Physics-
General
Easy
Question
.A rod of glass (
= 1.5) and of square cross section is bent into the shape shown in the figure. A parallel beam of light falls on the plane flat surface A as shown in the figure. If d is the width of a side and R is the radius of circular arc then for what maximum value of
light entering the glass slab through surface A emerges from the glass through B
![](data:image/png;base64,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)
- 1.5
- 0.5
- 1.3
- None of these
The correct answer is: 0.5
Related Questions to study
physics-
An optical fibre consists of core of
surrounded by a cladding of
. A beam of light enters from air at an angle
with axis of fibre. The highest
for which ray can be travelled through fibre is
![](data:image/png;base64,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)
An optical fibre consists of core of
surrounded by a cladding of
. A beam of light enters from air at an angle
with axis of fibre. The highest
for which ray can be travelled through fibre is
![](data:image/png;base64,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)
physics-General
physics-
A prism having an apex angle
and refraction index 1.5 is located in front of a vertical plane mirror as shown in figure. Through what total angle is the ray deviated after reflection from the mirror
![](data:image/png;base64,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)
A prism having an apex angle
and refraction index 1.5 is located in front of a vertical plane mirror as shown in figure. Through what total angle is the ray deviated after reflection from the mirror
![](data:image/png;base64,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)
physics-General
physics-
In steel the young's modulus and the strain at the breaking point are
and 0.15 respectively the stress at the breaking point for steel is therefore
In steel the young's modulus and the strain at the breaking point are
and 0.15 respectively the stress at the breaking point for steel is therefore
physics-General
physics-
Hail stones fall from certain height If only 2% of the mass of the hail stone melt on reaching the ground,, the height from which they fall is ( g = 10 ms-2, L = 80 cal/gm and J = 4.2J/cal)
Hail stones fall from certain height If only 2% of the mass of the hail stone melt on reaching the ground,, the height from which they fall is ( g = 10 ms-2, L = 80 cal/gm and J = 4.2J/cal)
physics-General
maths-
=
=
maths-General
physics-
A fish rising vertically up towards the surface of water with speed 3
observes a bird diving vertically down towards it with speed 9
. The actual velocity of bird is
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RTcIqFRSfWQxsjz7J0csL8mFzlZQQlE1Qypiy1Uiyu6LDFFJSHQlolRUlZUCc1UiLXrBcWoOIas8CUUh6RgPXkbnOV0RCNZpX7eBG8wjN6MQ2ko6D81j/rAErKMmHxMFncZQDFYmmtdDr66KPThgAu65DlpQwUnHK98Y1vrN72trelKZ9nPvOZSTHtyuEec3kpj/FqHBXTpkjyM741DtYhxC6hEqVzj8TiesuB/J2kYV4XrQnLi0lxlwEaNiWjMHbUaPAiw5R5CJSFInJJI1FAz3upF0UUlLJDiAL7rU8RLZgwvSOoZWw8xlq6T/42M9hcwA0X5RYMwwdrXFKmCfNjUtxlALeSteWiUmDurWWJszRyz5iOsXpKQtv41xsDuOEUqAth+cNCdlnmIXiO5fWseeWPfOQj1b//+7+nRSH4GfIkJsyPSXFHQINsa5Rxve23UDRzsBTNeNWWOEosAmycWgr0jVG52lxUQSdjXxFe1s8Ji2h3dQgUjYU1LvW/JYwscBvffaD4rLtn0dNhiFJ7neZpp52WOin8KStextKfMIwpOFUADY9ryRWUgNUBDdN4NcasFCJ+850ForCf+cxnUgPX2AV1RGQpW7x6ssTyoWcJIwXBh0UU3GSRZgshTNlQZlM0XdFe/IoKWwWFZ/njJXgeAj7D9UfHAg6vF/E8F9x88znnnJMU23g7PwzdZ0k5JwxjUtwCUFqWzHjuP/7jP5KVpHQU0EIHY03jVi6rxhrznZREBJbSUljWkSvrXToiv2ha/2usOdSgKS1FEYxyAoWpIEpjbGtbnzXK8hP9pSw6A/w1EZ2G5ZOUnlXMeYYhXvyOjqkl88n48fYCUXPKy8NQTiu45KGzITN8xRg9MJTXhHZMilsAikthKKDTHygFhTPO02i5iZ/85CdT0IYVpAhAWS2eoKCsIGuogf/iL/5iOrHCmFAkmNWj1EONmDKwlBSd4rJy1hDLU7QZLTRYUtFibmwOv5nSCSvIVQ5Fwyt4Jp/bbePJtfAY8K1zwhtF1iFZrUU26JKPTx0F3iUdnPx0NMqQW/u2/Casj0lxC6BhaYismbEqBaW4rA0lsFuHYsdKItZIo2SBrFJyv3OGNWARWG6tkxaNTbnSQAmGFkOA6SH0dA4smU7Dwghvjmc1XXciRd/iCPnITwfA4tpjK8jEKnoODVYxUiCUyieZRCdg2aMos7OnHM0aZ1C94AUvSHPPOhJRcC4+70RnZnxvV5M8KX+sl54UtwyT4hZAY6IEAkPGbxo8K8dSUkaBGMqioVLmUEDjUEr8lKc8JT1jDCqARMkoOAul0VK4oeNf8OB3issqUhyN3/rlUFy0/OYe+XYpgevhMrPMsY75sssuS0EzPPIMdAwUWzl4HeHm6pRypaZ0vJBI4aqjj64xMd4oKcurkxNg01nIy8ovIE+0JgxjUtxCaKTcPtMulIxLqNFTZNeNM61ECjcUKEdYQIom2qqxsrYUn5Jp3JKG3aVogbBy7sNPU3EpVn7PENzHfdex2A5oDC3oJLGG3FpuMEVjJSXKzb12XfJ/ntxrXCsQx8pKXHLKHh2KzoASU2geh/LjgeVuuvcT2jFtMiiEhifY8sEPfjApjS1tVh4JVvnNGmFWFUJpQrTx/ZhjjkmbBd75znemfay5K1uiaDnked5551VveMMbqpe+9KXpALdwN8cCnyyqcSdlpbgU0F5eyhnjUhaYcrPQFD7y83x8covdHyd08CrIhUL6XyeGdx2F7+4xJvZd59XndUx4AJPiFkJj05i9CFpjNs40fjOO5R4b12nMfWhT3FkUDRZTcQOaArqsoOkcwwCWN9xln37zf7jPudL6pHiUlBJSynCZldWQgEcSlt5vENdgHv43JkyKWwhiEmgSWY61xlxUY1Xb4lgVjbUPD3fFDShrpPx7/G+szwJT3hzy5gpTynzI0PYZ/0P+/4QyTCunRiDcPVMf5m+N01heCxCGlHYlgSLFWFnSwVBISTlF2JWZi2tcmifXucPui2c8LwU9tEN5J6WdDZPijoDGx5oY6wmsmPoQpAo3b2MBZWsqdK6gkzIuPSbF7UC4h3mKBRUCKaK4XGTjtwkTlhuT4naAohrHiY4KyFBaUVaroKwNtic1XyY4YcJyYlLcDhi/mnc98cQT0zSQFVMWC7CwLK3lhdzCCRMeCkyK2wLW1lSH1UPHHnts9Sd/8ifV8ccfn6wrF9nifmO8ydpOeKgwKW4HRD4dQSpZUCD4YmG/NcdWQ01KO+GhxKS4LaCUpjMsTXQUqfnX3/3d300L6bnHlHrChIcSUwvsAOVkWR1xaqGFUyOs9BljafOIdBtcN60UK5AmTCjFpLg9oKQUONJYpbWu17JBytkGq58sn7RskvJOmFCKSXGXCBTXCivrm+2oMbUE0RlQWtsB7aKhvL5PmFCKSXGXCBSUq21Ns/XN9uJSTtdFpCn0v/zLvySLHCcmTphQiklxlwgU0dpmymuJpLOhnKls1405YdsBzRP73XrnjW3Z5IT5MCnuEoJLbLO94JYN+CyvTffOID7llFPSiQ8W5dvV494JE0oxtZYlBKvrbCenY1Bg+1m5zk6IsDLLS6ltUpjc5AljMSnuEoJCsqQWcXj/DyU1P8yFdlSLkx6nxRwTZsGkuMsA87+OurE5gaLGm/UEpSYXecIsmFrNMsAY1vpmyyUdEuel0466mTcgFZZ6stgbHybFXQawqqyusa7D0J2rvBhj29i0PkWkNz486MypWO3jXTdW88Tp9hMWB/b1Oq/JKRrGupnoR0Nn4Picv//7v09jZa8gocDz0Jyw9FA/6klH/