Chemistry-
General
Easy
Question
0.1 ampere current is passed for 10 seconds through copper and silver voltameters. The metal that is deposited more is..
- Cu
- Ag
- Both (a)& (b)
- None
The correct answer is: Ag
Related Questions to study
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,iVBORw0KGgoAAAANSUhEUgAAATMAAAAfCAYAAACLQSqnAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAqDSURBVHhe7Z1Ji9VOF4fLdy+On8BhIQqKOIDDQsEBV+5UdCEoigOCirMuBFEUdSE4gYILZxE3tiiCLnThCAq6csCFuHL+Av3mqc6v/8d0cm/SN0l3364HiuRWkhpPnZycSuoO6YxwgUCgm8WLF7sHDx64J0+euDlz5sSxA5enT5+6uXPnukWLFrn79+/Hsc358eOHmzlzpvv48WMc07/5X7wNtCH37t1zQ4YMcW/fvo1jisP1hGPHjsUxXYM9GZcFA2Ljxo1u5MiR/prp06f7wSWUFkHoN8eqhLKRz/nz5+OYLq5cuRLvNadZ/eqEfl6+fHl3+40bN87HoZD37t0bn5Wfhw8fumXLlvl9pak+oY6KK0MOSgHLLNCeRHfizrFjx3ZGghzHFKejo8OnMWLEiM5Pnz75uO/fv3dOmzbN7zeDMkQDwl9D2LBhA08C/6TFb/IR7BPHsSo5evSor1taXcg/ssziX9k0q19dkDd9RP4qC+VSHagrZS0C7aJ6pPUJclWWHJRBUGZtCkKM8Jw7d84LuUWCjjBxDIFE2NMgHQmiHQx23won6UkxvXnzJlVgOcfmxzlWcbBPXJVQZhSZysjWkixTGnnrVwf0M/XJoqgyo05WUaX1Sd4062qn8JjZply9etUtXbrULViwwP369cs/copNmzb5bTSg3YcPH/zxZpw+fdq9ePGixyMZrFy50k2ePBlJdwsXLnSnTp3y8c+ePfPbMWPG+K2YMWOGe/ToUfyrC3w6emxhv2p4hKKslDtSAu7mzZvxkfwUqV/VPH782D9WlgXts3bt2vjXf6iPCLt27YpjG1NXOwVl1oZ8/vzZXb9+3ftPEKDoDuvu3r0bH3Xuxo0bbvPmzW7UqFE+2EHAtQhqEs47cuSI27Nnjz/HglN5/fr1fn/q1Kl+C3/+/In3ejJ8+PB4r4vozu+VIYH9qtm/f393mSOr07dJFihw2oh2Yav656kfNxH8Q7q2Ff9lI37//h3vNYfyW99ams/rwoUL/kaYRH1EiKyqOLaLVtqpDIIya0OOHz/urS0J66tXr9zZs2e9E7YZKD8ENQ0GP3dT0rcwYHEM49y1d+tZs2b5bVL5MTs2b968+Ff9oOijRx43ZcoU3z6HDx/2v631arlz5447dOiQb5fo0ch9+/bNx+ep37t377wFyLVsmSWtgvnz5+eedaT81BfLvKOjo4d1hMLl5pW0pJrRSjuVQpRxoI3AP4Evwvp75O/ArwL4QvCBAcca+S7wf1nfCX4Pzre+EtKWnwzfmT1fDnb5S3Aacz0+K2Brrwf2idM5ZUKalMfWlzjKpDZJKxMQzzm2XM3qJzhOmyV9c2VB+pRZ9VJZJQdZznpk4tq1a/GvLjg3GZfWJ1lpttJOrRCUWZuBwCkIBpHiEG4GFMLFb4SK41nKTNfZ4wwAq8yUPluO2fMRXgRb6bBvB7Qtm9Bvm0dZ2Pw00Cmr4thPKxP10EyhpVn9QOmTblXKDFA46lcCyoP8dDMjJPsxqbSANJL11PXqk6w0W2mnVgnKLOCFHqUWSIeBqQHKoLSDtxmcK4uYNBjE/QGUmBQZ5RIomN6WsZV2KoOgzAY5CJzulrJUAv/CAFUbEYoMUhQGj1Nch8VTpWWWFxSNrQ9BUNc0ay0PrbRTGYTPmQKBQDfMQg6Uz5eSBGUWCATagqavZqR978U3VprmZ1/H2BdMfyue64uQ/I6LLWnoHR2bNuURHLfXFIX3bfSeDIHXDTRdn0xbZQF7jY1vhK2DDaS1b9++XK9RDGZsm9OWYPvIysVAwY4zZEBYWbFjrN1hPKreyZDav1hmWfB8z/O+nHogH4v1r+BATpt54jquLwL5kJ6dxtXMiX0Gx2GdVnye94kv6ptQWVUv8sbHYeul6emkb0k+CDl685KsA3VXXN3+hoEGbUX/ECz0I2GgoplUjTdBPYvK10CHMUC9bVtoDCZfm4GGyixNWIA4O6DpgDRlRmHS4huBIFJYKTJBvB3g7FtFIKT4iiAFmHR88tuWX2knlRlkxTciqw7EFW23wYj6Q4OcG1hS+AcayD03VSvr1G8wygNtYMekbmBZbZE56hEMKyiNIPG0DChM0U6gI/NMDZepzMgvjwVZhzKjw4jTqxKyjonjmCy3/ijcCF7yhlA16jvaBmu+aB+URZl1l1yg2DSAkzf3voby1G0B23ZJI9Nnps8uJk6c6Ld1wPpGfIZjv++rA77L4zOdvobPPfgIPBqUbtu2bT6OD6EvX77s9w8cOOBmz57dq7Wp6oBv+U6cONHtw6oDPoCH8ePH+8+F+moxxTLrvnPnTv/xO/2MPPCJUNFPi6pG5anLh8fY4FO5SKFlt0Ws1HogLZjnToeVwLlpoYgFIcuHvJuh8mWFInB+nnKqfFmht5aZDWl3YeWb5ifob8iSrNNCk7VatP3Lpsy6q8/7y0u2acgarsNCY3w2cyGU9qF5lBka5J+AFq2aZJ6REMRHqoM8kvm2gtKIlJhbt26dvyunffS8ZMmSeK9a0maP8gY+3sa6XrFiRZxatTDri2WNNbt69eqWZ4HT6pQ3lFl3WZhVP6XYlX6LhtGjR3cvYlDl6rqMBZ4UWVqKD+CzyFRmkyZN8tuvX7/6bVlglmpana19lWHChAl+++XLF78ti+SrHnbaGxgIVbwoaF/1QGiaDTTMZz1iaE2wvsAq6aIhsk78igmRdRKnVi08hu3YscMrtJ8/f7qTJ0/GR3pHWp3yhrrrXgYs35RWlzwhspL82Ikss8oe7xkzW7Zs8cZSs5t5pjLjjwzg0qVLfmthgPZWE+NTuH37dndDsEaWQOsSxznJgY8yyrPWeBoXL170W4Q9elTzS77Y8uNrwSpK1olyaM3zopDWrVu33PPnz33aLGyocrQr9BkL+p05c6bwu4W9gTs2bcvSRNwIdu/e3aNv66LuuvcH8OGyVht1rgrGDH1s86CtMRCSZCozFAsOSMw7rS5KIlg1JG5JKh7BomwMYgsKBac26WOBYC1ZDh486E11GkrpolQwZS1ZC779/fvXb63Fh7WjxpB2Hzp0qN/CmjVr/B1169at3WsuMSBYwM+itJOonO/fv/db4E718uXL7nWhmGAYNmxYfLSLZB1IB4VN+7I+lZB1nPeF3L6C1Um3b99ey2CmLVatWuXlRdDP6scsmayKsusuOWy0sGFfovJVqciynP6NjILIYswGJzWON84jRJaTd7jKEaf3wgjWEYgTVPFpTkyO49RLc+jh6CYfXU/+pI2DFWzaHBNywBLPNg3STnNYci3lVLpcz2853ZNpqyxg28fGi0g59airrYMN1Js2F43yHazQBmqvLJmjrQYqts8J1GswYsdjWkjSJ99mykSMCuuXYcZSqwPu5mj6Iv8d2CpYCKyRzx0sc0o5EAi0TGmzmUVAf+Iz4xEz758itIoUWZH/RGwVKbKkmRwIBMqndmXG5AHPwviSIlM6jq0WlArOWRQZ+eKDq8NJLEWG5UmdezuBEQgEmlO7MuM9KmYsedR8/fp1Le+iMZnA+zC8F0O+dbwDhcJk8kR/msFkRyAQqI6wnlkgEGgL+sRnFggEAmUTlFkgEGgDnPs/glYXmZarZCMAAAAASUVORK5CYII=)
