Physics-
General
Easy
Question
The vibrating of four air columns are represented in the figure. The ratio of frequencies ![n subscript p end subscript colon n subscript q end subscript colon n subscript r end subscript colon n subscript s end subscript text is end text](data:image/png;base64,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)
![](data:image/png;base64,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)
- 12 : 6 : 3 : 5
- 1 : 2 : 4 : 3
- 4 : 2 : 3 : 1
- 6 : 2 : 3 : 4
The correct answer is: 6 : 2 : 3 : 4
Related Questions to study
physics-
A ‘pop’ gun consists a tube 25cm long closed at one end by a cork and the other end by a tightly fitted piston as shown. The piston is pushed slowly in. When the pressure rises to one and half times the atmospheric pressure, the cork is violently blow out. The frequency of the ‘pop’ caused by its ejection is (V = 340m/s)
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D111/jzp07OgVU3/2TUCXiyZMn48SJE0bj3L9/H48fP67DnFkPIuJ6RjwIplAoBJNZoVBAoVDAw8MDISEhcHJywrx585CYmIh27dphyZIlyMjIQG5uLpKTk3Hnzh1UVFRAo9EIpzUQqvj111+xY8cOybDGUOEREcsEiqLg7u6OyMhIJCcn48yZMxg9ejROnDiBmTNnws/PD9OnT8f58+eJgEWwLIusrCwkJCQYjCN3zzl59uSbGOJ+HVDlMcYvYJ88eTIGDhyIXbt2Ydu2bTh69Cg6duyIDRs24NVXX0XHjh2F6/n9tZra/HNNbpcAkJqaqnNOmJwgLbEMEM8/iwfDePO7a9eu+Pjjj5GVlYW33noLv/76KxISEtCnTx+8/PLLOHLkCDQajTDvbGwj98aIfiWoD8uyuHDhAv788886zpl1ICJuBPC+3mq1Go6Ojhg8eDB+/vlnJCQkoLi4GKmpqaisrERiYiLy8/Ob1OAXTdPw9fVFZGSkwTgURWHRokVG1xw3ZIg53UgQtzb85vDjx4/H+PHj8eTJE1y6dAkLFizA/PnzMWbMGEybNg39+vXTORpH392zsRAUFIRBgwZJhsm5L8xDWuJGgNTcs3jUW61Ww8/PD5cuXcK8efNw/vx5xMXFoby8HKdOnRI2jG+Mbp6822XXrl2NxgHkO0ZARNwEELfOM2fORFZWFtavX4+8vDyEh4ejR48e+PLLL1FcXNwoRWyKhTF8+HCj/tUNGWJONwF4t0x7e3twHAelUgl7e3u4uLjgxIkTSEhIwKJFi5CWlobDhw+jpKQEDg4OUCqVgrkpV5fEmuCtlpUrV8r2N5KWuAlgzN3T19cXq1evRk5ODj777DPcvHkTfn5+WLhwIa5fvy77ltlUt8t+/foZ3cKnIUNE3IQRL57w9PSEn58fXFxc8Prrr2PTpk0ICAjA559/ruOnbcmunvUxKk5RFGJiYnD27FmDcWiaRnFxMZ48eVKHOfsLSzfrk6f9QLAY8eoqfpN8hUIBV1dXzJ07FzExMUhKSoKbmxsePHiApKQkvPLKK+jcubPQx+Q/Tb2fl5eXcC6TflhtDher7bXivrD+HDkfVlBQgOXLlyMpKckq+aoJ/WuVSiWioqIQFxdX61VpRMQESdzd3TF79mwwDIOcnBysW7cOCQkJiI6OxhtvvIH27dvXurDFxMToHKzGY0sRA0BWVhZOnz6Nd955RzKcZVl89dVX6N27N4YMGWKVfNWE/rVpaWn44YcfzEqPiJigg7jlYlkWSqUSAQEBOH36NNauXYukpCQ8evQIX3zxBYqKitC6dWuTxfzhhx9KjhLbUsQcx2HZsmW4cOGCzrGlYhiGQWRkJFq2bInWrVtbJV81oX/tjRs3kJuba9bacCJigg5igYlPNGzdujXmzJmDKVOmoLKyEunp6Xjrrbcwa9YskwqyeMdQKRGbmqfahAG65rMh859lWRw/fhy9evUSzuGyNF81oX+t+HTG2kIGtggmwbccbdq0QYcOHeDn54eXXnoJixYtatCrpmiaRu/evTFx4kSDcSiKwrJly5CRkVGHObMeRMSEGhF7gPEthbu7O5YuXYrvv/++wXs69e/fH++++65kGHG7JDQZxNNRHMfhyZMnWL16NSIjIxv0qij+kPHevXsbjSNnMRMREwwite0Py7LQaDSYOnUq3n//fYSGhtbK06mu54nFAjW0npjjOIwaNQrdunWr07xJQUanCVaF7+vyIjh8+DCWL1+OFStWYMaMGfj444/h6+uLzZs3m5Terl27wLJstcElW08x/fbbb9Bqtdi1a5dkOMdxwtRSamqqVfJVE/rX3r5922y3TyJiglE4jkNOTg4++eQTHDt2DIMGDYJWq0VgYKDB0WYpGIZBREQElEplnR5jwzuyAEBkZGQ10VEUBZVKBa1WC4qi6mWQju+qjB492qzriYgJOm5/Ym+sCxcuoHPnzjhx4gSKioqQkpKCkJAQ0DQtLFs0tTVSKBR48OBBtZMhAdu2xOLjcQzNwWq1Wjz33HMYP348PvjgA6vkqyb0r2UYRligUtu+ORExQTglgRdwdnY24uPjsX//fixZsgTTp0/H9OnT4eTkpDPAxc9rmlqQmzVrBkB6ntiWzh6HDh1CRkYGlixZUk3IHMcJrbBarUbz5s2tkq+asORafcjAFgEAhKNO1qxZg+HDhyM3NxdfffUVXnvtNTg4OMDR0VGWo7csy+Lnn39GcnKy0Xhy3rKItMRNDP0+H8MwOHv2LOLj4xEVFYWgoCB8/fXXCA8Ph6OjIwDomNhyFHJNu11SFIWMjAzBUpAbpCVuYrAsK2zFc+7cOYwaNQojR47En3/+iWbNmsHb2xtRUVFwdHTU2dRe39lDTpiy2+WuXbtw+fLlOs6ZdSAibmIUFxdj27ZtOH/+PIqLi0FRFL777jscPnwYI0aMkLVYpaBpGn379sW0adMMxqEoCgkJCcjMzKzDnFkPYk43IqQ2uuMHrPg1wRs3bsTdu3cxd+5cvPfeexg+fLjk8amNRcQA0KtXL3Tp0kUyTK5dBDGkJW5E8CYjbzKXl5fjwoULKCgowMGDB7FmzRqEhITg2LFjePvttwVTmb+2McJxHJKSkhAQEGA0jpzFTFpiGWOoj/f48WOkpqZi3bp1yM7Oxrx58zBr1iy88MILaNmyZa125JA7prhdAlWOID179qzr7FkFImKZwp98yBdOlmVx6dIlPP3001i3bh0+/fRTjBw5EikpKQgNDYVKpUKLFi1kO41iS2iaxieffAI7O7v6zopZNI3quBHCO10UFBTgyy+/xIABA9C/f3/s2bMHU6ZMwYULF7Blyxa88MILkn3epoKpu1326NEDS5YsqePcWQci4gaK/sohlmWFQaqSkhLs3LkT5eXlWLZsGRYvXozu3bvj8OHDmDhxIlq1aoWOHTsKJrNc+3rWgKIozJo1C7m5uQbj6O/5JTeIOd1AEa/R5UedT506hU2bNiEtLQ2lpaVIT0/H//3f/2HevHnCsZy8cImA/+Lo0aM4dOgQli9fXi1M3ELL9VmRlrgBU1FRgczMTMTHx4NhGKxatQo//fQTZs2ahXPnzsHPzw8eHh5wc3MDIN9CaEtYlsXly5exc+dOo/GI2yWh1hjaDYNhGJSWliIuLg579+5Ffn4+unfvjqioKKxduxYODg5Qq9WSrQcRsTSmuF3++OOPgpup3CAirgf0T1EoLS3FTz/9hH379qGkpATLly/H9evXER4ejrFjx6Jnz55wcHAQ3B8BacFac2VMY0I8uCX13FiWxbp16/D8889j+PDh9ZBDyyAirgcoisLDhw/BcRzu3r2LiIgI3Lp1C507d8bYsWPBcRy2bt0KhUIBrVbbpEeXLYWmafTv399oHIqikJSUBJZliYgJf8HP4fJrbrVaLYqKipCZmYk9e/bg1KlTeOmll7Bw4UKMGzcOwcHB6NOnDxwdHXUW2/MLxQnm07VrV3h4eEiGydlTi4cMbNkAfjS5srISeXl5+OKLL5Cfn4/du3cjJiYGf/zxB2JiYjBlyhQ4Ojri448/xvPPPw+1Wq3jWST+NORxRDAOx3HYsGEDgoKCjMaRs5hJS2wmhlrHiooK2NnZYe3atdi8eTNycnLQrFkztGvXDi+//DKCgoLQqVMnKBQKYXCrMa0aamiY6nY5ceJE+Pn51XX2rAIRsYno70MlXmzw8OFD/Pjjjzh48CBycnKwb98+PHz4ED4+PnjrrbcwdOhQtGzZEjRNo3Xr1kJaTcV/uaFDURTefvttODg41HdWzIKIuBbwAtZqtcjPz8ft27fRo0cPDB8+HFevXoWPjw/Cw8NBURQ++