Physics-
General
Easy
Question
For the system shown in the figure, the acceleration of the mass m4 immediately after the lower thread x is cut will be, (assume that the threads are weightless and inextensible, the spring are weightless, the mass of pulley is negligible and there is no friction)
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/471592/1/944349/Picture67.png)
- 0
The correct answer is: ![open parentheses fraction numerator m subscript 1 end subscript plus m subscript 2 end subscript minus m subscript 3 end subscript minus m subscript 4 end subscript over denominator m subscript 4 end subscript end fraction close parentheses g](data:image/png;base64,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)
Related Questions to study
physics-
Given
. The coefficient of friction between A and B
= 0.3, between B and C
= 0.2 and between C, and ground,
= 0.1. The least horizontal force F to start motion of any part of the system of three blocks resting upon one another as shown in figure is ( g = 10
)
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/471632/1/944343/Picture56.png)
Given
. The coefficient of friction between A and B
= 0.3, between B and C
= 0.2 and between C, and ground,
= 0.1. The least horizontal force F to start motion of any part of the system of three blocks resting upon one another as shown in figure is ( g = 10
)
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/471632/1/944343/Picture56.png)
physics-General
maths-
maths-General
maths-
is equal to:
is equal to:
maths-General
maths-
If the chord through the points whose eccentric angles are
and
on the ellipse
=1 passes through the focus (ae, 0), then the value of tan
tan
= 0 is –
If the chord through the points whose eccentric angles are
and
on the ellipse
=1 passes through the focus (ae, 0), then the value of tan
tan
= 0 is –
maths-General
physics-
For a certain mass of a gas Isothermal relation between ‘P’ and ‘V’ are shown by the graphs at two different temperatures T1 and T2 then
![](data:image/png;base64,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)
For a certain mass of a gas Isothermal relation between ‘P’ and ‘V’ are shown by the graphs at two different temperatures T1 and T2 then
![](data:image/png;base64,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)
physics-General
maths-
maths-General
maths-
If the chord joining two points whose eccentric angles are
and
cuts the major axis of an ellipse
+
= 1 at a distance c from the centre, then tan
. tan
is equal to
If the chord joining two points whose eccentric angles are
and
cuts the major axis of an ellipse
+
= 1 at a distance c from the centre, then tan
. tan
is equal to
maths-General
maths-
P(a cos
, b sin
) is any point on the ellipse
+
= 1
Now if this ellipse is rotated anticlockwise by 90º and P reaches
then co-ordinate of
are -
P(a cos
, b sin
) is any point on the ellipse
+
= 1
Now if this ellipse is rotated anticlockwise by 90º and P reaches
then co-ordinate of
are -
maths-General
maths-
Normal to the ellipse
intersects the major and minor axis at P and Q respectively then locus of the point dividing segment PQ in 2 : 1 is -
Normal to the ellipse
intersects the major and minor axis at P and Q respectively then locus of the point dividing segment PQ in 2 : 1 is -
maths-General
physics-
Given graph gives variation of
with P for 1gm of oxygen at two different temperatures T1 and T2. If density of oxygen
The value of
at point A and relation ![b divided by w T subscript 1 end subscript & T subscript 2 end subscript text is end text](data:image/png;base64,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)
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)
Given graph gives variation of
with P for 1gm of oxygen at two different temperatures T1 and T2. If density of oxygen
The value of
at point A and relation ![b divided by w T subscript 1 end subscript & T subscript 2 end subscript text is end text](data:image/png;base64,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)
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DdxLJK5Mq1UGn12MdcVEHcdidj1t0SJmTVoshHKUQWqZDFLD2y3IgXoa+qgjotBXkLZiGbx7bduiEsv//gAbp0646+/fohMiqKMoDUA+qtuNXE/ke/iNu0O8UoZ9YdQbwKVVIJZDeuQ2Q+GgWzpkATGw15pRaXHR3Rvn0HmE+cKHgVRN3HqMTtacttKhM3mZrEjXg1NGmpKN6xVRA36eH90OfnIj0vH3ut9qFnz15Ys3YdJJSUsl5gVOJm9Rtxk5K4Ea+I4kEQciaMQs40c1QG3ANUSjyIiMSSZcsxfMRIHDt+HHK53LA2UZepHXHT66DTVgqdEZVa9rdhMasQlmuF5VVvPfU3iRvxJvDhVlKnK8jo0xX5KxYDhQXC8htu7hgzdhymTp2OmzdvCrGgRN3nDcRNjyp1OSqKc5EvykRmZhYys7KQlS1CtigHubm5yM0RQZTNlvHlWZnIEuUiu0iKMoUWbyNxKYkb8SZoMtJRYrkLmQN6oZS5pDB0GtjZnUbXbt2xePFSRDArjjoT6gdvIG5yFER5wuuoBQ4fPoojju5wdnWBp5Mtzh7chs3rNmGTpQ1OOLnB+cZNuDkcwakje7Hx4HVcuZsF5Vto7CdxI14bJlgVPreRv2gucplLWuHmKizmd9CuXbvR5Kem2Lp1mxAiRdQPXlPcuNmVi0fOVtg5dihmL1qLTWdccOHKZbgdXYB1Qxvjm398iS97zsbsI9dw2ukqrp3ajB2rpqLvqI3YcCgAMnntjxYgcSNeF71KCfGxwxCNHSF0KGjiYoTlUqUKK1asxI+NGgvtbbyJhagfvKa4adjdkIxQr0s4vPUYHK77IzotBxlZqcj12wW7SY3x1Z+/wGeDtmCzrwhR2dkQpUYj3N8VB3Yeh8P521Aqar/dgsSNeF20JUUoWLkYmQN7QepwAXqFHDq9Hsnp6Zg+YyZatmoNp6tXDWsT9YE3ELc8ZKSnIPRhHkqkT4lIxjl4r+yMVp81x09TbXEiDZAZqvi8DKKYxxDFxqPqLbwBSdyI14HPIK+MjkLOpLHIGj4IypBgYblKo4Gfvz/GT5ggBO/6+NBEMPWJN3BLtULvqIoJyC+dA0z0Us7Ac3kntPy0GZpMtsGxJKDEUMvRsW2qKt9OqhgSN+J10Jawe+XqFWQzlzRv0VxoMzOE5WVSKS47OGDM2LGYPGUKHjx4ICwn6gdv0KFQA3oVkHQat5YZxG3ScRxN0KPoLYeAPIHEjXgd1EmJKN5tAdGkcSix3gd9aamwPL+gAAcOHoTZKDOsWr0aj2Oq2+GI+gGJG9HgkQcFIHfGZOTNnY5yT3dAWZ06PDMrE+vWrcew4cNhtW8f0tL5FOJEfYHEjWjwSK85CRlAClYthTo5kd3H1TdsUnIyZsyYicGDh8D+nD0KKAykXkHiRjRoqsSlgiua0b0DSvbvhU7xy9CqmJhYDB06DAMGDMStW7dQUVFhqCHqAyRuRMOFzyQfFYGCNcuFXlKpo4OhopqQkBB07doNg0wHIywsjK1O83DUJ0jciAYLt9Kkzo7InT0N+UvmQx7ob6ipxsPDA61bt8HoMWORnl7dg0rUH0jciAYLz91WvHcHRGOGC64pT1L5BJVShfPnL6B58xaYMXMWysoozVF9o3bFDcxsT7OH14rqIN4mU07Cht0v1R3rbx8SN+JV0OSIkDdvJrKHDRQSVHKxe0JhQSEOHz6C1m3aYsXKlc+dpIiou9SyuGmY5WaHW0vboem/GuN78+M4HA8UG2rfNiRuxMui1+mgDA+FaNRQiMYOF0Yo8GVP4NNK7tq1C92794CFhQXNUVoPqSVx00NXWQGpKBqJlxdiW68/439N/hN/aDUXU8/F4V6GBFJVlTCu4W1C4ka8LFWSMqG9LXv4IOQvmYfKvFxDTTUPHz7E+vXrYWo6GIcPHSZxq4fUmrhVKUuQ98gLd6xnY0X/b/HTN1/jq54zMdHKC45hucgv15K4EXUGYV7SfbuRM3E0Sg5aoaqszFBTzV0/PyxevEToTLC3PycMNSTqF7Xmluq1KshLsiGKDUaYrxs83d3gdicYgY+zkFYoh7zy7QsNiRvxssj9/ZC3aA7y5s2A7MY16A2jEjh8KknXGzcxbfp0TJ02DdddXCgMpB5Sy21u7xcSN+JlkTo5IGv4QBSsWwlVTDR7Of8iXlzcLly8iFGjx2DBwoXw9b0L3VPtcUT9gMSNaHBwISs9dAAZPToKoxJ+65JyceOJKQcMHITVq9fgYfhDYRlRvyBxIxoWVVWoFGWjcP1qZPbpBonDRTCzzFBZDReyPXv3okvXbti6ZRuSk5IMNUR9gsSNaFDolUrI/e8ib8Fs5Ewcgwo/X0PNL3AXdOOmTUL23b17LZGfn2+oIeoTJG5Eg6JKLIbkrB1yZ0xC4YbVUEVHGWp+gYd9LF22DI2b/ISjR4+hvLzcUEPUJ0jciAaFNj8PRZvXCRMvi22PCy7qbykrK8OsWbMFcTt3/jy0NJVfvYTEjWhQ8HxtfOo+PstVhbcndBXPWmWZmZmYYD4RzVu0hKvrDcNSor5B4kY0KHjmj6wh/ZAzdQLUSfHPdCbw9rbo6GiMNBuFdu07CGEgRP2ExI1oMOhkUkgdLiJrUG8UrFwCrfjZlA5qtRoBAYEYNnwEevbqjeDg6pmwiPoHiRvRYFAnxKHEcpcwy1Xpof3QPTUq4QkymQxubu4YPmKkUMLDww01RH2DxI1oMMh9fVCwdEH1kCsXZ2G+0t9SXFyMS5cuY8RIM0yZOk1wUYn6CYkb0WCQXDwnJKYs3LQGysiH0NfQC5qbm4vjNjYYYWaGxUuWICEhwVBD1DdI3IgGAReykv17kNG3G0oO7UNlQc2BuRkZGcLohJGjRgmBvKmpqYYaor5B4kY0CLRFRShYvQwZvToLg+Zrckk5iYmJWL9+A8zMRsPSygrZ2c/GwRH1AxI3wujhQqaMCEfunOnIHmEK+b3nh3c8fvwYCxYsFMTt5ElbFBQUGGqI+gaJG2H0VJWJIbt+VRhylbdwDlSPIg01z8Iz8E6cNFlId3TlyhWIxWJDjRGh1/N/NcCXs2L4X82wWr1OiAfU6X5v3drgN8d7hQOSuBFGDx9iVXLAEjnTzFFitQuV6WmGmmcJCgrC0GHDMJqJm6enh/GNK9VXQauUoUIiRpm0AuVKDTRqJVQVEmGGL7GM/V2le45oaVAlFSEvKQLBIY8RFl8EifItJvHUa1ApyUJuYihCwqMRllQKsfzlh8KRuBFGjyohTpgnIWfKBKG9raq0xFDzLH5+fujeoyfGjBkrCJ1GozbUGAm6KmikeShMCkWk3024Xb2Miw7OcHL3x93wVKTkyVCurUncdEwUc5EbegXXrddg0ZqD2HrhEVJK3tb10UKrECH7wSU471+OFRussc0xEQmFL5/uncSNMHoUIUEQjRqC3OmToAx5wAyC50/24uXlJUznN278eMTGxjI3yNjuIT208kIURznj9oGpmNm3GRq36o9us4/D6kY8EgvlUNbo+6mhKIpF+Pk12GrWEj91nYzBOwLwMO9tTXmogKI4Eg/OrcaGIc3RpsdUjNgXgZAcEjcSN0KAC5nM1RmZvbsIAbza38nNdvXqVfzUtJkwf4JIlGNYalzotXIocu4i6rQ5Jv30P/jj/zXDjzMdcSSwCCWKStTs+GmhluYi0XUn9pt9i+9aDUPnDXfxQKQ01Nc2aqjLsxHjugs7B32NZm2GodeOUARkkbiRuBECXMxKjx1CVv8eKNmz44VWW5VWi1OnTqFxkyZYvGQpZDIjzuOmT4MkaCs2D/gSjX4YCFOrGNwSGepegDrhBjxWdkL3XqPRc5PfWxS3asSPnXFlThv07WWG/rvDSNxI3AgB5l7xkQiFm9cjZ7wZJOfPGCpqRiqRYN/+/UIet/UbNqCqypjvn0yUh+3AdtPv0KzJEIywTsTtl0g4rEh0g9earujVdyx6bfZDSI3ipoeOXTvdy/RsVlVCyy7z8660NP4Gri1ohwF9R2EAiRuJG2FAp4Pspgvy5s8SXNIKn9uGiprJzhZh23YLtGzVBrt27zYsNVK45fZgO7YO+hZNGw/GsANx8PiVF86USZmD9DBf+N10hYe3L257eeLaoRXYOLo5GnUzR58tfgjLfdLmVonK/DikRfrjnp8PvN0c4HThHM5eYX8/LkTezwazGhpxGpKDfHD3lhvcPN1xy8UBjg6ucPKJRXReBZ6WS0nMdVyd1xb9+5C4kbgRP8ODd0ttjgjjSYt3W0AdF2uoeRYe3xUbG4d16zegW/ceOHT4sKHGSPkdcatSpiH3wXmc2bkBa1ZthsWBQ7Dasx2bp/bFkHZf4YPWE9F3WwAi8nlvqQaV4mTEel6Ek+0x2Nja4Pj+dVg/cySGDzLHhI0OsI+So6SyCjp1ItK8D2Mve+HMnrcOm60P4OCOeVgwbhQGj7eAxfVYxLJdPnlySdwMkLgRT1NVUYHCTeuQ2b8HyuztnpnC72mqqqoQHPwAS5YuwyBTU5w++2IXtt7zQnGTIPueLRzWTcOi9Yex3TEMD6IfIyoyEF7H5mNRj6/xWfPR6L09GA+5uKmjkX3/NA4eOAfrc/cRlZKEpLgI3L+wGdvN2qB9p/EYvjsAvnkSyNKvwG3LcPTqNRkj1jrCKyYasY8u4czqYRjaqi9GrnXBhVRAbnBpSdwMkLgRP8NcUnVmOnLnThfErcLHC3q27HlUMivP08sLs+fMwZixY+F09aqhxkh5Rtzi4SG0uTGnUBYID4vpmNHbDDOP+sPtqZyesojTODupOVq2G4neO0MRnqtAZdZl+O6bgHFzdmOBdQAexMQhPj4RETcOwGZKC7T8vDkajzmKo4/ykZviBt+jqzBv82Uc8S1kzqwUiiJvOG8chFGNGqHz1NPYHQKUkbj9GhI34gk6hQIV/nchmjQGIvPRUD1+ZKipGT7jlaOjkzD0aubMWfD09DLUGCm/FbeDCfAsYsurcqF7tA/7zE3RseMSrHKJQ1z1FgKKmKu4ubQTuvYai367QxGWU4oyf0ucmt4Wg8YuwKh1djhywg6nT5/GyQNbsWvRBIw1nYDxK8/gTHQxciuKIU6LREh4Ih7FpSE/7T5CPa2xfWIH9Gn0IzrOZOIWzMTN8OiSuBkgcSOeoC3Ih+TcWWFu0oI1y6FhVtyLUKnUQhiI2ahRzDVdisDAQEONkfKMuCXiNrfQ5ImQ3ZiHpb274Psum7DJJw1PR4jIY67BY1VX9Og7HgP2BCM0OxtZ11Zh18hWGDz/IFY5RCMoNBwPH4YjPPQBQoMC4e8XhPsRKUgRayB0P1SkIe3uFVw9aQvbS4647nMex9aNxPg2TdFrlh12BTFxMwTbkbgZIHEjnqBOTECxxRbkTpsIsc0RaAtfnN1DqVRi//79Qnvbho0bERX17HymRkUN4ubNmyQlsSg+PxmzO7TAl53XYPXtNDz9WqiIcYb7yi7ozsVtLxe3DKQ7LcXmIW3Qd/Fl7H9BVnY+RaKiJBlp/mdgt2MdVq21xuHrgQjOjoCv/RIs69ICA2faYicTN7HRiJteJ/RWvakUkbgRT1AwqyFv1lTkzZmGcg936MplhpqakcsV2LR5C3r07IW9lpYNIEllOqQhFthmysVtCIZbJ1eLW3kipE6zsbjjD/is6VRMPheF0KeGLChimbit6Ixufbi48Ta3AhR6bsDOYU3QavBGzL+UgfzfPnZleVCVFCBTXIpEnyM4v2okhk7bjeX2cciUKaCqSkW4/Tws6dQc/Waewq6n3FJprAuc57fFgL6jMXBPOAKzX36g/nsXt8qiRGTesYerxz24J2hQ9gZD1UjciCeUe95ClmkfYcC8Oj4Oeu2L3/gVFRVYuGgR2rRtB5sTJ4S5FIybbCjDd8KCi1uToRhxJB13pWyxLg/a0G3YPeR7fPHP9mg55yJOJVTiydWrSnCCy8IO6NhtHPrteYioIjkqY0/g4oymaPZjJzSdcBjHggoheqJB2lwke97EHXc/3M9IwN0z87CqT2M0HnUYG/0M6yAGIYfGYHLLpug26xwsw9jvZ+hQKE9wg8ui9hg0YAxMraLwIPfln+n3LG5qlISeweVZnTFkxBJMtktDtPj1BYnEjeDwIVZl9qeR0aMjirZueGEIyBOKi0tgPrF6ImZHR0eoVG9rQPj7Ro8qjQKKwiAkO87G7DZ/xT8+ao+2K7xwOlIMsUIMbZE7PHcNx5Afv8LnTcZg6FoHXAmOwsPoBAQ77oCl2ff4oVEPtJjnjGuPi1BReh8RJydjSruv8MlXndFhmiW2nffGHf/b8HY9hyOWp3DCMQAPc5MRfmUJ1vT8Cj90nonRu70RGBONuHhnnFvdH0O+/xxNBqzD3IvZiMyVo0IhQ27gCRwf8z1aNe+Bdstv4Vq0BArtywx9eK/ixoRHn4D4a0uxuM0n+Offu6P9gmtwTa+obnR8DUjcCD7kqjI7E8V7diCzf0+ITxwVwkJ+j+TkZAwbNgzt2rWHr6+v0ExilOh1zEXMRGbAKThv6IeB3/8Zf/xbI3w1xAIrTocgJLMMsspiFEWcxfmlvdG30df44htmqQ2dirFzN2PpnImY2e9b/PBdC3xruh2bnR8hsaIExUkucN00DCObfYpPPv0WX/zYAs3adkdX05mYsecGriaUoVStQPmDwzgzowXaftcIX7QYArNF67HK2hobF47BhJafolHTXui6+AKO3UtHStZjRF1ehXW9vsRXn7VEo3HWsHRPQpbs5XK6vT9x06mhy3SE794BGNToU/zB5Ct81Xsttt7NQdrzxza/EBI3Asz9lAcFoGDVUuRMHAuZ6zVDxfPRarUICg5Gv34D0LNnL0RGPj9Tb72HiZtGWojCmLsIdj4Km72bsWGrJXYcvw5H3wQkFCgg5+upc5AfeglXrZZiyfSpmDJnLZbvPIVDR47h5N612LJpGzYeZaIVkgHexq/VlUIcfROeh1dhzfRRMBsyBINGzsbMDXY4E5CB1Cd+bUk0Etz34+DKWZgxfSEW7zqFw9d84ep0Dpd3L8X61Rux/oQ33KPzkVuYjswQZ7ge34Od2w/A6qw3PKNyUKh4uef6vYmbXlWEnGu7cGFpH4wb1wvfffUNvmw0GEMtg+CW/XLK/FtI3Ai9SgnJlYvInTUVhWuWQxH8+yEdsvJy3LhxE3369hMmYuaTxBg3PF33k9TdT5ffpvHWQifPR0FmMrsmWcgukaNMKoFYlIn8QmatKZlQ/irVuJ6tX4TSjBjERkYhKl6EHGklVL96DJlbrCpDWVYiUpPTkFIgZ88p2465w+X5qcjIzke2WAM1cz2FlOfC92T1T74jX2bY0+/xnsRNDlVxGNy2b4Tl0kXY77ADS2cwt/TzpmhkdhS7fQuq3x6vCIkboasoF1KJi0YPR+mhfdCkphhqnk9+fgFOnz6DAQMHYeas2cL0fsSbwOTnV6L3fng/4qZMRmnkCexcsQur97ojKDMUD87Nxuymn+OzRhMx1joIUSqeZ+DVIHEjeP62/EVzkTW4nzCrfJWMdwG+mJSUVOzda4lhQ4dh/YaNEIleIrEZUed5L+JWlX4bceeXYY3FaWzxkKJQrgAeHcaZiU3Q/PPWaDHDFicStSh+RemvFrd0mOxNx5R7Uihfz7sl6jGaqCjkThiN/DEjoH/JQNzY6FisXrUaY0ePhc2R45CW/n7vKlH3eQ/ipkDuvfNwXjMX20554EqR0G/K7kp/RNiYwezHL/FZh8WYfjkbcZJXU7d9XNyOZMLESoTJ99VvHBRM1DPkKihuuKJg7EhIlyxi/ubLxapFPAjHlMlTMcV8MjyuuwMqeisaA+9Y3LRMxB4zF9QCK0dMx/KdZ3Ep6jEiHj9GdLw7PI5Nx5SWn+Kf/+qDjkvccDNFgVeZW2d3tBR/OhCF71Y4Y56tE67F+uFaeiCupwUYCv/b8P/ku/DJfogi5S9v6SJFGcIKEnAjPQjXU+89tf5vCq9L8UNEUTKq9NUSWqAQwysrlO3Xl63z9LGeLv5sW394Z4cjXpyFispf0vLFlWYIdXy/NW/LCqtzYecTXZwKuWFb3sAqKi/CHVFE9bapzzs2P2df3M2JRJm6On023zanohhBeTFwTb//4nNO4ed8D1HFKXjSmpJbUQKPzBDhWj73nPk5sf36iiKRLs2Duqq6sUGrq8KjklTDOb/ouH7C75FYls2+b/W11rB9pEpycZtdR+Gc09mxMwJxx88JUVuWI2JEb9xZOwMu4TfY/u/iXu4jyDTVrbhVOh0yZQXwZ8tcMtg5ZwRgy5n9aN+9C3qOGIjNFw/CIc6H7ZMfm30v9t0fl/wyFaCoogjumQ9Y3e+fs39utHB9+bly5JUqhBcmCnXPv9Zsn2zfbhnB7Hr9khq3XKNALLtHhOstXK8XHJv9HgG5j1FeyTyiBsy7FbcqCfSp5+BiNQ9jRi3GzGW7YX3yBGxOnsQJu+Ow3r4AiwY2wY8fNcY3vTdj+51MpL+C8bYlTo7Pdnthlul4WIxsiZ4W/fCvk8PwD7uh1eWUodgOwT+O9EAHp3nCTf6ER8VpWBl4HP+2H4N/HO/3y/q/LTYDWH1fLPQ/BLW2Om7Fhz1ozS9PF/Yr7L+m7U6aCtt2u7YYp+LckSf/JZeMRdj56nq23xq35YXVfXx6BLaGnEUhE2JOFXtwPNjD1uPaEvzjWG+2j8E1b2vLlrPv1sNlKSKLk3/eNpA9BLN99+HTM2Zs//1r3pYXG1Zn0w8r7h//WdD5A9jo4uQXn/OJQcI5D7ixmj14AZCoK4RtFexBXxN8ktUPFPZb47a8sHP6/OxoHHrkjMqq6rB3GXvQLyf5oD37/YRzPs3WOzcCIzb2wXnTFjjVvxFGL26PT46w38mmJ/rdWMleJpnCtlxc+UvI3NsCH9mPxIdnBuGDue3xl28+xp97fIP/s+iJD2zZ/s6w+4Z/L/bdNzw4JWzLcWbi8d2FCfjHUXbOp553zvycBmCkxyb4speJsqr6HuEvg3n3Dgp1QqlpW77Poz3x1bnxsE/4JTMJf4EdfHQVzRzYPXaM3SMvusfY7zHEbT1SJMY5wc3L8k7FTVuejWzHzTi1bTkWn/DCaa8ghAYHI5iXB2EIDnCBn800zOz0Db78fjCG7AuER4HQ9/JSbEzQ4ssd3ljdoTvsf/wP9Bv2MUxWfw2TXd/AZAf73G4o2/4NkzV/xX8f64NbTBiekMduvmUBR2Fi2QIm6//B1v3ql22eLps+gcmGf6L/jVVQVlbblo7sbWti3Ynt9//Y/p+z3ZbPYLLxI3xlP449JPd+tiZ4l/dMX0uYbP1c2G+N2/Ky/kOY7PwBSwOOoII94Bxufd3ODMPHdiNgsu7vbB9f1LztNracfbe/2poKFsWTbbkFNMvXCia7f2LHZvuvaVteNv5L+O7Db234Wdzs4z1hsr+tcC2fe86bP2XbfYyml6fBTxQFpbb6evHPcV7bDPUf1bwtL+s+YL9fE2wJPfPzcVVMLK4yi+0vTDiFc97Bjr3nB/SY+CUcWn6M1f0/w59XfMuuN/udN/wNH58ZIVhMHG5FPWYW49jb7Nh7G7Hjs/MazI7/0Z9g0p395hvZvbLTcL/w78V+6/Fe24VtOTYxN2Bi1ZIdl53z8+4Pvs9NHwsvz4iiJFQaLDfuGZjeXMvqeD0rNW3L98nPaW9z7I9yErbjSJi1feyxC/7jaC92H7Brwu/hmrbn9xD7Pfg99rTF2RB5h+KmhjL3Adx2bsGB3adxLUuDPEPNL7C3et5VOK7ojm7f/oTGo49jl18FXnYOoq0JwEe7gjCqw3Bc+NefcKzbt5i6Zwx63FqJ7q5L0f36kupybRG6O8zAZJ9diP7NDcDN/qHuG1j9TLbu4l+2ebpcnY/ujnOwO+KS4CJxHhTEYbTnFmG/3Zll9vztZmN98ClkV/ySpYKLm22sG7o7LxT2W+O2vFyZjT6uK9iDfc+wZTUZzH1ZxKzI7lfYsfk+atrWcM5cROPLsgxbVsPdPtOba9j2s2relhf2oHZ3msseOMef3UNu9Y64tbH6Wr3wnOdge9g5lCglwnYcLjJH2cMq1LP91rgtL+w7DWAvkZvsOz5NEnNT59zd//M597Cfjr3TuiKsQ2McX2iKwVfY+fJzvjKTWUsHkMZc4idodVrhZdT/5iq0OzkB/x7dAR98+SkaT+slWMDdbxjuFf692Pc7En3dsCWz0Jn7P8R9nbDf598f1ddqz8NLkKl/CWpSMSv/ABOs6npWatqW75Pt29RtLbMwwwxbVhPFLO5pd/YY7jF2bjVtz39/9nss9j+M7PJCw5YNk3ckbnroVdHIYi7NpuWW2LDfD3Gy52QB0SUi/MRUTG/2CT790RxmVoEIL69C5UuYbzsT9PjznjD80GM6dn/4AUI6NEOagy2SpDlIkojYA/GkZCOJuSkZsvyfLYkn8LaNVGmuUP/L+r8tfPssoZ3tyTAd3gbG25ReZjvujmr1v260LmYP/pP6mrdlhdUlM1fjiWv3BO6ucbel+thsHzVtazjnzPIC4SF7Gu7mcQvuhccW9pvF3GGxYSt2rSoVTDRe/lpxS/EJ/K+iJ+fM9lvztqywbbl7JX1KJDj8pcIfXn7sxIIURN++irh5k5E5chAyHc8imW8rqT5nvt6Ttr4nSDUVSCzNgut9L0yaMx2t2rbFriP7qu+Tn+8V/r2yf9UuK1yr3z1nvh2/VmU/3x8c/je33qrPmZeatmWFnTM/xhPL/gncYs1iv1/1sZ+3ffU58/vhyYu3ofL2xU2vhrokCYmeW3F4YW+06TUbQ9begl9SKROE3yiWTgN58UP47RsL8y9N8N8mf8PfOs/HovP34ZsoRomq+qF4Hnvjtfj/rKLwx2EbMOurxkho1xKws2MG4WuO5yLqB/wZvuwI8dTJKF69DIiOqV7+EkQGhmPRnAUYNnQ4PG96GJYSxsDbFzedEsqcUITYr8GWqaYYOH45Zuz3gvujAiZWv7HdquSQpAfC7+RKrB3ZHr3atEKbgTMxZdc1XArJRw4zWF4kblaxKpgcjIPJtJPo124QvJo3RsmcqVD7+zFfhLr3jRWdiFlXK5ZAZDYEZefP/u6s8k9QVMhx7qw9xo4djzlz5yHAP8BQQxgD78Byq0KVUozSrDgkRIYh/FE8YjKKUSBVMVfhN1Kl16KSuWyl2UlIfhSKhyFBCA57hMjEXGSXqpgLaVjvOVg9VsDkaApMVtxCk/6zsPubr/CwbRPIDu1n/sTvR6oT9RCdDvLAAGSPHAzRBDMoIx4KU/q9DGKxGNu2bcfAQabYyj7j4p6eLYCo77zDDoW3j9WjcvzhRBZMdkXjr6M3YfBHH8P5g/+GZP4M6BLjmc6S9WZsaPPzILY9jszBfVGwdjm0RXyWk5ejoKAAM2bMRJeuXWF3+nQDSFDZsDAucYuS4j9sc2FyKBt/mG6N5l98Ddt//hlFowZDceUCtMUvf+MT9QP5vbvIWzQHoqnjIbl8Hjrl0/OVv5iEhATBauvUuQu8fXyE6f0aFHo1VDLmVbEXRH5ODnJFIuTkF6CgpAylZRJIpVJI5WwdnqFDVwlNRRkkhfkoyGPribKRLSpAXrEMUuZS/Ww26CuhU0shKy1Efl4+cnJy2X6zkJfP/i/RQP4OL7GRiZsE/99JJm5HcvGn5efQtVsfHG3fDLEDeqKQPQBq5uYSxgOfh1Rsa4PMgb1QuGE1VHExbOGLWmV/gWfave3tjU5dugoCx4WuYVEOdW4w7jnY4MgeK1gfY59WO7Bn4zps2mWNvcdOw97xBlyCM5BcJIW8MAoR107ilKUlDticwPFD29m667Fy23nY+aYiS4vq6IeyZOQ9cICT/SkcOn4Wp47vx/4N87B+015Yuonw8B1GpxiduP3BRgQT62x8vdMdk2cvxBazIbjUoQ0Su7aD0u4EdBW/DqMg6ie8iYFP18eTUmb26QqJ/Rno5L8OnXgR+fn5wlwJXbt1x6w5cwUXteFQiYrsAITbr8a6efMwddlBHLA7j9PHtmDHnEEYzK5JF9PZmLPvOs4FZSEt9SFSbmzGOvNRGDh6FTbZnsfFc3tgtWQEBnUehTFrruKaSAupVg7xAye47ViObZZHsdfJBVcvHcPJ5f0xd8okTDwcj+tJhq/wDjA6cTM5ngWT/ZnoaheObfuPYOqYkVj04/cIb9cCijXLoQp5wKzxVxmxStRF+LwIEoeLyDEfLcxypQwJNtS8HJFRUVizdi1MBw/Bnr2WKJP8EmBs/JQg1WMX9pm1w4Dxm7H4aiGSSypQLotFjOsarOzRCK07TsekM+l4UKRFZaYHIg6ZY9TIORi2yRuB2YWQiR8h5NIiLGjfHD2G7cTW+wpkKfORcGEHdow0x6pjrnBmLmtJeRnkj+zg78iswasZuP0O84Aan7gdzYCJVRrG38qB4y0fjBw5DP2++Qb3Rw2HbPJ4lFru/N05LIm6jzopCfmL5iF7hCnKbI8LkzC/Ch6enhg1ejTGj58AZ+drkCsayiBz7jwm4eG52ZjX/Cu0M7PCen/upHIqIX18EsdGNkLn9mMx/Fg6wkrY4ooY5N47gxPnb+Pi/SLIFAWQZd7Gtd1jYf7T52jVfz2W35YjTcFE8sIKrOrUHH3HrsKymwmIFGK+c1FZGovIBClSX+1neiOMT9yO8HxuqZj/QI6w+BTMmDwBnVq1xvWVy5E1ZjhyRg+F4q7PKzU8E3ULnUIOmet1ZA3qg9yZU6CKjoJe82rW+ElbW7Rr3x6LFi1GTEysMI9Cw4CLWwbinFdibbdGaNdvDeY4lCBdaOhXoST8GKyHMmus+2SYn05BmNCBXAVoCiBKiEZE4H08uOcJPx87HFo7CmNbfIX2QzdghacCqewFUfbwNC4t6o2hnTqizcD5mLH1LM7cDkF4Rj5ypTxxAd/fu8H4xI1n4t2TgsXhaqQXlMJq+yb0GmSKbcuX4z6z3PKG9EPZzq3CA0HUT1RRESjcuBZZQ/ujxHofqpjYvQoymQwbNmzEj40aYfeePZC/QludcaCGOMIeTsv6oH+fiRi8+Q58smRM4FOR6L4d60wHwWzKXuwPKUeGMLhHC700ATE3jsPWwgIWhy7D8YEv3Bw2Ym2fpug3ZBWWuCmQVKGHTp2NotCzOLdhLEZ1/AlNf2yNpr1mYvrem3CNl6KExO31+EXckrEgRIFCmRJ3XJ0watIkjGQuiNPa1ZCuXoqiUUNQevzIKzVA10t4ALVaAUW5BFJJGcRi9imTQ67SQKNRQSWXQSZly8skkEjLUa6orJ6Yw7B5XYTPSSo+eRzZQ/ojf+kCKB68Wlubhm0fHR2N6dNnoG27drh06ZKhpoFREY8cP0tYLJqL8dO3w9LOEdevn4X9sb2w2GkH25sxSJDw1LLMWc2NQKLrLuxcvRLz1p/BWe9HiCnMQlzgQewd3BKDBq/AYtcKJPw8qb8YRXE+8Dq9BRYzB6Ffq2Zo1mUSRu/ywg2203fV4m204jY7QIoylRa5qQlYvmqVMDDaascOSK5cQsFIU+ROM4fifsBLR7PXO+RFkCUHIuTubdzwCoDffeYahAcjKMAH3u6uuOF6C+53AuEfxJaH3cf9ez645eIDn4A4JEnUrzVBz9tGX6WFKvYx8ubOQFa/HpBePIeqV+wI4LFb5y9cwPDhIzBu/Hj4+/sbahoSemhkicgNtsOZA7uwbsM+7D9wDMePnoDtBXe4RRUi5+fh2HrIgo7i0pwO6DJ0OSbYZqE6S5wYOb5bsaV3E/QcvB7Lb1UgtZy9NJUSFJVqeVpahgKq1FvwthiMMR1b4YveW7DySiLeVai0cYrb7mRMv1uKiio+u7YaJ06eRNMWLTF32XLEedxiLs0a5A0biCL2qUkyzvgmffYDJJ9fjq0rl2DielscPOuIm7fO4rT1Miwa1gO9e47CsGVHYHn6Ktxc7GF/eDtWjp+DRcuPwj6hFL9OilQ3qMwVofTwAWQNH4j8xfOgiqnOS/cq5OTkYCV72fXp2xfbd1ggJeX3Z8cyPjQoeugMt61TsHLtdqy288a1W77wv3MHvvdCEBKTjvQSlcHCUiPX0wL7hn6Ln7rNwWibNIOrmoL4KwuwqOO3aNNvLbPc8hFfnIHkSH+4XItEgsjQQaMvhdx/G2zm9EeTXmsx51QE3tX0O0Yrbnz2K4XBv7rDfrRBg4dgyOgxcGBuSOFtT0iXzEdW/x7MxTn2yj1t9QFl/D2EWy/Gjp3szexwD+6B4YiOuYVbp2djerMP8ek/O6DFnHM46haOx1H3EXTbCedXLsWOdZawjijAozqWSEWvrUTFbQ9kmw2GaNxIlLvdeK2YRT7h8oCBA9GzVy+4ubmjvPxlswUaExoUBNjizMQW6N+J3QdDZmLMlNmYN3smpk+bgqlTpmLS3C3YdMoHd5KLkBB4CqenNEH7H1vgu/4rserAaZx1u4BjWydjYvN/4rvveqHH6vM4ec8Ll212YvXYedi4+zycQxIQnfgYsVc2wHrRBAxaYIe9t7PxrqbfMWpxkxuSjqSmpmL79h3o1acvlqxeg9SEeOhuuiBn9DAhTkp61QE6IwsFKM9IQoKHG4Kj4xGv1UOt10Ovz0ZOyE5s6/sDmjUajgG7wnE3q0rIM6bXqlAZfQ+JAXdwO02ChDp2OdSJcSjavF4I2C3euR3a1xgHykclODo5oXWbNhjFXnQN02rjaFEWfQ3Xl/fD6I4/4rumrfBTi9Zo1ZqVli3QollTfP99a3QYugzLHWLhF/UQobZzsHJwWzRv1g09xszHHMuT2GlpgW0Te2JYt57oO3cXdri4w/74Lmw1G4Hps9Zh3SkXXHK+gguWG7Bz8y7suh6D+7m/yQT0FjFqcStnDzWH39R3fO6gX/8B6MYEzjcgEGDWmuSoNbKZ9ZY3axqUYaFCY7WxUCmvgLSgCDKl2tD+wSlAYYQldg1ojJY/jYKp1SMEPJ0OWSNDpbQURfJKyOpQZAS30MQnjiJ76EDkzZ0O+d07hppXg2f92LR5Mzp36YINGzdCJmuIVhtHhrzIW3DZswXWB47B5qYHXD084OHhyYoH3FyuwGH/MuxdNx8LD9/DuRApCjMeIu72eVywtYOd8x14Raay6xmN2LtX4eZ0FVfuPMTD9HQkx4XjgZsrPFxccdPTG563feF9JwhBUalILVGyZ9LwFd4BRi1uUs0v/X58eM2cuXPRvGUrWO7fj1z25q9KTkTZ+lXI7NsDhexTFf3LZDHGiQg5obth0b8RWjQZiUF7HgqWW12GW9RczETjRyLLtK9gZVeV8sjSV8fR0RGDhwzF6DFjcN3FBVUNMUtMZTk0WZ64ffYANm13wvXo57j2GS6IPLsO2+38cDaaR8BxmHWvqEBFJe9mMKBTQq3RQikYZHypHtoqHarkYsjys5CdlY98me6VJ1ivDYxb3J6acZ5nfLA/dw6DTAfDjN3crp6eQuCn/mEY8ubNZALXDSX79qAyuy42pdcW9UzcdHooH4ajYMViZA3oiaJtG6F5zd9Hyaz3zVu2oHmLlli/foPgkj6dArzBoCyA3M8CRxaPRo8JVthyJQrpYikkzIrl7Y8ymRRSST4y/J3he+YYzvvGIYC9S15LnPQ66Nhv+L6ucoMRN05KairWsRu7afPmWMM+JTz4k4lehet15EwYhazB/SA+Ym3Ew7Pql7jxF02J1R5k9uqM/IVzoIwIf62cfGq1GlGPHmHc+Alo1boNHBwchKaKBkllGdQRx3FhRT90bdUJLXuMxcSFG7B22x7ssdyNnRZbsXUbu0f22+PszYeIEJWjlLmS9fE10KDEjU/Ie93FFe07dMSgQabw8fODmqcfFzMT+solYZxi1pD+KDt76qVTVdcv6o+4aUuKIbY7+XOG3fKbrswQeL3vypNQWh8+jB49e2H8BHOhx7ThUgl9aTTi3A7g4NJxGGtqiv5DxmHMpFmYOW8R5i9ZieXrmdBd8INnsgKSOtT2+qo0KHHjJCYlYdnyFejSpavwmZhc3WOmLy1B2cljyB42gD1QpiizP40q8S+TJhsH9UPcdMw9Kr91E9njRiBr6ABILtq/UaLRCCZmY8aOQ08mbseP2wjpjho0ukpUKsSQ5CcgIcQH3tcd4XTFCQ4uPvAKjsHjjAIUSBWQ11OL7QkNTtyUCiV8fe8KDctt27bDZe6iGEYpcDdIfPQQc0/7Inv4IJQxy8G4YuDqvrhxt7PC2wu5MyYJSSiL9+54o3ZQqVSGs2fthbY2ngEkNjZWGIJFPEGDSmkJSooKUVBcDpkRZQNrcOLG4QOnt27bJtzws+fMQVh4uKGGCVxWJsTHmMAx9zR7BBM4WxtoMjPYU2cMjc91W9x0KpUwJC5//mxk9u6Coi0boH6F7Lo18eBBCGbNmo227drD0tJKaH8jGgYNUtw4d+/exZQpU9GufQdst9gByZMxiuxB0ubmCJOOZJkNFjoZSvbvhSYtlT19z99f/SAHuWF7sEMQNzOY7o2AX/aLzknLLKkKKJUKVCh1b3V2RG6xKUKCkb9oLhO2rihYvQzKsJA3GvvLhczKah86duqM6TNm4F6DHEfacGmw4lZWVgaHKw5C50Kv3n3g7n7rV0NxKkXZEJ+1ExqzuXtUtHEtFMH32cNWn12aQhRFWQlBvC2a8CDeaNx/gdddWZqEnIBL8PK8C7c4NfLe1mh6pppyfz9hvCi32PKXzBOETv8GPZpc2CIiIjFypBlatmoNe/tzwlR+RMOhwYobJ5sJ2Nq1awWXZdq06QgOfvCrBlRtmRhSl6vImToBmX26I3/5YpTf9oC25PWCSN8feug1CqgkEXjkugTzWn2Mjz7sijZLbuJKRClkKi1+O/k/R53hjwSbOdi7yxrrveR4/Ba0QSeTQX6PCdvCOYKwFSxbwFxTf+h1b9YMkJGZCYsdO9GhQydMnjwFsbE0J2lDo0GLG49QDwsLw8RJk/FT02bYsXMn8vKeHo/E1pGUQX7XB4VrliOzfw+Ixg5HGbPoKnPeVW6DWkBXyQQ5BTmhZ3BhyyD0++av+M8/Nsa/B23DxnMPECGSQswu1W+vli4/AmLHFbA5dAxrPOSIqmVN15XLUO7uitwZk6uFbdVSKIICa2Wc7003d/Tq1Rt9+/bH5csOQjsr0bBo0OLG4SMXLly4iO7dewiZIs6cOYOKil/7XzyPmPJhGIp3bBayv2aPGIzi7ZshD/BHFXtA6zx6LaqkIiGBoJ/jIRzcvh7LVu3AlkNOcPSNRWJhBWTsUj1jK5UmQuttAYezZ7H5thzRtShumvRUlNmdEBIXZA7sjaL1q6rb2LRvPlCHh/ssWboMjZv8hNWr1yA3N69hjkZo4DR4ceNkZGRg//79aNO2HYYOHSaEijwTLsAejsq8HJTZ83Y49kD26Yq8+bOZ2+oMDXOB3qR96J2g1wkiXcXEgwu6RsM/tdBqq6Bj51bjo1+agEqv7bjMxG2Lt6JWxE0nr4AyOgolByyRNaSfMF60ZN9eqBPihWv8pojLyoRe0c5dugpjSD29vAw1REODxI3B3dP4+ATMmTcfzZq3EEIHQkJCDbW/hg/NKvf2EjoYeE8qf0AL168WZj7XyY0rbRJKEqBh4nbpTLW4PX5DcauSSiFzc2EvhVnI6NcdokljUXbudK31RCuYO+vj44N+/foL7ahnmCjzjiOiYULiZkDHHi4/v3uYYG6On5o2xbJly5HE3JvnweOvSq33QWQ+CpmmfZA3ZzrENkeFNiM+dMgY0OeHo9RhMax3W2GhUzFCXjOemacs4m596bHDyJk0BpkDeiJvwSzIblxngld784U+fPgQc+fNE3pHFy9ZgnRmkRMNFxK3p+Du2rVr1zBw0CDBRd26bbvQ61Zjew2z9vjwLHmgv5CtIntwX2QyayRv3ixIHS9Dk5oiuGD6ejxlnC4vDNlXVsN6zwGsdspB6CuKG8+6oi0sRLnXLRQsXyRcH2HGKqvdUD1+VKuuPB8/unv3HrRo2UoYP+p79y4F7DZwSNx+Q2lJCc5fOI/uPXoKGSR