Maths-
General
Easy
Question
If a1, a2, a3, ........., an are positive real numbers whose product is a fixed number c, then the minimum value of a1 + a2 + a3 + .... + an – 1 + 2an is
Hint:
In this question, we have to find the minimum value of a1 + a2 + a3 + …… + an-1 + 2an. For solving this question, remember the inequality of A.M and G. M.
The correct answer is: ![n left parenthesis 2 c right parenthesis to the power of 1 divided by n end exponent](data:image/png;base64,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)
Here we have to find the minimum value of a1 + a2 + a3 + …… + an-1 + 2an.
Firstly, given is
a1. a2. a3….an =c ------(1)
We know that,
Always A.M ≥ G.M
So, A.M =
And
G.M = (a1.a2.a3……an-1 (2an)) ^![1 over n](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAAjCAYAAAB2KjFhAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAJhJREFUeNpjYCAM1IC4FogvMFABLAbiNCD+z0BFMGrYqGFDxrD/WPAoGOzgPwV4FIyCQQHqgbgEiMWBeD4QfwPid0CcR45hq6AaQQbZAzETEEsD8Q8g5iLVsFvQZgE6ALlOmBSDQK74gkWcBepdkoA5EO/HIm6JQxwviISGFbHieMEkIE4mQRwvWAfEXiSI4wWgGOMgQRwMANIqNUS92dJtAAAAYnRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtZnJhYz48bW4+MTwvbW4+PG1pPm48L21pPjwvbWZyYWM+PC9tYXRoPuobFZgAAAAASUVORK5CYII=)
From, A.M ≥ G.M, we can write
=> (a1 + a2 + a3 + …+ an-1 + 2an) / n ≥ (a1.a2.a3……an-1 (2an)) ^
Cross multiply,
=> a1 + a2 + a3 + …+ an-1 + 2an ≥ n (a1.a2.a3……an-1 (2an)) ^![1 over n](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAAjCAYAAAB2KjFhAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAJhJREFUeNpjYCAM1IC4FogvMFABLAbiNCD+z0BFMGrYqGFDxrD/WPAoGOzgPwV4FIyCQQHqgbgEiMWBeD4QfwPid0CcR45hq6AaQQbZAzETEEsD8Q8g5iLVsFvQZgE6ALlOmBSDQK74gkWcBepdkoA5EO/HIm6JQxwviISGFbHieMEkIE4mQRwvWAfEXiSI4wWgGOMgQRwMANIqNUS92dJtAAAAYnRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtZnJhYz48bW4+MTwvbW4+PG1pPm48L21pPjwvbWZyYWM+PC9tYXRoPuobFZgAAAAASUVORK5CYII=)
=> a1 + a2 + a3 + …+ an-1 + 2an ≥ n 2 (c)^
[since, c = a1. a2. a3…...an]
=> a1 + a2 + a3 + …+ an-1 + 2an ≥ 2nc^![1 over n](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAAjCAYAAAB2KjFhAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAJhJREFUeNpjYCAM1IC4FogvMFABLAbiNCD+z0BFMGrYqGFDxrD/WPAoGOzgPwV4FIyCQQHqgbgEiMWBeD4QfwPid0CcR45hq6AaQQbZAzETEEsD8Q8g5iLVsFvQZgE6ALlOmBSDQK74gkWcBepdkoA5EO/HIm6JQxwviISGFbHieMEkIE4mQRwvWAfEXiSI4wWgGOMgQRwMANIqNUS92dJtAAAAYnRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtZnJhYz48bW4+MTwvbW4+PG1pPm48L21pPjwvbWZyYWM+PC9tYXRoPuobFZgAAAAASUVORK5CYII=)
Therefore, the minimum value of a1 + a2 + a3 + …… + an-1 + 2an is 2nc^
.
The correct answer is 2nc^
.
In this question, we have to find that minimum value of a1 + a2 + a3 + …… + an-1 + 2an. Remember always the inequality of A.M and G.M. Always A.M ≥ G.M.
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and reflected ray ![O P](data:image/png;base64,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)
![](data:image/png;base64,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)
In the adjacent diagram,
represents a wavefront and
and
, the corresponding two rays. Find the condition on
for constructive interference at P between the ray
and reflected ray ![O P](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABcAAAANCAYAAABCZ/VdAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAARVJREFUeNpjYMAO9IB4LhC/BOJPQLwQiLVwqP0BxP+h+AsQrwJiRxxqGWqBeAMQmwIxExQHAPFDIDZHU6sCxBeQ+GxA7ALE97E5phqIZ+Kw1BHNIAaopUuxqE0G4hJkATUgvgF1KS4ACiJBJH49uiFQ0AHEOcgCPegCWMBuILZF4oPC1w9NjSgQ3wJiYWTBK0AsT8Dwx0DMh8QHGSKJxDcG4qPoEQoKim8EDGYB4g9oev5AU8k7qKHNaJbBY/kTAcNDgXgxEh+UcvYzEAFArvhFIDKPoiXFSCCez0Ak2ALEiTjkKrEk0UlAnEas4SrQpBgPDV8QMIAGBba0vw6IvRhIALLQbA+KoNfQDGKJQy1IDQfDQAEA8+k0isiZVGcAAABTdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPk88L21pPjxtaT5QPC9taT48L21hdGg+VjfoXwAAAABJRU5ErkJggg==)
![](data:image/png;base64,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)
physics-General
chemistry-
Select the rate law that correspond to the data shown for the following reaction.
![](data:image/png;base64,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)
Select the rate law that correspond to the data shown for the following reaction.
![](data:image/png;base64,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)
chemistry-General
chemistry-
Select the rate law that corresponds to the data shown for the following reaction.
