Physics-
General
Easy
Question
A light ray gets reflected from a pair of mutually perpendicular mirrors, not necessarily along axes. The intersection point of mirrors is at origin. The incident light is along y = x + 2. If the light ray strikes both mirrors in succession, then it may get reflected finally along the line:
![](data:image/png;base64,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)
- y = 2x – 2
- y = – x + 2
- y = – x – 2
- y = x – 4
The correct answer is: y = x – 4
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physics-
A glass prism of refractive index 1.5 is immersed in water (
= 4/3). Light beam incident normally on the face AB is totally reflected to reach the face BC if
![](data:image/png;base64,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)
A glass prism of refractive index 1.5 is immersed in water (
= 4/3). Light beam incident normally on the face AB is totally reflected to reach the face BC if
![](data:image/png;base64,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)
physics-General
physics-
A slab of high quality flat glass, with parallel faces, is placed in the path of a parallel light beam before it is focussed to a spot by a lens. The glass is rotated slightly back and forth from the vertical orientation, about an axis out of the page as shown in the figure. According to ray optics the effect on the focussed spot is:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKMAAABfCAYAAACEPHfiAAATXUlEQVR4nO2de1hN2f/H35VuKh2pZMJRjuiCYTBPlHtlhIbBjIyMeYyR0ZiR6XGd4jGmcUnylEuiQuMe41JGMV2UW0imkTqTRCe6iNLtnM7n94ef83zPdDvpnLM39ut5/LHX/qy13jnvvfdaa6+1tgYRETg4WIAm0wI4OF7DmZGDNXBm5GANnBk5WANnRg7WwJmRgzVwZuRgDZwZOVgDZ0YO1sCZkYM1cGZkGUSEiooKpmUwAmdGFnHx4kWMGTMGvr6+TEthBM6MLCArKwseHh44ceIEDh06hCtXruD+/ftMy1I/xHL8/Pzok08+oby8PKalKJ2HDx/SV199RTNnzqT79+/L0iMjI2nevHkMKmMGVpsxKSmJxo8fT0lJSTR27Fim5SiNZ8+ekZ+fH7m6ulJ6enqj82KxmPr06UMFBQUMqGMOVptx2LBhdOvWLSIimjp1Kp09e5ZhRe2jtraWtmzZQk5OTnTq1KkWY0NDQ2nx4sVqUsYOWGvG7OxsGjJkiOz43LlzNH36dAYVtZ8VK1bQkiVLSCKRtBpbU1NDVlZWVFxcrAZl7IC1HZiYmBjMnj1bduzi4oJr167h+fPnDKpqH7NmzUJSUhK0tLRajdXT04O3tze2bt2qBmVAQ0MDhEIhhEIhSkpK1FJnI5i+GprD3t6eioqK5NK+++47OnjwIEOKlMPkyZPp9OnTCsVWVlYSn8+n8vJylWrKysqioUOHEgByc3MjkUik0vqaQ4OIfWtg8vLyMH/+fPz1119y6cnJydi5cydiYmIYUtZ+rly5gqVLlyItLa3FuLKyMgQEBODo0aMAAAsLC5XoefHiBfLz8wEAWlpaMDIyAp/Pf+Pyjh49ij59+rxZZkYugVbYunUrbd68uVG6RCKh3r17K9TmYjOjR4+mS5cuNXlOLBZTcHAw2dvbU1RUFD158oR69uxJFRUVJBaLlf6vvr6eoqKiyMTEhADQ8uXLqbq6+o3Law+sNOPEiRPp7t27TZ6bOXMmXb16Vc2KlMuff/5JLi4ujdLj4uJo0KBBtGrVKqqqqpKlL1u2rMmLU5k8efKEYmJiKCYmhrKzs1VaV3Ow0oy9e/cmqVTa5LmgoCAKCQlRSj1SqZT27dtHn3/+Oc2dO5eEQqFSylWEoUOH0vXr14mI6N69ezRx4kSaMWMG5efnN4oViURkbW1NtbW1atPHBB3euHGgIoRCIXr16gUNDQ0AQElJCbKzs2XndXR0cPLkSQwYMKBd9YhEImzevBkZGRkwNzeHt7c3CgsLUVhY2K5yFWXKlCnw9fXF4MGDkZaWhk2bNmHkyJFNxlpYWMDNzQ379u3DwoUL1aKPCVhnxsuXL2PEiBF49OgRNm3ahLy8PPD5fJk5GxoacP36dRw5cqRd9RQVFSE3NxcAUFdXh9TUVLUOaRAR7t69i3HjxiE9PR2ami2Psvn5+cHNzQ3z589Hhw6s+9mUA9O35v/i6elJbm5u5O7uThcvXmwyZvjw4fT48eN21/Xy5Uvy9fUle3t7cnV1VetjmogoOjqavLy8FI738vKi6OhoFSpiFtaY8fbt2/TFF1+Qqalpq+Nw8+fPp8TERDUpUx2v30E/ePBAofh//vmHHBwcmm1Pv+0w/gYmLS0NHh4e2LJlC1avXg0ejwd3d/cW8/Tt2/edmGLVoUMH/PDDD9i4caNC8f369UPfvn0RGxurYmUMwdRVEB8fT66urrRw4UL6999/iYiovLxc7n10c5w5c4Z8fHxULVEt1NTUUK9evRR+B52RkaHQ/9HbiFrvjESE48ePY/To0bhw4QIiIyOxY8cOWFlZAXg1ydTBwaHVcvr374+srCxVy1ULr99BBwUFKRQ/ePBgmJqa4vz58