4EChvk3sePMGlOj4W0ssXhMBTkdlQZA8fKKRREh8/LFgsOmX9zEChlxdClhKC6MhohKSWo/AVvG5taYkgakVbNyB71FDBhc9fMh8ShwuC8NcmFcwyPMtc0B49ewptbfzvhpk+nHgaErca4O00R44eRZeu3dC5cxehgZpPLPIieFyWOjYGZSeOI3fmZGQxV5Xn++eCV3bmFOQB96BJSYZOJjVsYXzwyZK5cPHkkqVHDiJ31pTqcbpjhqPYcheU4WG10hv6NOXlFXBzdxfmRWjVpjX2Wlq+8GVENBxI3J5DYUEBjhw5go6dOqFTp86wtraGSPTi2DbuglaViaGOY5acw8XqJItD+gsxXDxfXMmeHajwdIcmIx06lVLovayNHsL3ik4nDJHSFhWiwu8Oitk55ow3Q0avzkzch7BzthBGH2iLimo9jTtvLuAdCBPMJ6Jps2ZYtHgxkpOTG2aGXeIZSNxeQHZ2thAiwsWtQ8eO2LNnD1JfclKRKrEYigdBQuhI4bqVyJ02URC4nHFmgstavHcnpE4OUEY+rLcdEDxjijzAT5hBjAfgisxHM7d8CHKnT0Qhc0d5SnB1Yvxr52F7EXomqiEhIZg6dRoaNW4ijB19wP5PEE8gcfsdeO6vAwcOolOXLkzgOmHb9u1ITEwUOh9eFj6aocLLo9qqmTQOmf17Cu6aIAJb1gl55Mo9b0H5KBLqlCRo8/Ogk0rr1ITR3NLkOdV42IaKfc/yW25C9pT8lYuFNrXMfnz0xggUb1kvTMFXySy5twWPQQwNDcP8+QuE0J2x48bhjq+voZYgqiFxewl4hLvNiRNCJtdmLVpg1arVr5zNlSdgrGRurepRFMrdXIUwkvxlCyAaMwxZfbsJ4RE5k8ehcMNqlNkeR4WHu7Au7218nz2uvEdTw763PDgQksvnUbRtE3Knmgtixns/uVgXblwLyfmzUIaGCCmjdBVvtzGfp6havGSpMGSOD4z3un0bciObmpF4c0jcXpL8ggLYnT6NfgMGojmzFmbMnInbt72FwNFXhaf34e1uFXfvoOyMrTCUi8d98QH6OUw4cqdPQu7MKcibO0Nw94p3WwhT20kdLzEL8JaQnYTPts7zzHFrio/R1Fe+ngAK7YQyKSrzcqFOSoDyYSgq7ngLLrPY5giKLbYwEV6I3NlTkMMszZzJ45EzZTzy5jPXeudWSK9cEiZx0T1JGfUW0WorERwcLOTga96yJUaMHIlr16833PkQiBdC4vYKcCFzvnYNZqNGowmzGnjq6qtXnZlll/v6jdh6vTBQXJORJgzQl9jbVYvd7GnIGjZQaJjnhY+E4JZd/qI5gnXHXdzS44eFCH+p02WUu9+E3O8uFGGhUMXGMKFKhIa5uJrUZOZKplSXlGSokxOhiouFMuIhFAH3BPeSCxQf51l60EqI2eNixgWMh2/wY/OhZtzlLFi5RAhv4W4nHxuqUzJhf0cdIjzcw8/PD7NnzxaCrEeameGmmxsUSqVhDYL4NSRurwhPaskDRBcuWiREwnft1h0WFjsQFxdvWOP14UG/vL1Nk5wkdDTwVEDS61chPnlcCKUo2rJe6IHNmzdDEB/RmOFMAPsja2Cv6na8QX2QzQRRNGooRBNGIZetwzNu5M6ZVl1mTELOxDEQjR4mxOLxcZ3cHeb56vhELHwQO7cYeV41LqAllrtRdtpWcKPlD4KEUBee546nKXqX8GBcNyZk48ZNEIRt/IQJ8PT0pEwfxAshcXtNHkZEYMOGjejWvYeQzXfu3HnC6IbfCxd5HfiYTE16mhAQzOcXkHGX8ZSNMM8qD5ItWLNMyGCbN3uqIGi8V1Y0bqQQkpFjzv7mgsYL781ky3jJmTRWiMfjlmDB2hXMxdwG8VFrSC7YMyvwhpAsspKHrDCL6X2SmZUlzIEwZMhQofNg6rRpuO3tzVzU+jvyg3g3kLi9JnwsKu9ouHTpMszMRqNxkybCsK2DB60RExNT+xHy3Ptjri8PghUmk1apBHdWJ5cLnRVVpaVCrywPvVBxlzP4vjCYv8LXGxU+XtXF7w7kQYHC/J88Fk+TlSEk3uQCxgNw9czF0zMriffSvs78oLWJkn2XhMREWO3bL3TkNG3WXBgvyvPvkbARLwOJ2xtSykSFz8fAZzHv3acPWjFXdey48Th1yg5ZzOp4L/BZvis1glgJ4ldRXl2YGPJAWh4jVpfhs567uLhg2vTpzPVvJaSB37lzFx4/fkzCRrw0JG61RGZmFk7a2mKk2Shh0H2ffv2xZu1auLreQGJiEj2UL0EFE2Ce2YPHFQ4bPgItWrbE0GHDccrO7pkMyQTxe5C41RK805C7opFRUdh/4AAGmQ4WMsH27tMXmzdvwf3AQGHMKs2Z+Sw8ILqgoAA3b97EnDlz0aJFS2HGqjVr1+F+UBB1HBCvBYnbW4C7ozdu3BQeTi5yHTp0xIABA7Bq9Wo4OV1FTn2af+EtU1RUhBtM1JYsXSpk9eCzkZmbm8PW9pQwqQvPEkwQrwOJ21uED93ik5Pw2CwucDw7LI+ot7CwYO6qKyIjowSLpaEN9OajCVJSUoReT0tLS4wbPx6t2rQRsrCsXLUagczKfZXhbQRREyRubxmpVIq0tDTB5Vq3bj369x8oDBviYjdl6jScZBZKRGQkZMylNfZJTPj5cUvN+44PNm7aJEzI04S77r37YN369XC/5YHMzExKMknUCiRu7whunfEQkYsXLwkzMo0aNRp9+/ZD3379hU6IZcuXC64YnxXd2BrPuXXKRxccO26DefPnY6CpqRDewUNn5i9YgNOnzyAmNlYIryGI2oLE7T3ArTk+RvLQocNCLjLeu9qseXP0699fePh5hwQPhQgPfyi4b9y95Z0Vuqq6//Bzd1IsLhPaHXnoBp99iufCmzVrljCP6E/NmgvuJ596z/XGDeoFJd4aJG7vCe568Qf70aNHQoM6T2c+kwmAkFG2dRuhDBhYbdkcZOLAhx/xIV4SSd3N5CsWi4VsKbydcdPmzTBjFikfvdGyZSvB9Zw9ew4OHT4Mb29vJCUlUy8o8VYhcasjcNfN19cXx21sBBeVD8rnbht34YYNH47Ro0djypSpWLZsBfbssRRcORcXV8GNjY6ORlZmlhBq8rbj6TSVGhSXFCOZWZShYWHw8PCEvf057N1rKfR4Tpo0Seg0MTUdLEyxN3z4CCxatBhHjhzFvXv3IC4tNeyJIN4uJG51CN7mxN06ngEjNTVVcOkOHTkiiMaQoUPRuk0b/NioMZq3aImevfoIAjh/wUIhjs76oLUgMjxTRnBICOLj45GWni64h3z+B24lFhYWCrNE8VEVXAh5EgBuPfHCXWX+f2598XW42PJsJzwbcTrbT0JCAoKCggRXkqd+2mO5VwhtmcwEt0/ffkIaKP7d2nfoIPR+8u905coVwTLl++XnRbO+E+8SErc6jFwuR7ZIhEfMMuMN8nxg/rFjx7Fly1YsXrwE06fPwFgmcNxK4g307ZkLyNvveNZg3n7H851NnjIFCxcuxOo1a7B12zbstbQSrChbW1vYnzsHB4crTIQchY4OPmsUtxyt9u1jx9giWIkzZszEKGY19us/QJhZqm379kKAbe++fYT9T5o8WciIu3HTZqHDwMXVVRBBnq2YrDTifULiVs+oYm5nTk4uwsLC4ebmjjNnzjI3dS9WrloliB3Pc8bdQR4Q26NHT/Tp01doxxs8ZIjg3vKe2TFjxgqpucebm2PixMnMlZwMc/OJwnyfXCz5OnzY08BBg4XeXC6cfKrD/gMGYvSYMcIogg0bN+Iwsyqdrl4VxCw7W8S+G03MQtQdSNzqKbxtjXdK8ASavCeVu34lJSWCyPBeSn9/f0H8eOO+7alTsD50CLv37BHcRR6Kwl3defPmY8bMWcLkKrNmzxZc3BUrVmITs8K4YHIr8fz5C0LAMW8v4/vlLi53Xbkby91nngWXxs0SdRESNyOFx9XJ5QqhfY23naVnZCAxKUmItYuIiEBoaKhgcfn7BzDh8kdAQKAQnhIeHi6IGO/NzMrKFoJuuXjSdHlEfYPEjSAIo4TEjSAIo4TEjSAIo4TEjSAIo4TEjSAIo4TEjahGr4VWrYCiXIZyPmKhXAG5mi2rqkJVpQqqChkq+GiGcjnkSg00VXrQ1SXqMiRuDZ4qKEsykfnQHyGBAQgIjUR4ZCQePQxB6P178PO9i7v+QQgKj8TDyChEhQXiwX1/+ATH41G6FBotDaki6iYkbg0eGbKCruDC6plYu2ojNttdg72TE9zP7cLBlRMwetBwDJ22HutPXoX91eu4fpYt37YI5osOYOfZSIhllDGXqJuQuDVoeGCuCI+9TsFqznxs3nYYp70e4E7gfTy8vhWHJjXHD3//HP/qMg/zzgXANSgEIT6X4XTKAjPnbIPFfg+Ulimqd0UQdQwStwYNt7oykRR9H9edmKBF50ChqRTSGmlTLuHOhj7o8nUzNBptCcsIBbJYXaVGhfLSTAS6e+KBVwCUchI3om5C4tag4ddHBomkFKI8ORSq6qUCudcRvH0gev7QGs3MD+NwAlBiqOIoSotQXlgAXRWNKyXqJiRuRA0wdzXTCf5bBqDH963QdPxBHHysQR5dTqIeQeJG1ACJG1H/IXEjaoDEjaj/kLgRNUDiRtR/SNyIGiBxI+o/JG5EDZC4EfUfEjeiBkjciPoPiRtRA+y6ZV1FwNYn4mYN65hK5D9vGKmmHEppCYrKFChX01hTom5A4kbUTK4LHhiCeJuaHxGCeIsNVT+jk0NbloKU8Du4dekcLtiewUXPUNwXqSChIafEe4bEjfgVen0VtCopKiJO4PqCNmjx8Vf4dMBmrPctQbysUkh19DPaUqiz7yPQ/RKOWazH7sXmmLvxMDbfyEWymK498X4hcSN+hU4jRUlKMEJt52N97w/xyR//iP9sPAZD9/jgSng+8pnA/XxVtcxyE2cjOzMVcZFeiHDbip17DmPF0RhEZz09losg3j0kbsSv0GlkEKc/RKTLUZzaMheL58zA9FWW2HEhEF7RhSgsr8TPtlsVu74/Dy1lTmvqJVx3cIDVlXQk5qkNywni/UDiRvwavQ46rRoaRQUqZBJIJGUok5ZDJldBqalievacDgNpNkqDr+Hu3fvwStWgSEUdC8T7hcSNeHM0xajIisXjsMeIyyiDlC2qqq4hiPcGiRvx+lRVQFWcgMS7l+BkdxyH7d3gcDsGsamFKFU81TZHEO8BEjfi9VHlQPzoEs7vXo65U2Zi3qLVWLT5JA5eCsGj/IpfmuMI4j1A4ka8PpVlkIvCEOLjhqsOzrjhegPXbwXAJzQdIqmaXFPivULiRhCEUULiRhCEUULiRhCEUULiRhCEUULiRhCEUULiRhCEUULiRhCEUULiRhCEUULiRhCEUULiRhCEUULiRhCEUULiRhCEUULiRhCEUULiRhCEUULiRhCEUULiRhCEUULiRhCEUULiRhCEUULiRhCEUULiRhCEUULiRhCEUULiRhCEUULiRhCEUULiRhCEUULiRhCEUULiRhCEUULiRhCEUULiRhDEG6PXVUIjl6FcVo5yVSUqq3TQaTXQKCsglyug1BpWfIeQuBFEA0OnN/xRi+iqVKgozoIoNgwR9+/grrc3bvv6496DcIRFRuNR9GM8jklAfKoIohI55FWGDd8iJG4E0YDgwqao1EHOSm2KnF5fCUVJOtJ8bHFx/RhM6NcT3YfPxcwdp3D0wmWcO7IdOxfPwIxZq7HiiCduJZdDbNj2bUHiRhANCD0TNJVWj/BCFc7Ey+CcWoGkMg3UVW+qdHpoFWKUhNrBdUlbtP/wz/jvb4Zi0I7rOOPtB59rJ2C/3RzmvTqgbdfJGL/dDc6xJZC+BSvyCUYrbjN8i6FmPyJBEM9yM0OOHi656OSci00hYnhkKpAhqxQMAs3rCh1TTn3BXSTZjMGon77B550XYcGNPERWVEKjlkBV6IUbm0xh+uUX+LTJNEw6GoRIhR5vy0M1WnGb7VfCXyYEQdRAKLPchrjn4x92mfj6bBY6X83FZJ8iWEVKcDdHCYnqNb0eSTCyz03FxFaN8W3PlVjhI0Xiz89hMZIvLsCyZn/GP/+3NdouuoQreVWQGGprG6MTtz8cSYfJ3hT2VsrHuYRyXE2VU6FC5TdlH3tW+t/Ix/+ezITJ/lRWUvCHo+lodFGECbeLsI+JnHumHFHFaohfRehKA5F2ZjLMWzbCt92XYalHER6rDHXQItdtM3Z1/T98+acf8NMMW5zMqkKRoba2MSpx28N+EBMubpYp+I9j6firbSb+dooKFSq/Lf/Hno3/scmACRM0wds5xAr7/AN7bv4fW/4Bs+haXBFhum+xYCTElqpRodHhdz3WX4nbcizzLEFsJa9gG2pFeGQ3F4ua/w2ffNgV3VZfw3XmYEmFDWsfoxK37eFlMDnAfqSdyYL1ZrIjCSYWVKhQeabsYs/IPmaxcWFjgiaIHDcM+P8PssKtOetU/IVZdk0uiDDGqwAXE8uRW1EldEo8l9L7BnH7Ed8wcVt6W4JkvlyXC3HESRyd1BJtPvocn3RaiYUX45GkAQTtewsYlbg5pVag38189HDKZW5pHnq75lOhQqWG0vVaHn68JGLixaw3LmpPCrfgDjJhYwLH3dR/MCvvx/PZGOyej5OxMmSVa18cQsLFzX4KJrb+Hv9uOxVTTwXjVmwyEkOd4XlkLuYP7YHuA+ZgyoG7uJWsemvCxjEqcZOodUiRVCKmRM3MaI3wd6qUChUqvy2BeSqse1CK7y5kMwuNCRoXtadEjltsrR1zMM+vGBeYxRZZrEaBour3Q0aYuKWfm4pJbb/H500GYciaw9hxwg4nDu6G1c4dsDhwDnYe0YjMk6PibSobw6jEjSCIl6NEWYXtYWX4wj5LaKM2sUrB/xxPR8srOTC/XQQLVueYUoGIIjXklb/X0PYUpYFIFyy3H/Fl6/GYcOAG7L3vwdfHF74BEQhPLkHBzx0MbxcSN4JogPjnKDHUvQD/PJ2Jz+2y0OxyDsZ5FeLgIyke5KtQrnnNUJBnOhSKEKM21L1jSNwIoqGh18MxuQJdruUKbW/bQ8W4lalAgliDQuZ6vnYQL0fM3NKzXNwa4zshzq0MCe9gHGlNkLgRRAOC93RqmXgF5SlhHS0R2tN4G1ytIQtBzvmpmNSqEb7psQIrvCVIfA8ZQTgkbgTRgOA9nbxTQKHVQcP+U2uD5/U6VGmUUKbdRITlIAz65p/4W/MpMLdPgn+BCqpK3TsfMETiRhANCC4wb+J1Pg+9TgFpbhzirm/HsYk/oOlfTWDyr65os/gSrL3TkFIoB9O3dwqJG0EQb4xep0R5fhKSfC/g6v4VWLtgOqYt2YK1x2/B6X4m0osVeJVO19qAxI0giFqAubhVlahUKaCokEImlUAiK4esQgmFWiu085FbShAEUQuQuBEEYZSQuBEEYZSQuBEEYZSQuBEEYZSQuBEEYZSQuBEEYZSQuBEEYZSQuBEEYZSQuBEEYZSQuBEEYZSQuBEEYZSQuBEEYZSQuBEEYZSQuBEEYZSQuBEEYZSQuBEEYZSQuBEEYZSQuBEEYZSQuBEEYZSQuBEEYZSQuBEEYZSQuBEEYZSQuBEEYZSQuBEEYZSQuBEEYZSQuBEEYZSQuBEEYZSQuBEEYZSQuBEEYZSQuBEEYZSQuBEEYZSQuBEEYZSQuBEEYZSQuBEEYZSQuBEEYZSQuBEEYZSQuBEEYZSQuBEEYZSQuBEEYZSQuBEEYZSQuBEEYZSQuBEEYZSQuBEEYYQA/z+cKF9jsjWYzgAAAABJRU5ErkJggg==)
physics-General
biology
Legume plants are important for crop production because they :
Legume plants are important for crop production because they :
biologyGeneral
maths-
The limiting value of (cos x)1/sin x as x → 0 is :
The limiting value of (cos x)1/sin x as x → 0 is :
maths-General
maths-
Let f : R → R be a differentiable function satisfying f (x) = f (x – y) f (y) " x, y Î R and f ¢ (0) = a, f ¢ (2) = b then f ¢ (-2) is
Let f : R → R be a differentiable function satisfying f (x) = f (x – y) f (y) " x, y Î R and f ¢ (0) = a, f ¢ (2) = b then f ¢ (-2) is
maths-General
physics-
A thin equiconvex lens of refractive index 3/2 is placed on a horizontal plane mirror as shown in figure. The space between the lens and the mirror is filled with a liquid of refractive index 4/3. It is found that when a point object is placed 15 cm above the lens on its principal axis, the object coincides with its own image. If another liquid is filled instead of water, the object and the image coincide at a distance 25 cm from the lens. Calculate the refractive index of the liquid
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)
A thin equiconvex lens of refractive index 3/2 is placed on a horizontal plane mirror as shown in figure. The space between the lens and the mirror is filled with a liquid of refractive index 4/3. It is found that when a point object is placed 15 cm above the lens on its principal axis, the object coincides with its own image. If another liquid is filled instead of water, the object and the image coincide at a distance 25 cm from the lens. Calculate the refractive index of the liquid
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dWdVZ29/xc/GNGSWz3Dsk9emhZ7hDyI+DcUO7xI0kePqhRkad/Lz3EjEZ7cVxL9+8yKvqZUIQcDkXoLdH9n7jm9tFYzjtsoLjUdmeSpE6e0NLcSpnN5ciP036JaCvydFrNbKOb12v1HKycvMMGSQSFC+eb1EtQXRd4Xf0oFCGHQxH65Vj5fL+kzzVpt1PvkDoVIZTbYqKA7Y5OKG2PJ+TngOIVlPCjV1F4ySI95IprLGgWOLHd2yXbfFNbS8C7jvwwFCGHQxH6hZgVKEwrUyePSWDKBKvEdtgAie3YItm7zVqG++3S1npDyM8F+z9lrbS8q+fKQrOn6T6jZ1BfddpIHT0spWCg7dHkTVCEHA5F6BcA12SPR1LHj2mbZzgmo7QWOXtNk9D5gLxjEO0g6kErd6TkvEMHiLt3VwlMGmdV0D1+aHkOMir6HhQhh0MR+nnA/61o/mbwekMjMxQgBKZN1JRJ0ee1Dp8S8h7QqMhE2HkULhz6Wrvuevr1NNdgFwnOmqr9qPQaZEfXv4Ei5HAoQj+RSkU3i9G6Ob5nl/jGjLQaz5mVKFJy5QS7nZIPBw6xwlkB7SLcvT4XV9dOWgyDvlRaQYf27yxaUChCDoci9BMwNzNEJnfntsS2bhRf/SDx1PWS8ML56oKMFs7seEo+JJqei1rt4ONf7NE+VDgUDVPcyKrlkjpz2koNZ9kQkSLkcChCP0y7vRE6m2J1Cet92O/g7EZ42SLJXrkk5ViUAkRsA+4b6tB9+aJE1q3WBRLSc+joGt+7S/LPn30/PdfBIiSKkMOhCP0wlbKJgHB48E6zJUCD+hkR6i/hNSsk13yLB1CJY9CF0sMHEt+1XQUITfS8QwdKZP0a7WdUCoc7nPi0QxFyOBShH6KilvrZG1clsmqFiX56WxY8WzbqzY40B6x6CHEKECKUa2OvKLRwnrj79BB33x4SmjPDOjht7nWNihgJUYScBEXoDcAFIRaVzPWrElqyQPd/YLMf2bBWsvfuSjnH/j/EuZQScXPtXpOoiYJ8o+rN9dtb/JPGaXoO543QvbcjlXJThBwORej7lOPmJr54Qfd9NAIaNlBiWzeppxd9u4ijQZBjFlGI1AtoJX/kkATnzdZUMs4WhRbNl9QpExV5zCQMO6kOAEXI4VCELNqLENDjBX1cVIAG9BbfyKES37nNMiFlBESqCFTQFUMBydy8JuHVy3VB5e7+mZZy67k2r7vNlbu203MUIYdDEWrDiBD2gJDGwNkLT11PtdNHc7H88xYeACRVizbPe3hfYmYxhbby6O4Lp3fd34TFFM4U1TAUIYdDETIYAUKePH3xvIQWzxd33+5qw4O2DPkXz2jDQ6oXc21r/yEssiIRSTedleCsaeLp3dVE+n0l0rhMMpcuSCkcqtn0HEXI4XR4EUIRQjQimWuXtQgBq0Rv/SBLgFAF19YFlZBaAP5z6fPntOITh1vRNC80b5Ykjx6WwssXNXm4lSLkcDq6CMEuH10rdQ9oYB/dA0LaovCsRUteCakpcPYtmdIFVnzfbglMGW9d