVKuzevRu5ubmYMmUKEhMT73rqHpfLBZfLdUrXM3vAYrHg7e39l/6GEIKWlhYUFxdj9+7d2L9/P7y9vfE///M/eOKJJxAaGnrH73M4HMTHx8PPzw/Hjh1DSkoKevbs2WqCN5vNOH78OAQCAXr16oWMjAwsW7YMa9aseeDi1l/BIYKnaRoFBQXYtGkT/Pz88OGHH973981mM44cOYI9e/YgOjr6vsfkWG/2448/jqioKGzbtg07d+7E1atXMXHiRIwdOxZyuRxisdglt5w5GpqmYTKZbGsZO3fuxPXr19GnTx/MmzcPiYmJd53UcjgcdO7cGfPnz8exY8dA0zSUSiV8fX3/VLsTa3m2xWKxvWiatn1hKIpC9+7dERsbCw6Hg+joaLz77rvIy8uDv79/qwneIbU01tprPz+/B/ZFoWkaFEXB09MTjz/+OP71r38hOjr6gWJlsViIiorCwoULsWPHDiQnJ2PdunV48cUXsXPnTqhUqjZ36p090Ol0uHLlCqZPn4733nsPhBB8+eWX+Oabb9C7d+8H5sN79eqF+fPnQyAQYP78+cjOzn7gJJYQArPZjKamJpSUlKCurg5lZWXQ6/W2kNLT0xOdOnWypY59fHwQFhaG2NjYVs3iPLKHp2kaTU1NMBgMoCgKKpUKwcHBf3jU8Xg8CIXC+wpeqVTi0KFDuHbtGmbNmoV+/fpBIpH86ccmm822nQD+/vvvY8KECfjxxx+xdu1a7Nu3D88++ywGDRoEf3//dlVO8CCsma6srCzs3bsXFy5cgJ+fH5YuXYo+ffogODj4Ty/8WDN0bDYbhYWFWLFiBd566y307Nnzvn9nMBhQXFyMsWPH2spObt++DYVCYZtbWJ8SZrMZWq0WQ4YMQYcOHVp18vpI72Sd8Fy/fh1BQUG2czilUukdmy+AX8R4L+GSX89FPXDgANatW2e7ATKZ7KEmkUKhEHK5HMHBwYiOjsaRI0dw+PBhfPXVV0hLS8Pjjz+OhIQEhIWFPVRuua2g1+tRX1+P/Px8ZGRk4Pz58+Dz+Rg6dCjGjRuHmJgYeHl5/eVrzOVyERsbi5dffhkZGRm4ceMGEhMT77tJXigUolOnTrb5G4vFuuskmqZpVFVVobKyEkOGDLnnPoiH5ZEEby099fPzw4IFCwD84gGMRiMoivpT30yapm2LIz///DM8PT2xYMGCVqlv4fF4tjnA8OHDkZqail27diErKwudO3fG6NGj0a9fP/j6+kIkEoHH47WJmu57YV18MhqNUKvVuH79Ovbt24fTp09Dr9dj+PDhGDt2LPr27ftIbQZZLBYkEgkmT56M/v37g8vl4vjx40hKSoKnp+cf4m0WiwU+n//A0MSarEhLS0NSUhKioqJsayatJvpH3RT7ZzYNE/LLAQRLliwhr7322h3/rtfrSWFhIVGpVCQvL4/cuHHDLpusaZomFouF3Lp1iyxdupTExcURPp9PevToQT755BNy5coVotFonHpIw6Oi1+tJUVER2bFjB/nb3/5G/Pz8SEhICJk8eTK5evUq0ev1rX5tjUYj+frrr4lcLidLliwhtbW1D/U+NE2TlpYWsn79enLp0iWi1WqJRqMhZWVlrXqIAosQxywv6vV6fPrpp2hqasKnn34K4Jd9mJmZmVi4cCFGjhyJGTNmICAgwK5LzSaTCWq1GmVlZcjIyMCuXbvQ0NAAgUAAmUyGYcOGYcSIEejYsSO8vb3vKFdwNSiKsoUtGRkZOHz4MIqKiqDVasHlcjFs2DCMHTsWCoXClulo7ScYIQRFRUVYtmwZTp8+jQ8++MC2gPdXqK2txebNm3HgwAF4e3tDIBBAJBJh/PjxGDFiRKulkB2WhzcYDLbif5PJBB6Ph5ycHPznP/+ByWRC37594e3tbfe6Cj6fD6lUCm9vb4SHh2PQoEHIzMzElStXUFBQgB9//BFHjhxBfHw8OnfuDIVCgfDwcPj7+0MikYDP5zsl7CG/Zjr0ej1UKhXKyspQVlaG/Px8XL16FTU1NRAKhVAoFEhISEBiYiK6dOmCgIAAu07QWSwWQkND8eabb0Imk0Eul0OtVoOiqL/Um8a6GBgZGWnL+giFQiQnJ7fqwpPDPPzNmzdx4MABaDQaTJ06FTKZDEePHsXGjRsxduxYPPPMM05r3kPTNNRqNXJzc5GdnY2MjAxcu3bN1nRULpcjPj4e3bp1Q1xcHDw8PCASicDn821L4Gw2+5Gbk5Jfa0gsFgsoigJFUTCbzTAajdDpdLh16xays7ORl5dn20lkNBoRHh6OAQMGoG/fvoiPj0doaKjDn0rk133DxcXF2LdvHwYOHIgePXo4/Yib3+MwwVuhKAotLS3Iz89HTEwMPDw8XG5J32KxoKqqCmlpaThx4gRu3LiBsrIyNDY2ws/PD71790b37t0RExODoKAgyGQyyGQy+Pn53fUJda/P9vtLb7FYoFaroVQqUV9fj9raWpSXl+P69es4c+YMysvLweVyIZfLER0djT59+