ugjANXd/kiLW7dQFAWlUgmlUml0dLpv376Ijo7G3Llz6yGXlkFELIIfhJI6hIsX7tdff43Dhw/j8uXL8PX1xcmTJ/Gvf/0LXbt2haenp841PMamNwi2haIozJw5EzNnzpQMF289JFeIPfc/+L2QeT9llmVx48YNfPvtt4iIiMCaNWtQWVmJAwcOIDAwENu3b8fx48fh4OCAsLAweHl5QaFQQKFQQKlUCjtk8P1dYjrXHwcPHsSsWbMMhsvd7ZK0xP+DpmmUlZXh7Nmz6N27N9avX4958+bBzs4Ozz33HNzd3dG5c2ecOXMGKpVK2HuZ0LBhWRa///47Dhw4YDQecbtsoIhfiv6AlHj3xq1btyI1NRXHjx9HcXExdu7ciZCQEHh6emLIkCFwcXER4vPTQAAZVZYLprhd5uTkwN7evh5yZzmNWsTAXxuj8y+rsLAQv/zyCw4ePIiLFy9ix44dOHLkCAoLC4U9p3x8fODg4IBu3bpBoVBUM7eIe6O84CtbQ0LmOA7//ve/ERgYiNDQ0HrIoWU0ahFzHIeKigrk5eWhoqIC7u7uCA4Oxq1bt+Dl5YUhQ4bgyZMniI+PF3yTxS+bCFX+0DSNgQMHQq1WG423efNm2NnZERHXFbx5xC+SByA4T9A0DYZhkJubizVr1uDYsWO4du0agoODsXHjRixYsADdunWDt7c3HBwcqo0ii+9BaBx07NgRTk5OkmHi+X+5IksR62+3UlpaiqtXryIzMxPff/89ZsyYAVdXVxw/fhxDhgzBokWL4OfnB5VKhVdeeUXHjdGYFw9B/nAch+TkZKxYsQK3bt0yGk+u771BithQrch/r9VqUVBQgJ9++glBQUGYN28ekpKS4ObmhsDAQLRo0QKBgYE4e/assPmZ+PAv/mXJ+cVZgrHfLX72NT0b/fckNVWjP7hoSrrWhPeq06+w9fMSExODvn37WvW+4i6Zpb/ZWDoNUsQ8fGtbWVmJH374AUuXLoWdnR3Gjx+Pa9euoby8HJ988gnUajWio6PRu3dvODs7486dO9i5c6dVTqyT6hvb8jS8ukhboVDA1dW12oYCHMehuLgYDx480BnQM5Q2P2DIcVVnGG/btq1aBcGyLM6ePQuFQoHNmzdLjujb8lREALh06RI0Gg22bt2qky+WZWFnZwetVouOHTvi3r172LJli1XyRdM0XF1dqz1Hc9PmOA4eHh7o1atX9bicgZSioqJQUlKCtLQ0gzeqCXPEIJ57raiowNGjR7F8+XKcO3cOarUaGo1G53rxNeLaz1piaGwi5tFqtTqHq4kFLl5GaSxtftpNfPKEeJyCj0NRFBQKhc6OJLXNt7ki5h1uSkpKdPLm7OwMACgrKxPiqVQqKJV/tWuWviv+flJz0LVJm3cWeumll7Bp06ZqcRtsS8xxHAoLC5GTk4Pc3Fw4ODjAx8cHZWVlOm6NYtGKp5KIiKXDgSoBFxcXSzqrsCwLjUZj0m/mvyssLIRGo5F87uLKwcvLS9J7zdYtMU3TuHLlCkpKSoTv2rRpA5qmkZeXJ1zv7u6O1q1bWyVfvFXDewJaCk3TcHFxkQyrNxGLayf9lvPWrVtITExEUlISaJrGxIkT8eabb8LDw6NarabvvKH/vTk0ZhHzz0+/cIlXZfHiljK39WEYBpmZmbh161a1AUcemqbRqlUrjBkzRtL91NYiBoDdu3fj7t27wv9HjBgBpVKJ9PR0oZIZMWKE4P9uab4AoLKy0mBf2Bxz2tAOL/VqTnNc1TRRUVERkpOTsWrVKuTn5yMiIgJvv/02fH19hdrdWO1tS6E1RhHbIl8k7dphbtpSlQLxyicQZE6dmNO8mQb8NdUDAP/973+xbt06rF69GiUlJYiMjMS7774LLy8vHd/mupySIBDkRp2JmDedFQoF8vPzkZiYiG+++QYAEB0djX/84x94+umndex+Il4CoWbqbGCL4zhcv34da9euxcaNG6FWqzF9+nT8/e9/N7gTIYFAqBmrilh/xBmoMp9/++03rFq1CikpKXBzc8OHH36ICRMmCOI1d3CAQCDYoCXmnQS0Wi0uXLiAlStXYt++fWjTpg3i4uIQFRWF5s2bC3H5fi+BQDAPs0XMe6PwThYMw+DkyZNYvnw5Tp06hZ49eyI2NhZffvkl1q9fb9D9zA0mZecAAAUHSURBVFT4ATHeoaOsrAzbt2/H4sWLERAQgI0bN+rEb0pTTFJzr1qtFizLIjs7GydPngTHcXjxxRfRtWtXnTlh/p51OVUjrrT1fQQsTdvUcJZlkZGRgZiYGEycOBGzZs1Cq1athEaIX5YqByyeYiorK8OBAwcQFhaGl19+GQzDIDk5GUeOHEFERASaNWtm8cMQb2Cn1Wpx/PhxhIWF4b333kNgYCAWLVqk46nV1P6k4CtNV1dXKJVKfP7559XGHsTuknWZX3032fr4YxgGgYGBmDp1KtatW4egoCBs27YNpaWlsuve1dgS63uNAFUvvKysDGlpaVixYgUuXryIoKAg7N69G4MHDxamh6y5iyDHcSgoKMD8+fOxfft2VFRUoH379tBoNPjwww+rxa+phjaG+FqpdKyVtjnhUqxdu1Y43pSH4zgolUp06dIFN2/eFBbG86KnKAp3797FO++8o3ONLfItFaZWq4UK3tpp1za8V69eyMjIwOTJkzF06FB8+umn8Pf3N3hNQ8MkETMMI2wMV1xcjNTUVKxcuRJXr17FyJEjsWLFCjz33HMAAJVKJVxrSWHXh3cTdHBwgFKpREVFBTiOQ1lZmWRl0ZREbAyGYbBr1y7ExsbqzL3zlazYNbCuREzTNO7cuYO8vDyrp21qOL/QgWEYFBcXC4OyN27cwB9//CGr0yBM6hNTFIWioiJ89913SExMxM2bNzF27FisW7cOPXr0EEw3Q6adpfAFzt3dHStWrMCkSZMwe/ZsZGdno3nz5li0aJGOzyuf56YiYkPPnWEY5Ofno6CgAOHh4dV2MfHw8EBqaioA1DhmYU2h8TuwiPvkdS1ifkxgy5YtiIuLg5OTEz744APMmDEDTk5ONivLtsCoiDmOw7179/DNN99gzZo1KCkpwYQJExAbGwtvb28hnik1uSXwJhfvCNKvXz8cOXIEKSkpmD9/PubMmYPk5GSb3Fuu8O9k37596NChA55++mmd7wEIQqrrPbH598h/1oeIGYbBwYMHMX36dERERGD+/Pnw9PSESqWS3YyJwQUQEyZMwPHjx1FZWQmO4xAdHY0333wTbdu2BUVRJm3XausWTaPR4MmTJ2BZVpi2slbacmqJpa7llxMGBwejZ8+eiI+PB0VVHWki9d6s0beU0yIFlmVRXl6Ou3fvokOHDkJDIXVyh7n5Noa5aUu9O4MtcYsWLcCyLN58801MmzYNLi4uwkn1DWXTdJqm4eDgoLO4nVCFUqnE48ePce7cOSxcuJCcQKEHx1Wd/dyxY0fBGpFT6yvGYEtcXl4OrVYLZ2dnk2sEqTi2bNGk1r1aK225t8Qcx2Hr1q2Ijo5GYWEhlEqlUAmTlrgKqTlq8bORS0tssHpWq9VwdnY2OM/WEGho+WlopKamIjw8HKdPn9ZZ7E+ooqGW69pCbKxGSnFxMQ4fPoyWLVti69atRlthgrxpsHtsESzDzs4O77//Pjp16oTRo0dDpVJZfQ6a0DAw2Cc21ic0OfE66lvKNW1zwk1Nm2VZwc9cfMSq3Pqtck7bGNbsExsUMYFAkAekT0wgyBwiYgJB5hAREwgyh4iYQJA5RMQEgswhIiYQZA4RMYEgc4iICQSZQ0RMIMgcImICQeYQERMIMoeImECQOUTEBILMISImEGQOETGBIHOIiAkEmUNETCDIHCJiAkHmEBETCDKHiJhAkDlExASCzCEiJhBkzv8D5GIMFmQZLGEAAAAASUVORK5CYII=)
A ‘pop’ gun consists a tube 25cm long closed at one end by a cork and the other end by a tightly fitted piston as shown. The piston is pushed slowly in. When the pressure rises to one and half times the atmospheric pressure, the cork is violently blow out. The frequency of the ‘pop’ caused by its ejection is (V = 340m/s)
![](data:image/png;base64,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)
physics-General
physics-
A source of sound is travelling at
along a road, towards a point A. When the source is 3m away from A, a person standing at a point O on a road perpendicular to the track hears a sound of frequency ‘n ’. The distance of O from A at that time is 4m. If the original frequency is 640 Hz, then the value of n is (given velocity of ![text sound end text equals 340 m s to the power of negative 1 end exponent text ) end