Chemistry-
General
Easy
Question
Which of the following noble gas was reacted with
by Bartlett to prepare the first noble gas compounds -
- He
- Xe
- Ar
- Kr
The correct answer is: Xe
Related Questions to study
physics-
A set of
identical cubical blocks lies at rest parallel to each other along a line on a smooth horizontal surface. The separation between the near surfaces of any two adjacent blocks is
. The block at one end is given a speed
towards the next one at time
. All collision are completely elastic. Then
![](data:image/png;base64,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)
A set of
identical cubical blocks lies at rest parallel to each other along a line on a smooth horizontal surface. The separation between the near surfaces of any two adjacent blocks is
. The block at one end is given a speed
towards the next one at time
. All collision are completely elastic. Then
![](data:image/png;base64,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)
physics-General
physics-
The blocks
and
, each of mass
, are connected by massless spring of natural length
and spring constant
. The blocks are initially resting on a smooth horizontal floor with the spring at its natural length, as shown in figure. A third identical block
, also of mass
, moves on the floor with a speed
along the line joining
and
, and collides with
. Then
![](data:image/png;base64,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)
The blocks
and
, each of mass
, are connected by massless spring of natural length
and spring constant
. The blocks are initially resting on a smooth horizontal floor with the spring at its natural length, as shown in figure. A third identical block
, also of mass
, moves on the floor with a speed
along the line joining
and
, and collides with
. Then
![](data:image/png;base64,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)
physics-General
physics-
Find the velocity of centre of the system shown in the figure.
![](data:image/png;base64,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)
Find the velocity of centre of the system shown in the figure.
![](data:image/png;base64,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)
physics-General
physics-
Two blocks
and
are connected by a massless string (shown in figure). A force of 30 N is applied on block
. The distance travelled by centre of mass in 2 s starting from rest is
![](data:image/png;base64,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)
Two blocks
and
are connected by a massless string (shown in figure). A force of 30 N is applied on block
. The distance travelled by centre of mass in 2 s starting from rest is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAATYAAAB/CAYAAABlnO65AAAgAElEQVR4nO3deXDTZ3748bfuW7JlWbYsW75twARjYyeEECCQA0jI1TTJ7rbb/aPbYzqdnXam13Q63c50dqZ/tNt0Z3psJzNpu9PNNNndYbdkQ7IJJAECGGywwcb3bVmydVi2dR+/P6i+vxgM2GDwwfP6EwvpkfTV5/scn+fzyDKZTAZBEIQNRL7aDRAEQVhpIrAJgrDhiMAmCMKGIwKbIAgbjghsgiBsOCKwCYKw4YjAJgjChiMCmyAIG44IbIIgbDgisAmCsOGIwCYIwoajXO0GCA+XiYkJhoeHCQaDpNNpAGQyGQaDAYfDgcPhwGg0IpPJVrmlwnomApvwQI2MjPDxxx/T2tqKRqNBp9OhUqnQ6/Vs2rSJxsZGGhoaUKlUIrgJd00MRYUHyuFwUFZWhtvtxul08swzz/Dyyy+j0+l4//33+d73voff7yeVSq12U4V1TPTYhAfKZrPhcrlIpVJUVlbS3NyM0WhErVYzODhIT08Pbrcbo9GI0Whc7eYK65QIbMIDpVar0ev1aDQaioqKKCsrQy6X4/P5yM/Px+12k8lkEGUChXshhqLCAxUKhfD7/ZhMJqmnFo/HOXHiBD6fjy1btlBdXY3JZFrtpgrrmOixCQ+U2+3m0qVLXL16lXfeeYdPPvmEQCBAcXExR44cYdOmTeh0utVuprDOiR6b8ECNjY0xNDREY2MjBQUFhMNh+vv7GRkZwWg0snnzZhQKxWo3U1jnRI9NeGBSqRSjo6P4/X6+/e1vU1hYiNvtRq1W09bWRn9/P7t370aj0YhUD+GeiMAmPBDpdJpQKEQgECCTydDY2Ehubi6VlZUUFxfzxRdf0NraSmNjI7t27UIuF4MJ4e6JwCY8EOl0momJCXQ6HXV1dVgsFik5Ny8vj1QqRTgcJhKJiBVR4Z6ty8CWyWRIp9OkUilkMhkqlWq1myTcQSqV4tq1a2g0Gnbs2IFSqSSdThMMBhkYGCAWi6HX67FYLGIYKtyzddnfz2QyRKNRQqEQc3Nzq90cYQkSiQTnz58nmUxSX1+PUqkkHo/T09PD+++/z/T0NIWFhVRXV4vFA+GercseWyAQ4Kc//SkVFRXU1dWtdnOE2/D7/bS1tXH06FE+/fRTiouLGR8fR6vV0t3dTX9/PzMzM3zjG9/gyJEjmM1mMb8m3LN1dwX5/X4uX77Mz3/+c8bHx0XO0xonk8mQy+Xo9XqamprYtGkTRqMRpVKJyWRi06ZNHDlyhFdeeYWtW7eiVqtXu8nCBrCuemypVAq3201LSwtnz57l+eefx2KxrHazhNvQ6/XU1dWRn5+/6N9zcnIoLi5+wK0SNrp1FdhmZ2cJh8Or3QxhGdRqNVar9ZY3IDHsFO6HdRPY0uk0V69eJZVKsX37dhwOhxiGrgMymQylUolSuW4uNWEDWBdXWzQaZXp6mkAgQF5eHnl5eRQXF4uyNoIgLGpdjAOmp6f57LPPKC8vp6ioiEAgQGFhoQhsgiAsas332ILBIF1dXfzyl78kFAqh0+lwu91Eo9HVbpogCGvUmg9sQ0ND9Pf3o9VqmZmZYXp6Gq/XK23JEQRBuNGaDWypVIq5uTlGRkaIRqPs27cPuF7PS6FQUFhYKIoRrpBMJkMikSAWixGPx0kkEqRSqXW1Z1Mul6NSqdBoNKjVatRqtVhxfYit2cAWCoX44IMPcLlcvP766xgMBgA6OjpoaWlBoVCIPaIrJBaLMTIyIu0EGBkZwe/3E4/HV7tpS2YwGCgvL6eqqoqamhoqKyvR6/Vie9ZDak0Ftkwmw/T0NBcvXuTLL7/E5/Nht9uxWq1oNBppWHrlyhXg+sEgJpOJ0tLSVW75+pPJZIjH41y5coWWlhb6+/tJp9NSekZhYeG62oyeyWQIBAKcP3+eCxcuYDKZePTRR9m6dStOp3O1myc8YGsqsAF4vV6uXLnChQsXsNvtwPVhRiaTYXJyksnJSWZnZwGYmprC7/eLwLZMqVSKaDTK5cuXaWlp4cqVK0SjUQoKCigsLMRut2M2m9dV7lk0GmVychK3243H42F4eJhEIkE4HKa+vl46NEZ4OKypKzeTyRAKhXA4HBw+fBi4fg6lWq2WTg3/av5aeXk5ZrN51dq7XsXjcSYmJvj+97+PQqFg37597Nq1C41Gs9pNuyePPPIIcD3IeTwefvazn/H+++/T3d3Nd77zHbHY9BCRZdbYDHEwGCQcDpNIJACwWq3SIsGNf9Pr9RgMBvR6/aq1dz1qbW3lP//zP9FqtdTU1LBp0yZyc3M3TI8mnU4Ti8XweDycO3cOr9fLCy+8QGNjozQKEDa2NdVjg+ubonNycpb9N2FpJiYm6OzspLe3l1deeYXNmzdjtVpXu1krSi6Xo9PpKCsrY25ujkQiwdGjR7Fardhstg0TwIVbE9/wQ6arq4uenh5ycnIoLS3dcEHtRjU1NdTW1vLxxx/T398vErsfEiKwPWSyqRxVVVVotdrVbs59p1KpMBqNWK1W/H4/Ho9ntZskPAAisD1ksqvKZWVlD0Vgk8lkaLVaXC4XgUCA8fHx1W6S8ACIwPYQyeZ6ZVM7HpZqtWq1GrvdzuzsLD6fb7WbIzwAIrA9JDKZDKlUilgsRiqVQq/XPzST6NnFhEQiIebYHhIPx5UtCMJDZUXTPWZmZpicnGRoaIhQKEQoFGJ+fn4lX2JFWCwWcnNzycnJoby8HJvN9lAkb66xlEVBuG/uObBlhzihUIienh4uX77MuXPnpK0tfr9/Jdq5ohwOB8XFxRQXF/P4449TV1dHSUkJRqPxoRmeCcJGds+BLZ1OMzU1xU9+8hMuXLhANBqlrq6OpqYmbDbbmkyo9Xg8TE5OMj09zY9//GOcTif79+/nueeek6qICIKwft1zYOvs7OTEiROMjIxQUVFBUVERTqcTo9GI0Whck9udcnNzcTgczM7OUlJSgsfjobW1FblcTlNTkzgOThDWuXsKbNPT01y6dIkzZ86wdetWmpubKSsrW6m23Tdms1naPF9TU0NXVxcXL17kk08+kZI512JAFgRhae56QimTyXDx4kW6urrQ6XTs379/XQS1GymVSrZs2cKTTz7J1atX6ejowO12r3azBEG4B/cU2D755BOCwSDPPvvsup6bksvl5OTk8NRTTzE6OsrJkydXu0mCINyDuwpsyWSSUCjE4OAgqVSK6urqdZ3FLpPJMBgMbN26lWAwyLVr11a7SYIg3IO7mmOLRqNMTEyQTCbRarUb4lAVlUqF0+kkHo8zNTVFMplEoVCsq/LY90smk2F2dpb5+Xni8TgKhUJaHLqxym4ymWRubo65uTlSqRQGgwGj0XjLfamZTIZMJkMkEiGRSCCTyTCbzeJzF+7JXQW2ubk5Ojs7MRqN5OXlrXSbVoVcLsdoNKJWq4lEIvh8PnJzc9d1T3QlpNNp4vE4H3/8MSdPnqSvr4+8vDyee+45nnvuuQX1zdLpNIFAgA8//JDjx4/j8/k4cOAA+/fvp7Gx8ZbPPz8/T1tbG4ODg2i1Wl5++eWHYoO+cP/cVWCLx+P4/X5UKtWGuQBlMhkKhUI61SgajUrlyB9m8/PzdHR0oFQq2bVrFzt27KC7u5u2tjaCwSDf/OY3pR773NwcH3zwAdPT0+zcuROdTofX6+Xy5cvk5+djt9tvKj8ei8Vwu90cP36cQCDA5s2bxQ6J/5M9bOdOu3csFgtbt269b8nl8XicUCjEwMAAcrkcm81GaWnpor3qubk5hoaGmJubIzc3l/LyclQq1aKPjcfjDA0NEQwGicViwPUshby8vAUjgdnZWYaHh6WioUqlkoKCAux2u3RMwI3uKrBlSy/L5fINd7xZ9uJIJpPiBwYkEgkmJydxuVyUlZVhNpv5/PPP+clPfsKnn37K888/j1arJZ1OS0GsqqqKw4cPU1BQwNGjRxkbG+PixYvs2bPnpsCW3bkyMzPD7OwsiURCfO7/Jx6P09XVRVdXF7FYbEEwSafThEIhwuEwLpeLLVu23JfAFg6H8Xq90glxoVCI3Nxcdu/ejcPhWLBo6PP56O/vp7W1lXg8jsFgYGhoiMceewyz2XxT+5LJJGNjY4yNjeF2uxkZGWHfvn3s2LGDiooK6XGRSISBgQF6enqYn58nJyeHxsZGaTpkMWL/kHBbGo2GsrIyysrKsNlsqFQqdu/eTW1tLYlEAq/XSzQaJRQK0dfXh9FolB6v0+lobm6moKCAX/7ylwQCgZue32AwUFlZyZEjR6TDWITrsnOPX3zxBUePHiWZTEp/SyQSdHd3c+LECU6dOkUqlbovbXC73Zw7d47jx48zOzvL2bNneeedd3j33XeZmJhY8Ni2tjZ++tOf8vHHHzM2NsbPf/5zfvd3f5eBgYE7tm90dJR/+Zd/4fvf/z6ffPLJoo/p6Ojg4sWLjIyMSOee3MqKn3mQ7bJevHgRm81Gc3Mzdrv9pknmwcFBzp8/z5dffimtSB44cICcnJxF57UymQxer5euri5GR0dpbm5ecGKVcH9otdoF1XZlMhlqtfqmnnooFGJ4eJjCwkLy8/Olf7dYLMjlcgYGBpZVMqizs5OzZ89y9uxZAF588UVeeOEFAIaHhzl79uyiP4Bdu3bx2GOPsXnz5mW/17VGo9Hw+OOP09PTw+joKM8//zxqtZpQKMTU1BSPPvoop06dIhwO37dhqFqtZtu2bTQ0NKBWq6mtraWtrY2+vj7m5uaA68c5Tk9P09rais/n44/+6I+wWq1cu3aNL774glOnTqFSqW66cWk0Gurr66mtrUWn03H06FEGBwc5ceIElZWVPPbYYxgMBnJycti5cyder5dwOExNTQ1btmy57XbNFQ1s8/PzDA8P88UXX3D27Fm2bNlCXV3dgrmqTCaDx+Ph2rVr9PX1SacjeTweTpw4wd69eyksLLzpuTOZDF1dXZw8eZLx8XEqKiooKChYyeYLi1AoFDcdcZjJZFCr1VgsFqxWq7Tg4na7KSkpWTDczC7IhEKhJfUqMpkMyWSSkZERJiYmUKlU2Gw2LBYLqVSKcDjM6dOn6erqkk6cunr1KmNjY9TV1aHVau/7vK/H42FgYIC+vj6sVit2u538/Hxyc3PR6/WoVKoVeZ3s4dWVlZU4HA7KyspIp9NEo1FisRjbtm2Tgsr9Cmxms5mcnBxpHjU7NPV6vdL7TCQSDAwMEAqFyMvLo7GxUfoeZmZmOHbsGE6n86bAplAopMVHl8tFSUkJJpOJSCTC+++/j9PppKysDI1Gg91up7CwkFgsRnFx8R0X9lY0sIXDYTweD4ODgwwPD+NwOBZ93JUrV+jp6cFgMPDmm28yOztLS0sLx44do7q6GpvNtuhhvWNjY/T09OD1eu/YFRXuj0wmw9zcHAaDQdobrNPpiMfjzMzM3PSdLyfQpNNpEokEExMTBAIBiouLOXjwIJs2bcJoNBKLxfD7/Zw9exadTsef/dmfAfDOO+/w2WefcejQIXbv3n3fT36fnJzkxIkTvPPOO5SXl7N161a2bNlCRUUFdrsdk8kkvW+NRoNarb6r9JVkMsnAwAB6vR6n08ns7CxTU1P09vYyPj5Oc3MztbW1uFyuRQNbNgDeiVarRaVSLfocX72hzM3NMTY2RjQapampSeoxxWIxurq6UKlUVFRUoNVqpaT3oqIiWltbeeKJJ27bBo1Gg8Ph4Pnnn6ezs5Nf/OIX7N69G71eT3Fx8bI/vxUNbLm5uTz++ONs2bJFuuhulE6nOXv2LEqlkueee066609PT5PJZBgbG6OwsJCioqIF/08ul/PCCy8QCAQ4evToSjZbWIZkMklPTw/5+flUVFSs6CHL8Xic4eFh/vVf/5Vdu3bx+OOP43K5pNfI9lZKSkrIzc3FYrEAUFZWxtjYGPF4fME81P1SVVXF9u3bmZ+f59y5c7S3t2M2m1EoFJhMJoqKiti6dSvbt2+nrq6OioqKW64M3k48Hqe9vZ35+Xny8vIIBoO0tLSg0+l48sknUalU5OTkkE6nF33uzs5OOjs77/g6DQ0NuFyuW+ajzszM0N3dzbFjxxgYGMDlcvEnf/InUk8+Ho9z7do1FArFguGhxWKhrKxsWSlTtbW12Gw2BgcHefvtt5HJZLz66qvLvs5WNLAplUqUSiVarXbRN5NMJpmfn2d8fByXy0V5eTkajQa5XI7FYqGoqIhQKEQwGLwpsMH1c0VvnFPr6enhvffeA65f4Nu3b6e6uhqFQsH4+Djnzp1jbGyMcDi84P/V1tby2muvreC73/ji8TiBQAC/309OTo70OQPS0PTGnnY2WXcplEolMpmM6elp/H4/8Xh8QQFQpVJJTk4Os7Oz0oKFTqcjFotJq3C3GwZ6vV7OnTt3z8EvnU4zNDSEyWSSzlHw+/1kMhlUKhVDQ0P09fXR2tqK3W7HYrFgsVhwOp1UVVXxyCOPYLFY7viDj8VinDt3Trr5z8zM0NHRQUlJCUVFRahUqkVHNlnRaJSZmZk7vp9YLHbb1KZsSfl4PM7IyAgej4fPPvuMXbt2UVhYSCaTIRqNotPpFrRHoVAsu7eq1Wqpr6/npZde4t/+7d84ffo0+fn5PP3000t+DnjAByYnk0lmZmYIhULIZLIF0V2r1eJ0Okkmk0ueZJ6bm2NgYIBf/epXOBwOtFot8/PzUo24q1ev0traSigUwufzMTU1hcfjoby8nNzc3Pv1NjekdDrN3NwcHo8HvV6P3W5fcCapTqfD4XAQi8UWDH9mZ2eJxWJSj+Z2lEolZrMZi8WCx+Ohu7tb2q6XTS3K3tx8Ph8tLS3IZDLGx8cxGo0UFxfftiqLz+djYmJiRU6qCofD0g08u2sCrs83Zeeh+vr6kMvlZDIZTCYTNTU17N69W1ogu11gyw67Z2ZmKC4upqqqCgCr1UpeXh4Oh2PF5vLuRK1WY7PZaGhoYHZ2lr6+Pv77v//7pmvgRtlUnuWm7zidTvbt20dbWxsDAwN8+OGHbN68mWg0uuQg+UADWyKRIBgMLnrHVKvVy97FMDY2RigUYs+ePbzxxhtUV1dLX/aFCxe4cuUKlZWVHDp0iOnpaY4dO8bPfvYzfvM3f5PXX399Rd7TwyKZTBIMBhkfH2fnzp033RjMZjOlpaWcOXOGqakp6d/D4TAKhUKae7mT/Px8Xn31Vd566y28Xi+PPvooBQUFUs9eo9Fw4MABTp8+zdtvv01vby/bt2/nxRdfZPv27bcNFpFIhFAotCKJ1/F4nEgkctvnikajqNVqtFotPp+Pa9euYTQaaWpqwuFwSEPpxfj9fgYGBmhsbGT//v0cOnQIuB7wdDrdogts90u2x7l161aefvppjh07xre//W2efvppampqbvn/kskksVhs2YFNqVTicDj4zne+w1//9V/z8ccfU19fTzgcxmazLe05lvWKa0Q0GuXy5cuoVCrMZjO//uu/TnFx8YIeQTweR61Ws2XLFmn4WllZuaS7XDYbPhQKbZgE5OzdMxAILOtCy2QyxONxBgcHicfjNDU1YTQapd53Z2cnNTU1mM1mKioqePfdd7HZbPh8PgwGAy0tLXg8Hg4dOnTbXnIsFmN+fh6FQkF+fj4HDx7k8uXL/Pu//zvf+ta3KC0tJZPJSEUKjEYjf/EXf8H8/Dxms3nRlKIbVVVVUVlZyf79+5f8/m+lu7ubv/u7vyOZTJJKpaTzSzOZjLSSXFtbS21tLdXV1VRUVEi90eyq3u0EAgGGhoZwuVzS6i9AcXHxqm7zs1gslJaWUldXh1qtJh6PYzQa2bRpE16vd0Gu4tzcHG63+66G/tndBS+++CIKhYK///u/p76+nl27dlFbW3vn/7/sV7wHCoXilse+JRIJAoHAkvLSUqmUtEJUVFQkTS5+9XmNRiMajYapqSni8Thw/cMyGo23DW6ZTIbp6WlOnTq14TZip9NpRkdHl1yuPbv3M9v7jcVilJSUAEg/ZpPJJC3JFxQUsGPHDqLRqLTA4/F4KCwsZMeOHYuWtspWiWlra6O7uxudTseFCxekAgSnTp3CaDTy5JNPUlNTQzweZ2BggKmpqQXfY3Yi/ZFHHqGwsHDRG1I2+D722GN38/FJJiYm6O7uJhQKoVQqcTqdFBYWUlxcjNVqxWKxkJOTQ1lZGS6XC6fTSUlJybLSULK7OA4ePLggsLlcriXfbB0Ox5JSbPLz85c8OZ+dN9NoNFgsFgwGA2q1ms2bNzM5Ocnw8LB04wyFQkxOTlJVVbXgPSyFTCaTErxDoRDnz5+ns7MTh8NxxxVWeMCBTaVSYbFYpC84u+9LJpMRiUQYGxujurr6jjk5CoUCi8VCf38/yWSSQCCAzWZb8IUXFRVJJb/tdjupVAqv10tpaekdf9ihUIgrV64AbJjglslkSKfT+Hy+m/LSbiUb2E6dOkVPTw/BYHDB351OJ7/xG7+BTqdDLpdjMpl48803b9oEX19fLwXEG4VCIbq7uxkYGCAYDJJKpTh9+jSVlZXSHNann34qDb8MBgOxWIyrV6/S3d0tPY9Wq6WoqAiDwYDVar2vp46Nj4/T19eHyWSipKSEqqoqtm3bRl1dHdXV1VIKzHKvnWy6y/z8PD09PVy8eJFf+7VfW3Czv1UK1WLKy8spLy9fVhtulJ0/zAar2dlZvF4varWagoICcnNzSSaT1NTUcPLkSYaHh6W/Dw4O0t/fz969e285ZE2lUkQiEYLBIPPz84RCISKRiPT9uVwunnjiCWmRcGhoaEntfqCBTalUYrFYsNlsZDIZJiYmpNWdWCyG1+uloaHhtnMPcD3nJRsAx8bGeO+993j11VdxuVzSYyoqKohEIvT29vIP//APUmLfm2++SV1d3W2fv6Kigj/4gz9YdNP2epUdiv7t3/7tolubFqNQKHC5XPzhH/7hoitn2VXK7I1KLpeTm5vLkSNHeOqppxaULbqVgoICDh48yBNPPEEymZTm0dRqNclkUpoLzfbAA4EAR44c4ciRIwvmmbI3RqPRyMzMzH0NbNXV1XzrW9/ijTfeQKPRoNPp0Gg0UiDO3qyXKxKJMDw8zGeffcYHH3zA6OgoLS0tFBUVrdpiV3t7O6Ojo9KCXmdnJ8FgkN/6rd+Sfm8KhQK73U5dXR2BQIAf/OAH5Ofn09HRQVtbG2+99RabNm266bmze4RbW1s5duwYZ86c4fjx4xiNRpqbm6XHlZSU8Du/8zvSLpSlWPHAlr3rZHsI2WEg/P9M6rq6Onw+H5cuXSIvL49AIMD4+DjJZJKioqJbThBm5zPg+ofZ2NiI2Wzm008/lVbPshd7f38/k5OT7Nixg7q6OinLedu2bbftsclkMinTOXvn3QiyGf0Gg+GmntetZLdPLWcYkQ12Sx3uqlQqaa50MV+9FrxeL59//rl0HmxRURFKpVLas5qdXL7fq4XZQ4qyK7Ur1av/anGJiooKaQV4NavMyOVyEokEoVAItVpNVVUVubm5bNu2TfpuZDIZKpWK5uZmjEYjvb29KJVKtm/fzs6dO6mtrb1lhe1sKonZbObgwYPo9XoikciCx2i1WoqLi/nGN74h3fju9JmvaGDL9rq6urrw+/3EYjEuX76MWq2WKgHIZDK2b9/O1atX6e/vl96Ix+Ohuroap9O5aKJgJpOhvb2d/v5+otEoHR0d7NmzR0rm+/zzz4lGo2zfvh2Xy8XExAQDAwMUFBSQn58v9Sq6urooKiqioKBgQxTIfJhkA1g2DSK75UqtVpNOp0mlUuj1+vt+EM+dFinu5Xmziw5Op1O6yd5pBHM/5efnk0gkMJvNUoApKipa9LdTXl4upaNEo1Hy8/OprKy8ZS5b9sZZWFhIc3Oz1Eu7MYUkGzgPHz5MLBa75Tz9V63oN+T3+zlx4gTf+973pH8bHh7ma1/7Gs888ww1NTVSYJPL5YyMjPCXf/mXOJ1O9u7dyze/+c1b9g5SqRQ/+MEP+PLLLwH44Q9/iEwmIzc3l8nJSY4ePcqlS5fYu3cvv//7v4/RaGRycpIf/vCHNz3X17/+dV555RVRTWKdsVgs7Nmzh2PHjnHs2DFpvqWuro59+/bx3HPP4XQ6120vW6fTUVlZSWVl5Wo3RZKt1LJUFotlyYsz2cT8HTt2LOnxiyXt38qKBjar1cqBAwcWfBDZ3tqNw8vy8nJef/119u7di1arlTYT32pOS6FQ8Md//McL5odcLpe0Pw2uXxhWqxWj0YjBYGD37t1SRYiv8vv9a/KEeuH2dDod1dXVfP3rX+fw4cPSbhKTyYTVasVms22YwqfCvVnRwKbRaHA6nUvahGwymTCZTEu+O8lkslv2sL76etlUELfbTTwep6GhQdrqkV1BvXz58gPZUyisrGx+2FJXdYWH17pM0L2dVColZW0HAgFpMUKn05FKpZicnCSdTostVYKwgW24wKZUKsnPz6ekpIT+/n7+6q/+Sqq64HQ6aWpqoqmp6Z7zewRBWLs2XGDLZiw3NDSQm5tLU1MTcH2uz2w2S5UR1usEsyAId7YhA5tSqVz2ao4gCBuHOMxFEIQN564CW3YzezKZ3HAlurP1o+6m4ulaJ5PJpDMIfD7fQ7MynEwm8fv9aLVasaL6kLirwJbNQA6Hw4RCoZVu06rIlp1OJpMoFAqMRuOGKVkE14OaXC4nLy8PnU7HxMTEkurhbwSxWEwqRrnUel7C+nZXgS17FmR2V/7dVMlca1KplFQEU6fTLVrmer2Ty+U4HA6MRiP9/f1EIpF1/73dSbYc/eTkJDk5OeJks4fEXQU2tVpNfn4+er1eqoO/mht1V0K2nrtGo6GwsBC5XL7hhqJwvdhitvLCzMzMuv/e7iQQCODxeNBoNBQVFS0481TYuO56jk2n09HY2IhGo+HMmTM37chfT9LpNKFQiDNnzkjnIm7EoAbXS8BkTwLq7Oxccn2r9SZb+bejo4OrV69y6NChFT9VS1i77mqsld1t//jjjxONRmlvb6e8vCkdMPgAAAwsSURBVJyysrJ1VzEjk8ng9/vp6+tjYmKCgwcPUl9fv9rNum+sViu1tbU0NTUxMDBAJpMhk8ngdDpvqkK8XsViMYLBICMjI/T29iKTyTh06BAlJSUb4v0Jd3bX37JMJqOxsZGamhpmZ2f51a9+tS7v/slkkqtXr/L5559TUVFBfX39hs5/U6vVVFRUcPjwYRQKBSdPnuRHP/rRhjqE2u/3c+7cOf75n/+ZYDDIoUOH2LZt26qW/xEeLFnmHmaPk8kkQ0NDXLhwgZaWFmZmZqTTbPLz88nPz19ywcEHyePx4Ha78Xq9dHZ2kkgkKCkpYf/+/WzatAmbzbZhh6Lw/yfUOzo6uHbtGt3d3XR1dZHJZNDr9WvyO1sqt9tNKpWioKCAuro66uvr2bx5Mw6HY0WLQgprmzQUjUQiBAIBJicnl3XnjkQiUmmi7NmT7e3t0uHJazFlIpt/l0gkSKVS0vFi2VLiAwMDq93E+y6dThOJRLBYLLhcLsLhsLRKul4XFGQymVS6yG63S2ddDA8PMzExsdrNW5RSqcTlci3pAGVh6aQem8fjoauri5aWFubn55f1JGq1Wpq/8Hg8XLp0Ca/Xi8fjwefz3ZeG34uioiKcTicFBQXU19ejVqsJBoPMzs6u2x/13TKbzRQUFOByuaQj9dbid7YUMpkMl8uFVqslEAjQ39/P7Ozskk5qWi16vZ6nnnpKKrktrIwFPba7zUZPJBKMjo5Kp1s/8cQTmEymB3ZS9XJlD3Kdn59ndnZW6r09bEENrp/9GI1GmZiYkHrZ6zF/L3tYTUdHB6lUilQqRTweX/PfaSqVwufz4XA4RGBbQVKPbWZmBq/Xy8zMzF3f4RQKBSqVCq1Wi1arRaVSrclVqGxgi8ViRCKRDZFgvBLkcvmanT5YinQ6veDAn/VAoVBgs9nIy8tbdxkFa9k9LR4IgiCsRWuvOyUIgnCPRGATBGHDEYFNEIQNZ/0tf62y7OpbOp2WJtsBafVtLS6W3E46nSaTyazbBQNBWMz6+hWuAfF4HL/fz9DQ0IJ8r/n5eebm5laxZXcnGo0SCoXWfFqEICyH6LEtw/j4OC0tLRw7dgyHw0FeXh42m42KigpisRgWi4WGhobVbuaiUqkU4XBYOlA4FArxxRdfSHXKXnrpJXHAjbBhiMC2DBcvXuSjjz6iu7sbk8mEWq0mHA4TDAaRyWTSifRrTSwWIxQKMTk5idPpRKvV4vP5OH78OKOjo2zevJnDhw+LwCZsGCKwLcP//u//0tfXx1tvvUVVVRUmkwm3283bb7+9prP1/X4/vb29XLt2jT179uB0Opmfn2diYoJAILDazROEFbd2f41rVLbIZnay3WKxcOjQISYnJxccFHLjQTfZIgPZM01TqRSzs7NEo1HUajVWq/Wm10okEszOzuL3+zGbzZhMplv2qvx+P4FAAI1Gg9VqRa/XA9d7a+fPn+ejjz4iNzeX4eFhjEYjpaWlHDhwgPb2duk5AoEAsVgMjUaDyWRa08FaEG5HXLnLYLFYmJ+f59133+XZZ59l06ZNWCwWampqsFqtKBQK0uk0Y2NjtLe3MzY2xo4dO5iZmWFoaIj+/n727NmDy+Uik8lw7do1hoeHycnJ4cCBAxQWFqLVaonH40xOTtLR0cH4+DipVIpQKERtbS3Nzc0UFhaiUCiIx+PMzMxw7tw5PB4P4XCY6elptmzZwvbt26mqqmJgYIBz585J9eYUCgUKhULquY2MjBAOh7l06RKTk5NMTEyQSCR45ZVXKC0tXbP7fQXhdkRgW4bq6mpaWlr4p3/6J+bn53nmmWeoq6sjNzcXl8uFQqGQClf+x3/8B+fPn+dP//RP8fl8tLW10dbWxvj4OM3Nzdjtds6fP8/nn3+OxWLBYDCwf/9+NBoNMzMznDx5ks8++wyfz0dBQQFnz55l8+bNJJNJnn32WYxGI6FQiCtXrvDjH/+YSCSCwWDgwoULVFRUMD09TX5+PoODgwwPDzM5OSnt4y0tLZXeU/YQm9bWVgYHB2lra6O7u5uKigpyc3PJy8tbxU9cEO6O4rvf/e53V7sR60VxcTF2ux232825c+c4ceIEV69exel0YjabpSFma2srFy5cwOfzceDAAfbv38++ffuoqanh+PHj6PV6XnjhBfbt24fVaiWZTNLf309jYyMWi4Xu7m7+/M//nL179/J7v/d7PPvss9TV1dHX18dHH31Ec3MzZrOZvr4+fvSjH1FfX8/LL7/MK6+8wjPPPENLSwsdHR0UFRXxyCOPANfTVPbs2cObb77J3r17UavV9PT00NHRwdzcHL/927/N/v37sdvt9PX1SYVCCwsLV/lTF4TlEz22ZbDZbDzxxBPodDra29tpb2+nt7eXf/zHf+Sll15iz549FBcX09DQwJkzZ+jp6SEnJwe73Y5KpcLv9xOPx1EoFDidTgwGA06nk97eXoaGhkilUni9Xvr7+zGbzVRUVFBdXY1arUar1XLlyhX6+/u5du0aGo2G3t5eTp8+zeHDh6XS13a7nccee4y2tjbOnj1LXV0dZrMZo9GIxWIhPz+f3Nxc4vE4gDRfaLfbycvLk9JYEomE9BhBWG9EYFuGTCaD3W7nhRdeoLGxkS+//JKPPvqI06dPo1arUalUvPHGG2zatAmn04lcLkev16NUKpHL5dLp8lqtVipRo1QqF8xj+Xw+3G43BQUFWK1W6VSl/Px8SkpKsNlsTE5OUlhYiNvtluboLBaL9HpbtmxhamqKwcFBotHobd+TTqdDr9dLB7kolUq0Wu2620EhCF8lrt5lyO4ukMlkOJ1OXnvtNf7mb/6Gr33ta3R0dPDee