iAlJQVJSUkuk2natWsXPvroI1AUhe+///5P7YpyJA4VvLWSb8mSJbh69Sr++c9/YuzYsS6XGbF6Wb1eD71eD51Oh5aWFhQWFiIjIwM5OTm2x7a1NyOHw4FIJIJcLoe/vz88PT3h6ekJDw8PeHh4wNvbGxKJBHq9HhqNBmq1+o6fjY2NuH37Npqammyb0dlsNrhcLng8HhQKBQYMGIBevXrBx8cHEokEIpHI1qnAVVCpVNi9ezc2btyIadOm4bnnnnOptnsOFXxzczO2b9+O5cuXY9y4cZg9ezYiIyNdyrvfC2vPSqVSiaamJtTW1to8cV1dHerr66FUKqFWq23L5taf1o0YUqkUdXV1d6TauFyurSuYWCyGn58fAgIC4O/vb3vJZDL4+/vDz88PXl5eLn8mVV1dHS5evIiIiAgUFRWha9euiIyMdAnH5jDB63Q6NDU14fTp0zhy5AgWLVrU6qtozsJsNkOlUqGhocG26mwymWwvo9Fo2xVGUZTNM1v31/L5fAgEAnh5ecHPzw9SqbTNrwmYzWZkZmZi8eLF6N+/P15++WUEBQU52yz7C54QYmuDJxAIbOWerhJzMtgHmqbR0tKCWbNmITc3FzNmzMDcuXOd/jS3u3vV6XQ4deoU3n77bXTq1Mk20WNo37DZbHh7e2Pp0qXYt28fevbsCb1e7/SzWu3q4QkhqKysxMyZM6HRaDB//nwMGzbMpSYxrQkhBHq9Hjk5OaioqIBarbZtvrDG8YGBgZDL5fD29nbYTn1nYjQaodVqUVZWhi1btuCpp55CcnLyX67fby3s5uGNRiOMRiMsFgsSExMxePBgJCQktFuxW+FwOJBKpdiyZQvS0tLQo0cP9OrVC3w+H1VVVaiqqoKXlxdGjx6Nrl272m2rnKsgEAhsO85Onz6NnJwcLF26FD179nTO/K3VihR+A0VRpKysjGzevJmcOXOmXR5AcD9omibr168n4eHh5PvvvycqlYoQ8kutS3Z2Nhk7dixJSkoiq1evJkaj0S2uj0qlIqmpqaRTp05k2bJlRKVSOaVuqdWDKYqi0NzcjH//+99Ys2YNLly40Ka7ATwM1vDl9x5MIBCgU6dOWL58OeRyOTZt2oRTp0455LBgZyORSDBq1Cjs2LEDkyZNglKpRF1dncMb2ra64M1mM06ePImSkhIMGTIEzzzzjNNn5s7gtxsafvtvfD4fYWFhGDhwIHQ6HVJTU+12KLMrwWazIRKJEBcXh/Lycrz99tv48MMPoVQqHSr6VhM8IQQqlQrV1dWIjIzE+PHj8Y9//ANyudwtBX8/hEIhoqKiwOPxcPbs2bt2G2ivcLlc26ELP//8M9LT02EwGBw3fmu9kVarxcmTJ5GRkYH58+djzpw5TK79PljrbtRqtdvttY2MjMSCBQtAURT4fD5aWlpsbVLsTat4eJqmkZ6ejvfffx/nzp1rlbM/2ztarRY0TSMwMNDtHAOLxUJERARWrFiB5ORkbNmyBYcOHXLIiSyP7OEJIdBqtUhLS0NQUBBmz56NDh06uN1N/CvQNI3y8nKYTKZWbzTUVrD2BWpubkZ2djbS0tIgEokwePBgu9bvP5KH1+v1trLZSZMmYe7cuejfv/8j7Zds79A0jYqKCpw/fx4SiQRPPPGES1U7OhIWiwWZTGY7dOHcuXMwm812DfEe2sObzWaUl5dj7dq1CAsLw9SpU//QodcdIb/p4muxWGAwGGwnpVgsFmg0GmzZsgWFhYUYM2aMzUG4IywWCyKRCKNGjUJsbCx4PB4qKirg5+d3145xrcFDC76yshIbN27E9u3bsXDhwnZR9fiokF+34ZWXlyM/Px+NjY04d+6cLSd/69YtXLhwASaTCbNmzWqzzVtbGy8vL3Tp0gWlpaW23kFz585FTExMq4/10CpVKpWoqanB9OnTMWHCBHh5ebWmXW0W8mvz1tGjR6Nv377w9PSERCIBh8NBVFQUhg8fDolEgoCAAIjFYrcXO/D/C3VBQUF47rnnsGfPHkgkErz33nutfo0eunhMqVSiuroaQqEQkZGRjIf/FWurwN9fVusOJmYyf28sFgsqKyuxbds2REdH46mnnmr1RkwO39PKwPAgzGaz3ZwDI3gGt6Lt7iFjYHgIGMEzuBWM4BncCkbwDG4FI3gGt4IRPINbwQiewa1gBM/gVjCCZ3ArGMEzuBWM4BncCkbwDG4FI3gGt4IRPINbwQiewa1gBM/gVjCCZ3ArGMEzuBWM4BncCkbwDG4FI3gGt4IRPINbwQiewa1gBM/gVjCCZ3ArGMEzuBWM4BncCkbwDG4FI3gGt4IRPINbwQiewa1gBM/gVjCCZ3ArGMEzuBWM4BncCkbwDG4FI3gGt4IRPINbwQiewa1gBM/gVjCCZ3ArGMEzuBWM4BncCkbwDG4FI3gGt+L/AHIbCJSd3sYBAAAAAElFTkSuQmCC)
physics-General
physics-