text](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJcAAAASCAYAAABW4kwSAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAA15JREFUeNrtWV9kW1EYj4mImRF5iJgYUzVVUaYqZiZMzURNmaqZqtKHqdlbVc1epw8zfRhV04e9TVQfpsZUVO0h1MzMVKjZw0xeYvYQV4TsO/wyZ9/OOTc3N7m50vPjp73fvefec7/zO9+fm0jEwsKMUeIT4ifrCote4zVxmdiyrrDoF9zE9Yz40LrJoh/iEvhAzJ6FF/WLPHGfWCc6xArxBTHpMq5gmN9F4ktiGdyCbRD+09GPz68Rj6y43FEizhJjkm2C+M4w5gLxq2F+B8QZJsSDIfP5EURmxdUFfhvOiUi0pJnfPeKmwi6i4fwQ+fwR6q+/uIKdWjeExwJ2ZQN/ZzxMoKU5Fg4/Rdo5JGYUY2+iDW7g2sUBikv46URz7roUhVTzKxKnNem3yGxPiavEFARZJf4k3sH5BPE5sQaxr7Hx68TvxCbmshqguHI8Gh9rxNLGFBZ2HMfjOM75EJcQ1gbxMmyLEJiMqxBy+7ljWIiWR6e40Q0pzK8iLbAMkTo/S++iumeNpVh5bJXZ3kBgx4hqUdz7GzENP83BnsHmTEnC2tY8q1f1mQkxHt3r2A06FBG5eCTb8yGuPLOdQ3SS8UqTMoKKXNypjw1t+IrL/JqG5/D3rmD38zX5AeGo7GmpY7s14BT6z/vcxaTmDXVGzE2hXaRFt+tEKoiHoOZKwEdlpGkZWfgu4kNcDttkYrOfV2w+k12u7T66ZKJAxdXudLaRhkY7XMxGn8XV7EFB34u0KPuozGzieKSD+VU1qSrO0uIU6l9VadKpPY2urYQ5B4mYqelZg/LDELkc7MwwdYuOR/HKpcVtxf2mWUEvsseO4jqv9jjqwAcB+ydn+ryiqn2KijAr0sSuItJwMWz6EFcJXZiM5ADFlUU91E1nNYvMwLHDyhHhr2XFdV7t7Zr1fsA+WkGjpsSSIsxOojsck5x8qlh40cUs4P8RdD1zPsQlQv574iWItoD6JghxHaJ+ieLZeXRrCz7a9hKagigi/7qiQ97VdKRe7ZMocZIBi+u/j6jtEC4iz77UefDu8ARR7QsiF0cGzmogNOZ8psUI6r89pCMhrImAxHWD+BbPdSCMgs9vQglEEwdF+JaiJqppmphO7L+kdSzhU06QGIqffyzCiaH44doifNjgtd8fCVshMO2rGo4AAADUdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG10ZXh0PnNvdW5kJiN4QTA7PC9tdGV4dD48bW8+PTwvbW8+PG1uPjM0MDwvbW4+PG1zdXA+PG1yb3c+PG1pPm08L21pPjxtaT5zPC9taT48L21yb3c+PG1yb3c+PG1vPi08L21vPjxtbj4xPC9tbj48L21yb3c+PC9tc3VwPjxtdGV4dD4mI3hBMDspPC9tdGV4dD48L21hdGg+1tZL/AAAAABJRU5ErkJggg==)
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)
A source of sound is travelling at
along a road, towards a point A. When the source is 3m away from A, a person standing at a point O on a road perpendicular to the track hears a sound of frequency ‘n ’. The distance of O from A at that time is 4m. If the original frequency is 640 Hz, then the value of n is (given velocity of ![text sound end text equals 340 m s to the power of negative 1 end exponent text ) end text](data:image/png;base64,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)
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)
physics-General
chemistry-
Faraday is equal to :
Faraday is equal to :
chemistry-General
chemistry-
0.1 ampere current is passed for 10 seconds through copper and silver voltameters. The metal that is deposited more is..
