Physics-
General
Easy
Question
In the set up shown in Fig the two slits,
and
are not equidistant from the slit S. The central fringe at O is then
![](data:image/png;base64,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)
- Always bright
- Always dark
- Either dark or bright depending on the position of S
- Neither dark nor bright.
The correct answer is: Either dark or bright depending on the position of S
If path difference D = (SS1 + S1O) – (SS2 + S2O) = nl n = 0, 1, 2, 3, .... the central fringe at O is a bright fringe and if the path difference
l, n = 1, 2, 3, ..... the central bright fringe will be a dark fringe
Related Questions to study
Physics-
In a Young’s double slit experimental arrangement shown here, if a mica sheet of thickness t and refractive index
is placed in front of the slit
then the path difference ![left parenthesis S subscript 1 end subscript P minus S subscript 2 end subscript P right parenthesis](data:image/png;base64,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)
![](data:image/png;base64,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)
In a Young’s double slit experimental arrangement shown here, if a mica sheet of thickness t and refractive index
is placed in front of the slit
then the path difference ![left parenthesis S subscript 1 end subscript P minus S subscript 2 end subscript P right parenthesis](data:image/png;base64,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)
![](data:image/png;base64,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)
Physics-General
Physics-
Following figure shows sources
and
that emits light of wavelength
in all directions. The sources are exactly in phase and are separated by a distance equal to
If we start at the indicated start point and travel along path 1 and 2, the interference produce a maxima all along
![](data:image/png;base64,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)
Following figure shows sources
and
that emits light of wavelength
in all directions. The sources are exactly in phase and are separated by a distance equal to
If we start at the indicated start point and travel along path 1 and 2, the interference produce a maxima all along
![](data:image/png;base64,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)
Physics-General
Physics-
Two coherent sources separated by distance d are radiating in phase having wavelength
. A detector moves in a big circle around the two sources in the plane of the two sources. The angular position of n = 4 interference maxima is given as
![](data:image/png;base64,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)
Two coherent sources separated by distance d are radiating in phase having wavelength
. A detector moves in a big circle around the two sources in the plane of the two sources. The angular position of n = 4 interference maxima is given as
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHAAAACGCAYAAAAFKw5PAAAVK0lEQVR4nO2de1BU5/nHv7vsujcWTFBgXdlAIyUsS0DXG7uMuoOhjCKSYBnQpM7UIXYmHdrYscmMdeI002naTqaVmBkv0ya1o02NGCM6xsuypAUToMiCoCighOUmLAjs7Sx7eX9/8GMbo4S9nAVWz2fm/LPznud5zn7Pey7v+7zPYRFCCBhCFvZcB8AQGIyAIQ4jYIjDCBjiMAKGOIyAIQ4jYIjDmesAfMFms2FoaMizjYyMgKIoTExMgKIo2O12OJ1OcDgc8Hg88Pl8LFiwAHw+H88++ywWL17s2QQCwVwfDi2w5vOL/Pj4OG7evInW1la0t7djfHwcPB4PAoEAfD4ffD4fHA4HYWFhno3NZsPtdsPlcnk2p9MJiqJAURRsNhvsdjsiIiKQmJiIlJQUyOVyREREzPXh+sW8E/Cbb75BTU0NGhoa0NHRgbi4OMhkMixduhRRUVGIiIhAeHg4xGIxRCIROByOZ+NyuR4BHQ4HnE6nZ7NYLDCZTDCbzRgfH8fw8DB6enrQ3d0Ng8GAZcuWQalUQq1W47nnnpvrv8Fr5oWAZrMZtbW1OHv2LLq6upCSkoK0tDSkpqZCLBZDLBYjPDwcXC4XLBYrYH+EEDgcDpjNZphMJphMJty4cQNNTU1obW1FfHw88vPzsWbNGoSHh9NwhMFjTgW0WCw4duwYzp49C5FIhIKCAmRlZWHx4sXgcrngcrmzFovD4YDD4cDQ0BC0Wi3Ky8thsViQn5+PkpISiESiWYvFJ8gs43Q6ic1mIwcPHiTp6elk9+7d5Pr167Mdhldcv36d7N69m6Snp5ODBw8Sm81GnE7nXIf1ELPWA+12O4aHh1FRUYGTJ09CoVCgpKQE6enps+E+IPR6PY4dO4aWlhZs374dW7ZsQVRUFHg83lyHFvxLqMvlwuDgIKqrq3H+/HlIJBIUFhZixYoVwXQbFK5fv45Tp06hv78fubm5yMzMRHR0NMLCwuYspqAKaLVaUV1djaqqKtjtdmRlZWHDhg0QCoXBchl0rFYrqqqqoNVqwefzsX79emRmZs7ZMQVNwIGBAZw7dw43btxAYmIiXnnlFSxdujQYruaEnp4enDlzBu3t7UhNTUVeXh5iY2NnPY6gCHj9+nUcOXIEMTExyMvLg0KhAJ/Pp9vNnENRFFpaWnDu3Dncv38fu3fvnvVbA+0Cnj59GsePH0dWVhYKCgqeqF43HT09PSgvL4dWq8VPfvITbNu2bdZ80yagy+XCoUOH0NjYiJ/97GdQKBTz/iWYTsxmM1paWnD48GEsX74cP//5z2fl4YYWAS0WC/785z+ju7sb+/btg0wmo2XEJNQghKC7uxu/+93vIJPJ8OabbwZ9ACBgAYeHh/H+++/DaDRi//79iIuLoyu2kMVgMODdd9/FokWLsGfPHixatChovvwWkBCCnp4elJWVwWQy4a233kJCQgLd8YUs9+7dwx/+8AeIxWKUlpZi6dKlQbkq+T2hazQacfLkSfT392PXrl2MeN8hISEBu3btQn9/P06ePAmj0RgUP34JaLPZcObMGRgMBuzbtw+rVq2iO64nglWrVmHfvn0wGAw4c+YMbDYb7T78ErC8vBx6vR4lJSVITk6mO6YniuTkZJSUlECv16O8vJx+B76OfldUVJBXX32VNDQ0BDaM/pTR0NBAXn31VVJRUUGrXZ8EbGhoIBqNhlRXV9MaxNNCdXU10Wg0tJ78Xgs4ODhINm3aRA4fPjzv5sRCBafTSQ4fPkw2bdpEBgcHabHp9T3w0KFDUCgUeO211+Z0+iSUCQsLw2uvvQaFQoFDhw7RYtMrAT/77DMYDAbs2bMnpKeC5gNCoRB79uyBwWDAZ599FrC9GQU0GAw4ceKEZxaaIXCioqKwZcsWnDhxAgaDISBb3ysgRVG4cOEC0tLSoFKpwOGEVB7wvIXD4UClUiEtLQ0XLlwARVF+2/peAZubm9Ha2oqsrCzExMT47YThUWJiYpCVlYXW1lY0Nzf7bWdaAcfGxvDVV18hISEBKSkpfjtgmJ6UlBQkJCTgq6++wtjYmF82phXwzp076OzsxIYNGxAZGel3kAzTExkZiQ0bNqCjowN37tzxy8ZjBTSZTKivr4dEImGGyoJMcnIylixZgrq6OphMJp/3f6yA9+/fR11dHTZu3PjErOKZrwgEAmzcuBH19fW4f/++z/s/IuDExASuXr2KJUuWhETS7ZNAeno6lixZgqtXr2JiYsKnfR8RkKIoVFZWIi8vb1bXJjzNcLlc5OXlobKy0udXikcE1Ov1sFqtWLt2LW0BMszM2rVrYbVaodfrfdrvEQHLy8uxdetW2gJj8J6tW7f6PGf4kIDDw8P4+uuvkZ2dTWtgDN6RnZ2Nr7/+GsPDw17v85CAFy9ehFwuD6kVqk8Szz33HFJSUnDx4kWv93lIwAsXLiA3N5f2wBi8Jzc3FxcuXPC6vUdAi8WC+vp6rF+/PiiBMXjHunXrUF9fD4vF4lV7j4BNTU2QyWRBTUJlmJlFixZBJpOhqanJq/YeAaurq6HRaIIWGIP3aDQaVFdXe9XWI2BNTQ0j4DxBo9GgpqbGq7ZsAHC73ejs7ERqampQA5uCEOLzkJEv3L59G6+88gru3r0bsC3y/yVJZpPU1FR0dnbC7XbP2JYNTBbXkUgkQV+073a7MTw8jBs3buA///lP0Py0t7cjKSmJluVtNpsNVVVV6Ojo8Gu2wB94PB4kEgm++eabGdtyAKCrqwtxcXFBWxLmdrsxNDSE1tZWXL58GQ6HA7/97W9p9WE0GlFXVwcul4v6+nrIZDJaZlKEQiHi4uLwpz/9CTKZDJs3b0Z8fDwWLlxIQ9SPh8ViIS4uDl1dXTOuOeEAkz1QJpOBzaa/eKHb7UZjYyP+/ve/49y5c5iYmMAbb7yBEydO+GxrxYoVWLly5SO/j4+P429/+xuqqqoglUrR2NiIPXv2PPaKcuvWLb96v1gsxoEDB/D5559j27ZtKC4uDtpSOjabDZlM5n0PNBgMkEqlQRFw6n43VU2QzWbDbDbD5XL5bOtxlzBCCJqamnDt2jWUlZVhwYIF2Lt3LyQSCRYsWPBIe6vVioGBAZ99j4yMgMfjgaIojI2NBfUezmazIZVKvcpY4wDAgwcPgjbzHhYWhoyMDCQkJGDTpk2or6+HWCzG22+/TYt9l8sFvV6P9PR0LFu2DHq9HrGxsXjmmWce216pVEKpVPrko7OzEx9//DFKS0uRnZ2NlJQULF68mI7wp+WZZ57BrVu3ZmzHASbPSqFQGNRl0bGxscjPz8fatWvR19eHu3fv4gc/+EHAdt1uN0ZGRsBisfDgwQOUl5fD5XLRmsM6NDTkKdgwGwMdLBYLQqEQVqt1xrYeAUUi0aysa4+NjUVsbGxAuZDfhsvlIicnB7m5udBqtYiIiIBGo6F1bXpaWtqsppawWCyIRCLvBbRYLLOeMk9X3RgWi4VVq1ahs7MTbDYbbDbbUzuULuYiL0goFHo1HurpgQKBIGQrS7DZ7JCtuPs4WCwWBAKB9z2QzWaDBKlkGkVRuH//PiiKgkgkQkxMTEjn2jgcDgwMDHhO+ujo6KBUoSKEePVWwAbguWHSLaLNZkNFRQVefvllKJVKbN++HV9++SWcTietfmYLp9OJqqoqFBUVQalUoqCgAOfPn6d97TshxPNg6U1jsnPnTlJZWUncbjctiw6nuHnzJlmxYgVhs9kEAGGxWCQjI4MYjUZa/cwWRqORqFQqEhYW5jme5cuXk5s3b9Lqx+12k8rKSrJz584Z2wa1B5rNZrS1tXkGZQkhaG5unvXBYbpwOBxobm72DEIQQtDW1kb7GCkhxOsHy6AKGB4ejqSkJM/DEYvFQmpqasjeA7lcLlJTUz33JhaLhaSkJIjFYlr9EB8uoWxgchZ4aGiIdgHj4+Px1ltvIS0tDUKhECtXrsQ777wTsotlIiMj8c4772D16tUQCoVQKBT49a9/jfj4eFr9EEJgNBq9GjTgAIBMJkNLSwvtAgoEAuTl5WHlypWw2WwQiUSQSqUhu1CUw+FAo9EgKSkJZrMZAoEAS5Ysof09kfx/GTOFQjFzTMBkOtvFixe9mkD0FYFAgOeff552u3PFggULaO9x38XtdsNgMGDz5s0ztmUDk5e67u7uoAjI4Dtutxvd3d1enShsAJBKpRgdHZ21GWeG78dkMmF0dBRSqXTGtp5XfYVCgYaGhqAGxuAdDQ0NXt3/gG8JqFarodPpghYUg/fodDqo1Wqv2noEzMzMZAScJ+h0OmRmZnrV1iNgUlISbDYburq6ghYYw8x0dXXBZrMhKSnJq/YeAXk8HlQqFaqqqmgLpqenB7/85S+Rn5+PgwcPBq1q7Wzxm9/8Bvn5+di7dy8tOaeP48svv4RKpfI6xfOh+Yq8vDycPXuWlkCsVitOnToFLpeL/fv3w2g0orW1lRbbc8E//vEP3LlzB/v374dcLvdpBZEvnD17Fnl5ed7v8O2RbbvdTpRKJS2j6w8ePCBvvvkmKS8vJ4QQYjabid1uD9juXFFaWkr+8pe/EEIm/yez2Uy7j1u3bhGlUunT/xR24MCBA1NihoWFobe3F11dXV4/BU0Hm81Gb28v3n33XcTGxuLFF18M2SE0YHIctKSkBCwWC5mZmUHJYv/oo48QHx+PjRs3er/TdxVtaGgg2dnZhKIoWs6q2tpasnr1avL+++8Th8NBxsbGyOjoKC22Z5sHDx6QzZs3k4KCAmK1Wsn4+DgZHBwkFosl4LlUiqJIdna2z9V8H5mzT0xMhFQqDfiVQq/XY2JiAsuXL8eOHTswOjqKvr4+XL58GceOHQvI9mzT3NwMm82GyMhITz5rc3Mz/v3vf+P3v/89KisrA84y0Ol0kEqlSExM9Gm/R65pfD4fL730Ei5dugS1Wu33XNd7772H9evXg8PhoK2tDWq1GhEREXj55Zdx5MgRv2zOFR9++CHkcjmioqLQ3NwMhUIBuVwOsViMkZGRgGcjTCYTLl26hJdeesnn/JpHeiCXy4VKpQJFUairq/M7qNLSUty9exd37tyBRqNBQUEBFi5cGJLlmn/xi1+gt7cXTU1NkEgk+NWvfgWxWIx79+6BoijEx8cHdH+vq6sDRVFQqVQ+T3Y/1mt0dDQyMjKg0+mwcuVKvyZgVSoVVCrVQ7+ZTCa0traira0N9+7dC5mvvcjlcvzxj3986Lf+/n5UVFSAxWLBYrHA5XL5JeLY2Bh0Oh0yMjIQHR3t8/6PzVsTCARYvnw5rFZrQMVIvwuXy0VMTAyKiopCPo9TKBRiw4YN0Gg0iI6O9nthUHNzMywWC9LT0/26FE97yiQmJiI5ORlarRbJycm0rAng8/lISEgImZ73fURGRuLFF18MyIbRaIRWq4VcLscPf/hDv2xMe9rw+Xyo1WoMDQ2hsbHR7yAZpqexsRFDQ0NQq9V+Jwd/b7+Xy+VQqVS4fPkyuru7/XLA8Hi6u7tx+fJlqFQqyOVyv+3MeOHOyclBX18fdDod7Ha7344Y/ofdbodOp0NfXx9ycnICsjWjgFFRUXj99ddRXV2N27dvB20NxdMCIQS3b99GdXU1Xn/99YDXMXr16LR+/XoolUp88MEHfi1PZvgfAwMD+OCDD6BUKmkpa+b1s29xcTE4HA7KysqCuj78SWZiYgJlZWXgcDgoLi6mxabXAkZGRmLv3r1ob2/H6dOnaXH+tHH69Gm0t7dj79699GWn+zpq3tTURIqKimj/kOGTzvnz50lRURFpamqi1a7PAhIy+SHD4uJiotVqaQ3mSUWr1ZLt27cH5cOZfo3Arl69GiMjIzh69ChEIhHWrFlDz+XgCaS2thZHjx7Fjh07sHr1avod+Ku81WolR48eJevWrSNXrlyh86R6Yrhy5QpZt24dOXLkCLFarUHx4fcciEAgwI9//GMYjUYcP34cixYtQmpqakhOF9GNy+XCjRs3cPz4ceTk5KCwsDBolS5YhAT2Zj4+Po6PP/4YN2/exE9/+lMolcqnWkSXy4X//ve/+Oijj5CSkoKdO3cGdeYlYAGByWIGp06dQm1tLQoLC6FWq0N2FW4gOBwO1NTU4F//+hfWrl0b1J43BS0CApNLoj7//HNcvXoV6enpyM3NhUQiocN0SNDf34/z589Dr9dj48aN2Lp1a1CKB34X2gSc4tq1azhx4gTYbDZ27dr1VHxAS6/X469//Svcbjd27NjxSCZCMKFdQGCy/ujp06fR2dmJH/3oR8jKyqKleu58w2w2Q6vV4tKlS3j++eexbdu2Wf9oSlAEBCbzX2pra/HPf/4TfD4fpaWlXi/YCAVu376NsrIyUBSF4uJirFmzhvZqFd4QNAGBycpGXV1dqKiowLVr1zyP1HNxoHRhMplw6tQpfPHFF1CpVNiyZUvAWWmBEFQBp3C5XGhoaMB7770HNpuNN954IyQ/caDT6fDhhx/C7Xbj7bffnh+vTEEZHpgGt9tNPv30U5KRkUEKCwvJlStXiMlkIg6HYzbD8BqHw0FMJhO5cuUKKSwsJBkZGeTTTz+lvSRZIMxKD3wcn3zyCT755BNIJBLk5ORAoVDg2WefRURExJye1S6XC+Pj4xgZGUFLSwu++OIL9Pf3o6ioCEVFRXMW13TMmYDA/6oZTuXbJCcnQ6FQICEhAYsXL6a1bPJMDA8PY2hoCPfu3UNLSwtu3boFHo8HjUaDLVu2zNuPQc+pgFPYbDa0tbWhpqYGHR0dEAqFWLhwIaKjo7F06VLExcVBIpFALBbTUpSWEAKTyYS+vj709PSgp6cHg4ODGB0dhdVqxbJly6BWq/HCCy/MW+GmmBcCfpvBwUG0tbWho6MDXV1dIJNzlgAms6Gjo6MRHR3t6aF8Ph98Ph88Hg88Hg8cDgdOpxN2ux12ux0URYGiKE8PGxwcxODgoKcaLovFAovFQnx8PJYtW4YXXnjBrxT3uWLeCfhtbDYbent70dvbi4GBAYyNjcFiscBiscBqtcJut8PpdMLlcnk2t9sNNpuNsLAwz8bhcMDj8SAUCiESiSASiRAZGYnY2FhIpVJIpdJ539OmY14L+F0cDgfMZjPMZrNHRKfT+dA2JSCHw3lomxIvPDwc4eHhT8xge0gJyPAowR8uZwgqjIAhDiNgiMMIGOIwAoY4jIAhDiNgiMMIGOIwAoY4jIAhDiNgiMMIGOIwAoY4jIAhDiNgiMMIGOIwAoY4jIAhDiNgiMMIGOIwAoY4/wcEDVRm0wZGtQAAAABJRU5ErkJggg==)
