Chemistry-
General
Easy
Question
Observe the following sequence of reaction and answer the questions based on it
![](data:image/png;base64,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)
Which of the following compound give benzoic acid on KMnO4 oxidation
- w
- y
- z
- all
The correct answer is: all
any mono substituted benzene oxidises to benzoic acid
Related Questions to study
chemistry-
Observe the following sequence of reaction and answer the questions based on it
![](data:image/png;base64,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)
Which of the following statement is not correct
Observe the following sequence of reaction and answer the questions based on it
![](data:image/png;base64,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)
Which of the following statement is not correct
chemistry-General
chemistry-
Observe the following sequence of reaction and answer the questions based on it
![](data:image/png;base64,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)
Compound z is :
Observe the following sequence of reaction and answer the questions based on it
![](data:image/png;base64,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)
Compound z is :
chemistry-General
chemistry-
In the Hofmann rearrangement an unsubstituted amide is treated with sodium hydroxide and bromine to give a primary amine that has one carbon lesser than starting amide.
General reaction :
![](data:image/png;base64,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)
Mechanism :
![](data:image/png;base64,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)
If the migrating group is chiral then its configuration is retained. Electron releasing effects in the migrating group increases reactivity of Hofmann rearrangement.
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)
In the Hofmann rearrangement an unsubstituted amide is treated with sodium hydroxide and bromine to give a primary amine that has one carbon lesser than starting amide.
General reaction :
![](data:image/png;base64,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)
Mechanism :
![](data:image/png;base64,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)
If the migrating group is chiral then its configuration is retained. Electron releasing effects in the migrating group increases reactivity of Hofmann rearrangement.
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)
chemistry-General
chemistry-
In the Hofmann rearrangement an unsubstituted amide is treated with sodium hydroxide and bromine to give a primary amine that has one carbon lesser than starting amide.
General reaction :
![](data:image/png;base64,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)
Mechanism :
![](data:image/png;base64,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)
If the migrating group is chiral then its configuration is retained. Electron releasing effects in the migrating group increases reactivity of Hofmann rearrangement.
Arrange the following amides according to their relative reactivity when reacted with Br2 in excess of strong base
I) ![](data:image/png;base64,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)
II) ![](data:image/png;base64,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)
III) 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)
IV) ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAARkAAACNCAMAAAC0Tv7EAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAMAUExURf////j4+Pv7+9zc3JeXl0ZGRjMzM15eXqCgoNvb2/39/bKyslRUVAwMDAAAAFlZWeLi4nl5eQMDAw0NDS4uLiwsLDs7O+Hh4fz8/Hh4eBoaGoiIiNHR0fHx8YGBgUVFRfLy8oSEhFNTU9XV1YaGhuTk5BQUFAICAp2dnQ4ODtLS0qmpqS8vL9nZ2RcXF2FhYVhYWGdnZ4CAgBAQEMjIyOvr6yEhIXBwcL6+vpaWlhkZGW5ubr29vRsbG7m5uZiYmG9vb5WVlefn5x8fHzg4OK+vr0BAQC0tLcnJyQoKCj4+PvT09H19ff7+/lxcXK2trdTU1IKCgrCwsE9PT/n5+QEBAYWFhR4eHk5OTo+Pj2BgYCUlJcLCwt/f31VVVT09PU1NTXd3d2JiYgkJCXt7e+/v78XFxWhoaFtbW19fX7q6uu7u7igoKB0dHRgYGOnp6YqKirW1tff394uLi5qamsTExKGhoZycnPb29iQkJKWlpebm5l1dXe3t7QsLC/Pz83x8fI6OjmlpaQUFBejo6HJycs/Pz3R0dBMTE2tra7u7uw8PDxYWFtjY2FFRUWRkZM3NzXV1dcPDw8rKylpaWsDAwM7OzggICMHBwVBQUCYmJre3t42NjdfX1wYGBvr6+kJCQikpKfDw8HZ2dkRERAQEBN7e3jk5OTY2NqSkpCIiIoyMjDIyMpKSkrGxsSsrKycnJ0pKSqampiAgIMfHx0NDQ2pqauDg4Kurq6ioqOrq6ra2tgcHB5mZmREREZubm2VlZdPT08vLy0dHR6KiokFBQWZmZpGRkRISEtbW1pOTk+Pj41dXV7+/v0hISH9/f56enrS0tJ+fn9DQ0ExMTH5+ftra2lZWVjo6OktLS3p6ejQ0NN3d3SoqKjAwMBUVFaqqqiMjI+zs7HFxcaenp7Ozszc3N/X19VJSUjExMcbGxnNzc66urhwcHOXl5aOjo2xsbImJibi4uJSUlIODg4eHhzw8PD8/P8zMzJCQkElJSTU1NWNjY7y8vG1tbQAAABE7eqAAAAEAdFJOU////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////wBT9wclAAAACXBIWXMAABcRAAAXEQHKJvM/AAAI7ElEQVR4Xu2cO3asOhBFHREyAc2NtYg1E8ZBxBwgZBQEDIPwnhKi+aj0w+1ri9Z+z3fhbmhQ6ah+0P7KZDKZTCaTyWQymUwmk9mZ+rao+kn/ltmYq3KlkvqVjKKGTYauqoqyLLJsDsAwgyCLSFGW7fpaBsAc1aYUbNd6MyPLstebAA4nryfNXBZ6i5iGstKbH09VjnpLIcph0ZsfjuzOlmnKUujNDwfL5+RzYZmD2/lkYJmrZrJlFFfN9NkymqtmxmwZjbxoBhXCrDc/nbbsDrndgtJJb348qJoOuR1y4CwZDRzNvp7mIZeUO4hGuqSU9XBaWh8PhFIObS2qDk6m0S/+eaa2aCO410KYEKpXRDo9PZJ6DDdrnmWsxqoakxGMqveGLhisiu5TGrmiLCPmUSJNuyOapV8bD3062e/UxfWRZrjSG6IR61lkWSajuDjJAIjmhhMWunRKp9N5rfb8kGjiR6ctk5BmkLjHdh7bO6LZLDOkYpnlUgaH0CByR4smOc2Md1YGSsLo5n+fmGaWW94UR0U3/1PTTHVHMqopFyuaxPzM3dsbEE2s305MM9XdTB+iieyxpOVn7t8Ro1ZUXH6YlmaKstNb0SANKqKGuPuZO47tP4Nk9nZ5Fy2apDRTRE77CZRbUUdrP/OVgp/pv9XCx7KIUlxKmum+d9cHho0JbNoyqLX/vGWiuw8XZBclmnQ0g4F9865PXAsrnXwGYfdbksEgo/qeyWgmtsfJEdXC2izz5zXjaVjJZp5n/DRz4xhITN8zFc04e5zTPGLMmsHxVQFUF8Gi2f3M386BR7vznLbvB+x0thiEXe0GPpOIZiAZ2zLoEYwhhbHXjMjoUFj37HgiWliJ+Blr96FpSSLVfHh3EgUZp2MtMAaLJg3NYKr5cKueWDDdykJ361lxUGEZJpo06qbKUgzSOAc2y0Eo41WDNwKjP84om7/tfSmksKXkhKU0WIrMBu6HMw3VCGEZ46RcVlvPfus0/eEqmp4SBznr++LE6Zd30pZsXUBLqbKeUUId3LNSKL9Cqgyyejm0OIX/i1+UXO/RsFUCP7Uf/Xc85CRvLFqLZBZctbPjAtO0zPsQjb+ZsWAvyoumHqPmPuUE9tm92moZXN1uGUdoVUz1MAzduDnMegh8/K3gPQNNqlOj56l80QeIBoduS1HiPJ7lRyfaPxOWwb/N0TIezfSkTGJYv7KJ+BG0+FDtcPtREeSZe0txzRvsBKy3W6Pz9XVgPIxtM0S0ZnCyoZqnhpaukifEHqIZTAiXgdA8eRcFjM9cEVanrwXWHmVaD4V7CnEt7T7PnJ9xWQaG0Z9P2TyNNVAzmHjOgLDrfmYr/ErAqx7RnL7fJL2xDOt96janx2nGsZowvpdXgbbo5kiYZhBluQ9F0h7ShcJ8MILDsnevD0y4Q/0GpJn9mNXP4By79V2r6fSAOgInbBKmGcFbIMSNAlwSV1zj1E7B4QL94euASiu2Ib400wpRKwREYLMMtHaYJSkoFwrSDA5khY+x+byoAguHGSMu2ykaR2XPoTSjlgIdpf3MFm80NstAW4aqgzQj+CHgWsIaLfxyollxLRe8HeICXxRqAcFjkN8+akbjOB0sY8j3oJnJBj6flbUnQdix9NUhxWHR5zAhn3FRpNRvcchVM2o94bDVz0Az+0egYHdYxnjroBlK2mywsj55fifrdRpgWuxMF7dPEtBvcdQ4ibLM6tVemjnEJrsH9mimQnLMY5H1KVtwsgr9Cma51GdgoNEd1uBUFKLRb3EInGQVJtZupeciNJ/xaIZmhf2B+dgpR4IQbBmuT6OG4ACnVadX4ELJTtdrO/y8hIn1JNaWyVkzztXk0owdi6MJ1gyJwwxi5Gac58ZpX2Ukrt3j7Tc/o46DzslMOGo/r7bMIoTRhN2PVdQC8xgUm86z9+I0I07YsO2IFRrKl7Q5sLPnXKibNmXjuLUDcNaMWk19Wc2VUbdDZrsZYE9oOUgzlOyac85qkAVTYoZ98pSMuU/Aol1NARcbHiue5p2CifIzR8vATPiMAq8vRjcNsX73aTATbBKmmS82CQ62zO4CDuDMvsHC7dLsEwMzMxcObh5GUHNxusJ1NS0YtGyNImyN9YTEJl1YmGZINKYRcF7v2BSIv4ZlcLAzA16RjaioLVD7L1L29W69uVa/THW922D/pTZdFrnCal6WhRq0Ki4EagbL0/w0rIej37LD7UgBRG96kMudHqSDluvn7/LU6ypQMzTtZoKP5RxkVpzkuhgQ124/B/k9oA62oSFFAbnAP+lYEaoZ8lHGjogBQfMOC17Nj5f8nuMnQAhjDUNMjdhvLzQi8EutMLWRlsFXmJ7VhNkNNg058geofP3keCAa4zOpJNSbDoTpqbGo2SL150ECMXSDM/eO5pwnKpgxm0BtV+9Nt5ve61WD6VUj670rGU7TmGe4C6+nMfeBO/8tyfwMa2V/Ai7EZxro4+pSEKvCwn0qwAyGChHb3KahdPSiD6Q373eDv0trpq0omJ2moU7sNRGCNd/rAX8frsOxUO5odcOUa1+XIKkoLIdKCPZrgsjzLaqRgmqeq8ywv5lOpw48BDMoUg1rGrKZ8XQHQlzoU3opwX4duaFy+FDUrkwzwnU5GmkLXn2eZJRoOOepCtWinptlNcTUzCO5ZubvDCGVZoz7AJCKcEtBPRxFtGM91uohKVAbglEPwoQ1dVJD2v5K7/pE8BGzcQZIMqa9HgFSWkuWtvRtp2/+DF1L7XcTap15cuZkoTux1kmfpkX9P9n26IN6nIliF40fKiV/p2H1X+BvxQbxaMmo4d1sIVCR9WDJKNHcm3imIfEsEHlvzTx1Hx7VsDJhuhEhIEt8tmTuioa6D7ejWiqc/9pzIOPTepwcwU/OHHhkw8rkxl+6emCPk2OJrpghs0+QjKWF5eKRPU4Ovu9ph3qcj2xYmQQ/RLHy0B4nB0TT6T8xHsLnSEYVQVE8s8fJsXT0uEXof8N7n31o/naYW8dK/3p+1v/fyfLwyvQbvNnSmUwmk8lkMplMJpPJZDKZTCaTLl9f/wCDvrcWX0yiJQAAAABJRU5ErkJggg==)
In the Hofmann rearrangement an unsubstituted amide is treated with sodium hydroxide and bromine to give a primary amine that has one carbon lesser than starting amide.
General reaction :
![](data:image/png;base64,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)
Mechanism :
![](data:image/png;base64,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)
If the migrating group is chiral then its configuration is retained. Electron releasing effects in the migrating group increases reactivity of Hofmann rearrangement.
Arrange the following amides according to their relative reactivity when reacted with Br2 in excess of strong base
I) ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAPMAAACuCAMAAADUOMskAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAMAUExURf///+Li4rq6usPDw+bm5s7Oznt7eysrKwAAAAMDAzIyMm5ubrOzs7e3t0lJSRcXFwgICCQkJJGRkZOTkwcHBwQEBDExMVZWVmFhYV9fXycnJw8PD8vLy5SUlAEBAWdnZ7+/v9/f33h4eAsLCzo6OuPj4/7+/pWVlQICAigoKKqqqr29vSYmJkVFRdra2t7e3hgYGAwMDNHR0UFBQf39/aampkNDQ9zc3BUVFREREWpqapubm2xsbOzs7DMzMykpKYmJidvb2/X19aioqIuLi93d3fLy8qenp4iIiC4uLqysrJiYmHV1dWNjY3R0dB8fH+Xl5dLS0q6urgoKCoKCgtDQ0CIiIuTk5O3t7Tw8PAUFBXd3d+rq6rS0tC8vL8/Pzzc3N8bGxuDg4KSkpGJiYsnJydXV1fz8/Ojo6A4ODjQ0NLa2tiMjIwkJCRAQELCwsDAwMHNzc1hYWBkZGcDAwM3NzVVVVVRUVBQUFE5OTtfX1+7u7mVlZevr63Jycvn5+bKysioqKsTExAYGBvT09ExMTBMTE8jIyO/v7zY2NmBgYDs7O1tbW/v7+6Ojo6GhocXFxfb29j09PVFRUfHx8a+vr7m5uZKSkvf39ywsLG9vb7i4uLGxsdjY2EBAQCAgIHl5eX19fRwcHOHh4V1dXRsbG4aGhp2dnWhoaNbW1o+Pj9PT0xYWFmZmZnFxccrKypqamoSEhICAgB4eHlNTU0JCQvPz84eHh21tbUdHR5eXl62trb6+vsLCwvj4+LW1tXp6ek1NTXx8fH5+fn9/fzk5OTU1NVdXV1BQUPr6+kZGRi0tLcfHx4yMjOnp6YqKiqmpqVpaWp6enoODgxoaGqWlpSUlJURERCEhIfDw8D8/P6KiohISEk9PT+fn59nZ2by8vLu7u5+fn8zMzDg4OHZ2dmlpaUpKSlJSUsHBwZCQkA0NDY6OjpaWlmRkZIWFhUtLS6urqz4+Ph0dHXBwcF5eXmtra6CgoJmZmYGBgVlZWdTU1EhISJycnI2NjQAAAK7JbnUAAAEAdFJOU////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////wBT9wclAAAACXBIWXMAABcRAAAXEQHKJvM/AAAIa0lEQVR4Xu2cS7ajOgxF02QszCCd9FgrI6DDPOgwJsZDm8UkaNY5xgk/GX9SVYbE+72q4uYDlo8sSyI3t0QikUgkEolEIpFIJL6Apu8bffgjDFWZZY82/x2z++6eTZSjfujbGWnto25baJ0N+sHvhia3A726qGD7L7g3TC5zfXwbyuxR6OPvpcBSXliJGej04feSr43cTMF30mbZKlbj57enfynNIytXUavPsqc+/FaKcrN+4eu/YPNK59+wee3bv2HzOvX6AZsb2LyK07D563NupJu1PlRU2f3rs08kIfdFEvIDrg2eS6GRb69D2neCrCSrtJ05Vnc/HX43BYx+VENTjMg7s0o/GodiAPzL8U9wadDQ1qxkr+QRt2XAndOP8ODTQ2ry8vFYdNMwPPhgk2n6Af/FLiIHGNHVHsA1W/3eqwKZ/RoWI4QOE6qpW+UhRR03gKGM9dw1mEWGCd3o1ghcK+Z6brxlnoQOCrvF2+a7+jkSSAH9O80IvqvU2ZVZ55ipNnMj/+GzUR0i9Dl0DpI5IO5NnELn0HDEqQpIl0+hM51UjcIXCu0v1Rl0ZtYZtlP673DkDDqjog3MLm41ygR96M4JdG6QRYYmRMxYvW9DnEDn6pNqAWWhd6Mjvs68SxZeFVJo375lfJ0h8yctqYC3R9d5gMyfNJgD3h9d55AFuYJCKxOcia1zyHpc4x8PYusctMGu8d7eI+vMROrT2/zeaVxknf+CzP5Cx9U5LF/e4luWxdU5sADe4tkliqqztVXQ5G+O3IFtFg+ho+p83BFqevWBzBePymy2X58lps7HHWreM9zQGe3y6qdF1PnII6GxsrKuntX0P16MKaoMVjO1cQ6GEXU+kDlXFnbj4ulGfcw8u9fyMLHpOUfDeDpzhzHkjErjbq/byKmQG2AsNVyTm1nn/30fA5mEobjAM9ldnA5151hWGs+4Ct2oTaDhzcnpgf+FWWZKdjctTs6HaDRLDfcsdng+yvqpPrhuo+jzxdTgJ/pIUxSL9xaFYY1uQAkoZ50DJsMcoG8jnhaN5gldbED2VzMykNKhIMM+uAg7uApntirLxRDr0qnjzMJAlIV36w63HVO4p+M4VaVP+lGb9y3+zaa7skcwP55Ngp8pm1fbROeW7+NN8vLDE5YegilJx3BchOYNhFYNsWB0sCrNfGeeTG0z3jkPATK5bHrG1UdPMq3lF7ju0rPeOAnNK7/dBEO3Nmk4xXOWZ9DZpVODi4kO7FZo4YrSb45AQXubCYOei2221m2jhQrd/AHoWed51t10ZmgWwxTO5VIsGBTFSre6ar1aAFVX2WyGDE/YrScqXGdkTaJpdDy7zEY3wfBsF0fs9KxeaTMGrFecwWa7zpBZDnSYT6cmKFe95CeI+ZYuES7tXowoYHNFMSb3mG1eXN9FZ8gsD83RtdV+xUtvQTZpmXGM2WFPXjL59cu75/X8qLsXd6dIKMvMLdbFtdU8i3JZJw0vEAOJGaWz0onGzjqvsO7P8EB5T4FMjqmU6ZXGVfNCj9kDrTD0oJizztU4jrn6H6WPTWdGGvklOKFTJgUw7aJedACkvyY4WVtH0E/JNC+d+S/eOeu8Ws8WnbkWDUvKMYcjmH3xJNwFDxhw9ZWD4JgFqpHqbTO1zU02W3Ru8DY5dGIfcY6pyCbEEoWZ5QHDxkGarhux1My0s82YrrLA+bXN673KohUjlbimJu9xAyeRbFalS2MEI8OMTyYo4C6tfs7AbLMan9YZmq9stsZtXMgUgNxtho/qwyVGH3oDB1mIAoVsYXy2mepqvUSdi/GgI40VJMUqL5tFnZnH2WyAd76T9bXoMq+dmailr3XeruemurfPhzEG4zSSM3xuM4ZiPwM0eozD0A+508sXOk8R0qDzQA8bzSULwoYQdXFGx+0Zr8XA9eEMTuByDwemIotQAd6q8lpnOsZ+PWOdIfsb2H4ozN8UgLmTIh1cx7wg1sBD9xKZSpctI4pD8uDwbQzlsoNUl+rLEJ6r3lBbvrTKD0pTuRiAx7g6tzQ9hpmUKPKqHZ1agDcV7Wem3t/6QYZ3xfA4cBwWA3svxKPWoD9BL9690li6/C/G+6FkshtiYTisR4B1tXs7Fp5Du+If0lqmnBFwv3bh3G5KYW3s1iLcParMlfXyEHqfPTBb0YeHcBFsV65TN+wf0mfdwF/w0z9KiJ1P194Q8wp9+IIZrWc34O+CCEoOO0/Y4vbPyxv3Drjx9mVY4VFl5heS9Xl/fAuMmu4yNcYhexQTXsXiwrX2jghzwJ0yfNC2x+bYqLbLQjzZ+WBDfe/IiG2WJmIvvE90mjMiLkGO/vC3kqHyPhBgppwCfnQYavdbGmUUb0dNqKe3jsDd3iV3PgEQWkiQEaGyzuTeoskNZPa8OxEPCC1koKz1SnmbHiWT1dboWpBFB7mFsDU1/H3uu3DzbICe0mcQsF07Nw/jYxgtv5wwK6u+eX9qoymKnB8MkL6ckovhMjIroeUG1vQtC2X5qHJkNyOqclXm18I6Z8P8QjKrZFOOPk0FVTfI30BKmY82t9Nx4Jf99HnHN6uPBc5wx3PtrpwEo9CgGZ7Vi6doMGAcND13UrjPfJJOXFBmlTYG/A7zGzmvOTnDR0IzPY/aEQqD9UGw0JT5AjXkFhYIoXUgZY7aEQoF+XVoWwf5WtyOUCjhBf8nLhIZqhUUez/wkNiErkqG/IvKrIQO2WQv0xGSCPvqCvZMLtIRkghKmi8tM1Z0QNZ8qY6QhNwlOoQV2UWD9oR/eXSxjpAETeDHRsen45+rdYQk1k0RJy7VEZKg0H5crlWwJ4fLwmnd/7p0AEskEolEIpFIJBKJRCKRSCQSiUQikUgkEolEIpFIJBKJRCKRSCQS/5rb7Q9n86cLLevI9gAAAABJRU5ErkJggg==)
