Physics
General
Easy
Question
Here is a cube made from twelve wire each of length L, An ant goes from A to G through path A-B-C-G. Calculate the displacement.
![](data:image/png;base64,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)
- 3l
- 2l
![3 l](data:image/png;base64,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)
![fraction numerator l over denominator square root of 3 end fraction](data:image/png;base64,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)
The correct answer is: ![3 l](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAANCAYAAACgu+4kAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAALpJREFUeNpjYIAARyDeBsTfgPgHEN8C4glALMyAG4DUMsE4+4E4CIjZkBQYAPEOHJpVgPgSAxHgEw7xACBeTkizEhDfwCFXD8TluDSKA3EiNBy8cKhZBXUFCviPhgvwuA5kuDQuSUGo6SeB2B6LPBM0BggCHqgh6MAcGmtEgR9YxCKBeD4xmvWgfkUHk4A4DV3wIBCHAjEL1I+glHkfiOOxGLAOW+zYAvEWqJN/QP3og8Nl74CYg4FaAACysSSx8Esj9wAAAFN0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW4+MzwvbW4+PG1pPmw8L21pPjwvbWF0aD5JIro5AAAAAElFTkSuQmCC)
Related Questions to study
physics
As shown in the figure a particle starts its motion from 0 to A. And then it moves from. A to B.
Is an are find the Path length
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAUMAAAC8CAYAAADigMx/AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAFxEAABcRAcom8z8AADexSURBVHhe7Z33UxZ4tub3P9it2tqt2t3aX/beO3fm3jszPT09M90TOmdzRFQURAGRpAKSVMCAAcEAioBkwYgZiQqIgDlnBRUMgKCgBAV99vscYW53T6uI6X3hfKoouyXjy/Oe+Jz/AkVRFAUqhoqiKAYVQ0VRFIOKoaIoikHFUFEUxaBiqCiKYlAxVBRFMagYKoqiGFQMFUVRDCqGiqIoBhVDRVFemiePH+OxeelNqBgqivJSNDc3o+r6ddTV1XX+Te9AxVBRlG5DITx08BASExJQsq+k8297ByqGiqJ0m8rKSixfugyjR9li9aoYPHz4sPM11o+KoaIo3eZAeTm83D3w6d8+RlBAICoqKtDR0dH5WutGxVBRlBfS3t6OhoYG7C0oQFBgIEYOHw73KVOwc/t2NDY2dr6VdaNiqCjKC2mor5eocO+ePdhhBDByyRJMdnbGvNA5uHzpUudbWTcqhoqivJCL588jYc0aFJjIkF3kgwcOwNPdHXZjxqKwsLDzrawbFUNFUZ4LU+TioiIEz56NbVu3yv/fqK6G/4wZ+PbrbxAXFycptLWjYqgoyjPhYHVVVRU2b9yEhWELsDVzC2pqanD92jUsX7oUI4cNxwwfH5SWllr9ELaKoaIoz4SjM3l5eYiNicWunTtx+tQp3Lx5Ezdv3EDJvn2YN2euSZXHIHb1arS1tXW+l3WiYqgoyjO5d+8e1qalSb2QESLF8f79+/LCLnJBfgHs7cYjwM8P169f73wv60TFUFGUn6WlpQXnz51DakoKtm7ZgsampyM0TIe7UuJLly7Be9p0OE2cKJFjfX29/L01omKoKMo/wLW7w4ePIGblSswNCcWmjRtRV1fb+dr/5MqVKyYq9MfXX3wBdzc37M7Kwp26Ojx58qTzLawHFUNFUf4Bdod3Z+3G3NBQhM4Oli5ydXX1j0SO/33+/HmsWLZM6obOkyYhKSEBFVcqrLKZomKoKMqPoJA1NTZKilxSXGxe9sl/NzTU/2j1jvVDjtgcPXIE+bm5yDMvRw4dQs3t2yqGiqJYP4z4Hhmha2trxcO2NrS1tqLVvFD8fihyjx49QotJp9lFpkhy/rC1pcW8fZumyYqiKNaKiqGiKIpBxVBRFMWgYqgoimJQMVQURTGoGCqK8g+wG8x1O47OcJawvKwcOdnZ2JKZidL9+3H37t3Ot+w9qBgqiiJQADkiQxG8cOEC8vPykJSYiLlz5oiR69DBQ/DFp59iymRXMXnlul5vQsVQUfowXLurqKhEWWmZ2HOtXrUKc0JCMM1rKtxcXcXanyauPtO94enhgW++/BJ//tOHmOrhif29wLbrh6gYKkofgFEfhY8u1fQiZOpbZsRsixHAmFUxmBs6R0RvrO1oEwEOxmibUeb/PRC+aBHWZWTgwIEDOH36NDLS0zF29Gg5CMVVPX6sx096hyCqGCpKL6e1rRVXK6+K/2DG2nQsWrgQHm5ucu5z1IiRcHRwgK+3N8Lmz0dszGpkbt4sN5EpfjwNWltbKxsoTKF5CyV97VoMGzLEvP8oMX3tDS7XRMVQUXoRFD4aKhw7dgy5ObkiXEuXLkXI7GD4z/Az6e50SXGZAk/z8pLoLnZ1jBx5OnTwoHgWtj18/i3kWzdvIi42FqNtbSWdPm4+V29AxVBRrBDuBTc/eCB2Wbdu3RIRO33qtLhSp6akYvHCRSJUTHsHDxwEW5P2enl4YEl4ONZnrMP+khKJ+u43NcnOMfeKX6b+RyPXeXPnYpSNDRLXJMgpAGtHxVBRrAiaIty+fRsnjh/H7qxdRojWYNGCBfD18ZF0d9yYsXCZ5ATf6d6YExKKZUuXYW3aWuTm5spFuwvnz4t4vmonmDYMHLVxmzIFk52csXXLVhFVa0bFUFEsFDncXl+PK5cv4/Chw5L20oKf0R1TXg93N7i6uIjLtOOECebPSZjh44ulEZHYtGGjHGm6du2aRJFvgps3b8g5gCEm8qTb9cULF+RrtlZUDBXFQqCQPDCpLzu+dJDm0fYtmzMRHRWF4Fmz4eY6RdLd/v36Y9jgITL7xxnAxIQE5OTk4Mzp0xI1Nt67J51j2nC9SSstfmxGqF7uHhgzyhapySkSdVorKoaKYgHwdghNUtnJXbZ0qUl7feEwfjxsR47C+HHjZNDZz0SDYfPmyygMu7gcfD5uxIjjLU3373d+pLcLa450wXae6GS+xskyr2itqBgqyluk3aSs9XfqUVlRiRMnTqC4qFiOLcXHxRmhm4fpU6dhkqMj7MaMxfixdvBwc8fCsDCsTU1FYWGhSZmvoKW1tfOjWQZ1tbVYvnSZjNokJybJRT1rRMVQUd4gTx4/lvk8Nhc4r3fi2DHs3L4DMStXISggEPYm+mPKazNiJFydXRA8cxZWrVyJbVu2SsOD9cLbJvW829BgUt8W87Esb8CZ6TKF2t/PT9L5wr2FVtlMUTFUlDdAff0dnDt7FnsL9sigc+SSJQj094eXh6dsdnibCHCGjw8CAwIk9eXcHtPN0tL9uHzpktT9rIk7d+5I08Zp0iQsXLDQKk+GqhgqSg9hxMdj6rU1Nbh29aocTTp86BBys3NMWpsmtb9ZQTPhNtlV1ttsho8wKfBEzDLR35q4eBlNOWfe595d60wrf8r5s+fg5ekJDyP2bKy8qS72m0LFUFF6AC2sOLNXuHev7OtGmMiPs332duMwYugwWXWbbNLemYFBWBYZKZsgdIE5dvSYHF6/efOm1NaseRTlpzCVp8iz0cNomIPZ1oSKoaI8g4dtD2Wz4vLly0bEjmJPQQE2btgg9T5uXwT5B5hf/Bmy1zt96lRMNVERV9xYC4yMiESaiQ4L8gtw5syZXrO/+zwo7GfPnpU5R19vHxQXFne+xjpQMVQUA1M6SXlra1FRUSFpXm5ODpKTk2XOj+YGbBBMnDABw4cMlUFjdntZ94uMiBBnF0aJdINhvYwNBKbRvcniqjtQEBkV8qh8SlKyVaXKKoZKn0bW22qerrdlZWXJRgVHXOjqMmqkjRiacs5v+rRpCA0JkUYIU0GOwxQVFknEePHiRUl7OXP3JoecrQWWAzgeNN/8HFlHtRZBVDFU+hT37zfJdgfHVnZn7UZqSoqYGnCNTfZsXVzg4uQEJ8eJMugcaFJeNkI2mPS4uLhYHKDv9ULL+9fJqVOnxCCWQ9hpKaninG0NqBgqvRambPThazIRG0c/mMJmm+iPae8Pu7wDud42ZAhcOtfbkpOSTHSTb6Ka8/J+TJ9pbMAIp6+lvT2BddYN69ZLGYE7y3wCsYaIWcVQ6ZWwbscNj6xdWYhdvRrBs4NNxOcsllbjzC+pq8tkBPj5yXZH3OrYv6e9J0+eRNX16yKASs/gk8a5M2dle2bksOHI3JyJevOkYumoGCpWDaM//qKx6UGT0aLCQmRu2iQCuDBsAQL9A8TggJsejFTcp7hhwfwwpKamydYEB5xbmps7P5ryumgyqfGSxeEYbiLueSbaPm1SZ0tHxVCxGphqsUPLyKPVpK10aKFRAV2aV0WvFOGbMN4eQwcNxohhw2S9jQ7Pq1fFYPu2bTIQLTb2NbUy48fUlx9Pef2wMcWNFHos0l0nLze38zWWi4qhYhVwS+Pc2XPYs6cA6WlrTdSxGH6+MyTSYzpGV2eOubAWyDGYNfHxIpI8esToT5sebxdG7KX7S2XukmNIaampna+xXFQMFYuCkRq7jxxV4aYGR1fYzEhfmy6uzbNnzoK7SXvH2I6GzfCRmDTBUdbbWPfL3r0bZ8+cwV0rdU3pTTCKv3r1KsLNk9Z3X38jT170arRkVAwVi4EiyF1dplSc95sTHCIjLiOGDRdXF+dJTrLd8XS9LV22O9gkqbhSIaaifH9GJIplwMHz7du2y7+fn6+v/Nta8r+PiqHyTmjqnPdjGku3FjY85s+dJ6kvB5y9p06X1HeapxcC/P0RsSRCbnnIetvp07hzx/pcUfoibGpNNf+GnOHcuXOnRc8cqhgqbxTO5bU0t8hu7s0bN00UdwUHDx6UhkZsbKwcL2fNz3akDYYMGiwHjTgAzVlAiiTdn5kysyDPj6UbHtZFZUWFGL9OcXUVn0b+W1oqKobKG4MDz+ze7isuln1VjrrQy89u9BiMMS8ccg7w88eiBQsRZyLDLZmZ5m334aRJffl+HHi29otrfR3uem/csFHEMCQ4WEagLBUVQ+W1wPSHnn60qOJu6vp16xC1YgXmzZmLmQGBYm/Fzi8HnxkJhgSHmNQ4Flk7d8n71NTc7vxISm+Cw+ssbdDOzMPdXWzPLBUVQ6XbMEXljB+HlCl+jNzoWXfk8GHs2rULSQmJWDjfRH+daS+Pl3PjgytZdHZZv3499u/fL1Ff15xfl7uL0jvhhT4+2XFPmZs/LHtYKiqGSrdgzY5rahxc3rljhzi3sN7HtNd+3HjzMg5TXCZjhrcPQmcHIyJ8iRwHyjIiyXkzWuCz48vUWek78An05o0b8rigAxDNMSy19KFiqPwIHjCiizOPj586edII2X7s2rkTiYz6wsLg7+snaS7t6znrZ2tjA0d7B2l6sFDOE5YHyspRVVWlEZ8icFso0jw52owYgbjYOIttoqgY9mFkva396eU2pqw1t5/6+rGLy25uoJ+/DDXzehsHZ/kycvgIqf1xDIZpMQ1QOerCTjHNEVgj4sfTrq/SBacA1q9bL3VD1pBZVrFEVAz7KDQipbVS0d5CrEtPx7LIpWJjzyFnOo1wzIW3PNj5nezkjKCAAKxYvlzqfiyIc36s2kR/LS1qcqA8Hz4t0gWc92CYQeRk51jkk6WKYS+Hz8psdty4cQMXjfgdOXwEebl5SElOlh1ePjgZ/dHYYFD/AWJyQHeX6V5TEb5okRHKDBmNqa6u6vyIivJyUPiOHzsuJrrMKjhqY4m+kCqGvRQ+ACmCNCil+CWuSRD3YY62UPgG9OuP4eZPp4mT4O87Qx6oSYlJyDFpL6O+yitXpLbDi2dsnijKq8Bto5VR0eJik2Aei5ZYT1Yx7CWwVvf39bYtWxEbEyP1GUZ+06ZOk9U23rT1cveAj7c35prXxcasRubmzTLozG4vHYqf9SDl8GxBQQFOnz7d+TeK0n34+GGNmTvmPKOgYqi8MkwvmpubZcaPNTseIyovLxenZgogx10oeKNHjRIr+3Fjx8LXxwfLly3D5k2bpDtM0aR4drduQ5FMSUmBl5cXtpjPoygvC2dT6W/IWjQfo3wMWxoqhlYEZ/S4zsTDRPT0W7hggdRgONg8ZpStuLpwvW3xokVIiI+X/V+KH6O5q1crUVdX99IND6bIiYmJGDFiBJydnSU6VJSXhSNbnDwYNniomHHQmNfSUDG0UPhMyu2Oo0ePyoMoIz1d5vhCg0PgbwTPZ7o3PD08ZLKfriDzQuciPjYOu7OycOwY19tqXrljx3EbbozY2Njgs88+E1Hk/KCi9ISysjLY2oySQX0e57K0JoqKoQXwdMWtRVbUKGI0KC3Iy0MqO74LFhrR85QH0aABAyUCnGrS1YglS7Bh/XqJ/CorKuUCHCPHR4/a8fg1TS1QiH1Miv31119j5syZMohtiSMRinVAA46JnSdYD5QfQJuFbSOpGL