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,iVBORw0KGgoAAAANSUhEUgAAAXEAAADvCAMAAAAzQhQRAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAMAUExURf///wAAAEpKUvfv7+bm5nNza4yclISEhAgQCEJCQsXFxWNaY0IZWr2c5hAZWnNjEKVjWr0QWlJjWozOWoyMWozOGYyMGcXO3ntze0IZEMWclHNjQoRjpYyc74ycxcXv3u9aWu9aEO8ZWu8ZEO+cWu+cEMVjWr0xWr1jpb1jhL1a773vWr2tWr0Z770xlL3vGb2tGYzvnBBrGb3OWr2MWr3OGb2MGSEpKd7W3qWcnO865u86re8Q5u8Qre/eWu9j5u/eEO9jrTEpMbWttb29te9ae+9aMe8Ze+8ZMe+ce++cMYwQGWsQGRkQEO+t7+/epe+tpTo6Me/ee++E5u/eMe+ErVJrjFIpjIwQWilKWqVjKb0QKRlrjBkpjJTO74xrzowpzowQpVJKjFIIjGsQWghKWqVjCL0QCBlKjBkIjJTOzoxKzowIzowQhCEhGYwxGSnv3imt3invnCmtnAjv3git3gjvnAitnGsxGSnO3imM3inOnCmMnAjO3giM3gjOnAiMnKWtpUJrKb3vre/exe+txb1rzr0pzr0QpYzOrRBKKb3FlEJCEEIQMb2UvUJrCL3vjL1Kzr0Izr0QhIzOjBBKCGNrY1rv71Jr71Lva1JrrVqt71Kta1IprVrvrVqtrYwxWlIp71LvKVKtKSlrWsVjKb0xKRlrrRkprZTv7xlr7xnvaxmtaxkp7xnvKRmtKYxr74wp74wxpYzva4yta4zvKYytKVrO71JK71LOa1qM71KMa1rOrVqMrVII71LOKVKMKRlK7xnOaxmMaxkI7xnOKRmMKVrvzlJrzlLvSlJKrVqtzlKtSlIIrVrvjFqtjGsxWlIpzlLvCFKtCAhrWsVjCL0xCBlKrRkIrZTvzhlrzhnvShmtShkpzhnvCBmtCIxK74wI74wxhIzvSoytSozvCIytCFrOzlJKzlLOSlqMzlKMSlrOjFqMjFIIzlLOCFKMCBlKzhnOShmMShkIzhnOCBmMCBAIMYRahHtSY+//Ou//vUpCYwgAEOb//wAAABlF4n8AAAEAdFJOU////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////wBT9wclAAAACXBIWXMAABcRAAAXEQHKJvM/AAASnklEQVR4Xu2dTZqqvNPGCaGNiTMmshPCVJgyYPhuInvIJthqj+R6UxVUQOVDefyfxvrZx8av9vRtdVFJKlUBQRAEQRAEQRAEQRAEQRAEQRAEQRCfRVubwSVvbyuZtUeAslb5I15rf/AALn/aI2IaHbNMFUXMCn+bx9IfILq83K9K//0RPPxtj4gZCMYb9y3f+ZtBErcHiCjhQUec+O8PKdL2gJiBYM5dRM6cL7edjfOiaE375+C/8xTdjgoi6x7hNudwM7K5he+FgWtiHqB41vEkYOM5K1tvXreKo6Y8YVWcmSqJdxJeoU2dV7U7sBU8h5iHYIkTsr3hSMIgCAWaMNxqfcwBnErD4Yn8XEfBEfz7r3B3Gic52fgSnI1z0VFcSFXdwpXWxpXBj4AzEN44B6RYFqg93Jc5H56TH18A+vGjcxGtWe9Y+AueQmHE19p4VuEJlDN4JHXmDYrHDF6SMUU2vgjB3GnTEbeBtzgF0d4JGzK4FTsf40jxBNkqbtwzQXGLiifOo1OssoSEOQMPovrkzBX0/IFY5Rw7T+2iEw1XcIpsIxn0Kr/4gPsMjPsDaEoXVv5QPD4fZUq5EzWOdGJn1oUpbRAZJoJsv0sMnBvBqeA3Lpj7OJJ9xZ3vcdorKUTsfL42pX8eMQMe8UhrzcFBwBV3uKAED93d/knSO5UGn+ZewP0TnNYajN/d8p6JeIHGXVquB8dbuH69r3NErE4N/p34IJcJAIIgCOKfh1cUWX8WznoLEsR/jp85IT4HZ+0SBPE2upbWB9Yqqds1tSK+zBheIBtfjUIKUeHCvDWFCmsYpCdxLljvTNmQ4qsRO/tuYCqwgHlWDlcCEiIKWJC4QYqvS+jkTHC9pq4C7qdY+8EJ+fE14aJ0XhsX34OijBTYObgWuL5ANr4ikQSf3UqqWBExXECGVbMOI4q3k+XEbLhy9t0qnjOlW8XbteMkEe6req64gvVNYhnHMw8O6KhzExy9V5F+7TgJARn2FefGr/4AvBxLhCMGWEwrLJiTFtfdK3ddofb98HDgVRrZ8fJh/5nEKJaBS0iNi7jBbCOTt4EhhogdBrGKLW8rmCHZ+AJ4lgrrE5XzNBPeJdeVrSFO73AXq5zb4akjpEmuRaj8mnyf55Ci4tA5pqN0uFO8vMksMCOIWJc7xZNbSqI2tH6/Ps1wzKlvswBRf0KAWIU7Gw/atCxHNAhriDW4V1ykV+8d0war9blX/FhefUl8ag+I9Xgwd7i/+pK8TXwmVuTexgPc8oNEJYWHq/NAcet3pAApOfLVeaB4Z9hZnygiX5tHa0Dt7KIjo1Hn6jyycedWWtPm+9ssC7EKD9fym/Kqc3g1d2IlHike/F51thStrM3DtfzOBtv9cLKReJOHNq7212Fnd02IWIOHindms8itzIcXxXVForisSBTFYNz+WPHOJDktL88lj2VsYjDQIg1thdGHSLM4Ha66PfDjQX4bdgraED4PLp1Z8183So9gj702TvICVpt9UtyVxzYeldcT5hGXqIkpmgydQc2adrVSOqH9WbC3zPAst7Zzwow7lUGI52j01zVzZ0GUNEuDNu+w6kcfjxW3t1IHmox8AcbZp5dUXbPgoC7WjSe5te2ng4Rk5LOB4jWt28hvmZ7exkXtSOpneYcGn4uQkc9GYIRy8ja+15dMTz+EF/HBXeLDE8V97pyHPPlMRJvSiYuVdRVEDHMRBxI/Ubwz7HRGfqmNSDyn4RIM/MgD61xLw8/OvjHl0Dl0fMKFx3480JdyfIAvkEWMAlWBrDAwRs9klvnctp9YZYMclCfRoYsPu/fTwHMarlShVI3yqrBqIw83EB2cBZ8qbrs5uMWlmi3xNk8V17dhpyO+pQ0R7/EkHnfInvvx4yjifZ7a+CAmzH1oSbzNc8X1vjexe6B4ZR2eK85NLwpvYC6MeJ/nfhw3PHeRt0lz4nWe23iQDfZojTyVmM+IjNFwHd/S2XMFxgxXDkeaJPkKjPjxoNdFBSHJ32fMxtX57lRJkr/LeA2