Chemistry-
General
Easy
Question
An aqueous solution of ethyl alcohol:
- Turns blue litmus red
- Turns red litmus blue
- Does not affect the litmus colour
- Decolourises litmus
The correct answer is: Does not affect the litmus colour
Alcohols are neutral and do not influence ![p H.](data:image/png;base64,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)
Related Questions to study
physics-
A reflecting surface is represented by the equation
A ray travelling horizontally as shown in figure and becomes vertical after reflection The coordinates of the point (s) where this ray is incident is
![](data:image/png;base64,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)
A reflecting surface is represented by the equation
A ray travelling horizontally as shown in figure and becomes vertical after reflection The coordinates of the point (s) where this ray is incident is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAO4AAACdCAYAAACzWERNAAAUTElEQVR4nO3deXxU5b3H8c/sk8xkspCErCSyKrJElMUFikhZRaq4REVrtYoWS21vr3qvF62ltLa1bq20eq8bKErdUKQorldulT3RoLIvCZCNZCaZyWQyc+ac+8fAhCFgiSFMTvJ7v155vTIn55z8Jsx3nuc8z3kGg6ZpGkIIXTHGuwAhRPtJcIXQIQmuEDokwRVChyS4QuiQBFcIHZLgCqFDElwhdEiCK4QOSXCF0KFOCW7N2ie4amAK6RMf5J+VCtDC3tfmcOGUX/Fxpfqtx64u39AZJQnRrXRKcDPH3MmfH5yOq6aBoMsMmNFqzVx8791cnH3iX/lZ5RZuXP1bAkpLZ5QlRLfRSV1lI1mzfsEPHa/z8OLdhIOlLP2ikGsuSvzWo/5UsozqZjcvbnu/c8oSopvovGtc6znMmTeWbxY9zsqVr1I5+lrONp949x2e/byxaw0AD29ehqp9e5daiJ6sEwenIq3uTc5XmbswwOTL8771lz1a8mr0+22eCt7Z83nnlSaEznXuqLK1iNvmjqff5GImpZx4t9pmD899sypm28Mlr3RqaULoWSdPBynsL89k1g9HYvuWvRZ9uZxAOBizbc3BMtZVfd255QmhU99y1fndqZ4vefvNrzCn7OXtxktY2N90wn2blRZKanfw+wvmkGi2MX/tszxzyd2sq/6a13b+L6OzBndGiaeEpmmgaRiMMh0uTi9DZ3x0jfL1X7mm+C9UF93Ow4/PZUzqiV/YqqZiNER+XlK7g8nLf0nNrW+1+VlX5P/8n7iffZrc/34h3qWIHqZTWlzz4Dt4/cs7TmrfbwtmVw4tQNjjRvV6412G6IG6djKEEMclwRVChyS4QuiQBFcIHZLgCqFDElwhdEiCK4QOSXCF0CEJrhA6JMEVQockuELokARXCB2S4AqhQxJcIXRIgiuEDklwhdAhCa4QOiTBFUKHJLhC6JAEVwgdkuAKoUMSXCF0SIIrhA5JcIXQIQmuEDokwRVChyS4QuiQBFcIHZLgCqFDElwhdEiCK4QOSXCF0CEJrhA6JMEVQockuELokARXCB2S4AqhQxJcIXRIgiuEDklwhdAhCa4QOiTBFUKHJLgdpAYC8S5B9EAS3A5o2foNyoGKeJcheiAJbgc0ffQ+akMDwV07412K6GEkuN9Ry9ZvCG7bCoD72afjXI3oaSS435H7maei33uXv4FSWxPHakRPI8H9DkJVlXhXvh19rIWCeJY8H8eKRE8jwf0OPC88A4oSs63h5SWofn+cKhI9jQS3ncI+L00frCZp5hXRbSk334ql8AwaX1sWx8pET2KOdwF6YzAYKVj1EQazGe9bbwCQce98AMINnniWJnoQCW47GR2OE/7MlJxyGisRPZl0lYXQIQluB2Q8uBBzXn68yxA9kAS3A0wpqZgze8e7DNEDSXCF0CEJrhA6JMEVQockuELokARXCB2S4AqhQxJcIXRIgiuEDklwhdAhCa4QOiTBFUKHJLhC6JAEVwgdkuAKoUMSXCF0SIIrhA5JcIXQIQmuEDokwRVChyS4QuiQfK6yjqiaRl1AxR0I425Ro1+NQZVgWCOkamyoaaHQZcZuMmI1gskANpMBq8mI02LAZTHgUzRGZNhItRlJTzBhNhri/dREO0lwuxBN0zgUUNnmDrGpJsCOBgVPi0qFT6HCq7DPp6BqkGg2kGozYjdBIAxF6TasJrAaDSzf3cSUgkTS7SZCqkbpoRaCKgxItuALqexpVKj0K1iNBrwhDZMB7CYDZ6VaGJBioU+SmXyniTNcFsZk2Umzm+L9ZxHHIcGNk2BYo6wuyKaaFjbWBPj0YAvV/jCeoEofpxmjAVxWI9cOdDK1IIF8p5lr3qvh5UkZjM9LBOCx0gb+rzLAa1MjHxHbrKgs+1sTz0zIoFdCJHDXr65hWC8r95wb+V8WHinxsK66hWVTehMKa1T5FfovqeC6gU5CGuxrVHi4pJFDzWF8ikaG3ciZqRYcFiOzBzkZk2Wnr8uMwSCtdDxJcE+TqiaFNZUBXt/ZREltC3u8CkkWI+dm2sh3mqnwKXx+ZQ79ky0kWoxc+141IzJs/PuISOAUVaPGH6Z/ijV6zgqfQr6ztUWs8CokmAyk2VuHLvb7FKYXJEYfl/sU8p2Rf3aLyYDDYiSowpwhLhItkeOmvF3JveemcN1AJ9s9IT6o8HPfWjd1gTC3fFiLw2JkdG8bBS4zNw5yMqq3HZN0t0+rDgfX89JitEAA1xVXYUpNPRU1dQv1gTCry5v5oKKZTw82s6tBoSjDiqJqDE6z8t7MbAqSIi3Xqn1+1lcHGJZuix5f4VWYeUbr/1NU2RTGYIDsxNag7vcpjOp91DG+MPlJsa1hhVchPyk23ONyEmLOkWYzRkMLUFYX5IGRqSRZI28sG6pbuDg3gfd/kB3tKazY08SCDR5e2e5D1WBcbgKT8hOYUZhAYXLrm4voHB0ObsJ5oyifMYm6R/6Ac8o0kouvJ2Hk6FNRm66omsbmmiCryv2s2udnXVULCWYDPx2WzBPj0rkg247LauSyd6r4fp8ECl2W6LH7fQp5zth/iiMhPKLcp5DrMMe0bBU+hVn9HDGPj26BVU1jf1PsuY89735fONoCA9Q1hznYFGZIr9bwfXKgmfG5dgCsJgPnZtpYtsPHVf0dLJ2cyZeHgnx8oJk3dzcxb00dg1MtzOrnYGZfByMyrNKt7gQnDO6OgX3adSItFMS7YjneFcux9CnAOW0GzomTMTqdJ30OQ30FfeoDBHfvatfvjpdgVRUNzSEe/LCGN3Y3oWkGJvVJ4LazXcwdCg9t8vC7C9Jijqk4qqt6xLHBDasaB5pi96vwxobyeMdVNikUJrW+IdT4w4RUyHWYY445+jzHnqOsLsgZSWaSrJEWWNM0PjkQYN7w5Og+zYrKM197eWt6FkaDgaIMG0UZNnwhjZAKPx3m4q09fi558yBhDe4Y6uKms5IYnCYt8anSKde4ofJ9uP/2F9xPLwKbDYPx5KaLEzWV/wm1UP7KpZ1R1ikTViGkaqhhhYOpeexpVOiTZGHj1bnRqZWntzS2CSicKLhh+hzVClb7w2ga5DhaA+YNqW1e+Ol2EwNSWoP6k6HJhFQt+thiNDBvmAurqbXFe+SiXhQd1SU3GeG8zNbzltUFGZbe+nibJ4Q3pHJeZusxr2xvIs9p5sLs1m3uQJg/lTSw4tLejM1J4OoBTh7e7OGprxqp8IYY+fcDFDjNXJBjZ+GYVHonyvBKR5zwrzdge/lJnUBTFHYOHwShEAAGmw3n9MtIKZ6NveicdhVTUruDyct/Sc2tb7XruNPh6/ogi7d6eeLLRhJNBm48M4kr+zuYlGVj00YP2z2hmPnQ/T4lpksK4A+p1AXUNsE90KRwwVEhSLMbeXlyZsz5fjw4iZvOTIo5bnNxXszjZFvsG2SvBBOPj0uP2VY8MLYHdMtgV8zjqQWJjM2xt/6OmiDjc+3R8GuaxpNlDcwd6orpAj9a2sCo3jbGHr5+bgqp/LHEw/MTM5lakIgvqDJheSUfVPhZstXLZWc4uHagkx/0TcQoXel26/DbXmDzJgiFsPYbQHLx9SRdPguTK/lfH6gDnkCYl7b7eO4bL9+4Q1zR14HDbODNab256KgBnorjhLTCp9Av2RKzrbo5TJIldtQXYMHoVM5KbW3l7GYjVw+IDZjBYMByGqZU+6fE1lw80MFlZ7SOSpceCrKzQeH6Qa311TWHeeyLBlbPzI5ue7KskX7JFqb0ifyddjaE+Ko+yK4b8mkOazy0ycOsVdX0dZmYOzSZWwa72rzxiBPrcHCV+kPkvfRqtxqQ2ljdwl/LGnhuq4+RmVbuHJbMrH4OEswGbIv2xAwsQaSre06Grc228bkJMdsKk8xsuS6/zWDNyN52uiqjwYDT2lrvmakWPr48G8dRo9B/Km1gbI6dMVmR5+ENqvxhs4dlk3tHn+v969z8ZKiLrMPX2w0tKnPOTmJifgJPfNHIvZ/Xc+0AJwvGpMVcNojj6/BfKGnK9FNRR9wFFJWl230sKmtkuyfErH4ONODTWbnYDncTK7xKmykZiLSux44Kn5lqiZmqgUirqfcXZYLZ2OZNqsqvsHBM6yDc4180MCTNyoS8SJDXVwf4+EAzz1ySAUDZoSAr9vrZMTufHKeZjAQTl75TRWNQZeCScmackcicIS4m5icijk/fr6JToLY5zF/LGnmk1EOu08xdw5O5doCTb9xB3i1vjoYWIlMyOQ5Tm5sNqvwKBccE8s/fi7227M6evSQz+r2qaTxa2sDy6bGt7bxhyWQcvpvrgfX1zDnbRY7TjKZpzF/r5t4RKdw3MpW9jSGmr6hi6ttVzOzr4P6RKTHz2yKixwZ3qzvIo6UNLNnq43u5dlQNXp6UGX2RVBwzvwlHpmTa/sk+uzK3zfVsT2U0GCgtzote86+vDvB5ZYClkyLh3lzTwuryZnbfGGl9P6ho5mt3kJUzsgBQVNjdqPDpFdn8fWcTY149SFGGlUcv7MXo7K57SXG69bjRgNLaFi5+8yBFL+8nrMKGq3N5fWpvvCHtX86buqxGJvVp232T0MY6eqCuMMnCikuzoosV7l/n5s5hLjITTZHWdp2be0akROeNH1zv5oZBTs7PTuDRsemsnNGb9dUtXLz8IDd9UMN+nxKX59TV9JgWd11VgN9s9PBhhZ+QBh/NzGbs4cGj7e4giWYDKUeNah5vpHhaYSLTCuW6qz0yE01kJrYO0g1Lt/JvRZFZh1X7mtnbqDB3aGRK6uv6IK/vamLr7Pzo/k+WeblzmIufD0/mv9a6GbCknGkFiTw3MROXtce1O1Hd/pmvrWxm0luVfP+tSoakWfmiOB9FJWaAZX9TmDxn7D2++U4zE44ZFRYd99vz06Irl94r97NgTGr0PukH1rm5ZXBSdACvtLaFd/f5uXdECgUuC4u/n0Ffl4UvDwXpv7icp7Y0Ej7qhpOepNu2uFvqgtz3eR0r9jZz13AXr0zOJM1uYktdkBSrEac1dgVNniO2W/yzou4xF92VPTa2V/TN8qu6IP/Y52fnDa2t7bFTSCv2+KlvUdk5O49PDrZw15pDLNzo5oWJGVyc17N6Qt2uxd3VEOKG1TWM+vsBchxmNGDh+WnRa6zIvbmxIT14uMUVp9fRPZxcp4kVl2aRfTik66oiU0h3H17WqGoa969zc995KTisJqYXJvKXcb2obVa5dEUVcz6upa45HJfnEQ/dJrg1TQrF71YzZOl+7GYD22bnc/tQF73sRhLMx7Sux4T0R2dFJv5F/KTYTEzIa700+dV6N3cNTyb9cLf6jV1N1LeEufXsyPWwpmks2OBh/sgUvro+n2p/mH5Lylmwvh5N6/7dZ903M8GwxqKyRuavqwegpDiXMw/fPvjFoZbjrsQ5erUMIDe8d0FX93dyxeEli2E10trOH5kanVd/v6KZbZ4Q7w5Lxmk18vrU3hS+UM7DpQ1sqAnyt/Hp5HTjXpRun5mmabyz188v/1mPzWRgztlJlNWFoqGFyFzssa3rdQNPfpmhiJ8fDW5dUPHm7iZawlp0kcWRmzbuGZESHat4ZYcPq8nAjmvyufuzega/VMG84ck8ODq1W64H1mVXebs7yJS3q7jlw1r+rSiZkmtySbKa2oR0/3GW0A1MtTIwVdaF6slF2XZWzsjCcri1XbnXT7lP4SeHp5EUVeNX6908MCqVzEQzz0/MZEpBIn8s8TDjnWqq/d1v7ldXwfWHVOavreecZQc4K83Cjhv6cNsQFyajoc0CcYCCJDMT82VKR++yHOaYntQjpQ38x7kp0WmkxVu9mAwGrj/cmzrUHGblPj8rL80mxWZk2Mv7+cdef1xq7yy66Sqv2NPEvE/ryHGY+OzKHIYfc/9qhU9hTFbsttuGxK41Fd3D8xMzozMDwbDGrzd4eOj8tOg95H/Y7GF8bgIT8iNfS7f5uG51DbMHOfnjhWkxg5V61eWfQYVXYebKKm7+sJb5I1NYM6ttaOHIXKxu3odEB/RJMkcX37+83UeSxcDVAyIDWdV+hUVljfx6dOsHF143yElpcS5fHApy7rIDbKkLxqVuAFVTT8l5umxwVU1jUVkDQ5ZWkG43sW12PjcPdp3w0xIWjkljXK7chN7TTCtMZOWM7Ojr4qFNHib3SWiz9LDQZeGTy7MpHuDk/NcOsHirNx7lcucnj/Pguuc54Kvt0Hm6ZBO11R3kxx/WUukP8+b0rJj5vROZ2dfxL/cR3c+RpYIAjUGVp7Z4WXdV7nH3NRkN3D8qlfOzbFy/uoY1BwM8Ma7Xae06j8sdxrXvLWDBhsVMLxzD7UNmMrlgJEZD+2owaF1otnpTzXbOW3ZbvMsQupYNVMa7iHYpTMrix2dP55bB08hy9DqpY7pUV9lqkjlW0VH6Ci3AXm8VD21aysKNL9IUaj6pY7pUiytEd7e26ivOf3Vu9HFRen9uH3IZ1w2aSJL15BdKdMlrXCG6q/f2bSDRbOOaARO4fchljMo66zudR4IrxGk0tFdfDt78