![](data:image/png;base64,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)
Select the rate law that corresponds to the data shown for the following reaction.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAWQAAAB7CAYAAABD7PraAAAgAElEQVR4nOzdd3Qd1bnw4d+005t675KL3G1ccMHd2KaGEhJCaAk3kPrd5CaEVAgkhIQkhJAQQguhdzDFYBsMNjbGvduSJVmWrF5Pb1O+PyTAxgZyc5Elm3nW0lqSzpyyZ+a8M7Nn7/cVgtG4gclkMpkGnTjYH8BkMplMfcyAbDKZTEOEGZBNJpNpiDADsslkMg0RZkA2mUymIUIwDMMcZWEymUxDgHmGbDKZTEOEGZBNJpNpiDADsslkMg0RZkA2mUymIcIMyCaTyTREmAHZZDKZhgh5IF5UU1V0Xefo8XQCkiwhieYxYODoxKIhmuobiGmgo5CWkU5GZhqK0L+ErqFpGiAgSjKS2P+AkaSnq5P2tk6ShgCinfyiXDxO+0l01Nbo7eqko62DmA4IFvIK83E7bQi6hq7375GCiCxJiP1tN3SN7tZGugIR4kkdu9NNelYuXqeCMHiNGQIMDF1HVbUPv8uCgChKyNIn7BWG2rcduvyIzlSKctKOXt7QMRIhDja0YlicpKSmkuq2H/+ldA014qehpQPZmUJqaipu24CErSFhAFqms3Xlk6zbWUcw8eF/BUcGZ521lAkjCv/jV26v3cmummZw5zHr9DEoAp/zL8xHGBrB7lr++qtfcFh1INt8zDn/S1x6wVyUvgWo2fgyq9bvIyT6GHvGQhZPLOt/coKqzat46LHl9MSSRIRsrv/NjzmtNA/rybKSjQT733uNex58nqDoxG7P5uu/+AHDg342vP4Guw73ACCIEg53KsPHTmLShNFkOCT2vfUkT769j9bOAL7cYXztezcwpcyLcLK0fQBoiRhdNZt4bPkGgpE4ADZXCqPPWMqCccUo8scF5Th7N77Gg0+8hW/yhdx0zUJqt27gYFeCjOJKJlZkondVcefv/0bMU8lXvnE5sz4uIGsqgYMb+e3tD+MdvYTrLv/C/ykg97bWs2v3Pnp0H3PnTMZpkYfUCccABGSNDS8/xB8fX4tfTKEwJw0AMaWM4ZVjqcj1EEtqWB1unFaFeDRINJZAkK24XA5iwV4SuoQk6OhqkpgKTq8Pu6ixf83T3Pz35VC6hPvKs8l0eXHalA/P8j73NCKBdtaveo2ewtlMm1SI22Hte8jQMZIBXvrH7dzxwmZ65WymH5Q4Y1wZNqmv70qxOfE4bdRXb2N1TR2X9wbRBrU9/1sqLYeqWb92Dd7xi5iS48UqCHQf3sPz99/J45sOU1AxEpcRoK0rRM6oOfz89ts4d3Q2st1DmsfK1g072V3fy5Ir4hiGwec5IhtakmBTFa88+xibd1UTw0b52Cl8peg0Zo/IIBRIgCghGAaxWBRdUEhJTcEqa0RCftpaWkl0+YmGenj9od/x8MZeplz8AwovPx17LEJ7aytxNZdwNI6aTBAK9BKNJ9F0A0mx4nA4cVgMYl0NrH3rTTK0Mi4JJyjD2fcB9SSBYAjNEJFkGVFPYsh2RDVGLB4jlkhiIKJYbPh8XiRUGnat47ab/kCNMJaHy3Mpy8zEZVUw1DjBQIBYUkO22PF43NhtlhN+wjdg5/6CPYVRZ1zFnT+8EBEQrS5S7SrrXnmSzfW9DJ9xNosmFlK97hXe3n4IZ85ozv/CXLa9+CDb2mWKsj00V++iqgNmX3AFc0vgjfXbqDlYjxF4iwfusTF53hdZMLEYt10ZqGaclERJYvisi7jhh5cwIi8F6DvTiDZt4eWNTYR0K0oiRNXqZeztvYqxKRIW0cmkORdQMXIiL/3letYdOjjIrfjPOX2ZzPnyt/nlJVNx2hTqOgEEPKm5XH/X80wTN/PLn93IxsaDbK5q5YIJhUz7wnVMmVeDEmrjyY2BwW7CkCDb3BTPvowH/pjCVd/+CbV6Kd+68TYunzkcrX0fDz+zAt2VTZ49yrr1mwlZC/j6d65jbKGbvJJRzJkfxTm8hPaa91i/q46DB3vRVzzNfXoti84+i2kzZmOkllOQ7iISbOelh+5hc00bveE4rvQips4+k7PnjIbjTiY2MKIdLH/6ORpDFipPG0WsdidG0RmUJHayat02ag53kNBlMopH8aWvfoUSR4Qt762jqq6eZi3BQ/f8nXHTz2PxlGKC9dt47sXl1DT78RWM4vyLL2RyZTFOi3Ri1/lAvbAR81O7aTm/vmUfApBWPp2vX34eLrvGysfu4e4n1nDLDxbz+N330W4p5b9uOBuHHuWdFx/kX+92YEvNxWeH5kONPPfqOm773fepauomEotj9LawfcsW0isXkVD1gWrCKSWZiLN59es09CaYsuh88tV6lm3Yw/LVe6lYOgKLwzLYH3GAGcSiQd5b+RyHY7uoaY1QPuYMlk4p+/Snfl4JAqJsxemwI0kioiBjs9uxytDRvJdH/3kfdZ1xsjLTceh+dte2URey86efXkTjrvX8675/kb7YTeXcOB3+KPF4lM7GA2zbAuMnVfL4A/ehFs2j+LQJpKVF2LD+PSLeQoj3smH5O6xY9SZtP7uNL6YeJyAbBka0jeXPPMprmw/iSfNgdXiYd1Uhicg6DhzqJSlIhDsOsPz5p1izq4Vbv7WIjvY2AtEEqtbNrq1bsGWPQat6kScffZ52Wy7TRmWx6rE7WLNpH9f/7HouOWPECV3lA9Z9IkgyiqAiCAKCIKCrSRSbh1GnL+a7Vy6Bxne46ee3Uh1wsPCCyzh/agkiOslYlISSype/8SP++qdbuWZhJf7m3WxtcjJ38iiyU1PIrlzIzbffzmXzK82z43+LTiIeZNUrrxNTUpk1bz7zF5yORw/xysuvE47E+DwkNNGSUba8/Sqr12+nNxiipaGObbtqUAf7gw1hgtD/8/7Fu9D3m6GrxGMxskbP4xe3/ZHbb/seOXqElvoqegNRtGSSWCxKUoOyqedxxshMUlLSmXreN/jtrTcxrdiKocaIxROoGjhcGXzpisuZMLyIlJQUbIqBv7uTPXUtGPrH7J2GTiIex5pawhd//Acef+Rf/M+XZnLakktZumg2pbkZOD2pKEaEhoPVxOVUZs2ZT1GGF3v2eH522+1cu7CYvVveY29bmIphw8jOLqIkXaKhaivbd1SdsPX8voG7Xak4KZpyPr+4/iJEwOJKJSfLi0u0MGrWmeTaH2B7U5CMcbMYP7qMdJ+DeCAMgGBxkZWbz/DyXBqHZ2NoMcJJEbvNit1mxXD7KC4tJUWEeMhPd1xFVKy4XQ70RAR/MIpsdWB32LF+7I2Hzw89ESHYsInXN9YTCDtZ9cJTuPHjD4XpePtV9nZehs/nxiGfyv2lAhabh3Ou/G8mZ2tseOYunnhjL48/+AIXnDWVnFP3xv2AcvvSKSitoFBMkmoX8CfjaPqHdx4EUcTpy8Blt2K12vCmZVFcXITRcpj3B15osSBdtTv5+9/voynpobAgBbvTjdIVJZ6IY3zK6YLNlUJ+STmjK4djJDp5+B+P8fTaKhLWFHJTXbhsIt1qAkGx43S5cNstSLqTwtJS0rt3EwmHSBrQ1dVNp8PAUzaVM8o8lGR5B3LVHdfA7Ya6TiISpKOjAxEQAjHcDitqsoMNry+jKe6mclQRveEDrFm3heljSkh///5TIkxrUwN79nazaU8Lkj2NkqIsXO