hW9rKFcsSiljeYlTx+MFjllWXzFviFcb8+F18iGiKyydR16nWS5bWjVEbjx6ucDbyfFt2Jq4UAlqcOHQVhr4RRx7LcNgfb1Txu2FnS8yu/YOIK1nqEyAULP8I2KNp4arthXJlXPHDXXzoyRlt2X+A76uUYNOZ0gntN64NHMWoH38UH3pUSL077qkyZ4fc+MZKkJIFg3Ze9m163Mb581V8cQ7JswxAG48YKp6bS5pVv/jehOLDlLkuR1mSN+9TgX36zmwuitZtYbJLc8KWCcV3Y5PioqRqcT2wnS/3Nm4rZ+Po1w8Dqx3143duv09zYMPcgK8mRYVjVDg2zoOjjXubdwYaOw5xPG7jbf24pyjJhtWevxjfstrXjzi7yCKEUA8ytJDskBx+6qSeUHxQAfQedSbNPdyyGJeGpdE6hlBOp0mUXSpIXsPpCcWLcnIWRTDSHIiS+oBGHiRC+Ng5Ooi6FfzGhB8P9v6HjCIkC9fWfLNh0ESs4mKbwSD1MeDP1xwS2WSz02WTiu9m/upuFFqK1bITd/LZaPfPM6l4dG73gk7SgHPJVhKKm8HG080wPq8C+Irx8wBDl6uIHnXq526LSRvvlkWYQVOEZi/t26LrDdv4lOL5rRrfTPL4dy/z93x69Pu9igd+rLoMG5esSoZFABagr3WMtsa0Hw/qqWHnY/KdYefqVVOP9l8bq8BqUnuwGJ3F5lxJq5b6Jff/2uwi0wzF9fmd8aQW9W/JZK2OS4xW/7Bk+cf0J5iheFC9u9MtEqIqmYkP6tIefopC7MRG52pm+PEgW+UvvEiSfbkv41hhz/2vZY6N+y4ga8BVUofMsKquc/6dus/rXdhpErQCnGf1wXjdkyPnWw1KnjBL8fu05rdAHxVF9hAfmHM0JvlJVPM1ws/x4y8MO+fCtVZxGJbn0pSVSMRO82bj0s+ycdVpEvSfwI/6uAtlaFhpTFkLIbLNrirNUjxIP1UJQR/VsZZSVuxsjPnz59Yms9lwsnue4tnH93IeleOvDzt5XOZ2ONs9y48HR2itSiwFy7cPC9rMs/EgpbzOF/A1ajp92xxze4nHj3ZLEOMc9ziOqfsKz1S8uNU/JObS5h0mg2LL8xTnnWp8xEywbz5kUPmFmURKFwCHkhl3JTFhU7jvUkLWucIj+Cx4DM+LtRt23h52txwxBOkW74TgUeORhKUb97Md8Ha3hyP33b0RvLmAA9zwouDA/XR3mLn/TCghHVjDfyvEIscHePUsk/gXac30kltr3QjPfSWscldCwC9dQPZWAkJpPML0cHxaEikWFO4+/zDP8LXwsMJnwk9u4GGRgKQZvAhnW28Pc/8wvMb/dBxU4X07uLPAN4KfHuER/nR8n7/71+W7cFxyay/M8yru88K/EGIJCgq6ZcOemzMVX3s26zsQ5U6gd+0wM1Zxf/Xn9oBYgNZ3GW2zFdedas3EG8xWPKhmJdkSUzSzFRe4MZR4l/k2HpFbWYV5c4fIf+1WtLU2d/+yKxCSb475Nv7fuJXCWmHSCr72zJNW7oJfm0z2XKD46m5FWVmx3+pUidwZd154/vzCzwQLFA9Oz7eML0cnKTMH+33nhgV+fE23EiWlybZuzY9ZYuNRt9PBW6i9r7HzjSxR/K4czquIQcmRxzwYIW+BRYrn67gVO5y/fASvjWFiexslmiV+PAhWcSsR9PebgsOWObXf4ITlIhtfx63Uc/ZcKPxUstWyev8dlileDGfXX2HOTq6Go9Tr5VH/OyxTPDDvp8MNM2bGOGywv9kyP75GR9pBS9YxjltsQ7TQxt8f6S9Y2VB/NxNM7y7juyKD7IcOCxUPzHvRQ8PN7KkCVf01J15I49sS2KrOcH2zOaRC9JM2lyqev1mhoJztU2pIqvhbm4WU9V3zNJSWxIX8AnI9f2R32nmhHw+CdNknNEDM3htasyy34q+V9wtRcd/8PnXuwLcK6214WGrjC0tRDJgf7UUnmVbp6f3Q6LP41mzec2bGGTsOGfuueKni75w7+ea7TqLirRXnqQu2UCyBA8e6knhZqriLkV9dDNNm8+kAqHjjPbVyNu7Tando43a32wn3b7Hi/OVt+ulW+5QVic+Y7Nu48ypH71X6SzmLFX953Ck2OGT3NDyK/B++P3NKtOnKnfF875N+dLI0VnH+qd/UcC67b+hj62u+K5h+UmcXImLLzWsdVSRabuOBL2m+EPENgifMh95xqhSqxFOphz2UXlDcnpcbuR501N4kuk5q7zkLkbQuNPMp9TdesfEXjJy/OTuwJZb78eVG3pDgN16y8aVGToJ3eUnxHLuAzIUE7/KajQfhgtmVaPtDzUW84sedilC0fx5k4X1etPGgZjNTSbj5v/aI8LyoeDvzOwlZ+JBXbTwoznOyhUjwe17z44663W4+xpEEv+NlGw+C6c6ogpHg97yu+NR8d5N9w1zKYt6wcagfMhKvROE3zBa+wMt+3JEP5iG7ZKYiwR/xjo3DXHv92Jfrmq25aWhTvKV4ULCHHTas+VKPoq57DIpL81Ke9R3Bezbufp68L7ySmXOyub0NM2i4TGK/z1ibQ+zLctowPsjevN87fhz5OZ9sR1+9M+efqbBxm0SVMz5dOkd73Ds7xjS4HJYSRDfh5F0bd0T1uayxWKjKxC9jWJnpG8kwGE4YDwT2SKvTgPuKnr3x+fuKO81zyZgxhu2rsPhWvZ3B4dImKO7T4CBFyLcGrzojwcV5h0/gUGdWfa/aNyBZxQdq6lxwPwj0SVktb/txokcN6d6t4sy2igtQ/GBOp/RUpSvZ+HejkqQtElhjNpBf9VJlFHnFsXeyyqzNbJaR4mvgonD0qIcDpl/5lO/6N2hOqHhPZFJ8PbiAsUkWuRMmDAAh6RB76WJW3BXy46txZKyOQwkd6eqyUL5CZGXUtZ04slasQrggWYgkadPfst1lcL/bid6QkxT/NKT4p1m81414E7LxT0OKfxpS/MMsrCFEvA/Z+KchxT8NKf5pyI9/mi+w8WLYO+N/yxcons8paPk5vsGPh/+Y4pv24w1XKoivimseaAWrA9BIW6soCBTe/CQbt3FVJqL2BSAcmbG70kCFSyVNHVdGiSosP5uvN7c/59+k4VAEWl3S2BueGsWDmPGAJ3Bn9auCQL5S1+EN+L91WlmZGPcU3LxKCqsxR+juivkMBhaAfUmUz9GwMnHU8DXvIro35l3ET+fGrMuPmP8fai/uJZ1bSQ0hIUraUfwEd0ZQSimBjBLc5PHx82pexyFe4vCA1xNfJyaHd019Vay6u2/iSzIzvGvyi5W9m7DMaE7wK940RcW1aVrFT/8LG19M1k3omod6oT7Wxfcu4MEeAQtZDFjapcHmQpD8GuR7d4U5OyeowvtvxY4PwP/qMvLl5YVfKYBzvlc8CNMsS0qj3PnKPSpYFQXcMOuMwH0WUen8i2Uma4vP/KPgKWcZBf5tL+KVEzp7VHBBFU5tCLy1i7v1EXJR1RHu0seAw013n8+J/WcRDyxpAvsZG9/qWO4zNh69YOP7jRYVeUHxfPmZ8yUbX/7X9yd44cxZ/LYH83nFxn3wvT308tPMCy/hdvkE0wtvQxAEQRDEhshE1g3ZuJ1YPOGJyGDmqMWKrJ5eblFCJJ0wRbg3bQ+foYUQvSgl2kpH7INUqlP2SpcTITMPQ6V8PW4gcy8/TPagSEyh4/IqeV0rex4Ps7PS6qRbS56f/D7hP08GvTn5rYhHo+W44jWMNBVru5oqLMyNO79G8HvErg1wMpgpKUY/Jr8N2xe1R9x/64Xx6r+IRFOrO5LdllYe0HBf9fMy9FZo7FPdHzMs+lzAspijwfca77xXYEMpfatLF1/2Cf95vH8QnZJ741P57cyIb0Z0UU/AzrsRfP9P1a1DbOXoh+Tn3vm1fFRWuHeecv1/A99bSHT2gk4pjs6gt2QUlWK80o2f4j52HHEWjre9kjhLds1IyNx3vhE/LvHX6Ck++sfbKt6ruiCnZrDbKhk9I81HvYrfj60vZ/GyznPBDpsoOSLRikSnT0o8mujR1gCAFi0terolnJ8KPt6CFUCOTa/7NdSr6z7m1sbsvpDUXyQ+43Vn1n/cxnkFBs1vgcYRlnW9O3+KxR5R9eVTCtG6veN4gjpDMCTacy0SbcSP4++BTZSK2MtWd3/Ne9TeWWoNRmvBtpNSRC4+nxgDQb8/BZ8Sj907nUHr4haRPgJiKB8ixu3zri7mr2PLUELWWGCxzRhPZDlq5EEhZY2OG0UpTWqMzx8ZQVcyxoaF+AHrJJaHcNxF8KqS3l1Bxhug055T+sNw0Y0BuDP0qfMTFr/o0Y6HRtj1XIKaHOS7U2t/kE8QxHsEwf8DBs9BeKv2+xEAAAAASUVORK5CYII=)
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,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)
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
physics-
A rod PQ of length ‘L’ is hung from two identical wires A and B. A block of mass ‘m’ is hung at point R of the rod as shown in figure. The value of ‘x’ so that the fundamental mode in wire A is in resonance with first overtone of B is
![](data:image/png;base64,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)
A rod PQ of length ‘L’ is hung from two identical wires A and B. A block of mass ‘m’ is hung at point R of the rod as shown in figure. The value of ‘x’ so that the fundamental mode in wire A is in resonance with first overtone of B is
![](data:image/png;base64,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)
physics-General
physics-
The length of the wire shown in figure between the pulley is 1.5m and its mass is 12 gm. Find the frequency of vibration with which the wire vibrates in two loops leaving the middle point of the wire between the pulleys at rest
![](data:image/png;base64,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)
The length of the wire shown in figure between the pulley is 1.5m and its mass is 12 gm. Find the frequency of vibration with which the wire vibrates in two loops leaving the middle point of the wire between the pulleys at rest
![](data:image/png;base64,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)
physics-General
physics-
In a sonometer wire, the tension is maintained by suspending a 20kg mass from the free end of the wire. The fundamental frequency of vibration is 300 Hz
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)
If the tension is provided by two masses of 6kg and 14kg suspended from a pulley as show in the figure the fundamental frequency will
In a sonometer wire, the tension is maintained by suspending a 20kg mass from the free end of the wire. The fundamental frequency of vibration is 300 Hz
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)
If the tension is provided by two masses of 6kg and 14kg suspended from a pulley as show in the figure the fundamental frequency will
physics-General
physics-
A train A crosses a station with a speed of 40 m/ s and whistles a short pulse of natural frequency
. Another train B is approaching towards the same station with the same speed along a parallel track. Two tracks are d = 99m apart. When train A whistles, train B is 152m away from the station as shown in fig. If velocity of sound in air
, calculate frequency of the pulse heard by driver of train B