ypWxgDqcLxYLKbIyEgaMWIE+fv7U1lZWZNxERERFBgYqFCZNjY2ypTIKC9evCA+n0/Pnj1TKD4lJYVGjhypYlXqR+l3RolEgoSEBABAbW0tQkNDMXLkSJSUlCA+Ph4BAQEwMTFpMq9IJIKlpaVC9WhpaUEqlSpNN5MYGRnBy8sL27dvVyjeyckJAJCamqpKWWpHqWaMj4+HjY0NcnNzERgYiLFjx0JLSwuXLl3CsmXLYGho2GJ+kUiEDz74QKG6unbtytxUJxWwZMkSRERE4OXLlwrFr1y5Ehs2bFCxKvWiNDOWl5dj9uzZKCsrQ2BgILp3746UlBQsXLgQurq6CpUhEokUnp3SrVs3FBcXt0cyq+jSpQumTZuG3bt3KxTv5uaGkpIS3Lx5U8XK1IdSzPj48WOMGjUK5eXlqK6uhrGxMdLT01FWVtamcoqLixU2o4WFBUQi0ZvIZS2+vr4IDQ1FfX29QvErVqx4p+6OTZqRiHD58mXcvn27xcx5eXlYsGABvv76a7i7uyMgIACzZ8/Gp59+inXr1sHc3LxNYp49e9Zse/K/mJubv1OPaQCwtLTEmDFjsH//foXip06dipycHNy7d0/FytRDo5ecRARPT09IJBI8efIErq6uWL16tVzMnTt3EBgYiJqaGvj5+cHR0VEpYqgN83z19PRQW1urlHrZRN++fbF8+XK4u7u3+pTQ0NCAn58ffv31V0RFRalJoQr5b/c6MjKSfH19iejVZNaJEyfStWvXiIgoLS2NPDw8aNasWZSZman0rr2tra3CsWFhYUqbSsYW/P39ydDQkACQmZkZ1dfXt5pHLBaTjY1Nk1PP3jYamdHBwUFu7UlCQgKNHDmSXF1d6ZtvvqHc3FyViWmLGffu3UubNm1SmRZ1U1lZKZttDYA0NDRo165dCuXdsWMHeXt7q1ih6pF7TNfX10NDQwPdunUDESE2Nhbbtm3D3bt3cefOHYXHANWBrq7uO/WYTklJgUQikR0TEYKDg7FgwYJW886bNw92dnZt6gCyEa2AgICA1wfFxcVITU2Fp6cn5s2bh/Pnz2PXrl2IiYnBoEGDUFRUhIMHD8LW1hZbt25FWVkZnj59igMHDsjSnj59irKyMuzfvx82NjYICQlBUVERnj9/jujoaAgEAoSFhaGwsBAvX75EZGQkrKyssGvXLly9ehWOjo7Yt28f+Hw+IiIikJeXB4lEgr1796JHjx4ICwtDcXEx8vPzkZiYCBcXF4SGhqKwsBBVVVWIioqCtbU1du3ahQcPHqC2tlauPKFQCLFYjL1796Jnz57Yt28fcnJyQESIiIiApaUlDhw4gL///huamprYs2cPunXrht9//x137tyBtrY2wsPDYW5ujiNHjuDmzZvQ19fH7t27YWpqihMnTuD69eswMjLCzp07YWJiglOnTiE9PR08Hg87duyAsbEx4uLikJycDHNzc4SGhqKgoED2suA1L168QK9evXDhwgV0794d27dvh66uLpKSkhAfHw8+n4+QkBDo6+tDJBJhz549mDBhArZt2wZNTU1cuXIFJ0+eRN++fREcHAwAuHHjBk6cOCH7vaRSKW7duoXjx4/L0iQSCe7cuYNjx47Bzs4OQUFBqKurQ3Z2No4ePSqLq66uhkAgUJoZ5e6MWlpaskHXXr164erVq7hy5QqAV4PM+vr6EAgE0NHRgUAgQNeuXWFkZCSXZmFhgc6dO0MgEEBXV7fJNGtra5ibm4PH40EgEEBfXx/W1taQSqVyaVZWVjA2NkanTp1kaQKBAN26dUNRURF4PB709PTQu3dvmJuby+rQ09ODtbU1TExMYGxsLFcej8drlGZoaCiro2PHjuDz+dDX12+UpqOjI/t7DQ0NwefzoampKZfWs2dPSKVSGBgYQCAQwMjICD169IBEIpFL6969O6qrq2V/U35+PjQ0NOQ6cRoaGigtLYW1tbUsjsfjwdLSErq6utDT05Olffnll/Dy8pIZxMTEBPSqGSb7HUxMTKClpQWxWCz7vUxMTKCjo4O6ujpZWpcuXdCxY0fU1NRAW1sbAoEApqamEIvFcr+1mZmZ0owIQL4DIxaL5dptz549I39/f+rYsSNFREQo1KBuD21pMx44cIDWr1+vQjXqJSEhgXg8nqzNCIAGDhxIrq6uCpexdu1a8vf3V6FK1SI3ztihQwcYGhoiLy8PAMDj8TBo0CBMnz4dL168wKhRoxASEoKamhrlXhFvQF1dHfT09JiWoTScnZ2ho6MjO+7UqRNWrVqF8vJyZGRkKFSGj48PIiMjUVVVpSqZquW/7jx79izNmjWLpFIpVVVVkZOTk2y7trq6Otq9ezcNHz6cfvnlF6qoqFDqldGvXz+FY0NDQ2n79u1KrZ9p9uzZQzwejzp27EiDBg0iqVRKx48fp2nTpilchp+fH23cuFGFKlVHk1PIVq5cScOGDaN+/fpRVFRUo/MSiYRiYmLI2dmZVqxYQU+fPlWKmLY8poOCgig8PFwp9bKJ9PR0Onz4MNXU1BDRq+W09vb2Cq9lLi4uJisrK1n+t4lmtzcpLi6GtrY2unTp0tJdFWfOnEFwcDBsbW0xe/Zs1NbWoqCgAKNGjZJNmlUUe3t73L17V7YSsCU2bNgAPp8vtznUu0p0dDQSExMVfsvi4+MDW1tbLFq0SMXKlIyyXH3s2DHq0KGDrPGto6NDa9eubVOnx9nZWeG77Pfff08XLlx4U7lvFW1duFVQUEACgaDd242oG6VNIfvss8+wbds2AK8GpEeNGgUPDw9oa2srXEZbpoW1ZbrZ205bF2717NkTzs7OOHjwoIqVKRllOruhoYHGjRtHnTt3puTkZJozZw5NmTKFLl++rFD+JUuW0Pnz5xWKdXZ2ptLS0vbIfato68KtnJwcsrOzo4aGBoXi79+/T0FBQRQUFERZWVntkfrGKHVrAk1NTSQkJCAxMRGPHj1CdHQ08vPzsXHjRqxduxZLly6Fm5tbs/ktLCxQVFSkUF0lJSUttmffNf534dZvv/3WaryNjQ1sbW2xe/duTJo0qdk4iUSCPXv2YPPmzZBKpfD19YWxsTEePXqkTPkwMzNrdZK12vZnFIlE2LJlCzIyMuDj44OpU6c26qhER0fj4cOHjaas/RepVApbW1vk5OSoUjLrqKysRP/+/XH79m3weLwWY7OysuDl5QWhUIjhw4c3G1daWorbt2+joaEBurq66Nq1K2xtbZUtHevXr8eQIUNaDlL3rbisrIz8/f3JycmJoqKi5BrZ6enp5Onp2WoZubm5bXoz8S6xZs0aWrduXYsxBw4coAEDBlBmZia5u7u3ujF/YWEhubu7EwD66KOPKCcnR5mSFYaxRfyVlZW0adMmcnR0pNDQUKqpqaHKykoaMGBAq3ljY2Nlcy7fN0pLS4nP58vt3/ia+vp68vHxoUmTJsmWvaalpdHw4cNbLff1S46qqirGxigZ297E0NAQy5Ytw6VLl6CpqYlx48YhLCwM1dXVrS5Bzc7Ohp2dnZqUsovmFm6JRCKMHz8eZmZm+OOPP2SPcUdHR+jo6CApKanFcjU0NGBgYAADAwPmXrMycgk0gUQiof379xOPx6PFixe32FOeO3cupaSkKKVekUhEQqGQhELhW7Oh0uPHj8na2prq6uqIiCg5OZns7OwoLi6uyfgLFy40uVMu22DdBvOBgYHo1KkTDAwMEB4ejgkTJmDgwIFyMd9++y1CQ0PbtU/htWvXEBYWhvLycowYMQJLlix5qyZexMXF4cGDBygtLcWcOXPg4+PTYry3tzcGDhzI6s1GWWfGlJQUhIeHIzo6GlKpFIcPH0ZmZqas511RUYFz587B09Pzjeuor6/H6dOnkZubC21tbXz44YcYN26csv4EtSCRSBAeHo7w8HDMmDGj1fgHDx7Azc0N2dnZCn2HhhGYvTE3prq6muzs7Jo9HxMTQytWrGh3PVKplA4dOkQ9evSgzp07U3Bw8FvzmH7Nxo0b6aefflI4fs6cObR//34VKmofrDMjEdHgwYOb/RDPjz/+SLGxsWpWxE7a+tGi7OxsVm82yvhmoU3h5OTU6INEr0lKSpJtfPS+Y2hoiLlz5yq8YZStrS1sbGxw8uRJFSt7Q5i+GpoiPj6e5s+f3yj98ePH9PHHHzOgiL2UlZU1O+7YFKmpqeTs7KxiVW8GK++MDg4OyMzMbJSemZmp0Gai7xMmJiawsrLC9evXW419/vw5YmNj0b17d1ZuJ8hKM1paWoKIIBQK5dIPHz6MyZMnM6SKvbS2PV59fT2Cg4MxceJEODs7IyYmptVPfTAB+xT9P9OnT5f7YGVtbS0SExNbnPXzvuLi4oKKigrcuHGj0bnDhw9j9OjRsvXWHh4eDChUEKbbCc1RUFAgtybm0KFDNG/ePAYVsZsTJ07Q1KlTZcfJyck0ZswYWrNmDVVWVjKoTHFYN+j9v/z8888wMDDAokWLMHToUKSmpsLU1JRpWazF09NTtvB//fr1GDp0KNOS2gSrzVhdXQ1HR0cMHjwYw4YNg7e3N9OSWM39+/eRk5Pz1rarWW1GAMjPz0dGRgamT5/OtBQOFcN6M3K8P7C2N83x/sGZkYM1cGbkYA2cGTlYA2dGDtbAmZGDNXBm5GANnBk5WANnRg7WwJmRgzVwZuRgDZwZOVgDZ0YO1sCZkYM1cGbkYA2cGTlYA2dGDtbAmZGDNXBm5GANnBk5WANnRg7WwJmRgzVwZuRgDZwZOVjD/wEI81v/cWlPSQAAAABJRU5ErkJggg==)
A slab of high quality flat glass, with parallel faces, is placed in the path of a parallel light beam before it is focussed to a spot by a lens. The glass is rotated slightly back and forth from the vertical orientation, about an axis out of the page as shown in the figure. According to ray optics the effect on the focussed spot is:
![](data:image/png;base64,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)
physics-General
physics-
A ray of light strikes a corner reflector as shown in figure. As the angle of incidence q is increased, the angle between the final reflected ray and the incident ray
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)
A ray of light strikes a corner reflector as shown in figure. As the angle of incidence q is increased, the angle between the final reflected ray and the incident ray
![](data:image/png;base64,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)
physics-General
physics-
A ball of mass m is attached to a rigid vertical rod by means of two massless strings with length L. The strings are attached to the rod at points a distance L apart (see Figure). The system is rotating about the axis of the rod, both strings being taut and forming an equilateral triangle. The tension in the upper string is T1
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)
A ball of mass m is attached to a rigid vertical rod by means of two massless strings with length L. The strings are attached to the rod at points a distance L apart (see Figure). The system is rotating about the axis of the rod, both strings being taut and forming an equilateral triangle. The tension in the upper string is T1
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)
physics-General
physics-
Two identical resistors with resistance R are connected in the two circuits drawn. The battery in both circuits is a 12 volt ideal battery. Which statement is correct?