5D2js6ZOSFK247tvGORzRmBgZKustbHrzhwQbInJBQLI2IlBu/OdnZKC8rl2fWN7nexppkREQEPvroI0yZMkVu4aoQKq8CTRq4p+7m6maynVw03rMsb0MVw7cEa2+3jXjR7be0tFROWPI+76IFCzB96lRZYh9sIj++OIyzx2wTiTHt3bVjpxHLw6iurhbxfCFP2vGk6RpuXjqCg2UlKN5biH3FRdi3vwRFhSUoO3IeF2pb0ficD8XidmpqKgYNGoShQ4eKCYOivCpXLl+WMo+nuye2ZG7Bnbq6ztdYBtYhhiYiYVRiLXEJxwa6Vtw468dbEKyXbNywAUsjI+XZ0W7MWBG+b7/6Gl9+9jm++PQzDB08WGqBdHSm0wejRr4/0+juYX5GbbVoOJGJrFWBCPRwgbOTC1wmmz9NtDnR0QMzwtORfvwurj5jV551HH6tw4cPx1dffYWMjAwxZlWUV4VuRfS0ZI2bR+a5/mlJWLgYPsaT5lrUXb+CisuVqLhxF/UWbnpSW1cr5ysZ+cXHxWGOOLu4y0qbxxQ3eE+fLnc8OOfHut+S8PCnTZEZMzDD11fOXYbMDpG0mA8YmiV03+WjCc31p3BoWwLiprsh0NEBbkEBcJrqhQnDRsLJ1Qdz1+1B9pVm1D5DX9l8mW6+RjZMWCe0ZGdixbqgGHLriWK4PmOdimG3eNiAu1dP4FTxDuxan4zUNfFYE7cG8YnpWLspBzn7T+NcdSPuvcO5zYePHsrx8quVV41gnUJJSYkYHMTHx2Gx+QfniMtkFxeJAMeOHiMX3RbOD0NaWpqMxnDWjw2Thrt35b+PHDki2x+JCQkijh5ubnBynCT3PzaYiJJ2+fycz+ce7t89j0MmHd6yKBoZC+Yhec92LFu3FmFeQVidugXFt+7htnlCaf+ZMJuDsWFhYfjrX/+KadOmydekdULldSGR4QKNDLvP4wbUn9qJ7BW+CHAcg3FjHOHs7g0fH294T3aE01g7jHcOwqy4PORebEL9WxRECgPNKikaXFl72vR4erycnn4cch5lYyOzf2x6rI6JEYHkUDSHo29UV0tjgjW5jh+MFTA1ZfTHQWjOAnKk5oBJVcMXLhLThNE2oxC1fIUYKzxfnNrR0d4iJgyndmRhd/Qy5JzMw9qCXVg6Owrb8g+DgzE/9yNjKrx27VqpEQ4bNkzqhN2PSBXlxagYvgytdbh3ajO2LPaA5zh7OLoHI3h5CtI2bsO27VuxNSMRyZEzEexihwkO3vCKyMaOM3dMPPTmoC3V2bNnsbegQEwL6NgcFBgoTY9pnlPlihvrfExz55vUd3XMatkG4cjL5cuXZOSlpzBFXr0yRvaHbUeOMml3vAjmi2nB2T3ZWB++AnuP78LW4ixEhKYg/8AFdF2uffwDRWSNk9EqRfCbb76RbROKsqK8TlQMu80jtF4rQnmUC6bZ2mKkZxxi9l5FRUvnqzt50ngJFdnhWOY6CsOHGSGKK0H53cdofcX5zYdtbZK2suPLLY+TRoj27tmDDCOAy5cuxaygIBl14W4lra0oUMGzZmNN/BoZimaXuNG8/+tOK5sam7Bj+3ZJt708PCQifW7E1nEP7XfysSl2BfwDE5BzpBAlheuw2HMWolevQ+G1m7jS2IGWH9QMeXvYz88Pn3zyCWbNmqVCqLwRVAy7BQXkOq4VRyHacQjG2QcjcFMFjtc/fc2P6TCCeAgHUvzhP2wIxk6NRXR5I279RDS7S/ujRyKAx44eFYt6jrNQ5OjrN2r4SFl145bHbCMS3ABhKskZqaNHjkrqS1NTdnzf5OI5tz54OJ11xDXx8bhqHlTPpOky7u2ZjYUBPrAJyUfOuWuoLk1EzPjvMGbQeLhG78b2ay242/mDbWq8h3nz5kmdcLqJcCmMivImUDHsFkZIHpTiaIovvAbYwj5gHTKush3wLFrQcDQN6zwHYsy4AHimXMTZ+hdf6mfkx6jv0KFDMrzMFbforgtuJvXlziTHXrguxLofB56XLF6MtNRU7DFpMp1daIn/tmlvb0d5WZnUJt2nTEHJvn2dr/kZHlSjqSwRmelpWJZTjTN3HuHRtWIciJ+FsKAwzE8rRWlNm4nDn160W5eRjn7ff49BgwYjP3/P04+hKG8AFcNuYdK+69uxL8IV4/tNhsuSHOx5ADzPUqD1Ui6KF47GBDs32Ifvw4EbPw4N2aTgMjgjNx6yPswLbnLLIwHhRuA4xsLbHWxQ8JKb22RX6eLS1oppKSNFRoy838A5P0Z+77KzeqP6hrh90HyVBgzP5PEjPL7fYCK+RtS3PkEbv+SOB2hvumV+Hndwq+EhWFF4aL6nvXv3yjzhgAEDpctdd+c2Otruo7H2Fm5er8C1a9WoqmlCY2uHvI+ivAoqht3hSRtwYR3y503EyAHT4LaqCAfNb9/zLEXbrxbjSLQjXOxcMCY0G4XX7v8opWb05GcEj2ambq6u4uY83s4Ori6T5Zg1PdU4B8hBaN75PXTwoOwEc/+2ob5eojFLoq62DvPnzkW/774TK65XhWLPOuHHH3+M4JC5qDUCCBixPJmDndFzEe49Ac5OXnCauQ5ry2+g5um7KUqPUTHsDhTDixlPxbB/98TwUWURDkU5wNluMsbMzUHR9Qc/EsN1GRn4/Xu/w3//r/8N/+t//E/83//9f/Av/++f8Lc//1WEkcOfFBWKQs3tGrS1Wq6bMyNSHl3iip7D+PHIy83tfE3PYINkrhHWzz//HFOnTsXBg523bFuu4nLZVmyMDcfSmVMwcXA/fPG3sXCNykPePRNtv7vAWOkFUAx16PqFmDT5xk6ULJ0C+37OcF68G/lNz0+TH5zfhfy5NrAf5wnHZeU4fOvHqyms8TmMG2/E7y/484cf4S+dL3/7y19lBW70KFtM8/JC2Lx5iFsdi8xNm1FUWCjRIQ0QWE978OCBrNSxe8tI8V1ZDjFSZd1yqqenDHTza+wprHlu3rwZ/fv3x8CBA7HHpMoSBT8xqXDNVdy+dhVXGu7hzt0bOLo+HItHDcLUBWuRctV8HW9xplPpfWhk2C3Mb1nLUZxcH4QZg0fAbnoi1pztQP0ztecebpfFYo3LANg6hMJ3wzVc/Mk6yu1bt7G/pEQ6xJmbM5GanIIVy5YjZHYwppl/DO7q2tuNw6gRIzDYiMKQgYPEHdpp4kSZIQwJDhF36LSUVFmtYwODrhu02Or+rvDrgZ/bxdlZvjaO8bAe2FNozso6Yb9+/ZCUlITGrjlII/RP7jehta0DTwsET1B/IgsbQuchYWMhys2nbNHIUHkF2Lycb4IPiiHva9fW1Ha+xjKwEDEktbh9OAmpXsMxfvRUuK08hMKKVvzjxIyJ1m7mIGeFO9wGj4JDQDpSTrai7gVZLiM8NiFOnjwl5zEZCcaaiDBs/nzZF+ZRdI7R8Op//+++x4Dv+2H40GEimJwv9Jk2XbZK2H1ev26diBJFineGeXWu6noV7tTdkWjydY3ZsE5YWFgkjR3eLp47Z45sp/QUzkLSn5C2XEyTuQ3zj3TgyYPruH1uAzKWhpoHbhTidp+VzRXVQuVVuHTxkuzlc1qDQcrdhrc/mfE8LEgMO9BRexTn1vkh2H4EhtqFIDi1HPurmtH0qF1SufZHjWiqLEFZkh+CxttgyNi5mLPhBM4axXzUzd9Ufhx2iLkZwu0Sdpw5x3fh/AVxa2EnOSkhAUsWh8udVw83d4zrdJjpOqQ+wERVXSc1GWXSdGHVylXYsH6D3BQ+deIkbt64gWYjjPx8FEem2N3pRvNt+PZ0umEqwQh2sIla/Wf4SaTb06iUdcI5Rky//PJLMWI4ePBg52t+SjParhZgX4wTnL/6I373oR3GRRSgoObJzzwxKUr3OXP6DNymuMnvFDe0GKBYEhYkhoaOJrRVFWNfUjDmTLaHk5MHPGcuxIKl0YiOjkJU5Hws8PeAl70DJrnPQ2jqAZRcv4/XaWTDkRzWMvgsxhvD3ELheh3T7CgTFTI64ywiU1aKIY+sj7G1xaiRNiblHmmE82nHmuc3F8ybj5XRK5G+Nh3Zu3ejrLQMp0+dkkiS4z4U4nuN92SXmDVKphH5efkmYl0t78+tkxHDhsv6X3FRcTdX8f4RCiGPv3/77bcYMmSIjNQ8+4HYhkd3zuLCnrVICRgN5+8/wReTIhC46xaqHuiAjdJzjhw+LL6d3KRi3ftNLir0BMsSQ+ERHt48gpNbl2FVkAvcJoyH/QQnI4yTMMnBHvYObnALWImYnSdwoq79uR3n1w2jPArLeRq0mmc2iSKTkhARsQSBJvynCI4dbVJtEzX2//579Pv2OwwZOFgeABziZnTHmuX8ufMQGb5ERns49MyrYZs2bkKMiS69p3mLAA4xkegU8/F4XvHSxYudX8HLw685KysLo83XRbPWNWvWdH9fumIbjkUMgo29H4ZHnsXZWu2gKD2DGU/Rnr1SevL19pbMydKwQDE0PGnDw7tVuHHxKI6VFmBP9k7s3LETu7L3Yk/ZCRy/cAM37z5kD/qdwEtfdK6mqFAc6UJNGy6OvzDV3rVjB5ITExFhBG/2zFlys9hpEs0WbPC9ic5o5vrNl19JbXJg/wHSvGGtctiQobC1sZUbERwM370rC9cqr/b4GZTvR5OJrjrh/PnzxXGn2zTsR91WT8wIWgqXuEpcqtPIUOkZ/H3Zmpkpd3y47vqgh1nOm8QyxfCntLfIwaRWy5qD/hE0aaDQMP2kCHEchqkwHauZlvLeMLdfaOgaGBBgokiXv0eR/YwofmEE8pO/fYyvv/wSI4ePkFSCx6DiYlZLis6ZSM4XHigvl0YIm0EvivA4RhMaGioGDO7u7nLg6Zk8bEJL5UGcLMlBVv4+FO4vQ1lOOnLWLMTy1FykHWnCHcs7datYCWwGJsSvkcc76/HMWCwN6xDDd8qTp02X1lap2VFgeLuB9T7OTVFgaMq6PiND0mY2Pn4KUwQ2UCiSnFmkezT3o9lR4/ApHySRSyKk00ZTCF7A44NmYP/+GGCEks0bGsS6uU4xbxOAxQsXiaHEFvNMy02brs2ZW+bjsqPNHWzeR7506RIcHR1hZ2cnn++5tNSh6fA67IwLQ8jCKETGJpqvKwnx8ZnIOlSJykcsYChKzzh96jQWmcctpzOSTNb0Qz9PS0HF8BlQwB40N4shKy/DFRUVY+uWrUhcw07zYgT5B0hXzGG8vURynua/ebqTA9vdgaLIaJJpNt/nmhFRXryj7T4FjmUBHoyKCA+XzRPvadOkhmg/bpzsU7OmyJspPCHKjZrpU6fJ7nLMqlWyYsjGzz7zcZKSk5G1e/fzbb/I41Y8qjmF8+XZRqRzsLvwIMqPXcKZy7dR2/SQk6CK0iP4u0SnJ/p+8oX/zb+zNFQMfwZGgRTAdenpsvHBiI1iM9HBEcOHDJXjTR/87n382y/+Fb/4p3/Gb//j1/D19sEZE6G9zn9kdrZZj+TXsq+oCNtMqp1gxDh80WLM5LxWpxjT+NVmxAiJKHli1MXJSey+Zvj4yMR/XFycCPXOHTtQaFJ2Xts7f+48qquqJYr8acry5GGblCR0rlB5HTArYqlnonnS5s2f06dPd77GslAx/BmYClM4uK73/Tff4sM//gl/+uCP5uUP8vKH938vYvjer3+D3/3mt/j8408lgqNDDmuGnAV8naLIBxM/JovQFMj7TfdlRpIpudxOyc5B+tq1chpgTkiIfN0c+xliUm0WrAf2649B/QdIA4cdb4o76zYU1m1bt6G0ZL+cFLhdUyPiyFGf5uYWPHzUbr4PbZoorwbLQ3xs8sk6cc2abmdPbxsVw5+BkSGNW3ds2ybd4K+++BK//Od/wa9MJEgBpBD+8fcfyAuF8aM//AmTHB0lraVPIgWKg9wvTE1fA4+NWLGWyRom79LSnJVjP9yQYdOFTRs+G9OvcbrXVKk70qV7PFcRbWwkxeesJBs6vj6+CJtvIsnYOGSa9+WpAxpZMIW/f7/n5wuUvg1/nzhOxrLO+ox0i30sqRg+B0Z3rOPFx8dLiM/0+P3fvidpsQji+x/gIxM1fvXFFxhjOxpeHp6YNXMmwubNx4rly5Eqe827ULKvBMePHcdlI1a3b9+Slb23RddsJPeqy0pLO2uRydLVZjOGkeK4sWPlnAFX/vgnU2/XyZNluHxWYJB0teNjY5G5eTMK8vM71xBPyGA6bzvfbWiQqFVRfgqzGgYGLCMNHzpUlg/e9m5/d1ExfAEM8Zk2FxYWyh0UDlIzIqQo/vrf/h2ff/KpHINiR5hD0xRC1vK458w1Og6ZMhJjaspUgbW74qIiqdkx1aWI8MHBz8MHzpuCH5+fi0J87+5/Nm649cLoLy8vT3auV61cKfvaNL/lKiA3a5hms1zA7vaokSOlJslTqBEm1U5OTJIueun+Uomm+T0xEuAVQQoxP68lFsuVtwPnCfl4591wZ/N7wAaheUB0vtayUDHsJvwF53F4ih5FghEhPRI5PM3uLbvOFy9cxMEDB7E7K+tpDY8nBebypECQbJ/w2ZG7zDwmT8EUQTEpbIqJ1BhB0mCW4zpvM3Lsgil9fT3vQFfipEm1eQeamyvcj44zUeFiEx3y7ICXpyfcTNRIQeSdmAn2DpJy0zXc3c3NvI2/RJJcKdy4YaMY53INi0Pp9fUNb1TwFcuD415cQKAQctrh50bPLAUVw5eEEdWunbtE2OiPOMBETdxd/rk0kZFRTc1tqePlZucgJTlFutOs3VFAOCLTdXAqwM/PiMgCubXM6LEgL19EhAPWrNnV1tRIbZCR1tuGkV3X7rTcjzGpTnpamlicsSzgNnmKmFnwaiA3ajgjyf9nCs6O9pzQUCyNjERiQiK2myiSZQO6/bAEwV8ORqiMvtl8UrHsXXB1laNhDAC4dtpgnhAtFRXDHsDND44HsDHBX3hGi8+z1mLURQ9