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAPYAAACoCAYAAADTlhNPAAAgAElEQVR4nO3dd3QU1QLH8e/MbEs2vRJCCKH3Kk0QUCkCiigiCIgN61N59mfHrlQ7KqCgKB0UlCIC0qQTeggQCGkQ0ssmW2feH4FATIAFElO8n3M8h70zc/dO3N/eu3eapGmahiAINYpc2Q0QBKH8iWALQg0kgi0INdC/Nthq8nImvruIeNcFZTkH+eXLSXw6eSorjljK8d2cxHw7hV/OqOVYpyBcXPkG2xnPvv2ZVPmPryuRxeNe5ps/DpF1LtjOGL77z5sc7vgYTz7UlL9eGsuCRNclq3GbM5a1Cb60D/zXfo8K/7By/aTlr/uUp974iRPllIeK4SJx0dccCm6Dj3SuTCXj18l8nXMDd7Y3I/t24/a2h/nsy80UlsM7OmP/IDOyN7WVcqhMENxQfsFWU1m+cA2pu+czf4+93Kotb66EBXwb14NHevhSnGsK+GvlBpz1mxChABho1DiSMxtXs7+MXbGn7Wfz7mRcBSfZsWIp62NzUIH8uI38+vNqYjIvHLM4iV2bQWTvcBTAmrSTlUt+Zt2uXRyKL8/hviCcV27BdsUtZHPoczzSMoFfflpPlfzIuk6ycHo8PR7tjZ90YXky8Set+AYGFv9BDN7eGE4lkOS4sAKV7H3zeG34bYz9ZBbTp8xg+cqveHbwg0yaOZmPpv3G+h9eZNiYrzhaPMQ/zJ8Z9bgxXMEVN4vXP4mlfrf2eGyezKdrsqr+zxahWiqnYNuIXrCfBncPY9jdnclf+RMr0qraR9ZF/LxpJPd+jBsD/rbbmhWbA4xGw/k/iAZoDmwlemwZv9Z3cGfXWuDZnOGvvs2bE97mzuA97JNH8taHH/LhB6OJPLCVPWe/2ZyH15AZ2ZtwGewxW9l0JIFMatPlsdcY085c4Xst/DuVT7Bz1vDz6c7c0dxI+G3D6SmtZ/7ik1Sln9rqmUVMmH2C7I2f8+F77zJp8QEsGdv4adJsdhX44+sjYbPZi3tQ1VqAzcMPP4/SdSk6BZ2nF0YA2Qtvs4LZ2xsZkMxmPLFjdwA4iV2XQWTvOsiAxw33Mkw/h9E9evDAhwcxN/T/9x6WECpUOXyuVFKWzWVXVhzzJnzAxGn7cAY42T1/Dged1157uVHq0PWmlvjoFHQ6BZ0iIyEj6WQkuRatW9QiMyWFopG3i+SkVJQmrWmpv4b3dB5mXUYUN4UX/ZlVpSVj5m1k6fjbYMULjHpuIeIImFARdNdcgzOWJVsa8ua0N+hiKiqy99Nz2x2LmLNxLK1vrBrDTTnwekY9f33xa+uqFBbGhHDP2BG0M4Dz7iFEPrmdvbbbud6Yw4GD2dwwbDDhZcxka5qGxrlT7LWzr4tfni0DZ8wasurdSe2zX5+2Td8yM/gxnhz0MlODLQx4J55MFUJEty2Us2sOtuWvH4ltPprHTOfLDK1GMrT9ND77fin/7XkPoZf44Fqzs9FOxKHYLj5wt0kSnu3bouivpfu8NF2rJ3jr7rF8PWUhOSHbWR36Cq8NqVVqSGM5uoYVu06TbV/F8uhGtExbyvbkQk6tnc/2tt2xLdtEvO0YGxf9Rd3CDOrdFX6+DlcCS159jIz+XQjJczH4hXtpfO1frYJQinQtV3el7ZjJey9+wNHr3uCtZ4dzXVhR95Z7eBmTnx/LzH0+9HjyPV5/ciCNPMuuI+9gNBlTPoM9scVlqsuFrJzvKlUPE16fTyGkTevissyMDGx2Ox4eHvj5+V3tLvyNSk7CIRJd4TSN8i+H4YwgVI5rCnZ50FSVlG3bcM1bhPHgYQBOG3SciaoLQJPTafDkY9Tt1fP8NprGuNdfJyk5mToREbz19tuV0nZBqKoq/dedJMuEd+2KsXVr5NijyLFH8QsMpPdnn9D7s0/wPJmEh69PyW0kia7du5OckoLVaq2klgtC1fWPjjYLCws5ceJEmcsC69Ut/rfLpbJ9wwZ0kkSky4UzKYUzSsmmGrKyiD9+nF6t2+ByuZAkCVkun+8pm82GLMvoK/A3vSBUJLeG4pqm8dUvM9mefqR0BSo80H4Qd97Yh4ENgtGVkS2bC2Zs3s9Pi9ew6a8jWMuYKOvWLpghE8cXnebp70ehZ9EBZI9TqVjatEL115FS4CQ0JR0pKJDTviYi4lLwTEjCEhWJ68F+1LvncRTDRX7MXwGr1crjDz9E127dGT5iJD4+PpffSBCqELd6bEmS0NX3Y2HSzlLLTOi4w3kTsXui4bevUbauKLWOo+ut2PJy8fFvgKZT2R0dX2qdLp0CyAoLJeBUKmRl45GVXbzMJzcPV/RxvPp3wW9rMiQkow7ogWdCEgDmEyfJSM5Ekksfm0pMTGBvdLQ7u1nCsWNHWbd2DZ9MnsjwESO5/6ExRETUvfyGglAFuD0Ud2mXP5NCk65tKJwSUbso2BdzwfndhU4XPoqC4irq/eMcJprqjKU22bZlC88/M/aq22SxWJgx7Ru+nT6NAbfexptvv0tISMhV1ycI/wS3g+3O5LkmXXaVS7IZDG6va+B8qAE8L7LtLQMG0rFT5ytuy/czv2XGtG8AUBSFWwfdzphHHhWhFqoFt4NtUvSEmQM5ZckouUCSOHnoCLW8MqhnL0TTm5AcpWeqE7f9Rc5pL0zGsieksrOzOeRtppVOQed0Il/QPTs1DcKDMOtkVIpO7nKoGoWB/hT4+5EaHEjbW28ts14vLy+8vLzc3c1i8fHxeHt7M2LUaO574EFqh4dfcR2CUFncDvaZwlyGN+xOgiWTFEsmx3NSSC3IwijpcGoaqapKPVshrhYd0Sl6sOQUb6tKMjGFDgolGw5bDv161UKSoNBqJzOr4OwQW+WMzcrzHVtxKjmFNxs3w8fbi+/zcolPTmJ4/1u58/H/oEwycnTEfYRkW1Cj6uHRohnd3nwVSbrG4cIFcnJy6HXjTXzy+ZdX9aUgCJXN7R/FA4I7UbA+hYJZh3i7xWheDRrMoJg6PKW/mYdHPkj/IUOJbdKXl/blsSKoPd7PfMLH9gge3pvPnrqduePuu3nw/v60bJJL/JEFdO8SxOjh7fAx7EO2buaO23vQ/e67WL9hA4pBz9S8LOYp4DLqqVs/igPpmezauxeb08npsFAKGkeRXbcOGR5GFEVBUcrv9iS+vr7ce9/9ItRCteV2sEM8/fhl5gJUhxNjoYQr1cKi6T+x8ZfVmE2eKHo9Jwrt/LRoMbsPxiB7++Ph48vSX38js8CKrCjodQp790QTf+I4OVlJ6PUKyUnx5OVlIUtOGjRqgJeXF5qmERIcgsnsSb7FQm5+Plank507d/LSc8+x0OVgtoeRaaqdz44cLtfeWhBqAmXcuHHj3FlRr9djNBoJCgrirqF3EVW/Pp4enrRo3oLOnTufXUdHaGgtRo0aRUBAAAD16kUxctRIjEYjsiwjSRJGo5ExY8YQHl4LVdUIDgrm9ttvx2QwsXvXblRVY/iIe4ioW5dff/sNWdExbPhwRo4aRf+BA9FUlZH33ounhwfXdexEZGRkxf2FBKEaKvMElffeHsfs77+vjPZA8QWQRb2wqhadVSZd46E0QSgvjz3xH8Y++1xlN+OSypw869PvFozG0seEBUGA7j16Xn6lSlbpV3cJglD+xPhWENw0b86PHIk9XNnNcIvosQXBDRaLhZ7Xd6ZVm7Z89/3sym7OZYkeWxDc8M1XX5Kens66NX/w1+ZNld2cyxI9tiBcxpnUVHp260phYQEALVq2YtmKVeV2/X9FqLotE4QqYsqkCcWhBjh4YD9Lf15SiS26PNFjC8IlHD0SS9+bepW6ujE8vA5rNmzCZDJdZMvKJXpsQbiED99/r8xLlpOTk/j+u28roUXuEXfYFYSLsFqt9LulP/1u6Q/Ai889A8D4SVMA8PH1rbS2XY4YiguCm3p260Knzl2YMPnjym7KZYmhuCDUQCLYglADiWALQg0kgi0INZAItiDUQCLYglADiWALQg0kgi0INZAItiDUQCLYglADiWALQg0kgi0INZAItiDUQCLYglADiWALQg0kgi0INZAItiDUQCLYglADiWALQg0kgi0IbrLb7eTn51V2M9wigi0IbkpPT2f/vn2V3Qy3lHn74ap+41JJkiq7CYJQpYkeWxBqIBFsQaiBrupJINYzZzgycRIFx4+j/e2Jg4qiFP87IzgI7w4dyDsUQ0BCApIsA0XDaEmSQL5gSC1LNBg7loB27a6mSYIgXOCKgu2y24n/7jtOfDEVl8VyyXVzWrZg4AcfEBMTQ5eRI1n61FOYf//jkttkbdlG/Wf+S4NHHj77JSAIwtVwKz2apnF6zRo23dKfo+MnXjbUAOGjR2M2m4mOjkan09FwzBhcl3sfp5O4CRPYft/9FKamutM0QRDKcMlga0DesWPseOBB9j7yGNaTCbg7H52fk13871OnTlGYn+/mthLZf21hy623kbpmjZvvJgjChcp8KJ+madhzcjj22eck/fADmvNyfW1pOfWjuPmnH3G4XCxcsIDQrVvx2br9iusJHz2KZi/9D8VkPN9ocbhLqASNouoSGhrKpq07Krspl1VmsBOXLePYpCk4MjLK3EhTVexWKxJFvXoZawASWR4mdE2bYD9+gsCc3Iu3QpbhbFgNRiPyBRNwAOamTWg9YTzmOnWKGi2CLVSCah9sVVUvuZE9O5utw4eTKMuEyxLY7BwxmsgIDCAoOwedToexoIACby8aZWeDpuEwmUgvKMDXZkOTZY4YjDR2OlBUFQ+TkVhJprGm0fK9dwns2KmMloJ04Yy6IPzDqlOwy5wVv1xw8lwu8kweRDlsyJLEYQ8T/u+8R6c2bUiJP0HtelHsmziRZuvWoBgNHJcUojQXniYTux99jMbXdyUoMRFdRAQHlyyhy/LfaK5qKDodkiSL4ArCNbqqY0peioK3006yTo9TgzqFVmyFhdgKC1EdTlSXC01TiTN54JIkwl0ObCYTp1QVv6AgQupEEBgWRkidCPzNnriQOGY04lRk3J6dEwThoq7qBBWLy0W23UGg3YIqyyTqdKhWK/k52WSlp6EYDOTn5NA0IwOXBEl6A3UyMghQNfanniblxHHOJCWhaRrp2bnUtxYSUVCAJnFVE3WCIJR0VT22hyzjbbeRbtCjyQq1bDZ8/P0JrBVGUFgYYZGRmL29STaZQNUItdlRdQYyNfAPDaV2VH1CIyKoHVWfQB9vUDUSDQaq+LUnglBtXN0ppapKnk6Hv90BQLpOR/zUqcQFBeLKyUFv9sJ45AjNrFY0JNJ0CmEOO75oHN+4EenMGc5kZZEREEBaTAxRQC27AxXQLjLPLgiC+y56HLussvTNm0lasBBXbi4F27dToCh4qhqcnUXP9/DAy1p47mgXeYqC99mhtapTsLlceACaBvkGA14uJ5KraNtcRcbHpWJs0Rydvz+SJFHvkYfx79C+eDa8uNFick2oBNVpVvyywXZYLCQvWULCD7MpPBb3jzYOSaL23UNp/MLzGP39LygWwRb+edUp2BcdiuefPEnCD7NJWbgIV14l3Q5G00iZN5+01atp+NJLRNx5h7g4RBDcUGawVacTp8VC2ODbCRt8OwBrJ06iQcyhEusdMplobrWWKNtlNHCdzV7il3KM0UQzW8n1Ykwmmlttxb+pJWCHwUBHu4MLz2fzGzoU3wH9AXAUFmIwm69mPwXhX6XMYMs6HX7Nm5co8wgOIisjhGyXilkCnaoiaRo7kAjo0KF4vUJZ4ph6Yaw1chSFOJeL8wepi8qOnf19nZ2dTWB8PAadQqbZC4dOR3ZhAcE6PX516+LXvEV57rMg1Hhuz4rXstvJK7CQa/LAQ5KRHTZqabBJU7n9fy+xYMECIiMj6RwaSmxsLL6+vvj6+hIREcGqVavIM5lo27Ytx44dw+Fw4K2qmAMDkSQJS2oqeV/FEuFhRHKpqAYD6XYHIZIE2qVPbxUEoTS3gx0nyTRXIaigoLhsl9GIt91GSEgIbdq0ASAhIYGCggK8vLyQZRl/f3+8vLzw8fEhLi4OVVXx9PQkMzMTm81GYGAguTm5RKlODsue9HA4IS+XCIMeCfAUR7+E6iQ/huU/ruRYvhNT89sZ1b8xnu4sK2duBzvAaOC0rw9pioIfoHe58HK6cEoSM558Ej3gUVgIgD+QbTSRbrdxWtMwAnbAZvLAWmhBkmS8zpadMBopzM/H4e9PkKLjtF6P3aDnTH4+4XoDHopMcPnvtyCUP+cRZj39PtlPf8XYluksePw+Hk2eyowxzTBcalkFNMXtYBtdKlZVw4ELl8OBzuVC73QiuVxs2bgRPWC+oDc3hobS1N8fP1nG6nRi0umweHqyafduvC64eqzQZCJfgiahtTDa7agGPS7JiF2nB72u6JJOQagGrBu+Ylr6dcxqZQbFzKAHuvH5fz7lj6FTuWnXxZcN8C3/trgd7FMOO6Gpp9HZ7Zy7svqw0UhuWjozThwvtX7//Hza1AojA40Yo5FmNhu+Oh1zExLIsdlKrd9HZyDGoKdjlhMNjWAJgk3GohNeBKHKc3H68BEyiCqeIjY2a0ZU7qdsO1hA84suszHgemPJquxpHNiWQMD1TXHtWs++gvp079EU34I4/lq7D2vDnvRqHnDJ88HdnzzTJA40aULnmTM5dSKesKh6NAVeatykzPWTPM0UfPYpLbt0wXx2/U3ffkfhU0+WuX5Mx+voP2EipxNOUqtuJPm5uewYehc3yjoxFBeqAQVvfz+k4/s5kAf1/QBVxaUVYMmXL7Gs5CSSmrWXxe+O5dU/Injo0SbYTqey++dVzB7xMl1zY0izHmX1/2bx4C+LeKSRUmZL4AqCXag6QVWRJOnsfzJFZ3aXPbul01QkWUFSiv6TFQVZ05AvctaYrCh4eHthMnvi4e2FqrrQVFXMigvVhn/fexn0xZNMeXU6XqOiyPpzGYfVENrW1uHf4eLLLiT7t2HQXd347I90mo14jdv87OzSRzN6r8wnP44nRIslJGYA23ZbeKSRz0Xb4nawM2UFk83GqfiTpCYloVEUUqNadrCDC61knTrNqeMnSEtOQgJ0p5IxSBLWsjYoKOB0/EnSEpNA0yjMtxCkqpjFJV9CNSEH9uO9JXNZtngTsXFOGuss5NXtQa/GOmTDxZeVoigoejNmE4CMt5cZxeyNtwyoZjw9wWG3X7Itbge7gctJtMFIWL16AIRF1UPSwHGRHjjFywv/sFrUrl8fSZIIi4riaEQkBa6yr7eWPcxn69YIqxdFfk4OcZKEVdx5QahGlOAODH60A1g28Wb/BK5/9CvaGi6/rLy5HewUWUHLyODAZ5+Sl5VNhr8/ubKMx0V6VA+7jfRffuHg7t0k5+SQ6euDc98+9LKMs4z1HckJbP52BlJ6BhkB/titNgyKjEvkWqhu1DTWvvcW2zt+yIx76qK4u+wcTStxbwKtxGutuOxS3A52BlC/IB8WLKAWgATpeiORRkOJx/qc4+1SabllM2yBNL2eEIeDUMCk02Mvo9dunJZG4uzZdHY5Kd4LnR5ZDMWF6sKWycmDW/l9yQqO13mDWY/eQIjsxrILWY6w7rddpGbZWP3rbhq0SuPX7ckUpqxh4bZ2XG9byl/xNuLWL2JH34fpWKvsCbQyL9sUBKG0y122qWYeZf8pA5ENI/Ezur+sIlykx7YQv3klG2Nz8QhvTZf2nuQXNKZp5MWn1y/Pxrbx9/Cx/BKznu9cIWfbCEJlkgMa0SbgypdVSFtKlahprHltJK+tgSYd2xKUtoRn+9zB5/vOn1RiPZVMujtHoaynSCleUU/9G0cwrEf9q7sfkyAIbiuVMTXlZ6YvDWHk1iF08gRataNtgIvPzw3YXSeYP3EODd9/haBLDilcxM+ZwILGH/BCkBGQCe54F4MrYCcEQSipdI+tN6Iv/JPpk/4g5ez0tV+vodxSVweWw/z8vzFM+H036+fNYVO8C3CSEbOWpQsWsHzzUXJUAAtHFr/IEx+tInrdXOZviMcF2E7vZvOeMxR39vYzHFizhCW/rCMm/YK5clsqezdGc8aZzdE/f+a3LScpQBAEd5UKthw6hP8+1ZKEaffRf+ATTF17kkLP9lzXygByIC06NsZsCqFRhw7UD1BJmv84I8cfo267CI5/MoQRk6NxIuHfqhONvIwEN76Odg38yNj9PS8OHcxLC47gANS01bz76PvsMDWhoX4zbw4ewuStOagZ0cx7YQhD/zuZLz94m2nLFvPxg3cybvUlnv0lCEIJZUy4m2n/9FyWfv8i3e1/MGH0jfR/6At2ZKrgEUzdMB90Oh9qN2xMbR+J7AyVFr370qphO3pdF8yJg0ex4Ulw3dp463T41G5Io3A/QtoP4/ZOgWffsIAtU95gS7OHuLdbc1oN+B9vDMrjmze/Jsa3HYPv6EygaqLtYxMZP2kqY3sVsnvbES59ro0gCOeUEWwnTpeBOr3G8sWqDfz0Rl90G97jideWkVFqwkxHy8c/5fGgVXw68QtWHi1EU10XfcC9QX/2J73zCH9tPY1P4LkrVHQ06tAWn2PR7MsFdDoUUyAhPjKgw9vbE4fVJu44LghuKhVsNe0X5izLLHphqEWXR77g6/+2Izd6G0ccf1/bwo7xd/PSttY8+PxYhrYLdO/RIpIJo1HldGLS+bPQPEyYzP74ma5+ZwRBKFJGDvPYOPNrduace62hOjX8Wl9HIz2g6JBtBVicaSSe2M/63w9jqB2Ol/MMsXHpuOw20pJPAzKKbKPA4iQtIQELF5wGpzTklttak/77AjZnA6ikHT6O523DucGToiu6tJLP3han0QiC+8o4pGwi1OcE0597gvnBPugKUznlvIWP3xtMkAxqkxvo4fs879wfwMtTXqD3nR1Y9PEQhu68kxHtWuO3diFzDvbhtd5N6NbTj1feGk3Aa5N53LKClXvSOSP9yuqYVgx45HPGp73Ip489xebW/ljVQUx+pQdeuTH8unw3aWkKK1fsJaTeMf7Yl0GavJy1sa3o3+Til6oJglBEnFIqCG6qTk8CETcUE4QaSARbEGogEWxBqIFEsAXBTSajCU/PirrFf/kSF1oJgpsi6kZQL6p+ZTfDLaLHFoQaSARbEGogEWxBqIFEsKs6NZmV49/h5xMXXFqj5nDo5y/4ZMokvvkttlyvVXcems5nP58pxxqFyiCCXaW5SFr4Bm9MXU1M1rlgO4md8TjvHOrEmLFjaPLXizw3L+GiV9RdGSdH1iTg2z6wXGoTKo+YFa/CXIkLmXEwmFY+x4rL1IxlfDI1m27z2mOWFboObsvbY79gy6CP6O5xjW/ojGVdRj0GhV/LTSuvQEE8W1f9yf7TFlQNJElGNnoRVK8d13drScg/cDfPmkr02FWV6ySLp8XR/bGe+F7w0ISCTSvY5GhA44ii8BkaNaZu6gbW7it9Gwp72n42707GVXCSHSuWsj42BxXIj9vIrz+vJiaz5AX2zsN/kBnZm9oKYE1k14rFLFu7i+iD8RVzayrPenTpF8WJmR8yN6kpd9w3miE3N8K24hkG9h3LLwnlMw75NxLBrpJcJMyfxslej3Gjv1Si/NSJk9j8Agk893/O6IO34TSJiRdeLK+SvW8erw2/jbGfzGL6lBksX/kVzw5+kEkzJ/PRtN9Y/8OLDBvzFUeLs+Mkdl0Gkb3roLjimP3Kxxyr3522Hpv49OPVZFXUsxGNtQgLUNB7B+DvacY/sgvD3nufwdpiJn6zldIPXBbcIYbiVZDrxFy+S+7Df+8JQC7xBEMNq80ORiMG+XyZhorDZgfMZ8tk/FrfwZ1dp7A2oznDXx2Mr30nuuhh7JO/ZNaHoWhHQjl861b2WJ6gkQ/gPMyfGfUYFC6D7RA7Nh4hYiiEdX2cl3T7i2v+R8gGjHqNwoJ8cdecqySCXdWoZ/j5ox+ID+zO1Pc2gnqSQ5YMPGdPZI76JN39fMFmw36uB1WtFNo98PUv/QNb0SnoPL0wAsheeJsVzN7eFD200YwnduxnO3rn4TVk1ruDcBnw6ME9w7/jqRHd+K37SJ5++VmaVujYTsORn01mdjaKJYmdc95hXmp77ht1A+KGOldHDMWrHJnw62+ihY+CTqegUxRkCWRJQZZkQtu0pFZmCqfOBtKVlESq3JSWLfXX8J5OYtcWDcNlAFWh+aML+GP5RAZKy3l5+DMsSa3I55Rr5Mb8xuwZ3zDjyy/4bslhvK7rTmN/8fG8WqLHrmrkILqMfpEu515bV5IyP4bgkc8wrL0BnMMYHPkEO/bYuLWbkdz9B8jpMZxBdUrPZGuahlY8mNXOvi5+ebYMcMawLjOKwbXPBsm2kVnfhvDw07fz/DfB5Pd9m5OZKoRWVNBkAjuO5Onn2hV9IC07GX/nnTz5oJ25q16jg3ge1BUTwa5udK145N27eX7qJJZkh7Dz91q8OO6uUpmzHF3Dil2nybavYnl0I1qmLWV7ciGn1s5ne9vu2JZtIt52jI2LtnFjl61kRd1J7eI6XCQufJmn0wfQMTQX1x0vMqLJP/hRMbemzw2RfD09mv0ZKh3CRM99pcStkaopNeckMQkq4c2i8KvOX8/OGD4eeAvLe/3M8pfP9ti2GL64eyCf2Z5g4a/P07KK7N+AvjdTL6o+X349rbKbcllV5E8mXCnZN5IWrSq7FecV/rkBKTfvoss1sxFdl67ozRfMrxfEsXnJLNaecHDaMZmX86Lw01tIOrCXpICH+PjNp6tMqKsb8WcT3GaxWDgeF0dgYCC1w8OLy61Z2SS88wEBR49fdFv5ujbYVCe1+9xyvtCzAd1GfsjSkR9WZLP/lUSwBbd9Mnky8fHxeHh48NHEiZhMRQejTP5+RM2cRswzL6Dc3BNJb8Cwew/+x0/i9PQgx88X35F3U6tnz0reg38PMSshuO1kUhJbd+ygUdOmxaE+R6kVSu0z6TQbPozmDz2AZDajHTqMsjOaY40bUOvmm5F1oh/5p4i/dA3lcDhYv24tnbtej7e39zXXp2kafV8HpToAAApESURBVBo3YcmsWXjn5RO/+o9Sy71STpXeDrDVrXPN7y9cGRHsGiYnO5uffvyBmd/O4LqOnejdt9811xn7y8d4frWOngcPsyWqGTmxsej2H4D9h0lrEElYA2+caw6D3UHWwCGoIcF424rO8s4MDyM1x8XDT84oVa+iSHS+rh4P3HsTo1o2xFDGxacuSWZbag5z/1zLlCVlz0bXDQjjncdfueb9rElEsGuIk/HxfDt9GvPnzqGwsOharAP79/HdjCs/NNOt+w00btK0+HVuQgEBBw8D4GMpwOVpwPjnVlBVfMK8MexJRMkuetiblpSMlJTMuUtXnDoddpc3m3ecKPU+UZEBdHAVPbJp8rCbMMZsLt2Y