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)
Two identical resistors with resistance R are connected in the two circuits drawn. The battery in both circuits is a 12 volt ideal battery. Which statement is correct?
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ImWeDv74/i4mKxe1ZWVvDw8JBK+TExMQgPD8eSJUuwfPlyqY/2iQhRUVGIjIyEl5cXfHx82r744AM65SDk2bNncHd3R3FxMdauXYvs7GzU19cjNDRU1McbPXo0UlJSUFBQgM2bN6OhoQGrVq2Cubn5Z9draWn50cJYaW6S4vP5sLa2xs6dO1FSUoKwsDCp1vxycnLg8/mYNGkSwsLCUFRUhNDQUOkYXZJ2uiP2Ad8/HUsoFJK+vj4FBAR89FxNTQ1FR0fT8OHDadasWVJZwdFWZL0ts66ujmxsbOjOnTsyi1FTU0MTJ06kkpISqZTXZfqAAoEAAoFAdF1SUoJVq1bBwMAABQUFSE9PR1paGrS1tTlUKVuUlZWhqakp9u8gbVRVVaGmpia1d/B1yib4HS9fvkRRURGSk5Nhbm4OPz8/ZGRkICAgAE+ePMHy5cuRn5//WVMvjNbRqWvAN2/eIDs7G3v27EFoaCh69+6NESNGYNy4cZCTk8PJkyeRkZEh8xciMtpOp64B+/btCxcXF9y4cQPz5s3DqVOnMGjQIISEhGDbtm3IzMxEXFwcVq5ciTlz5sDV1ZXTXXICgQCxsbFSG0E2R01NDY4ePfpRAlmavHvrqTTotDWgQCAQ9UOCgoLw/PlzBAQEiH4uJycHa2trJCUlISIiAidPnoSHhwfu3r3LlWSsXbtWpuYDgClTpkBTU1OmMZydnVu9YepTdMoasKKiAo8fP4aioiKKi4uhp6eH5ORkeHt7IykpCbNnz4aCggIOHz6M0NBQ9O3bF+Hh4e2as5QGc+bM4TR+R6RTJqJboqqqCjt27EBSUpJoYMJlEprRMp22Cf4UV65cQXp6Onr27AlbW1vOX07DaJkuZ0A7Oztcu3YNCQkJyMzMhL6+PtavX//R0nVGx6DLGfAdJiYmiIuLQ05ODlRUVGBubo45c+agoqKCa2mM9+iyBnyHiooKmpqaMHjwYCxcuFCi06YYn48ua0ChUIiEhATY2NhAR0cHmZmZsLe351oW4wO6pAEzMjJgZWWFsrIynDt3DgsXLuz0byfqqnQ5AyYkJMDNzQ1aWlowNzf/7BuQGK2jy+UBgbdzxMePH0d8fDzMzMywfv16riUxPkGXNOD7cHk2DON/0+WaYEbnghmQwSnMgAxOYQZkcAozIINTmAEZnMIMyOAUZkAGp0i0JH/w4MH4+uuvZa1FJnTlfcBdAYlmQl6/ft3247c4Rl5ens0Hd2AkMiCDIStYH5DBKcyADE5hBmRwCjMgg1OYARmcwgzI4BRmQAanMAMyOIUZkMEpzIAMTmEGZHAKMyCDU5gBGZzCDMjgFGZABqcwAzI4hRmQwSnMgAxOYQZkcAozIINT/g/P2/NlLCI4egAAAABJRU5ErkJggg==)
physics-General
physics-
The equivalent resistance between the terminal points A and B in the network shown in figure is
![](data:image/png;base64,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)
The equivalent resistance between the terminal points A and B in the network shown in figure is
![](data:image/png;base64,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)
physics-General
physics-
A hollow conducting sphere of inner radius R and outer radius 2R has resistivity '
' a function of the distance 'r' from the centre of the sphere:
. The inner and outer surfaces are painted with a perfectly conducting 'paint' and a potential difference
is applied between the two surfaces. Then, as 'r' increases from R to 2R, the electric field inside the sphere
A hollow conducting sphere of inner radius R and outer radius 2R has resistivity '
' a function of the distance 'r' from the centre of the sphere:
. The inner and outer surfaces are painted with a perfectly conducting 'paint' and a potential difference
is applied between the two surfaces. Then, as 'r' increases from R to 2R, the electric field inside the sphere
physics-General
physics-
If I = 80 mA, determine the magnitude of the current in the
resistor
![](data:image/png;base64,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)