02JEHF39XMvn37KMzIpXv7S7yxtQlf2RQuOnsqbVtW8Mzb1ZRNWcDiWROwml80YsFedq1+jaounfxRFVhlAUOzMqw0m437tvLa+lpGZqfg8NmOeW4i4qe7tZGqg21INh9jx1Xicdk5GWO3IIrYnR48Xh2nzYJgaMSjUTQDDI4esWMYGmqkiz37qunwx0jPK6akpAiP7cT2KQ4mXUsS87ezt/oQvcEIMaOX5vpa6ovcWI88axUEBFFCfn/VHBM/BWRZhmSU9sY6qqqqSBM1tP7eRi0WoHbzq7ywcj1jzvsu8+aNYkukif0NDcd5reMQ6L/5qmOED/P0cyvY2mnn3P/6AjPzBapWP0VP/weTJAlZBDXQyb69+0haEzicbpy2booqJ7Fw5khkPU5PMElJUeb/af39JwYkXNmdHnwOidZty/jB99/sW1++En5+w/fJju3ioRfW4xm9lN98fy733PE3Nq1axguTpnD1jCwA9GgPz/3zz6xxCLS2dlEyaQnnzyjC2FtGfqqL1sZ1/OKH17Pwqz+hqHolz7ywi/yZFhbOq2TNs/dwz7J2vlMxFd0c8wxAOBTg3a1VuNJK+Natf+a8CaU44x0cWP0gF/3gXva99y49C0aSd5yA3NO0myf+9Aee392LFtb40d//xZJxBXisJ8+6lS02nB4vDkuEp+74MS8JMXq6urFmD+fsyy4gVwYJOPJuhJaM07pjNT++8X56/UHyx83h+p/9hElFvsFqxgmnJ+O07VjBb+9+lI6IjkgLyx64G6v9R3wxy4LXl4Ld7cQiS0iiBV9aOrrHhUVRsNod+FJS8brsiIJEcVkpvnca2LPyQW5oWsvXrv06drcP2ePCbrORmpNLZloK3VVreOi+jQS6OnD6fHicdiRLAl9KCh6XA+XI8cyigtvjxSd4sPefeQlWJ4WZqVT5u3j3xUeodkm06z68HjcWRcGZmk5JVhrbW2r47U+uZ+KZVzNp6unsrDrMuy89TNP2PCQtShAfF1+dzZyplSd0nQ9AQJaYdfE3STvtAiLJDw9vos3HiIJUkj3lXPeTX1M0ehrjSlIozyth78EObI4YEa3vgCjavZw2bSajC9MRvIUsPusshuX6ENIu4Sc357B63Vb8mo3TRuRSWHE1PxnXizOrFDkRZuPGbRRMvIJpoyrwWU7C07jPnIHNk8qsi65j+BdSmDe5nHSPC9GwM3rp1/mbVEnSm0ea8/g39Q7teI/qXpmv/fA3tD58DW+/s4fJxel4Mp0nuB3/udSCsVz2/37GjI5g39mcIGB3pVJcMZyR5YXHPdtPxKJsXL8MS/lirpsqsGXNbt7YU8+kovEnvgGDRJQtpJZN5urrXERifZMKLA43RaOKSPFkcf3Pb0JKKaIo3YNTqOC/f/0n4t4iKvJzSDqW8tNfjcCePxqb1cr8r/0cpXg6m/fUI3tyKBs2mh/88lcIrhzGVI4kfWwxD8gFvL2zmYLKceR5LcSjSdLKx5KanuCnv/RiyyynIK1/vLIgIDjzufw7P+SspJ2RpZkgyAjOYfz8jjuY8sY6miMK5aMnkKI24ZeyGFGUSaYrix/dejujXn+L5oDOuMmjmTthCfMWncX6dzeyp+YwkiudYaMmMHXKuBO+zgcgIIuUjJ1OQaXKUX3xgoRFFsEoo0IzkC1WLLJIyegp5I/QECSJZCzQdzatOBg3/UyuOmcaoihjd/QfGe1expy+iIqJs9EMAbvThahnUlipIxgxuhreZVONwkXfu4jywozP7aQRXVV594lfc+7Kh/nSN/+b7/3X+UyfvxTV6OuHFwVAkLF78pl/9rkYkoxVjrL84dv4ze8epKGzk2i8AOifdYmARZZRFAk1mUAf4jUN/O0N/PNnV7P8z+Xc9M+/sHBkIZPOSGfsESNyBFFCURQUSSQZj/HKnd/lruc3sKe6EU/RBMAgmUwiylYUC8iCTvxzNqJHlBTcucM4c3HJB9tcEEUk2YJFNJi7IBdEGUWREYV0Zi05F0NUsFhkcI9kfm4FgqQgSyJSSj5zzr6E0xclEUQZh9NBcebivq4ORUHCzumLL2H8PBXZYkHqH/8tSgoWCeafmY8oySjK+zfxBQSrl0kz5qIjIB/x//TS8VyYOxLVEJBlBUmYgC7IWC19cxYKKqdxeck4NN3AanditcikuidyXlElSxIqiBIWixWr9cSPPBqQLguL1YbF+gmPH/G7YrWh9C8roTH7gq9jb7MydfxwfD7f0UFVkLDaHVjtjiP+2d8EXcLjKeSbN9/GojnDSTnlh3EdhyCTkjWc7978ezriYAgORk0cjl2WsSkf3dR9U6cdLlffnwaUjprGV6+xEtYBJY2x+ZkIegWpwlpeevZhggd0zrykFJ/zEzbuoLIyevpSbrgpnaAqIshehmV4scpK32X0xzxLlCQqpizmy+6xBKJJvBn5TCxNI+6fQuDvb/JKu05UzuZrpdkntDWDThAQZQsO+fjfJbt89Agnu9P14R+ShKx8+DxBUnA4FRxHXFhZ5CP3SRGb043tYy68HPJxRlMJEjb7sTP8ZIsNl+XY7rf3KVYbXutHHpcklE8KWifIkCrhZOg64f6ZenaHHfv/5ghlGOi6SjSuYbNZPrc5M3RNJRaL9V+dCCgWCxbLv5OTwSCZSJBIJPvuowgiNpuVuL+VXRvX8vq7VciePC657CIK0r1YpaF4/WGgJpMk4on+/mARq92KLEmf3H7DIJmIkVA1DKMvQMuShOY/xDPPvUpdS4Dy8aczf94ZZHs+hwd60wkzpAKyaWgyDB1d10HoS8gzFEPxQDF0Dd3o63cWzSn6pgFmBmSTyWQaIj6f1/Umk8k0BJkB2WQymYYIMyCbTCbTEGEGZJPJZBoiBjjTg0Ffjm/z7vSJpiUTaAhIooT0SeV2AAydpKoC/Ym+j9lcx9+OhmGgayqqpiPJCpIoDol87n1lh5IgysiS+Mn7n2Gg6xpJVUeWZURJPGoUiaapaJqOIIjIsvxB+3RdRVU1NO3DySKirKAcURrqVKJrKprel/FDVuR/axilYfBBdrij/q/3T7qR+ta3OBR2miFiAAOygaapRGMaLufHD9I2ffYMQ6etfh9NQZHcwiLy0j2fuLwWC1C9vwbV6qOsrASX9egEOrqmEY/FURxOpCPKZmlqnM6mOmoaesgpH0l+ZgrWQc86pBML91K9dy9CagkVhVkf5Dk47tJakkB7A7sPdlE8fCTZqR4+TBCo09taT11jBxZPFsMqirErfQ/GAx3s31dNS0/4g9fyZJYxamQxKUN24sx/Lupv42BDG5otnVHDjz/d/Ei6ppFMxBEsDixHjlk3dBKRbnZs24s7fwRFeWk4LGYGsPcNyLC3cE8ze7a+x9p33mZjeDT/vOUK7BYzb/GJ0NvRxLN3/pRNkWLyXDHa/DB63gV849wpx5zV6IkIgfr3+NltD+PKK0aKdtGj+rj6+z9ifJ4DWQtzYO9O1rz5Fq+8sZ8fP/RPxqWIWEXoOryXV//1INuiqZRn29ix/l0KZlzApZecT2naIB2AjRhb33qFhx54GteoqdC0g3DePK64eDETyo7N3BVsr2PTiqe4e8Vhpo/PZ+eWfUw7/6tcfO58HGqQVf/6HetabWSkOOlsqKEp7OI7v7iJsdlWOvYu5+/3v4TfW8rEkgwA3JkjmTN7PGmnUEA2dJ1dK+7nn6/uRvH4sKp+Dqul3HrTf5HutHFM7jsjQd2e7ax/awVvvL2Di39xHwtGerDIAkbCz64Nb3L7X56icuYMOva+i2fMOVx4/mJG539+kjZ9kgE5NIligvbD9TS3ddMU7sEc6nyCJEMEO3bx5DsBfnj