Osm2jl0WSldZCB3qUoNTQoiTI8EVQofkGleI00xVAgRawmgYMNnsWNQALSEwWuzYT/ID8KTFFeI08+/5lCd/dB45uZP4XUkjtat+wfip97Bsi5uTvZNZBqeEiIeGNfzn5GLeveB33GrYSu+f/4Yr8k6+HZXgChEngZLfM3Xa4yT/ZiNv3JLTru6vdJWFiAuVxpowQyYMpvSxX/NOdfuW+0lwhYgDZftSHt88kvtfeIYFQz7i5/NeZE87Pl1WgivEaeYre5E7bnyKhqKzSDOnc97Fw1FX3cvsn73AxpqTa3nlGlcIHZIWVwgdkuAKoUMSXCF0SIIrhA5JcIXQIQmuEDokwRVChyS4QuiQBFcIHZLgCqFDElwhdEiCK4QOSXCF0CEJrhA6JMEVQockuELokARXCB36f/tJy35mvP4ZAAAAAElFTkSuQmCC)
physics-General
physics-
A particle is dropped to move along the axis of a concave mirror of focal length f from a height f/2 as shown in the figure The acceleration due to gravity is g Find the maximum speed of the image
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)
A particle is dropped to move along the axis of a concave mirror of focal length f from a height f/2 as shown in the figure The acceleration due to gravity is g Find the maximum speed of the image
![](data:image/png;base64,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)
physics-General
physics-
The co-ordinates of image of point object P formed after two successive reflection in situation as shown in figure considering first reflection at concave mirror and then at convex
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)
The co-ordinates of image of point object P formed after two successive reflection in situation as shown in figure considering first reflection at concave mirror and then at convex
![](data:image/png;base64,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)
physics-General
physics-
A beam of light strikes one mirror of a right angle mirror assembly at an angle of incidence 450 as shown in the figure The right angle mirror assembly is rotated such that the angle of incidence becomes 600 Which of the following statements is (are) correct about the emerging light beam
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)
A beam of light strikes one mirror of a right angle mirror assembly at an angle of incidence 450 as shown in the figure The right angle mirror assembly is rotated such that the angle of incidence becomes 600 Which of the following statements is (are) correct about the emerging light beam
![](data:image/png;base64,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)
physics-General
physics-
A boy is walking under an inclined mirror at a constant velocity V m/s along the X axis as shown in figure If the mirror is inclined at an angle q with the horizontal then what is the velocity of the image?