Two sheets of thickness d and 2d and same area are touching each other on their face. Temperature TA , TB , TC shown are in geometric progression with common ratio r = 2. Then ratio of thermal conductivity of thinner and thicker sheet are
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)
Two sheets of thickness d and 2d and same area are touching each other on their face. Temperature TA , TB , TC shown are in geometric progression with common ratio r = 2. Then ratio of thermal conductivity of thinner and thicker sheet are
![](data:image/png;base64,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)
physics-General
physics-
Heat is conducted across a composite block of two slabs of thickness d and 2d. Their thermal conductivities are 2k and k respectively. All the heat entering the face AB leaves from the face CD. The temperature in °C of the junction EF of the two slabs is :
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)
Heat is conducted across a composite block of two slabs of thickness d and 2d. Their thermal conductivities are 2k and k respectively. All the heat entering the face AB leaves from the face CD. The temperature in °C of the junction EF of the two slabs is :
![](data:image/png;base64,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)
physics-General
physics-
One end of a 2.35m long and 2.0cm radius aluminium rod
is held at 200C. The other end of the rod is in contact with a block of ice at its melting point. The rate in
at which ice melts is [Take latent heat of fusion for ice as ![open fraction numerator 10 over denominator 3 end fraction cross times 10 to the power of 5 end exponent J times k g to the power of negative 1 end exponent close square brackets](data:image/png;base64,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)
One end of a 2.35m long and 2.0cm radius aluminium rod
is held at 200C. The other end of the rod is in contact with a block of ice at its melting point. The rate in
at which ice melts is [Take latent heat of fusion for ice as ![open fraction numerator 10 over denominator 3 end fraction cross times 10 to the power of 5 end exponent J times k g to the power of negative 1 end exponent close square brackets](data:image/png;base64,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)
physics-General
physics-
The graph shown in the figure represent change in the temperature of 5 kg of a substance as it absorbs heat at a constant rate of 42 kJ min–1 The latent heat of vapourazation of the substance is :