0.1 ampere current is passed for 10 seconds through copper and silver voltameters. The metal that is deposited more is..
chemistry-General
chemistry-
1 Faraday of electricity will liberate 1g atom of the metal from the solution of :
1 Faraday of electricity will liberate 1g atom of the metal from the solution of :
chemistry-General
chemistry-
During electrolysis process of fused CaH2, H2 is liberated at :
During electrolysis process of fused CaH2, H2 is liberated at :
chemistry-General
chemistry-
Assertion (A): Carbon exhibits catenation to maximum extent.
Reason (R): Valency of carbon is 4.
Assertion (A): Carbon exhibits catenation to maximum extent.
Reason (R): Valency of carbon is 4.
chemistry-General
chemistry-
Statement - A :Carbon has two unpaired electrons in its ground state.
Statement - B :Carbon forms 4 covalent bonds in all its compounds.
Statement - C :Carbon exists in ground state in all its compounds.
Statement - A :Carbon has two unpaired electrons in its ground state.
Statement - B :Carbon forms 4 covalent bonds in all its compounds.
Statement - C :Carbon exists in ground state in all its compounds.
chemistry-General
chemistry-
The end product ‘Z’ in the following reaction,
is
The end product ‘Z’ in the following reaction,
is
chemistry-General
chemistry-
Identify Z in ![](data:image/png;base64,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)
Identify Z in ![](data:image/png;base64,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)
chemistry-General
chemistry-
Westrosol is
Westrosol is
chemistry-General
chemistry-
Consider the given figure showing that possible levels of the energy of
ion depending on internuclear distance versus potential energy of the system .
![](data:image/png;base64,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)
It may be easily assumed that the ground state of the molecular hydrogen ion,
corresponds to the lowest level which means that
Consider the given figure showing that possible levels of the energy of
ion depending on internuclear distance versus potential energy of the system .
![](data:image/png;base64,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)
It may be easily assumed that the ground state of the molecular hydrogen ion,
corresponds to the lowest level which means that
chemistry-General
chemistry-
Which bond angle
would result in the maximum dipole moment for the triatomic molecule XY2 as shown below.
![](data:image/png;base64,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)
Which bond angle