+/d82skEgnm5uaYmZm5qcek0WgwGo3IZDLi8TjxeJxMJkMsFltQIFSj0Yhj5oSHmghsy3DixAk+/PDDBf9mMBjYuXMnDodjRV7DYrGQm5tLX18f4+PjC7ZpxWIx4vE4TqeTkpISrFYr6XSavr4+3G73gsep1WoqKyulnQaCsNGFQiHpvBIxFF2G9vZ2+vv7cblcFBQUoNVqmZmZoa+vD5vNRmlpKZlMhunpaUKhEMlkkqmpKYLBIEqlEo/HI+WmTU5OYjQaCQQCTE1N4fP5CAQClJWVUVFRgdFo5PLlyzidTrZt20YkEsHj8aBQKKisrMThcOByuWhoaODUqVNotVr27duHUqmkp6eH+fl5qUS7QqFALpfj9/uZmprCbrcD13PfpqenUSgUBAIB0uk0fr8fn8/H9PQ0wWCQSCSCVqsVpzsJa172eIOKigoR2JZjdnaWgYEBTp06RXl5OTqdjqmpKT755BOqqqrYu3cv6XSa7u5uvF4vcrmc3t5eiouLUalUdHd3k06n8fl8XL58mYqKCsbHx5mYmMDn8zE8PExZWRmbN29m165dDA0N8Ytf/EI6nyEQCFBcXExVVRUWi4Xq6mpee+01/uu//ot0Oi0l1vb19WE2m9m5cydmsxmz2UxOTg4TExP09/djMBjQ6/WMjo7idrtRq9UMDQ1hMpkYGxvD5/MxNjbG+Pg4gUCAgoICUf1DWPOylXdApHssi0ajoaGhgf3793PlyhUuXrzI8PAw1dXVHDx4kObmZuRyOf/zP//D4OAgZrOZcDiMTqcjEAjQ0tIi9X6mp6cxGAz09PTg8/kwGo2o1Wry8vKoqanhkUceQS6X4/V6uXbtGqlUioaGBo4cOYLNZkMul2M0GqmsrMRgMEhHBwaDQZqamnj66acpKSlBoVBIc25Xr15FoVCQyWSYn5+nvb2dSCSC0Wgkk8lIQTYSiSCXyzGZTFitVikhWBDWsmQySTqdJi8vT5x5sBzT09Mkk0lyc3Pp7u5mamqKVCpFfn4+paWlWK1WUqkULS0tC0oaFRUVIZfLGRsbk/5Nq9VSUlIiDVVlMhk5OTmUlpZSVFREMplkYGBACjQ5OTkUFxdTVFS0YKtTKpViaGgIt9vN3NwcBoNByrczGAzA9dJE09PTdHZ2YjKZpDMsR0dHCYfDqFQqcnJykMvlRKNRZmZmgOsrsU6nUwQ2YV2Ix+PSWbkisAmCsOGIVVFBEDYcEdgEQdhwRGATBGHDEYFNEIQNRwQ2QRA2HBHYBEHYcERgEwRhwxGBTRCEDUcENkEQNhwR2ARB2HBEYBMEYcMRgU0QhA3n/wHmV+kbdTWkXgAAAABJRU5ErkJggg==)
physics-General
physics-
Three rods of the same mass are placed as shown in figure. What will be the coordinates of centre of mass of the system?
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)
Three rods of the same mass are placed as shown in figure. What will be the coordinates of centre of mass of the system?
![](data:image/png;base64,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)
physics-General
maths-
If
then descending order of ![a comma b comma c](data:image/png;base64,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)
is
If
then descending order of ![a comma b comma c](data:image/png;base64,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)
is
maths-General
physics-
A disc is rolling (without slipping) on a horizontal surface
is its centre and
and
are two points equidistant from
. Let
,
and
be the magnitude of velocities of pints
and
respectively, then
![](data:image/png;base64,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)
A disc is rolling (without slipping) on a horizontal surface
is its centre and
and
are two points equidistant from
. Let
,
and
be the magnitude of velocities of pints
and
respectively, then
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAL0AAACaCAYAAAD8fkm+AAAdSklEQVR4nO2deWzT9/3/H45jO3YuO86FTQK5Qw6SkEAKIaWhlJu2aGxdaVdppdW0Ter6T6f9U6lT1a3an+uktpO+m9aLTYOutGkRUAJNSmg4kkISwOQkhxOcw47PXLZ/f/CzV9YTsOOP7c9DspAj9fN+xnn25df7eL3eEq/X60VEJIqICbUAEZGlRjS9SNQhml4k6hBNLxJ1iKYXiTpE04tEHaLpRaIO0fQiUYdoepGoQzS9SNQhml4k6hBNLxJ1xIZaQCQwOzuL3W7HYrEwMzODy+ViYmICj8cDgNPpZGZmBrfbfdt/Fx8fT3JyMjExMf738fHxqNVqNBoNSqWSlJQUJBLJkv9OkYxo+jvE5XJhs9mwWq3YbDZmZmb87y0WCxaLBafTeZvpHQ4HFovF/96HSqVCrVYjlUqB/5peo9GQkpKCSqUiJSWFxMREkpKSSEpKIjExkcTERGJjxT/d3SIRjxZ/Nx6Ph9nZWf9rdHQUg8GAwWCgt7eXK1euEBMTQ3p6Ojk5OWRnZ6PVaikpKfEbMy0tjRUrViCTyW579sTEBENDQ8zPz/vfj4+PMzAwwMDAAJOTk/T19ZGdnU1xcTGFhYX+V3JyMkqlkri4OORyufhtcAeIpv8epqenOX78OM3NzZw4cQKZTEZ5eTmrV6+mpKSEyspKNBoNMpmMmJgYYmJikEgk/n8B//v/xev13hb9fe99L997g8HA5cuX6ezspLu7m+vXr6PT6di+fTvbtm2jtLSUhISEJftMwh3R9N/A4OAg58+fp6Wlhf7+flauXElhYSElJSWkpaWhUqmIj4/3/xsbGxvUSOtyuXA4HDidThwOBzabDaPRSFdXF11dXQCUlpayYcMGNmzYQFxcnBj5vwPR9P8fl8uFwWCgubmZkZER5HI5Wq3Wn5osW7YMvV6PUqkMtVQ8Hg8zMzMMDw8zMjLC2NgYExMTWCwW5ufnWbt2LbW1tWRlZX0tpRIRTc/k5CQGg4Hu7m5MJhNzc3NoNBry8vJYtWoVK1asQKFQhFrmd2I2m+nr68NgMHD9+nUkEgkqlQq9Xs+qVasoLi5GpVKFWqZgiFrTLy4uMjIyQltbG21tbZhMJoqLi3nooYcoKSkhMTEx1BLvGI/Hg9Vqpbm5mebmZqanp8nOzmb9+vXU1NTctlIUzUSd6d1uN3a7nbGxMY4dO8YXX3yBWq3mJz/5CQ0NDaGWFzAmJiZoaWnhxIkTTE1NsX//fioqKsjIyECpVEZ1zh91pp+amuLIkSP87W9/Y926dfz0pz+lurr6ttWWSMGX+58/f54//vGP6PV6fv7zn1NXV0dcXFyo5YWMqDG90+mkubmZf/7znyQnJ7Nr1y6KiopIT08XxOQ0WLjdblwuFzdv3qS1tZXTp0+zfPlyfvSjH7F69epQywsJUWF6o9HIyZMn6enpIS8vj5KSEoqKikhISPjG9fNIxWg0cvXqVS5fvozdbmft2rVs3bo1qj4DiHDTe71eenp6aGlpYXJykry8POrr68nIyAi1tJCxsLDA1atXOXfuHCaTicLCQhoaGqLqjE/EHuBwuVxcv36d1tZWJicnqa2tZePGjVG/dCeTyVi9ejWpqamcPHmStrY2vF4vNTU16PV65HJ5qCUGnYiL9F6vF4fDQU9PD4cOHWJxcZH9+/dTVlYmLtf9D06nk5aWFg4fPkxNTQ0NDQ1kZ2cLfl/iXok40zudTj777DPeffddKisrOXDgABqNJtSyBI3BYODPf/4zycnJPPXUUxQVFUV0qhNRpp+amuKDDz7g6tWrbNy4kU2bNpGUlCRG+O9hfn6esbExPvnkE65du8bWrVvZuXNnxBo/Ikzv9XoZHR3lX//6F/Pz89TU1FBVVUVqamqopYUNbrebGzducO7cOa5evUpxcTE7duxArVaHWlrACfuJrNvtxmKxcPjwYbxeL/fddx9r1qwhOTk51NLCCqlUysqVK1EqlSgUCtrb20lMTGTdunWkp6eHWl5ACWvTe71eLBYLH3/8MWNjYzz66KNUVVVF/EQsWMTExLBs2TK2bNmC2+3m3LlzKJVKampqIiqIhPWuhM1m49KlSxw5coQ9e/ZQVlYmGj4AJCYmsm/fPpKSkmhvb6e7u5u5ublQywoYYWt6t9tNR0cHBw8e5Omnn6aiokKsHgowzz33HHa7naamJoaGhoiA6R8QxqY/e/Ysra2tVFVV0dDQQHx8fKglRRwymYynnnoKpVLJO++8g9lsDrWkgBCWpu/u7ubixYvI5XIefvhhVCpVxC6vhRKJREJWVhabNm1Co9HwxhtvMD8/H/YRP+xMbzQaOXXqFAAPPPAAy5cvD7GiyEYul1NcXExNTQ3z8/O8++67WCyWUMu6J8LG9B6PB5vNxvHjx7HZbFRUVFBZWRlqWVFBQkICpaWl1NXVcfbsWTo6OsLa+GFjeqfTyZkzZzh37hy1tbXU1taKO61LiEajoaamhurqaj799FMMBoO/X0+4ERam93g8jI6O8sorr7Br1y6qqqoiuvAj2Hg8HhYXF7/WZvD70Gg0/OIXv2BkZIT29nbGx8eDpDC4hIXpR0dHaWlpIScnh/Ly8ojaKAkFk5OTXLlyhZ6enrualD733HN0dXXR1NQUBHXBR/A7svPz81y9epXTp0/zq1/9irS0tKir9AkUbW1tfPLJJ4yNjSGXy7FYLBiNRl5++WWqqqp+cK1BSUkJeXl5GI1GLly4QE1NTZCVBxbBu8dgMHDlyhVyc3OprKwUd1zvAofDwZEjRzh06BAKhYKGhgZ27tzJ1q1bUavVfPDBB/T29v7g56lUKjZt2kRMTAzNzc3Y7fYgqg88gjb93Nwc7e3tDA8Ps3v3blQqlRjl75DZ2VmuX7/OG2+8gVQqZcuWLezdu5edO3eyd+9e9u3bx9mzZxkcHLyj55aUlJCdnY3JZKK9vT1I6oODoB00NDTE4OAgSqWSdevWhVpOWHLz5k2OHTvG8PAwDz/8MBUVFf72HzKZjIKCAiYmJrDZbHf0XKVSSWVlJcuWLaOxsTGsNq0Ea3qPx8Pp06eRSCQR1YRpKfF1PP73v//Nb37zG4qKim5LDz0eD2azGalUelfLv4WFheTl5dHV1cXQ0BALCwuBlB80BGt6s9nMhQsXUKlUbNiwIdRywhJfn06z2cyuXbu+turlcrloaWmhrKyMzMzMO35+bGws+fn51NfX83//939hs2ElWNN/+OGHZGRk3PZ1LHJnmEwmBgYGkEgkXyubnJ+fZ2hoiLfeeouKigqysrLuaozs7Gzq6+s5fvw4o6OjYbFhJTjT+1rRnTp1itzcXMrLy8XDZHeJVColNjYWr9fL4uKi/+eLi4sYDAbee+89cnJy2LRp011FeriV22dlZVFQUMCXX37JxMREoOQHDcGt08/OztLR0YHb7SY7OzviStWWEq1WS25uLjKZjJMnT1JVVYVUKmVgYIAzZ84wMDDAM888Q2lp6V0fzZZIJKjVanbv3s3nn39OWVkZer0+wL9JYBGc6e12O42NjaxevRq9Xh/2S5SLi4uYzWaGh4cxGo0AFBQUkJSUhEKhQKVSBS19S0lJYc2aNaxfv56jR49y8+ZN4uPjGR4exmQysXnzZvbu3XvPRzp86/YHDx7EaDQyOzsr6JRUUKb3rSY0NTXx6quvsmzZslBLuicWFxcZGhri3LlznDhxgpMnTyKVSjlw4ADLli0jMzOTqqqqu04tvo/Y2FgqKir43e9+x+uvv87nn3+OXq+nqqqKH//4xxQVFeF2u+85fZTJZCxfvpzMzExGRkYwGo3k5uYG6LcIPIIyvc1mY2BgAICcnBySkpJCrOjeuHnzJi+//DI3btzg2Wef5aWXXiI1NZULFy7wpz/9idzcXLZv3x5UDVKplOTkZIqLi3nuuefQ6XTI5XJiYmJwu91MTEyg1Wrv+ZoeiUTCgw8+SGdnJwaDQdCml7700ksvhVqEj4GBAU6cOEF+fj73339/2JYAer1eZmdnef7555mbm+PJJ59k+/btaLVaFAoFqampmEwm0tPTqa2tDZoOq9XKpUuXOHjwIK+//jqHDh1iZGTE3/qwu7ubL774gry8vID0+ExJSaGxsRGZTObv+S9EBBXpTSYTly5d4vnnnw/rIu/FxUVaW1sZGRlh27ZtNDQ03NY0KT4+nr179wZ9VSouLo6VK1eya9cucnNz6e7uxmq10tTUxIoVK8jNzaWuri5gwSU9PZ3MzEysViuDg4Pk5+cH5LmBRjCmn52dZXJyErPZHPatPObn5zlx4gSZmZlUVFR84wrUUhhCLpeTmZlJRkYGVVVVDAwM0NfXh8PhQKPRkJubS05OTsD+55PJZOTn5zM0NERPT49o+u9jenqa6elpUlNTUavVYb02v7CwwJkzZ1i7dq1geuF7PB4SEhKorKwkKSkpaN+keXl53Lhxg76+vqA8PxAIJukyGo1MTU1RXl4eain3jK/Sy+PxhLyk0Vdb3NHRweHDhzl8+DBnz57FZDIF5YBYXl4ecOsC6q/ehi4kBBPpfaavq6sL6ygPt5YKV69ejVQqDfm2vNPp5Pz58zzxxBNMTk76N/0ef/xxfv/73wc8jdTr9SgUCvr7+3E4HIK8mlQwkX58fByLxUJRUVGopdwzCoWCxx9/nNbWVt555x06OzuBW13ZhoeHaWxspKenZ0m0DA4O8tZbb2E2m/01sWNjY7S1tXHhwoWgRGO9Xo9Go6Grqyvgzw4Egoj0vl1Ll8tFdnZ2qOXcMzKZjAceeACj0cjFixd58cUXkUqlyOVyGhoaqKioQKvVLomWubk5TCbTbUXgCwsL2O12rFZrUMbUarXEx8dz48YN1q9fH5Qx7gVBmH5mZoa5uTni4+PDdm3+q8TExJCRkcGjjz5Kbm4uAwMDOBwO5HI5hYWF5OfnL1nf94SEBAoKCvj000/9P5PL5aSkpKDT6YKSSiYnJ6NUKgXbLUEQpjeZTACCWekIFDk5OeTk5IRUQ3p6Otu2baOrq8s/uVyxYgUPPvggubm5QTG9Wq1GpVL5zxoJDUGYfmJiAq/XS1paWqilBA23243D4cDpdCKVSklISCAuLi7ok3aNRsPmzZtRKBScPn0at9tNTU0N9fX1QZtkpqamkpCQQFtbW1Cef68IwvTT09MAS5bnLjVerxez2cwXX3zBxYsXSUhIoL6+nvLy8iVpWqVUKtmyZQtbtmwJ+lhwK9LHx8djNBrxer2CW40ThOl9kT5Sz86PjIzwn//8hz/84Q/Mz88jkUgoKCjgwIEDPPvss6GWF3AUCgVKpRK3243NZhPczeyCUOJwOAAiYhL7TRgMBj766CNu3ryJ2Wxmenqay5cvc+7cOYaGhkItL+BIJBJkMhkKhQKbzSa4TSpBmN7lcgFEbH9Kq9X6tUmdy+XCYrGEXaOkH4pEIkEqlbKwsCC41iCCML2vfvNez3QLFa1W69+e95GYmEh6enrEXuwsk8mIi4vDbrcLLtILIqdfWFjwfyVGIgUFBTzyyCP09fVht9uRSqUUFRVRV1cX9tVh34ZcLicxMZGpqSnBFZQIwvQWiwWNRhORF/UC6HQ69u3bR25uLu3t7SQkJLBhwwZWrVoVamlRiSBMHw0kJiayYcMG1q5di0QiQS6XExsrfvyhQBCfuu+P