Physics-General
Physics-
A beam with wavelength
falls on a stack of partially reflecting planes with separation d. The angle
that the beam should make with the planes so that the beams reflected from successive planes may interfere constructively is (where n =1, 2, ……)
![](data:image/png;base64,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)
A beam with wavelength
falls on a stack of partially reflecting planes with separation d. The angle
that the beam should make with the planes so that the beams reflected from successive planes may interfere constructively is (where n =1, 2, ……)
![](data:image/png;base64,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)
Physics-General
Physics-
Two point sources X and Y emit waves of same frequency and speed but Y lags in phase behind X by 2
l radian. If there is a maximum in direction D the distance XO using n as an integer is given by
![](data:image/png;base64,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)
Two point sources X and Y emit waves of same frequency and speed but Y lags in phase behind X by 2
l radian. If there is a maximum in direction D the distance XO using n as an integer is given by
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALMAAABxCAYAAACeNJJMAAAT+UlEQVR4nO3deWyT9x3H8Xds53QuO87pJA5xEqiTQJICAQIECFCOdKNrWTdN3YQ0saps2vHHpkpDk7aitX9s1doJdWiaKk3axsQ0IZGVjgJJIwgjKcudkBA7zm3HSbATx3F87Y8JayxAaZvER36vf5CM8zxfmw9Pfs/veiJ8Pp8PQQgDkkAXIAjLRYRZCBsizELYEGEWwoYIsxA2RJiFsCHCLIQNWaALEIQnsVqtmM1m3G43AFKplKKioke+V4RZCGrnz5/nT3/6ExKJBKlUysjICH/+858pKytb8l4RZmHVLSwsMDQ0hNvtRqVSoVKpkEge3eI1GAycPHmSF198kejoaN577z2+//3vc/nyZWJjYx96rwizsOo8Hg+jo6O0tLQwNjaGQqHgmWeeobi4GJ1O53+fw+HAZDKxe/duIiMjATh+/DjvvPMOVqtVhFkILI/Hg91ux+12c/fuXS5cuIDVauXgwYP86le/eui9Y2NjqFQqsrOz/Vduo9GISqUiMTFxybFFmIUVNzc3R19fH5988gmtra0sLCygVCrR6XSo1WoqKyv50Y9+xIYNGx76uYGBAWJjY0lISPC/9v7773Po0CHi4uKWnEeEWVgRY2NjNDc3c+vWLW7cuIFKpaK0tJT9+/eTl5eHUqnk9u3b7Nq1i1OnTqHT6ZBKpQ8dY2JigpSUFP9V+Ic//CHNzc1cunTpkeeMEFNAheXgdrsxGo3U19dTX19PW1sbubm5HDx4kNLSUjZu3Eh0dDQxMTFIpVKcTicNDQ0UFRWh0WgeeQP405/+lHfffZeYmBgkEglHjx7lrbfeIiUl5ZE1iDALn5nP58Pr9WK1Wrlz5w4ffvghV65cAaC8vJwvfelL7Nu3j6SkpMcew+FwIJPJ/Dd2y0GEWfhUbrcbh8OB3W5nZGSEO3fu0NDQgNFoJDc3l+rqavbv309WVtaSHobVJMIsLPGgx+H+/ftYLBbGxsbo7u6mpaUFt9tNeXk5e/bsYePGjU+8+q42EWYBr9fL3Nwck5OTjI6OMjk5iclkwmQyMTY2hkwmo7KykrKyMrRa7UO9C8FEhHmN8nq9TExMoNfr0ev1WCwW7HY7DocDiURCRkYG69evp7S0FKVSSVRUVKBL/lQizGuI0+lkcHCQtrY2+vv7sdvtSCQSIiMjycnJIScnh8LCQtLS0h7ZjxvsRJjDmMfjYXJykt7eXpqbm7l79y5yuZyoqCjy8/MpKioiPT2dtLQ0UlJSlvTzhhoR5jAzNzdHd3c3t27dorm5GZfLRWZmJjqdjuzsbNRqNUlJSahUKuRyeaDLXVYizGFgZGSEpqYmLl++TEtLC1lZWWzdupWqqiry8/NJSkpCLpcTHR0d8lffJxFhDkFutxuDwUBdXR1Xrlyhq6uLwsJCjh07xvHjx1EoFEgkEiQSCREREYEud9WIMAcpn8+Hx+PB5XLhdDqxWq10dnbS2NhIfX09LpeLyspKDh8+zO7du4OqvzdQRJiDiM/nw263Y7PZsFgsGI1Genp6aGlpwWazkZOTQ1VVFdXV1WRkZAR0tC0YiTAHmNvtZnp6mrGxMSwWC11dXRiNRkZGRpDL5ZSUlLBjxw50Op24+n4KEeZV5vV6sdlsjI+PYzAYMJvNjI6OYjKZkEqlxMXFUVpaSnl5ORqNhpiYmECXHDJEmFeBw+FgeHiYvr4+BgYGsNlseDweIiIiiImJIT09nfz8fHQ6HSqVKtDlhiwR5hViNpvp6elBr9fT1NSETCZDqVSSlpZGVlYWmZmZ5OXlkZKSIq6+y0SEeZk8WKTZ3t5OS0sLra2tJCYmsnHjRhQKBSUlJaSmppKamopcLn/samTh8xNh/gJmZ2fp7Ozk448/5ubNm7hcLvLy8qisrKS0tNS/5Cc2NlZcfVdBUIf5ypUrvP766wwMDADw2muvcebMmYDWNDw8TGNjIxcvXqS3t5fc3Fz27NnDvn37UKvVxMfHExkZiUwmW1MDFsEgKBe0+nw+Ll68yLvvvss777zDjh07AEhOTmb79u3U1tau+Pm9Xi8ej4fFxUUGBwf58MMP+fvf/47NZmPHjh2cOHGCyspKFArFitYiPL2gvDIPDQ3x85//nJqaGr7+9a/7X3/zzTdxuVycPn16Wc/n8/lwuVzMz88zOzvLzMwM/f393Llzh9u3bwNQU1PDzp07KS0tFf29QSoor8x9fX2kpqZSUVHx0OtWq5X09PRlOceD/l6LxeLv6zUYDNy9e5e5uTnUajVbtmzh5MmTpKenizZvCAjKME9OTuLxeEhOTn7otWvXrnHu3LnPfVyXy4XZbMZoNDI5OYnRaGRiYoKpqSlUKhVFRUXU1taSk5MTtEuDhMcLyjAnJiZis9kwm82kp6czOzvLG2+8gVarZdOmTU99HI/Hg9VqZWhoiL6+PoxGIwsLC0xNTZGUlIRaraampgatVkt2djYyWVB+HcJTCso28/j4OL/5zW8wGAykpaUxNzdHbm4u3/zmN9FqtU/82fn5eQYHB+nq6qK3txe73Y5MJiMhIYGYmBjy8/NJT0+noKAApVK5Sp9IWA1BGWaAe/fu0dvbi8vlAnjipiImk4n29nZu3rxJT08PcXFxqNVq8vLyUKvVpKenk5WVRXJyMtHR0av5MYRVFLRhfhKPx8Pw8DAff/wx//rXv+jt7UWlUlFRUcH27dtJTU0lKSmJ5ORk/9ZOQvgLmTDbbDba2tq4du0aDQ0NuN1uioqK2Lt3r7+/98FImwjv2hSUYfb5fCwsLNDf38/169f53e9+h91up6ioiMOHD3P06FFycnJCcjm8sHICHmav14vT6WRxcZGZmRn/JJ3m5mbsdjtbt25FKpVy7NgxqqqqAlmqEORWPcwPrro2m43p6Wmmp6fp7OxkZGSEzs5OpFIpO3fuZNu2beh0Ov/evB6PJ6xXFgtf3KqE2ev1Mj09zcTEBKOjo0xMTDA+Ps7w8DBOp5OsrCzKysrYtm0bWVlZjzzGxYsXOXDggGhaCI+1YqMELpeLsbEx+vr6uHfvHjabjfn5eRYXF0lKSkKr1fLCCy/4Z5p9mrNnz5KcnEx1dfVKlSyEuGULs8fjYWZmBr1eT1dXF3q9Hp/PR3R0NE6nk+LiYrRaLfn5+SgUis/cZKipqaGurk6EWXisLxRmu93OwMAAra2tdHR04HA4iI+PJyMjg/z8fDQajX9p0BedaVZbW0t7e/sXOoYQ3j5zm3l8fJx///vf1NfXo9frSU5OprCwkPXr15OWluZ/SGF8fPyyboPqdrtxOp1htz+asHyWhHlqaoozZ85QV1fH1772Nb773e8yOzvL1atXuXHjBiaTCa1WS0FBATU1NaSkpCCXy4mLi1vx1RU9PT1ER0eTn5+/YucQQteSML/++uucPXsWm81GVFQUSqWS1NRU9u3bx969e9m+fTsKhYKIiAikUumqLg26cOECN27c4O233161cwqhY0mb+aOPPsJmswH/7ZHYsGED//jHP4JiK6jt27fz9ttviz5n4ZGWTGI4fvw4qampAGRmZnL06NGgCDKAUqlk586djI2NBboUIQgtaWbcv3+fc+fO0dDQwMGDBzlx4sQjn1MsCMEm4HMzPqu5uTk6OzvZvHmzWBkiPCTk5kpOTU3xhz/8AaPRGOhShCATcmGOiooiKiqK1tbWQJciBJklYbZYLBw/fpyJiQkADAYDZ86coampadWLexSFQsFXvvKVp5rPIawtS8KclJTE3Nwcly5dwmaz8de//hWXy0VxcXEg6lsiJiaGqqoqdu7cGehShCCz5A4qMjKSn/zkJ/zgBz8AoLOzk3PnzgVN9xyAVCplYWGBhYUFsTnLGnL58mWampooKyujoqICjUbz0N8/sjfD6/VSUFCAVCqlv79/1Yp9WuPj4/z+978nPz+fb3zjG4EuR1glXq+Xmzdvcvr0aerr68nLy+O1117jlVdeISMj49Gz5i5evIjH4yEuLg6HwxFUV2WA1NRU1Go1g4ODeL1esYA1DD3Y/8/hcGC325mZmaGvr49PPvmEhYUFIiMjycjIQKfTkZKSAjyimdHZ2ckvf/lLGhsbeeONN6irq+Oll15a9Q/zJDKZjHXr1uH1ellYWBCrT8KEz+fDZrMxNTWFyWRieHgYvV5Pd3c38/PzqNVqysvLycjIID4+nh//+MdUV1cTGRkJ/F8zo729nV/84he8+uqr7N27l0uXLnHhwgV++9vfBt0ooNvtxufz+T+IEJrcbjdms5mhoSEmJyfp7+9nYmICi8VCfHw869evZ8uWLaxfv56kpCTGx8c5f/48u3bt4tlnn33oWA9dmScmJnj55ZfZtWsXEomEqqoqDAYDTqdzVT/g05DJZAwPD/t/3Qihwev1YrVaGR4epr+/H6PRiMPhYHJykvj4eFJSUqiurkan05GTk7NklNfhcPD8888/cpu2kBvO/l8XLlzA6XRy7NgxMWk/iDkcDgYHB+nu7vbv/yeRSPzP887PzycjI4PCwkJ/+/dxFhcXH7voI6QnN8TGxtLd3Y3FYhFhDjJms5mOjg6ampro6uoiNjaWrKwsNBqNf/8/tVrt3//vaefFP2n1UkiHubCwMGibQWvNg6dtNTY2+vf/UygUlJWVcfLkSVJTU1EoFCgUihXbQi2kmxlut9s/cCJm0K2+2dlZ2tvbqa+v5/r167jdbgoKCti9ezeVlZUolUpiY2OJi4tble7TkA7zA3a7nZiYGLH6ZIU92P+vvr6ev/3tbwwPD5OXl8ehQ4eora0lNzeXuLi4gD1lK+TD3NnZyfvvv8/3vve9JcObwufj8/lwOp24XC7u379PS0uL/2FFVquVyspKjhw5wpYtW4Jqw/aQ/91cUFDA0NAQ09PTIsyf04PwPnjS1vT0NB0dHQwNDdHe3k5ERAS7du3iZz/7GcXFxUH7tK2QD3NMTAyVlZV4PB4xtP0Z+Hw+//5/Y2Nj/j+HhoZYWFggMzOTTZs28eqrr6JWqwNd7lMJ+WYG/PdGRCKRBLS9FgpcLhfj4+Pcu3ePe/fuYbVamZubY2FhgcTERLRaLWVlZWRnZyOXy0PuuwyLMAO0trZSUlIiejX+h8fj4f79+xgMBrq7uzEYDLjdbiIjI3E4HP79/woKClAoFCH/3YVNmE+dOsWpU6fQ6XSBLiWg5ufnGRgYoK2tjY6ODubn55HL5aSlpZGWlkZmZiYajQaVSvXQcxbDQWj/V/wfSUlJ3LhxY02GeWJigtbWVhoaGtDr9f4mw9atW/37/z0YtAjn7suwCfOhQ4e4fPlyoMtYFQ+etnXt2jWuXr2KxWKhsLCQHTt28PLLL6NSqZDL5cjlciIjI0Ou7ft5hU0zw+v14na7l3Xn0WBis9lobW3ln//8Jx988AEul4vnnnuOPXv2UFFRgVKpRCaTIZFI1kx4/1/YhBn+O6PK6/WG9LpAt9uNy+XCbrej1+u5desWH3zwAWNjY2g0Gmpqajh8+DDZ2dliUcL/CaswX7p0iWvXrvHrX/860KU8Na/Xi91ux2azMTs7S0dHB83NzXR1dREXF0dZWRkHDhygqKgo7G7YlltYhdlut6PVahkcHAzaq7PX68XhcDAzM4PJZMJkMjE0NERbWxvz8/Okp6ezadMmysvLKSwsFCtpPoOwuQEEkMvlVFVVYbPZgirMTqcTs9nMyMgIIyMjTE1NMT09zdTUFHa7nWeeeYYjR46wefNmMjMzA11uyAqrKzNAb28v69atC/gD32dmZvyDFXq9HofD4V+zmJaWhkajQafTkZmZKUYul0nYhdnn8zE4OMi6detW9bwejwez2UxbWxs9PT0MDg4ilUqJjo5Go9GQmZlJbm4uGo2GpKSksO7vDZSwC7PL5eLUqVO89dZbKBSKFT2X3W6nv7/fP0VycXGRxMRENBoNhYWFZGRkoFKpyMrKCvmh4lAQlt9wZGQkt27d4vDhw8t6XKfTidFopLm5mY8++ojx8XFUKhWlpaV8+ctfJjMzE6VSSUJCAgkJCWIG3yoLuzBLJBI2b97M7du3lyXMDoeD27dvc/PmTa5fv8709DTl5eUcOXKEZ599lpSUFP82u2t5wCIYhF0z4/Py+Xz4fD7/vg4NDQ00NzdTV1eH2+2mtraWr371q2zcuDFsRxlDXViG2efzMT8/j1QqfWwX3YPVFfPz81itVoxGI62trTQ2NjI5OUl2dja7d+/mueeeW/WbSeHzCcswz87Ocv78eTweDwcOHCA7O5uoqCg8Hg9WqxWLxYLZbMZgMNDb24teryc2NpaSkhL27NmDVqsN2qVBwuOFZZgnJyf5zne+w9WrV6mpqeHb3/42crmc8fFxTCYTo6OjGI1GiouLqaiooKysjPT0dDHaFuLCMsyDg4NUVlZiNpuJi4vj0KFDbNiwgYiICNatW8emTZvIyckhPT090KUKyyjsejMAIiIi/P26MpmMkpISTpw4QXZ2tujvDWNh2RGanJzMK6+8QmZmJvv37+fFF18kLy9PBDnMhWUzw+v1YrFYGB0dRaFQkJWVJbrT1oCwDLOwNoVlM0NYm8I2zBaLhdOnT/Pmm2/6B1Feeukl/vjHPwa6NGGFhG2YVSoVJSUlDA8PMz4+ztmzZykuLuaFF14IdGnCCgnbMANoNBoUCgV/+ctfMBgMfOtb3xKPKQ5jYR3mvLw8oqKiqKur4/nnnyc3NzfQJQkrKKzDHB8fz9zcHNu2baOqqkr0M4e5sP7XXVxcJCEhAa1WS0JCQqDLEVZYWF+Zp6amcLvdpKWlBboUYRWE9aCJ0+nEZrMhl8vF7j9rQFiHWVhbwrqZIawtIsxC2BBhFsLGfwBtlK1nxaWPEAAAAABJRU5ErkJggg==)
Physics-General
Physics-
Two ideal slits S1 and S2 are at a distance d apart, and illuminated by light of wavelength
passing through an ideal source slit S placed on the line through S2 as shown. The distance between the planes of slits and the source slit is D. A screen is held at a distance D from the plane of the slits. The minimum value of d for which there is darkness at O is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJ8AAACVCAYAAABGgCiGAAANkUlEQVR4nO3dfUxTVx8H8C8UWl5KaYUORgF1IbgJTBhKeNmgmxAci8wFtyl7kckmZiHGaaIze0Ezt2RZZG4zajI2A4hzMFimsqCGKQuOjc2JIFJwskqhGiGMl2JbKL3PH4T70EdEprec8vD7JCb23N5zfhe+nHt723vrxHEcB0IYcGZdAJm7KHyEGQofYYbCR5ih8BFmKHyEGQofYYbCR5ih8BFmKHyEGQofYYbCR6bU2dkJi8Vil74pfGRKn3/+Ofr7++3SN4WPTKm2thZGo9EufbsI2dmpU6dQVlZm0yYSiXDw4EEhh2HujTfeuK3ttddeQ3x8PINqZi9BZ76mpibcvHkTixYt4v99/fXXQg7hEA4fPmyzjVqtFm1tbazLmnUEnfkAIDg4GMuWLRO6W4ciEolstrGpqYlhNbMXHfMRZih8hBkKH2GGwkeYofARZih8hBkKH2GGwkeYofARZih8hBkKH2GGwkeYofARZih8hBkKH2GGwkeYofARZih8hBkKH2GGwmdHRqMR+/fvh1QqhVQqxZEjR2C1WlmX5TAEv4BoLrBardBqtfzjvr6+SZ939epVVFZWoq6uDmKxGOfPn0d3dzf8/PxmqlSHRuG7B4mJifjmm29s2lQq1aTPHRkZwT///IOYmBgsWrRoJsqbNSh896CqqmpazwsICEBqaiqKi4uh1WqRlpYGX19fO1c3e9Axnx3NmzcPmzZtQnp6Oo4dO4ZLly6hvb0dpaWloO/eoZnvnkzndhnNzc24ePEiMjMzERgYCKlUipGREXAch8bGRjz//PMzWbJDopnvHkzndhleXl4oKirCihUr8N5772Hp0qWIjo7G/PnzERgYyKhyx0Iz3z2Yzu0yVCoVDhw4gFu3bsHV1RX+/v6QyWQzWabDo/DZiUgkwsKFC29rP3v2LM6cOQOTyYTNmzczqMxxUPhmmFqthlqtZl2GQ6BjPsIMhY8wQ+EjzFD4CDMUPsIMhY8wQ+EjzFD4CDMUPsIMhY8wQ+EjzFD4CDMUPsIMhY8wQ+EjzFD4CDMUPsLMpJ9ktlqtMBgMAMY+Du7p6TmtziQSCYqKilBUVMS30XUL5E4mDV99fT0yMzPh7u4OlUqF7777blohys3NRW5uruBFOprp3i6DTG3S8G3duhV79+7F008/jZqaGjQ1NSEhIWGma3NY/+Z2GXNFf38/fv31VwBje8vg4GCEhoZOuc6k4ZPJZGhqakJsbCySk5OFr3SWm+7tMuaKzs5OFBQUQKPRwMvLC4ODg1AoFNixYweCg4PvuJ4TN8l9G86ePYtjx47BaDTipZdewuOPP37HDsxmM06ePIkLFy7wbYsXL8aKFSvg5eUFq9WKAwcOoKenh1/+xBNPICEhARKJBP39/di7dy+/zN3dHU899RSWLl0KALh48SKOHz+O0dFRAGO3oEhNTeX/qqqqqnD+/HlYLBYAgFKpRGZmJuRyOSwWC8rLy6HRaPj+g4KCsH79egCAXq/HyZMn0dHRwS+Pj49HSkoKAOCvv/5CZWWlzW517dq1CA0NBcdxaGlpQVlZGb/M09MTr7/+Oj92bW0tampq+OUhISFIS0uDQqEAMHbx+dWrV/nly5Ytg1qthoeHBwBg165d/DJnZ2ckJiYiKSkJANDa2ory8nKMjIwAGLtI/cknn0RUVBT/O6yrq8Pw8DAAQC6XIyMjg79gvaKiwuZ6Yx8fH/6Qqbe3F6dOnUJraysKCgpQV1c35YXu27ZtQ3d3Nz799FPI5XJcu3YNe/bsQXR0NNatW3fH9Sad+dRqNaKjo7Fz504UFhZOGT5nZ2coFAqb3Y6Pjw9EIhH/2N/fHxKJhH8sk8ng5OQEYGyKnrium5sbpFIp/9jDwwMqlYoPn7e3N9zd3fnlcrkcKpWKD59CoeDHdnJygo+Pj03/SqWS/79YLIZSqeT7Hu9/Yi3+/v42L7gmjj1+TDyx1oljy2Qym+W+vr5wcXGxeWwymWy2xdn5vycgJq4rEolsjrvd3NygUqn48Hl6etrUKZPJEBAQYBNOsVjML583b55N/xO328XFhf+5Tfy9TebKlStobm5Gfn4+5HI5vx0BAQHo7e2dcl1wE3R2dnKfffYZ19PTw3Ecx7377rtcdnY2R+auuLg4TqfT3XF5cXExt337ds5gMPBtXV1d3M6dO7mjR49O2bfNzKdUKqHT6bB8+XJYLBY8+uij2LNnz9TpnaCwsBCffPKJTZuLiwsaGhqm3cdsEB4eflvb7t27sWrVKgbVsGUwGCCVSvk9GQC0t7ejsbERa9eunXJdm/CJxWLs3r0b77//PjiOg6urq81u5m56enqQkJCAZ599lm/7f/yFaLValJaW8o8PHz48Z0+3PPLII9iwYQM2btwIDw8PdHR0YMeOHcjKykJISMiU6952zCeRSO66n5+KWCye9knp2WziNrq6ujKshK2kpCTk5OQgLCwMJpMJfn5+KCgoQGJi4l3XpXu12NHg4CD/StrPz+//9q6kW7ZswZYtW/71ehQ+OzGbzTh06BBKSkogFovx3HPPIScnZ07sFaaLwmcnBoMBJSUl+PLLL+Hn5weNRoOBgQEK3wT0qRY7cXZ2hoeHB2pqaiAWi5GUlIQHH3yQdVkOhcJnJ1KpFG+//TZ0Oh0++OADXL58mXVJDod2u3bi6uqKlJQUBAUF4YsvvsCff/6J7u5u/P333xgaGsKbb75pc25sLqKZzw4aGhqwdetW/q0ys9kMFxcXREZGIi0tDX/88QfjCh0Dhc8OIiIi0NDQAG9vbzzzzDOIiopCRkYGvL29odVqJ32HZC6i3a4diEQiVFdX39Z+5coV1NbW4pVXXpnzu1yAZr4ZVVFRAYvFghMnTtA3EIFmvhm1fft21iU4FJr5CDMUPsIMhY8wQ+EjzFD4CDMUPsIMhY8wQ+EjzFD4CDMUPsIMhY8wQ+EjzFD4CDMUPsIMhY8wQ+EjzFD4CDMUPsIMhY8wQ+EjzFD4CDMUPsIMhY8wQ+EjzFD4CDMUPsIMhY8wQ+EjzFD4CDMUPsIMhY8wQ+EjzFD4CDMUPsIMhY8wI/g9mTs6OvD7778L3a1DGR0dtdlGvV7PsJrZS9DwRUREQKPRoLW1lW9bv369kEM4hJdfftlmGxcsWIDQ0FCGFc1OThzdk59MIT4+HqWlpQgMDBS8bzrmI8zM2PdwjI6O4vr167BarQgODhakz5aWFuTn50On0wEAvLy88PHHH+Ohhx4SpP9xAwMDMBqN8PHxgYvL1D+yW7duobGxEbGxsYKMbTKZUFZWhpKSEr4tOzsbK1euhJubmyBjAIDVakV3dzckEgnkcrlg/U5lRsKn1+tRVFQEiUSC7Oxswfq9du0alEolsrOz4eXlhfLycuTm5qK4uBg+Pj6CjePp6YkTJ06go6MDa9aswYIFC257jslkwo8//oiqqiq88847go1tNpvR1dWF9PR0JCUlobm5Gfv374dSqURiYiL/5YL3y8nJCWazGQUFBQgPD8fy5cshlUoF6ftO7LrbHRgYwIcffoj4+Hi0trYiKysLMplMsP4vXbqEBx54AOHh4QgLC8PGjRvh7e2NtrY2wcYAxr5LbfXq1QCA6Oho5OXl4fr16wCA4eFhnD59GitXrsSuXbuQk5ODoKAgwcY2Go1oa2tDVFQUwsLCkJGRgbi4OGg0GlgsFsHGcXJyQmBgIFJTU7Fv3z6sXr0aP/30E8xms2Bj/C+7zXwGgwFqtRotLS0wmUw4cuQIKioq7qvP8PBwnDt3DgDAcRz0ej3UajW/+7nTLjElJQX19fX3NTYAjIyMwGg04qOPPkJpaSm++uortLS0YNu2bejv7wcAqNXq+56Nzpw5g8ceewzA2MzX19eHkJAQAGN/CP/bf2trK2JiYu5rzHFWqxUmkwlWqxU///wzhoeHBel3UpydHTp0iFuyZAn31ltvcTdv3hSs3xs3bnAbNmzg6uvr+bbLly9zsbGxXE9Pj2DjjBsYGOD27dvHPfzww1xOTg7X3t7OL7tw4QL34osvcsnJyVx9fT1ntVoFGdNqtXLV1dXcq6++yrcNDg5y6enp3OnTp7nR0VFBxhk3MjLC1dfXc2vWrOFSUlK477//nouMjOR0Op2g44yz+6vdrKwsnDt3DkuWLEFVVZVg03hXVxekUil/XKLVapGfn48XXnhB0OM9YOx47pdffsGNGzdQUVGBgwcPYuHChfzyyMhIHD16FHl5eTh+/Dj6+voEGZfjOGg0Gn7W6+vrQ3FxMebPn4/FixcLdrw3PpZer8dvv/2GtLQ0lJaWYtWqVQgMDIRIJBJsnIlm9Dzf0NAQLBYLvL2977uvyspKfPvtt4iIiIBCoUBdXR1kMhny8vIEf7XW29uLoaEh+Pv7w9XV9a7P7+zsFOS82OjoKDZv3gyz2YyYmBh0dXVBp9Nh3bp1iIuLu+sr7387ll6vh7u7O3x9ffn2H374AcnJyfD09BRsrHGz9iRzQ0MDqqurYTAYAAAKhQKbNm1iXJWwrFYrCgsL0dHRAQBwc3NDWloaIiIiGFcmjFkbPjL70TschBkKH2GGwkeYofARZih8hBkKH2GGwkeYofARZih8hBkKH2GGwkeYofARZih8hBkKH2GGwkeYofARZv4DEHCYmBwpyDsAAAAASUVORK5CYII=)
Two ideal slits S1 and S2 are at a distance d apart, and illuminated by light of wavelength
passing through an ideal source slit S placed on the line through S2 as shown. The distance between the planes of slits and the source slit is D. A screen is held at a distance D from the plane of the slits. The minimum value of d for which there is darkness at O is