would result in the maximum dipole moment for the triatomic molecule XY2 as shown below.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAecAAACZCAMAAAAijAJjAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAMAUExURf///wAAANbW1u/37zoQWq2trRAQWrWMnLVajEpajObWEOYQ5uZaEOalnMXFxRAZIQAICIyMnL1aWnMpWnNaMYRarRlarRljWoRa7xla75xaWnMIWoRazhlazrWU70qtWrXvGUqtGbWlGUrvGbUZrUoZrbUp3kop3uaUMeYxpeYZMYTvnOalY+ZzpeYpYxBjGYSU70rOWrWEGUrOGbUI3koI3uaEY+ZSpeYIYzExMe/m72NjY0JCQubWnOac5oyclObe3oSEhLVa7+bWc0pa7+Zz5uZac7VarUparebWMeYx5uZaMealvbVazubWUkpazuZS5uZaUq2llCkhKRkZEBAICEpSSjoQCObWvea95lpSWlKM71KMrRmM7xmMrYzO74TOaxmMa4TOKRmMKYQpjBkpjFKMzlKMjBmMzhmMjIzOzoTOShmMSoTOCBmMCIQIjBkIjGNaEHNajAhajAhCWnNra7W9teb3Kb0pGZwpGb0IGZwIGXt7c7XvrUJaKeb3e3ula0IQMb3F5rXOa7WlzkqMa7XOKUqMKbUpjEopjOalEOYQteYpEITOrRBCKYSlzrXFlLXvjEJaCHulSrXOSrWEzkqMSrXOCEqMCLUIjEoIjOaEEOYQlOYIEITOjBBCCISEzntSWlLv71Kt77Wla1KtrVLvrb0pWhmt7xmtrb1aKXMpKRnv7xnvrYzv74Tvaxmta4TvKRmtKYQprRkprRnva4SlKRnvKYQp7xkp71LO77WEa1LOrZwpWpxaKXMIKRnO7xnOrRnOa4SEKRnOKYQI7xkI71LvzlKtzrWlSlKtjFLvjL0IWhmtzhmtjL1aCHMpCBnvzhnvjIzvzoTvShmtSoTvCBmtCIQIrRkIrRnvSoSlCBnvCIQpzhkpzlLOzrWESlLOjJwIWpxaCHMICBnOzhnOjBnOSoSECBnOCIQIzhkIzoRaEJRajClajClCWr3v773vzrXva0rva+b3xbXvSkrvSkI6EHuEUkJjY0I6Y4Slreb3/wAAEP/3/wAAANrmsbEAAAEAdFJOU////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////wBT9wclAAAACXBIWXMAABcRAAAXEQHKJvM/AAAKv0lEQVR4Xu2d3ZLbLAyGgzOcOsnlAJ4B38Ia58D3ER/5xr8dp/NJgO1sm7/ddRJM9Gw7E9w2uzV+kRCSsiIIgiAWBw/kbpT7QesGREIUlgGV0G7ERYWjTroRkQ5Gw8zaUvqZlbLcMpXTNCeIBkWX4fVq1bG9CS+JqJGtN7LB5JovozOYT8aK4U/byvLwkogbs7fAxgaTW1ZuWE2S/RsOgu78S6mYokV7GfRcwcRZxTM3NK06MrH78KNzwOQy4QWtbXhBLIC+rNnJ8qtrcX2j1IIr5lxsWMIvy56IDlMw1gzulGzYLry8wLqDvRQ+CromJ2xR7I6ToPU05ZfIBUO7nAvrbTqxEEwDPrSf3Uzc4UHDrhkE3TEVxsRC4BXz2pQdO9z2oHGhV7qqyAlbGuBDu01xfp8HrS2zlSUnbHGAD12DoPvD9oYT5gFnDR6My3svIlL6DnbN+eqjCmb6FhjmPnHCpOnDKyJGwnkEkAlW70yxvTOMaeCvn8xzu1ectliR8ifTezXODpjcqrD3hjHhsTjZVPUlY/ZTZxQDjQ/ZdrD2Tl4X+tAnwxvA3z7Vc1aKGv61aknUcQFStoxVjZ4kiAeO4XziNjnMM/8TBojRLky+1+ScRQNKGeXXtacLLUj0/kNGVP9fnrnMS3GEZ4csdRRIoxtUXvOP8kp236YKyb/Y5wF4a0w3aTQFUF4MSFmgHe7OJPscvqFnDHGfC5PA+zs7fyBL/TrWo96yc9tdcJr/leg5ZM7VlrFid3aFhm+yIUv9OkYpf7HKJ3TgWoWX1zGqskfL6iEH5W9k3oGlrpcrasPLcqFeRpBycV7KjvLLVukKkmvN8evyvbjoBCwBXoimqYq7jVg0TFI+3Qr9Ra/Y8Xv/tStvBjMNovaWemnREy6KVhouqoVN9OQFXwlCS4kha5XJ+QLVfTZa6qtPRGTkwiXLrPiikt9QyrCCXrbKHnnAgBYu7LMW0fiFpL713aOiDDmssvFZcAugN1x5q3xNyojUTaNUA18zF0v9AVEvylJP2VB8u4xECtmW91vItfv1ECTHSPpSRF36HEcgs6yM/ye+W8rPYBS1if7GqfEwJxe3UyJfDO5gUcoqGgl5UR/PBuKiohkyIlfrA4t74Z6kHJOfC+43npFt4hZ1W7Em/Hh9941A8NMBKbsIczxSnpCtgmXGijJeS80t+2/44e4OBD8fL+XtvozBKp8j9wffKlZRc8aUWa37lYS9JttGOc8yL4st3MS4Q1CSH5z7HaeoQc/V4XBQ+Bt+zAgdbi/lGqzyozZIc9HnGvtfoKjDlXiAeRYwxx3+AhsTW4r6IGXFY5byhGxR1Da+PTXMs0KTB7/BD4tsngcHu7x8GBUdMiu9qHlUlnoH8zysh11U9hmlHG5YuLIUJEf3mxUx7alBz/vhpynvPZB/PL33arZFtA72VeKz1LkY4yRmH0ucZLlSnjDOUtdFLO53M8U9q3HKXwpIGZY9lHLsDvZ1ZKbx6DSSp7Vjm3COkW8icMNO3JhwZcnI1oV3YthTw8IdZldvh5Orl2FGq7xsKU+gpa5jeG77wxDgblj3Up8H1jmUsk1DyhOTS/lSUQ+JBtqO7fBegXEHfClJeQJFDRutF4ta24obs7M32ms9knXuDuwTscrnmCzS60TNC1EUQr1MzcZl1W3jP6v/FevhNOZ1z7LhWr/KI5Swpm3gv98kK+WJcLr6akv9AsAquxP6tKU8EYGon09wsDfvIOWJ8XDmPR7tXrYY9lpABt3sgKgFiFq8g6inPJtw4b0YRK2TfshRyjVKOcoUm+eAeY3YDqNLVdQyK1HKtvl4TymP9OYj1PQmKGqsQIPH+K2lPNHnrhoQRD1jPeclenm94nc+QtjLvpeDfZXecHdL9o/pRtdLY/JW77pOAVhPqLpup9vcmKln4syAlF2mPUn5K0PjqpnbYUiTc901orK1Kw0+oba2EqrTPJ89h22IYDdv6mBfx3w493tfziRqKVt9KNAkIDCpRdFggTBIuikKmPrhDwpV8hkXEixlxVkGOxSuEF8J7reYwVKbXCuMPzG2ETCPsEi7VXoNYlvJtZQmy0HppQrPgRVN186hazlVjy4xp+9phD4cv7PUYAQabIrIqqKDGR6M8Jkbv5ZZy2Fd37oH4vBb/wBLWbEZ4/L6trwA737/2IOBZRO3rKzad3euxuCntaXCb7oV6uf7u9CMEWtGScp3YXZu7St+UI/n1wOMMX5zvqThLimvhqn+ife09lXpFTnY3wEXwO9HGEJfnkr9zK3qTV7u0Wp8ey1BKcM/jLz8O07Cnvr+vrE+rxRWgV+Z9rZ0kdjvbIlCVfrce8K3Yei1c5e6jDvenSMuYVyTeivKux6wG31VibsYb+KN9VC6WS7mKlCChwYTIW6fFqP88VGkDxv4Lb4b3XWhOi3Xn3OeCUl3Zlodrs30GkyLtxSvzBFOBxA1tpi8JGrZgiGvP2c/Lsjd8n1xK4yRWi/lW6In7gVEXaH7faZ0R+YHeAhm1fKA3yqBpv81BrALU/jskZTnxmjc8oAf/PXGGuxQCxvtMJybDDULdjoMA1jK6qRMEewHgKJGCZ1YanC/YBoe2V20d6u3KKcHCazykO4UrhAz04OoMQ4yWOpcWTCgD77dfYYzDUuGK4XyUt5WJOXHMvS4wYTgHO74J398Jdq6xecJ+ziP6chZevVvsRFEbRvORfWkg/y+bY7K+PICsspPIxTZiuLkE/cejClL7KuD5UIU9noe+LENKGr1nHzZP7kPkFHY6/lMHVzChYcxFQmRlF/BOtOfwf0OVx4BWGX8JulWpS+BSWqPsdTw/hjchPcnB/vF+HrTh+htaHRHUo4CL2psMTmn/fQnVkeSckQMLSbnq3HxVjm5tk/Lx4u6nsVST1aZHOwIyfXebXJ/qUFflb4hKceLF/Vv+q8ZtytHq0zBzZjBHjegRvEjNcrh05k+6GPM48c7yt/f8/om0ijlcIGIHOxx801Ry+EU7JFJC8TseFFjoOweUYOUnVX+O0GIiJ8pieuWqEM+6bu2fVo+3v22n9dq6vyxV+0SVIhl0rska8wBudCNrp9Sw8MVYqmEoon97h9L7Vsk12/YjDFN0P12lvo0GwTr37yDTVJOBxA1rs9gqb2ovYPNSMrJMYlaklVOm9BisnGHUSTlhAk1jk7KdOSYMuh+nVZoEckiySoTBEEQBEEQxLyspTGZQfwYhngBGzUTCSFLUewL4OBae69hiJS0kU4MV8DMNvtQGu/ONaq9Jj0nxtqUMNHNGCMxeyYoLJYkMNEb92nuiH7lR30TjyQrGBs+rr+tNty/IpIjF2Hl7k1hS3+NSBBdsy2u3KY4YjswIlFkt2XVB8z3dnLIiAQxzkR/2MFME4nSCnYUVUWudupoTOYlVzt5+gPM8y4MiGQxik27aCJVZGlFxZgidzttuG0MBxNdUlpvyrQCXO2+ZGwDu2giVdqqQlfbNIwJMtHJIputD3eOgW4iQeTBqhDVxl005ZIkSrctxmZC5ZHZ8SyaSAjcUU3hTgx0k4lOEW2PpwLOYRddUJg7MSQ2qThpAme0AgvNREeR7qSQeyx7ZmMSCQc1OxpyxlJCNhYZ0wB5BQP4soriYklhMmT8AOneDQHaRCcG6ZYgCIIgCIIgCIIgCIIgCIIgCIIgCOIJrFb/A6b75ppdca2aAAAAAElFTkSuQmCC)
chemistry-General
physics-
A long rubber tube having mass 0.9kg is fastened to a fixed support and the free end of the tube is attached to a chord which passes over a pulley and supports an object, with a mass of 5kg as shown in figure. If the tube is struck by a transverse blow at one end, the time required for the pulse to reach the other end is
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)
A long rubber tube having mass 0.9kg is fastened to a fixed support and the free end of the tube is attached to a chord which passes over a pulley and supports an object, with a mass of 5kg as shown in figure. If the tube is struck by a transverse blow at one end, the time required for the pulse to reach the other end is
![](data:image/png;base64,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)
physics-General
physics-
A plane progressive wave is shown in the adjoining phase diagram. The wave equation of this wave, if its position is shown at t=0, is
![](data:image/png;base64,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)
A plane progressive wave is shown in the adjoining phase diagram. The wave equation of this wave, if its position is shown at t=0, is
![](data:image/png;base64,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)
physics-General