7xZR5Rda9/BQrXnqFJQsmU2AXjuqOiEXCrF32GP70KXzlwrm4Y4dY/ujDvPD2NkZdPA1JEuntaqe+oZmejhai2ofVdByeLGZfcg2TseJzygxPi/HMmm3snXUGpWm5g9L8eHczOzZvpqdgAd+5dDFG13BuvuVRdlSWU1ma+ZFirQZtB/fz/EvrmPPVmzhnXBojU+7n1S2bmTBpAhPzXYxfcAkjZDc2i8zh3Wt58O4H2FbdRmVGPsl4hKTgYPTM+Zw7qRgAxWrHdkrle9XR9QCvPPUSqdOv5NwzxqJ21PGX3/2RtVWXcGalgvuYdKQGwc526usbCAR7CMa0/u+/QKC9ke1r38Q+6Ry+fPE8grU5/PWRt1lfMtIMyP0G5KaexZHDnCVnc+a0YcceQU0DRouHCdTto8M9jNHF+ZSUD6eiKAc5sJ9DHUk+WnghHo+xfct2Rpw2naKiEspLy5g0poBNm/ahaRqCaGHMtAUsXTSXdOfRW9LuSaOwbBgjyorIzs7F61CQBI55jxMp1N1CS2eU0gljKC/MpWLsNEodIVqaGwkfU61Vo6WpldaAncnTx5GTV8SI0eOxx7vZ3dyNbLGSXzGGogwPsUAPbR09KFkjKM50fZD4JuLvYN+Wd1m9Zj2769pQDZDkU2iPN1SMWCObalQqSwuoKC+nIL+A0dmwf18Dsfhxaq0ICsOnzOWsRbPJch99peDvPEh9S4Qx48ZRkJ1F5bjRpCgqjVU1J6hBQ9+AHM4lxYrT4cDpsCF8LooDDQ16MkGopwfZm4okiAiIOOwKFjFJwB/HyFc4Mg27pqp0dvop93qQFQWLYMHlctLT0Ylh6CBasTkcOF0OlI/JXWHoGv72et55awv23DMYljl4ZzqxSC+xhEFqigMQQXLjtWr0xCJEVYOjOj4NlUg0QlSz43VLCCLY7V5EknT1ftgvnAh18OozD7FuTzuj55zP6AI3siRgc6WR7pHZsG4FB9+FpJLBN370I2aPLcFrO0W653QNI9xNj27DLluwihBVZHweB13d3WiqCsekbBKxOZw4nQ4sytEHp1gwSCiepNztAgFEhxMrGomg/4Q1aagzh72dQozj/Ha8R4/6W+j/+eBxg383WYWh60TDflY++GtWdxYyd9EihmU7Pv2JA804+o+Pb46AYAif2Hx7WhGXf+tHfPeri2hceR8vb20mltTJrDiDG35/Dy889zQP3f83vlQZ5OFHllPd3PuZN2ewHTu65v0H/nev05/A86jNY/wHr3MqMwPyKUS2WPFmZZDs6UY3dMAgFIqR0Cz4Uh0f+WIJSLJMdlYK/h4/alIjEY/T6w+Slp2FIHzarmHQ297AU3/4AU/VF/D9/7mWOWMLB3WHcjhTcdolunsigA66n86QjMPuwql85FsvKLicTuxKmN6gjmFAJNyJJljJTPkwjaQoW/H40ikdVsG4Qjfb9lSjqmpfRjhZRpEVbHYXZeWlJKNhYonkiW30QBJlBE8W6WKUiJogYYCaTNLtD+LIyESS/3cX2A6PD59DoTsYAgP0cIiILiJ6UgeoASefAfn+RAMd1NYcoKq2kVB3M1u37qI9GEU1ey8GlGjz4CoeR1FwI29sP8Du7RvYtKeWWPoEhmWISAR5/Paf8dBzb9IWNrDb7cw8YwYbVyxjz749bNu+mTfWH2D2jIn9NdAiNB2soaqqhk6/n+qdmznY3EU0odJ+cDfL7v0NT2w3mD1rAlpvM/v2V1Pf3DVo7XdlFZGbYWffGyvYeqCBLStfYH/cS25hCU5Rxd9Vy63fu4ZXt7cQiIvkF+VTkp7gxedW0lhfxZqVbxG2pDK2OJNoOMCKZx9h4469HDx4gF1bt7Jufw9jRpYhyxLVG9/k7bXvsPdAHfUHdvH8q+9RMGoMuWknvjDmgBEkRCWf2eNsvLd1F5u3bqdq707W1EqcNr4Ah11m75rnueuOO9ha29P/pATN9QeoPlBHc0c39dW7qG5oIxJPkppbTmmhlzXLX6OmqYW1K1fSmbRQPmb4oDZzKBmYW8J6L9s3beNQwMrYPJUN727GWTaSVNenP9X0fyBZ8WVWcu2Vi3nvndepl5LElSKuvHIh6VYBwQAjHiGSNJBFsFhcjF96BYt7XmTdypchGSN16oWcN2MYiixiaFC3dyv7G9qoGFdJ09Z32Go4KMj0IhlJ2iI2iovTCLfUsL3jIJLFwbBpSynOTRuU5ivONKYvOJuunud49dmnMMLdzPzilUwfV4oiCEiSgJZMkjD6Jr9kFI/iq1+7lIdfW8czXVvp8Kez9LwzKU53IegRot2H2VbThCAYBP0hJl/0DZZOLMCqSCiE2bFhJ1EsGIkIUvkirjlvMlneYxOmn7xEBMnB4q9+g1fe3MjKV5sRtSRzvnwtU4o82GQRWdAJhKMo7w/eNnQa925ld30X+cNH4z+4me1uhZK8dJzeHKYuvpjqh5/j+SceI9zVysyzLuSMMXmD28whZEDGIauJGLFYnHhSBQQQRJxuF5bjzgIzfZYMQ+8r0NlYR2dEID0zh8w0b1/5LAwiwSCCbEGx2vonQBhEejtpONyMJrvIycslxW3v69bTVSLRKLFY4oN+P6vDhc2igJ4kHo0SSx5R8l2SsVptOO2DNw5XVxOEAr00HmoAVyYFeVm47FZEwUDXNEKBIFanu7/skEEyHqWnvZmGtiCZ+YVkpHqxW2QMXSceDdLZ1kKHP4bDm05eTiYue1+C+mQ8gr+7i/aOLqLYKSkpxOOwIn/arMiTkKGr+LvaaGnrRrd6KS7MwWFREIS+2oOqpiFZHFgVEdCJhsPE4gn0/tmdstWBw2ZBlkQ0NUE40EVdbSO2tDxys9P7t89gt3JoMPMhm0wm0xBx6h3OTSaT6SRlBmSTyWQaIsyAbDKZTEOEGZBNJpNpiDADsslkMg0RZkA2mUymIcIMyCaTyTREmAHZZDKZhoiBmTpt6ETDQULhKKpoJTPd90EOWdPAMwyDUE8HUU3C7nDi/pQSWnoySk9vEEO04PL2TYl9XzIeIRQMEU0apKRnYJXF486qUpNJBFFEkgY7H7BBIh7F390Ddi9elx3LJ+Qo1jWVRDRElz+GJ8WHw25DEvrWoZqIoxnGB9nNBEFElGQUWUIQQEvGiIQjBKIq6RnpWKShUVNwIMQjAUKROLpoIS3V+4lncoaWJBQMEorEsXlS8DqtH9bNM3TURIyOji5snlScDnv/LFITDEhANmjYs4Gte2rpCcVIaCK+3GEsnD0Jr9thJqwfYPFIiJpta9ha1UQ4oeNML+K0yRMYUZR1TJZDQ0uSCLWz7u111LR0owsyOaVjmDZ1IhkuhXDXQbZs3E5DRw/RaBKLK5VZCxeRl+r+oLacrmt0N+5j1eot5I47ndMnDGPwsgGrdDYdYtM7a2n0x0C0UDhmOqeNKCDd6zxm6UTET+fhKla9s5NoQkO0+Zg6cwYVxXlYSLBr/UqaAhqaAYaaIJFMImSN4byZlWiRLqr3bGfT7np0RBwpucjXqrgAACAASURBVCxceAapXjeWUyi+GIZBZ8N+Nm/eSkNHEEFxUDhsHLOnjcamSMfsU8lwJ/t27mDb3jqiCRWLw0vZ+OlMqsjBZTXoamtmzeq36QwlMESZ4ZNmMbqikDS3WXcTBqTLQmfXxg10xi2MmzKNkWkhbvmfG1hX10pc//Rnm/4PDJXutlp+//OfUkc+oyuy2L/mOW69d3lf+aWPLK7GwtS99Qg33vM6rvwR5NnDPHfXzby6vYWkqtN+aDu1zQGyhk1g+sRSVt39E/76zCbaA/G+t9NUov52XnvkT/z6t3/i1bXbiQziRHw9EWDNS49y16OryRs/izy9lrtuv5O1uxo53q7X3biXR++4lVeqksyYMYHGd57k/kdeoDmY7K+YIiHLEqIokgh1se+t53jizZ2EYwmadr7GfQ8+TbOYyenjC3nxz7/k8XU19EaPU0XjpGVg6Aneevi3PLWmlrTiCrLlNn51wy3s6wyTOE55mN7aDfz2T/ezL+hgxozTUPe/zM9vu59Dbb0kwx1seOUh7nh8A2NmL8AV2Ml99zzE+uq2QWjb0DQAAVli8eXf5aqvXMT4UZWMnX0R8wp7qGuOEYyaaTMGkhHvJdS4iW3idK46ayqnzzmLhaePRahZzd4u/ZjySpFwmBWvvsrMi77GjKlTmDt/ERfOruCVletIqklKJpzLlVddxoKp4ygbNo7LLppNU10NPaG+ihrRQAebnvkDL3eXMSo3lZRBru0Zbj5IfZOfEeddzeLThrP4imsZTgv1B6oIH7PrGTTU1LK9Qefab19NxcjT+MoV52IJtrK1thmL1cG4WWeyaPFSzjprKcPy06g/3MsXv7AEu93CljfX4CwYxaUXnc2wUVO59qsz2Lx2M43tp1KCeg1Da+GV1a3MX7KARQvmMHnmYs4s7Wb1xmaC4WMPPk0N+7CklTF15ulUDh/GhZdeQLKjmWQ0SsfhavZWNbP4qmuYVFHCRV+9mkyph22b9g1C24amAbm4kmQZSZIQ1Cixtt1sbE2jLMeG23aKdrANEVo8RrC5BTk9F5siI0kKXo8DCyE6u6LHFJtVVZXDhzvIyMrCZrNitzvJyEihpbEZQzcQRQlJkpBEgVg8wjtrN1FQXoHP5SQRaGH/xuX8Y6uTH177BYqzvINe+CEU6iIYUcnO8yGJEpI1g2x3kkDQTzjx0aUTBIIhQgk3mRlWJEnE481B1iM0dwUBPmh/vLOWXTt3EBv1RRaN8mGVYjS1hlDsTtwuBUmWycrMIdjeQiAcO+HtHjC6ihFsoTluJ8VuxyFLWGxWstJc9LS0oCWPTcZfMfU8Kp2N3HfT9Xz7ht9x+90vsPjSL5Odk0nE30VPIEluWiqSIGDx+XCJOvGu9kFo3NA0cL1dWoymuj38/U/3MvqCqxmXl8YxBWpNnyld10nEE0gWC+/XxZEkEUkwSCRUPprXTzd0YolkfypKEUEUkGSJRCyOcUQHR3dLPetfuJft0ulctGAUGS6Vqt1beOi5XVzy1UsYmZ+CVZEwDANjEKucalocVae/lpsAyCgSaJqK9tHGGzqqqqKhoMh9i4uSAhjE40dWRNXYv3k1W6v9XHTxmaTaRERBI54w+m/y9b2ToljQtDiadkw11ZOXYWAk4yQECUkUEelLp2lRZPR4/LjV5OPBbgR7GsUjRpHvSHDoUDOd3b1EY3G0ZJKkYfRtHwGQJEQMOE5g/7wakFEWhhql4cAOnv/Xw7T6JvGday4k3ec0x9gNMFGSsbudaNFI/5fFIJlUSeoCdoflmBEAoijidtmJx/oCiaZqJOIJHO50+irNGXQ2HWTjqmd4flOAL3/ze4zKS8FpidPR3oI/lqTzwCaePhBhx+FuvJvfYdXocZw/c8QADd/5ZBaLC4ssEI0lAQOMGJGkgKJY+LDeZl9JepCwWiwoQpJY3ABJIJmIYhgiLpflg9cMd9Sz6u0dWAonMWNkQf9zLbgcIhFdI5k0MAyDaDSMxeLEYhmMlg8QQUSwuXCQRNU1NEDXdCLROLLThSge+42u3fgKtVoRX7r8C0zKE9i66lF+fOeTBBZPwG23Y5NFovFE3+ZJJFANEWxDoA7jEPHZx0gjSWvtNv75t3+wscPBpV+7nFxbAj2ZQNXMu3oDSbI6cBeUYu2uo6U3QE93J4dbu4grOeSmWxEElYN7tlHb0EpUBYvFwojhpRys2kd3TzftnW1U1zQzbGQJoiQS6Gpm1dP38vjKfYxfeilLx2X1VdxISgwfN4OvXLyYrLRU0lJTcYkJJFc6GW75+DVWTwCXL5M0r4WG/fV0B0J0N+/nUMBKamomLhmS8SC7N23gcHeUpK6Qnp5KqiNI1f5mQsEATYeqiEluyj6onK1Rs+FlDkTTOG3ObHJc/VFdsFJekUPE301zcyehUIB9VbWkFpWQ5j52NMdJS5QRnPmMyFA51NFFW1c3vT3d1LREyS/NQ7Eq+Nsa2L93H93Bvj4hf2cnejLZd7Uk2ykdMw6PGkJQk7hTc8lJs1JdW0cwEqWtvp5eVcBXkD/IDR06pBtvvPHGz+7lDNA7+P33/psNTSpjJozCf2gfO3fupCtiJy87DZv1FDqDGGIE2Ypq2Dn8xl9Z351Komkzq97ZiX3cOVw5bxii4ef337iUd9pdVI4fT4ZDINcLd/3jSSS7Qs2Wt3ltYwNfuuY7DMt2su2pm7h72W48xSPJoJsdO3aw71AHWTkFFBYWUjZsGMOGDWNYRR57164jb9Iczlo8E/sgdSYrLhc9h6tZ+dTTJNPz2PHCvWyLl7LknDMZmeOgq2UP3zznbBJjLmZYfio+u0a0cRv3r6iiyBPmoXuexDPqDM49cyYexQDNz50/u4WcMy7g3AWn4/6gUKqAw6Gx8e01rD/QhStezx1/fYUvfOe7nDYsF7s02L3pnxURBDuW4DZeeLMaf6iXhu2reXGPk+u/fxGZLgubnvsbd/zjCXwjzmBYrhu7rLLsuWfZUd+NU4qy/KF/0JA1i7MXTacwJ5Wov5kH/v4MWRWFrHr0rzQpIzjnvAUUp5v13WBAKoaotDU0EEzoyBYr7++bis1LZpob0azVMqA0NYm/o5lD9bW0hSA9p5CyolxS3A5Ao62+DtWRTmZaCoqooyWjtDQe4kBdA5rsoqisnLycTOyySKy3hdbuCLoofTC5QpAsZGSkY1WOvCGg0XH4MDhSSEv1DGLXlEE0HKCloZ5DDY0YzkyKS8vJSXNjt8poaozG2nqcuWWkOi2gJ4gFu6mrreNQa4CMvAJKS4pI8bqQBUBP0FDfiDs9G7fb2fe/fmo8Qk9nK3V19XSGdArLyiktzMNmVThl4nG/aLCHlsP11Dd1olt8VFSUkJeViiSKRHs76OiNkJadh8smo8UjdHW0Ul9/iI7eCOmFZeTn5pLhc2KRIBYJcfhQHXV1h7Gk5lBaVkZmigebxbzBBGYJp1NWIhYmqYsoioJF+ZSrEl0lEouDIGG12jjZy8JpmkoiGsVQbFgVGekTTgIMQ0dXk0RiSaw2G4oi/9ujRQxdI5lIEE/qOFwOREEY9JEmA0VTEySSKjoSDrv1k9tp6CTicRJJDcXeN1Pyw+X7ahtGwmFkmwNF/uTt83ljBmSTyWQaIk7ycyGTyWQ6dZgB2WQymYYIMyCbTCbTEGEGZJPJZBoizIBsMplMQ4QZkE0mk2mIMAOyyWQyDREDNI+5L+GKYfSlNRAFAeFUrW0zJBno+gd1hz4sn/NxSxvGB5m7hI9sq/cf+7TteOTzB1vfZ9YBAUH4tLJKfRnqdAMEsa99wkcee3+g/pGv9cF6OWIYf9+6OzXLOBmG/mEpK1H8tybAGIYxJPaHk8mABOR4JEBzQy3VNQ1ExBQmT51ElteBYtbOGnCGoZOMhanatoH6XigZPorywixsysdNTdUJtDWwbcceEtZ0Ro+pJDvNjQioiShdrYeprq6hIwSVk6ZQnO3Dqhw988rQErS3dSE7XKT4BnPqdF+du56OJrZu2gbp5UwcXUGK23H82WCGTjwa4vCB3Wyv6aBs3CTK8rNw2xQMXScRDXKoZi/VB1uxpOQxdmwlWSkuBCDUUc/mTVupa/0wIX160TimnlZJtu/Uyl6mqwnaG6vZU9WA7srltImV+OzKJwbbWDhIKBjBlZmFVeSUncH4WfuMkwsB6Ox4/XFWbapBsDmIte3l7r88TNa4yaT7PKdUvbGhR6e3o5mHbvsxGzps2NQO1ry5htqglQmVhccESi0epnPvG9xyx2NEJDv+Q9t5beW7OEvGk+O10lm/jpdeXU9XUkKKt/PEP/5CMH0suelenFYJMFATMTa+dC+/uOVuemw5jB1dhmWwvn16mK1vL+evf30YMauQnt0reXFjCxnZ2eSmuY9Z3N9Wy7oX7ue+Nw9RmGVlxROP0hy3k19SjKLFWPfC/ayvC2KxyhzasZZnl60mdeTpZLoVeg+9xwsvvYXfnsvIomzcbjdubwaFBRlYP6Go6snG0DW2vHwvDy3bSMQQ6anbzOMvb2P86RNxWORjCt4asR62rFvNU/96iPueWMPYRWeSZhGOWxjXdKwBCI8CGSNmcM6557BowXzmzV+A1LyRzTV+4qo5S3sgGckIgbYdPLuug3lLFrHozCWMypFY+/LLNIWMY0o4xaJh3n31Sdoclcyev5BF82eRE61i2dpdJFUNq7OABWedw5IzFzJv7nwqfQFWvbmZzlBfVYx4OEDDjlU8v3oHPe3N9Pb0MJgV5WI9bWzbuIHujCmcveRMzj57Hl2bV7J9Ty2x45Rwaqvbx/OvbmDs3LNZsGgJC6dksXPjRmpbehElmdLxszn3rKUsXLCAmVNGE699jz2HetB0nUQsREyVKR43hblz57Fg4UJmThmB2zJ4JV4/exq65mf5My/jKp/EmYvPZM7sWYT3LGfd/h6i8eMk4xdEwsEgra3tdLY0ElaP3e9MH29AAnJh+XDystJQQ90crK3Bkj2cUYWuo7JlmT57ejxE6OA+ulPHUJmbTl5BKeUF2dgjNRzsSBzzxYjHYmzbupOxU6eTm51LUUERk8aXsnXLHjRNJTW3jJKSYvIyUrDZHbiddkRJQjAM1FiIzuYDPPb4KxTM/yIVWak4BvnEMNzZRHtPkvLTxlKQ4aNg9DTKnBHaW5sIHxM7NFqa22kPOpl2+mi8vgyGj5mIS/Ozp6kTxWKluHICeak2Qt0dNLV0IOeMpDjTiSgIiIJEItJL9bYNrH77HbburiUQjh23mOpJy9Aw4o1sOShQWZJLSVEBmVk5TCxW2L+3ob8QwNEEq5fZZ1/MF5bOIdNtptr93xqwDoRQVz0v3PN7brjxDrwzvkhljg/XqXTyMARpiQTBXj8Wtw9REAEBu03BImoEArGPlNwx0DSN7u4QLrcTWZaRFQW7w46/q/uIZQ2S8QjtDXt4Zd0hps+YQLrHTk9zNa898S+asubxlTkjSffY0XUdfRCLEESjfmJJA7fbBgggOPHYNGKxCLHkR0s4JYnGosQ1O26XiCCCzeZGMFR6/ZEPX7PjIPffcQt/fvQNsqedy+QSDxZZwOJMIcWhs33F0/zp97dw7Te/z6tbDhKKn0JVp3UNPdSDX7BhlRUUASRZwu1yEO/tQT+VylUNEQMWkFPyRvG1X97Bs0/fh7riNp5eX0fHsacpps+QIAiIonRUPTyj/+fYcjsCggCiJH4wGqbvCQai9OFddENTObTnPe689Xeknf8Lzj2tkDR7iA3r3+LVAx4uP3M4LU1N9AQDdHZ20dbRPWhniYIoIgoc1Xrd6B8d8dFOTOH9ERXGB6MH+kZmHL2u3AVj+ent9/Lnn11F4M2/8ODqWiJxjcyKmfzwN3fxzNPP8OQTj3PjBbk8/8zr7G/qGvB2nkiCKPbVvTviYG7oBkjmnbqBMCAB2TAMECQUiw2nK43yIg8NB5uJHecSx/TZkaw2PNmZqJ2tJHUNw9DwB6LEVBvp6XZEAWKRMPF4As0AWVbIy02nq7OLRCJBLBqlq6uXrPwcBEFEV2PsePsF7n/gcdIWfpufXjGfVLcdQbRRUjGamaN87N68iXff3URDd5img9XsPtCKNlglnNxpOO0SHW0BDHQMtYu2kILT6cYpg65rhIMBEqqGbih43C6cljBd3Sq6DsFAG5pgJbv/BqBhGAiihMVqIzUjk5J0G7UNTWiahiBKKBYrDocDh8NBSoq3v0zZKdRhKsqI7hyy5QjBRJyobpCMJ2jv9OPJykaWFZKJOLFolIR6SnXWDJrPuJPHACPEmlfeJCw5ycxKIdhSzbt1MPPcfFwOs09pIIlWN57i8Qw3XuLVd7YwKlVnw84apKKplKWKiIR44W+/JVY6n6VnzsVjdzBjzhz++OaLbEoP4wzV8sbmw8y76HJkWaZu8zIeePAx2qwlzLElqd7xHgdd6VQOK6Z01FS+XDCqr5qzEWD/a8uxjhzLlDFFg1Yxw5FeQHGuj2fffp23K2zoje9Sp6YzsbQMh6gS6m7gb7+6lTFX3cyskVnklxQzPMdg2TPLsE7LY9OKtcTdIxlbmE40HGDNy88gZ4/A55Jp2LWBTY06cy8qRpElajeupLpLw5ueiRRtY9nqvZTN+C65qceO5jhpCRKCJZf5UzN4773NeOQERkc1mzt8fHNcHg67RM2GZazcXM+s865kQmkKRtzPvn3VbN+1j6a2NrauexvbmNGU56ZgP5UKwA6QAVhDBpHOetbuakC0WUlGw+SdcRlnTczH6zA7kQeUZMOTPoxrLp3N8nUrqNZiCN5SvnzBUtKtAoJhEO7pJBCKA2CxO5mw5DLmND7MuhUvoakqaRPP4ZzTh6PIIlpvE5InA58Ajfu30rgfrCkF5BcWkZHqw+Hy0ncQ9jFh8mlIo0aQ4XMP2jhkxZXB5NmLaDn8CC8//xx6qJsZl1zBlMpiFAGiaPR2dxLqq8dJesEIvnz1V7jr0bd4vtlBp9/HuV+eS1GGGxIBupuq2bn9AKJgEA4nGHv2FSyZVIRFEdHivWxbv4mAbkHUYsRzZnLd0glknVJjkEUE0c78S67E/9IbvLasDkUUmfKFq5hc6MamiOjxCJ1dPejvd2loCXZtWk91S4DSYXlUvbsalyOLspyUwW3KSWJgKoYYOuFgL73+IIbVS26G91Nni5k+O4ZhEOpuwR+XcHt9eJ3WT15ejdHW3oEu2UlLT8N6UheFM0jGo3S1tWI400n3OlE+YVywoWskwn6aO0KkZmfittuOGDNrEOpupzuUwOr0kpF25KQXg3gkSG+Pn4hupSAvA0k8dUs4JaIBuntD6JKDnEzfKdvOwWaWcDKZTKYhwpw3ZzKZTEOEGZBNJpNpiDADsslkMg0RZkA2mUymIcIMyCaTyTREmAHZZDKZhggzIJtMJtMQYQZkk8lkGiIGfnK5YaCDOVPvBNOSCTQEJFFCkj7luGvoJFUVEJHkY6tA8H5GNOHomWiGYaBrKqqmI8kykigNiXpyuq6jJZMgyUiS+Mn7nmGg6xpJVUeW5aMz3ek6x8yaOqJGoWHo6JqGqhkoFsspXRVD11Q03cBAwKJ8StgwDDRNRdN0RFlBPmr/M/rKYyVVxH9n+3zODGBA7pvCGuzpole1kZeZgtVMLjLgNDVJNNhN0+HDdIVU0nMKyEpPxeuyHbuwYaBrCTpam2lqbkWVXeTl5pCRkYYi9eW+0DSVcChIwB8iJb8Quwii0FdvLxTw09LSQk8ggiMlm/ycDLxeN8qgRSaDWCSEv7uDQ40tYPNSVFiA1+M6bk1BQ0sSCQdpbjxER28Mb3Y+uRmpeN1ODC1JR9MhwkkDTe9PYiqIKM40CrJ8iHoCf283zY2N+BMSGXkF5GWmYrcqp9y04kQkQGdHG00tnQiOFPJyc8hM9Ry3TqGhJent6aajpYl2fwxPWhZ5eTl4nDYUsa9KTU97Mw3NnYjONIoKcvF5XFjMepvAQAZkQ6O9fid/v/knrBIX8Oit36A0L23A3s4EYBDxt/PS337C3W+24xAjyKnlnHP19/jGkrHHBApDSxBp3cEN1/2Y5qSCmtRx5k/it3+4kWGpVkQjSUdzPe+sWM4jj67kv59cxtQ0EZsEPc17eeyPv+OJHd1kp9hoaepmzqXf4nvXXEzOYFUiMFSq31vOnX/4CwdUH/S2ULH0W3zvqvMZU3Bscpt4sI2Nyx7k+jtfJjsnhQ6/zJeu+3987eJ56IFO/nHjdaw7FCOSBD0ZQ00mcM38Jk/96jKskVoeuONOnl13gPQUB62xDG7/82+YOjzvJM8FcjTD0GnY/CK//OMTNAdi2K0yntEXcNeNV5LqtB7T55kINvHA727mtU0HsTod9LR3cMY1t/CdC6eT4xGo3vg6v7rx94Q8OYTaW5h64Xe49soLqMg4lZIy/ecGKCAbtB/cxapH/sr+qA2cA/Mupo/QwvS07+Te18Pc+o87KUmxsOaZh1n+9JMsmTuGAuvRxSYjIT+rHrsbceIV3HzJLLzxQ7z22MM89Mp7/PJL07EZYXZtfIc31m6iKxw/6q18uSO5/Bd3cYmqI4oCtRse4bGVu9hYM4vzxhec4Ib3SXYdYvPmHcQn/BdPfGsBRqCK6398L5u3VDCiYCYfPUw07tvOc6+8x3W/+xcLR3ipWX0PL+7awq7J45laksF3b3+Ea/trwjVXv8ez9/yN5ITRKIrMjhVPc9go4Ld3/5wSd5LX//FTnl21i7w0H2VZrkFp/2dPR9fCPHHf44y74Jv8fO4kEi3V/O03v2LV/gtYOioNj+3okFy39TX2h3L52i+/zdxyL/4Db3L1H/5/e/ca21Z5x3H8e87xcXyLb3FsJ3FuTXqhaRsqVlE6OjQQGxuUyxAMxDQhbUOTkLYhTRp7103TpE1I08SGNG28KAKEYGthUCgklN7oSumFlaRN2zRNnMZx4tjx/XLs47MXCb2swKQpIaZ6Pi99eay/bf2fx+c8Pr8dPPy1VdhySY4f3E/jPU/y9MObKFw4ylPPvkP/oR6Wb1m/RDXWlkX5nZCePMuevj5OGGt55NZ1mK5KqxAWg17IkTk3RNLTxTK/n+amEJ2hRpTcOcJT5asy9bRSiYGPBuhYs57m5hBtoTbWrAhw/PgZdL2KpNrYcOtd3H/3HfhsV36GqtmGu8FHMBjA729ERceo6kjS0gXrZWaniM7k6Fq3gqZggOZla+myZ4lOTZC5KlmpQnRymmjaTk9vF4FgkI7lazAX4pyKziIrJtwNAfyBII0uE7NTEU5VVvDd29diMRuc/Pg8VrePts4QAb+fNau6iZw+xVQquxSlLw6jglEc5dgodLUEaG9pIhjw0+1XGR4apVS6OnDC6WmikhrlxPFBook0iekYvlA7FquFdHyMsUiWnlXLCfj9tC/vwq1oTA6PLEFxtWlhV8iGQTkX49B7bzEQd3Dvlg00RN6dP2gvLiq32KpljdxsEsXlxSTLSCjYrGbMskYqXcIwVC7P3dH1CjMzabpcTlSTCbNkxu5wkIzF5+KMFCturw+/vwGrevWkKkkSRlUnFRli756PsYY2c13Q+QVWfKVPMvU8bhsgg6keV51OspCnqBtckbJrVMgXChR1C06nCUkCq82NTJlEMn/ZqAbRkQGOHBmk55v3s6a5HpUs8aSGHDBjtSrIZRmX20MhO0uhqH3RZS+eqo6RT5CsWrCpKmYZTKoJt8vGSCKBrleAKy/t6gp0sqa9nn37Xmdb5ASzo2fo3fIENmsd+WyaXKlCl8MBEih2O2aqlDOppamvBi3o0tUwqmQuDPBi3zn8oSasFBkZj5JLTjExnSCTL/3vQYT/nyTN7YS4bO4z5uPQPutEtiRLFwNNjfkHX5U/9xn0colU7AK7dzzH4WSI2267hXb/0v1cl6TLp5u5E3FzlUmfuh6Ye08u3WfMhwte/l7pxRRH9vQzpnm577b11EkgYVz93KrBtXc1ZAmQka74Qs3XKsmfWu3sdJiJnIPbv/Mg39jci9epcurQ+2ilEtJ8juOlsebHFbssLlrwY8hauYrfUaB/+zb6KiVy8XHGJuHZF1r52eOPcH2nf6FfUpinqGacfh96OoxWqaDrZTLZApphweWyIklQKuRBMWFSzSiKSsDvJjWbRNOaKGlFkskU3sBqJEkGjItJ0oZhUK1WqBoqBhKGXiYdj9D/0p949kCRn//yCTau7cT0ed1/kVltXuwWhdl4Dl2vQiVJPKvgtDuwqhLVqk4xn0e12FAUFYfdgc2UYzaloXsUctkZKpIZv+fSSY/k+Ee8++84oU33s7bNPXejZCXQYCWpFckXyrikCvHEDDZXCw7b54cBfKnIMrLDh8+kkdNKlCo6mqYRT+Wx+3zIJhOVcgldN5BNZlSTzOB7O6j4bmLTzbfSGzJz4/oQ9235Nanpe/E53TitKvF0Gr1apZJJk69KWJzepa60ZizoClmSFfyrb+FXv/8jzz//PNv++md+95MHWbn5QX7x+MOsafMt5MsJ/0W2OrF3rCMwdZgPRyKMh09z4nSYYv1qVgZlFCnL35/+DS/+cx+xnIHFamHjphs5tq+fkbExzpwZ5MDR82za2ItiUkAvMzszxWR0imyhQDQ8SiyRoVypkowM8frffstTb8R47PHvE7TpTEUmmEnllqx+ZyBEwGdjYM9eRqdijBzdzcmii2BTG06lQiYxyh+e/CnvnJgmo8k0h4J0NBTp7ztCPBblyP79FOu89LQGmFsKltn98jakph7u+PpXUC/OMyprN1xHbjrM0eNnmJmeoG/3YTp71xH0upas/gUnqUh1HXx1FRwfHObUSJjx82c5NFzi+uvbsVlVTh/cyV+eeYYTo0kAGppDTA8P8NGp08RiMc4PDFByNSHVWWgIdLKszcX+3fuZTiQZOHSQeMVCx+ruJS60dihbt27dupADSrKCqqqYzWZURaKcjnA66+Hbm3tx2j9lL6ywcCQZVXXQ4S3xe4Nw9AAAAvNJREFU6ivb6XvvAOm6Nr73g4dY1eRBocThnTtIuVbQ27Mcp1WlsaOb3NBe3nzrbd4/PoK7904evfdmvDYzkpZi1yvP8Y9dB8jpZcJnBonTzOplQfTEGDt37SOWSTMxMsSHH/yLD46dJGdtZX13YEnKl5U6PJ56MkN7efnVnew7cp4N9zzKnZvX4bGrlAoJ+ra/RsOGu1gRdOByuWhvcbB7+0u8+XY/53Je7n7gAW5Y3oxZrlKZPcsLrw9wy5Z7uGFVK3WX7ZWtb2xBTo3x2vbt9O85SKV1M489dDshXz2ma+YfIhJICqH2VoYOvsMbO9/myOAYG+77IXfftBJ7nULs7DEOnxxn5fqbaPZacQU6qMuOsWfXTna9u5dj50s88KMfs6GnA0e9C2eDj8mjb/HKjjc4NBhh410P8a1Nq3FazUtdbE1Y1Agno6JRyqeZSBs0N7qx1omQ08VW1cuUsrMMD4+QyOn4W9pobg7isqpAhYnRMRSrC5fXh1U1wNCJjo0wHplCMzlobgnR1tKIAlDOMRmdJhZP8UnIuyfYRqPHCaUM8ViUeObSeQHZbMPjbaA1uHT7zbV8mkQsyvBoBCwuuru78LrqMZtAK+YJj4zgaemm3mHFLOvksynGhs8ylSriaWqntcmP12kDo0pVyzI6mcbtceNxOa48ZlotE5+OciEcJlmS8bctoyPovSa/41Utx4XxMBORGJLdS2t7B00eO7IskZqJkitqWNxBvA4zGDrxqQiTExPEMiWc3iBdXZ3UW1UUWaKUzzATDXMuPI3J0ciyzlZ8HhfifyFzRKaeIAhCjRDzkiAIQo0QDVkQBKFGiIYsCIJQI0RDFgRBqBGiIQuCINQI0ZAFQRBqhGjIgiAINcKUvZauTiUIgvAlJlbIgiAINUI0ZEEQhBohGrIgCEKNEA1ZEAShRoiGLAiCUCNEQxYEQagRoiELgiDUCNGQBUEQaoRoyIIgCDVCNGRBEIQaIRqyIAhCjRANWRAEoUb8B3QAPJpTkAmLAAAAAElFTkSuQmCC)