C+rddv3ZNjBq6UlPeYmZqygjSZ/p0TJwwASOHDxdhYbTFI1W8jEfnbo7FUBwpHO9CNCiKFH1+/3fu1Em9sLKiUuqRR48cQX5+vkm118usIwfDGRF7urvDwd5e6kV84mDpgKk2o0qeZeDMJps8T1Pt/fKzYar9LkRfef1wZtbRYYJsXfF35qdjXJaEiuErwIbI7qzd2FuwRzZAeiJQXNtjrY3NDTF+MCkF95I5R8hBa+41808fb29ZcGe6TV9F1h/T09Yie3e2pOb8WhqMSL5rGL1WV1fJnvb+kv1yhItR5MroaDH2pLhLR3vSJDibl8nOzuIXyYFyd/P3/F5DZs+WGzX8WXDLZo/5+TJKvnzpMupqa7VZYwVwf59zrAwU2JDjhEJPXZfeFiqGrwif6VgkbmlufuVGAd+fgspIknvOtPti9EjLf0ahNJjlOhPTUDZm+IzLdH3h/DCp69HOn8VqClFX+kmxZQ2yvf3ddPC6vie+8OvgEDlrrwUF+diwYQNWmSiSp1o5G2k/bjyGDXlqrts1F0nBnOHtK42plSuisNYIK2uyfALgbOTf1xDv3JFUvms3XHm3sIHGyQW6WnPrhCbFlo6K4WviVYXw5+gwQstfcO4yX750Seps+00qyQdZanKynDFgtOXv6yenTmkVNtpmlBFJBxFJ2oQxeqThLLdj7tTfeSNf58vCJxBGCYzyWF6gqPF748hOnux5s6u9CosWLJLj/d7ml4nlCA6Ss87KEgJHmViU9/PxRfiiRTLMyxOqNMBlLZK1XRXFdwf/ffnvwn8rPpFzT97SUTG0UrglwiFrCsiObdslHVkwf748C3OAmi+ce6QosgvM0wFMvyWC3LRJurxcy2PqSeOJdgua/Wp/1C71VbqPl5eXSVd7rRF1ij83bHimgSdgHcbZw3G8g4xt0C+S0aWvj48MmC8w0TKbUay17jJPHkUmYmadlrORjJjfRce+L1FlnuRYA2d0z1IJn9QtHRVDK4ZRHqMs1tBoccZnYx6+5y4zh6PpsL00IlLqjBNNSk2/RHHAGTNGLMLYtOFlwK2ZW6R5QWFkes4GDT8Wx4neZcH78eOn3x/LBvxaeEZBImXzPTLSLTKpF7/2NfHx0rDhvCfTam7V8IYN5yO7GlGsRXILgrOgFEhu6HBTiKNEjFA5OM7GENcdH5qfp0aVPYc/R9rN0ciEg/2sZ1tCRvIiVAx7KRQzdns52nDwwAEZ1WFEyEI20xaOuwT4+//9UiAFg7ODFJTIJUukNpefmydjQVz1s0RxaG1plVoh64Znz5yVOU123FlGYCQZHRWNBWFhmB00S9Jp1q+YbvN7tTNPCEy7GUEHmCcLml8kmFR729at4vZDWzSef3gbK5W9DT4ZB8+ejSmurkhPT3+la45vExXDPgYjLIoHD0Lt2LEDa+Li5aAVbzI7jreXW9MUCEZSs4NmSroZJauFKTJfua+4WBogVy5fkVSWhg49GvN5/AhPGipxq/IcTlyqwuXKm6irq8fd1o5uH/d6EYwiGfnxlk1eTq7UItnV5vAvU2rWVmkeYGc7GpMmTJAut+90b5mdZC12OTvaCYni0My6K0sSp06elPIEU23+knd0WO6oyLuAWQobY1zr5M+RTuuWVIJ5HiqGfRCmLIx4nq7m3RUXYu6P8qrfHpNeM42kANKkgiMvfGCzu2tj0s/Jzi4y+rIqeiWyjDiyrscI7aVpqUNjSSw2LZ+F6QsTsTRuA3Zn5SLv4BVcrGkVQXwdmkjXHa47ssvM9K3BpMP8frkxxEbL/n0l2L5tO1KSkmSchzdqWGvlUDx3tZlq8ywDh8i5fTPXRNQro6JEWCmwnK9kE6hraJxiwM/H9L5HTxJWDL/nU6dOS316tHmSYfPOUveQfw4VQ+VH8Iwqu9dME1lHZPGboz3cNmFExUFqzjvy0D6v/+XszpbxnZelo/E8zia6Y9bIz/HpYBc4TgvCnNkhCJy5GgnZp3He6OvbmCZ83PFYbMuqqq7L98yzCnm5eWJKkZRIgeT3HSprhjNMqk3ziqlGLDkTycYNGzlMv2eZKDpiSYRs2dAWjdcMT508JaNEfaVZU1NbgyjzREEh9JsxA0dNRG5NqBgq3YKRJO+usOlAa7M1cXFIWpOAYpM2s/nwcrSi+Xouts0cg4lffYchTiGYvTIWMVErsHB2FBJ2HMaJZr7Vu6e1rVXmGFkHK9xbiM2bNiN2dSzCTBrNJwTWH2lmIVZoJnpk5MyOPiNMekauXhUje+oczudgPd2LGJFyxZI1ycbGe72iLsnvgSUU+/HjJZPgsDynFKwJFUPlpWAayEiqpqbG/DLXyOmCl+44d1SgpjQK4Q42JooIROiWUyirvm1EpxrXLlWi+vZd3O8wUVvnm1sCTPcY4d1tuCvfe9X1Kqmbdm3a7Ny+QyLo6BUrZECcmzYsMdiNHi3pNlNt7qG7T5kiZQaaeHAVk13Xo0eOypomx6WsNbXmHOFyE0UzKmQGwdEaa/teVAyVt86TmmKcTvOCm+0kjA/cjOzqJxYRBb4KbEyx686o70D5ARnd2bh+gxzukvXKwEDZIKJJh/fUaZJuc16SfzKSDPTzl00crlmyWbXDiCtTbToIMYrkE5Cl0t7eIZMKPDnB74PfvzWKuoqh8pbpQNORNOwKHg27iaHwTjqNyw96d6OBKSSNLS4aoaTvY9cOOkecONbT5RvJNUs2qRztJ8jNHabanBPlQP3mjZvkyBdPz9LMguuWrO1ytIiNoTaTznMu823DLSka/bJmSjHkaJI1NU1+iIqh8hbhL+tNXNwWhuWOw2A/IxkrSppxr4/MN9O8gDvsbDhxBpQej2dOn5GONHfKKZJpJipcGb0SixculmPrjBxdJjnLqVge/WJd0s3VFbNmzpK0lB1bnpo4fOgQKiuvGmF8u2YIXBNdGBYmgr565SqJYq0VFUPl7fGkGWjYi9wlbnAb5ACP5XuQdctETi8Z0HBLhDUqdruPHDqM69euy5B5b4CjTvSN5Gxkfl6+GOTGxqzGgrAFUofkVgfF0NPdQ6JHf/N37PAzimSaHRG+RFJzemLSYp/1zJMnT4ppMKPI1xm1sVMeu2oVbG1s5GvggD9XKa0VFUPl7dFeh8fnUpEx0w32Y+Zi0fYzOG+E8GWSZM5IsoHBKIoCMDckVJzCd5tf/KPHjspAeddKIRseD9seyqyhNcHvkTW3H60imicA+jwymuSmDYWOUSEbMZzr42wkD3uxUTNk0CCJJCmcnBWNjIiQtFy2a4qKxQ2Js5H8OfJjcjhd1hDN53r8+MVhOr82vi8H9u3t7ESc6dRurelxFyqGytvjYR0ent2MbTHLEBK+A1mnatCTeI4RDo0m2LXljN8UF1c42DvAYfx4MWwIDQnBahNN8Zf/QFm5pG4ciO4tULTu3m2QwfFLFy/KRhBrkVyf3LJ5s5jlshGzeNFi6ezSWJVjQHRUZz2SmzfsatOBmls2aalp2L0rCwcOHJDtGkanz4ORK+dOhwwcaER3NNZnZMi/ibWjYqi8PdpNpFZzFueOH0HJ0euoutuzHjIHwxkB0kWZ92dWmF/8mUEzxSSWN1loHMtIqcsIl/N+4tazcZMYWDCy4ubMrZu3JCLqbXD8iTe8ORvJWuSWLVtkLpRmFky1uZ89aYKj+XlxYNxT/o71SboecS+dZhYcE+KTyZ6CAukOnzt7DhUmKuU6Imuag030SUf2lORk3DSi3BtQMVTeHib9e9LxSNKptkeP0dPmJ9NIGkfwl57GukyJ62rrxB2l3ESC9DVkCsfIkU7hcqlwwECZ9+PJV14q5ClXuVRYWCTdWUY2TKuZkvLrs3bXGv6MmGbz++H3xXlQpsScDWVkd/ToUXli4JMJh8h5xEs62xMnwWbkSEm3n65fOosFHO3T6A7EsgQNhieY6DIjPV1SbH6u3oCKodKrYD2L3VpGMezSMrLhDBzvPjMy4sBzkPnl5kohLxTKyYHJrhJFMoLkreuc7Bw5aXnzxg1xbO6tUCRpOMGzExz85hPDzh07jMhliBckb2uzU0yHI/7c+DOiWHIuMjMzU+qGvQkVQ6VvYKIXRn9sHrBLyzRwES8VTuWlQjvYjholtzrYpWVnlFcMKQi8JV2Ql2dS60NiE8b0nB+HEVdvRp5UGhqkJsk1QkbbyUnJEnHzJg1nG3sbKoZKn4IpMMdwKGic9WPKyCiw61Jh9IoohAYHy1U/muAOHfx0EFrceszf8x40hYEekVw5Y82RwtFbUsWfwqFqNp+4AcNTCnxhRNkbUTFUFANrhBzJYaOAjRkKHruyXKXjdoWvj69cKOQLo0n6IdIwlr6HnAPM3NR5jIumsCZ9fBM1x94quJaCiqGiPIeuzuzhw4elnhYfFyd3WDimMmrESLlSSMdsL5Nec+6RIydMwelSw9SaXWtxqKmhQ02jjMX0FIohI9t75uP01ujsXaJiqCjdgKLIGhpTa26/cKtjX/E+bNuyVS7zcfODzs5Mr1mDZGrNIWjemuHISlJiArKzs2WPlw7hPY0c2RwqKCiQ8wYUV+X1oWKoKK8AIzUaJvDUKQfBOW7CnWEONNME1mOKm8zy8VIcDU/ZnJk/Zx6io6Kwzrwt94o593jp0mUZfXn8glSYNTuOwvBWzdrUNJzjCpyVjwFZCiqGivIaYArLaI/iyBVANhy4zcH646aNG7EyKlqE0GniJAzvvFLIo1TcoOHVPgpcZuYWlHTefeZYD4WP84E/PIx//8F9GYr+/ptv5SRBmIk6Dx06JJ9Pa4qvhoqhorxB2G1mQ4VGsFyb45F71h55c2XFsmUihAF+/rJHPMFhAsaNHYtJjo4S+dG+i7dW6LBNgXxohJapcWxMDL76/Au8/9v38Pknn8q2Dd20aeul9BwVQ0V5B3BOke7WHNGh6QQbM7xjzUiRYujkOFFSbN5dodkCrxQmJiZKh5udbIrhB797H7/6xb/iD+//Xq78cUuEKTc3cpSXR8VQUd4RXd1hpsG0/KeIsUHD/V9e3mNNMHJJhOwOc+d6xLDh6P/d9/j0bx/jwz/8EX/8/Qf44L33JUL80wd/wOeffgYPd3cZC2Kazc61ps7dR8VQUSyQ+033UV1V/fcbK7TIok8hU+IvP/0c7/36NxIRUhT5J///33/5K/zRiKLtSBtZPSwqLJIOuNI9VAwVxUqgOC6LXIpvv/oav/yXX4j4/cev/k1efvPv/4Hfv/c7Eca/fPgRxtiOlqYMx4Be+mBXH0XFUFGsBDry0H7rrx/9WYSPqTEjwz//6UNppPCGCq25aKTAyJBnTek+3fzg+TZlTKV/+CLrheaFf7KLzT/7AiqGimLhsPZ3tbISCWsSpHZIQ1UaSnDIW7waTQTIvWo2YooKC3Hk8GG5rcK9a94u5qjPs2DUyB3r0tJS5OXmyO3j0yY1p+vP8WPHxJSBH5NnA3o7KoaKYuFw++XsmTPYtHHTU+HLyEChESiKFi242lrbOt/y5aHQ8pgUd7C5Yhi+aLHUKGkMSxHk2dLwRYuQnpYmJwf4tfRWVAwVxcJhmkrLLN5lpvhxU+VBczMevYZaID82fR+DAgLw3ddfiyEu1wWbGhvF2YcRJuuUvPWcEB8v1/B6KyqGitLH4aH6QH9/fPbxJxIZ/hCKJdNvzj3ydgrXB3srKoaK0sehGM4MDMSXn30uYvjD7jPnIHNzc0UMeXWPq4W9FRVDRenjiBgGBeHLz7+QNLnLDYdCyNvIK6OiMHwI78dMkLspvRUVQ0Xp41AM6bJDMeSqH/enZdh7/35poFAEaSqRnJgkmy29FRVDRenjUAyDZ8+WfWfuRfNq4K6dO5GclCQH6nmP2tfHR1YEG+obeu2Kn4qhovRxuiJDimGAn5+M7PAQ1Anz98VFxYhZFQPv6dPl/EFeTp7eQFEUpXfS1UChGNKx+6dcvnxFjsx/8elnEilWVVX1yuhQxVBR+jgUQ84Zspv8c2JYV3dHZg35erp1c9/5TRy8eteoGCpKH4e3pDlnSGuwn84ZNre0yL0VHtv/yogh1/9q6+p65b6yiqGi9FEoaPRSPFBeLmnygO/7Yd6cuai4UiHH8rkPXVZahkgTLTra28Nn2nTs3bPnhXdarBUVQ0Xpo3TNEfKQ1bLISPjP8JM5w5SkZKSmpIoxxKrolVixdJkcr6JxA9cCeysqhorSR+GmCV1tLpw/L0elSveXijlDfl6+DFdz9S4vNxcHDxyUvejejoqhovRhujwMu+jyM/zhS19BxVBRFMWgYqgoimJQMVQURTGoGCqKohhUDBVFUQwqhoqiKAYVQ0VRFIOKoaIoikHFUFEUxaBiqCiKYlAxVBRFMagYKoqiGFQMFUVRDCqGiqIoBhVDRVEUg4qhoiiKQcVQURTFoGKoKIpiUDFUFEUxqBgqiqIYVAwVRVEMKoaKoigGFUNFURSDiqGiKIpBxVBRFMWgYqgoimJQMVQURTGoGCqKohhUDBVFUQwqhoqiKAYVQ0VRFIOKoaIoikHFUFEUBcD/BzzYD4JkAoZ6AAAAAElFTkSuQmCC)
As shown in the figure a particle starts its motion from 0 to A. And then it moves from. A to B.
Is an are find the Path length
![](data:image/png;base64,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)
physicsGeneral
Maths-
Assertion (A):