![](data:image/png;base64,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)
The graph shown in the figure represent change in the temperature of 5 kg of a substance as it absorbs heat at a constant rate of 42 kJ min–1 The latent heat of vapourazation of the substance is :
![](data:image/png;base64,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)
physics-General
maths-
Consider the circles,
and ![S subscript 2 end subscript colon x to the power of 2 end exponent plus y to the power of 2 end exponent minus y plus 1 equals 0](data:image/png;base64,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)
Statement‐I Tangents from the point P(O, 5) on
and
are equal
Statement‐II Point P(O, 5) lies on the radical axis of the two circles.
Consider the circles,
and ![S subscript 2 end subscript colon x to the power of 2 end exponent plus y to the power of 2 end exponent minus y plus 1 equals 0](data:image/png;base64,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)
Statement‐I Tangents from the point P(O, 5) on
and
are equal
Statement‐II Point P(O, 5) lies on the radical axis of the two circles.
maths-General
maths-
Statement‐I Angle between the tangents drawn from the point P(13,6) to the circle
is 90.
Statement‐II Point
lies on the director circle of S.
Statement‐I Angle between the tangents drawn from the point P(13,6) to the circle
is 90.
Statement‐II Point
lies on the director circle of S.
maths-General
maths-
The common chord of two intersecting circles
and
can be seen from their centres at the angles of 90°& 60° respectively If the distance between their centres is equal to
then the radii of
and
are‐
The common chord of two intersecting circles
and
can be seen from their centres at the angles of 90°& 60° respectively If the distance between their centres is equal to
then the radii of
and
are‐
maths-General
maths-
If the two circles,
and
touches each other, then‐
If the two circles,
and
touches each other, then‐
maths-General
maths-
Pair of tangents are drawn from every point on the line 3x+4y=12 on the circle
Their variable chord of contact always passes through a fixed point whose co‐ordinates are ‐
Pair of tangents are drawn from every point on the line 3x+4y=12 on the circle
Their variable chord of contact always passes through a fixed point whose co‐ordinates are ‐
maths-General
maths-
The locus of the centres of the circles which cut the circles
and
orthogonally is ‐
The locus of the centres of the circles which cut the circles
and
orthogonally is ‐
maths-General