jM/8zP3XR2P9RTXKp6/+7u/S+f/Whzg2uSKzQ8yFEm2tNFOo3mVDD1Rah2sRuAsrKmeHv6wCMfQyeGC3uwwK9Y75dFxnBYKONza1MWE+UGhuLXeFXT22WenXUZeYUKRZ0HQs2TSOc+2G5paYoWnpZP9KO3cSjvVEno5Lf/rtB0Ob9g0K9ZTXAviuXMsQzA1xFxpIbswtvBjUFpRsFR5oKsT9La/E044oXr1q1+dAlQizJStJN9mHqy2lVdvetObqhe/+MXVX/zFXyRas+w0Wgr5zyv3xa439+jsSuIB7tUBDm38IG/0+njtouU7L2lWrKe4rAAXWUMLhoaEmJNokOtFKX1AdwxtQLeEdmBsHiX8q1znD1t04U1/ljqaFjr00EOr5z3veWms27V7CNrK4Dt3y/nOv/7rv14dfPDB6ZQO18cobtBt0m/DGNmgV0Iz0KQ97/NNoEV51EMMV/rup4w6RnVD2aHJH3rqDU2fbfTcp/7RaZ557X6HDs6KQcVtY6iJnKExCNpLlU8JzUDOw2Lmo+LtEnJ2lU0F3qVjQYbD5n7rt34rHRzepbh98tGwLKP8tV/7taS4XgHlviErkWOMfKBELn08tyHuy2mP4SvPp4s/ikjRTjrppOrzn/98OgCQnNruR8sqN3PtDpr3lopm/USe3htlGatDBHNDB36Xr9e1mPrzTmSxiOg0pEVXXAvh9SSObHFavuhl89R6wChf3dTGM57xjHQQdoNcJ6LwDmKztc1b3NoanR5LFNb8p0PaKIJK6INn0Pb6S7tyrA9uCjaH3lAFqSzrh0saP1qi7nhXBsOLJl/usUrKpwZzxhlnpO19KtTpGr/3e7+XVlCRYVuZ3KeRffWrX01Bw7wO9OLiEF6JQva//Mu/nPh38uSQfPBDRjY/kI/6xX+bfPDmEAHvSeLa9ckm6NrGyBtAv0vu6ofcNWz8x7t98e6sr6g37bHteSitN3L026mnnpriN+j63kXXwhgr3bx9EX9diqvj9Ab+OBy/CbKIJa+8q6hnz0pLoriYJUAvbDY9pGJzeEwBKOuBBx6Yxm0qOBgbgkIBYXIfo/C5MNGiqHbP6LGMCylCl4UKqCgQGUebApuKiTxz4FVP6E17RxxxRHofUFsn1QRalFBkUBk00q7GoFzxQi3ejMZmQQa5eSG1TQjK1JSbhqlT+NjHPpY6CFN16EcSSKQkGoCphcMPPzxFK9saUQ7PkpHgFk9Ax6DjzOUTvBiHa8Rce50MRewCujwB9D7+8Y8nSyTy3SZ3sgq5azvPfOYz03X56uCi3sitr94E+dSbzz7e3O93cpZ3U9Y5yEa7i+h/GzyPFlm31R2QB97D7fYd3CstiavsM167SJHbGkNUFNePculR2grQBs+6l0XxTh4V3GYp3Med1PNplAQxlEcISM/KUimHyuqCSnLsql5fQ23jow0qDO/KQNmDr8jfp8bH2nK/uMzeP/uqV70q5aNDZCm5Um0dnrLqHCinZ+UH6GoIxs2m7nQAb3vb2+5fC13CPxp5/XY1evWrc9bIhqw5mpL2E1a8S+7Kija56/C1obg+pt7IEW8l9UYJJTz2AQ9oDSm4+kGvrWMJeB6dvByuSUuiuOHiYKqvoPF4SWNpwrORB/Tlg36D1UGgF6kEUVGl90NfHhTCFJDkPTte4Gyca2zL4no7O0ux7777JlevOQzI5dOkr5Pkjv7Kr/xKOjL2T//0T9M9odylGKpfwEdp/fbx3IY22vF8KWapt4cSeJXmUdxB6YRgu1IwMQtC0EGjjX6kWVBCN08wS+XneUSeEmuJnjXKXEFWhXLyIMy9vuxlL0vuHgWP/HPk8gn6kUf8n98zC5q029IY2l08d6U22qXPRoJZ6m0lo0hxS9I8aKPXlmZBG52uNAuaNPIGxbV0SiTrylXWuOIeysu1FXRjbVkYv7Uhp5+naLTg+yxo0uxKY9FGoyu1oe2+rrScUIdDaTlQ7o9MGA3WlML6bAY5VLBAGytsDNmnuGOwXA1nY0LUizG5OjNM6UoCiotVl30YHOO2wfWSQX5YnlkKMTToB3SHAghdwDv6Q3nMUwZAP6KK//zP/5w2Bfz+7/9+itJGlBjtMfl4RgMSvbUAw8opY1xueJ880M+DJCXAf7PT6YJ8S+sjZD/UhqCUbmmdjuET0KUXDviLl8C1PUtOgmSCnKbOuui7Li1pcKoN7hGm7wqDg0JorNEDjYEGJn+R2q6Ghjd56OUoxhhERUQZ5NcGfEcvSym6ytoH/MvLs5Y7/tM//VP11re+NU0DaQCQ51OiJPh3r+CUBRgHHXRQ9Y53vCPl0Raccr881IXUVa9tiHroq2tAM5dVF9xH3mhKQ50VvqMd9ckGXbJWp+Td1W7Qwx966JbUqXKJ6h933HHprDDKi2+0Ar5ri6b2fuEXfiHN25JdG33XpGVVXIU1jWHdrZC/xue+uDfImXg2TSHiaQFFabSTUAV1Pve5z90/Wd4mJA3EFJS9rRYH4LsE+NQAvOf2s5/9bJonjSBSIMqAb3OYhxxySJqKGmpkOUImFkmobAsKvKLTFI5xrUPiQiamRCxCiHygLx90lV89vOUtb0mN0Ika11577Xrz1XgmU/Vh2kl9qMOuhh0IGvIQ/Tbn2zYXHnzix1j+5S9/eZqb7apvsveb+j399NOTEvjeRldSB2RjDp9suugqo7l0dWoNtzbs+bxeyULcgXJZF2BBj2tSH/BGH8wOsLoxddlsMxTc4g101a97Qj45omxLGlVug4KoAMLCrOT/5nf35YUrhWc8m9OM/5vfZ6FPaDn9ZsrLoJzujefGwrMSemiF3Jr5uEdZxpbH/V11Edfi/yjHmDw800arec1naRn87l58e66Lblx3b/Deh6CZ04j/8+/ucW8o0BAooOdM25mDt+Dj53/+56s3vOEN9yff7YmOzlcHM0t7KcVoi+ua3/S+eu223ioqJlyzEqHnwBKXp8+Vkgdh6unlMUZInlXOcKvaygD4Zp3kobJnARkpB3CVbcP7jd/4jTQVFNfH5oN/98YmA66yl5JB0/NwL8jDM9IYqGtyUg4y7pKzfCgGd1G9DAFNqat+AU2JbNAdakdooYnnIVc5hlhj202kLoSM+ujG78s+xnWdAPoKAATZpRRDQH+ooiAa1FiUlgHtrkZQAvQ1EI0vD0697nWvu3+MC/Lpa8Q50KSAglNcZe6vTQaUvk0e7g/6Y+ujVE4wpgyl9QvoldZBCd0+PofK2Ve20md9SsvuKsuUILkDfWlsI8nh2TaazdQnyD6UlmEepYU8n6DlU9JJ5vnMU5agk9NsXpulPkrlJI0pQ2n9SuiWooRuG586vfBIuhLPrsubcN3vbc/laVbPrYleixu911BPQljIdFVaSS8YGKLVhrFWQRrbiIN+iSyatFUWq2u541FHHZXcWhY3poOgtAzBu0YQFte2vj/+4z9O+WiYXUC7pOEsZR20yacPaEp9mLVOAb+etXpNIDTc9ybcRzEFy0z14Cnk45PO2KjR97w6M28f74oSwJoVg4obFR0FzBHXJMw2fwfX0MgbTBudgN5wTAWgFXzmdNryiGvoyye/vw9RhmhAOS0IOq6h3eTfs0OKC3kebfxD0B+ruOj1yalZhjHyAfei71PK+c9pS6UW1L0hk5xGIL82C88Q8jj55JPTdE9Ez10PoK3+BJ3MYghEGfrQFff5tNfXq2VsKhG7iHoE/LHIVtG99rWvTVOB6NlcMStaFTd2i9j5ImRv6kQIvAkFtipI+FuAxCohCJKYt0PEjhj7em1ra2T3IOiNTL/EweElFUwAplxMWUSovq3y5OtevZzDyfFM6CqlD+4hC0riZV2mL5oNJGgrv2kZ+0PjOqDh9y7F9Tu6tiHaaG/OsAm0yNoySXOEppScXxUnYAwproaDtv2j6lXjapOTOjD9EnXQZ8EhaJD9aaedlhp+21Y+95mKsUb7+c9//uBuHvdLpna0QVM92mbOM5koM7lbD276kVUs7Rgg+LRt8qyzzkptVD45//iUjxVu2qd8yFM+7vNpby5eWW0yy5/Hp+/4NHWJhu+mM2dFp+L6pLAnnHBCarQaUy408J3roJKd6NCcu1JYtD796U+nt9VpMF2VhZY1uzaY25+pAQ01GmB5NMgPfehDSfjNOdkAntxrDg99HU0Ivw/u0ciddGCPqC12+Go2ID2wikDbXKZrUVZy6FJcFeh3nc8nPvGJ++eum0BPY6dUhx12WOocKG6cgDGkuBr0l770pWRVWIVmB4d+1MELX/jCdPicOtAO+uAZZdBwtRWf6qDZcPHGRTSXbNrENs0+2iEXc+AOC7BmoNnZoKt+WEIyZ8lEi0vaTRvkiT66bfCbOpVyPsD35rUm8uflsSRRZZ8ERfFi6qcNhMsSUGCNMwdGCZHSq8yhRqASLEbQs/m/S4A55IFP4wt8hrK0wb2UlwLgeUjQEMLGv43rytDky3eVrvzkoAw5yKjP4kqsOllTqK6Ghw7+KYCkQy21uPKQXwyD1Gdb+fHJMo6pAzC2y9tKG238oY33Uto8NnTx3KUwaOFXvaqHUp5zoJN3Nl1Au62NeT5SFzwbz/tcsukgBSGUvgIFIyqrQep+BI2+QkHQGtNjeqaEz4D70W8Tfh80OmmoYsgB/fw+z/UpLviMPPoQsmZBx45x/U5OQ2UYWweAZmlbQdv/fXyAe9DE9xDPZCKtBOBXWrLpIMTD8nYlCh4V0QW/u6/t+TwFrTFQoSV8Roqeeyw0iqEy+N19Qw2yDcqg7G1089Rm8UuAJ+UuKcPYOoAxbQVKZOSeMXLfmDBsoibcDw1J71/iPUx4+EBdqTN115fmqdfSPBar3UyKW4iwcqUu+XJiFgu8sSBkQ2nUXVcKxXL/LPIMpW2jHWkxFbd3jBuZGJ/JtKvBRmE9O9Zl8Ry6kUdXwdyHNldrrKvrWfTlM6uriTeRTScQirw6K0p4X4Wgh2+RZfc1EeX7yEc+Ur3vfe/rnMcdAtrRAIxxrVX2JgM7XeJNBuQTqbSc0bCG6hdN8puFZ7S7nlOf6hbtIYQsc3oxbpaakL+pNmcgm9UQRIN4NupO0M+siKkega7SdowP9zpPzO6hCOzmspQHPgQuTUNqO74v+nRQHpzCVIwl2gQDCo4RoXgNagw8K0/RSJ9dSokXikHAGsJY4B/9WZ7Ho7KZmvjN3/zNNI9qz6X5OPTwjDZF9NkE3jU20z3HHHNMWqts+qzrLOMuoC3qrE7IwlZBnQB+3v72t9/fWEJO6qQEGrM0VL9oSmNA7kG70dTuh/rQbqS8wbeBDNDzGW3F8/jyfFOerpHT+9///jTPKkItj7gveBLp9k4np2XaCI/vEpALXTHlaTrMkcaezWWPT/VvDt4BCqYMfV/0BRihuIibAjF/qdGyOJjIheNxQsOU+TmHSJf2VugQuvliZwfrFQkWzWYe5hRNsmvwsd+zwXorVJJk/7C9pa9//etbzwduVmQgriuj85MpnblmZbX/VMOIMvzt3/5tivT6nvMPePBmPXj3u9+d5kkpegnQ8jzaziu2r9ezOjt7cE1t2W/rHmc2W+CgcfAM1EWXnPBJDmQTc9TqH52AZ7UDjdmWNnOlUFLH6PBQjj/++NSgmwsz0PadpeM1oE2B2joQMqAMlJCCqEvtFG8sl3lcZ0s353E9J1/H0JrS81uzboAsWFq01HWXAWkCLeUw986yq5OmvKOceLNckqfmuXmWPG72Z7aVZMCwHk3FyExBKZNexPykhqFBRPJdz2E5FxfA9zFQAIWNA7lVXE4/8lBICifhoymcIaCvbJTNXGJUTAhVo/AJ0TlJ+W8qX6+tA5FURNyncVBM1s6CgJx/32OPJitr+sbB65SkBOhDzCXrLCxgcOCc84fJx15ReZCTRSZPetKTEn99DRBd5bdaSB2QS5xfncved/Wrw4zGVip//JrHx4vOJZcL2j51CurFJ/m10Q4567DQpGjairZnWkXb87y6yp/3f9SJMjAwPptJuUKhov7HwBwypW+jH9fwoM7Qx5eOYlYUjXGhcVsrxhY2x1LT7wKayksB/K9xqUANQIelJyUTQmfdWA/b6LoOMW8rB1osg1VL//AP/5BePTLLGBfQ9wyrEEfX6Ai89Es+uYUdQ7tE/jCWXyihPS+vs/D1UAH/0pJv69Mg9Fp6+q7k97BYY0HoGnZfHn5rc0FLgbfm83GN6/nXf/3X1Tvf+c70ShGNX5ldd0bUu971ruoLX/hCErR3mlpv21TaKEMb75Hm4R/wm8vJ/1GGyMO1sfmU1q/7xiJ4bqMZaQztkHPO76y8rWQUaZqGzOqwwl3J731uWR8oADeyLw+/uaetty0B3prP+991LiIrKypoM4T7NDiNRNm5wayjsSSXTnSwyYfvQzJCdx5EGSIfn3E98nANz2OwlPUbPLfRjDSGZ3LOZTD2+Q0Fs5nIBjRwvfxQr62nnNXilPTcEh5K8wnFNR4UeBEAM74Hz6PFygpGGUO5X0OZpQHnwJ8UkdAm/2MtZt6JLIX1LK1faSxtKOGZvLSBNpTw5veu54cQba8vD7+Nrbd5sCiKG1ZJ0MB4sS0ZL/a9BGoIelXBmTbaeZIP6zgmnwicRDQxrIRgkzKZ9vHuH6AkuaKMhWdj4byAWZN/+ZElHsY2ArQFEQWDmnTz5Hf3lZYDL0P1GwltnV8pbfe5f4h21yYVzwuszfp8CbQFddaXxzz1NguKg1Nt8Lve0jSRbW/cTA0yfy7IiwTbQ/rKV74yRdkIoxR6PFMhxp+mLFS0PNry4c6K2DqMTQTa9UYRH4QoA7p22rC6Au16UdvgKK+T+0JxZwH6emzTGKaCRCBFQ3UuUQY8+p8b7j1DpkZ0Jm2NzX06mXyTgeCURuPNgI4+xTcZN2XEKoig2rpnXzI6fZ2c+wXobBQ3XadtQE4X5O1ePJtX9lJoZe6jrV7Vpb3U9vLKJ5cJoKsueEUOfreflTwjPwplKsueb7w1Fcd3ZRTV1fZE3+XR1yYC6MjLEMpGe0f5Mgq55Y56E+HGmzwMu/o6Cc9ISx6c6gOmCUcPrschSIVrJr+5x72zgLBVMjpt9KX4LfIpqRxQORTeWFd5RI8pBeGraHNv7lkM4Al/Td4jsR7zyAnPaPTJiRwpdal83KcjR7eNXp7cE402V6A+BM+ez9tP/r/fo7Nv0s15a2t/ZOH3vk6kD55TJ2j0tW98lMp0XsxlcQMaWaQuxtHSU0UaC7QJMM8j+Gt+p2Ty8L2kDMYnevs//MM/THmwsLwH85YWSgzNhw4BP6yPbX2mg377t3/7/gUYTf58x7tnunh3Pbe4rCeL6zn1pgxk0pRLIOogZDQEdNCU4nv+XP7dZy7/IXg26tb/Eng2p4teyCSn23w+rpU+X4K87XUBzTyPPuBLmsfiLoriuo/bMlRZCo5+I8siEEg0iCFEI+sTdA6Ka7z5N3/zN+k0DS42oVoCt99++6U80ZsV+A7FtR9XB2Hpm166CbLBd59FJOOm4sZ+XFAXffWALvqlZSqtX0Ab3bCOQ0Av6raPdsikrU7JNsrehpCjtlfaJnIod5S/CyX1FvC79JC6yoAJQuFOcMO60jyuhMbg+Ta6zTS2gvCkUozPNB6BDFHkGCPPUtl9UI4uWbk+tnPDcyRyGqoHv4/piErrV3JPqdIC2u4fok1mXfWAt7ZnIqEtzVqPnhtqe+iPrbd5sCiKuxKhkeulw4r4JHSBBTs4BEME1Py2FJWB5nJV8saOqGtWk3VuS34bsvp9CKvclUf81me1x2CjVVxKw+qE8ugxHdgm4mtJo8jrUintYiFvZPH/rA1vQ0bUNYvIcrYlv5W4uV1gldHoyiN+C6s/bz0VjXH1RDGGcC1/JL5LhDOLO4JGWL8uzJOPZ6K3Uzk+bRiwh9IUlbJ6y5vdHUL6ph1MQYxx+SDyaMpI2fS6XkFiB9Gs+3HdG3kYl9vw8OY3vzntrLFcM8pHNmN4D9n38ZLLXxspBbroez5oBPLv6lRqwu9Bw2cbgo5yo5HnQV7WoZtuyt8umcP9ZhV4WXa3lZ4wCniSp2CmmIMgp2fzPNDHv6GY9uWkTt+XdD8uJpxpiyG+vNubTLlP5NVCfPNZY4CWII1Nzibvo1G0CVc+dlfYwUK4vjfYbwVaymDsav6UUprvtGHAnKlAjzOTzZ06tlUenimhDe5lsc2dkp0y5HLCpwZkLvDEE0+s/uiP/igprqmFZjm74D7yIadQeFsJ3/ve96ajWn/pl37p/nzIhoyUs68MaGjsZCNp1DnfgaCh87GjhQxLI+3m9fEc0zE57ciL/A1RTLvJI+fZ79od5bPIoU2h3K/ceIsdOEFDB6eD/uhHP9p7fK9nBSLts6ZQ2n8JKKD6Nneufq0H0BaaeeBPMMrrQnW0+CLHWdGruIgTvMZmgUXffly91eGHH54inG09ZxvQUSANUMTVgdQqpw3ywY+AkdPg5aOShxqPPAjXRmcWyin0Fjk4df7YY49NSnDAAQck3vfee+/kKo8Fvlhwe2X17JQAvyGn+CRLsGlhlv24FkBEA4y5SVvyKJEykYfGb4mmjsGWuT7LQfbqmWzUcduZ0RBl0bhtZ2Tlhzabu18iDzw7y7lp7dANy2MKzn7a5n5csnXY+oc//OG0yELn5blA8KbedGBeeWkaLyyv3yi+WQOfzfLFPfig8DqQZudRAnxpu+TZpiPqT1nwGbGT2CI5C3oVV8VqIBqKaRLXm0yBgurlWS97QccUmsA0dI1Sx9A2RRJwr4ZpCaJ88FeSF37t9KFcXBUN3QumuTeEHS5S7PMdwz/gi1La3G3DuF49h0pzjzK658///M9T5zNGcYF8uGMWiGiYLNknP/nJ1JkZl7tPGXznjlG0vk4UXxqy+pU07qZVBPJwTcOOaTIKVtJBU1jbD3ls4U3lQBctUXxBQS5r3hnjUbtz+Lu3JITXl8P34I3yaiNBw29oaKM+m2ULuM8zeGxr40NQv9qjPLqALpmRuf/nmQ4qGuNiCGN9hcEIhtoqvg8h2MhjCO7H45h8PBMVp1wgL9fQQCuuzwP0Qk65WCMvFj7OnJrl6JqQk0+9t07gjW98YxqTt505VQJ8oinhpcl7Dr+pZ7LquieHe5Q9eO6C+6JBN+G3vNxt8gqeZ22Dyw28Sks+j0sQlEWFdSUCw8xYgYXQQ3mGEj7G5uPeZsOIBhjzb4uBKAOaOb/xf56/MoyFZ9C4++4Fq4B2yC/P02+l8nFf0PJsTqeZWDtJOUv4D97w3EYvkrzRbENOI5dlnoJn97i3tOwrGUWKSxgqdyiVVGYX2uh1pVnyiTIE8jLNw3eOoNeXAtG4XCvNP+7z4f8Hvj9QluigSmlC/nxbit95YoYCa9asuT8WMaQkQ7QjDfG7WHQ2FBQp7liEe9SX3DMrwnUaSvP0vCV5hFvcBWNY40bWIEc8p5GZghJgkh93ukk7b4h33LGuHqdfUyvOZfV494qkSKwvxL3Gksa+FDin15WGyhBwz9q1N1UXXXRJdf75F1ZXXHFNXS5Ta+11XUq3icWQew703D/L883n2pJ7HgoUjXFL4X7PeZ77ogdsA2HmkdAGC51AH00KEfsru55FV6AmdvyUwr0sFosiUNbmwslTGUTTRQmVpY0PQSSBN/cI/YvcHnnkkemcKONS00febud5WxFN3ygfHoxhBZcEXRawSXXVVddU5533zZrm92rZbVcr0g3VUUcdWb3iFa+sfud33p5kIkIvemsbW99cdJSBnB6cz/rYdFOdwia10n6n+spXzq07m+9Xu+/++GrvvZ9al22r+g7WcMF9DrryVr9DU1KBkLvoLLm38Z3TxnOX3AN+E0fI20pJvYF2jBeybGvHnqO05IYWOZbCs9KSB6dKobGJ/Nl3GnsX20ChTL0I0GjQTYvUBYJyr32y5s1MX7Qplp7QPKZIq6kR3xvF7IR7WUBHlopkkkXbsyrdtIN9v8rSdNPITvnJQfTaPdxMimvRh6kaEVf05amRKx8a5Gi6xd5OU1ULVnWTWraXV6ed9uXqa187v24oq+v7Nqvl8Nnq4IOfV/PxknR0KdlKZgG4tBpuG/+uUQBTEl7W7CDwvnEmrFlzZS2Tb9Zluvy+9mHT/jW1YtxYd9R3pHvcqzGTjci5CLc2NQQy4C1YCGNOXR00+fad3NE05+7sry6eo62Yr/eKV/PA6ih4U2+i2G31RrlNQWkD6k5H0uTFfYyCuV9Hw5rSck/zvjbEffMobu/xrFFhpXC/hmLaRY+pYShcJKF+jcrUEYU1pUOQbT1aGwgUXZXKBVV4z4dljTz0gFap2PxOoJ4rhXuVnzWkeHrS4DsviykMymcqydxfs8LIggLq7VW+qRxKbFO2BoU+OTnDihzkEfyzJo4u1UB1QEH61ltvS8syv/WtC2urt7auIxvKNbRNalqX17QvqC3t7qlBqgdeD+uS850nnYWpE/kv5LN+GSgU3HzzTck9vuKK62rZO7HittolvyZ1RvJet+6OWu7bJXpoRf2SW5NuG+RF7oYO5C7fNp5D7mSjHXXRjrbC49FW0NdWPG+RRl+9AR54TCxusx1Hkj/lQ0u9jYV6nhWLanGBEqJB8fuEqkdUOWOUCtBEW6U0e8sAviVKJ58x5XBv0PfZ1angW1IGeTQRPLAiTojkIVhgomGycjoUJ4E4oJ2ikXeUxXM57ZCRueILLvhmdcopp9Yu8RX1la3qMm5RW4Tv1x3EdbWSbFEdeujrkjXyXJuMgq8A2qtWyUdMgHwXrntGPUq33HJzcsEvuODbtSXSYXKPLd64o1boG2o53VorwyOr/fffpy7LXnWn+ajU2DVmZVjI7oE80W6rN7wOyT1kE3XbB3nkbQWasm1D8LdU7TjoP2xc5cCQQAOEMgtC+ENQtK4GMAT0S8rfVIwm/MbtOvroo6tPfepTadyk0XFN7aW1IIQVaKPTvOa758877xvVSSedUp177jdrC/eEmt7q2rreWlvXe6qDDjqgOuSQF9WNYvekPJ6RQHkiLZBdaEALKd1Sw