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)
A boy is walking under an inclined mirror at a constant velocity V m/s along the X axis as shown in figure If the mirror is inclined at an angle q with the horizontal then what is the velocity of the image?
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)
physics-General
maths-
Let
, then the ad joint of A is
Let
, then the ad joint of A is
maths-General
chemistry-
If there be a compound of the formula
which one of the following compounds would be obtained form it without treatment with any reagent?
If there be a compound of the formula
which one of the following compounds would be obtained form it without treatment with any reagent?
chemistry-General
physics-
An object ‘O’ is placed infront of a small plane mirrorM1 and a large convex mirrorM2 of focal length f The distance between ‘O’ and M1 is x and the distance between M1 and M2 is y The image of ‘O’ formed by M1 and M2 coincide The magnitude of ‘f’ is
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)
An object ‘O’ is placed infront of a small plane mirrorM1 and a large convex mirrorM2 of focal length f The distance between ‘O’ and M1 is x and the distance between M1 and M2 is y The image of ‘O’ formed by M1 and M2 coincide The magnitude of ‘f’ is
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)
physics-General
physics-
Consider a disc rotating in the horizontal plane with a constant angular speed
about its centre
. The disc has a shaded region on one side of the diameter and an unshanded region on the other side as shown in the figure. When the disc is in the orientation as shown, two pebbles
and
are simultaneously projected at an angle towards
. The velocity of projection is in the
plane and is same for both pebbles with respect to the disc. Assume that i) they land back on the disc before the disc has completed
rotation. ii) their range is less than half the disc radius, and iii)
remains constant throughout. Then
![](data:image/png;base64,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)
Consider a disc rotating in the horizontal plane with a constant angular speed
about its centre
. The disc has a shaded region on one side of the diameter and an unshanded region on the other side as shown in the figure. When the disc is in the orientation as shown, two pebbles
and
are simultaneously projected at an angle towards
. The velocity of projection is in the
plane and is same for both pebbles with respect to the disc. Assume that i) they land back on the disc before the disc has completed
rotation. ii) their range is less than half the disc radius, and iii)
remains constant throughout. Then
![](data:image/png;base64,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)
physics-General
physics-
The resultant of a system of forces shown in figure is a force of 10 N parallel to given forces through
, where
equals
![](data:image/png;base64,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)
The resultant of a system of forces shown in figure is a force of 10 N parallel to given forces through
, where
equals
![](data:image/png;base64,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)
physics-General
chemistry-
On reacting with neutral ferric chloride, phenol gives
On reacting with neutral ferric chloride, phenol gives
chemistry-General
physics-
An air bubble in glass (m =1.5) is situated at a distance 3 cm from a convex surface of diameter 10 cm as shown The distance from surface at which the image of bubble appears is
![](data:image/png;base64,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)
An air bubble in glass (m =1.5) is situated at a distance 3 cm from a convex surface of diameter 10 cm as shown The distance from surface at which the image of bubble appears is
![](data:image/png;base64,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)
physics-General
physics-
The fig shows a mixture of blue, green, red colours incident on a right angled prism The critical angles of the material of prism for red, green and blue colours are 460 , 440 , 430 respectively, The arrangement will separate
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)
The fig shows a mixture of blue, green, red colours incident on a right angled prism The critical angles of the material of prism for red, green and blue colours are 460 , 440 , 430 respectively, The arrangement will separate
![](data:image/png;base64,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)
physics-General
chemistry-
Ethanol reacts with thionyl chloride to give ethyl chloride and:
Ethanol reacts with thionyl chloride to give ethyl chloride and:
chemistry-General
physics-
The minimum speed for a particle at the lowest point of a vertical circle of radius
, to describe the circle is
. If the radius of the circle is reduced to one-fourth its value, the corresponding minimum speed will be
The minimum speed for a particle at the lowest point of a vertical circle of radius
, to describe the circle is
. If the radius of the circle is reduced to one-fourth its value, the corresponding minimum speed will be
physics-General