/9XeLJFGTEwMCoUirItjIgVBTGR99ZlOpzPESkQChdfrxe12I5PJBLc5JQjTKxQKJBJJRN1KHe0sLCzgcrlITEwU1MYUCMT00ZDeRBui6b8HX71msM53i4QGr9cb8nLJb0IQpvftxPp2ZkXCn7m5OWw2G6mpqYJbpRKE6dPS0pBIJGHR8Vbk+3G5XLhcLlQqlX++JiQEYfqUlBQApqamQqxEJBBMT0/jcDhYvny54PJ5EIjpU1NTkUgkTE5OhlqKSACYmprCbrcLtt5ZEKZPT09HIpFgMpkEdzhJ5M6ZmZnB5XIJ9lyRIGYYWq3Wf5mvy+VasnP1MzMz2O322y4Ii42NRa1Wo1QqBbnyEA74TF9YWBhqKd+IICI93CoxS0hIYGRkZMnGfPPNN9mxYwclJSWUlJRQWlrKQw89xOHDh8X5xT0wOTmJzWYLeVH8tyGISA+3TiJqtVo6OzuXrOHTU089hcvl4tq1a+zevZvi4mJ/M6b4+Hj27du3JDoiicXFRcbHx3E6nWKk/z50Oh0pKSl0dXUtWaVNZmYmSUlJ6PV6duzY4b+qZnx8XLDtK4SO0Whkbm4OrVYr2Es1BGN6vV7vj/RLhclkIiYmBr1ej1qtxmq10t7eTmpqasT14Fkq+vv78Xq95OTkCHK5EgSU3mi1WlJSUjCZTMzMzJCYmBj0iWRXVxc2mw2v18vhw4eZmZmhr6+P+vp6qqqqgjp2pNLb2wsguGqpryIY08tkMrRaLRkZGVy+fJnq6uqgruJ4PB7a2tro7+/HarXy3nvvIZPJ+OUvf8mOHTvQ6XRBGztSWVxcpL+/H5VKJdgLGUBApgf8t+0dPXqUoqKioJp+dnaW5uZmGhoaeOGFF/w/F9qWeThx8+ZNRkdHqa6u/lohvJAQVNKl0+mora3lgw8+COqJS4/Hw5dffklNTY3/RnLfS+TuOXnyJMuXLxd8u3VBmV6lUpGdnY1Go6GnpweLxRLwMTweDw6HgyNHjpCens7KlSsDPkY04vV6/aYvLi4OtZzvRFDpjVQqRa1W88ADD9DR0UFOTk5AOyS4XC4MBgPvvvsuH3/8MTk5OeTm5opdCe6R+fl5RkdHmZ6eRq/XC37lS1CRHm4VlOzcuZMrV64wOjoa0GoqX+dgo9FIVVUVarVacN23whGn08mpU6dYsWIFer2euLi4UEv6TgQV6eFWQcm6det47bXXuHHjBlNTUwGLHAkJCdTV1VFXVxeQ54ncShctFgtHjx5lz549gj1k9lUEF+l9PWEeeeQR+vv7aW9vX7KxvV4vi4uLLCwssLi4KJ74/AHMzc0xMjLiXxgQemoDAoz0PrZv305raytdXV3U1dUFfUt7bm6OgYEB/va3vzE+Po5Op6OhoYHNmzdHbLvBQNDf38/Jkyf52c9+RlpaWlicTBWs6dVqNdXV1QwPD9Pa2sr27duDNpbH42FwcJAXX3yR8+fP43A4UCqV9PX1sbCwwO7du4M2djgzOztLX18fnZ2dvPLKKyQnJ4da0g9CcOmNj5iYGDZu3IhUKqW1tTWoPXEcDgfXr1/n+PHjDA8PMzk5yfDwMG1tbXz22WdBGzfc6e3tpbe3l/z8fPLy8sLmG1Gwpodb5zeysrKwWq10dHQEbZy5uTmmp6exWq235fE2m43R0dGgjRvO2O12Ll26xNTUFLt37yY2NjZsNvcEbXqpVMratWvJy8vj/fffx+l0BmVyKZfL0Wg0pKen+3PSmJgYNBoNWVlZAR8vErhy5QoDAwOkpqZSW1sbajl3hKBND7Bq1SpKS0vp7e3l0qVLQUlzkpKSqKqq4rHHHiMtLY34+Hi0Wi11dXXs378/4OOFOwsLC3z44Yd4vV4efvjhsElrfEi8YbA7YzKZOH36NG+++SZ///vfg1Jl73a7mZmZobOzE7PZjFqtJicnB51OF3Z/1GBz7NgxmpqaqKmpYe/evYJr5vR9hIXalJQU1qxZQ15eHidOnGDr1q0BTzukUikajYaamhoWFhb8F4WF2x80mPgCw5EjR6iurqa2tjYsP5+wUBwbG4tOp+PJJ5/kyJEjZGZmEh8f728SFSgkEknE3nB4r3i9Xqampnj77bfR6/WsWbMmLHZfvwnB5/Q+lEol69evp6ysjM7OTjo6OsTel0vIxMQEra2t9PX1sXnzZvLz88M27Qsb0/suYnvssceIjY3lwoULXL16FbfbHWppEY/VaqWzs9O/SVhWVkZiYmKoZd01YWN6HyqViieeeAKZTMahQ4cwmUyhlhTRLC4u8uWXX9LW1kZWVhZ79uwJa8NDGJoeICMjgwcffJDU1FRee+21UMuJaK5du8aZM2fweDw888wzYbMB9V2EpeljYmIoKCjgvvvuQy6X89e//jUoVVbRztjYGB9++CFxcXE89thjEXOje1iaHm6lOSUlJdTX13Px4kXOnz+P2WwOtayIwOv14nQ6efvtt1EqlWzcuFGwLfruhrBYsvw21Go1a9asYWhoiDNnzqBQKKisrBRsZ61wwOv1YrFYOHbsGBaLhR07dlBWVhaW6/HfRthGeh9qtZrHH38chULBxYsX6ejoEJuv3iWLi4uMjY3R2tpKc3MzDz30EOXl5RGT1vgIi2MIPwS73c5f/vIXpqenqa+v5/777w+b891CYGFhgbGxMU6fPs2JEyd4+umnWbduXURu1kWM6X156CeffEJzczPZ2dm3NXES+W4MBgMHDx7EaDTy61//mtLSUqRSaUSs1vwvEWN6+G8+2t3dTUtLCyMjI7zwwgssX748onLSQHP06FFOnTqFTqdj27Zt5OTkCL6jwb0QUab3YbVauX79OmfOnMFkMrF161aqqqrECe5X8HUx+PjjjxkcHCQnJ8dfuxDpASIiTQ+3GhANDQ3R2NjI/Pw8paWlVFdXk5mZGWppIWdhYYHBwUGam5sZHh6mtLSUDRs2oNfrQy1tSYhY08OtdGd6epr333+fiYkJCgoKqK6uZuXKlYLtnR5srFYrvb29XLhwgd7eXhoaGti4cWPYHy24EyLa9D5cLheNjY20traSlZXFrl27yMjIICEhIeK/yuG//Xymp6fp7u6mqamJ2dlZDhw4QHFxcUROVr+LqDA93PrDd3V18Y9//IPGxkZ++9vf+s0f6SwuLjI6Osqrr77K0NAQO3bsYP/+/Wg0mqgzPESR6eFW14OJiQn6+/s5fPgwLpeLTZs2sXnz5rAtiPgu3G43N27c4KOPPuL48eNs27aN9evXk5ubi1qtDovGTMEgqkwPt1YtZmdnuXLlCleuXMFgMDA3N8eqVavYsmULer0+7FOe2dlZLl++TGtrKwMDA6Snp1NWVkZZWRk6nS7idljvlKgz/VcZGxvj0qVLXLt2jZmZGSQSCTk5OVRWVrJy5cqwmtz56le7urq4dOmS/9SpVquloqKCtWvXIpPJojKd+V+i2vQ+JicnaW9vp6mpifn5eXQ6HcuXL0ev16PT6Vi2bBlKpVJwhvF4PExNTTE+Ps7Y2BjDw8OMjIwwOTlJXl6ev7wyEo8S3Aui6b+C2+2mra2Njz76CIPBQFJSEmvWrKG8vBydTkdycjIqlQqlUhmS+lC32838/DxOpxOXy4XZbObatWt0dnbS09OD3W5n69at7NmzB71eH7Y1rMFGNP23MDExwblz52hsbKSpqYmUlBQ2bdrEhg0bKC8vJysr67Z7qoJxZ5XX673tZbVa6evr4+LFi7S3t3P69GlWrlxJQ0MDDQ0N3HfffQEdP1IRTf8tuN1uZmdncTgc2O12enp6aG9vp7u7m+HhYQBWr15NeXk5+fn5ZGdnk5mZSUJCQkDGNpvNXL9+nZs3b9Ld3c3ly5cZHx8nPj6ewsJCCgsLqampQafTkZCQgFKpjOjzMoFENP0PwBdlJyYmmJ6exmw2MzU1xeTkJBMTE1gsFqxWKw6HA5lMRl5eHklJSaSnp6NQKL73+R6PB5vNhslkYnR0FLPZ7O+lqVKpSE1NJS0tjdTUVDQaDRqNBrVa7X++0OYaQie2p6eHlpaWgN7tFOn47q4aGxtjbGyMqakpzGYzdrvd3+teoVCgUql+0Fq41+v15+o2m425uTnkcjlpaWkkJCRgt9v93zpi94d7J9Zut2MwGJifnw+1lrAkIyPjtl1dX1rkdrtZWFj4wRe5SaVSZDIZcrmc2NjYr50NslqtQb1bN5qQ2O12b09Pj9g0SSRqEHN6kagjOs/XikQ1oulFog7R9CJRh2h6kahDNL1I1CGaXiTqEE0vEnWIpheJOkTTi0QdoulFog7R9CJRh2h6kahDNL1I1CGaXiTqEE0vEnWIpheJOkTTi0QdoulFog7R9CJRh2h6kajj/wE4x/rOcKg4BQAAAABJRU5ErkJggg==)
