Class 12th Physics Part Ii CBSE Solution
Exercises- Which of the following frequencies will be suitable for beyond-the horizon communication…
- Frequencies in the UHF range normally propagate by means of:A. Ground waves. B. Sky waves.…
- Digital signals (i) do not provide a continuous set of values, (ii) represent values as…
- Is it necessary for a transmitting antenna to be at the same height as that of the…
- A carrier wave of peak voltage 12V is used to transmit a message signal. What should be…
- A modulating signal is a square wave, as shown in Fig. 15.14. The carrier wave is given by…
- For an amplitude modulated wave, the maximum amplitude is found to be 10V while the…
- Due to economic reasons, only the upper sideband of an AM wave is transmitted, but at the…
- Which of the following frequencies will be suitable for beyond-the horizon communication…
- Frequencies in the UHF range normally propagate by means of:A. Ground waves. B. Sky waves.…
- Digital signals (i) do not provide a continuous set of values, (ii) represent values as…
- Is it necessary for a transmitting antenna to be at the same height as that of the…
- A carrier wave of peak voltage 12V is used to transmit a message signal. What should be…
- A modulating signal is a square wave, as shown in Fig. 15.14. The carrier wave is given by…
- For an amplitude modulated wave, the maximum amplitude is found to be 10V while the…
- Due to economic reasons, only the upper sideband of an AM wave is transmitted, but at the…
Exercises
Question 1.Which of the following frequencies will be suitable for beyond-the horizon communication using sky waves?
A. 10 kHz
B. 10 MHz
C. 1 GHz
D. 1000 GHz
Answer:10 MHz frequency will be suitable for beyond the horizon communication using skywaves.
10 KHz cannot be transmitted because the size of the antenna will be large for this apparently lower frequency.1 and 1000 GHz are very high frequency wave which will penetrate and so cannot be transmitted.
Question 2.Frequencies in the UHF range normally propagate by means of:
A. Ground waves.
B. Sky waves.
C. Surface waves.
D. Space waves.
Answer:The signals having Ultra High Frequency(UHF) can propagate through Space waves. These can neither travel along the trajectory of ground as shown in green nor can propagate by reflection in the ionosphere as shown in figure in red. The UHF signal propagates as shown in Blue in the figure.
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Question 3.Digital signals
(i) do not provide a continuous set of values,
(ii) represent values as discrete steps,
(iii) can utilize binary system, and
(iv) can utilize decimal as well as binary systems.
Which of the above statements are true?
A. (i) and (ii) only
B. (ii) and (iii) only
C. (i), (ii) and (iii) but not (iv)
D. All of (i), (ii), (iii) and (iv).
Answer:Digital signal obviously use the binary signals i.e 0 and 1 only and no other signal other than these. It is also a signal that represents discontinuous values and it cannot utilize decimal values (0 to 9) which are continuous.
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)
Question 4.Is it necessary for a transmitting antenna to be at the same height as that of the receiving antenna for line-of-sight communication? A TV transmitting antenna is 81m tall. How much service area can it cover if the receiving antenna is at the ground level?
Answer:No, it is not necessary for a transmitting antenna and the receiving antenna to be at the same height. Because in this specific case of transmission there is no physical obstruction between the transmitter and the receiver.
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QNPv/5z5ewAiWIslKDbZ/i0tb1xuDolX9mA9mVp+ma9BgLUPYnQdfiO6tD9kxX23GA45WvfOVlPUwS1BlnnLFQIGLSzoxlhx12KCUVZS37f97OM2k/7bq1owB3v33N5vuZz3xmSSjjCdlpp51KAZDY3pVH1LKQ125+1uJJDWTXgsqr+IyhgvH2Q/Yt4FUcyibRdXafLvWFxXkVplhqE58VLx1qrZ7wUim7OvepBiZBTSlNW7V8xNL33HPPArZ4YVqvxuqMtPW6GhRoILsaVF3lPiO7M1tZ4j6Eq8xUpfBs4Yhs2FUezrrtPk7FiQIMkQiF7jwItrfkxBb/13KVn76qP9zFcS6sfnz6rJec2ew5MpfDPRt/x/2e6++oR0z5qreLuKbvLNwYo9/z+/i+fp++yc7JPuuWGSZ4sbwe0ZmSKwPcvx/96EcX9SC+bz8zV7JKXZLi9t5775KkppCJuWTp5vlq3qoJJmEGL2kgO4OTMsmQ8oJT1EBCiricxapAvIQLC7UJwEmoOXwNgEVHzd+EHi9BbkHjcfHJAM0A6wCxuq86IzVA2/eUJ+MIEI0+jMl14dmYZt7j2kmqE/WNedx7L28G5uvuoIU58hF/tZ1LEQ//D0Us3gpvcf9br7Zf2dbF8jWPMr43Vqx9vqg+26NtIDvb89M7ush6jR8tXhmnCg8o86cG7i9+8Yti2ba2PAoQmrVFF4en1z2PszT6ChTUfdRbQOL36JuQ9ndsLYrr4/txYxhliU4Csn3gvZRnLm9WZvfu7JHAO7wWKmnZu6zYR262Qe24444leY01a4uUuteqdIm1t/U7u/M8zcgayE5DrY14bW1tZMEWeySdyKLYgYID9kW21ijQKLDxKRDFRYBmxONV5lJti3s4so1V7LKXWZOJ3KzYjT93KzGCBrIrQcU16GOUtWDhKsMHZJ3Y4lgyx6NF9SHDa9sB1mCS2iMaBSoKiL0eddRRJc7Ky2R/sy1Yec+sW3ihDj744IWynMprZjd88xbML2s1kJ3fuVs0chmn0WwTUJnHYo6Wk2jWySu312gUmHkKKBaiQhYFeK+99lpUQSwPXgKUyl1ajq3P/Au2AY6lQAPZsSSazQtqy1SRBBvfJVmIz9ku4LzSOMIsYouhHTfNeDbntY1qvimQ6zpba/ZVH3300QVoh9qHP/zh7phjjumU4VTa0iETzVU833yQR99Adg7nsi/5xD47CRYKu8tSVLRAokXWjhvAzuFktyHPFQXqUpwRbw2lOEA41qI61k5xkjXu9KXnPe955aQkhz20tj4o0EB2jucxW7MKytOEHfrtiDR1almzshXFesINlTNl5/jV29AbBWaSApF5Hnus8xrt2yrFgnW04Kte9aoCrJKflO+8ylWuMpPv1wY1PQUayE5Ps41+R5+rl6tY2r/SbQ78VvDdmaPHHXdcAV+uY61tbt/o09cGsI4pUK/NvKUnCpDEd05nAq5CPPe73/1KchQlWdnFtvd4/TBJA9n1M5elNJujzr7xjW+UbGMAG4eJO5g7Fyb32hZ9PsptHZGivcoUFGiZ51MQa4JLw4oNMA3vUV5r9rHzNClScdZZZ5WjDL/4xS+W3kfFbyd4fLtkxijQQHbGJmQ5w3HcmvblL3+5bGS3F8+h3GeffXZ3+umnd/vss89C97n0X3zZhO2G1K/j331ehHEuQb329dN3Xz2CcQlqtQsyx/5yX7mfPrdl/q4uiDGOL8b9vhyenrd7s+UadAnQze/iwIBPfOIT3cMf/vByDJ6YrHVKEV6J+tjzRrf1PN4GsnM+