3SKMd5dyb1cs+aS2qpeUrveFrBYh7t13fHsWbus29b1tzA1dfvtIsx31Aq7dd0hPap28x9XW/6FQ8C33dZLvvvLFcj568MDPK9Powm02tpKFw+BpeAlEPc/bFzlQF6YvjQP2ui1pVnRRqstDSEsA8trTB5jWuc9eU0IdzWUa4i2Brj11lvVlnXbWoHX1vQurRXsnlo5Hlm7qdw+9xgnczsdj3NrTfee5C7jwferrrq6VsBran7W1jRur/m5tXYJr0uu+3XXXV+7wI4f+kH6/eKLL6nOOefraUx96aVX1gp6d01ruzqvHVO56uZd012wNnfddXcqm2j3DTd4jQyruGVN6/bavb68Hp+vSR0Y1/Wuu+6s6WyR+PIs3kK5lLtNFs00BrM+3/ZcW5oV87jKS6K4E9aH8a6GrfFyjePgM9fHeB4Uc8stt0oN/fbbb6sV5cr6qgj0znUj4uZvUivLHSnyfNNN1kZ7Ydk29fUfpjHp+ed/q7ael9TKK07gtSk31hZ1Ta2k36k7gqtqpbu1vn5breDX19b2qprfq2slvrnOb8u6w9ip9g52SfQWFG2h0S64natqhbyndqudLcbCr647FZHw69JyU0sqfYqM3333PYnG5puvSm54RJK1vc024+mUu50rGUs2xlU5obx9ShwkZumB0B2Th8odi+jNu+jPwz9EGfr4J8/Y2EBpRYy5kngrKVOeh8Rqfe1r36iOPPIDtZLeltzX7bbbIbnNd9/tFIrba8u4VfXkJz8hBel0EKzqhRdelKZzNtlki3Q/WqLCt912c/2/d+DsVFv17Wue7kltQYDLJ+g0Fizs+nEDcgvXWZm46dK6dbfV7enauhP5Xoo8a6wCcnvvvU/tbWxfdxLXpvy33HJVCjjhdZ4G3YeQXfzfxNh2EPTaaAWCVk4vvi+Zq5wjZ6CZAvn/JYj7FTyn15bmRV8egfz/UjSfb0vyXnAtF46PtUhfI807xlKgB6ZFKJex5403UsRV1U47PbpWum3vU6wFK3jvvY4wvbO2pLcky+n/e++lgKvTPciJTPu+ahVLvqpWPqd2WlZp3tMJDg4k9wqV7kPJlYNSr169RcoXXe6zRRoLkW+Hhm9TK7OdMVsmq3zttTdU3/72whiaC6+TWL16VRoOKF8T8mimUoTcAnn9RArk/w8BD006kSA+27AkFtenRQjmGo1LWIwuGKOYgtEYhdr7mA1EgU1vmPvlLvVZHr23qQY9cowLh6CRccHsBBLa1yG1gVLFDhUh/lLXNcpAPjEnK4LZBD40RHmYppJKp8HkgaY5WbIyTeEantXPmWeeVTf6G2t6u9Sy2Tsp2O2331rX17r76S/Uh80Eq+v7tqmt29apzlyPuopP9a6ufca1EuCp/ps+F+RC+fHwwJAr8ouEP5HptWuNe+2VflQ99t+/OvDAZydvxHP4XIhM91s1MuqqN/KXlzoSZwi3vAl5mb4yvSPqv1CO9WUQ13kw6kW0vy1v9+mozSKYQVBnUXZp0aPKGCEIc3S2jdnHaj6yTXgep1QWDNhjaiN6ScOPntvkuAOtzXPKuysPympM6FUhlFceDdbXA/eQwnr3rqmY2A+b54EG4VLaI444Iq1g0vOXIBqEbWtWRZmn1SiibIC+BkFZvbfWYgdlcX2If/CsuUSLAchKYwnFYtE233zrurN8Ut0InlZb3F3re2+rretVdX090IlEXiLBO+64SxoPr169ZS0HZYgTFhd49gz6Pkv4g4X7uMqCSurFjMFdtSdwXd1ZhjwWFFp+Ibctttiylv0j7nPVv1ftuuv21QEH7FvX836psYOym5MOfiR04hMohI5RZ5jLPkDxtRdt2eHrZIhefu8CP1ukDkMdWbiDfpdCyt/+YPVOT8gs+AG/k6s5Z3vHLfgw9xvtVloSxdV49ehhrbosrscJhsW1IoXAGyRboZCEpQfUE8pLofLCB9ATgbQowfiI5XJtKB8Vw0JZRWT9LovrmaaAKbjJeCuaKFhbb9yGKIO5WXIy0d/sfNDHh4alUViUIL8h3gNooalx6NzIScO7+OJvV1deeX3dWHeqO829am/kMXWn4UDw6+u6u6nOkyzvI3IfRHrvvturOJ0cYoHIlrUS71h3JDvX/D1wagQXWbkWvi9cW1DsB2T+YP4tdV1Xe0031vwZyzpF8q7aE7kydSTK4HkdxyMfuVOKSmvUXGoewrp1a+vfqmqfffao9t13n9SGdKbkdvrpp6e3KKi/LuXQLiialXLaCaXMgY62pY4EB3UEytekpR1zXxkGhsjvDy7nAlz3PJ7Mb7ftY/acfJVDvfNGl9ziRnAKIzIPNG5dD8FQXoA+xL1DeQQ9vzUFXgL3S220IehFYx1DPy9DH/34reuePngGfXVjWsnKKQv9r76aB2H8aTzINb2l7tU3q13OHevGbBHE6rpMC/l5fu3am+uO8sra5b46RZ2NY405d999z1rxd6vzubdWNCfyr6vvF73eOnUyGiUFdG3bbbdP7vammy6sqApQ2ksvtfngklpx7kwKeeON3r1kk8W6Wgab1gq7Q83X7ikv4+VaMnX+m9VewNZ1h7x7td9+T0+NmfKFTC1/5GkwHm2dIsXV2T7nOc9Jrz5hNZuKC+4NmoG8LnK62sEQcno5nSbc4/f8nvi+pIobBcoL1kSQaJAqQgl9WIw8oC2feWgHhsoxL/8SpbUp4cwzz60b8i21Um2XlOmmm7xR/ua6AT+ievrTn1Y9+9n7pl6eK0oZZamBG4s7f4m1vuiiC2tP57u1MotI71GP6Qw/7q2/X19bJHPNq5Ml3nrr7eo2cWethNfWyri6Vjpvbt81KeYDZdkkKenFF59Xj7e/m+5jWa+//qq6c7msVuob0j0U9zGP2b3aZZfH1vwIZG1eK/KOacXV/vs/IzXkvLMBSpS7yU2EbJSPEnXJH+K3vnvG1NOs9PwvLaniTnjooR4kbtnJJ3+mOuOMM+tx4Z21oj66du22qRXANM429VDlqbW7uXft6j2xtloLc71RvZ5Xp8bghg/cbuumRXUtrPjhDxeWJq5eLfDFFTSFZdzK2i9cd23dOpv2FzoDVtQ6aRCIMp41P7vtto7MubvuHL5eW2GbTdYmXnbYYcd6qLBHzd9TksXdfvttq7322jPxzDXlSuIzb5K+Dymk+6XcUvbd30RDBYpRkkcb7eB3UtwNHOpBsvzw1FM/X5199rm1Fbuttnw719byMXWj3622mLulQIjxnnhDNI68etFgmUCw0RhNuuyyK2prfmNSkN1227Wmu0OtiDZCWEl1c90JbFHTf3S6tmbN5bXSX1Xff0OKhZgNMFbdZhubMB5RdyQ71Z+mfO6urfCVdVuyaeDW+p5NE4929Oy5517Jshr324ywyy67prFgDFXmhXLmyj5E01BgLPo6E9cjz7Yy+S4tu+K6rgF0/Q7IYjrvBccg6A/lQeiNIhQBXcKXuoBulGNsHkP8j6WNjnoRyFuz5rspSCVK+cQnLgS87MhxD1qRZ9Bvq4O4z292KVnuyHo+7nGPr5V/l9QOzK2uXfv9NOaMUx252ZYviqBbDeX7lltuW3caj687jB1reqLXq2oaO9U87VD/xvW1ImqzxKPgoqkRY9EcTTkF3yWyaUKHImAkGNlW9oBgFBkaI+tESuuB627Yog7Iqe055RXlRlunlMP90rIrLsbd16c0FILrQzh9ytEGwo48ugSPN3QFT+QxBiH8KENXHuirAHn47CprE+iRXx9tPOCbjNAuAZ5Nj0ixSAZvGkZEqiOhL6EfLmgTyuc6WpTS/5QUP76LviqH7xq2snCzudtc7Ysvvqi64oor6wa6fZpmMt5eu/Z7SVn32GNhFZStfsFT1Jfk/5xfKZDL3f+lcC+ZfPnLX07HCZuxiHYc5c/zobRODDXFKCZAvkNQZ7wVU0vxTl55Rh7okxOl1UnZqSWPuA5R3mVVXI1AgMNWNW5WVHgAOd9N2XCLrBLiuilcCVSYxkEoTjHES9AM+K5SuYXmRs29lggd0FHBKtWGfBPosaihCZPxhG9u2uKPkjKQD55t4zMm1fjb+I/pIZFQ1qyENhrk43kWD/+sZXNhid/dZ2rD3LeIK3n1dSKRwJSJaRif2gF6AfeQn0/WxLrrnXfeNdG3BtnSyVWrHKO7S5JZRIjRsS9ZlFi7UV+RXyDyoVCU3gu70dAmS4AeGsbujsI1TefZZj7gGt4stiAf3kCXfHJE+9Q5WHsdU0s58MCjsIjDZhL1HNfjU1pWxcWQBQe2qKlYjcZ9cW+QU6mYdnI7JS4Vvh6NMJwK/8UvfjG5JAQTeUSh8aHgDtF2SDd+S4AG4VMq84OEH4tLmmWwUCJOOLAijHI1xLUeNGA8H3/88SkCbAzombAc/lcejdO8t95e56AhD9EGvHve+cpkFGcNhzKhIblPHcTb4clrqHMI2eiYLYrxybrHbxA8ks2znvXMmvbL7uvUuLULDditAlchUzR18DoaUzv5YpugC6EAOnodgleRGgN7dgyUkzyDXptcI1+8aXNNXroQtNDP20OeR5N21H3AvdKyKq5repzmGCLuRc7/GFYBKtj/jWw64VlCMX7Q6PETz+Z5EIbGaIkiJSilD+hokMrps9n7By3WM05NkFdJHujg2Skd5IR2XA+go1JZXfyXjq8AHTJH21iurw7wH3XQbDx9yGWDdtCD4BNtHgn+1W8T7ot7PauR6yDVKZ7z3wJxDT1ytyhGRxjXS6GsUd4m3838pCjjGEQeTXr5d3TbaEe+yz7GBQ1vCEhHoxqLplC6MIvQAyV5zFqGpaQNaMtjCLPkgXakPqAdqQSlPMM8sulCV3lK+S9BM4822iGzh0RxhyoV2pguRQl9WOo8ZqW/0uWzFPyX8gzzyKYLOo3oUNvox3UdxiydhucjD2jmkdPniS2p4kbqAxJNJksRtPvyCNpLnccs9EtoB+bJo5R+/lmCEv7n4Tv/bEMfzyXPQx+NgN+0bS57n1JSOq66ocBYoBt5dPGiLLxV+ZgWmxVFihtoMuM31+JzLOLZvucj/1no5+ijE79Fhcb3xQa68iilH7x29eA5+srXBfd6Tup6ru+3PuS043sTfb8FhvLPaUSeTVAUcnf06xlnnJGWflKu/F7PUlaRYNFssyHk7r4SUHZBN7u4Itoc9ZZDPEbgzTSRwOesaFXc2B1EgTER0z5NKLigjekMUzKlR3FCVIgFBaY25NkmJEIXYLG7QvSVgPp6zBwEJ4hjGsK0SURImxAAERk132ZaoLSydG54t3Ona48n4EOwxRSHSLJpiBI5KXusTza10Rdd1egE0WxP7NvZEsCTAKOdUw6F65INXk27mdoTLCqRDdoCUM551pjVQZMX37UdkW+7siiMa5LnNXzl7qs3cK92ZxGK9kEOzXogR3znistV9WzAM9pBKK4ZETIsbWuhuKLxobielyDKT3GdsU1xTdXNik7FVbC+/bge891cod7JwWdC9wraINmKEFrffly0CMQ2Ly8DNrWkIUWkdggqYqn24+KfTEwpnXrqqUmx8JvTBvTdq4HaeubIGg2tpEFo2DqG44477kGNoQm0RKbNSWoQz33uc9N9XXn4jVzNYZvWM7VEifOGHHWo0/TKTlMzOh51NATKI3psSsyUngh7UzYUKeSu7XhFq3ukqDflNh/bVm/gXuWw1NP7de15bWsfIQsdgLqVd1sbDbmgIY2FfOWhQ0c/8kDX/z4l5VO36mtWdLrKPjVMc7UE3xWswgQrZZKZVWmQ60QUhjWntBolgeZ5+F1jUsE6BQqs9yzNw7MEyaqzXG0KiZaGZspEw/SpkoeATzLCO4uVT3HkiDJoCOaCYzF9SRmUVaPFf9RJWx2gpcHpEAQ8NOS43gU85fWL/zbaeDXlo5FR4hLZoK296BgoINpNBM/kTSY8HtekqDeGQ72h1Ya4V6elbUhodvHoNzKNcubycS3y1w6lsUBDHnhq5pF/R5uSs+6zYnCMi4khINEgMwpLnUcJfWh2HCVwf+kzs5ahlH8Ym8dSyd79aJfIpkvRxpYbnZL83NMsT9u1eRB8BM2cvk9pnqjyoGQWszBtKBH0vCgpg3uWg5dZsJR1sFS0x8iy696xvJXm2UZ3seWAXk5zsekPWtwJEyYsLkKpl9TiTpgw4eGHVsVdbLM+YcKExUVvVHlylSdMWBpQu0WNKovMmTYpCftPmDBhdjRPxhiD9RQXWi5NmDBhkTGPR9uquBMmTHh4Y4oqT5iwAjEp7oQJKxCT4k6YsAIxKe6ECSsQk+JOmLACMSnuhAkrEJPiTpiwAjEp7oQJKxCT4k6YsAIxKe6ECSsQk+JOmLACMSnuhAkrEJPiTpiwAjEp7oQJKw5V9f8P8NBTno7gigAAAABJRU5ErkJggg==)
A fish rising vertically up towards the surface of water with speed 3
observes a bird diving vertically down towards it with speed 9
. The actual velocity of bird is
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)
physics-General
physics-
The image of point P when viewed from top of the slabs will be
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)
The image of point P when viewed from top of the slabs will be
![](data:image/png;base64,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)
physics-General
physics-
A cube of side 2 m is placed in front of a concave mirror focal length 1m with its face P at a distance of 3 m and face Q at a distance of 5 m from the mirror. The distance between the images of face P and Q and height of images of P and Q are
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)
A cube of side 2 m is placed in front of a concave mirror focal length 1m with its face P at a distance of 3 m and face Q at a distance of 5 m from the mirror. The distance between the images of face P and Q and height of images of P and Q are
![](data:image/png;base64,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)
physics-General
physics-
Two transparent slabs have the same thickness as shown. One is made of material A of refractive index 1.5. The other is made of two materials B and C with thickness in the ratio 1 : 2. The refractive index of C is 1.6. If a monochromatic parallel beam passing through the slabs has the same number of waves inside both, the refractive index of B is
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)
Two transparent slabs have the same thickness as shown. One is made of material A of refractive index 1.5. The other is made of two materials B and C with thickness in the ratio 1 : 2. The refractive index of C is 1.6. If a monochromatic parallel beam passing through the slabs has the same number of waves inside both, the refractive index of B is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAcgAAACACAYAAACP3flfAAAgAElEQVR4nO2d6W9b2X33v3chL3eKFClSC7XLkiyPZFu2Y9meGduTOHZnc5pBmqYFGiBFUARtgPRFX/VFgf4FLfq6QNA2fVEY9Sxx6pnxPh7L8iJb8qKNkqzF1GaKpLhe3uV54efc0LLk8SKJl+T5AMYkvOLlucs533N+22FUVVVBoVAoFArlGdh8N4BCoVAoFD1CBZJCoVAolDWgAkmhUCgUyhpQgaRQKBQKZQ2oQFIoFAqFsgZUICkUCoVCWQM+3w2gUCgUVVUhiiKy2Sx4/umwJIoi0uk0AEAQBJhMJgiCkM9mbjiqqiKbzSKZTEIURbAsC0EQYLVawbKvtn5RFAWiKEKSJPA8D47jkEgkIIoiGIaB0WiExWIBz/NgGGaTrqi4oAJJoVDWRFEUbbB91cE6F1mWkc1mwXEcOI5b81ySJGFkZARjY2NobGyEyWTC4OAgxsfHkc1mUV9fj927d6O5ufmNBnhZlqGqKjiOy7tIqKqKZDKJ2dlZ3L59G+Pj4zAYDGhtbcWRI0dgsVjAcZzWbkmSAABGo3HNtmcyGdy7dw8LCwuoqamBxWLBjRs3MD09DUVRUFdXhwMHDsDv98NkMm3ptRYqVCApFMpzqKqK5eVlzMzMYNu2bTCbza91HkVREIvFMDg4CJfLhZaWlucGZ0VREI1G8eWXX2JychLZbBYTExNYWFiA2WzG7Owsrl27hmAwiF/84hfw+XzaKvNViUQiWFpaQkNDAwwGQ95EUlVVSJKEa9eu4dq1a0gkEpBlGVNTU7h69So4jsOBAwfgcrm0+zM0NASj0Yjdu3c/125FUbC0tIT/+Z//QUVFBRYXFzE7O4twOAyO4zA/P4+vv/4aS0tL+PDDD9HQ0JCX6y40qA+SQqE8hyzLePjwIf793/8d4XD4ueOiKCIUCmFhYQGiKK57HkmSMDU1hfPnz2NqagqKojxznJgYv/nmG8zNzWH//v146623UFNTg48++gi/+tWv8Ld/+7dwu90YGhpCJBJ57hy5ZLNZzM/P48mTJ9pqMZfR0VGcOnUKiUTimWOyLGN+fh7T09OQJOm5720GDMOA53kEAgH86Ec/wq9//Wv8+Z//OYxGIy5evIgnT54AeCp+g4OD+PbbbxEKhdY8VzQaxe3btxGNRrF3715s374dgUAAP/7xj/F3f/d3+MUvfgGj0Yj79+8jEols+rXloqoqVlZW8OjRI6TTae35KYqCUCiE2dnZF75D+YSuIAsUWZYBACzL5t1URCk+VFXF48ePceXKFfzqV7+CqqpQFAXZbBZzc3OYnZ1FLBZDY2MjnE7nmudQFAWjo6M4c+YMbty4AY7jIAgCWltbUVVVBY7jIEkS5ufn0dvbi8rKSuzbtw+1tbUIBAKaiVeSJFRUVMBut8Nut3+nuffJkycIhUKwWCyoq6uD2+2G0WgEy7KYn5/HzZs3kclktHOHw2FMTk4imUzC5/PB5/Npps3NgmEYsCyLffv2obu7G4IggGVZ1NbWoqamBqlUCpIkIZPJYGRkBJ999hlCoRAymQycTidaWlpQUVEBjuMgyzJmZ2fR19eH9vZ2NDY2ory8HK2treA4DslkEoqiwO/3o729HQ6HY1OvbS3S6TTGx8cxNjaG6upqVFZWwmQy4fbt24jFYviTP/mTvK7o16OkBJLMCvX2EF4FVVUhyzLC4TAURYHX6930zpwvFEUBwzAF/bwKGRL0IcsyRFHEkydPMDMzgwsXLiAYDOLAgQPo7u4GwzDIZrNrnqO3txenTp1CMBjEo0ePMDQ0hJ/97Gfa4J5KpdDb24tkMon29nY0NTWBZVltdTEwMIAbN25AEAQcO3YMVVVVALDu7wGAw+HAlStXcOvWLezevRt79uxBfX09nE4nstksstksZFnG0tISpqen0dvbi76+PvzgBz/Azp07wTCM5u/bDBiG0XyxFotF+1ySJKTTaWQyGTQ1NcFisSCZTOLKlSv4/PPPkUwmMTo6ipGREfzVX/0VXC4XGIZBKpVCf38/0uk09uzZA4/Ho5mxp6encevWLQwODsLtduODDz5AIBDQfpOssjd7xWwymeBwOPDb3/4WNpsNhw4dQmdnJ/r6+pBIJHDkyJG8CPd3UTICqaoqUqkUZFmG2Wx+bR9GvpFlGU+ePMEXX3wBVVXxl3/5l0W5ipRlGZFIBBaLBSaTqeiurxAgk5NYLIbe3l58/vnn+OqrryBJEn74wx+iqqoKQ0NDa67oeJ5HR0cHjh49iocPH6KlpQW/+c1vUFdXB5vNBqPRCEmSsLi4iK+++gqHDh3Czp07tXPNz8/j7Nmz+OKLLyCKIvbt26cF1oyOjmJpaWnddsuyjEAggL6+PvzLv/wLysvLceLECRw7dgzRaBTxeBy9vb24desWzp8/j3A4jBMnTqCsrGzd69koVFWF1WpFQ0MDnE7nM781Pz+Pe/fuIZlM4v3339cmER999BE+/fRTdHV14Ze//CVsNhscDod2D0OhEAYHB9HR0YEdO3bAaDRCURTMzc3h9OnTuHz5MrLZLHbu3Km1gfx3cnIS8/PzLzRbb9R1i6KI1tZW/O53v8Pp06fR09ODqakpNDc3b+pvvwmFqRKvAYmSm52dRU9PD9xu93N/Q/wSZrNZl6syIhpXrlzBtWvXEAgEMDg4iJqaGrjd7oIMgc+duNhsNk0I4/E4Tp8+jd27d6Orq4sKZJ5gGAZLS0v4v//7P1y9ehWjo6MwmUz49ttvsbKysqafDwAsFgv+4R/+AaIowmw2o6OjQzP9kfMuLCzg6tWrsNvt6Orq0o4BgMfjwfHjx/HWW28hGAzi4sWLuHLlChobG3Hu3Dlcv3593T7KMIxmmpybm0MoFEIikUAqlYLZbEYikcD//u//Ynh4GOPj4xBFEf39/VpQ0GaupmRZhtvtxt/8zd9oKyZZlpFMJvHtt99iamoKJ0+eRCAQgCAIyGazWFlZgdvtRltbG+rr67XrVhQF4XAYn3/+Oex2O3bv3g2Hw6GtwCsqKvDxxx/jwIEDuH//Pr7++mtcunQJx44dQyAQgKqquH79Or7++ust8bmSYKOpqSlEIhEkk0kkk0nU1dVt+m+/LiUlkMPDw7hx4wY6Ojo0gZRlGalUCrFYDKFQSAuz1uOqTFEU3L9/H7/73e8wMjKCe/fuYXx8HD/60Y9w9OjRghXIubk5LCwsoLq6Gi6XC2azGfF4HKdOnYLJZMJbb721qbN6yovx+/346U9/CovFopknDx48iKNHj8JgMKz5bAwGA8rKyjAwMABBENDU1KSlJxA3wfT0NC5duoSDBw+irq4OBoNB+77NZkNzczMaGhrQ1NSE+fl5DA8PIxQKoaenB62treu2l0wkz507p/nydu/ejSNHjiAYDMJms+FP//RP0d/fj9///vdYWVnBrl278M4777yUj/NNUBQFDocDXq8XwB8niAMDA3j06BH27NmDt99+W7OaEJ9vTU0NKisrNcuXqqrIZDJ49OgRzpw5g7/+679GY2Oj1naWZWGz2dDW1oaWlhb4/X5MTEzg5s2b6OzsRCAQAMMw6O7uRmVlpRbTsFmQFeTDhw+xuLgIQRCwY8cOLCws6HIxQigZgVQUBfF4HJFIRPNfkOiqmzdv4ve//z3a29vx3nvv6TaRluM41NTUoKamBul0GidPnkRbWxvq6uoKNq+JYRgYDAaMjo7it7/9LU6ePIn9+/drwRvxeDzfTSxpiEmwq6sLzc3N+Pjjj3HlyhVMTk4iHo/jxIkTsNlsa35XlmU8fvwYoijC7/c/M7ivrKzgzp07qKysxP79+2G1WrU+l7uaYVlWE5THjx8jk8mgo6PjhZPBpaUlXLhwAbFYDCdPnsSBAwewfft2VFdXIxqNwuFw4O2330ZPTw9++MMf4ubNm+jr69OE/3VTWl4Wcp1EAMfGxnDu3DnU19fje9/7Hlwul/a3oihicnISdrsdZWVlAP54fxYXF3Ht2jXs2bMHO3bseM6Hp6qq5u+02+2oqqpCJBLR/KsMw2Dbtm1oaWnZ1OsF/hikc+7cOezevRu7du3Cnj178N///d9aMQg9UjICCfwxciybzeLJkye4fPmyFnDQ1dWFrq4uWK1WxGKxvLaT5/l1K2mYTCbY7Xa0tbXhnXfeQV1dnVY1A/hj8nE2m90Ss8lGIAgCOjo6MDk5iX/7t3/D2bNn0dHRgVgspsuJSilB/JA8z8Pr9cLpdKK6uhpTU1OQJAlLS0sQBOE5wSKBHyQNxOVy4ezZs4jFYvjkk08wMjKCW7du4YMPPkBTU9Mz1XPu3r2Lu3fvorm5GTt27MDMzAzu37+P8vJyVFRUrLtqJcI7MTEBk8mEn//852hsbNQiJsnEl6xg3W43nE4nGhoasGvXLiiKgpmZmS3LkSR+wm+++QaiKKK7uxsAcO/ePXzzzTd4//33YbFY8PjxYxiNRgDAl19+iYWFBRw7dgyjo6O4cuUK/vEf/xGNjY3aebPZLHp7e3H37l10d3ejvr4ejx49wu3bt7Fz505UVFRof7sVQXAkqHB2dhbvvvsuampqEAgEYDabYbPZkMlkdDtWlZRAEpaWlvDll1/i7NmzGBgYQCaT0cw/Foslrw9LVVXNpJXrkwOedqiVlRUwDIOmpibNHJmLoig4d+4cBgcHdfvSrYZlWaRSKYyMjOD69eu4e/cubty4gYWFhXw3rWRhGAaVlZU4dOiQ9h5yHAez2YxAIAC/369NYNYbYBmGgcvlQn9/P/7jP/4DHo8H3d3dWmBOIBBAS0vLc+JqMBgQDodx5swZXL58GclkEiaTCQcOHIDX632hCZTjOHi9Xvj9flRUVGjpHaSNPp8Pu3fvhtFoBM/zWgk7r9erWZe2ypyvKAoePHiAvr4+LC8vaxWLIpEI0uk0jh49CrvdjvLycty6dQsLCwuoq6tDV1cXJiYmcOvWLbS1taGpqem5cYDjOCwtLeH06dMwmUxIp9Nwu904dOjQMwK5VZjNZs0HbbPZwPO8VlZQrxY7oEQFUhRFxGIxLRdKlmXE43GEw+EtT6JdjSzL4HleS1bOfXFkWUYsFoOiKKisrATHcchkMs/MqFVVRTgcxtzcHGRZ1u2LlwvDMEgmk5iZmdGeRywW27KEbcrzcByHtrY2/PznP3/G5EeOkZxGYO20KSKoO3fuxPLyMu7cuYOjR4+iu7sb/f396O3txd///d8/s/IBnorjtm3bkE6n0dvbi2AwCJfLhXfeeQd79ux5ofmTYRgtQnS9djU3N8Nutz9joWFZFkajUfMLbkWfIStsk8mEtrY2zM3NYXFxEQBgtVrx9ttvo6ysDGazGT09PYhEIlhcXER9fT16enrwn//5nxgfH8cvf/lLmM3mZ9rM8zza29uhqiquXLmCubk5eDwevPPOO+jo6HgmtWQr4DgObrdbi/sgbWVZVit7l+t/1hMlJ5CqqqK6uhq/+c1vcOTIEZw/fx4PHz6E1+vFJ598go6ODs2ckS/ITH31TJakeESjUXg8HiwtLeHixYt47733tJBxjuPwZ3/2Z/jxj39cMOISj8cxODiIL774ApWVlejq6kJTUxP+6Z/+qSAEvhhhGAYejwcul+uF0aIvgmVZtLa2orGxEZIkQRAEiKIIp9OJ999/H9u2bXuurzEMA7PZjN27d6Ozs1Ob5BkMhpceRF/UrvLycrjd7jVrsW7lu0bM1j09PdizZ88zQTK518uyLLZv347m5mathqwkSaitrYXVakVTU9Nzz4dhGDidTuzduxc7d+6EoihgWRYGgyFv6W1r3VuO43Dw4EGIovictUwvlJRAklkbz/Ow2Wzo7u5Gc3MzJiYmcOPGDSwtLUEURZSVlemimPFqWJbVVohnz56Fz+fTKpzkOv43O8hgIyF5XIuLi2htbcWJEyfQ0dGBdDqdd3N3qcOy7BubG1cLG8mPbGxsXHdQJDtPbMZEVU8Rky97nbn3kIxh3/ve9wBg3VgFsirO92T/RTAMo0XT6jUvXZ+t2gRYloXdbofb7dYc8BaLBWazGR6PBzt27MDc3BxisRjKy8t11ZEIHMchEAigtrYWAwMD6Orqwq9//Ws4nU7difnLQAo2S5KEhoYGtLS0aAnQoVAINTU1sNvt+W4mZQPhOA4Wi2XLzXzFAvH56rHqzKvCMIzuU9MYtUSm6NlsFkNDQwiFQti7d+9zfhUAms9Lr05jIijxeBypVAqCIMDlchV0jiApVg3gmdluLBbTqofs2LGjoK+RQqEUJiUjkKqqIp1OQ1VVLYJtrb8B9F2rlZhUc3OcCp217rskSYjFYrBYLBAEQdfPhEKhFCclI5CUwqIQJisUCqW4KRkfJKWwoMK49WzFrg5bCbkeuiOMvtHz86ECSaFQoCgK0uk00um0bgerl4VUy8lms0in0+A4DiaTqajEv1gwGo0wm800D1JPkH3uRFHc9G1eKBuH0WiEIAhF4XfVCyTwa2RkBKFQCNlstuAFEnjax1OplCb49J3RD+T9MplMqK+vR319vW4DI0tOICVJQjQaxczMDOLxOBXIAkEQBPj9/i3Z7b1UIKvGqakpPHjwQNuEGyhME3fuPoeiKGrbqNGVo74gudrl5eXw+Xybujn1m1JSAqmqKqLRKEZHRzE8PKzt/0jRN4IgoKKiQtsRntTNpbw+REQmJydx48YNpFIpAIUpjARiWhVFEel0GpIk6dq/VYqQ8nperxc+nw8Wi0XXz6dkBFKWZSwvL2NsbAzBYBDpdJrm1ukcsnm1z+fTigbouTMVEqlUCo8ePcLg4KCutxt6Fcgeiel0umDqEJcaFosFPp8PXq+3IPzCJSGQxKw6OjqKiYkJunIsEEwmE/x+PyorK7WyZHTQezPICmt8fBz3799HNBotir5A4gqIOBbDNRUTDMPAZDKhoqICHo9H2xBa7/256AWS7C4+Pj6OYDCIZDJJ/Y46hxRr9vv9qK6upuXmNghSLGN2dhb37t0rKnHMZrOaz5GiL4g4ErNqIRX+KHqBjEajGBsbw+joKJLJZFEMCMWO0WiEz+dDbW0trdm5gWSzWUxOTuLmzZtF0xdWB+RQ9IWqqloMgc/ng8lkyneTXomiFUhZlpFKpTA2Nobx8XEkk0ktWophGOp/1CHEge/3+1FTU/PMPnfFMJjnC7JyDAaDuH//PhKJRL6btCHkmlWpVUh/kJWjz+dDRUWF7guTr0VRqgTZAHl4eBjj4+NaOsfS0hLGx8chimLBLPFLBVLZn5hVbTYbncRsACSVY2xsDA8fPkQkEimKyQb1OeqbXJ9jRUWF5nMsNIpuBamqKpLJJEZHR/Hw4UMkk0nt2OzsLKampuDxeOhegzqCFJD3+/0IBALaHnf0+bwZxPw4MTGBwcFBrKysaKXXCpnVqRwUfZGbylFZWVmQK0dCUQmkqqqIx+MYGhp6xudIBoRMJoN4PE59FTpCURSYzWb4/X7N50jy2ShvhiiKGBsbw7179xCPx4vmnuamclD0h8Vi0VaOet6w+WUoGoEkPsehoSEEg0FttkzI9WUVQnhxqUDEsbq6GlarNd/NKQpyy8cRs2oxkJvnSFeO+iPXrOr1emE2m/PdpDemKARSURTE43FMTExgZGRE8znmiqCqqqioqADLshAEoWhm04UKwzBatGpVVVVR7JCuB4jPcXZ2Fg8fPkQ4HC4KsypN5dA/JpMJHo9H8zkWA0UhkPF4HGNjY7h//z5SqdRzAwL5/y0tLdi2bRsURaFRb3kkN/S7traWrhw3EFI+rq+vT6uQU+jiuFb5OIp+IBWvvF4v/H4/zGZz0SxAClogycpxdHQUIyMjmjiuBwkHNxqNNEIyT6wuH2e1WumAtwGoqopUKoXJyUkMDAwgk8nku0kbAi0fp2+IWdXv92sVcopFHIECTvOQZRkrKyuaOK72OeZCgj7m5+cxOjpaFHveFSqrUznoc3hzFEVBJpPB+Pg4BgcHEYvFimKQItdFUzn0SW6eY7H4HFdTkAJJUjlIPclYLPZSJlNSYiuVStEVZB4g5eNqamrgcDioOG4AxPw4PT2Nu3fvIhKJFIX7gGx4nEqlIEkSFUcdIgiClspRqHmO30VBmlgTiQSGh4cxPDz8nWbVXGRZpp0tT5CVIy0ft7Fks1mMj