If I = 80 mA, determine the magnitude of the current in the
resistor
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMUAAACKCAYAAAAaNo5JAAAXQ0lEQVR4nO3de1RVZfoH8C+XBDVR5JoE6nhDBEZFTVtA45VJTUHGBkNBQYTlTJKipml5HSzFvBWjBDiBFKsstcTGSxphiop44S6UInKT2+FqwOE8vz9Y7J9nn4M6ybl4fD5ruVbsd+/3vG/wPWe/e5/9vnpERGCMCfQ13QDGtA2HgjERDgVjIhwKxkQ4FIyJcCgYE+FQMCbCoWBMhEPBmAiHgjERDgVjIhwKxkQ4FIyJ6FQoWlpaUFBQoLC9srISN27cgPgLwc3Nzbh06RJaWloeW3dJSQnS0tJQWlraZe1l2klnQpGfn4+pU6fiwIEDcttTU1OxceNGtLS0YOHChZDJZADag7Jw4UIYGxsjMDCw0z/28+fPw93dHTExMaioqMCBAwfg4eGB69evq7xPTENIh3z44Ye0cuVK4WeZTEb29vZUVFRERETLli2jffv2ERFRUFAQJSQkEBHR4cOHae7cuQr13b59m0xMTOiXX36R23748GEyNzenkpISVXWFaZDOfFIAgLGxsdzPOTk5KC4uho2NDQDA3d0dR44cgUwmw9GjRzFixAgAgJubG77//ntIpVK543fv3o3+/fvj1Vdfldvu5eWF33//HZ9++qkKe8M0RadCIZadnQ0LCwvo6ekBAKytrZGVlYXKykpUVFTA3NwcAGBhYYHm5mb89ttvcsfn5eVhwIABCvXq6+vDzs4O9+/fV30nmNrpdCheeOEFGBsbCwPs1tZWtLW14YUXXgAAGBkZAQDa2tpARGhra5M7fujQoaivr1dad0tLC4YPH67C1jNN0elQDBw4EJWVlcInRWFhIYYOHYo+ffqgd+/eqK6uBgAUFRXByMgIdnZ2cse/8847yMrKQmZmptz2zMxMPHjwAAEBAerpCFMrnQ7FiBEj8OKLLwqnOdeuXUNgYCD09PQwa9Ys3Lx5U9ju4+ODnj17yh3f0NCAy5cvY9euXbh69SoA4MKFC/jss8/w008/oaioSL0dYmphqOkGdBWpVIri4mJIJBK0tLSgW7duMDAwwIEDB7Br1y68/vrrkMlkWLRoEQDgX//6Fz744AMMGDAAJ06cwK5duxTqnD59OiwsLCCVSpGamgoXFxecPHkS58+fR3JyMmQymRAspjv0iHRjipvy8nLhE8HU1BQvv/yyUCaRSFBYWAhnZ2fhVApoHxdkZmbCwcFB4coV0D5Q7xhnWFtbw8LCAiUlJaiqqgLQPmaxt7dXZbeYBuhMKDpUV1ejb9++f6j8UWUdnz5M9+nUmKKxsRGzZ89W+DpHh9zcXPj7+ystS0pKwpo1azqt28fHB01NTV3STqbddCoUX375JaqqqpCYmKi0PCoqCufPn0dubq5CWWxsLBITE1FbW6tQlpycjNTUVERHR3d5m5kW0uDd9C43ZswY+v7772n06NHU0tIiV9bQ0EBWVla0adMmCgoKkiurqakhS0tLWrx4MW3fvl2hXg8PD/rPf/5DI0eOpObmZpX2gWmezoQiPT2dHBwciIho06ZNFBkZKVe+f/9+8vX1pbq6OrKysqLy8nKhLDIykhYvXky3bt0iOzs7uUBdvXqVhgwZQlKplLZu3UoHDhxQT4dUqLq6mlatWkXm5uZkampKXl5elJaWpulmaQ2tHWjPnDkTeXl5T7y/oaEhVq9ejUWLFqGhoQGurq64cOECevToAQBwdHREbGwsxo0bh1WrVqFnz57YuHEjAGDMmDHYt28fJkyYAE9PT8ydOxe+vr4AgDfffBNTp05FUFAQamtrMXHiRFy+fBmGhu1Xs7ds2YLPP/9c7qrWH9XY2AhjY2MYGBg8dV2Pc+/ePUilUuFuPgB0794dlpaWwh1/VTM0NISPjw82bNigltd7UlobChsbG+Tn5z/x/np6eujevbvw8759+1BfX4/33nsPZ8+exdq1a3Hp0iUA7XewX3nlFfz666/Iz8+Hj48PsrOzAQApKSkIDQ1Feno6bt26hSlTpqCgoEC48rR+/XoMHToUfn5+yM3NxdKlS3H8+PEu6fObb76JtWvXYtSoUV1S36Pk5ORgx44d+PrrryGTyTB9+nQsWLAADg4OANovN/fv31+lbThx4gTOnDmD/fv3q/R1/ldaffOu413+jwgODsb48eMREhKCvXv3YtmyZUKZra0tJk6ciLi4OGRnZ8t9XcPNzQ2GhoY4e/YsvvjiC4SGhspdil2+fDk8PDwwf/58bNiwAZs3b36qdj7M0NAQ3bt377L6OiORSJCVlYWpU6di2rRpcHV1xdChQ9HU1ISlS5fi0qVLcp+yqmJkZNQln7BdTatD8TS6deuG5cuXY+3atUhLS8NXX30lVx4WFgYfHx/U1dUp3JUOCwvD1q1bkZOTg927d8uVmZmZ4bXXXkNERATq6+vh6uqq8r50tT59+sDPz09he48ePeDg4ICamhqYmppqoGXaQacuyYr5+voiJSUFixYtUrjxNnr0aJiZmWH06NGwtLSUK/vb3/6G/Px8+Pn54cUXX1Sod+XKlYiOjsaWLVtU2n6mGTr7SQG0P/ewb98+ODo6Ki3/5JNPUFNTo7DdwMAA4eHhmD59utLjXnrpJXz00UdwcXHp0vYy7aDToQCAyZMnd1r2qD/qBQsWPLJeLy+vP9wmpt10+vSJsT+CQ8GYCIeCCWQyGW7duoWmpia0trZqujkao/NjCvbk7t27h+DgYADt82h13Mh73nAomMDOzk7hOfXnEZ8+MSbCodAiRITbt29ruhnPPQ6FFomMjMT+/fvh7+/P4dAgDoUWsbGxwenTp+Hn5wd/f38EBwejuLhY08167nAotNDYsWPh4eGBM2fO4Icffuj0mXOmGnz1SYtUVVVh9+7dSEpKQnBwMLKzs4WpPZn6cCi0QFlZGSIiIpCcnIy3335b7sk+pn58+qRBHVPueHl54ZVXXsGlS5fg5+fHgdAwDoUGpaSk4Ny5czAxMYGFhQX09fnXoQ2Et6S2tjYcPXoU9+7dw5QpU4QFTYD2mfO+++47WFpa4vXXX1d4hPCnn37Cb7/9BgMDA0yaNAm2trYA2n/pHV8XGD9+vJq69OwICgpCYGAgvvnmG6xYsQJGRkZYs2YNZs2apZWPaWoaEUEqlap8YgVh4oKwsDD06NEDdXV12L9/P3788Ue4urriwYMH8PT0xMGDB3Hx4kXk5eXhvffek6ukubkZEyZMwPDhw5GQkCBsb2trw2uvvYbTp0/LTSqQkJCACxcuPHXj9+3bp1PvridPnsS2bdtQWVmJd999F/PmzdO5U6nbt2/jxo0bSsusra0f+ea5Y8cO5OTkIDY2FkD7/MHh4eFwcnJCY2MjQkND5favqqrC6tWrkZKSgm3btsHLywv6+vqorq7GunXrQESIiIhQeLrSEGj/4509ezbc3d0BtE9QHBMTA1dXV3z22WcYMmQI+vXrh1mzZsHMzAwBAQGwtrYWKjEyMsKyZcuwdOlSuflYr127hnnz5skFAgB69+6Nl1566Yn+Jz5PPDw84OHhgYsXLyI8PBxr1qzBhg0bEBAQAH19fbkFZAwNDRWWDngW3LhxQ+kM7wAwYcKETkORk5ODc+fOyf3dLV68GBs3boSLiwsWLFiAU6dOYdq0aUK5mZkZ1q9fj0GDBsHU1FR4A+3bty9MTEzw9ttvK33cWOlkaAkJCbRmzRoiIpoxYwZFREQIZe7u7vTtt98qHPP777+TtbU17dixQ9i2YsUKkkgkXTJB1fOisbGRPv30UxoyZAiNHz+ezp49S0REra2tdPz4cQJAq1atosTERHJ3d6ft27eTTCbTcKtVq7W1lTZv3kxxcXG0aNEiIiIqLS0lIyMjkkqlREQUHR1Nnp6eSo+fPXs2zZw5U66+JUuWdPp6SkMRFBQkrPz55z//mQ4ePCiUiUPysK1bt9KAAQNIKpVSXV0dvfPOO4/qK3tIWVkZrV+/nqytrWn+/Pl07do1pfsZGxtTeno6ERHl5OQQAPrvf/+rzqaqXVRUFJWUlFB8fLwQimPHjpGNjY2wz88//0x2dnZKj//5559JT0+P8vPzhWOPHj3a6espnJBfvnwZbm5uwumNiYmJ3HltQ0NDp1PSh4SEoLy8HMePH0diYiLmzZundD/2/7KzsxEYGAhnZ2c0NzcjLS0N8fHxGDlypNL9Hx6Ad6ypUVdXp5a2akJWVhbMzc0VTrdbWlrQu3dv4W6/+PTyYa6urnBxcRFWsz1x4gRmzJjR6WvKjeLu37+PgoICuYf2HRwccPfuXeHn/Px8jBs3TmllZmZmWLhwIfbu3YtBgwZh8eLFj+ovgPaZwt9///3H7gcA9vb2XTYbn6bJZDIEBgbi2LFjmD59OjIzM2FhYfHEx9fX12PLli3w9vbGG2+8ocKWdo1Tp07hyJEjT7Tv4MGDERYWBqB9WtLm5mbExcXh7t27qKysxLZt2zBp0iQ0NDQIbxKlpaVy442H6enpISwsDMHBwVi8eDFsbGweeQFDKCkvL0dqaireeustAMAvv/wCJycn+Pv7Y+fOnQCAu3fvYtiwYZ2GAmhfPNHe3h5z5859osuKU6ZMwaBBgxS2z5gxA0lJSXLbVD1jnTrp6+sjOjoac+fORWxsLBwdHeHt7Y2AgACMGTPmkceePHkSwcHBcHNzQ0xMjJpa/HR69eolt7oU0H7zMi8vD7Nnz5bb/vA8XBs2bBA+AX744QekpaXB29sbtra2aGxsRH19PXr16oWbN29izpw5nb6+t7c3Vq9eDW9vb5w5c+bRjSVqn4V6ypQpZGtrK/zz8vKSO6eLjIykd999l0pLSx97Dujr60u1tbWPP1l8hH79+j3V8c+a+/fv08cff0yOjo7k7OxMu3fvpsrKSoX9unfvTunp6ZSdnU29evWic+fOaaC1XeO7776jkJCQJ97/4TEFEdH27dspPj6eGhoayNvbm+rq6h55fEREBL3xxhuPfR2tnYr/eQvFwy5fvkyLFi0iU1NTCg0NpQcPHghlHaEgIjpw4ABZWVkJF0WeNf9rKHJycujUqVNy206fPk0xMTFK30DEJBIJXb58+bH7cSi0TGFhIa1YsYIsLS0pMDCQ7t27J5QVFxeTnp4eHTlyhIiIZDIZzZkzh8aPH0+FhYWaavIf9r+GQl1063bpM+zq1avYuXMnkpOTsWTJEoWBd0tLC0pKSnDhwgXo6+tDIpGgT58+OHjwILKzs1FWVgZra2terLILcCg0iIiQlJSEiIgIlJWVYcWKFYiNjVW6fHG3bt2UDsBNTEz4e2VdjEOhIR2XZI8ePQpvb28cO3YMvXv31nSzGPir4xqjr6+PgwcPIiUlBfr6+hg6dCj++c9/Kl25lakXh0LDHB0dERUVhZycHPTv3x/Tp0+Hh4cHjh8/DplMpunmPZc4FFqib9++WLVqFfLz8xESEoKPP/4YgwYNQmRkJE9coGY8ptAyBgYGGDFihHDlyd3dnR84UjMOhRYpLi7Gpk2bkJ+fjy1btjyT6+npAg6FFqipqcG2bduQnJyM999/HzNnztR0k55rPKbQoPr6emzevBmTJ0+Gk5MTLl68yIHQAhwKDZHJZFi/fj0iIiIwatQoDB8+XKeeN3+W8W9BQ/T19bFnzx4UFhbC2dkZ/v7+GDVqFBobGzXdtOceh0LDTE1NERoaiqysLPTt2xd5eXmabtJzj0OhRXr16qXpJjBwKBhTwKFgTIRDwZgIh4IxEQ4FYyIcCh3X1NSEe/fudVpeUVHR6WRqt2/ffuQ3dKurq5+6fdqIQ6HjPv/8c6xcubLT8g8//BAfffSR0rI1a9YgLi5Oadn169fh4+PTJW3UNhwKHRcXF4eMjAzcuXNHoay1tRWHDh1CfHw82tra5Mpqa2tx8uRJREdHK613165dKC4uRmZmpkrarUkcCh2WmZmJyspK7Nq1Cx988IFC+ddff43x48fDyckJ3377rVzZl19+CW9vb1RXV+Pq1atyZYWFhTh9+jQ++eQThIeHq7QPmsCh0GFRUVEICgrCtGnTUFZWpvCuvnfvXixbtgxhYWGIiIiQK4uJiUFgYCCWL1+uUBYREYGlS5di4sSJqKiowK1bt1TeF3USVjLSNmPHjkVJSYmmm6FWDx48QLdu3WBgYNAl9dnb2yMxMREWFha4cuUKtm7dimPHjgEArly5goULFyIrKwsAMHr0aOzduxeurq7IyMjA3//+d2RnZ6O5uRl/+tOfcPHiRdjZ2aGiogJOTk7Izc1Fnz59cPbsWcTHx+PgwYMA2lcP8vX1RUZGxmPb19bWhn/84x9PPMG22mh0KjamVt7e3nT+/HkiIpo/fz79+9//FsoOHTpEs2fPJiKi0NBQ2r59u1C2adMmWr58ORERrVu3jlatWiVXr7u7O925c4eIiFauXEkJCQkq7YeqcSieIzk5OfSXv/yFysrKyMrKihoaGoSy1tZWsrOzo8zMTLK2tqaysjKhrKKigiwtLamoqIisra0V5q49fvw4hYSEUElJCY0bN47a2trU1idV0NrTJ6YagYGBaG5uhpWVlbDEQocdO3bgzJkzMDY2Fk6zOoSEhKCoqAi2trbYv3+/Qr0TJkzAsGHD4OnpCU9PT5X2QeU0nUqmXkVFRTRw4ED69ddfFcokEgkNHjyYjh07plCWl5dHNjY2VFBQoLTer776isaOHdvl7dUEDsVz6FFrWiQmJgqLK4p98803nR7X1tZGly5deuq2aQM+fWJMhO9T6DgiQlFREZqamhTK6urqUFBQoLBdKpUiKytL4S63MrW1tcjNzYVEIumS9moDDoUOq6mpweTJk/HWW2/B0tISe/bsEcpu3LiB1atXo6ioCEuWLBHmra2trcXChQshkUgQEBCA+/fvK607PT0df/3rXxEeHo6MjAxs27YNnp6eyM7OVkvfVErDp29Mhb744gvh8mlycjIZGxuTRCIhmUxGI0eOFAbby5Yto8jISOG/O9ZNP3z4MM2bN0+h3uLiYurbt6/CUluJiYlkZWVF5eXlquyWynEodJj4foG9vT0VFRVRQUEBde/enWQyGRG1//FPmjSJZDIZ9evXj65cuUJEROXl5WRsbEytra1y9axevZrs7e2Vvp6JiQmtX79eRT1SDz590mEPT64mkUjg4OCAl19+GRkZGTA3NxcmbraxsUFGRgZqampQUlIiTO5saWkJqVSqMO7IzMzEwIEDlb6era0tiouLVdgr1eNQPCeioqKwdetWAO0zm/fs2VN4gEgqlaK1tVX4zlXH8mJtbW0gIrS2tsrVNWjQIDx48EDp68hkMgwbNkxV3VALDsVzIDU1FS4uLhg+fDgAYMCAAaiqqhI+Ke7evYvBgwejd+/e6NOnD2pqagAApaWl0NPTQ//+/eXqCw0Nxc2bNxVWXSooKEBlZSUCAwPV0CvV4VDouKysLLS2tmLy5MkAgLKyMjg4OKBnz57ClaVr167B398fADBjxgzhK+bXrl3DnDlzYGJiIlenVCrFhQsXEB4ejuvXrwNovxq1c+dO/Pjjj6iqqlJX91RD04Mapjqpqank4uJCXl5e5OXlRR4eHnTo0CEiIkpKSqJ169ZReno6BQUFCXexb9++TX5+fpSbm0sBAQFKryQNHjyY3NzcaMKECbRnzx4iItq8eTO5ubmRq6srjRw5Un2dVAG+o63D8vLyUF9fL7fN2dlZWGu7vLwc+fn5ePXVV+UG5U1NTUhLS8OoUaOUTuV55coVSKVSAICdnR1sbGxw584dlJaWAmhf3tjFxUVV3VI5DgVjIjymYEyEQ8GYCIeCMREOBWMiHArGRDgUjIlwKBgT4VAwJsKhYEyEQ8GYCIeCMREOBWMiHArGRDgUjIlwKBgT4VAwJsKhYEyEQ8GYCIeCMREOBWMiHArGRDgUjIlwKBgT4VAwJsKhYEyEQ8GYCIeCMREOBWMiHArGRDgUjIlwKBgT4VAwJsKhYEyEQ8GYCIeCMZH/A6s6tZfA/G+wAAAAAElFTkSuQmCC)
physics-General
physics-
Four wires A, B, C and D are made of different materials. They each carry the same current I. Wire B has twice the length of other wires. Wire C has twice the internal electric field of other wires. Wire D has twice the diameter of other wires. Other than these differences, all wires share identical characteristics. Rank the conductivities of these materials, from greatest to least
![](data:image/png;base64,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)
Four wires A, B, C and D are made of different materials. They each carry the same current I. Wire B has twice the length of other wires. Wire C has twice the internal electric field of other wires. Wire D has twice the diameter of other wires. Other than these differences, all wires share identical characteristics. Rank the conductivities of these materials, from greatest to least
![](data:image/png;base64,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)