II) ![](data:image/png;base64,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)
III) 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)
IV) ![](data:image/png;base64,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)
chemistry-General
physics-
The tube shown is of uniform cross–section. Liquid flows through it at a constant speed in the direction shown by the arrows. The liquid exerts on the tube
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The tube shown is of uniform cross–section. Liquid flows through it at a constant speed in the direction shown by the arrows. The liquid exerts on the tube
![](data:image/png;base64,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)
physics-General
physics-
A bent arc shaped sealed glass tube filled with water is accelerated horizontally with acceleration a. A small air bubble inside it is found to be stuck at 1 cm from vertical axis. Neglect surface tension. What is the acceleration of the tube.
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)
A bent arc shaped sealed glass tube filled with water is accelerated horizontally with acceleration a. A small air bubble inside it is found to be stuck at 1 cm from vertical axis. Neglect surface tension. What is the acceleration of the tube.
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)
physics-General
physics-
A pan balance has a container of water with an overflow spout on the right-hand pan as shown. It is full of water right up to the overflow spout. A container on the left-hand pan is positioned to catch any water that overflows. The entire apparatus is adjusted so that it’s balanced. A brass weight on the end of a string is then lowered into the water, but not allowed to rest on the bottom of the container. What happens next?
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)
A pan balance has a container of water with an overflow spout on the right-hand pan as shown. It is full of water right up to the overflow spout. A container on the left-hand pan is positioned to catch any water that overflows. The entire apparatus is adjusted so that it’s balanced. A brass weight on the end of a string is then lowered into the water, but not allowed to rest on the bottom of the container. What happens next?
![](data:image/png;base64,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)
physics-General
physics-
A cylindrical container of length L is full to the brim with a liquid which has mass density r. It is placed on a weigh-scale; the scale reading is W. A light ball which would float on the liquid if allowed to do so, of volume V and mass m is pushed gently down and held beneath the surface of the liquid with a rigid rod of negligible volume as shown on the left.
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)
What is the reading of the scale when the ball is fully immersed?
A cylindrical container of length L is full to the brim with a liquid which has mass density r. It is placed on a weigh-scale; the scale reading is W. A light ball which would float on the liquid if allowed to do so, of volume V and mass m is pushed gently down and held beneath the surface of the liquid with a rigid rod of negligible volume as shown on the left.
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)
What is the reading of the scale when the ball is fully immersed?
physics-General
physics-
A cylindrical container of length L is full to the brim with a liquid which has mass density r. It is placed on a weigh-scale; the scale reading is W. A light ball which would float on the liquid if allowed to do so, of volume V and mass m is pushed gently down and held beneath the surface of the liquid with a rigid rod of negligible volume as shown on the left.
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)
What is the mass M of liquid which overflowed while the ball was being pushed into the liquid?
A cylindrical container of length L is full to the brim with a liquid which has mass density r. It is placed on a weigh-scale; the scale reading is W. A light ball which would float on the liquid if allowed to do so, of volume V and mass m is pushed gently down and held beneath the surface of the liquid with a rigid rod of negligible volume as shown on the left.
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)
What is the mass M of liquid which overflowed while the ball was being pushed into the liquid?
physics-General
physics-
A cubical sealed vessel with edge L is placed on a cart, which is moving horizontally with an acceleration ‘a’ as shown in figure. The cube is filled with a ideal fluid having density r. The gauge pressure at the centre of the cubical vessel is
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)
A cubical sealed vessel with edge L is placed on a cart, which is moving horizontally with an acceleration ‘a’ as shown in figure. The cube is filled with a ideal fluid having density r. The gauge pressure at the centre of the cubical vessel is
![](data:image/png;base64,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)
physics-General
physics-
The figure below shows four situations in which a gray liquid and a black liquid (which we known nothing about) are in a U tube.
![](data:image/png;base64,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)
In which of the following situation(s) of static equilibrium must the density of the gray liquid be greater than the density of the black liquid? (circle all appropriate cases)
The figure below shows four situations in which a gray liquid and a black liquid (which we known nothing about) are in a U tube.