4+jv7+/aFI5VptVKfpDEAT4fD74fL6CT+V4EQUlkLIsI51O4+HDhwgGg680IJBKLQaDATzPF8VAUigQcaypqdH9/m+FAlk5klSOlZWVfDdpQ8gNyKHiqD/IOFrI5eNehYIRSFI+bmxsDGNjY1hZWXkulWM9VFWFqqoIBAJwu900zWMLMRgM8Hg8qKqqoj7HDYKkcoyPj2NoaKioUjlohRz9krsrB0nlKPaKVwUjkKlUCqOjo3jw4IFWPu5VBgSGYVBZWQmGYajDfwtQVRUGgwFutxtVVVWw2+1F35m2ikwmg9HRUQwODmqFxwtdHAFQcdQxiqLAYrHA6/WiqqpKM6sWe3/WvUCSVI7h4WGMjY0hlUq91nlIGbpsNgubzUbNrJsIyXMsLy9HdXW1FpBD7/ebE4/HMTIyguHh4aLZ+JvsNpLJZKg46hSr1apFqxazz3E1uhZIWZaRTCYxMjKCsbGx1w5fJ4Pz48ePsbCwgM7OTjgcjqIYXPSI0WhEeXk5Kisr4XK5wHFcvptUFMiyjImJCQSDQSQSiYKPxCb9UhRFLXiOviv6gvgcPR4PPB5PUaZyvAjdCiRJ5Xj06BFGRkaQSCReex9HYn5aWFhAMBhEW1sbOI4rCrOU3uB5Hi6XC1VVVXC5XHSlvkEQIZmdnUU2my2KSGAikLIsQxCEklqZFAqCIMDpdMLj8RR9QM5a6Fogw+EwxsfHwTDMG1VcIX5Ho9EIjuNgNpths9mKIl9ML6iqCp7nYbfb4fP54HA4qDhuICSAxWKxFE10J8uy2qQ3lUrR/qgzBEFAWVkZHA4HWJYtyeejW4EkD4NESm0EgUAAmUwGXq8Xdru9JB/4ZkHE0eVyFW3ScL5hGAYWiwWZTKYoyq6ZTCYIgqDlJ1P/oz4gkxaXy6VNdItlUvaq6FYgyYrEarVqaRpver7W1lY0NDRoM6JC9+HoBYZh4HQ64Xa7YbFYaDH4TYKE2QuCUPBiwnGc1g9JfjJQHNG4hQ7DMDAYDLDb7TAajSVtBdKtQAJPTTBmsxmiKG7IQ/J6vQBoJ9xoeJ5HeXk5bDYbAFBx3EQYhgHHcQWf98hxHHj+6fDDMAw1x+sEVVXBsqzmjir16HNdCyQZDHief6NBlzzkJ0+eIJVKaRUgSvnBbyQcx8FgMIDjuJI1xVAoxQCZdBXy5Gsj0b1Akv++yQMj3x0bG8PIyAg++OCDogp20AO0Q1EoxQNdPDxF9064jRh4yQpycXERs7Ozr11sgEKhUCilg+4FcqOhMyMKhUKhvAy6NrFuFCSgoaGhQUtHoEJJoVAolBdRMgIJAA0NDdqWSzTSkkKhUCgvoiQEkmA2mze08ACFQqFQipeSUAoSpDMzM4P79+8jmUzSqEsKhUKhvJCSEEjgqUgGg0FcvHgRyWSSriIpFAqF8kJKRiVUVUUikUAymUQ2m813cygUCoWic0pGIIE3LzhAoVAolNKhpIJ02tra4PF46GbJFAqFQvlOSkIgiRjW1NSgsrISgiDQNA8KhUKhvJCSEEjgj1u4GAwGamalUCgUyndSEj5Ikubx4MEDnD9/HrFYjEaxUigUCuWFlIxKMAyD2dlZ3LlzB+l0WverSJZldd9GCoVCKWZKRiBVVdV2utez/5FhGCSTSfT392N6ehqZTIYKJYVCoeSBkhFIABAEAQ6HAxzH5bsp66IoCiYnJ/Gv//qvOHfuHJaXl6lAUig6h2VZcByn/aN9tjgoqSCdtrY2VFZWwm6363IVyfM8JiYm0NfXB6fTiWw2C0mS8t0sCoWyDizLIpVKIRQKIRqNQlVVCIKAiooKVFRU0E3ZC5ySEEiS5uHz+eDz+bSgHb2RyWQwOzuLiYkJNDQ0gGVZKpDfgaIo2j3iOI76bjcRUmiD9J3c/63H/rTZqKoKURQxPj6OixcvIh6Pg2EYpNNpHD58GBUVFfluIuUNKQmBJMiyDEVRYDAY8t2U52BZFsFgEOFwGJ2dnVhZWUEymaQC+f9ZrwqSLMtYWlpCPB6H1WqFw+GA1WotyKpJqqoim82CYRhN7PWCLMtIpVLIZrNQVVXbY5VlWZjNZgiCkO8mbjmyLGN8fBxnzpxBeXk5Dhw4AIvFgs8//xwzMzNIJpMleV82CzJ+k/6xFf07rwKZO+vczItlGAaKoqC3txejo6P46KOP4Pf7dWX+SKfTGB0dhSiK2LdvH27duoVEIqG9EIXOm17DeisUnudhs9lw5swZTE9PY9euXfj+978Pk8lUcL6gbDaL6elpcByH8vJyWCwWXfjLeZ7H4uIiTp06hVu3biGVSmmrR6/XixMnTuDYsWP5buaWMzU1hTNnzsDpdOLw4cOoq6uDLMtoaGiA1+vV9p0txdX1ZhCLxbC8vAyr1Qq32w2e5ze9f+dVILPZLEKhEFRVhdPphMVigdFo3LSLXllZweLioq5WZQzDIJPJYGBgAI8fP8a2bdsAPDW3RqNRbUVRqCiKAlEUkc1m39jvm06nkc1mYTQan/lclmXs3LkTi4uL+K//+i989tlnOH78OPbu3atVTiqEe8hxHCoqKnDhwgWEQiE0NDRgx44dcLlcebV6KIoCi8WCpqYmfPXVV9i1axe6u7thtVrR29uLoaEhtLS0oLGxEUDxm1sZhkEsFsP4+DgeP36MkydPwu/3a5OZnp4eGI1GbaVdSrys5SbXTP+yfdNqtWJ2dhbnz5+HxWLBrl27tJiSzXKt5N3EyjAMbt68iVQqhe3bt6O+vl4zkW00HMdtyazjVVAUBdFoFAMDAxgaGkI4HEZ/fz+mpqZgMBh0GUz0shDx7+3txb179944Zdk6zykAABD3SURBVIXneQiCAJ5/9rVlGAZGoxH9/f24fv06lpaWMDY2hnfffRc//elP0dra+tx3XhWSJpRKpZDJZDbV+mC1WhEKhXDp0iU0Njbi7bffxo4dO2CxWPIy4KqqCqPRCJ/PB0EQsH//fhw/fhwGgwHz8/OYnp5GNBrd8nblC5Zlsby8jPn5eVitVtTX12vlKxmGQVVVFQAUdN99VVRVhSzL2r+X/Q7P84hEIhBF8aV/SxAEnD9/HhcvXsS+ffvQ09ODQCAAi8Xyxv18NWuejQwGmz0DYhgGDocDXq8Xn376Ka5evYrW1lYcPXoUDQ0NGy5kbrcbdXV1MBgMuprZBYNBLCwswO/3w2QyQRRFsCyLZDKpKzPwq0LeH0mSIEkSUqnUG/nVOI6DLMtrdoJMJvPMKnVxcRHpdBqSJG3IsybbpV26dAl37tzZtE23SRTkvXv3cPHiRaTTaVy+fBlHjhzBxx9/nBezMZnoLCwswOVywev1wmg0Yn5+HqFQCBzHwefzbWmb8gnDMIhEIlhZWUFDQwOcTid4ntf6aikJI/BHF9bU1BQGBgawsLDw0t81mUxwOBwwmUzf+bdEUBOJBK5du4apqSlcuHAB+/btw09+8hMcOHAAHo9nQ/vHcyONJEkIBoO4fPkyRkZGNGf8ZkAGUFmW0d/fj5GRERgMBpw9exZHjhzB3r174XK5NuR3AKC5uRnV1dWw2Wy6EEiWZTE/P4+pqSlUVVXh+PHjcDgcSCaTuHHjBv7whz8gkUgUtEiazWa8++67OHTo0BsPHIIgwGazPSeQ2WwWg4ODSKfTMBgMaG9vx969e7F79274fL4NmVUSU5DVaoXL5YLJZNo0gTQYDLDZbDAajdr+paSOcD7eW4ZhIIoi5ufnsbKygtOnT6Ovrw9GoxEulwvNzc2oqKjQRZ/aCoiJNZlMoqmpCSzLau82EcpSuRcANI0wGAywWq1wOp0v/V2z2Qyn0wmz2fxSf0/yTc1mM3ieRzqd1vrMZvjrnxs5yGwglUohkUhon20G5MaSmQHw1BG7sLCAcDi84QEqZWVlKC8v14XjXFVVLC4u4vLlyxgcHER1dTUAwGg0IhwOY3R0FNFoFBMTE+js7ITdbs9re18XhmE2zAdICj3kipMoilhYWEA0GkUgEMDhw4dx8OBB2O12CIKwoZ3GYrFg37596Orq2rRJi6IomJiYQDgcRldXFyorK3Ho0CG8/fbb8Hg8ePz48Za/u7kryNraWgiCgGg0ilQqhc7OTrS0tOgimGgrEUURkiTBYrFo76IkSRgdHUVFRQXKysryPsZsNZWVlaioqHil8bWsrAx+vx8Wi+U7/1ZVVUQiEdy9exdDQ0Oor6/H9u3b8f3vfx+dnZ2b4pp7TiBZlsW2bdvQ2Ni4JSsXEqZ/6tQp2O128DyP999/H4cPH4bRaMSTJ0825HcYhsHy8jISiYTmS8nXC0wmIeFwGHNzc5rdPhKJwG63IxqNYnFxEZWVlRBFEclksmAFEsCGmOpzzf65SJKExcVFtLS04OjRo5q5a6MhoeU2mw02m23Dzw88vZZwOIyRkRFIkoRPPvkEJ06cgMfjAcdxSCaTm/K734WqqojH41hYWMCHH36Izs5OMAyDM2fO4NGjRwgEAigvL9eVb3+zMRqN4DgOqVRKS8+ZmprClStX8M4778Dtdhe05edVYRgGPM+/dDAZ6cdkxVlWVvad708ymUQwGMTY2Bi2b9+O48ePo729HVarddNSotZcQZJySZstIKqqYmFhAZcvX8ajR4/wF3/xF3jvvfc0E2gkEtmQ3yGCdPPmTdy/fx8/+9nPUFVVlbcXWFVVsCyLlpYWtLa2ap+R+93e3o5//ud/Lukk7JfFbDajs7MTQOEXeM9kMrh79y62b9+ODz/8UDMnsyybt3eVJL4vLi4iFovB6XTCZDJBURT4fD48evQIS0tLeWlbvlAUBRUVFfB4PBgeHkZdXR3S6TSuXr2KsrKyvAVT6YHNum5VVTE/Pw9JkvCTn/wE1dXVmll1M/v8C6famz3YZLNZJBIJvPXWW9i/fz88Hg+cTic4jkM2m92U38tms7qZ2ZH7m3ufidk5t2pJqXa2l4FM6IoBQRCwZ88eGI3GNaN18wHDMEgkEnjy5AnKy8vh8/lgMpkQDocxPT0NURQ3NTVLj8iyjLq6OmQyGVy4cAFff/21Flx14MABeL3ekgvU2WwYhoHf74fH44HBYNiy1K289kCWZVFVVYXKykqYTKZNrxxiNBo3zZn7OqwnfiRwiVJa8Dy/IUFpG4miKFhcXMTk5CQEQcCTJ08giiKGh4fx4MED1NTUoL6+Pt/N3HIEQUBzczMcDoeWq2wymTYsKIzyPC8byLOR5PVJ8jy/pS+Tz+eDJEl59T9SKIVEKpXCgwcPMDAwgJWVFczNzWlRra2trfjBD36gBZiVGqR4AlnJkIktHVuKh5KY6hCzZXNzM+rq6mC1WqkJhEJ5CYxGI3p6etDa2gpJkjQrD8MwKCsrg8fjKdkV02pLDxXG4qNk3mxSDcRsNlNxpFBeElIEwO/3P3eM+sepKBY7+tkuYJNhGAYzMzPo6+tDJpPR1U4JFIqeISk2q/9RcaAUOyWhEiQadHh4GN9++y1isVhJRd1RKBQK5dUpCYEkyLKs7WdHoVAoFMqLKCmBtFgssNvtuknzoFAoFIp+KZkgHQBa9QWz2UxXkRQKhUJ5ISUhkCTNo7GxUctbopGsFAqFkj8KYZFSMiZWVVWRTqeRSCQgSRIN0ilAXmX3cQqFom94nofFYnmpvSDzRUkIJBlYg8EgLl68uGmb3ZYiWyVaZLcAnufps6NQChyO4+DxeOD3+3Vdy7ckBBJ4uoJ8/PgxRkdHtZ3tV+dC5hYJX/3AXvbYRp8v99hGn28jfmu9z9faWeN1foscN5lMa26WTKFQCgeyk5HH40EgEIDFYtF10GRJjTaqqkIURWSzWYiiqNnAydZekiRpn5EBnmXZ547lbrGSu0/hamGQZVnzdZJdJ4j/k3xv9TFSyzF3Vw9yTkmSnvnOi36LHFu9jyL5PLcda13XeufLPUZednKPZFmGKIoQRRGKooBlWfA8/0yiee51kWO510V+J3e7NZPJhLKyMl3PNCkUynfDsiz8fj/8fv8zG5/rlZIQSDLA22w2xONxfPrpp7Db7TCZTDh06BBqa2sxPz+PO3fuYGZmBqqqoqqqCj09PbBarQiFQrhx4waWl5fBMAy6urrQ0dEBVVUxPj6O27dvQxRFmEwm7N27V9sf7u7duwgGg1AUBeXl5di3bx98Ph8ikQguX76sna++vh5dXV3weDyYmJjAlStXIEkSTCYTWltb0dHRAbPZjNu3b+P+/fuQZRllZWVob29HW1sb0uk0Ll++jLm5OSiKAr/fj87OTgQCAczMzODGjRuIRCJgWRaBQADd3d2w2WwYGhrC0NAQYrEYzGYzWlpasHPnToiiiLt372JiYgLpdBoOhwN79uxBfX09FhYWMDg4iJmZGciyDLfbjePHj0NVVYyMjKCvrw+zs7OQZRmtra04efIkEokEhoaGcPPmTcRiMXAchwMHDmDfvn2IRqPo7+/HnTt3IMsyXC4XDh8+jEAggHA4jFQqhZqaGvh8Pt13JgqFsj4cx8Hr9cLn88FisRRENbOSEEiygqmtrUVnZydCoRDC4TAcDgcymYy2ikkkEohEIlBVFWVlZRBFEWazGdlsFvF4HNFoFDzPI51OQ5IkAIAoilhZWUEymYTNZoMoipBlGZIkIZVKIRaLaTuIkCIFoigikUhoFX0SiYRW9DiTySAWi0EURVitVqTTaW1VmU6nEY1GIUkSeJ5HJpPRVmapVArRaBSyLGvtUBRF23MzGo2CZVmUl5drK7ZMJoOVlRVEo1Fks1ntumRZ1s5HzNFkH01JkpBMJrXvCIKgtUEURcRiMYTDYUiShJWVFe3ek/MtLy/DYDAgkUhoq854PI7l5WVks1nwPI9UKgUAMBgMUFV10zdFpVAomwvP83C73aiurobZbC4IcQQARtVprG02m0U4HMb8/DxisdhrpWWwLIt0Oo3p6WmsrKxg+/btMJlMmuludbrH6kFYUZQ1NzV+0bFck+Xql+BljuWadcnn67Uv91jud1afb632vWrbc68517xMTKxVVVWwWCyaKJP7ul77c+/fWu0wm83a5tnkN0pZJGVZRjKZxNTUFCKRSMFHYnMcB4fDAQBYWFhAJBLZlE3SKa8O8fmTzYkVRXnGDfIqqKoKnufh9XpRU1MDs9lcUO9t0a4gyYprYGAADx8+RFlZGTo6OgDguYF5PSEhorPWsVyBedEDX+t7a51v9bnWOr7689xjuW1a/fvrte91277Wd1cH2pB7t9a1Ac8K+urvCoIAu92+ZbuGUyiUzYGIY2VlZUH4HFdTlAJJgl1CoRAGBgbAcRxaW1vBsuy6s6AXbd2z0ccK+bdetLJdvevDq/4WmblScaRQCh9iVq2pqYHJZCoYs2ouRSeQZBUiyzKmpqbg9/vR0tKCbdu2FUTlhlKFYRgYjUYarUqhFDjErOpyuVBfX1/Qk92iE0gSnMIwDPbs2QNVVbVgD4o+IStHl8sFg8FQsJ2JQqH8MVq1pqamoMURKCKBJD7HYDCIRCKBpqYm+Hw+zXxHBVKfMAwDs9kMh8NBxZFCKXCIOBaqz3E1hWcUXgOGYZDJZDA5OYlz585p+YCrk+Qp+oOIY6HPNCmUUoeUj6uurobVai1In+NqCv8K8DQiMhQK4bPPPoPD4UB7eztcLhfdsUPnkFQOKo4USuFCIv5zUzmKQRyBIjGxqqoKp9OJgwcPoqamBn6/HwaDId/NorwAi8UCh8NBA3IolAKH4zj4/X74fL6iEkeggAWSVIJJp9OwWq1wOp3o6enRdeFbylPMZjNN5aBQioDcXTkKpXzcq1CwV5PJZDA2Nobr169jfn4eAOhODzqHRKs6nc6icOBTKKUMz/MoLy9HbW1t0fgcV1OQV5RMJjE4OIhLly5hdnYWoijmu0mUF5BbBMDlctGVI4VSwJD6yEQci3myW1BLLlIWThRFLC4uwmazoaenBzU1Nc/VIqXoB5ZltWhV6nOkUAobg8EAt9uNqqqqohZHoIAEMjeXURAE7NixA6qqora2tiiX9sUCWTnSVI6Ngd4/Sj4gYy+pkENWjsU+9haEQDIMo22lZDabYTabEQgEAKy96wRFH9DycRRK4bHeJgYcx8HtdqOurq7oV44E3Qukoijahru3b99Gd3c32tvbIQgCNanqgPU6E6mQ43Q6aYWcDWJ1MfhCvqekXjLwdCsvWZZp3rJOIPvjyrIMjuM0n6PX6y0Js2ouuhZI4m8MBoP45ptv4Ha74XK5tH0cqUDmn9zi8OSZ5JpV6cpxYyEi8l1blekdVVWRyWS0HXZYlqVR6DohN9bDYDCA53mUlZXB7/cX3H6Ob4qu30hFURCNRhEMBuHz+dDR0aHVV6Wbq+oHSZIQj8fBcRwMBoOW50jFceNgGEYLjrDZbAU/OSTvhSRJ4DgOPp+Pukt0hsFggMFggMVigcvlKgmf42oYVac9TZIkrKysYHFxEY8fP35mRaLTJpc0RqMRgiDAZDLBYrFQs+oGQ4LUJElad3PsQkNVVc28yrJsyQ2+hQLP8+B5vijeuVdFtwKpKAokSYIkSZq/pRQfUCHBMExJd6atgHTXYri/uZtvF8P1FDOl+nx0K5AUCoVCoeQTatOgUCgUCmUNqEBSKBQKhbIGVCApFAqFQlkDKpAUCoVCoawBFUgKhUKhUNbg/wGtjbyUkG0GIAAAAABJRU5ErkJggg==)
physics-General
Maths-
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means
Maths-General
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means
maths-
If , then
by trapezoidal rule is
If , then
by trapezoidal rule is
maths-General
Maths-
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means
Maths-General
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means
physics-
A wire of length L and radius r is rigidly fixed at one end on stretching the other end of the wire a force F the increase in its lengths is L. If another wire of same material but of length 2 L and radius 2r, is stretched with a force of 2F, the increase in its length will he
A wire of length L and radius r is rigidly fixed at one end on stretching the other end of the wire a force F the increase in its lengths is L. If another wire of same material but of length 2 L and radius 2r, is stretched with a force of 2F, the increase in its length will he
physics-General
physics-
Consider the situation shown in figure. Water
is filled in a breaker upto a height of 10 cm. A plane mirror fixed at a height of 5 cm from the surface of water. Distance of image from the mirror after reflection from it of an object O at the bottom of the beaker is
![](data:image/png;base64,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)
Consider the situation shown in figure. Water
is filled in a breaker upto a height of 10 cm. A plane mirror fixed at a height of 5 cm from the surface of water. Distance of image from the mirror after reflection from it of an object O at the bottom of the beaker is
![](data:image/png;base64,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)
physics-General
physics-
One side of a glass slab is silvered as shown. A ray of light is incident on the other side at angle of incidence
. Refractive index of glass is given as 1.5. The deviation of the ray of light from its initial path when it comes out of the slab is
![](data:image/png;base64,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)
One side of a glass slab is silvered as shown. A ray of light is incident on the other side at angle of incidence
. Refractive index of glass is given as 1.5. The deviation of the ray of light from its initial path when it comes out of the slab is
![](data:image/png;base64,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)
physics-General