physics-General
physics-
A hollow cylinder with inner radius R, outer radius 2R mass M is rolling with speed of its axis v. Its kinetic energy is
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)
A hollow cylinder with inner radius R, outer radius 2R mass M is rolling with speed of its axis v. Its kinetic energy is
![](data:image/png;base64,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)
physics-General
physics-
Four identical bulbs each rated 100 watts, 220 volts are connected across a battery as shown. The power consumed by them is:
![](data:image/png;base64,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)
Four identical bulbs each rated 100 watts, 220 volts are connected across a battery as shown. The power consumed by them is:
![](data:image/png;base64,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)
physics-General
physics-
Resistors R1 and R2 have an equivalent resistance of 6 ohms when connected in the circuit shown below. The resistance of R1 could be
![](data:image/png;base64,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)
Resistors R1 and R2 have an equivalent resistance of 6 ohms when connected in the circuit shown below. The resistance of R1 could be
![](data:image/png;base64,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)
physics-General
physics-
In the two circuits shown, all the light bulbs and batteries are identical. If A, B and C respectively denotes the brightness of light bulbs A, B & C then
![](data:image/png;base64,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)
In the two circuits shown, all the light bulbs and batteries are identical. If A, B and C respectively denotes the brightness of light bulbs A, B & C then
![](data:image/png;base64,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)
physics-General
physics-
Two strings support a uniform rod as shown. String at end B is cut. Which of the following is true just after cut
I] initial acceleration of A is vertical
II] initial acceleration of A is horizontal
III] initial acceleration of centre of mass of rod is vertical
IV] initial acceleration of centre of mass of rod is horizontal
![](data:image/png;base64,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)
Two strings support a uniform rod as shown. String at end B is cut. Which of the following is true just after cut
I] initial acceleration of A is vertical
II] initial acceleration of A is horizontal
III] initial acceleration of centre of mass of rod is vertical
IV] initial acceleration of centre of mass of rod is horizontal
![](data:image/png;base64,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)
physics-General
physics-
The potential of point O in the steady state circuit shown on the right is
![](data:image/png;base64,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)
The potential of point O in the steady state circuit shown on the right is
![](data:image/png;base64,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)
physics-General