![](data:image/png;base64,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)
In which of the following situation(s) of static equilibrium must the density of the gray liquid be greater than the density of the black liquid? (circle all appropriate cases)
physics-General
physics-
The figure below shows four situations in which a gray liquid and a black liquid (which we known nothing about) are in a U tube.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAATAAAACZCAYAAACon2ZhAAAgAElEQVR4nO29eXgcR53//+45eu7RXJrRfSuOLdlBUuwkNjgJeMk+OSCw2UBYFsIDLCwsPGQ3bBZ4FsI38LCE54FAkifZODiEKziOcRzHUhzj2FYcS5F1H5Ys6z5mNCNp7qtnprt+f/g3vbItyTpGlgbq9Tz9PDqquz79qap3V1VX14chhBBQKBRKGiJZbwMoFAplpVABo1AoaQsVMAqFkrZQAaNQKGkLFTAKhZK2UAGjUChpCxUwCoWStlABo1AoaQsVMAqFkrbIUnGRQCCAaDQKnuevmVYqlUKlUkGr1aYi6yUhCALC4TBCoRCW8uGBRCKBSqWCTqdbdd7RaBShUAjxePyaaRmGgVwuh9FoBMMwq857qSQSCfh8viXZCAAsy8JgMEAiWf7zjxACjuMQCASWVF8YhoFSqURGRsay81ophBDEYjF4vd4l1RcA0Gg00Gg0K/LJlczOzi65LORyOfR6PeRy+arzXSo8z8Pn8yEWiy0pPcuyUKvVUCqVKbclJQJ24sQJtLe3Ix6PQyqVLpiO53mo1WrcdtttuPPOO69bI+U4DqdPn8a7774LqVS6qI2CIEAul6O6uhr33XffqvMeGBjA4cOHEQgEwLLsgumSDcVqteIrX/nKomlTiSAImJmZwb59+xAMBiGTLV4l4vE4srKy8IUvfAF6vX7Z+cXjcbS1teGtt95CIpFYtCyAS3Vm06ZN+NznPrfsvFZKIpHAwMAA9u3bB7Vafc16ynEcbrvtNnz0ox+FWq1eVd48z+Ppp59GJBKBQqFYNG08HofFYsGDDz6I/Pz8VeW7HILBIF588UX4/X4wDLOof+LxOHJycnDPPfegpKQk5bakRMDOnTsHj8eDsrKyRQswEAigt7cXGo0Gd9xxx3UTsHg8js7OToyOjqKmpmbR3h/Hcejo6AAhJCUCNjExge7ubmzatAlZWVkLpuN5Hk6nE3V1dfjiF794XQXM7/fjnXfewa5du5Cdnb1o+v7+fpw4cQKf/vSnVyxgw8PDaGtrw65du67Zs2pubobD4bjuAjY1NYUzZ87gn/7pn65ZFqdOnYJarcbtt9++agETBAF1dXW44447kJOTs2ja8fFxnD59Gh/+8IeRl5d33dpTOBzGm2++iT179sBsNi/6ELLb7WhpaUFNTc3GFbBoNIrt27fj/vvvh9FoXDCd3W7Hn/70J3Act+SueSoghEAQBFRVVeFzn/scrFbrgmmDwSD27t0Ll8uVkrwFQUBhYSEeeOABVFZWLpguFouhra0N9fX119U3STQaDe6//35UVVUtmq62thZjY2Orzq+oqAgPPfQQCgoKFk23d+9e1NfXrzq/5SKVSmGxWPDFL34RGo1m0bRerxeCIKQsb5lMhnvvvRcf+tCHFk3X0NCAiYmJlOa9FJLTAA888ADKy8sXHb62tLRg//79Sx4SLxc6iU+hUNIWKmAUCiVtoQJGoVDSFipgFAolbaECRqFQ0paUvIWkUCh/WxBCcOTIEVit1kUX746OjsLhcKyZHVTAKBTKsuF5Hv/93/+9pOURNTU1a2YHHUJSKJS0hQoYhUJJW6iAUSiUtIUKGIVCSVuogFEolLSFChiFQklbqIBRKJS0hQoYhUJJW6iAUSiUtIUKGIVCSVuogFEolLSFChiFQklbqIBRKJS0hQoYhUJJWy7bTieRSEAQBEgkEjAMg0QiAYlEAolEAp7nxX1/klFQZDIZ4vE4eJ6HIAiIxWKIxWKQSCRiJCC5XA6e50EIQSKRACFETJ88kmGZknkDl7brkMlk4nUYhoFUKkU8HhftS/5dIpEgkUiIaXieF+PVJYOUCoKARCKBeDyORCJxWX7JPGQyGRKJxGV2zo1duJhvkvklfSOXyxGLxZBIJMDzPOLxOGKxmGgfIeQq3wiCINoSj8dF3yynLObzzXz5Je87mU8yzyt9c2VZJO3keR4cx13mm6WWRdK3yfwIIZfZlCyLuX5I+jH592T6pfgmWRbJ9Mn8FiuLuXV0vrJI3neyjiTvLRkbdSn1NGlf0qZkumS5XKsskm0vWRbJmJ5LKYu5vkluiZP0f9I3yfu/0udJPy2VpA9jsdiSymJufjKZbNH9xi4TsPHxcUxMTMBms0GtVuPixYswGAzIyclBf38/MjIyoNPpMDU1BYZhUFlZiaamJkxOTiI/Px9dXV3Q6XTIz8+H3W6Hz+dDTU0NBgcHEY1GIZVK4fP5MD09DafTCY/Hg9nZWeTl5YEQAofDIcbCm5iYQFFRETiOg9PphF6vR05ODrq6umC1WqHT6WC326HVamGz2XDhwgXIZDLccMMNGBgYgFQqhdVqhcvlgtPpRDgchsfjQWtrK2666SYEAgF4vV4UFBSINm3ZsgVjY2MYHR0V/TE4OIjCwkIIggCn04nMzEwYDAb09vbCYDAgKysLg4OD0Ov10Ov1cDgcEAQBH/jAB3Du3Dn09PRgenoa3d3diMViKCgowOTkJHw+H6qrqzE6OopQKASz2Qy73Y5AIIDp6WmEQiG43W7k5uaCZVkMDw/DarVCrVZjdHQUNpsNUqkUDocDCoUCN9xwA9ra2pCRkQGLxQKHwwGZTIb8/HxcvHgRiUQCW7duxeDgIHieR1ZWFtxuNzweD7RaLQKBALq6upCZmYl4PA6n04nc3FwkEgnY7XaUlJQgEong/PnzCIVCcDqd6O3tRVZWFlQqFRwOB/R6PWw2G3p6eqBWq1FcXIzBwUGwLAuLxSKWeTQahcvlQmdnJ+RyOXw+HwKBAAoKCjA7O4vZ2VlUVlbC5XKJdWd0dBQjIyMoKSkBx3FwuVywWq3IyMhAX18fTCYTLBYLhoeHYTAYoNFoYLfbAQBVVVU4d+4cVCoVsrOz4XK5wPM8CgsLMTIyglAohKqqKoyOjiIcDsNoNMLhcMDn82F2dhZerxc+nw+5ubmQyWQYHR1FVlYWWJbF+Pg4HA4HCCFobm6GzWZDcXExOjs7YTQaxWuxLIv8/Hz09fWBYRjceOONGB4eBiEENpsNMzMzCAaDqKysBMdx6O3tRXFxMTiOw/T0NAoKChAOh+F0OlFWVoZgMIjOzk54vV44HA74/X7k5eVBJpNhampKrJudnZ3Q6XQoKCjA0NAQlEolTCYTHA4H4vE4tm/fjnPnzkEmkyEnJwderxehUAjFxcVwOBzwer3YunWrWHY2mw1utxvBYHDJ4dxCoRC6urqg0WiwdetWtLS0QK1Ww2azwel0ghCCoqIiDA4OIhaLobKyEmNjY4jFYigvL4fJZFrw2tLHH3/88eQv7733Ht544w1IJBIIgoA//vGP8Pl8MBqNeOWVV+DxeEAIQV1dHfr7+3HTTTfh6aefRmtrKwoLC9HR0YGuri5kZGTg8OHDePvtt7F582bs378fZ8+ehUwmEwNdVldXo7m5GSdOnIBGo8Hk5CTq6uqgVqtht9vxxhtvwGAwYGRkBMeOHYPH44HBYMCLL76IeDwOQgiOHj2K2dlZmM1m/P73v8fg4CBKS0vx6quvYmhoCDqdDsePH8fZs2chCAK6urrgdruRnZ2NtrY2nDlzBpmZmWhtbcWxY8dQXl6Os2fP4p133gHLsrBardi/fz80Gg2cTqcYTZplWbz88svw+/3IyMjAq6++CrfbDYZhUFdXh/Pnz6O6uhrPPvsszp07B6/Xi6GhIQwPDyMjIwNvvPEGjh8/jhtuuAGHDx9GfX09GIZBT08PGhsbsXv3brS1teHEiRNQqVQIBAI4cOAAGIZBNBrFn//8ZzAMA6/Xi6NHj2J0dBTl5eV47rnn4Ha7odFoUFtbi/HxcWRnZ2P//v3o7OxERUUFXn/9dfT09ECv1+Pdd9/FmTNnkJubizfffBNerxe5ubkYHBzE22+/Db1ej5GREbz55puwWq24ePEiDh8+DL/fjxtvvBGvvfaa2PM+evQofD4fzGYzXnrpJdjtduTm5uK1117D2NgYNBoNjh07hqamJphMJvT392N0dBQajQbvvvsuTp06BZ1Oh5MnT6K2thYFBQV45513UFdXB6lUipycHBw8eBAGgwHDw8N4++23xd7Bb3/7W4TDYSgUChw8eBCBQAA8z+PNN99EX18fbr75Zjz77LOYmJiAwWDAiRMncP78eeTm5uKNN95AQ0MDqqqqUFdXh6amJqjVarS1teHPf/4zXnnlFfzud7/DgQMH8Jvf/Ab79u3Dq6++ipdffhn79u3D/v37ce7cOSQSCVF88/LysHfvXvh8PrAsi9raWkxMTCA3Nxe///3vceHCBZSXl+P1119HX18fMjIy8M4776ChoQFbt27FkSNHxId2R0cHamtroVQq0draijfeeAMZGRloa2vD4cOH4fP5kJmZiXfeeQdSqRR+vx9vvfUWAoEALBYLXnjhBczMzCAzMxMHDx4UH3i1tbXo6OjAzp078eyzz+LixYswGo1obGzEuXPnkJ2djVOnTuHkyZOoqKhAfX096uvrwbIsRkdHceTIEUSj0SX1xGQymdhh2LZtG5577jnY7Xbo9XocO3YM/f39yMvLw8GDB9Ha2orKykrU1tais7MTN9xwA8xm84LXZsgcC2ZnZxEIBKDVaiGTyeB2u6FQKKDX6zE7OwuVSgWpVIpwOAyGYWC1WjExMYGf/OQn2LFjB/Lz88EwDNRqNcLhMKLRKLKzs+H1epFIJKBSqeDxeNDc3IzHHnsMkUgEkUgEer0eDMMgEAhAo9FAIpGIwhmPxxEOh8GyLPR6PaampqDT6UQ7WJaFWq3G7OwsJBIJzGYzPB4PpFIpWJZFLBbD9PQ0Dh48CI7j8KlPfQpFRUVIJBKIRCLQ6XSIxWIIhUKwWq2Ynp7Gvn37EA6H8f3vfx8zMzMwmUxIJBIIh8PQaDRgWRYzMzNQKpXQ6XTweDxQKpWQSqWIRCIghCArKwsTExM4ffo0Tp48iZ07d6KwsBBarRahUAgcx8FmsyEQCCAWi0GlUmF6ehpPPfUUXn/9dQiCgGg0Cp1OJ5ZFMm+v1wudTgdCCEKhEGQymdiDU6vVYFkWkUgEEokEWq0WHo8HgiAgMzMTPp8PhBAolUokEgkEAgGEw2E8+uijeOSRR3DLLbeAEIJgMAitVgtCCAKBAEwmkyhUBw8exC9+8QswDCNG1o5EImJZzMzMQCaTwWg0wuv1QiqVQqFQIBqNwufzobm5GTqdDizLQqvVisMLrVYLjuMQDodhtVoRCoVw+PBhOJ1OPP/883C73TCbzYjFYohEIlCr1VAqlZienoZarYZKpYLP54NKpYJEIkEoFALDMMjKysLk5CRYloVSqQTHcRAEATqdDn6/H7FYTCyL5NCvoaEBDz744JJ6GADw+c9/Ho888ggsFovY69JoNJDJZIhEIpBKpdBqtXC73QAAs9kMn88HAFAqlYjH44hEIsjMzMTXv/513HnnnSguLhbLWKfTIZFIIBQKiWXR19eHU6dO4atf/Sry8/NhNBpBCEE4HIZSqYRarYbL5YJCoYBOp4PP54NcLgfLsgiHw+B5Hnl5eZiYmIBEIoFGoxHLQq/XIxQKIRqNwmq1IhwOiz53u9144IEHcOHCBXGYuxhbtmzB97//fdx2222w2Wyw2+1QKBRinSCEQK/XizqRmZmJYDAInudhMBig1WoXvPZlQ0iz2XyZ2hkMBvFnnU437wVKS0uRkZEBrVZ7WcTrudGMLRaL+HM8HofBYIBOp7vs+sn85/t5LmVlZfP+fW6Y+ytvWKPRQKFQQKvVIi8vb9EuKcMwMJvNovOutDFJsuFemfdcSkpK0NfXB51OB4vFIvpnbvj5ubaEQiHRziujQc+1Y27088zMTPHn0tLSee1YzDcWiwVDQ0NQq9XIzs4W/T63zObmYbPZoFQqxeHitfK7st4YDAa0t7cjJydHnLOZi0ajEX3CsqwogiaTacFym5vfXD/NvYfi4uJ5z51bjknfRCKRa0bjns+GgoICsWyWUhbztal4PC7Wl+T/57s/lUoFq9UKvV6PjIwMlJWVgWGYq643N4+59zq3fRUVFc1r60LtP5FIQKFQzJvffKhUKmRlZYlR2Bcqi2v5Zj7oW0gKhZK2UAGjUChpCxUwCoWStlABo1AoaQsVMAqFkrZQAaNQKGkLFTAKhZK2UAGjUChpCxUwCoWStlABo1AoaQsVMAqFkrZQAaNQKGkLFTAKhZK2UAGjUChpCxUwCoWStlABo1AoaQsVMAqFkrZQAaNQKGkLFTAKhZK2UAGjUChpCxUwCoWStlwdFuavFEIIpqamcP78eTgcjgXTRSIROJ3OJUdcoVAo68fflIC98847aGpqglKpXDBdMvbenj17rqN1FAplJfzNCBgADA0NIRAIXDPdYpGAKRTKxoHOgVEolLSFChiFQklbqIBRKJS0hQoYhUJJW6iAUSiUtIUKGIVCSVuogFEolLSFChiFQklbqIBRKJS0hQoYhUJJW6iAUSiUtIUKGIVCSVuogFEolLSFChiFQklbqIBRKJS0hQoYhUJJW6iAUSiUtIUKGIVCSVuogFEolLSFChiFQklbqIBRKJS0hQoYhUJJW6iAUSiUtIUKGIVCSVuogFEolLTlssjcHR0d6O/vR1FREfR6PVpaWmCxWFBeXo7m5mZYrVZkZGRgZGQEEokEH/zgB1FbW4vOzk6oVCqMj49DEASYTCZ4PB5wHIecnBzMzs4ikUggIyMDbrcbAwMDGBwchN1uh8PhwKZNm0AIweDgIEpLSwEA/f39qKysRDgcxujoKMxmM8rKynDq1CkUFxcjIyMDw8PDMBgMKCwsRFNTE1iWxc0334y2tjawLIvc3FxMTExgcnISHo8HgiAsySnxeBwzMzPo7u5GW1sbKioqkEgkMDo6ivz8fGRmZqKxsRFWqxXFxcXo6OiA2WyG0WjEyMgIBEHAnXfeibq6OjQ1NaG3txcymQz9/f0wm82X+cbj8SAWiyEjIwMulwuzs7MYGRnB9PQ0pqamUF5eDpVKhc7OThQUFECv1+P8+fMoLi6GVCrF4OAg1Go1tm/fjrfffhs2mw3Z2dkYGRkBy7IoLy9HW1sb4vE4PvShD6GjowOJRAIFBQWYmZmBw+GAzWbD5OQkfve736GxsRGCIIDjOGg0GgiCgGg0Cq1WC0EQ0NraipmZGVy8eBHHjh1DaWkp1Go1RkZGYDKZUFhYiLNnz0Kn02Hr1q3o6OiASqVCdnY2xsbG4HQ6YbfbMTAwAIlEAqPRiHA4jFgsBpPJhGAwiEgkAqvVimAwiM7OTvA8j/b2dnR1deGmm25CKBTC+Pi4WBbvv/8+srOzkZubi+7ublitVuj1egwODoJhGHzkIx9BbW0tdDodioqKMDExgXg8ji1btqCnpwc+nw8f/vCH0dvbC7/fj5ycHAwPDy+5ETEMg6GhIRw6dAg5OTnYtm0bTp48iezsbFgsFoyMjEClUmHTpk14//33IZFIsH37dnR3d4MQgoKCAjgcDkxPT2PTpk0YGhrC6dOnUVRUhFgshnA4DKPRCI7jEAwGYTabEYvFMDw8jPHxcfT19aG7uxs33ngjpFIpRkdHYbVaUVRUhNOnT8NkMuHGG29EV1cXtFotrFYrRkZGEI1Gcffdd6O2thZyuRylpaWYmZmBz+dDRUUFhoeH4XK5sHv3boyMjMDlcqGgoACBQAAzMzNLbk8zMzM4fvw4PB4Pbr/9dhw7dgwGgwF5eXmiZlRUVKCjowORSAQf/OAH0dfXh2g0iqqqKuTm5i547csEzOl0orW1FRKJBDk5OWhpaUFJSQkyMzPR1taGwsJClJWVoaOjQyyE5uZm9PT0oL+/HwzDgBAChUIBjuPEShkKhcDzPFiWhVwuR2ZmJqanpzE8PIzz589Dr9cjHo+jtbUVGo0GPM+jpaVFrNCtra0oKCiAyWRCc3MzEokESktL0dbWhtzcXJjNZrS1tUGtVmPz5s3o6OiAQqGARqNBV1cXhoaGMD09DZ7nl+RwqVSKRCKByclJNDc3Q6fTgWEYtLW1IZFIgGVZtLS0oLS0FEajEW1tbcjLy8OmTZvQ3t4Onuexc+dOtLS0oKmpCcPDw+jq6oJKpYJKpUI0GkUsFoPRaEQkEhGvKQgCIpEIXC4XRkZGcP78eajVavFhwjAMMjMz0draCgDQarVoa2uDXq/H5s2b0dLSgqKiImg0GrS3t0Or1SIvLw8dHR3gOA41NTXo7u4Gx3HQ6XTo6urC8PAwSktLMTExgb1790KlUgGAaBMAxGIxqFQq8DyPSCSCG264AX6/H+fOnYMgCMjLy0NbWxsKCgpE+zIzM1FUVISOjg5otVpRhMfGxuDz+XD27FnwPA+lUgme5xGPx6FSqRCLxURB5zgOXq8XVVVVGB0dxblz52A2mxEKhdDa2gpBECCXy9HS0oIbb7wRarUabW1tKCkpQVFREdrb2wEAu3btEuuT0WhEd3c3YrEYCgoK0NPTA6fTiZ07d6Kvrw8ulwsA0NXVtaS6kqwvoVAI3d3d8Hq9KCwsRHNzM8rKyrBt2zZ0dHRAr9cjPz8f7e3tkEqlqKioQHd3NxKJBPR6Pbq6ujA+Po5wOIy+vj60tbVBq9UCAKLRqOj/aDQqthe/34/MzExMTk5ifHwcLMsiIyND9IHVakVzczPy8/ORk5OD9vZ2mEwmsCyL9vZ2RCIR7NmzB62trVAoFDCZTOjr64PT6UReXh76+/sxMDCA6upqDAwMYGBgAFKpFC6XC1NTU0sWMAC4ePEi5HI5duzYgdbWVlgsFuh0OnR2dgIAioqK0NXVBb/fj5qaGvFhsnnz5kWvyxBCSPKXUCgEjuOgUCggkUgQDochk8mgUCgQDochl8vBMAzi8TgYhoFWq4XH4xGfXksRCL1ej0984hN45plnIAgC4vE4FAoFGIYBx3FgWRYMw4iFJggCYrEYpFIplEol/H4/lEqlaIdUKgXLsgiFQmAYBhqNBuFwGBKJBDKZDPF4HGNjY/j85z+Pnp4exOPxa9pYVlaGH/7wh7j//vsRDodFO+LxOFiWhUwmQzAYhFwuv8w3EokEsVgMAKDT6eDz+fD888/j2WefhcPhuGa+EokEFosFZ8+ehclkgiAIUCqVYlmwLAupVIpIJAKlUglCCGKxGCQSCTQaDXw+n5gmWUZJ+wgh0Gq1iEajIIRAJpNBEAR4vV689NJLeOqpp+D1eq9po0qlwt13342XX35Z9A1wqdcqk8kgl8sRCoUgkUigUqkQiUQglUrFh8L09DR++tOf4o9//CPC4fA185NKpdi9ezf+8Ic/QC6XQ61Wi4J3ZVmwLItIJHJVWej1eni9XkilUsjlciQSCRBCoFQqEYlEwPM8dDodOI4Dz/Ow2+348Y9/jFdeeeWa9gGARqPBd7/7XXz5y18WbfT7/QuWBQCo1WpEo1EAgFwuB8/zCIVC6OrqwsMPP7yk+gIAhYWFePLJJ3HHHXdAo9GIdSLpj0AgAJlMJt5rsizi8TgEQYDBYIDX6wXDMOJDNJFIQKlUIhaLIR6PQ6fTiT/zPI/GxkZ8/OMfxxzpWJS7774b/+///T+UlJSI7UImk0Emk11VFoIgQKvVguM4CIIAlUoFhUKx4LUv64FpNBpoNBrx92TlBAClUjnvBTIzM5GTk4OBgYElCVgoFMJ7770HjuNgNBohkfzfNNzcvOf+fGV+8zHXvrk3nOx2d3V1LbkHluw9qNVqqNXqa+Y39+e5dpvNZhQXF1/mx8UQBAHBYBBnzpzBJz7xCRiNRvF/c6+xkE0Wi+Wats71TbKynz59WmxM10Kn02HTpk1X1ZWF8ruy3hBCYLPZIJVKl5Qfz/NwuVy4cOEC7rjjjmvmN9dPV5bFtc5VKBQghKC3t3dZPbBkOc+tm0spiyt9o1arkZubC5lMduVpCxIIBPDee+/hE5/4BORy+VX/n1veC7Vhk8k079/n+jJ5HYfDgdOnTy9ZvBiGQX5+PsrLy6HX6wEsvSyWQkom8W02mzjcuBbJCvmHP/wBwWAwFdkvyszMDA4cOLBk8QIuCdhCQrlcTCbTghVnPmKxGF588UV4PJ6U5H+tvC5evIjGxkZwHLekczQaDcrLy1ecp1QqhdVqvezBdS0mJibw8ssvL7nRrIZwOIyuri709fUt+Ryz2ZyS+iKRSJCZmblkcQcAr9eL119/HaOjo0gkEqu24VpMTU3h7bffXnL65JSRTqdbE3tSImBZWVlLFjDgUiV55plnYLfb19TpgiBgfHwcR44cWdZ5FotlwSfoctHr9UvugQGXBL65uRm1tbWYnZ1NiQ0LMTs7i5dffhmxWGzJ4qDX61FQULDiPKVS6bJ6YMClXsbJkydx/PjxJQvtSunv78frr7++rHppsVhSJmDJOSqGYZZ0jiAImJ2dxc9+9jP4/f5V27AYHo8HjY2N6O/vX/I5RqMRWVlZS76f5ZISAauoqBAnHJcCz/MYHh7GE088geHh4WVNBi6H/v5+PP/88xgfH1/yOQqFAlarNWVPjLy8PBiNxiUXICEE0WgUzzzzDBoaGtasl+p2u1FfX48jR44sy/8mkwlWq3XF+crlclRUVCy7kTqdTjzxxBMYHBxcMxGz2+04ePAgzp07t6zzioqKkJGRkRIbZDIZNm/evODwfD4ikQgOHTqEAwcOrNlDj+M4nD17Fi+88MKy/G8ymZCTk7MmNgEpErAdO3YgOzt7ycMCQggSiQTeeustPPfccxgYGEi5iA0ODuKll17CW2+9JU7mLoXc3FxUVFQsax5iMaxWK7Zt2waDwbCs8/r7+/Hzn/8c7777LkKhUEpsSeL1enHq1Cn87Gc/g8PhWHLvS6lUori4eNHX2tdCJpOhpKQE27ZtW1bPlOM4NDU14Uc/+hEGBgZSLmLT09P44x//iP3798Ptdi/5PJVKhZqamgXndVbCfffdt6zrCYKA6elpPP300zh27BhmZmZSZgtwaarh7NmzePbZZ2dDvAcAABmzSURBVJc1tAaATZs2oaysLKX2XAZJARzHka997WvEYDAQAMs6srOzyb//+7+Trq4uEovFVm0Lz/Okr6+PfPvb3yYFBQXLtueBBx4g58+fT4FX/o/a2lpSVVW1bFtUKhXZs2cPOXLkCPF6vSmxxeVykf3795Ndu3YRqVS6LHuKi4vJr3/9ayIIwqpsEASBPPfccyQ3N3fZPlGr1eRzn/scaWxsJIFAYNX+4HmeTExMkF/+8pdk06ZNRCKRLMuebdu2kbNnz67aJ3O5cOEC+eAHP7js8gFAqquryb59+4jdbk+JTaFQiJw4cYLcfffdRKfTLcsWrVZLnnrqqZTV3flIiYARQsjRo0fJ1q1bl+1wAMRsNpOHHnqIvP/++8ThcJB4PL5s5ycSCeLxeEhbWxv57Gc/S6xW67Lt0Ol05PnnnyehUChVbiGEEDI+Pk6+9KUvEZlMtmyb5HI5qa6uJq+88goZGhoiwWCQ8Dy/rPwFQSDRaJQMDw+T//3f/yVbt25ddkOVSCQpFfe+vj5SU1OzokaqUCjIPffcQ+rq6sj4+DiJRCLLzp/neeL3+0lvby/5wQ9+QLKzswnDMMuyg2EY8uijj5LJycmU+CRJIpEg3/rWt4jRaFxRe9q0aRP5n//5H9LX10c8Hs+y25IgCITjODI5OUnefPNNcvPNNxOVSrVsO7Zu3Urq6+tT6psrSZmATU5OkocffpjI5fIVOV0qlZKioiLy7W9/m/T09JDZ2VkSCoVILBabt8EKgkDi8TiJRCLE5/OR0dFR8txzz5EtW7YQlmVXZMP27dtJQ0NDqlxyma2//vWvSVZW1orsSorr3XffTY4cOULsdjsJBAIkGo2SRCIxb548zxOO40gwGCQul4ucOXOG3H///SvqJQOXnqa/+tWvSDQaTZlPvvGNbxCTybRin+Tm5pIvfOEL5MyZM2J94ThuQYFPJBIkGo0Sv99PxsfHyauvvkp27dq1ogcLwzBEr9eTxsbGlIwcruQvf/kL2b59+7JFNXloNBqya9cu8uKLLxK73U58Ph+JRCIkkUjMK2g8z5NYLEZCoRCZmZkh7e3t5Otf/zoxmUwrskEikZBvf/vbZGJiIuW+mUvKBEwQBPLnP/95xb2wZKWQSqVEq9WSBx98kOzdu5e0tLTM2wWNRqOkt7eX7N+/n/zbv/0bKS4uJlKpdMUFDoA88cQTxOl0psollzE8PEz+9V//dcW2JSuFTCYjNTU15PHHHyfHjh0j4+PjVzVYnueJ3W4nJ06cID/96U/J7bffThQKxbJ7XXOPW2+9lZw5cyalPunu7iYf/vCHV1VfJBIJ0Wq15CMf+Qj51a9+Rc6cOUNmZmbm9cnQ0BA5cuQIeeyxx0hVVRWRy+Urri8sy5J/+Id/WLMGGg6Hyfe+9z2i1WpX5R+WZUlhYSF59NFHyaFDh8jg4CDhOO6q/GZnZ0lDQwN5+umnycc//nGi1+tXVV8MBgM5e/bsgg/YVHHZSvzV4na78etf/xo//OEPVzXxzDCM+NmNQqGAUqmEwWCA0WgEy7Jwu91wu92IRCLgOA7RaFT8JGel+W3fvh0vvvgiNm/enLIJ/LnE43E0NDTgm9/8Jjo6OlZ1LZZloVaroVAoxE+mzGYzMjIyEAwGMTs7C7/fj1gsBo7jEIlElrxQdT60Wi1+8Ytf4B//8R9T9rYNuDQx/5vf/AY/+9nPMDg4uOLrJFe5z/WJXq+HyWSCWq2Gz+fDzMyM+M1lsr4s5+XOXCQSCWw2Gw4cOICampplrfNbKoQQdHd34wc/+AEOHTq0qmtJpVJoNBoolUqwLAuNRgOj0Qij0YhYLCZ+/8hxnNieotHoil+sSaVSPPLII/iP//gPZGVlrcr2a5JKNeR5nnR2dpJ77713VT2NKw+GYYhMJiNKpZKo1epVPTmvPCQSCTEYDOTAgQPE5/Ol0h1XMTs7S1544QWiVqtTZn/yHliWJWq1migUihXNKy12fP7znycDAwPLnntbCuPj4+Rb3/rWiuZYFqsvUqmUKBQKolKpCMuyq+pNXHlkZmaSH/3oRyQQCKR08v5KQqEQee2110hZWVlKyzNZX1QqFVEqlaseucw9lEolufXWW8mFCxfm7emlmpQKGCGEBAIB8pe//IXcfPPNKa00a3Xo9XryzW9+k0xPT69JA51LIpEgY2Nj5Ctf+QrRarUpFbG1OORyOdm6dStpbGwk4XB4TXwSj8dJQ0MDueeee1Y8f3o9D51OR+655x4yPDy85vWFkEtzyz/5yU+I1Wrd8PVFKpWSgoIC8tprr63oxcpKSLmAEUKI1+slr776KqmuriYKhWLdHbtYZfzoRz9Kent7STweXwtXXAXHceTixYvk4YcfJmazecOKvFwuJ0VFReT5558nfr9/TX0SDAZJfX09ueuuuwjLshu2oapUKnLrrbeSurq6NfXHXJIPvf/6r/8iNpst5b3rVB0SiYTk5uaS//zP/yShUGhNe6ZzWRMBI4SQSCRCDh06RD7wgQ8QtVq97g6eezAMQwwGA9mzZw85derUWrlgQXieJ6Ojo+Jyj40mYgqFgpSXl5Of/OQnJBgMXpfKGA6HSWtrK9m9ezfRaDQbTsQ0Gg3Zvn07+dOf/nTdehdJeJ4nMzMz5LHHHiN5eXkbrqcqk8lIXl4e+cY3vkHGxsauq2/WTMCSHD16lOzcuZPodLoN8fRgGIbodDry4IMPkpaWlrW+/UUZGxsjX/3qV0lWVtaKl36k+mBZllRWVpK9e/euyfKAxYjFYqSvr4/s2bOHmEymFS1vWItDpVKRD33oQ6Suru669dSvRBAEEolEyA9+8ANSUlJClErlhhB5qVRK8vLyyI9+9CPicrmuu1/WXMAEQSADAwPkkUceWdHi0rVooF/72tfIxYsXr1s3dzECgQD53e9+R3bs2LHuvgFAduzYQV577bXrMr8zH4IgEI/HQ3784x+T0tLSdfcHAHLvvfeSlpaWdfPJXBKJBKmrqyN33XXXhpieycnJIS+88MKaTzMsxJoLGCGXnqyzs7OktraW3H333evSBWYYhtxyyy3kpZdeIpOTk9e9d7EQPM+TYDBIenp6yHe+8511m6zNysoi3/jGN0hra2vKv0RYiU98Ph957733yD//8z+veEX6ag65XE5KS0vJk08+SUZGRlK2gDcVhMNhMjIyQn7+85+TioqKdWlLarWafOYznyFnzpwhPp9v3cQ9pevAFoMQglAohImJCbz//vs4cOAAGhsb4fV6l7VX13JRKpUoLCzEww8/jL//+79HUVERdDrdsrZzuR7EYjG43W709vbi0KFDOHbsGMbHxxGJRNYsT4lEgoyMDNx11134whe+gIqKClgsliVvJrfWRCIRTE1Nob29Ha+++irq6+vhdDrXtL7IZDLk5+fjvvvuw2c+8xmUlpbCYDCsydrA1cDzPDweDwYGBnDs2DEcPnwYfX19a1pfAMBgMKCmpgZf/epXUV1djezsbHGH5PXguglYEkEQEA6HMTQ0hLa2Npw8eRLNzc2YnJyEz+dLyaZ1CoUCWVlZ2LRpE2655Rbs3LkTNTU1MJlMG064riSRSMBut6Onpwdnz55FfX09Ll68iJmZmSVth30tkoE0ioqKUFVVhdtuuw07d+5EUVHRmizIXC2EEITDYUxOTqKzsxP19fU4c+aMuLd+KvaTk0gkyMrKQmlpKbZv3y7Wl4KCgmVtvLgexONxuN1u9PX1oampCSdOnBD39k+VmCX389+2bZtYX7Zs2bKuwpXkugvYXBKJBEZGRtDV1YWOjg4MDAxgfHwcdrtdjE6TDA4y36rg5ApsrVYLrVYLvV6PzMxMlJWV4eabb0Z1dTUKCwtTutXJ9WR6ehr9/f1oaWlBb28vxsbGMDk5CbfbjXA4jGg0Co7jFmzEMpkMarUaOp0OOp0ORqMR+fn52Lp1K3bs2IFNmzYtewvj9YQQArvdjq6uLrS3t6O/vx/j4+OYnJyE1+sVV5DHYrEFe2nJFftJn5jNZhQVFaG6uhrbt29HSUkJLBZL2vhkLsFgEBcvXkRLSwt6enowMjKCiYkJUcyS/knuQ38lUqkUKpUKWq0WOp0OGRkZyM3NxZYtW7Bjxw5UVFQgNzd3wS3N14N1FbC58DwPv9+PkZER9Pb2YmBgAFNTU2KosWg0Cp7nIZFIwDAMGIaBTCaD1WpFaWkpysvLUVRUhOzsbBQWFkKj0az70yFVkP9/k0OHw4HBwUF0d3djcnISLpcL09PT8Pv9oogxDCP6SKvVoqioCOXl5SgtLUVOTg6KiopgMpnm3T89nSCEwO/3Y3JyEgMDA+ju7obT6YTT6RQ/G0qKWNIfyR1PS0pKUFZWhtLSUrHnpdFoNnzvfDlwHCdG/kpGPHI6nXC5XPD5fIjH4yCEiG0pGYQlLy8PZWVlKC8vR25uLgoLC2G1WjfMtMKVbBgBW4xEIiH2OJLRTJIRZpKRkv5WScZwDAaDoqjP9c1fU6NcKoIgIBQKIRqNitGp5vpkow8L1xJCCDiOEwV+bntSKBRpV1/SQsAoFAplPv52H0UUCiXtoQJGoVDSFipgFAolbaECRqFQ0hYqYBQKJW2hAkahUNIWKmAUCiVtoQJGoVDSlg37wdfs7CxcLhesVqv4gXM8Hoder0deXh6mpqbAsiyMRiN0Ot16m3vd4XkeTqcTbrcbJSUlcDqdmJ6eBgDk5ubCZDIhEonAbrcjFAqJu3IwDAOXywW9Xg+bzbbOd7F6/H4/RkdHUVBQgEQigYmJCUQiERgMBmRlZUGpVMLhcGBmZgaEEGRnZ8NisSAWi8Fut8Pv94NlWRQUFECpVMJut4uf1KQ7PM8jFArhwoUL2Lp1K9xuN6anpxGLxaDX65Gbm4tEIoGhoSHEYjEoFArYbDbYbDZxRX4gEMDIyAgikQgsFgs0Gg1mZmY2zOd6G64HxvM8HA4H6uvrIZfLoVarEY/HcerUKXz3u99FX18fBEGA1WpFc3MzTp48CZ/Pt95mX1cEQUBnZye6u7ths9kgk8kQi8Xw1FNP4ZlnnoHT6YRUKoVUKsXAwAAee+wx/OUvf0E8HodCoYDP58Px48dXFcpsIzA5OYn6+nrxo3WZTIbTp0/jySefxMmTJ8XPhgRBwC9/+Us888wzcDgcom8cDge+853v4ODBg4hEIuJnackdUtIZnucxPT2N2tpaZGZmQiqVQiaT4fDhw3jyySfR2dkp+qG9vR1PPPEE9u/fL36SlkQqleLEiRN45ZVXYLfboVarEQqFsHfvXni93hWHXksVG0rABEGAz+fDH/7wB5jNZmRlZUGlUiEjIwNmsxkdHR3Q6XRgWRZ6vR6bN2/GxYsX8d57763pHlEbjeS2Mrm5uTCbzWBZFjabDW63Gy6XC3K5HCzLQqfTIS8vDz09PQAuxZNUKpUoKCiATCZDbW1t2oq/y+VCQ0MDIpEIioqKIJfLxXoyPj4Onueh0WjAsixycnLg9XoxNTUl+kaj0SAnJwcXLlxALBYDy7KiH3NycvDGG29gYmJi3RvoSpmYmMDRo0dhsVhQWFgIuVwOi8UCQgjGxsbEuKs6nQ47duzA9PQ0RkZGEIvFLvtWNNmByM/PR0lJCbRaLcrKyhCLxfDmm2/C6/Wu411uMAELh8Nobm5GU1MTNm/eDK1WC+DStjDJvYfm7kFUXl6OsrIy/OlPf4Ldbl9P068LyV0p9u3bh5ycHOTl5YmVLbmbgFKpFLv/EokELMte5j8AsFqt2Lx5M9rb29HQ0JB2jZQQgqamJrS2tmLLli1QqVTi/5INc+5uGxKJBEql8jLfMAwDuVwuBk5O+lGn06GsrAyCIODQoUMp2YPtehOJRPD++++joaEBO3bsEMs9WR+USuVlu0ts2bIFu3fvxuTkJC5cuHDZVjuRSARutxs1NTXIzs4GwzDQ6/V46KGHsH//flH01osNJWAzMzPYv38/ampqlrR9R3L3TAA4ceLEWpu37giCIO73ZLFYVhUlOysrC5WVlXj55ZdTsing9SQSieDIkSPgeR7FxcUpv77FYsHOnTvx4osvIhQKpWSTzeuJ3W5HU1MT8vLyoNfrr5leIpHgYx/7GCQSCd59912Ew2EAlx4UFy5cgEqlEsULuNTucnJyoNVqcerUKXg8njW9n0VtX7ec58HtdqOxsRGVlZVL3q/KZDLBZrPh+PHja2zd+hOPx/H222/DZDLBYDCs6lp6vR6lpaU4e/YsfD5fWvXChoaG4HA4YLFY1mRzPbVajeLiYtjtdvT29q5rD2MlnD9/HsPDw6ioqFjyOVVVVSgvL0dHRwfOnz8P4JKA1