chemistry-General
maths-
is relation on
given by
Which of the following belongs to
?
is relation on
given by
Which of the following belongs to
?
maths-General
physics-
Two magnets A and B are identical and these are arranged as shown in the figure. Their length is negligible in comparison with the separation between them. A magnetic needle is placed between the magnets at point P which gets deflected through an angle
under the influence of magnets. The ratio of distances d1 and d2 will be
![](data:image/png;base64,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)
Two magnets A and B are identical and these are arranged as shown in the figure. Their length is negligible in comparison with the separation between them. A magnetic needle is placed between the magnets at point P which gets deflected through an angle
under the influence of magnets. The ratio of distances d1 and d2 will be
![](data:image/png;base64,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)
physics-General
physics-
Two small magnets X and Y of dipole moments M1 and M2 are fixed perpendicular to each other with their north poles in contact. This arrangement is placed on a floating body so as to move freeely in earth's magnetic field as shown in figure then the ratio of magnetic moment is
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)
Two small magnets X and Y of dipole moments M1 and M2 are fixed perpendicular to each other with their north poles in contact. This arrangement is placed on a floating body so as to move freeely in earth's magnetic field as shown in figure then the ratio of magnetic moment is
![](data:image/png;base64,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)
physics-General
physics-
Find the resultant magnetic moment for the following arrangement
![](data:image/png;base64,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)
Find the resultant magnetic moment for the following arrangement
![](data:image/png;base64,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)
physics-General
physics-
A modulating signal is a square wave as shown in the figure
![](data:image/png;base64,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)
The carrier wave is given by
The modulation index is
A modulating signal is a square wave as shown in the figure
![](data:image/png;base64,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)
The carrier wave is given by
The modulation index is
physics-General
physics-
In the P-V diagram shown in figure ABC is a semicircle. The work done in the process ABC is
![](data:image/png;base64,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)
In the P-V diagram shown in figure ABC is a semicircle. The work done in the process ABC is
![](data:image/png;base64,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)
physics-General
physics-
Volume versus temperature graph of two moles of helium gas is as shown in figure. The ratio of heat absorbed and the work done by the gas in process 1-2 is
![](data:image/png;base64,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)
Volume versus temperature graph of two moles of helium gas is as shown in figure. The ratio of heat absorbed and the work done by the gas in process 1-2 is
![](data:image/png;base64,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)
physics-General
physics-
P-V diagram of an ideal gas is as shown in figure. Work done by the gas in process ABCD is
![](data:image/png;base64,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)
P-V diagram of an ideal gas is as shown in figure. Work done by the gas in process ABCD is
![](data:image/png;base64,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)
physics-General