![](data:image/png;base64,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)
Physics-General
Physics-
A monochromatic beam of light falls on YDSE apparatus at some angle (say
) as shown in figure. A thin sheet of glass is inserted in front of the lower slit S2. The central bright fringe (path difference = 0) will be obtained
![](data:image/png;base64,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)
A monochromatic beam of light falls on YDSE apparatus at some angle (say
) as shown in figure. A thin sheet of glass is inserted in front of the lower slit S2. The central bright fringe (path difference = 0) will be obtained
![](data:image/png;base64,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)
Physics-General
Chemistry-
Given
The number of electrons present in l = 2 is
Given
The number of electrons present in l = 2 is
Chemistry-General
Maths-
Plot A(3,-5) on a carteaion plane.
Plot A(3,-5) on a carteaion plane.
Maths-General
Maths-
If
is a non-zero number and
, then f(x) is:
If
is a non-zero number and
, then f(x) is:
Maths-General
Maths-
The integral
equal
The integral
equal
Maths-General
Maths-
If
log
f(x)
then
![equals](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAJCAYAAADU6McMAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAIzv8arAAAABZJREFUeNpjYMAE/4nAQwgMM+8MYQAAvYER7yMcYioAAABJdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1vPj08L21vPjwvbWF0aD4wTGvlAAAAAElFTkSuQmCC)
If
log
f(x)
then
![equals](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAJCAYAAADU6McMAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAIzv8arAAAABZJREFUeNpjYMAE/4nAQwgMM+8MYQAAvYER7yMcYioAAABJdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1vPj08L21vPjwvbWF0aD4wTGvlAAAAAElFTkSuQmCC)
Maths-General
Maths-
An incomplete frequency distribution is given below Median value is 46, the missing frequency is
![](data:image/png;base64,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)
An incomplete frequency distribution is given below Median value is 46, the missing frequency is
![](data:image/png;base64,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)
Maths-General
Physics-
In the adjacent diagram, CP represents a wave front and AO & BP, the corresponding two rays. Find the condition on q for constructive interference at P between the ray BP and reflected ray OP
![](data:image/png;base64,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)
In the adjacent diagram, CP represents a wave front and AO & BP, the corresponding two rays. Find the condition on q for constructive interference at P between the ray BP and reflected ray OP
![](data:image/png;base64,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)
Physics-General
Physics-
A thin slice is cut out of a glass cylinder along a plane parallel to its axis. The slice is placed on a flat glass plate as shown. The observed interference fringes from this combination shall be
![](data:image/png;base64,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)
A thin slice is cut out of a glass cylinder along a plane parallel to its axis. The slice is placed on a flat glass plate as shown. The observed interference fringes from this combination shall be
![](data:image/png;base64,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)
Physics-General