dbWYvfu3Ve91GAYBjfddBPOnTsHh8ORUvuXw4YRMI7jYLfbMTs7i7y8vCXviKnRaGAymXDu3DlEo9G0e1ouB57n0dHRAY1Gs+qGq1QqkZOTA47j0NLSAo7jUmTl2jM2NgaO49Zsp12GYcCyLLKystDQ0CD2SNKFoaEhhEIhZGZmLvkcrVaL22+/HfF4HLW1tSCEIBKJYGBgADk5OZcN04FLPsrLyxN3UF4vNoyARaNRjI+PgxACnU635NezMpkMOp0O4XAY09PTadWTWC6CIGBsbEzchG41JDc/lMvlGB8fT6th5MTEBBKJxFWNKpVIJBJoNBpMTEyk3TzY9PQ0OI5b1i6qDMPglltuQXFxMU6cOIH+/n4cP34cW7ZsgcFgmLc9ajQa+P1+BAKBVJq/LDaMgBFCRPFZbi+KXAoP91ctXkkEQRDvN1Wkk3gB/1fea93bJoSA5/m069WvtI7k5eXh1ltvRTAYxLFjx3D06FF85CMfWXQe7XqUw2JsGAFTKBTIzs4W9zpfqhjFYjH4fD6oVCoYjcZ1X1i3ljAMg6ysLMRisXlFZzkVied5MQBGTk5OWm0lbLPZwDDMvEO7VDWoZIwGm82WdvEDktG3FpoWWMg/arUa1dXVsFgs2L9/P8LhMAoKChbsyfl8PqjVamg0mpTZvlw2lIDl5uYiIyPjqqFgLBZDMBiEIAhXiVtyJfYNN9wAnU73V73fuVQqxebNm8Fx3GWVkxCCeDyOcDiMUCiEWCwGQogYSyAejyMQCFy2Vi4cDmNwcBAsy2LLli1gWXY9bmlF5OfnQ6FQXDV0Se6FH4lEEIlExOg78XgckUjkMt8kBZzjOAQCgcseCPF4HB6PB263GzfddNOGDDe3GHl5edBqtVet8YvH44hGo4hEIgiHw/MKWUlJCW6//XYMDg5i9+7dC4ZOS76htFqtsFqta3Yv12LDtHaJRAKz2YyqqioMDQ2J8w6EEAQCAYyOjiInJwfDw8OXhYVKRlq57777/qp7X8Cl+b477rgD0WgUwWBQ9AHP85idnRUbodfrFRvtwMAALBYLpqamxMYLAB6PBx0dHaiqqkJRUVFahRErLi6GzWaDx+O57A0hx3EYHh4WvzZIBq5Ifj7DMAzcbjfi8ThisRjGxsag1+vh9XoRiUTEB2MoFEJ3dzeMRiNuueWWtBOwyspK5OfnY3R09DKRCgaD8Pv9UCgUGB0dnfftamZmJv7u7/4OlZWVuPfeexe8d57n0dLSgurq6nX97GpD1drMzEx88pOfxOHDh/HJT34SOp0OPM9DrVbjy1/+Mr785S8DuPSkFQQBDMNgcnIShBDcdddd62z92iOXy7Fr1y7o9XpMTk4iEolArVZDEATodDr89re/BQBx+EAIwZ133ok77rgDwCUBTCQSkMlkmJ6eht1ux2c+85m0Gj4Cl4ZIu3fvRk9PD8bHx1FaWioGwP3Sl76EL37xi2AYBvF4HIlEAkqlEi+99BKA//MNwzDYtm2buPxGoVAgkUiAZVl4PB6cP38en/rUp6DX69OuV19aWoqqqiqcOnUKHMdBqVSC53nwPI9HH30UhBBIJBKEw+GrhocSiQSVlZV47rnnkJubO+/1eZ4Xwx1+9KMfXdce2IYSMJ1Ohz179ohvQbRaLdRqNYxG42XrnpKx7Pr7+zE8PIyHHnoIhYWF62j59UMul+N73/seXnvtNRQXF2P79u2Qy+VXfZid7I0mv2ZIIpFIEAgExO7/fffdl3YNFAA+9rGPIRKJoK6uDl//+tfBMAyMRuNV6RiGWdA3Vy5FSYre4OAgXC4XnnzyybQaWidRKpW48847MTMzg6NHj+KTn/wkpFIpTCbTZekWGrGoVCqUlJQseH2/348XXngB//Iv/4Ibb7xxXecIpY8//vjj65b7FSTX32zbtg1NTU3Q6/VQq9VgWVYUreThcrnQ2NiIkpIS7N69e0NFC15Lkg1Vr9djZGREjKA8N+DvYkcoFEJnZydmZmbw6U9/GhaLJS2H3smXPk6nE9FoFFarFVKpdMl+mO+Ix+O4ePEiOjo68NnPfhYFBQVpKe4Mw0CtVqOwsBCdnZ1QKBQwGo2QyWRX3fNC5y90336/H+3t7ZBKpfj4xz8Og8Gwrj7akHEhBUHA1NQUCCEwm83zjsM9Hg9CoRC0Wu2qV6WnI4FAAIFAAFKpFFardckixHEcXC4XlEolzGZzWjbQJMmXO36/H1lZWVAoFKsS40QiIe7kYTab0+7t45VwHAe3241YLIa8vLyUTBVEo1E4nU6o1eoNUX82pIAlSZq20FuQhf73t8LcoluqH/5a/SYIwqobE/XNtUkuU1lv4UqyoQWMQqFQFmNjyCiFQqGsACpgFAolbaECRqFQ0hYqYBQKJW2hAkahUNIWKmAUCiVtoQJGoVDSFipgFAolbaECRqFQ0hYqYBQKJW2hAkahUNIWKmAUCiVt+f8Ae+bHES40qkAAAAAASUVORK5CYII=)
Which of the following situations does not show static equilibrium of liquids.
The figure below shows four situations in which a gray liquid and a black liquid (which we known nothing about) are in a U tube.
![](data:image/png;base64,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)
Which of the following situations does not show static equilibrium of liquids.
physics-General
physics-
An ideal monoatomic gas is carried around the cycle ABCDA as shown in the figure. The efficiency of the gas cycle is :
![](data:image/png;base64,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)
An ideal monoatomic gas is carried around the cycle ABCDA as shown in the figure. The efficiency of the gas cycle is :
![](data:image/png;base64,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)
physics-General
physics-
The initial state of an ideal gas is represented by the point a on the P-V diagram and its final state by the point e. The gas goes from the state a to the state e by three quasi stationary processes represented by
i) abe
ii) ace
iii) ade.
The heat absorbed by the gas is
![](data:image/png;base64,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)
The initial state of an ideal gas is represented by the point a on the P-V diagram and its final state by the point e. The gas goes from the state a to the state e by three quasi stationary processes represented by
i) abe
ii) ace
iii) ade.
The heat absorbed by the gas is
![](data:image/png;base64,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)
physics-General
physics-
The P.V. diagram of a certain process (Carnot cycle) is as shown in the figure.
![](data:image/png;base64,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)
The process is represented as
The P.V. diagram of a certain process (Carnot cycle) is as shown in the figure.
![](data:image/png;base64,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)
The process is represented as
physics-General