u1nAOaDb2aAKkDuvlHZ87LHHlgPCn/GMZ5RzTV0Tra4cNU6gzzmpphp+0HWoCpLO6iSX+K4G1Sx482+57xoE4//jAGyUe7IP3PvG2NdHH9BmvqmJOW6cUxF/zi/uo0WmsfV4+OGHl9irzGPAaj+tJEUAu9122805BdrwMwUayK4jfth6663Llh1uJ2eeAtmrXe1qpfqTSlAKkku06BOWeevBpg62ATDTFMivAXcI/DLIDbHeEPguhVVHzWWfAuHd4+jESOKplYQhJWIp41vP9/QpSmjKTWybzj3vec/OUXgaS1amsV0BV7/61dczWTa5d2sgO+dTngXlFltsUcq0vfOd7yzFxZ1/+p73vKf7t3/7t/KWJ5xwQnfnO9+5HK+VWzsarZ8J+sBlOeA566xWhxBGJd8Muc1HWbuz/v6rNb5Mq9e//vVlfWrnnHNOd/zxx3d3utOdSlxWoyhP6sVYrfG2fleWAg1kV5aea95b7ZoKzVh28XOf+9xi0UZzDNohhxzS3f72t1+UXBFWWFgxa/4SM/bA1bLkL7zwwu53v/tdt9lmm5WTfZye5NQVR6EpJE/ZkSUuec1eSb/37YkOcgFByWvuuclNblIOgXdvJNh4hqPWFDaQTKN/H/upPW+lWx1+WOn+56W/IZA0186R/cMf/lBehTVrLzt3sfAOPth+++0XXnO1+HBe6LhextlAdr3M5P97DzVPWbRqoQJYW3dsDyBUJUTZ8G6bj1hQCOO+2OI6I8uqvA6lBZ2B4U9+8pPuZz/7WffDH/6wACn3X5w36xg6c+HM39/85jcF8Hzn/+6Ls0cNMo7SE6ObpqmFa94Ba4AvQPXdla985QK2/m9M9mP6qG0NxB2r5h7CXuUwp8NQBGSr269ZZ6WPGtemDgw58SzTAj8861nP6r7+9a+X4hPCOHiAx+kLX/hCISklKcdjW5x7mhUwu9c2kJ3duZloZLVQu851rlMWsJM/bnGLW3RvfOMbiwtKs5iBrK093Mb3ute9NnjGrC3svkPP60EPZdhORMAxFwHNCy64oCSPsUQAqtgZAQkwASpAtBXDhyW5MZrn9j1bmT7jn7QBV0oApUyBE4Arax0Q+82eTkAsboiv/L1S28CG5jHzQJ2Rna3nWQD47BXK47En1nF3mqQntNRssbv//e9f8ijQ2frVWtGYSTl29q9rIDv7czR2hFnwbLPNNsX6ALKvec1rFgD2W9/6VlnchKRN7y996UuLlUuQuj8soJUSmGMHPeaCnN1bC1K/5QMPajflpMKWVQeY7Fn87ne/W87k9a8DtAEpK/WnP/1pAVMAClDXe/OO8Z5o0ddYtkDCv4ABELOWWcf4jwXsX5XHgPW0PJXnPrvLA2yNqeaBWZmX8F5QSqJ9+9vf7p7ylKcUnpU97OCOF73oRYV2aOTvXXbZpSjHXPkBstPSbVZo0MaxmAINZOecI2r3FBfgDW5wg3Jw+9ve9rYS61GcQnyWu1hGo2xjiRbcxrKNCcIQCquVBFVbKePIPpRgFO9bC6BxwMpdixYsU/FO1h0A/eY3v9lRQFipwJSy0dpoCqCjD/rVzbzgJa7Pm93sZmXLmL9ZvLaX+dunrwB+3xxGMlYG27z/dNYs2cjMDrpwE59yyinFi8R7xG1P+aXQPeEJTyiWq0Pa8d3tbne7haSnDNKNH+ebAg1k53v+FhJjsoASlyXs7JE99dRTO5q0Rkv2N6tMk2384Ac/uGwbGAdSK0GmaZ9Ru65HJQHl8bFOxTtZYsCUi5dl7//2EM+DRcpKlMQ2lEyEFubYvyxuLutJ6bMScznUB0vOB637LGEAe+Mb37icrcpyYwWzfFl4kbTX13fmnUyTWQtv1Dz+9re/veQ/aEIOktQArXOflU+keHDpA2f7ZnObtXdbTb5Zz303kJ3z2e3bZmHhcgP7l9tT8svDHvawsnWHtSarkQVHo37+859fahy7ZjVbLXzGCZC+34dAWr1X1roPwCHMWO2AlcBfywb4uE79GwBijnzEMX0XQCSblMsQ7SVRabE31bU+uVpQDaKsHdfLWmaJs9aDH/TtN9Ymq9N4fCezleLhWv35FxjiC9exvFazSfSypSy2lXkWq1b+wE1vetPihga+joiz5xsoRauBdtYAqfbWoKn1RbHgIhbGMf+S1N73vveVusWa7wFtPnlHX+PWyGrOU+t75SjQQHblaLlReoqF7d8QsASUQhTARzvqqKPKVoHcAJA9e9zGNOgnP/nJ5edprc1pXjqDxLjnDP0OjFgBgBQ4ANbPf/7z5W+CarUbgQkEACPLixXGMvF/bneCknJjLsxBWKP+T8DOQou4q/nwN6WL9c/DweqnBKAl69jH78CYwsZDIOlrJZusbPu5faJxL+NjXhl/yyXgfkbbvjaKn/os/HH8N+79hvrM30swdKqO7VVCM7lJePIuttrhG27jOHknkp7aIQHjZmE+fm8gOx/zNHKUEbeKiyxesVlWi3KKNcASpIcddlixXLglX/ziF5dMY7Ha1WqhmU8L5EDVeIEqMP3Qhz5U4luSlVY6kzfiicCRJwCYskrjX9m0Yoyx/YVFgn7zlqDCWozsVvORS23m+Sfs8RA6s3BZZuaBNQpsWc+sYv8HwqxmoL0S3gPJeT6AF30pMsa54447llq/QAnw+n4cYMbvdVx3Wl7MtMnP7FMeZRML1+APiXR77rlnyeqnpEWzZ51yeOKJJxaA9S7RwiU+7t1Wa722fleOAg1kV46WG6WnerH7v8VqUzuhV1d3suD32muvEpv95Cc/WRY3i+HAAw8sVm3eEzmN5RmurXq7RbawJ9HMWVMsJ1bTueeeW9xqwDWEfWj5yyW2+DQg5UIFmqwkdACkMj4Brd+4ZCksk4x9uWOatfu9cw3IscXEvLJofSTt+OApc2UvKA+DOaQMmVNu/KXGwoF2WNVi6lzI4TVgESqucq1rXasoRH0JVRm4/B28ulSXbG3F1m5dSok4rLVICZFYd4c73KHwkPOdA2j9buw8ShSHUNb6DhSYNd5o45mcAg1kJ6fVzF+ZAVepNtnF++23XzlnVmIJMHnzm99c4mFiYLRoFgqLQIajJKkDDjhgA216XGwoC6v6vNoY0yiNnFv7/PPPLxbru9/97u69731vsbJXogFLQo0QJpy5dYGpZC9bmPy+2q2O1a328ybpf9ycjuvDfFI+fKJRXPBaboBVaEKMnJvfPFOYKIChTI17Vv27+32AN955wQteUEDXfN7jHvcoHhlgy9Xc56KveXIaZdJY+vILYoz6YplSDpU1lftA+aDMvu51ryvx80c+8pHFIwB8P/rRjxYF5C53ucui11zu/ExL03b96lGggezq0Xaj9ixphDBgUXB3AlHut2gEHiuXpRbbBVSf2W233ZYUG8ouudp9XROC29G4CFxChkAihFeiEWasUUKWe9G2CJYpS2GprQ8ka8E8SlDPqssvC/L8jrWltpzxs4QpdD6S76JxNwMg3hRHvgFdoBkgPO1cCSsIJfhowNXc3/3udy/1vAHvUPZy5t1pADeUy+zlYMmrR6xZc1GnmFdEU6/Yh9JnL3GUzuxz2TegnZYLZvP6BrKzOS8Tj2rISmK1Apqdd965O+mkk4p2/djHPrbs1ZPpSPPnygN4hI+zLGnaRxxxRNk7G27jIZdadrnlwQ4JZC40sVSAClgJU67r5cZVAajEGG5Mloy/JSNFpaKJCZkurIXbJJnRywGipYxxuffU4x2VubvcZ/XdD1QixsqSw4v+xRPnnXdesfTC2ltKQpv+bJ/xoXjhk1vd6lZl6xCFq++km3EWqveoPTX53VjtSidyEYvBsmR9xw3Mm8I7Iy778Y9/vNQQd5bsQQcdVKqyBQjrL4dYVoP2rc+1pUAD2bWl94o/rS8Bw3cAFuCwXgEoK5Vm/8pXvrI30QXYAtmTTz65xIke+MAHDsYhMwiNApfYLvKOd7yjxHsJn6EqQuMI4zlRPcg+S8oCUCU8xaCBahZU4/oLYRYJJnF9bYWPslgnecZ6vWacxTeNi5wLP7aQySVQMEUilTgssFRYRYhD6UGZyGK002Q4iw37OK8V/wNd9bxVWWLhxvameq5G8XZfYpK1E6fpeIc99thjg+kH9HhXiUXubGtCKKcOW0xDv/XKY+vlvRrIrpeZ/H8asNchAMQfLV6LWaYjwQJs+9xS4qCsXC4sMSPaNfdeTnKZ1NLh9mOlxvYgQEtYLiXjNLbGELyyn+9617sWC5sLcpKs0npqs1WewTS7C+OeISHXd23QfB2x0thXGWfdDyl/mb5B476kMqDjg1/tn91nn32KVQhcWbjyDd71rncVMAbEk/JXJFCJEystKkPcOnnUox5VlEv7lvsOROgD3PwdlzcvUHhQHve4x5UcCICam1DGK17xigLyXNneRx5EziwOfqrd9mMnpV0wkxRoIDuT0zLdoPoAgXbOcmXBWthcUuK0dRMT23vvvUt8SFLU5z73uVIFysHSZ5xxRrl8nCuUNs5i/tjHPlbcczJAo7jCNG9CwNl+xAoHrIQQ1x4FYdwY8nOGYooBrPn32jU8yoLIv00znmloMCvXTmpJBf36LDvvMhRWqMF26P64LkDX/+UY2Mpz6KGHluQh7ldWKj5ksdpSNEmLk45sRfrwhz9cPD+3uc1tut13372UJgXwObFrqE/Jg0ceeWRxd9tyJPwi38G6sh7yyTr6uOMd79ideeaZxaXs2Xg88iKC7g1gJ5nB+bimgex8zNPIUfZZDW5gjWr3uc99Fv7OtYm5bmnUYl4AkiUr85bA4foiBMR0h5okD4kdLArbbZbaPDdOBbJxH+Avp40DwCGrfJr7ljO+ebh3HC3iHcZ5OOL3ur/sSQgPQwblSWhE+fIRZ3V8nHguC/WDH/xgATtZvYBv0hZ7c08//fQCjIq0CJvImB6VhS7Mwltk7znFUIskQpnEALUuomFLj3XJms6/BZ3yYQiTjr9dN5sUaCA7m/Oy5FFlYRZa+Fvf+taSvWkvo+QLcUyas1gXTRqoETAyPh1zZkuPpkqN/aMsh2iyIQkhlWyAbFSVmmbAYqeEjG0LrAXPoxBMKtineVa7dvYpMM28j8q4xac+d7vb3Rb2ggNeoCvTt+9AgyHqKODvI5RC8fPZddddN9iiJCveQew8N9aRpD4NSHIdf+pTn+oe8IAHFMtb9rQ1xh3NRU6Z5bWpXcXur3MDZn8W2wiHKNBAdh3zhngTLRmAimeJsXIjyzSOfajAlvB50IMeVIBXLJf7y9+ygWnprAQZnzbSi4dJQJmmRe1egC2jkts6igdM2s+k7stJ+2vXzScF+tzKfcBLkfTRWKNRHIP79g1veEOxcCcpbEKp9LHtxn2UQt6fRz/60WWN+E4Ogr+5rymQxkOh5Y72PS+PTxyEIHkrjlTkns5VoIy3bd2ZT95sILu+5m2itxEbEu8BsBKgZONKROLSEnt94hOfWISF3wkhSRhRmF58SzLU8573vOLuIhTEuyZtMoG52GxjkGUJ4GWQ1hV5skCpE5PCIsix1CaAJp2B9XldzS/ZvRqVkoBnLnXJcpQ8pQlLqNPNogScivQLl0xyMIJ7fABmnNXMcnXouoIYxmYdWU/GJaGK0uq8WCdeKRDz8pe/vADwRz7ykZLMJzyjUlVfa7y+Pni4WbLrYx5734Jwsd1FUojYFdATP5WYBFwBaAijXLdYXIvFKnOTxs+KnbQBdu46AoVgk8A0lDxCiIRAzAIlx403pWSjSWm8qV7Xl7AWilmOYeYM8NoVjRclOPnIJlZ8BX8Lf3DfiuOOy1SmjH7mM58pH43yyZrlUsb7dVM/XFhG8iEF1xF3ceKOUMnQ+pjGjb6p8sQ8vHcD2XmYpSWO0SJlydLUASdhwHUmmcnCz9q+6jv2IhI2b3rTmwrATtpYqLe97W3LhytYabtJmvHl7RsBtHFOqt/nrfj+JO/drlkaBWrQyZnNuUhEWLRDVm88XX9CGD628IivylP46le/WmKxrNZJGmuWhYz/gSzwlnMQjeLJmuUdeuhDH1pczhGuaa7iSSg839c0kJ3v+VsYfVh/uUC/HxXBZ9E67g6Q2iTPZRWLW6EIrisAy8KdptmKoD+ZmLYLjasDXMdV8/aO2vro0+Kb+2ya2Vnf1w5ZeTmbOcdvJ7EKeXPCo8MlbO+rww5YoJNUnQK2PlFpTbGJfffdt+y9tY1OIQz7Z+U/WH/yJbIHqV4Pjd/XBw83kJ3zeaz3KdavI94jyUgmsIQNACvrUTzKoqe5x37BSUhBC5dlCWBlBEvmGNWyoOjbxuHecdtAsuUxyRjbNY0Ck/LMEJDJX/ChtLI+uZIlTU2yVU1ik7WlyWewVcfJV0I3b3nLW0qmMYXW1qCcue96ruqwxCdRDNpMzz4FGsjO/hxNNcK6eo5tBfb72Y5gcduoT5sGsirlTNJYwgSOJCauYHGk2Dzfd39fAtMkz2nXNAqsJQXqGG9WWGMc1lMALrBV+IIrmednkhKhir2I+bKGnYgFbCUcKlQhGbBWUluS31pywNo8q4Hs2tB5VZ4SQiInCtUPsqVAkodmC85TnvKUiTfoEwLiVdxb9rTmg77jOVlQTWo9rAoxWqeNAlNSIIco3NoHcNmaBIgyie973/uWLGKZyU79ke+g9vdQsz55kmTry0rWj0REoJ1zDuq9sXWW9JSv1y6fEQo0kJ2RiZh2GBnchtxLNuDLgLSXT1OCblyzt1YGpAQm5RVHVV/KMdba7dZcXeMo3X6fFQr0hTGCt/vcyYDR1pvnP//55RQpLmGnS8ltkGU8CmzFeTXeIVWpZO/LZwC6teIaCYC5v7auZoVrJh9HA9nJaTVTV/Zp4TFAh56r8sRFNWmWMBewDEnZkbT1ca3O3KwFRBMG4yjYfp8FCvTxcbYoMx9nxTa+p5QqP+rDNexgDO5hf/d5eeKdZRfLOPax7ii09s1KiOrLURgF+rNAxzaGYQo0kJ1z7sgLUnIGF5Z466RF0iVf2G5g7549rbVQ6dPka7cWEuZMzjknaRv+JkSBoQzk+L5O3Mtg5++cA7HDDjt0Prb+OCVIXW8lHcftu5V8aC+72K+D7Sm5fafybELTsq5edRBkp0kfH3dtxAyHNLvM6H0uyD4NctJZ6NsmMum9s3DdONqqVKN+8KmnnlrcwpPUZ1WFRpxWTVWJGKo8jUtkQou+I8kCYPO/s0C3NoZGgUkpMG47UO5nEg+NDPzHP/7xxTrlRna0nbDNqG1AUQXKPnXrWO6Es2fjnN36XbKczL+NkxeT0mS1r8vjj/KWfWGvofc0vnjXvG0xy/tRMqnGlBonhjx1k8x/TbuRlmykk+tYAWyCOAL1+eWHrJi4piZevED0Xwtqv/dpkK73/HhRxI3KRKwwrhug43nGOspds9pMtJT+s5Y8bmF7T7WFneJhW8CoxIvoy/4923mUlZMl7DCAUa3PYl3Ke7V7GgXWIwXGCdwtt9yyFH+xhUf948MPP3zhSL4heojxOtHHqVj22aqHbLucghajgDbk5bgxzcI8ZECrvQEBnoEJfWGxGlT7Ctq4L8Db3wqN/PjHPy4nNqmwlT0V8azVcsn3gmwQweANBripzSl2oKB1n4bQN7l9sYV871A1n6G+amuL9kfrY8kdd9xxBWSPPvrowtS2rfS5fGaByYbGULtq+0DOIrSN4Kyzzip78fx/XGOpoodtA8odyjjua6OylMc9o/3eKNAo8P8pkI0EcknOg/rhDtcQt5WV7ISeIUNAjXEZyco+yuznceKKjhOy5l0BHrJQJ/EqZFCtr8+/5b/R3j5nrvmcZDaqr5jNwJGlZnv3gmxoATEAFtPxxx9fyoKJG8SLqcepVJ/SfdqFF15YGIcGp25tXZMTg7HAZK7mlwOS+gIEsu5y871+beTWjAW42lqif3s3lTNTPeWpT31qAVl96Cu3eXGjhJbW55r17pQJZQ8VIR/XVGBise6///4lg3Fca3HVcRRqvzcKjKZADR613OFxU32NZUtJ5okad/CGPbk+8iee9axn9ZYtjbWbgWFW56q2TmOcLE0lLWGMA0bQTgUt8py8z41xIcGMwcCtng02ViuawhkV7zT3wx4eAfjBYMvj8FtYuOoHwCo4FhW5XLvUEq+D7uKsITjuTKxPcXnCHSgCM3vFpKDbf8mdfOyxxxYiCdrLlDvppJOKmf7iF7+4HKisRJkXVDFI7Vzlxo444ojuzW9+c/fDH/6wu+ENb1iy7W5wgxuU7z0HsMuQVUhBv7JmAZEC9wceeGBxAajCorSf5AETQ1NUn1fB7nlwn2Tm6RsvReOYY44pKf+TnN9KU3NYNA0Yo/WdV+mZ4ZYH6JGcsVRGmtUF3cbVKLCWFMihLM8dkj/2yj796U8va9S6Zmk5nGBUAyqPeMQjiiz0L6/UONmxlu8+zbOy8sE9DivIelug5Jcwqp7whCeU0pZySGwrhDNCXMrDMqgkegJZhha8IPcYgy95yUtKoR1HHSr8AW/s8SfnAq9U2tpnn30KcOrnZS97WTFg/C75zHZH8XBZ4+LjxrDUNuguzkSgNQSSexgwY03RMO5973t36t8yxZ1OoaoJwijfR8ADXX8T9I5+Cmvsrne9a4k50MxoF9wiYouy8VwLVIApFzVCIoLnYSx9AGnxDv3LqHU/zUNDqFwqcJat2HpseVFKlKDp2sBOoRnVMBClRZawYucUlb7WF+92nfvRe5ZptVQmb/c1CqwlBfrySeL5NejyuPkoTGHrHbkHbBgjfY0xwuiRUEWGkoP2so9KXFzLd1/Ks4S/GE/c6mqh81w+97nPLZgC5Fil5D/PnL3JwBZWcJ2zQP3mUAaWKPCVePaYxzymO+2004osRF99KGXpGqDO+KOomA/yVdhx9913LwANxIUcP/3pT5dxuOaZz3zmUl6t3DPRFh4D5a6ICiWsUoNFGEF5GpikGmY+0x3RmPl+D7endHYuZADNygQgLFSCXabrwQcf3B100EHlb9qM71VWYZWygMUj7OE8/fTTS1KA+GJk6wFfwAyAgTQNkQt5lttQTMKYvZdJFwe3HWDc4dKUC8xF6bDPrm/B5dhPPrHE88JF3azYteWYptCsLb3X6ml9yTqenRXceu4BJe8cmWf7D+/fKK+VLXpkI++iLT+HHXZYOYSgbrPIY/WYIgGTJfnwhz+8gCtrlqcS9lA4WJ3i2HCFUXfIIYcUmffLX/6y0MC7SxKDA7wC3MSMM0qI63nqYBasYPyJd5sn2KVMJoWFR5S3QD8AlzUs3HbyySeXZFFKwFLaRO5iiTOsJPEEjaWoyDzG4DsXD7W5Wvac6wIY8pFOgAAxlepjuXpp7tyddtqpU5lI1hfw9YIIgUCsMS8GwN0LgFnS+vCda7gBIusZwNB23DeU3LMUIi3lngyimalGxWy44tFCrIYLadxB0t6XBkcjowGOaqMS0+bNpb6U+Zi1e4YE7iihOIqPpn2/OpOyDxiyYtZ4ZFoKb+gqHkoEzfPK5ckbSB4CUQChbONQo5DbIgQcnPjDNZoTe4bmtS/Jcvo3XNodNS+FUQAX4AngpPizROX4aP615RDwsXS5jwGqD+VEI/NZ+sAXRn3nO98pwMp48BtPq34dlHLGGWd0J5xwQsERXs8DDjigFBBxH+uVseY5wqQsZjH0SDqb9q0HE59iu4wOAWgM0P8BGys0km9YuQYsuYaw9+JitggWFYcCMOK+sM4wEkCR9eVvDOWF3RuaA0biso4CC/71bBZZbNlBSJNjnHXG7VoLiEkBFi1jbFzgDlFn8U+yHWePPfYoWh/rfq3fb1oma9dvSAFzlhPN6izTGuBqgF3OnNd99T0rg3A7FWZ1ObhPmYkEKfFBOSunnHJKEfRDLWojK/HI6mOJ5VaDbfDALFi64RqXUa2R78YrFMlT6nt1n1mgYqX+nwt8cO/KzYET4rCUDVjAWNM3cAbY8oZgg+I78n+e9rSnlRoB4r9OFOMeFoclVyU8MegArWv6vASTcsVElixA9GLMaS8OdIFcEIV/W2Pec3e8+tWvLhqB72vXJFDM4CxeKzgNNJxqwZIT0wU0jozSvKh7EE4LoPa75/i4HhEjM4yFHC2shqFiCpMSa9Lr+hg6A2ruB0NJGOMiEV8e17gvuFC4xvsSmrKFtBxBPG4c7felUyDz4xDQDs1dFo5DPDU0sj4vSl4TfWGJGEfjpaXP97g760PmM/DxynF5cmcKv8k/GXU0pXgji8wWP8A0tKsg+C7LyLWa45oP4wD7MMSAnmsAqRClprgH97mQGE+mkCArFIjy5ElkghN4WF1pibBnn312qSvNK4BmcAI+uJb7l+dUrsuTnvSkEmaT/8OKZdxRVOALtzS8Yf0utY0E2dg3yVXL7GatQnVgiDGCOGKtLEmDZY05Vo3GwG1swLmABKLEYkYkAWxWLNcz897L2xIkAB0gG8RnpWrA3d/614wjiOf/xsD1gPjTCqKlErK+L5gk3r22VNCBhgpgVXkZ1TA/TQt9gSu6jbt+pd6j9bNyFMjCpc91OApYM7j6e6kKYwb42oKKLPPYHx+x+pWjQOtpiAIx90M0l+8igUdio8Qf7s6hcBKDw+/yX+wycLSlc6VrWRjPWur+z6XOZgZ4cjCMpzDaeOd4MyV9ko2w53Of+1wJLUpAojzIPJZVrC85QmQ9QGS1ciVvtdVWxSvKGhWv9hxGWGCW3CEeWTgF1PE8+no2L6wkNOMSsyV3l9MGs4tpEeErF0QGfsCQG4Mp7fiz2B9rYBFH9DK77LJL0Sbcpw+JTHE4MTMdWDP99cVVrJA9XzoXh6wwjes4jmhDhOc85zkLe1/teRL/lcourstX7nn6lJ0nOI7I0QgT41qrOG0IxKxcZAEqcUtig3hLMNbQJKrQhCbcRuOqvkQftZa6HAZp964cBZZqKcR8RggneysmHV1tPbivD6hz8lv2Qi117JOOb1O/rlbAclWjvK7JO94/xSnIOlnGozKRn/3sZxc5w8sIgPJxlXHKD4MlFKu1mIdsqRuDccnZYUlqQJW8t/sE5gA7W3x4O/EhkHU9y979tu3wsMIaeCJRicEmOVa8Fj7AKIqG/CFNThHaGIvtphp84IXlmpe8C6tkM+t7OW0wJpuPWfJicdJE38PET5n1YdrX12SXBeCNQLXruEF86pZjCkx5/vNoiIWAmt8QIxoNxydaCKSNkeJeCyaKBMYwuWIIoxqPARcFgOUeyS0z6VCspQnF5SyL1b+XN0jWPL4MD01YqAQsQOWmimpdscUqvEtLsTJHWcqEiq0jciokL2p9wLz6lNk0n1Cv4/r/qBLfkbc8WjyIQIELWfGEoSZeK84IsBSm4RWLps+1Mj76xuf5rEqf3HhPyb4wuvJv1oy60D51Y4DZ0lM3hTx8ogFyikfdgHfGmowjeQ6m4dJBSzYv4nHxoUke2BfcH7pvVDC+T8Mb9fzVjimF63tceS5p+VzgGH1cE3fg4okSlvn6nJCS43n1HM1CQsO499xUf2d50JZtWRhXuYuCxWUmIaNPuRpFw1wmM/OHvAdCmXeEUBGrsuGeh0UMyx7BUWsz/9aUudXj4uyRyms9nsgaAxQ8h/Z68v6NOjNa8g9Lj1eSe9X92lDoYRqZPQ0V6vfKQBaK5lIUvL57ajk4JBdHyculjGWRUtBHnFELJ4NvDXiTCIE84BwfinFEQQSWdA1gOS5VA08kD8T39URmgTMNQ4y6No9/CPzFEmiaPuPOdrUdJzIDs3Y5iq71XK22UrFStNuU+wGyqngBWIoUT46tAuaZBet388jC5eoKL0x26Y1SfEPj7ruGB4UXSGyKNQRk/S1z1fNZs3kNZQEY/fo31mYD2ZXl5Hr9ZvoO0Vo+i4pHYpTCdopVDO1QkGgp0VSCFCWLq7YPZPPukpV9w/9/ek7wUf2Onp1Dbq7LxkWMJ2e9Z2zIGBUyekiZ8CzPH5VBP61hV9NrMPEpE75Po4mXykwxauHFdQGi/h/f9Z3Gk11n/u4DyfzyQcy+ca2GVRfPq93qQWDvJLFJoJ5bcFQTP5YxDGCVW6sViCbIVnqZb9z+8ExkhhNywhuxLgJoQwBxDcZanJQPRilaABWQcqtFAh0Qj/GEdVNTqE+Zm3Q8G5fam87TuUO5kClt4pTKBQ41Z07LXWEE8JpFrLK+frlW3NDzQ5Hsi/vXGe8ZO+rYceb1kMlDHoDAkcy3EYah0OYT5nK/y81NGHkKzzgC1y6MumKQBS1D2OZowkLLoJQ1knipGiTjBWst3nX18/J4MsEz0VdqyUWf9Xj1LyMNuHK9jXIHSkJQu1SMNgp99I1vNazwlaJD62dpFKhrRWfBMip/wH220smclF0PHFm7sk8paLGOuA3tG7S/z1mmtioAVgkhmvwAW+VYsnYAUPSUneNBkalv+4O4sa0QLN4cp63X6tIo0O5aLgVqr6B5MX8KUpgz4QiVk4b21/KsSeyRGCWjVnJQ8F7I1tWSnTkpNOiQwa/Pe5flPd6UmyO2WuNUDbI1qMbzsrWc8aX2sGZ+X8qcjTy0XYdD2uoobTkGYnFLN7elJtfSrd0DeeDjntc3IX33h6U8TlFYCtHc0weuXDSKSRx55JEjq7S4Xya0MpLir5l5MnMt102x1Hdr960uBSzoUDqnSTqhsMpKp5RptidEdroMfDE32aeaNWcbBwBW6CR7owJk1fu2P1v2pARCTVyPcI5KO76TDCW7UwW3Zr2uLm8spffalWqOeCTUhZewagtLHO5S9+9e9QzEde1FlWjE/byarebFPpwZhS+KH7HU5TVQDvvwZCjOPIQ9Q0A8CTaNo9UgyNZ7pyRHcDHY8GtxmxRaMLPfXiObfe3LAjQyg2URW9w0YvuWpGN7cfdb2O6hWceRdPZ8+U1BBgexO0wgso71zSKkvdPQbQeKPVJeUJyBNmYflOcqiBFCbDU0sT6mkMFHG1RbeVSzDUd2tbiYzNHcQoNq4DqObef79yxkhBJYkHg89j3G3kHrS9ZlrDPC0vYErj2Z/LatWRMSmSi0al2r24rnFUS3FvUvsxSvifuyaqxJ1XBsXZBY5XkxJkoiUOWJMR7b66x7wKt/SkGfBTXfMzKfow9giLhin/VH7lKczCMFTVWjvoYHGERitZLgcqx2pRWr3B+etCcVvpCNku7wWBzywo0LVxgiLHRZxxJIyXvbSG3r0XgPbWfSYFNs4YQbnsHrQ5mAHfbb6s8zKKkUSpYxQ1CFqWi8P8orog08smV0KfXdJ4rJWqiqjtCMo8l4dC4iIOVy4H6KCZRBq3JGaMMm2CZqTGDyDFwjLLhU7beledNQCAuEkU0pPR1gEi5iB54Z5/7RrGXIIQ6Bo3h0NBaifbTqGAcgLjUum+/r6wMT2JYTR/ONWq4mSdKBqk1DLbsmRgXj51MstFEHP8ZiVXdWQRYu2gyyFC3CRrESMTO8ByC5bSW2ZGFAYSNMrVNrB4AG7wNpyTDRAmS5gVkC+rMPMaoI2X9JiMW5ztao51vTxsjiXWmh27hiegpkRa2OJUbsMaw5fET+SrKjKEnCHCpkQc6Sp2S0LOQ+q3apsrR+S/yq6ASQjQZnyFLZ7+S4kGNUFIwwXCSQnnjiiQVkKamKbvhXA8CUQiUWvS8lUbUofI4WPD68N3Ih1HAI7JCjYA8yoJeFrbgFfNOsJ316TrRJ6TDyFJ6IBSICgAUQBqcSh8HQJFiWtF+L0ckxtGSgCvmj9jBr1ctJ7LEfjzZOa0BgCT/6UaCCO4zLQqwS6Eoc8jwTzsL1fG4QAK4KB42FFo9IrEgn9dioTDBhqCiFNY4YfZp5/V0Ix8woxmQSCclRmcMsEYoC91wuklEzXVjd47YDTb8k2x2zRAG8FQUEuGBZkwRA1GT1O7DklQl+sX64yFzHNWxthgfJ+nAPYRv9hhAVlsgtcgRcS4ABWfcAUE1BgABY//cs17CMa8E8bl3NEs3X21j6FJ1xITyhAwoUS45hRBb3NfNMAWMk8WiQs7kNxeTHGST1s+xnhS1kPiuVYUS2A3d86vmSuVwHGCkHai6El9JJa7w17mGpMnZ4WXloWKzc5TAESHODwyjADB/kwMApa8i+WL/BDqEYIAuYeVQZgdYebxBLX6w7FI+gwzjP42AxikwQk6IIM8BT+MHCdZ4sc5v5bhEiEK0CoDLvTZTakAbpPouaBs6a4wamGdgULTBvkK4Hoqxjg0dINTi5QoC1F8MYAAi46cs9XhrRMII+VUhS1pGGEi3Aa1S8ty92O8S0nkuw2aM2qt6wJAJgD2AlOPW1WlA1K2G9icP+94lMfBaGxR0HcETIII7mCotULwDZOqSYsiwpdtYDQeM+/Bb8E2BbH88VCVdCKz6hPAb/R2GMGHWUQSVoGm/OD28OzZV5JJcZJCpGATByvK+xDFm1ZDuQyZnnwb/BP/n+SZUv8l8NYkUl9E2pxG/4GR8yTsh2YCq0KLmPYgB/yF/rBriq08yA807uE0Zh7DH0gDVAZQwx3hhyahbgfe9ALqsupQm1xCE0QiYytdU9lkBIQWFde15t3Uf+zxB3jEx8yhqLjeq0IG6pWJwmzKKV4ajUouZv2oSsLy8FhAEmwtOQuXyBsZf3kohn0PbvIU64PvwtBT3KIUZM1zPiKCfX6lvMIQ4vRkTCphYuk058Dcw1E+lfYhNrfNRRdDLfuBvEX9Gjbn3B//lZwm2ky6GAdRV8bo1ky3FUvwQOgQdcZQ1z3dL0rR+KXD4pa9z4jCFvTQihWfO07/O+w9xvA91xVJ6N3/P8xZyRT4CHweNoOGG6vgaAuW1ZfTyYUS0qeCf6zvJsUlkLG8huseI4To6s1CevThh0xhV5CfDAevEe7gd6MAioMsrwr+cbJwyCBbLuo5wkIPcM18CvXE3PO+WYq9i0D7xRH1lffe85zogb3MITBBer4bsWb6VBM7s/8pGPlDiNQVnYCCJpSYtN9r4DxkApNjbTUGgI3MrcT17I/ZI3HJzrRaIBXURAcPfnzdXxt7EBV24vrgGHF5swwqgWAEPZZhlU/Z0t2roPGXrc2vz1o5p3ZJVHLc5RANsE1WwIorUcRcTMPDMf2TVqDGJlL3rRi8o6EBqR2xC1va0hbj2NYNGC34f6H9pvmC0U/RBaPn18OqkwXUvatmdtSIFRIGDbDgOJ0SA/gFzua1y3UYlOXDIOWs+KWsjPcbI2+J7CSM6T3UKGjBduaoYTvmWIUSiBKmvSe+BFmAJsXRdbjljaMIlSAIOAp7XAPawPayQSqiJk4rvaiodZ3hWOcCGT47yzMFDOUL29rs8DWtNvZEzWxcxnQWMNyNIEIovL4CVS8GsH8AFXL+FFo/6q4DHNwmQKdoujsmC5iu3boym4JwMpQgJR7rE4ZScGH6c2eLY9g9wBzhAkiFi/XjxO8Il7Ru01zdrJULyBP56/3mQPNdYz0DchYb2G+y8nMTVg3bRFYbYiI740jiLWDX7nPq5PBeH2i7BKgGztNu7rP18b46gFZIBxzkDOfTWgHTdzG//37M7sk3XABMBJpgMq5GhfI4vJtkh6jQIWwQOeE0VV3D9OzgFYYM3b55lkufsVSyFn83Gq5LnfrAE8iR/Fc4XjuI9ZsXJwxGJ5dXh54ljWcD/Hwe368GwgG7kIxgtn4BcjkmXPlWynDC+uuG4+0zzebxL+HxuTFeOUoHTooYcWN6+BRrYXEAyTPPb70QQQlzCwbcCHxiJ2Ko6KEPz83F0Cy4LOkivCao3JZeUSHAGOwD1auIL1gSkOPvjgEhCX4RyaWAbsIXdX9BeaXmasYJA4TF1QvY5X5esF7gXwlUas+wmg3fjLrY1gFiiAr0NZU3OWyyu2qUU50UhGkgVs7eFvIRRrTy6AbXEy63lV5D1oPEFyBCid4RWqzx4Nvpa3wGogkLTwRNWWb5zTbLz1aS/jhOgs0LqNYTEFalmXLTH5MhKF7OrgSh4Kh5HjvI/AkVXbxwfjeAOfs14ZLyG7yW84wLADsAyVUP5CnsMj4CeDmNw3DpYw+Wsnitgumc0g4ibWB+szlEegDpvIct/nU4k8C54BVmORaCij2TpjNLp3KQfNjKz4ZHo8mItYEJgmgwgCyr4Hcohp8ftdo1Vwq9IofIATS1h6NBNeJvJ5551XJlAih4nVhxhBLimorqa9sASGLQg5biX7jGvY/fvtt1/x3bOIAbFnIkTO4h0XmM5gG39jPsklgDOUir4Fa8IoHyY1NvTnPkLjyf+2hb9pUiAUxtjXaIELw0gwGYqnshpkS7Iy8DxA5jaWsAL09GXbDVcWBdN+bWuGIkrA1MLOOpT4Yq+6rRLWleQrAiQLtZghY9ZX3h+b+XucMN00Z3o+3jrCFtl7Qbazau3+wB/2ivY1lh7ji7uVhzPk8ySu4uiPgieZCaDZI8sgw2fyb8h0iUxxvKfkJzxuu6dEW8lLEXKUmMuDCXCtCQVZXKcvGcmRF+S5cEWSLCyCU7lWAZyJc8l5JGGT9QbYyXmYB+tyy0rL0FqYKPEJaLHQaistHpa/JzhkZEWrjxgyebn6U1yX9/35TrwpYk71MUgmwSda31F5fYTIsYk68SgTiFuATx6TjTrv1bsReJih3qQ8ia9+PpZiG+VKUSAEEDDj3bFVgOcntOpwteElmrzvaeZCK5pMTAvfljEaNiWXgBOGoW0D7Fh7khQph3Hmc7wDRdR2CKEa7jYuP8ohAcMCiDyCcIOJ2Ul6sW+9Lp6yUnRp/awtBbKs6yuu4HeVongfyUC80hfbJyeFLvARfrMvNStgeGhU3V/gN3TiE9COM8j1STnE+32Y4ztg7VO3fMyq3ygR0eodH5G863f8LrdmkjZO0Rx0F4eLc1wHkwxiFq6J9xineYh9SSyR9TYEsJhD4glXdT7LNjOYv9cL7WZh/tbLGAK8gNtQUfahd6XsEhq14HB9Vkr9XwjGp6/ZASBj1CdarbjG965l+TbeXi8c2P8eOXckruBZjB0lEj7ztsi4hmIoR4eLlTcvDkAP72Fdo3t9U7H/7QYt2aEEoFFEGgoCT/v9NBMxjcU4LjaLWaRsR+WQvnFwQyuUwe2QWz2OBrDTzOKmde0kyRI1b60EP/UlvQxRPpJYavffUuTCpjW78/m2Q/MqRkkZ4yHhHs41rfObSlyS4SvHJh+GXvPtNPJ62nUyq5Qfm108zeIeunba76ch1rTjyy6MrJ1z+yp2IetsqHFpu6Z2X/eB7TTv0K7ddCgQnpQQIH2CpE8Q1QA5lBFfUzLAMiyLuC/H42rvTs4W1V89xqysrhdBuOlw4PCb1ryZrxQSEzaQCyCUxlVcNxnA8mUiWdSukb4Y7aQye+i6aYB6FuZ1LMjOwiBXYgwxMfWky6rk5uAOqbMn47kC3uoks3LFwTI41wJpJcba+lifFMi8MkpQ1MKuziXIZdwyaOb7UDB4PcfFspIZ23MyYGfeDoCuv5smuWV9zuT6fqsAt9gzHfMtAUgJQ2EIOQV952STobKTJcmq9RvFK4JimZeXSsVJQXqp/a/0fesaZMe5x2RiqnaiTuVQ4x620V+qek7fzoLOpGOuOCOxafcrzabrr79a2AyFG/q+73PBZYCtq/HE9dklmClaf5/BdaiO9rxZE+uPg1b+jbJ3JZS0KAaUz5dVlMLODq7hoYPhHQgvb0VoLU7KyUC78qOf3R7XPcgOaT0KYtj+I0tzqMlWkwQlfTxr89lKiO8DgBvAzi6zb+yR1W7ZzJv575qH+uJlfe7juo+hzM7cX35WHl9trdYCuG9MG5u+7fnLp0Af0PZ5OhSBUDPYXlX7ZvtqCNhWaXuZPdmSRG29qeWo//eF8KZ5k1mXuesWZIPwNLE6Td0mYxuYYwN+34QqOK1wdOzTmlQLmzdXxjTM3K5dPgUm4Y8h8B363qhqa3UpfeR+6jet+590PSyfYq2HtaLAJDyTAc32Mqex2WJGVvaVZLRDw29cy9zHOaM+PCbLVdgmWVNrRcO+56xLkK2183hxh/eKvyp0PVTT1aZjAGz/YX3IQCbgrGtPG5Op2rMbBRoF1g8FsqyrwwQMGDWD7TFl1Q7tzFBJivxVSUqcti+EMetgudQZXVcgiwFq8Au3l6oicZrEELEUyVDtJM6hra9rwLpUNmv3NQo0CswzBUL2RQ32+l0UrpB9rHjF6aef3vuqzv1WXcwOjdh7HcAaSVbrEWjXFciGu6ueKCnl9m4pkzjUVLph4dZls4as4vXIDPMsBNrYGwUaBVaHArWsG3LvqvikOpTCKLb5KLhfNyV2Aa2EqL333nuDU6NW5w02bq/rDmRra9O+LhnEdaH0THYJUCxYpbuijTvtfuNOW3t6o0CjQKPA2lJgKAM+j0LJUDFYxopkpzgEPV+j3rED16O6XpwGtbZvs3ZPW1cgS8MKLctmaecjKvQ8dDydmq1cyI5vykeO1QDbtiusHUO2JzUKNArMHgVyhnGWh/7uSy5lrZKv6m075KKvsXZlJas/sJ7rYs81yI4CPxNogocSnGyslmXspJ/c+vpsruHZW/RtRI0CjQJrR4EhGZgNm3o0jmNUkJ+n0Ak6fc2h6g638G8+ECBfO+9exbkE2VEJSA6S33///cu5iEMAqzyicwzjdJOY0Gaxrt2ibU9qFGgUWB8UGFUBbNttty37aFWKYtT0NWfDOlJOTkxfTYLY6tN3YtA8UHAuQRbR40zOPMFqZ6rO5CDsoeb4InWK87FMcW1sxm+W6zywbhtjo0CjwKxSIHZ6kM/OCpdR7O9TTjmlt+6x5FQWLyCO4xZDHs/7ro65BFmMVWs1amU+6EEPKgfCD7WHPvShZRId36X1uSEawM7qsm3jahRoFJgXCtQZyBKiFKOwn9YZtH15Ms4/vv/979+dfPLJ3W677VZeNdzRQ17JeaDH3IJsJq4N0I9//OMHAVZRCVt4uJEDYN1v4qLe8DxMVhtjo0CjQKPAvFCgL/xm287lL3/5Uvf4a1/72gav8otf/KJkHn//+98vCakB1uR0X3nH7IWcVbrMPciee+655RzDvhMhEN22HKnkhxxyyMIcREacesPNRTyrrNnG1SjQKDCvFMj1iOvTfHbdddeyl9bBAd/4xjc2eEVhPxnHdnw85jGPWfh9Xr2McwOyfX750047rTvssMO6Cy64oJcXt9lmmxJ/FYeN1rKH53XZtnE3CjQKzAsFcl3ivuIVkk7PPvvssgPkzDPP3OC1/vSnPxWgPf/884uM32KLLTaQ4fmmWQbgjQ6yo4LaWQOqr3vrW99a9rgOFfnffvvtS/xVJnHfZIQFOy9M28bZKNAo0CgwTxQYd+6wMrYveclLSm7M2972tg1ezU6RY445piRKqRClrryWZfcsg2u80EYH2VFMkzWgPGEOBVaMeqiK061udavupJNOWrRFp2/T9DxM0DwtqjbWRoFGgUaBcRTIBtNVr3rVkugkrGdXSN+Rebb2/O53vyuAvPnmmy8C2nnYdrnRQXYSoMvXvPKVr+wOPfTQQYB1woP6mdttt12ve2He08HHMXD7vVGgUaBRYJ4oYIsPoGWpykDua6961au6zTbbrJRsjOTVecmn2eggGwStwa/v/0cddVQhcl/haf3YX8VFLE08GlcEKzj+HSpuPU9M2cbaKNAo0CgwrxTI+1/DQyl7WAlcsl29+b7GooUL9txe6lKXWrBo/THLFu3MgGy2VvusTQHyo48+uvvLX/7SOwF77rlnOatwq622WmTBRr+5/NeoVPB5Zdw27kaBRoFGgXmgQF0HOWT0ZS972RKD3XrrrUv1J8eT1k0Y8Mc//nE55ac+AH5W5frMgGwmZgZcoApcBb6HiAhgTUreA5s1m9gPG8+YxEU9D8zaxtgo0CjQKDBvFIjM47Bis1HFZSwceL3rXa/ba6+9ut/85jeLXs+1kl7/+Mc/FhdzDbSzSIuZBNkglCA4grNQh5q9VieccMIigA33QbglxmW5tTjtLLJmG1OjQKPAeqbAKLmr8hP5rzCFAhV1e+c739mp4HfGGWcsOqJ0Fuk1syBLUzniiCNKIf+hdr/73a9YsNwMucXkTWqxTnrdLE5gG1OjQKNAo8C8UaA2fEJmZ+B94AMfWLyXBxxwQO9WzQ984AOlEBEXcj4qL3s8Z0G2b3SQRZA+UAwX8RDzcBEDYCW6suXq71kg7LwxfRtvo0CjQKPAxqBATkatn68evaQoQNt3APy73vWuTqlGyVLXuMY1yu05sWoWsGCjg2xfGrYKHwLgQw3BZRlHhllcN+/nDm4MBm/PbBRoFGgUmAUKDCW/7r777p0KUI973OO6X/3qVxsM9X3ve1+37777drb52HcbbVa2+Gx0kEWQcB1Icjr22GPL2YNR7SlT9GIXu1gBVyDr79xy9vAsMEwbQ6NAo0CjQKPA9BToi9U+5CEPKTL/UY96VPfLX/6yF2gZZrDDiT+jrOPpR7S8O2YCZOMVJDjZK9UHsKxWFq5i/9lyza8/LsFpeaRqdzcKNAo0CjQKrDYFIqYansmQ6yxa3w0lQ6lTz1Czj9bJa1pzF6fZetOb3lTKZg3tg7WFh7sgWt6iE5MRBSdWmwla/40CjQKNAo0Cq0MBoDq0l1YyFACV8FRbtO6BIf599rOfvcGOE6PdGDtJ1sSSratx1C/6+te/vpwd6Iijvnaf+9yn22+//Rb9pI+YjFxwYnWmvfXaKNAo0CjQKLDaFMjYQK5Htb5slcKDE088sRz+/oMf/GCDIdnSqZ98qEAk2GYAXysrd01Atn6Z/P83vOENIwF2t912K9t0nP2ardi+Sk6rzQCt/0aBRoFGgUaB1aNAn1zvK1oh69j39sr2HSpgW4/Y7JFHHlks3xyjDQNt9d5icc9rArJDZvpZZ51VkpiGLNh99tmn+Ncvd7nLLQLYtSbSWk1Ge06jQKNAo0CjwDAFckhQISJA6mD3ugSj65RetK1n//33Lx1urGzjNQHZvnKI3/rWt7rDDz+8F2ARg0tAtlg+rBehIv7aGLFRoFGgUaBRYNOiQA2UcMKRpxJi68pQ8nsOOeSQ7qIXvWiJ4UbW8VrXOF4TkA0tItjh+9//frfrrrt2X/jCF3o5xOZihSbikN6whKOflkW8aS2s9raNAo0CjQJBgTrH5xGPeEQxxh784AeXmsa5OfBdNrLzaA866KAFi7bGlNWk7qqDbBAkAtpOULDXaQhg73jHOy4KWNcvv1bB6tUkeuu7UaBRoFGgUWA6CsTBAoEB2XWs1vFHP/rR4iKum+vUX7jZzW7WwZdoYRVPN4rpr15VkK2ziGkTT33qUzulsPraDjvsUMpjbbnllgs/57KL079eu6NRoFGgUaBRYD1QoK5vDCTzCWvCj76zX7ZuvKeSpM4888zuFre4xQZAu5rG24qC7KjCzMx423Re85rX9M73rW996+7lL395d53rXGfR77NW7Hk9MGt7h0aBRoFGgXmjQL1VszbiHBRz1FFHlRKMtvjU7bvf/W6ptfDa1752A5yJXJ++raHLpdOKgWz2k/fti2WuA9G+tv3225fj6rbbbrvyc9+hAaupaSyXiO3+RoFGgUaBRoG1pUDelhN/X/ziFy+FKCRDvfGNb9xgQJ/85CfL/lpbfLbaaqvye71taKULVqwYyNb7kLLfnFah5nBfU9AZAN/85jdfZMLPUu3JtWWd9rRGgUaBRoFGgUkoEHHVDIy2fCpEoSLUOeecs0E3Z599dtk7e9ppp5XM4wDabNytJNCuGMiGBerfnP17+umnd09/+tO73/72txu87BWveMVSBusud7nLwm/1STrNgp2E1do1jQKNAo0CmyYF+izaa17zmsVafcADHtCdd955GxCGlXvta1+71MoPoB3CsOVSdUVBNpve/maaP/nJT+49NcHvrFtbeaLl+GurQ7zcqW33Nwo0CjQKbFoUyIlQClGoFvjIRz6y++IXv7gBIeCPOO7BBx+8YM06uzbAdqUMvBUB2ToGa5Df+973SqWNuhJHvOlTnvKUzv6mDLCA1UvWWWSbFpu0t20UaBRoFGgUmIYCgRk1MN7ylrcsO1Z23nnn7qc//emiLt3zzGc+s9t2221L8aPVassC2aHM31//+tfd0572tF4z3YtIpZZuHVqD7xAnADZrI6v14q3fRoFGgUaBRoH1QYFcCaoOOdq5IhnqwAMPLEUpchPGVKRCHPcOd7jDwk8rZcXqcGqQDY3Bi4TlWU+Tc1+lSfe1e9zjHqVosyywvubl8mEA64MF2ls0CjQKNAo0CqwmBeotPvlZ++67bwFYruH6vPLzzz+/eF0lRF3rWtdaOGYvA+1yEqGmBtmczSXBKVfNsBeWD5x53tcUm5DotPXWW68mrVvfjQKNAo0CjQKNAosooH7xl770pe7UU0/dgDJitpKgXvGKVywyAIfc0NOQdmqQDRcx1y63bkZ458KKtcbRQxmAZXvZyiOjK7flaAjTvGi7tlGgUaBRoFFg06NAYIwkp+c+97nlUBpWa91e97rXlb2zRx999MJPfaUXp3UlTw2yOV06LFkjoiF4gXy2XwCy67iI1Y6M1pcstelNf3vjRoFGgUaBRoHVogCcyWHNK13pSt3JJ5/cffvb3+7NOHby241udKPuYQ972KIh5ZjvtGOdGmQ9oAbICy+8sBwp5Pi6ugHYI444ottzzz03ANhpB9uubxRoFGgUaBRoFJiUAsARBmWP6VWucpXiMt5ll1022P3iOvHZzTffvHPogDat5VqPbUkgmx/KclWx6d3vfnfveztxRxmrfE+fCT4p0dp1jQKNAo0CjQKNAtNQoG9rD7ewWsYqQ+Vmd4xDBhwkIMwZbalgOzXI1jHU4447rriJ+9pOO+1UtvLkTOKwgluxiWlYpF3bKNAo0CjQKLAUCgy5ep0/66B3RmB9Du3HPvaxAsBO7bnYxS5WHrvU/KGJQbZ2EUt6evWrX132H/W1m970pt3xxx/fXe1qV1v4OVKnme95j+xSCNfuaRRoFGgUaBRoFJiEAkNWqGpQX/nKV0qctm6OZD3ggANKPpESwKtuyXpA3huregZzm2ldtzhySCWN3JY6yEmI2K5pFGgUaBRoFGgUmIYCm222WQHRz3/+89255567wa2nnHJKOeh9jz32mKbbRddObMm6KwLI/r785S9fag+roqGEYm6KUdz97ndf8qDajY0CjQKNAo0CjQJrQYErXOEKpX7Dfe97386Zs9EcHKAa1I477risYUwFsp4UxwHxU8u+2mabbUr28Nvf/vYyEN8xwftas2SXNVft5kaBRoFGgUaBVaCAo1bVMd5vv/26v/zlL+VQd4fb2MoTp/TU5RonHcbUIAsoM1ja+yo2y3f9ox/9qHvhC1/YXeYylynPb3thJ52Gdl2jQKNAo0CjwMakwF577dV99rOfLTFauUa3uc1tFoazVIDVwZJAts6yUlxZ4PhXv/rVwmnzYfF6SLNgNybrtGc3CjQKNAo0CtQUqA+4iZoOLNcttthiwVCM61Y9uzgPsA80bd71iVZbvG2KGwUaBRoFGgUaBWaFAn04tuWWWy4aXmz/AcBLbVNbskt9ULuvUaBRoFGgUaBRYN4osByA9a4NZOdtxtt4GwUaBRoFGgXmhgINZOdmqtpAGwUaBRoFGgXmjQINZOdtxtp4GwUaBRoFGgXmhgINZOdmqtpAGwUaBRoFGgXmjQINZOdtxtp4GwUaBRoFGgXmhgINZOdmqtpAGwUaBRoFGgXmjQINZOdtxtp4GwUaBRoFGgXmhgINZOdmqtpAGwUaBRoFGgXmjQINZOdtxtp4GwUaBRoFGgXmhgINZOdmqtpAGwUaBRoFGgXmjQINZOdtxtp4GwUaBRoFGgXmhgINZOdmqtpAGwUaBRoFGgXmjQINZOdtxtp4GwUaBRoFGgXmhgINZOdmqtpAGwUaBRoFGgXmjQINZOdtxtp4GwUaBRoFGgXmhgINZOdmqtpAGwUaBRoFGgXmjQINZOdtxtp4GwUaBRoFGgXmhgINZOdmqtpAGwUaBRoFGgXmjQINZOdtxtp4GwUaBRoFGgXmhgINZOdmqtpAGwUaBRoFGgXmjQINZOdtxtp4GwUaBRoFGgXmhgINZOdmqtpAGwUaBRoFGgXmjQINZOdtxtp4GwUaBRoFGgXmhgINZOdmqtpAGwUaBRoFGgXmjQINZOdtxtp4GwUaBRoFGgXmhgLrEmT/93//t0zARS5yke5vf/tb+ddH++Mf/9j97Gc/6650pSt1F73oRbt8bcya7y688MLuEpe4RHepS11q0WTqT/u7v/u78u9f/vKX7he/+EV36Utfulyf+/BMff30pz8t/17xilcs9/nbJ/52j36jzxhrjD3eJcbq33in+Dv6jGfmd65p4P1/85vfdFe72tW6f/iHxSyQxxF95/t/9atfdb/85S8L/S5+8Yt3f/3rX8u447mZ7r7/85//3P3P//xPt8UWW5Tr413z+PpWS36v6NO/v/3tb8vYPT9ov+WWW3Z///d/X7qJ++q/Xfvtb3+7+/GPf9xd5jKX6a51rWuVORtqP/rRj8r13m/rrbfurnGNayxcin54Rz/xnDxHmRb193F9zJdxx7zmsdRznOmReSj6z/Pexze5P/d4L/cEz2V6xdh8l3k0z8MQ3awFPPKP//iPhbfy+qr/znNV80/0n3kvXx+/e5Z3udzlLrcBb+XrXfPrX/+6u9jFLtZd8pKXXODXTNdYd0GLeHdjqOcprnV/rJl4h1jbNU3jnqB90DfT0m/By4PM2fNDLceMiayz/qy9urn+D3/4Qxk7esS7/vznPy//32yzzRbd4npzu/nmmy+s4/qZQUvr83e/+11ZozVPT8JD07z3PFy77kA2L6waXP70pz91J598cnfBBRd0T33qU7srXOEKC+CbJ8ti+MxnPtO99a1v7fbff/9uu+22WxCmeSH68j//8z+7I444ovvXf/3X7jGPecwisPE7UDjkkEMKE7/whS/sLnvZyy4AbGa4vLCCed2TQS9fPwS0sUjz4s8KwTvf+c7uyCOPLILw9NNP7255y1suAqYQFCFY4pnx3u9+97u7Zz/72YWOt73tbYtAyHSulZB/+7d/617xild0j33sY7s73/nOhY41DQHff/zHf3Q77LBDAbRotVA15uc85zndda5znW7vvffuzjrrrPIO5tK90Xe9+L/xjW90L3jBC7qXv/zlC31774MOOqjbeeedFwkUYHzaaaeV53znO98ptLne9a7XHXrood29733vAqxf/epXuze96U3dgx70oO6f//mfN3ifrJzU9OsDigyyMedxX8x/AF8W5HXffeAeL1wDSAbYeH7MeShA/h/PDR6qx//1r3+9+6//+q/uXve6V7n2xBNP7D7ykY8UHkPjDEZ5DDUgZbCr12J+Zv77nHPO6c4888zCCzH/WWnIzwMe1qn5e+ITn1hAuaaluQ+lM+71bwBspm9WZELJzPzXtz79HgCc59z3X/va17r3v//93Wc/+9nu9re/fXf3u9+9u8pVrrJACoD43ve+tzv33HMLyLnmdre7XVEaar73f+v0la98Zee9DzvssG7HHXfMZO0+9rGPlTkin8i43XffvfT93Oc+t7vf/e7XPfzhD1/E1+aZHLvNbW7TPfnJT170zPyuIfOsebTeb7/9NlDkFw1kE/jPugPZPmES84hJMQgwrC3Ueq6vec1rdgDp+9//fve2t71tEaPkZ3ziE5/o3vOe93SXv/zly2K3AGpBxOrJWn0WBH08lvuvr83CqF7Irq2t4dz/t771re6BD3xgueYud7nLomtrYMqgn8fDWveuAab6z2Osx/uFL3yhCEILt0/g++7Tn/50t9tuu3Wve93ruj333HNhAYdQiue/+tWv7k455ZQCrNq73vWu7uyzz+7ucIc7LAjZmvbve9/7ukc96lEFMP/lX/6lu+ENb1g08g996EOFFvjh8MMPL9o7BeWkk07qDjjggAL27tPfv//7v3cPechDCpg/61nP6q597Wt3r3/964ulC+hD0NXCrm+es/COv+vr+uhZg1ytqGTa1r/1/b8GPPfXFlQfL9V9Ecqf/OQnuzvd6U5FWcEbwCG8FkNzXvNNpkvm2aF3+f3vf9896UlPKt6M5z//+WNFtTl/7Wtf293qVrdatJZH8W7fOIbGma+t5zODc/wdioz7PvCBDxRe/MlPflK8S8CR8gao8Ctr9Ljjjuue9rSnFT619vDh8573vO4JT3jCggct04qRgDe17bfffgOQ/fjHP95ZG9oNbnCDArLWoTW1zTbbFH7PXi68bq0xUAJkg99r4rNgeQ3My01vetOijNdreeyEraML1h3IxtwQjlloWJSvetWrCrjutddei1y7X/7yl7uvfOUrRfO69a1vXdwr173udYs2d+yxx3ZnnHFGEf6YOLT7WEhcMpp747u8yDzv6KOPLtewYrXQmD2ThgjQMWPdLJTvfve7xc1Mg8xWQX7PvGBppoCfy4YFvu222y50S2mgET/iEY/oTj311EWPq4WZ53o+UKU1W9zaTjvtVATAla985YX70QBoeW/WC/oF/SkYGgHMYkVrblrXRbNwNb9Hq70QFvkxxxzT3exmNyvj0TLQb0C8//sFWjz96U8vAEtrP/DAA4u7S2M1ANOXvOQl3c1vfvMC8gQD4UXI8GLEnNDwKSXAHe2ArHvNK0FGQGk1wANtAhINWSrf/OY3ixWOt6KZDyDNPf3FL36xu8lNbrJgwXzpS18qVrP5985hMYUr0Jyw7nlTCETzEvSO/j//+c93559/fnmGvrlxc/POn/vc54prER1YeMasv+AJYzMWa+iqV71quS4ay0s4hAKHXo9+9KO7Rz7ykYsUD9eynIRgttpqq+4Wt7jFIl72bDRiEfvgWYK/z6qM577mNa8pND3qqKMKsEejFBurdzBW/KLpy/pDM2vDvTxbxly7Ro2H4iAscP3rX78AneZ6PKWfWpk3D/g61r4xWNvWyT/90z8teka+F+/vs88+BWB5T1icLHS89ZSnPKV7+9vfXuaHHLrRjW5UrHF8BWCBGAXTvNf8lxU/4/AuPHdahE6CZtka9p0x12Ekcow8je/RyNj1hX5+8+6us/55ecwRpRjfRWgmZOg4Q2MRk875f9YtyGaN0RzR2mhprJZYNIQGNyILiiAigFk7BLLFiclpv4R7bWHFvAf4EBJ9LjWLkuDGiBaIBUP7JygJ0P/+7/8ugu+hD31ocesYN0HhbxquxWdRc1UaFy0xGNUYMrMCV25Nz/BuwII1xh1EwGF6DWgAWe+U48jxTm9+85vLAqYEWICEhH4BDeFDADzzmc8swhIw0Gz1aSxoS+EgiL03oeoZL3rRi4o2DmTR2fvqg5CnuWsAj9DjVq5B39i