is divisible by the square of14 where n is a natural number Reason (R): ![left parenthesis 1 plus x right parenthesis to the power of n end exponent equals 1 plus to the power of n end exponent C subscript 1 end subscript x plus horizontal ellipsis. plus to the power of n end exponent C subscript n end subscript x to the power of n end exponent for all n element of N](data:image/png;base64,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)
Assertion (A):
is divisible by the square of14 where n is a natural number Reason (R): ![left parenthesis 1 plus x right parenthesis to the power of n end exponent equals 1 plus to the power of n end exponent C subscript 1 end subscript x plus horizontal ellipsis. plus to the power of n end exponent C subscript n end subscript x to the power of n end exponent for all n element of N](data:image/png;base64,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)
Maths-General
maths-
Assertion (A): Number of the dissimilar terms
in the sum of expansion
is 206
Reason (R): Number of terms in the expansion of
is n+1
Assertion (A): Number of the dissimilar terms
in the sum of expansion
is 206
Reason (R): Number of terms in the expansion of
is n+1
maths-General
Maths-
B=600!,
then
B=600!,
then
Maths-General
maths-
The arrangement of the following with respect to coefficient of
in ascending order where
A)
in
where
B)
where
C)
in
where
D)
in ![left parenthesis 1 plus x right parenthesis to the power of 4 end exponent](data:image/png;base64,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)
The arrangement of the following with respect to coefficient of
in ascending order where
A)
in
where
B)
where
C)
in
where
D)
in ![left parenthesis 1 plus x right parenthesis to the power of 4 end exponent](data:image/png;base64,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)
maths-General
maths-
A: If the term independent of
in the expansion of
is 405, then n=
: If the third term in the expansion of
is 1000, then n=(here n<10)
: If in the binomial expansion of
the coefficients of 5th
6th and 7th terms are in A.P then n= [Arranging the values of n in ascending order]
A: If the term independent of
in the expansion of
is 405, then n=
: If the third term in the expansion of
is 1000, then n=(here n<10)
: If in the binomial expansion of
the coefficients of 5th
6th and 7th terms are in A.P then n= [Arranging the values of n in ascending order]
maths-General
maths-
The arrangement of the following binomial expansions in the ascending order of their independent terms A
B
C
D ![left parenthesis fraction numerator 3 over denominator 2 end fraction x to the power of 2 end exponent minus fraction numerator 1 over denominator 3 x end fraction right parenthesis to the power of 9 end exponent](data:image/png;base64,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)
The arrangement of the following binomial expansions in the ascending order of their independent terms A
B
C
D ![left parenthesis fraction numerator 3 over denominator 2 end fraction x to the power of 2 end exponent minus fraction numerator 1 over denominator 3 x end fraction right parenthesis to the power of 9 end exponent](data:image/png;base64,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)
maths-General
maths-
A:
B:
term independent of x in
C:
then
A:
B:
term independent of x in
C:
then
maths-General
maths-
I The sum of the binomial coefficients of the expansion
is ![2 to the power of n end exponent](data:image/png;base64,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)
II The term independent of x in the expansion of
is
when is even.