9yOGaEdX2FJVirUVEVGEHE6HFSGkKQoFyd2/pyfNvageGjlM4l/slgJOmbMIgdQw6rTg80jq5HE1QkXBgmdgX6sV/e3b6k2HwoZaKFmgCDmcjipC5UxaxQZecLj5tJf/ts3aRIxNwkiHoFySUiiklj/hxiVaPefq9pkEp022yrh9PqmUqt+SiiLkcDqiCKHUGmmH2NbNegYIXnCRlcsk9+D+t1VwJlIipGZ57fouZ2H5c1+iG9ZYZdzdOklg5lRJHPxK8i+eV31lKEXI4XQ0EcI+T/7ZU4nt2qEuCOjHgiZh2Beq9VJVQt6EeiRmzH3R8kQSX39pBGiKFuf4xjdIdPsWyd29o9WjaFVfjVCEHE5HEqFKqah5cLRJ9o0eLu7e3SS0YK5kb1yznBAY/ZAODERGq+cuNElo6UJxm6gIizScm0PKrpyszkUaRcjhdCQRKpobLPnNIfGPH61ph9CiuZK5eoURECGvgQUZfBPDK5froW10Dw7OmS6pMye1rX21tS6hCDmcjiBC2gDMCE364jnxTxmvvflDc2dJ+vIFveH0MB8hxKJS0TYl+adPJLZzy6seRSjnTh78SoquVpEqSs1RhBxOzYuQuaFK0aikzzdJcN5Mtbb3j2+Q1PGj+v+EkB/ACA0sq3BsAW3sPQP6iH/cqDYvxQdSTlZHPy2KkMOpdRFCpIM9n+CsqeLq1kn8Exok+c1hK61QpRuthHwQ4MZdyGv7+nTTGXUUQTUp+mphzwg2V1qw0PZwp0IRcji1LEJIw8H9Gn1VXD07i7tPd4nv3S3FQIBngQj5qSA9F4noYi66Ya25j7pJ62cfSXDeLMmgxX08/sqfzolQhBxOLYtQ4eVLiW3fon1U0E9FbUlanrZ9lhDyc9BW9w/uS3TTOnNP9VcxCs6YLKmTx6QYDLQ9ynlQhBxOTYoQTElDIUl8vV+94Nx1vXQFV2h9aR28Yyk2IT8L3DHouQWD06LPK4nDB8Q3doTVn2jyOEkePaT9iXDw1Wn5OYqQw6k5ETICVAz4JHX6hN4ccMUOLZijqQS6IRDy9iD1VnC3SvzAlxKYNFa8/XvpXivah+cftXUfRnrOIVCEHE6tiRDy06kTRyWA5l29u2pBQubcGfP/0W/FhyJEyFuBPdUCChbOntZFnrZAGVyn+6+5O7e1kZ5ToAg5nFoSoYq2ZbghoTkzxdXpI/E31JuI6LiUTGRUbQfsCHE6cFjAQe/MtSvaDNLTp7taYUXXrZasEaJSIm7ddzYv+ihCDqdWRKiSzWmPFKzEPAP7mZuhTuK7d7QJEEuxCXlflJJJFR0YoMJzDmfxQovmWW4k0ajtnnMUIYdTKyJUcLVKfM8u8Y0apg26UBUHo9JvzwIxBUfIO6c9ysE+0bMnWoHqGVynxyHgy2i1hPDaeiSCIuRwql2ErJRAXJtzoRAB6QC4YqNZHRrT0ZKHkA9DJZtRJwU4LPjHjRZPXS8JTJ/8betwm1rlU4QcTrWLEPLO2WuXJTRvpuakg9MnSebCeamkU9YDWIRAyAcDFagF10vtRRSYMkELFmAYnNi/V4puV9ujDB/wvqQIOZxqFqFKoai56PCiueLu9bm2Z8DZIDgiEEJsolQy96BfUqdPanWqB0I0dqRGSPkXz6yzRB8QipDDqVoRQg66tVX3flw9OqsIxXZtlwI6QdKShxB7MfcnDoxrb6IFczQ150Hl3Ma1kkWTvA9Ywk0RcjjVKELY5ymFQ5I8ekRDfVfPLhJcOEdbFFOACHEO5ZjlYI9qOTSRhBhFVq2Q7K2bVh+v8vtPy1GEHE41ihAs5FPnz2qoDw+r0OJ5koaRIpvTEeIsKmWtjkNxgnfoQHn+238Wd9dOEt20XgrPnokUCm0PfH9QhBxONYkQvKsAmm3BVh4GioGpEyR19pSU4glWwhHiAPQ+NfdipVSWci4n+efPJL5vt3j6dpeW//O/5MWffq8tw3P37n2Q/SGKkMOpKhHK56Xockl8z07xDOyjztjY7ES/E0KIQ0C6PBaT3MMH2rsrtGKx+BrqddGIezY4f7Ykjx+VgrmXX/k5vkcoQg6nakTIrK7UvXffHvGNHKauCJFVjWot/yEuZELIj4Aze/G4FEzkkz53RiLr14hvdL02k4SLQnDuTEke+0byz55JOZky921B7+v3DUXI4VSLCKlH1eWLEpg4RtxdPpEQGmpdvWL5UxFCbKKixUClZMKIS4uWZaMCDmeEvPWD1b0Ee7ex7ZvN/XpZisHgB7fxoQg5nGoQIVzkuYcPJbJutR5I9dUP0o3OUjxmuy8VIR2Zci6rjSJxP4aWLRLf2FHiHTZAfKPqdaGI9g7Zm9f13BAcTDTyef/Bz99AEXI4ThchFBvgAk58tV98DSPEN3ywxM2qqvC8BZ+1HkQI+SBoY7tCQcqppJR8XiMw1yS2bbP4x4wQV9dOZpHYQwLTJqr45G7d0P3ais1tHShCDsfxImRWTzhnEJg2STwD+khkxVJ1y0aHR0LIhwXVbkWvRzIXz2u3YnjEoXMx7s3A1Il6eDx94ZzlFddunWUzFCGH42QRwooLTtjhFUvUldc/ebykm858K0AfYFOTkA6Puc/K6bQ61WNfB1FOcO4M8Q6qE1f3zuIdPlgia1bqHm0xHLKc6zXt1jZshiLkcJwqQpViQVNuKMFGjxLvkAHaH6gAE0RqDyHvHavgIGmimpca+cR2bNEKN+/IYeIdMVgdslEBlzxxXPJPH2uRUKXovD1aipDDcaQImdVTKRKW5IEvxTd8iAn3e0pk1XLJ3btjoiOWYxPy3sE9GApK+uIFiZoox98wXC13vEMHSGDGFIlu3SippjN6EBUOJnBGcCoUIYfjOBEyFz/KsbM3rklw1jRp7fyxuegn68flJMuxCXlfIPJBb66iy0Q+16/qmTzcgxAfd0+41NdLZHWjpM+f1YwEUnROSLf9GBQhh+M0ESrn85J/8liiWzbo6Wp0aYx/+YXeHOaKtx5ECHmnoAAIh8Gx2MOZHv+EBnH36aru9DAJjpn7MX3pgp4FghsC9murBYqQw3GaCCEHjeoaVN20fvoX8U8aqykBoTs2Ie8WZB3SKa1kyxiBwZ4rLHW8I4aKp39vPe8TWjhHkkcPmcc8ryrheR2KkMNxpAidb9KVWOvHf9YbIbZzm5qWllMpxkKEvC2lkpSiEck/eSSpUyckummdBGZO1XQbKt38UydJdOM6SZ08po8pxaK6F1tx8L7P34Mi5HAcl47LZvXCR4M6CFDrJ38Wz6C+uhGau39X89DtbtrVkI8mxHZwn5hRKVsHTUuBgKQvnpfwquXirR8o7h5dxN2vpwSmG/HZtllSZhEIF4RyjTiSUIQcjuMKE8xFj/2ffMsTbdWNVg3qvju4Tu3fUydP6HkF7B0RQn4cLbU2kQ9crVMnjkt03WoJTB4vngG9xVNnxGf8aImsXiHJ0+beevFcypnqKDj4qVCEHI7jRAgrtlJRKvmcZQd//54aInqG9hd3767inzBG4nt3a1Sk5xLoHUfIG4FLdSlixOfJE0mfPa1nevyjh2tTOVS76b20c5vl7eb3SSmVtBzpa6wvF0XI4ThOhL4D0ge5Rw8kvmeHBKdP0j5C8I+Di0LqzCndVEW/+mrNVxPyzkD0gpRbNifFgE9yd5olefighE2Ug8gHBQfY88H70TWNkjp13EQ+z/T+qWUoQg7H6SKkkVEhb1ZqXklfPCeRNSt0A9UzqE5LRxElZS5fkmI4aB7b9jWEdEAQxRQ8Hq0mRZl1aPZ08TeMNOIzRPxjR0lowVyJ7dkpmSuXpdj60ir0KRVrLvL5LhQhh+N4EWoH3RrjMa2SSxz6Wg1NXT06i6dvD7WMT500qzpzYcGxFzlwQmoZrLfgMA/hqRgxKYaCmrqOYx915lTx9Oshrs8/Ee/gARJaPF/vmWzzbSn4vG2HTDtO5oAi5HCqRoTaKZU0f40ybmymalRkhAhphvDKZdrRUdt9l7lXRGoXVIi+aiR36oT22oKLtWdwP/H07yP+MSMlvHSRtkDJ3riuB1FRedoRoQg5nKoSIeS824amHlytkjxyUILTJ4u7ZxetooPFT+LAl5J7cE/KUet8AyE1Aa77XE59FXOPHkrq7GmJbt9stTmBtU73znqcIWwin9SJY1JAyi2Ttop3sChD9IP7p4NBEXI4VRcJvU6xaFZ4Hm37Hd2yUYLTJqrjtm+sWQU2LpHk0SOSf/xQy1M1901IlaFN5IoFrQTFogu2OlhkIQuA5nHIBKDiLQhT0TWNkjhyQLJ3mqUUDGhRD6EIOZ6qFiFgblKkGbDq0zLUtavMjTlcXL0/F8+QOgkvW6RVQOjOSki1AREqeN0m6jlllViPGyWefj014kFhTmjRfInv3qlFOzhgqi3vuSf6N1CEHE7Vi1A7EKNEQs1P4/v2im9Cg1W40K+t3fAXu80K8baJnHxSgusCzxcRh6HFBkZAysmElPw+LcJJX7kksd3bJTBzshr6urp+onuggdnT1Ng3e/uWFfXksipY5PtQhBxOzYhQG+i6CqHJ3Lgm8T07dY8IZoyuHl3UFBUmjdl7dzWvXuulqaSKqJSlbCbLks8ruVs3JLF/r4S0e2lf3e9E5BOYMkF93lKnTppr+I4UPG4VLF7Hfx+KkMOpNRF6nVIwqAdaw8sXq0WJu9tn4hs1TCKNyyRx+KCWtOJEOXPnxA4QueCgaNHv10IaFBrETdQTXrpAU22w1HGbaN43Yoj6vGmxgavViM4bIh4GQT8IRcjh1LIIqWeWERkUJySPfSORlcvFP3GM+EYOVcuS0JKFkvhqn2Rv39ToCVEUIe8brXALhyX35JGkzzXpnk5kxWKN2v1jR4p/zAgJTpsk4calmkZGm4XCsxYpo8CGnok/G4qQw6llEWpH8+zxuBGjRypGYRMJeU1E5OryiXpoBWdPl+TBr8yN/vTVTa75debYydvQfg3p0P/Qw9QwCYWRaHjFUhOZ1+s16On1uVkcDZPQornq55Y+fVIj9WIgYBZHGabc3gKKkMPpCCL0OijXxmYu7Ev0cF9dLx1YfcKPDuWv2Vs3rHw7TpYT8ksxwoF0WymAdNt9PWCNvZ4wInITiXsG9tX9St+IoRKaM0NiO4z4XLoohZcvpZJMUnjeERQhh9PRREijIiMupVBICi1PJHXcREaL5mmrCNfnn+qB1+AcExnB5gTVdKGgFR0xKiI/CXOdQHxSKV3I5O7eMdfYUYmuXan+bXCCd3X7TNxm4ROYPlliu7ZJ5uoVjY6K5ppEU0ek6+AMQt4NFCGH09FE6LtoZHTtilmFblHnBe+Q/mbUSWAi9owWtOXkzeoUvfVxBgNFDNQj0g6uBUQs5rpAEzicV8uZxQu8DGPbt6h7QWDKePE1DBdv/WA9XBqcPU2bNKbOnZE8+vdwL/K9QhFyOB1ZhFRLzASCnHtJre9vqw1QeNW3p9FRmQRBQoUdUnWZWzekiHMZXKl2eFR/EgkpPH8uWRPNJA/sl/DqRgnMmPKqwAAebriWkOrFkYFU0ymthMM1VDbXnR4sfVO1G3lnUIQcTkePhL4FLSMK2k8fTcBSp09KdNNanUjgRuzq8rF4hw7UirrUiaNm4mmRciymOf9yLmdNJkzZ1SRqnWMWHbg+ELUgnYvuv3Bth/jEdu6Q4JwZ5vroL65unaS100fi6d9LgnNnSnzXdkk3ndE9IbQjKaNxHK4V8sGgCDkcitAbMNGRmkQ+vC9J5PM3rJHgrGm6gYzNZERHoVlT9eBg8uQxbZv8au+I1BzW4iSmBQOZG9e1UVx0w1ptIeIfN9KIzwC1iPI3DNdKy4iJpOP790i6vbTaLGwoPPZBEXI4FKE38GrlW9TJA+aReSM0OFOESQbeXa4ufxW3WgJZp9iT3xzWNsna6RWTDjaXWd1UfeC1N6+5RrhGeIruVsk139ZDz/Ev9kikcan4xzeIu3c3cXX+WN0MsN8TXrFYkkcO6XWCr4N7O8RLB64lRMmMlG2BIuRwKEI/DZzvKLpdWsSQ2LdH94gC0yfpShiTUGBCgwTnz5Lo5g1GkA6q2zEEqRSLaAoHkxFxFioJ2BOEUJjXqBSPSxEVbffvS/rCOW0EF9u6UcKLF0hw6kStboOBqH/iWD1YGlq6SOIoq9YzPXe1Zw+uE+IsKEIOhyL0E8GMhVWyWeEiVafmkhfPqyDBiSE4a6r4xgzX1Az2BmC7gtUxTCa1BNflYkrGgWB/B4sFtLxOfP2lllKjLQJcNZB6xesJ8UHlZHjJAolt2ajpuMzVy+YaeKzWUN8eJkW0Yz0vcQ4UIYdDEfqFGEFChINJCM7dGSNIKMnVBmMD+1hnQfp0F6+ZzEIL50l87y61X8k/eqCTHrq/asm3WTnrSlw7wXIGe5fougGpsHxeKigmMH/vYtCv/mv5lieSu9Osfm2xndsltGCOtgBBQQHc1909uohnQB890AzhSZ86ITmYhrpb1X2DkW31QBFyOBSht0e9wKIRKTx/pvtCMJqMbdsiofmztcwbouSp6y1es7JGtV1oEUQJPWDOq5XQK0FiF9h3hpqDYpGA18Xt0r0aLBQQmYZXLjXiMkG8KDQZhHbYba+Nea1Cc2dKdON6SR74UtJnTmtrbO3Tg5LqdMqIGqPZaoMi5HAoQu8A3XRuex+Y1TcipOzNa5ZNy5IFel5EN7O7dVJHb//4Ubr6jq5bredH0AUWvWNQkYdJE44OWs6rK25GSD8IUqQm0tEePOGQFD0eFQ24XahNzqEDEtuxVbuOhhbMFf/kcZouhV8b2nsg5RaYMEYiOAe2b4+m5VB6rYUlr6Nhlf6jH5LqgSLkcChC7weIByZG2PTnHz+WzKVLkjj4tUS3bNCDizg1H5g0xjrMOG60pvEQOcE5GY9JmBW7bnjDx67liRS9bp1kK4m4mSCzHa7yrlIpt6XVUia6iWqnXOyz5Z88MtHKVUmfPG7+ZvtMBLpZImtWSmjpQj2n4zcRjxYTmL+zf9I4rW7E5yJG/GO7d0jy+DeSvX7V/I2f6nPi/E9ZbZravjGpeihCDoci9AEom9W6pobM5GmiHFRSYZWOlE9s6yaJrFiqk6OvYYSaqbq6d9KVOiyEAmblHl4yX6LmcalvDml1nh6UTSTMRPkjQqQR2ndH2/9/KNq/V/v3xw/Q/r4O8zvosB72RsznSiYqRIQIVwu0cUdaDe2ug0a4/RNGi3dwnbh7meime9te3LCBWsUWWmCEfXWj7tclDnwlqaYzkr3bLIUXL1R0UH5Pb8DahiLkcChCdtC2XxEOS9FMhrnmW6+8xkIL51qT6vBB1n4F9pMG9TUfD7b87ObN0tSSruIPH5DUqeNG0M5K5sol7YuEg7Nqhok25pGwbqIjrYcqMKSYtAiiWDTz/geKpDC5owwa3xNnZ0wUV86kTZRofiYjpOiRUwr6pYio5ukTFWjsq6GII33ujP5dYKUU27tLD4iiXBrGn76xo4zQDNDiAR1D6vRvhpJ5RJkRIzyJfXvNc5zVlggoRiiavzfO/5COBUXI4VCE7EGDgJKZmDEpQyQiES1Q0MotMxlnbt2UJAocdmyV8NJFWqUFpwbtEIu9JbPi1yquup7iqx8s/klm1W+igsjalZZHGfaYTLSVuX7ViNNtnYhRBIET/DDZLJrXvRQKqk0RBKFihAGlxpV8TgSl5KWSlfLTKAU/7Ouj/f/NwGMw8DVIl5nngIM0xA8NBbE3hu+F75l/9lQbDObu3ZXc7Vt6lipz+aKkz5zUqDC6bbOEG5GqnG7ExAjx0AHixsHgnp2tCKdXVz0o7DERog9pzFnTtC2C/r7mOSDCSM8VXj7XfR304tHfr12A8TuRDgdFyOFQhJwJqrtK8ajkn7eoVUzq1AmJ40wSLIQWzjGiM0a8RpSQdtJh3kclHibvwOTxGi1gMg/OnyOhRQskvGyxTtjRdat0zwmN0xL79+g+lRZFnDxmxOCEpJtOS+bCORUHRFeZa1cke90MvP3OwOdwXiZzxQjJxfPqkYafM3nsiJ6lwbkb/Mzxndv1EC8EEo4DEFW4SyPqC5rIDmesgtMm6u8E40+0YEfk58OZq7bfzY/DwHNnSmTVchXm5MEDVpRzp9kIXKsKKSFvgiLkcChCDgURB864FPKWaaaJLuBfhlP5ORMpZW/f0FP9yRNHjZB8peeQsG8UWbNKTVZhqIlih8DkCWZyHy/+ieN0jwQRE/aZdEwxYjV1gro8B6djmMebEZxhBGzmFH0bmGkEAiLRPvDxzGk6AubjQPvj4ByNt+Z59PnMQPTmn2KeH6Jovi9aqyOlqD8Hvr9+b/P9zPOEjLAiCoJPX9yIDFJpyUMH1CwWER1SdDkTRSFtp5WDSOUhekMVW8FEYRq1mb8ZId+BIuRwKELVR/sBTPU3MxEAUk5oDaCpvCePJdt8qy3NdVpSx76RxKHXo5Kt6nUXaVyuh2hhzAoxgEC8ikLqB2lPJexHuQf01gOcSAPq6I9h7cO42wb2rvRr0Ppi/CgjbuNUrLB/FTIRT2TlMoluXKcN3FAGnfh6v0ZKqExDGg1imrlxTfeD0GLdqgRs28/C3hEO9ObpVE5+GRQhh0MRqjHMJK3l4W0OAXp2xu8zE7tHCq0vpPD0sbX5f+O6mfzPa8uK9vQZ9mVQGo6oCi0IUCiBkmdU8Olbfb9t4P3tGOYxO7dJfM8u/VpEZcmjh7WgAOk5OElj7wf7QHApgBM1/NnQ8hoRje7ZYE/MRHu0NSLvA4qQw6EI1SAQIlSkIWJC8UMRFXFmoDoNEYUZ6IGkaT5EUxCsVyNlFRb80oGvx/PgefH8KLwwQwsDULiA0V6hh6E/oxlMp5H3BEXI4VCECCG1DEXI4VCECCG1DEXI4XxXhO7cudP2GUIIqX4ymawRocMUIafyugj17NmLIkQIqSkymZwcOnhYhg2rpwg5kXYR+t3vfq+R0N27d9s+Qwgh1U8ul1cRGjJkqAwcNIgi5DQgQmvXrpXf/OY38vHHn8jx4yckGAyKx+MRt3mhXC4XBwcHR9UNzF+Y31paWmTTpk3So2dP6d2nr2zZulU/X8tUlQjhhVq5cqX86le/kn/8p3+SMWPGyqrVq2VFY6MsX7FCli/n4ODgqL6xYkWjzmMLFi6Suv518vs//EE+6dRJ1q1bJ62trW0zYG1SVSLk8/lkq1kZfPTRX+V//8M/yH/+5S/SvUdPHd269+Dg4OCoytE+h3Xu3EX+9d/+TX77u99Ln759ZdeuXTrv1TJVJULxeFyams7JjBkzpa6uvwwfMVLGjhvPwcHBUROjoWGMDB48ROqHD5dGExldvXpV571apqpEqFAoiNvtkUsXL8mRI0fk2LHjcuLkSTl+4oScOHGSg4ODoypH+xx2/PhxndtOmI+bm2/rnncezh017NBRVSKEFwIvSDqdlkQiIclkkoODg6NmBuY1DMxxuVxOisWilGFrRREihBBC3j0UIUIIIbZBESKEEGIbFCFCCCG2QREihBBiGxQhQgghtkERIoQQYhsUIUIIIbZBESKEEGIbFCFCCCG2QREihBBiGxQhQgghtkERIoQQYhsUIUIIIbZBESKEEGIbFCFCCCG2QREihBBiGxQhQgghtkERIoQQYhsUIUIIIbZBESKEEGIbFCFCCCG2QREihBBiGxQhQgghtkERIoQQYhsUIUIIIbZBESKEEGIbFCFCCCG2QREihBBiGxQhQgghtkERIoQQYhsUIUIIIbZBESKEEGIbFCFCCCG2QREihBBiGxQhQgghtkERIoQQYhsUIUIIIbZBESKEEGIbFCFCCCG2QREihBBiGxQhQgghtkERIoQQYhsUIUIIIbZBESKEEGIbFCFCCCG2QREihBBiGxQhQgghtkERIoQQYhsUIUIIIbZBESKEEGIbFCFCCCG2QREihBBiGxQhQgghtkERIoQQYhsUIUIIIbZBESKEEGIbFCFCCCG2QREihBBiGxQhQgghtkERIoQQYhsUIUIIIbZBESKEEGIbFCFCCCG2QREihBBiGxQhQgghtkERIoQQYhsUIUIIIbZBESKEEGIbFCFCCCG2QREihBBiGxQhQgghNiHy/wGG/2wD8tngpgAAAABJRU5ErkJggg==)
physics-General
physics-
A thin equiconvex lens of refractive index 3/2 is placed on a horizontal plane mirror as shown in figure. The space between the lens and the mirror is filled with a liquid of refractive index 4/3. It is found that when a point object is placed 15 cm above the lens on its principal axis, the object coincides with its own image. The radius of curvature of the convex surface is
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)
A thin equiconvex lens of refractive index 3/2 is placed on a horizontal plane mirror as shown in figure. The space between the lens and the mirror is filled with a liquid of refractive index 4/3. It is found that when a point object is placed 15 cm above the lens on its principal axis, the object coincides with its own image. The radius of curvature of the convex surface is
![](data:image/png;base64,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)
physics-General