1t3I6nw3tjA/FvseLrO9E7t0u+J9dIfD4eCh++4lIyMDgEMHD3Lo4EEG9usDQIuWLRk/aUqFvPe1EsGuAdLT0/jw/Xf5feUKXK7zvd7J+HjeeuP1K67vo4mTSwS7USZceO1YgUvFXy06xTTIW8WpVuDllW78Lq+oEzH0ej039+nDm6+9WqL84IH9APzv1dcq6J2vnQh2DRAUFMzUb6aTlpbG4gXzmTvnR04cP05AQCDPvvDiFdfXoWPHkgU+JX+jZ+cVcO5gl8WhUJH3Q9AMl67dQ2dEpeLOYx8xajTfzZhO/ImSI44ePXtxQ4+qO8svgl2DBAcH8+gT/+GRx59gx/ZtbN60kRGj7kWWr+3gh3XQQDL+3ID3yUQAHHY7hbXDwGolM08lJDIMZ54DjzPpJbZz6PXk+fvidJa+CQSAv68ndoeVU6dOIZWxXFN0uGyFpGWkYTle9ke1Q0hjbK6KGzHo9XpeevlVHn9kTInyl197o8LeszyIU0oFt+QmJpI47j0CTpxE0uvJCwslZNxr6L3MbPthJj/t3IPqctLPw4tgJGakp9KxcyfSTiaihTZlyepzNWkE+nvSuFEonh5GzIYzqLZDPOWVhU/sX2hmH6Tw+mh+wbgcNlxpSXwrNyfDLDPDPxqH5sTf5EOLwHpkWvPoFNoYvaxn8o3/rbB91zSNIbffyu5duwC46+5hTJzySYW9X3kQPbbgFp+ICKhTm6MZGaDIWCWoHRxETm4uqcG1wGSisMBCQsMotiUmYzMa+HzmTCZMmkj9qCbEHXuHqKgG9OjZj1OnUlgwbxpD7xlB1849aNb0fnb8vJjPT8u0ad6Cbm1asfdwLJt27aZFox48OWoUmo83jg/fIjMtg669uhMUFMyWNZtQD6XS59ZbLr8D10CSJF59fRxDBt+G0WTiuRdeqtD3Kw/iBBXBbd/m5TCvViBrmjdirubknXHj+OP334k7cQK73Y7D4aDA6STf5cSg12M2m8nLy6dZs4bY7Vaid2+n/y3d8fPVkZKSxOL5czAZiwbhG4/Hs+zPDRzPziGyx43M+3MjX8+Zi9XXF69aYXh7emE7k8e8GbMpSMyiT+sbOLn/GHO++R57qqXC971Dx47c0n8AYx5+hLDatSv8/a6V6LEFt3Xp0gWDXkfDRo3YsHEjQ++6i6DgYJb/tpw5c+fRoGEDWrdrS7PmzZn9w2xatmxFvchI9Ho9Y8aMQZKKQtyuXTt69OiJX4A/wcHBAAy5cwjHjh4j6Ozrvv364uHpSa8LTkPt06cvmZlZ3DPiHjw8PGjdujWRkZF06dKldGMrwCuvv4l/QMA/8l7XSvzGFspFdHQ0iqLQunXrym6KwEV67PfffZsfv5/1T7dFEKqFRx//D08/82xlN+OSygz2zb37oFPEKF0QytKt+w2V3YTLEkNxQaiBxKy4INRAVT7YdrsdVa3IW98Kl+J0OnE6nZXdDOEKVflgD7n9Nr747NPKbsa/1jvj3uThB++v7GYIV6jKB/v06VOkp6VVdjP+tVLF379aqvLBFgThytWIYLsq8OoeQaiOqm2wLRYL8+b8yOgRw8nOzqrs5lRbW7f8xYrlv4kvxxqmWp2Fomkae6J3M/enH1n2y88UFBTQu29fAgODKrtp1Va79h1oUj+SiLp1eejhRxg67B7M5n/0oblCBag2wbZYLDzz1H/4fdXKEuV//P47N3TtVKLMWlhIZpboxcsSHBSM3nD+yZznTk9KTEhg3OuvMXnCeEaMGs19DzxYLa5iEspWbYJtNpuZOm0Gv69ayfSvv2LXzh3Fy67v1r3EulmZmRw7evSfbmK10LxlC8xmrxJl8+b8VPzv3Nxcvp/5LZqm8dyLVf+6Y6Fs1SbYAIqi0H/AQPoPGEj07l1M/+Zrtm/dwkcTJ1d206otp9PJhvV/ciolhbDatXngoYcZPmIkPj4+ld004RpUq2BfqF37Dnzx1TckJyeRlpZWfF1vxVDJObSUH7YFMvqBGyj5kbdw4JfZ/JXsREPGp/Ug7ukeDthIWPMtM387QJ53C265/0FujjKVXX0l2rtnD0FBwbz86uv0H3grer3+8hsJVV61DfY54eEV/ZQJJ8nb5/HNu28z1/Nlht13Q4ljCa64n/jss4Uk6ySQ/Lip7WhAJXv1O7zyk0anduFk/PYJj/66l4m/TmVwFXvWc7PmzVi6fGXxTRCEmqHKB7tJk6Y0aNiwElugI7zTPYwZOJ8F6/6+zMLWRSfp/cMqhpYIbA7bU1rx3vRhRCqgjmyOevMzLF6TweBRFTmyuHKenpeeAW/QsCFe5fCIIOGfVeWDPXvu/MpuAgB6va7ULXJdifOZ+t0PHPg1hu3Dn2TsmBupYwDwpe99w4rXk/3a0CLSxB7Psu+RbU/bz47EALo0dbJ7/V4K6vfkhia+FMRt5M/9Vhr0uJlmAZXT07/wP/HonOqoyge7KpM8uvLExxM4sOkX5nw8mqHR45n71T1EKn9b0XqE4wU9GdDT628LVLL3LeD9Z15ibZ1HeLixldNndrL091kMf6kbuYfPYD26ile+f5hFC56g0d/rFYSLEMG+BnJQU67v15Tr+93N8NsncP+9H/H5mkFM6Hvh8NZFwqIlWEY+z8DAv/e6Mn6t7+DOrlNYm9Gc4a8Oxte+E130MPbJXzLrw1C0I6EcvnUreyxP0EhMVAtuqlozOdWYz3VP8dwdHhw9lFSi3Bk3nxnxA3hldEMu1uEqOgWdp1fRo3JkL7zNCmZvb2RAMpvxxI7dcZGNBaEMoscuN3oiIupRKyCwuETN3Mi0uU6GvTCIcPEVKvyDxMfNTaoKaGqJJzvaM5I4nX/27i72ONYdb87wfmfPW8/ZyXcf76DJ6NsIt+eQkxrDqjkryqxb0zS04pq1s6+LX54tK+89Emoy0WNflkr6/pUs2hSH7fh6Fqzuyn/6NQNsbJ84mIdX16Zv39b4SGbaPfgsvfwA216+emg047dkos4Yf7YehYaPL+Xvj6G3HF3Dil2nybavYnl0I1qmLWV7ciGn1s5ne9vu2JZtIt52jI2LttFnTGdCxQSa4AZxl9Jr4cwi/kAcOV6RNG0YXKGPkxWEKyGCLQg1kPiNLQg1kAi2INRAItiCUAOJYAtCDSSCLQg10P8BMzwQzzoH8QoAAAAASUVORK5CYII=)
A train A crosses a station with a speed of 40 m/ s and whistles a short pulse of natural frequency
. Another train B is approaching towards the same station with the same speed along a parallel track. Two tracks are d = 99m apart. When train A whistles, train B is 152m away from the station as shown in fig. If velocity of sound in air
, calculate frequency of the pulse heard by driver of train B
![](data:image/png;base64,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)
physics-General