Which of the above statements is correct?
I The sum of the binomial coefficients of the expansion
is ![2 to the power of n end exponent](data:image/png;base64,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)
II The term independent of x in the expansion of
is
when is even.
Which of the above statements is correct?
maths-General
maths-
: The fourth term in the expansion of
is equal to the second term in the expansion of
then the positive value of
is ![fraction numerator 1 over denominator 2 square root of 3 end fraction](data:image/png;base64,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)
:In the expansion of
, the coefficients of
and
are equal, then the positive value of a is 8
: The fourth term in the expansion of
is equal to the second term in the expansion of
then the positive value of
is ![fraction numerator 1 over denominator 2 square root of 3 end fraction](data:image/png;base64,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)
:In the expansion of
, the coefficients of
and
are equal, then the positive value of a is 8
maths-General
maths-
S1: If the coefficients of
and
in the expansion of
are equal, then the number ofdivisors ofn is 12.
S2: If the expansion of
for positive integer n has 13 th term independent of x Then the sum of divisors of
is 39.
S1: If the coefficients of
and
in the expansion of
are equal, then the number ofdivisors ofn is 12.
S2: If the expansion of
for positive integer n has 13 th term independent of x Then the sum of divisors of
is 39.
maths-General
maths-
I Three consecutive binomial coefficients cannot be in GP.
II Three consecutive binomial coefficients cannot be in A.P.
Which of the above statement is correct?
I Three consecutive binomial coefficients cannot be in GP.
II Three consecutive binomial coefficients cannot be in A.P.
Which of the above statement is correct?
maths-General
maths-
I The no of distinct terms in the expansion of
is ![n plus 2 c subscript 3 end subscript](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADcAAAARCAYAAAB5LjRtAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAWhJREFUeNpjYBgYYA3Ea4D4ExD/AuILQBzNMEzAQSCOBGIeKF8LiI9CxQYt+E+BXnkgvkQrh9UDcQkQiwPxfCD+BsTvgDiPTp4DgR84xEEx3AXET6HJeB0QC5Ji8CqoR0AeswdiJiCWhlrIRQfPWUKTJjaPnQPiViDmA2I2aCT4kGL4LSBOwyIOij1hGnuOA4hPQgsadNABxJMoSQ6gWPqCRZwFmjzxeYYQJgRAyWsDELvhcNdrUpMgOjAH4v04ksp+GuY5JajHVHDImwLxYUoLk0hoXiNWnBqe0wDi2QTysxe08GAgIvXA6kuMFABK08lYNOISp9Rz4tACjIWAOmMgvkFigD1EF1wHDSVixSn13BaoQ4gBF6AlJQu0tCzAUfDA8ug7bCUiB46SkoNGlT2xBZAstEXzB1rJ40pJoBJ9ChAnMgwzAAuYWIZhCvigyTeNYRiDH8PVY7ZAfGY45jdQjO2A9i7AAACCRFtkNGxj+QAAAH50RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+bjwvbWk+PG1vPis8L21vPjxtbj4yPC9tbj48bXN1Yj48bWk+YzwvbWk+PG1uPjM8L21uPjwvbXN1Yj48L21hdGg+ixPmuwAAAABJRU5ErkJggg==)
II The no of irrational terms in the expansion
is 55
I The no of distinct terms in the expansion of
is ![n plus 2 c subscript 3 end subscript](data:image/png;base64,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)
II The no of irrational terms in the expansion
is 55
maths-General
maths-
If
then ![a subscript 0 end subscript minus fraction numerator a subscript 1 end subscript over denominator 2 end fraction minus fraction numerator a subscript 2 end subscript over denominator 2 end fraction plus a subscript 3 end subscript minus fraction numerator a subscript 4 end subscript over denominator 2 end fraction minus fraction numerator a subscript 5 end subscript over denominator 2 end fraction plus a subscript 6 end subscript](data:image/png;base64,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)
If
then ![a subscript 0 end subscript minus fraction numerator a subscript 1 end subscript over denominator 2 end fraction minus fraction numerator a subscript 2 end subscript over denominator 2 end fraction plus a subscript 3 end subscript minus fraction numerator a subscript 4 end subscript over denominator 2 end fraction minus fraction numerator a subscript 5 end subscript over denominator 2 end fraction plus a subscript 6 end subscript](data:image/png;base64,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)
maths-General
maths-
If
denotes fractional part of
then ![left curly bracket fraction numerator 2 to the power of 2003 end exponent over denominator 17 end fraction right curly bracket equals](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAE0AAAAnCAYAAABKZsWMAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAbSkFbcgAAAkRJREFUeNrtWjFLAzEUfpQOIiIUKeJUKKWIk2sRKQXpIB26FCni4CLi4D9w9B+4iZODIA4ipbgUEREpiIhTcXN0cehQpBTOF+4VzjN3l1yj3uXywTfc5Th4X16+JC8BUA+LOETeIwucb2rIHrEm2e78/zOyChohhdxDPrnel5C3yDniDb0TbXdiEfkGGuLT9XyJLDueV5FXEu3ujvnQTbAyZY0TfQrWGXhfon0MloVHyO0oC7CCvKAAxn6y6fP9AnlanuNJbgwl2p2+thX1rGEZ00TO0PMSidLkfFtEtkg4CMi0dECmpT0ybRZ5iNyJ2/DLIV84GdamoHhwe1aZBBZtD/LMWBp9m2Y1L5RoRswgs5TB6xLt4JokHuMmWImGKM9vnOStw15p5tuXbB//k3XWNWV7bDCF7NIEYSCADHlP1UghhjwJVjBSiIEZ/DFy2kghhnnkOa2bDATRClhKJA5F8qmBzzeWD6OMwW95MKtbVTROijWKUSmsBIwmy4gWgRiHCRBtFMKrPT2bVSUeEiBaF/ilqtBp25ygF6JIHjZUDtEc+NerdEHboyISthN812e6QHmx0syeRrS/iXGU4CVHaHSQdfh+CqRqT3sA9nFfmNlZBVIUW0e1aOwA4wT4R2WT4BTsIzZZARpg1+1UoE+xZXX2E1a3uwP7DCLRkBGN3dtYBgNh0XbJAw0ERcvR/tCU0yVEYyfpFSOVuGgN2hsaCIrG1lE9Y/5yotXh58U/gwDRziDitxn/Q6ygrdE72HdDYoMvzmXdzoY5JpMAAACbdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1vPns8L21vPjxtZnJhYz48bXN1cD48bW4+MjwvbW4+PG1uPjIwMDM8L21uPjwvbXN1cD48bW4+MTc8L21uPjwvbWZyYWM+PG1vPn08L21vPjxtbz49PC9tbz48L21hdGg+o2oGLgAAAABJRU5ErkJggg==)
If
denotes fractional part of
then ![left curly bracket fraction numerator 2 to the power of 2003 end exponent over denominator 17 end fraction right curly bracket equals](data:image/png;base64,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)
maths-General