physics-General
Physics-
The acceleration of the center of mass of a uniform solid disc rolling down an inclined plane of angle
is
The acceleration of the center of mass of a uniform solid disc rolling down an inclined plane of angle
is
Physics-General
Physics-
A solid sphere of mass
rolls down an inclined plane without slipping, starting from rest at the top of an inclined plane. The linear speed of the sphere at the bottom of the inclined plane is
. The kinetic energy of the sphere at the bottom is
A solid sphere of mass
rolls down an inclined plane without slipping, starting from rest at the top of an inclined plane. The linear speed of the sphere at the bottom of the inclined plane is
. The kinetic energy of the sphere at the bottom is
Physics-General
Physics-
The moments of inertia of two freely rotating bodies
and
are
and
respectively.
and their angular momenta are equal. If
and
are their kinetic energies, then
The moments of inertia of two freely rotating bodies
and
are
and
respectively.
and their angular momenta are equal. If
and
are their kinetic energies, then
Physics-General
biology
Famous palaeonotologist/Palaeobotanist of India was:
Famous palaeonotologist/Palaeobotanist of India was:
biologyGeneral
physics-
A small object of uniform density roll up a curved surface with an initial velocity
. If reaches up to a maximum height of
with respect to the initial position. The object is
![](data:image/png;base64,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)
A small object of uniform density roll up a curved surface with an initial velocity
. If reaches up to a maximum height of
with respect to the initial position. The object is
![](data:image/png;base64,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)
physics-General
physics-
A uniform rod
of length
and mass
is free to rotate about point
. The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about
is
, the initial angular acceleration of the rod will be
![](data:image/png;base64,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)
A uniform rod
of length
and mass
is free to rotate about point
. The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about
is
, the initial angular acceleration of the rod will be
![](data:image/png;base64,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)
physics-General
physics-
A particle of mass
moves in the
plane with a velocity
along the straight line
. If the angular momentum of the particle with respect to origin
is
when it is at
and
when it is at
, then
![](data:image/png;base64,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)
A particle of mass
moves in the
plane with a velocity
along the straight line
. If the angular momentum of the particle with respect to origin
is
when it is at
and
when it is at
, then
![](data:image/png;base64,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)
physics-General
maths-
Assertion (A): If the system of equations
have non zero solution then ![lambda equals 5](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACUAAAANCAYAAAAuYadYAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAM9JREFUeNpjYEAAJiC+BcS2DLQF//FgrIAFiJcCsTCNHUUy8ADi2sHmKFA0nhtsjgKBo0Skrf9EYKo5KgOIS4B4Lg1D6hcQfwLibUBcBMQ8+DSoAPEGKPsgIcUUAlCmMoam3xtArIErLe0GYnEovxqI02gQfdiAGzQQMEAzEEci8UG+OMxAP/ADXcASiNdgUXifxmUWDOgA8V1kAVC6OYnD8i4CUUgOWAcNBCYo9oA6KAhZ0UJ0ASSgB8THqeyoUGh19geI3wHxKiA2ZRjsAABOiDy9zam25QAAAGN0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+JiN4M0JCOzwvbWk+PG1vPj08L21vPjxtbj41PC9tbj48L21hdGg+f1FJcwAAAABJRU5ErkJggg==)
Reason (R): If the system of equations
has a non zero solution then
is singular
Assertion (A): If the system of equations
have non zero solution then ![lambda equals 5](data:image/png;base64,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)
Reason (R): If the system of equations
has a non zero solution then
is singular
maths-General