9g2eHFyJia9krke/jgWBJP+ABDyhgm9td73rXMq/c/Czt+973vuWZhBFQ84kWVoV3DMVt3333LS5z/KGPAG/3xBgISNaI8RnH9773ve7qV796sUge/OAHl+6PP/747sMf/nABWUBFEUAX9OaSpiCYf7T37u7/4Q9/WFyeEZM238YVPILmXOSENje86wlHgAEEKQoaPuMypyABJcAGZM2dMbJGzQ3r3tgIVnQhQPGyZ3gnLskQ+sDUu3oPFq34PV5+y1veUv4WP+cKxct+F06wBgEAfgN+3nGXXXYpANoXnxTjJ7x5G7gjo3FVozeFDG2MlfLkWd6LcvSpT32q8EMABCsPnfCyRilBW+/gORRg9OIq/ehHP1rmBi95h2h4kwL/hje8obyH9c3TQVH1XNazZ0TYKfMhwARCFDU016wBViPrWzO/+PKlL33pgkfI+1m/6McwyIq2e9DN2kVLNP3gBz9Y3lsjdyjQ6K/f4NfwPoQxkMfpvay34HMKu3k1ft97lvWP5sIyN77xjQtvoZW1br1FKGTIC7Noga6j/6w7kM0xpJhMDPmOd7yjMAhNMVy3J5xwQgFdi+/ggw/uzjvvvBLLAIyABsNgOABs4QKtmkGyZpdjWsEjBIvFwWWCySxyQl0j8IDvy172srII73GPexQB52+uUS4kixlDA0XMbAGH5pj50MIh/IyVYLGgCSIWF82U0CJ8adgWrz6ytht9iac9/vGPL4kLxo0mhKyxs6YJVeMBLASTdyBYWVrAmLCh1RMwQDaSKgAJNz3N27t5RzElH4LAc8LSMJZMZwBAaAEJYBjN91od34rvuPEBA7r0NbRmNRFiAIfQ5vInqNGdhWEOgKR/CalQalhP3hmIEWKUspo3zDV+0oCqa974xjcWACK88YT5cA3rFki6hoJjngEAwcu15z58yauCvv6viUUCAQokHsHLlEMKBOHPYwCw8a8+gSFPDrpwfwNy4yDo9UmRMXfuoRDhH8LXmAEG2hif6+92t7sVqwU/mTsAahys+8c97nFFkQRKlCe0uuMd71iEfSgewJUSyaug4TvXuR7P3fOe91yI4+f5Q1d8jl4h9D3T/RrBzoq1vtHBc30ABW8JS5aXytqkYHsvyoS17H3N6a677lr4mWKInniDAgmcfMc9bv2YCzzvHvOPTykH+JpS5HuKFGXS/Ei4i4ZvJdRZp8bAq2EdvPjFLy7zRYnTfvCDH5T1mj0ggNiY9O89amCkZJsbyqD1KuQRIIuHWOXWkvG6Vgt5YD7ID3KTHMDr7o8+XYsn0N6ckyueAbABd/RnvJ5D+Qey0RrI9oqj+fqyFrqEE0FFUweUwbgECUGG6SS3WDDiPBYxMAGyEjoseuAT92a3YDAMzbGPeVyLeXOiBUFN6OrXPVyIFjJBj7FpgoQaIGIFimcS9CGsCIC6WSwED6FCwFkEgBUwWrQsIc+gqT/jGc/o9thjj97xEiIsH+OjXRPI4jMsKmOJhWhRszwAlL4IToAqkQgAhyvXIvMBdFxexkXLpd1auAS1Z1E8jJtWnoUQ+rCUWB7eJcf6+sA17iUcLHotuxMz3cJtbf7RDvABEPPjO/Euype5QzNWU4AsWrBwKWMUnHBL5v7NpQYMCHHj1QdFg3LHCiGo0JSlhwd5BghGCoDvjMm7AETC2u/4Eh14QFhvwEC/lCsKDGHqmYCQYqOF54RCpD8uSVY4C806IMTNG+sIABP4QAlg4SNrR4v4Hss2rDRjYS2iJ6HLZQ3krDljNvd4UH/WF8+K/3tPIGPtsHooABpvEp6y5iJZLq85PGetArpoxmKu9B0uccol17XrXWuceNR741NWmGvwJeXKe3umtWcsrkdTwG9dsWTvf//7l/t5HoAcUPShTHgPSYHWGuUFTT2H3ADePBuhCOSM5PCa6NdcWH9oFW5gAF17nLyHd+aqN1d1Qx98hQ9Y5Lw6FChyhFJnHq07ygn5qAVvs6LNHf4Nd7C1hF7h9qUAUVy8I16gPHkncigy8dEHH/B+UQRySG2+EGV5o113liyhXPv7MaFFgdkjLkGDZgkReCwkDROw3miRtDONqwdIAJRoOUko/o54WT0dFl52Z2JEi+M+97nPgisMw7uGBhhuLEDPJYc59U27dK/Fw01HuOvbYmNRYnIgxPoKIAJmBA+NWlwG07s+XM5AznMiI5lAoFQQ7jR8Fgph5z6WnBbva7ziZ/592MMetmBREIpoFyBrkbqHlR7jElsiCGNxB3ATJFlRib+51PURW2aCxujiU8eP/O655k3r+9336EdI6DsAESCzLCgBaIxugI2QFPskbEMoBt+4pq+FYCE4I1bKwvHurCkND7KmCSZ08Cy8CjwBrGaMhDt3JJc1KxsgmK8Ad7xNKaAQsUD9Zn6AKUHMYjbfhCQeiDi460JwUngIdgpmAJA+AbM+9UP5CBdhrBk8ENs1zJn3QNvYuoZ3Yt25Fm0Jd3yMLoAZf4Rr2JrT0C9a5gtKTSin8TuBj6/EiNHIGgZ0wMGcGjNlzRoBgp7lQ5FEa3NoPOhIGQ1eZY1ZPxQC4RugbewBiOhiLkJp9VyNEhX5G4Bb44IeyqL2O+UCSFNo9Q/o8aL5x8PZde598GyETGr+Myb8bwyUN/NtPeuHLKM44a8cw4/1Yg1T7PGo56Af2lDy0TDWjrkE4DwSDASyM5Qi1/BQeTYlxH31+u1dNOvwy3UHsgECWfPFcLTBnIofmmTEVGNuMR3GiEZgYOa84DOIB+MPuUAC9EPQx3OzqxYzh5s7kn8wvAXLwtKHxc+6wcSEB8EdjbXJpUTg1nviLCRKhvcnTNEiYj0sZkIzmmu4FFlDFpTfuP80FoK4auxJja073st3uWVh4D0sVJ9oBJ9nRQtAztfk/igWaF4vUs8eUm4Adlg0LIO+RkAQgGhEkQAuwEhIgcDz0Vj33OK29lBCWDda0JoAqZOesiDK/OQ68xDzHwleAfKheNR7DFkEgAotgl4BXPFuPCJoEok9rA0C2zgJ1aBfpnPmW7R0rX9Z2J7lvSObm2ta/9ZICGSKIZ7yTEI3b22JZJjaCqOEeT+87t8aQCKZcMhTEbyTPRTeE49yWxo/BVOLviOPgYKbx+M9eWViP7e5qWlPiTUmSgulFfBaF7wLvBGAm5JEGdSMj7KEJu4DkpQAClb2fLnWvAcd9BsuYfdYi+Ke5rneyoc25sDYRymZFDYhA+9FAXE9uuGNMDSCzkF3ijqlITc8zt0dsiN+wx/CDICWNyA3PI6+7g1+qXcx9C7MdfblugPZYOK8QAmFEGLxO4GDcWlguYmvYSbxClo911oIn765j+dg4qFN5DkpITTQDDIBsMYZC5zlxALAoO7XN4Z1jQzfADaMLFbkPWjVETuOBQxEjI1wAW7oEEJWgkdO4CBExeMIHIAKvGnfBArQZQFYLJFlaLF6DxZSZAv73XdRHCDonV1aQY+aXkP0i/nLik7Mhd/6ikqwRLhQbdsSI+MKrbeV8A7Q0O3hZU1y6Uri4tLMSgzlxVyw+sMC9fwARODSp2SZG7QA0nmPMLddVhjC4tBnfM81GSDve9YHIW6Lh34JVtaXuQprRAIT9ydeEM8zLooBwW1uWWNchQGi+mXhhFuS0JUB7T4CV0yTACXoI25rDHlcrguPQIBaxMr9a41RXnLjPqQ8ih+jRbgl45pYq0Oy1nzrN6wqz2H1AVh70fEipZTCxMsS40EzQOk9QwEDzkBOLBEP4GXXhJfCGHh2KOMsM40XCm2EN1i3PE5+j1gkXmOB4nn08VxjCKUg541YX4DbePsy/vVpLVEIeQaimQcfsqCv2AQeCeudt453wJpGM/xAYZcMqv8a+PBArTTyHnifiIH7HV/gD8oAWVI3stOa5fkJxcY6GRXmWWf4Wl5n3YFsTFIWeoSrBYJJLWoAhXFpn2KBYhBcZYSd2JK4AtcT4WPvGIbN1khmhFhYBBuGIvAIYt9buMZhkYVAZh1gvgyy7ovvLAb3SaZgUcVWGQskUvslPUSGdIwFWFqsFr9YrsZtxu3rN4kM7veOARQ09MiqjH4knFg0Em5oqeJ6Fiar1uJDS30QVBQRoECLpakTTNyL6Bzu9tCOQ5P1nIjThpCMRYdmfRVvzBM61iALLCx8igX6BcDrg+XHwvB+gAXAiLeGQJIUJT6GF7yHOSJ4PUN8jSAiLDVzKzlNy9YjIa6xIPsaoWq+uZgjA5Qb0HtzO3pv42cdBH3ME6vaHBKg+va753tH/UTVIsIf+BOilAWuRpY2sOCiw9PcxxqBHPFY8xPuVfNlTllZ4q/4HT08Sx9AXewOPQAF/gKCaG/8+N07ACpzHnMLFMwbGrjH8/AyUBOPdb81CWzNe6wPYw2FbMizEdvSxAKNG48BAQ09IlzBzetdw+2JbuaMJ0jWvTEaCwAA+PoFmHhf0hieoKQCcAlLYt/xDDxvrXi/yCMAJt6JEkFZt0aBkrADl7T5ydasvigolCUKkn7ExCUKWe9o5LnmH4jHbgd0IafQWkJRvW1Lv7EewkVsHbtHI9fCne+6oH14SKyBSOIMvvYs809umfeQM9YYOWHO9IO38Yzxor35Fg7LikBLfOoVF/P1ZXZZmVBAwF3GUpEEAbwsDkAmJkUzJTwxigXJVRKZeKw4DCOBQKv3b4bbT9/cauGWcp2sTwsDc+o39jf6f7bsMK7fgRjrUVZuJIVgTovKYglB1TcbNHYxQ5mPsSVGvxYp64wgYbVYQAFu0U/WWrnZvIOEGZpq7OFkvRAALEONsoIuXM4Ag6XGAjJW/YVLPQA9g6zvLEh9aKHlsjxZEUA+u9MBJgDk+vKhhHgGevpI3hED810IZv8nLMWJwtVLuIaG7/kEIGEZCTSUEcID8HAJR+wV7QGL5Jyw/AEDwUig5D2/mZaxrQHNCHA0QHt9oK0+AHhYc2iB/gQ9lx2hDpj87l7WNUUGoLjXmPA1HtEv+sua5XFguUq0iSQp4/LOPpJg0BrgAyVxSX2ExwQNKR9ip6xDY7I+zFtsDQHYPACAHN+bf+PGY+aecDV+vEyZoaRah8apfwCIN/Fq8H/wY7gkh/ZBAypuTzsGvC/XqphuJCd6F7QxVrxFuaQoGBdAMo8S2VxjHRo3xdXv1iswlOPgfrT3LEpPgDsgNQ88G5KiAJiGTwGy9eC7kCkUrYi5Z/7wfgCIsoTW1jxahYsZ7wJ6VqffWOmAO/icezYnf+W+jZuciVAJT4R39x05opkL/zc+LdYs+tfKbswbehqffeSaBCn0cH24tOUO4Es8wDPGK5ezn/tCK/OFMNONdt1ZsiHg80TGHkLaKYFH88e8GFRWLKDAlL6TRUnwRvEE34vZhRs3NPjo3+IGpoQLhs3PtRAtNNmKEZ9iHekju9xog9wtwN9vBCzGJyT9a1wsCZpoWIimOT+LUIxxi70QmAQ0gCWUNFYdYWMB5Puz1mpclA/WF2tVs8gJJf0RRsZHqFpsFj1vABqyiACaeE8sXDQGdlFAQn+8BMZFwGiEsYXIRWqBE+Y53gasPJMAIzApIt4P6Fv8AYKhIeekGHNn0RP2LHtKBnDVP4HGWoyGzpQLc8+b4Vpz6h3NG0EXLmcuUILYu4YlG27AGIdxARZgBBjdgx/MU1TuAbjmPyxk8w84NPNgDCxbvIGO+gYMAMK9+JI1iL/wIX7UgBjw8EzCFRjiA1YW+uuD4OOhsAYISXxBYaHIeG9WsbgjFyogxM/mQdgByKOFa9CAMPUsgh9NAagxeXf8BYjxBD52ve/9jt8APhpEI7QpusGnNa/jY4AX21eifJ9xmWMKid8pnngJjwBeY7P2XRPJaixBvBihCqECigglAg14FtA1bx3Dj4CYFcxlHImN5g5Pmhs0jQxfAEtBwue14uAeliWFR5YzjwAvm3UUCp2xWft4JJRcdDNXfTWGY234zbxrrGR9xrz6Dk/htVibFDMJdua03t6HZ6w79AK05ti/+CYUaM81Rgqx7ykh+JzC0RfGW5jwdf7HugPZPF8ZhIACjV1SD8YKd6vvfCxGTJOTCCwkmqBtCLnluILFXMdSap7J8QrCJAsU1wL22L4Q93L9+hgXhq+ZPlys+R0xt8VNgBpjHYPMyTzxHPfnhLBYfBZguMJzchirJlyn4oQWHmEQdYEJZG6iyHolWMLNFs9EM6AXjbVFYHlXCzbiufndABxAMH8EgbgcgekzrgETAkwjxCgkQxnH6OadfIwFLftiXmLUBAlLMMebsivMs8wbYdhXxpOAjQIE9TvgUR+Cuu/5rgeaOXac+xB24IXhEjV/wQsAThOPA3SAx7toLFxg6RpjM3bz5AOo+rZCEarc8VE0peZT/UpI8nFNnVREoPvkBswpRvWai/9TkliLFCJuVe59Y4s5xrd1QqN7AY6P9w6PS80HaK2fcOX39aMvYJP3fuaxAncftI88ivg9rMXamgOCPC1DLdzFLO2+Vsc5ZQfnUqbeyxrLjZJLkYtmzXJt5xbjNCfhIfM7xSSXV6zHJOyAjpSTLO+yl2vwZdfZD+sOZLM1kxnPYqLlAyGgiQGyFlgLQVmDLF8LiTu5j/HWgheGaiyPimv0VXHqG2vuo6+/IQETfRGYYjq0bK5uYM31ZfFG/GcaGo2qJ+1ZAA2oAHnegXqr1iTPyuUgx13fp9y4hyUUiWABWnUYwXW8G6wrLvA69j3u2fF7H8BGnDuXoYzra+HdV73HtRQZAEBos9qAJc+J64FQraAN7TXOvDDunWqAHXf9qN95ZMREAQeLN5clHce3+h1KsotnWg+T9DNqjEO0d89KxyVXur9Mh2nniTLFtY0XKYp1NbTmLp6WojN8fVicwYAAk3UaiSaxRzLiqP6Na2nD4nLic0NWzwy/+qoMrV4cBDNQpbRIHgM03KosnyhesNSB9C1EcSueBUpErbkv9Tnj7usbBxcu1xuXZq3Q5Ov9zmrOJRrHPW+S3ykKrJRcQ3iS+/I14shAVRYsDwEvAiuP8pJjzO4ZJRTXWmDG83gyhDTEBiM0MS0N2vWrQwHeH2Eahkz2NK01r6zO203f67qzZDMJakHMKuCewwShqWcgztogq5fQqTX6tRDu+RmTaqhLuWcadskLJJ5lbBJauOwi8Yg1WseJpnlOfW22ECUZSezKSRk5DjqKVkMLfNzC7+tT6IE7PWd19l0nfilGN+7Ep/qdM337QE68k5clu2b7LOlRa8F4xXrj4AT3Wx99SsMoGuX3rscdY68tt3E0n5RfrE/xxFCC+54/aV+jrlutfldibLPQR72H1zrlws+y05odcpXPwjus5hjWNcgG4fKiDjdQxGTitxxn9XcWoCHUV0o4jJvQSYE197OUe8YJlr4++wQOWq20tZaVn0x3AtUnxhELfNz7D/0+7r54dlZiMrjVyk2APtoSKgGw0wjqePfMmxls/Z73K/p/TsirQS3+n+kYoOy+uqhF/aw+oO/jnT5a5nU1ju8n+T0rE/oOpSArWyu9TsfxyCTjXs/XBH2C7ngqADb4flMFWPO+7kG2FpLBEEMWbAZm92KOvtjfSi/kWVuEtWCpheWQ1RL31duolvJ+edG6X5++y4laeYH3gctSnpvvqZUwz8uae/69/j6098xrQ+Op+am2EP2/Bt++eyaxOrNiUCuikf1av+dy6NjHS0vtL+Y+QDWvzT6aLfU57b7JKNCnhGaeCgVtKfkTk41g9q9a1yAbgqkGzj5hnIVT39+jmGm1p3mU4JzGQlruOEPw1vTLQrsez1KtgEzvDPAhZMNy82/trhr1ntMoR6FkZYEez8oaen7n/HcGhJoX6zEO0anPQgt6DFkH43gij6UPcPP8rgTfT0PzcTxaKz15/EvltXHPbL9PRoGsTGYezOt3Us/TZE+cj6vWNchOKsiGLKC8aLMFvNZTO0p4rLVg6dNIV2MMNb1HzcU0WvI0Yx31zEl5Y5rn9fHVEDj3PX8plnw9viHLcDnvsZx7R63hlex3rdf0enne0Drt815kBWm9vP8k7/F/AKkl0uxZ9pkyAAAAAElFTkSuQmCC)
(b) Height of the given antenna, h = 81 m
Radius of earth, R = 6.4 × 106 m
For range, d = (2Rh)1/2, the service area of the antenna is given by the relation:
A = π d2
= π (2Rh)
= 3.14 × 2 × 6.4 × 106 × 81 m2
= 3255.55 × 106 m2
~ 3256 km2
[As 1km = 103 m , so 1km2 = 106 m2]
Question 5.A carrier wave of peak voltage 12V is used to transmit a message signal. What should be the peak voltage of the modulating signal in order to have a modulation index of 75%?
Answer:Amplitude of the carrier wave, Ac = 12 V
Modulation index, m = 75% = 0.75 (unitless as a ratio)
Amplitude of the modulating wave = Am
We know for modulation index:
m = Am/Ac
⇒ Am = mAc
⇒ Am = (0.75 × 12) V = 9V
Question 6.A modulating signal is a square wave, as shown in Fig. 15.14.
![](data:image/jpeg;base64,/9j/4AAQSkZJRgABAQEAYABgAAD/2wBDAAoHBwkHBgoJCAkLCwoMDxkQDw4ODx4WFxIZJCAmJSMgIyIoLTkwKCo2KyIjMkQyNjs9QEBAJjBGS0U+Sjk/QD3/2wBDAQsLCw8NDx0QEB09KSMpPT09PT09PT09PT09PT09PT09PT09PT09PT09PT09PT09PT09PT09PT09PT09PT09PT3/wAARCACcAf4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD2aiiigAooooAKKKKACiiigAqjrWpw6Po91fXD7Y4YyeOpPYD3JwB9avVla3o8Gq/Z5bpnaO0LSrDkbHfbhSw77eo96AI/COrx654XsLxJTK5hVJieokAAbPvmtmud8IaNBYaZa3tuzp9rsrfzIRjZvVAN4HYkYB+ldFQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAVFc/8esv+4f5VITgEnOB6DNUotQt9S02ae0cvGPMjJKlSGXIYEEA8EEUAR+HP+RY0r/rzh/9AFaVZvhz/kWNK/684f8A0AVpUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAITgEnOB6DNYHh5JItH1BZoZYma7upVEiFcq8jMp59QRXQVFc/8esv+4f5UAc9oGnam/h3TWj1qRENrEVQW8Z2jYOM4q/8A2Zqv/Qdl/wDAaP8AwqXw5/yLGlf9ecP/AKAK0qAMj+zNV/6Dsv8A4DR/4Uf2Zqv/AEHZf/AaP/CteigDI/szVf8AoOy/+A0f+FH9mar/ANB2X/wGj/wrXooAyP7M1X/oOy/+A0f+FH9mar/0HZf/AAGj/wAK16KAMj+zNV/6Dsv/AIDR/wCFH9mar/0HZf8AwGj/AMK16KAMvQLi5ntrpLyfz5ILqSESbAuVB44HFalZHh/7upf9f838xWvQAUUUUAFFFFABRRRQAUUUUAV7+VrfT7maM4eOJmXPqATWTY2er3VhbzvrjhpYlcgW0eASAfStPVf+QRe/9cH/APQTSaR/yBbH/r3j/wDQRQBU/szVf+g7L/4DR/4Uf2Zqv/Qdl/8AAaP/AArXooAyP7M1X/oOy/8AgNH/AIUf2Zqv/Qdl/wDAaP8AwrXooAyP7M1X/oOy/wDgNH/hR/Zmq/8AQdl/8Bo/8K16KAMj+zNV/wCg7L/4DR/4Uf2Zqv8A0HZf/AaP/CteigDnr5dV0z7LMdWadGuoYnja3QBldwp5AyODXQ1keI/+PO0/6/7b/wBHLWvQAUUUUAFFFFABRRRQAVFcuYrWV1+8qEj64qWoL3/jxuP+ubfyoAxtMttXvdKtLqTW3V54UkYLbR4BKg8ce9Wf7M1X/oOy/wDgNH/hU/h//kXNM/69Iv8A0AVoUAZH9mar/wBB2X/wGj/wqW2sNRiuEebV5JowfmjMCLu/EDNaVFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFQXd5DYw+bO2FLBFAGSzE4AA7kk0AT0VWe/t0lijaTmWUwqQON4BO3PrgH8qkNzCt0tsZFE7oZFTPJUEAn8yPzoAlooooAKKKpWmrWl7GHhkODM9uA6FSXXO4YIz/CfyoAu1Fc/8esv+4f5VLUVz/wAesv8AuH+VAFLw5/yLGlf9ecP/AKAK0qzfDn/IsaV/15w/+gCtKgAooooAKKKKACiiigAooooAyPD/AN3Uv+v+b+YrXrI8P/d1L/r/AJv5itegAooooAKKKKACiiigAooooAqar/yCL3/rg/8A6CaTSP8AkC2P/XvH/wCgil1X/kEXv/XB/wD0E0mkf8gWx/694/8A0EUAXKKKKACiiigAooooAKKKKAMjxH/x52n/AF/23/o5a16yPEf/AB52n/X/AG3/AKOWtegAooooAKKKKACiiigAqC9/48bj/rm38qnqC9/48bj/AK5t/KgCt4f/AORc0z/r0i/9AFaFZ/h//kXNM/69Iv8A0AVoUAFFFFABRRRQAUUVS0/V7HVfOFlcLK0LmOVOQyMDjBU8igC7RRRQAUUUUAFFFFAHJXWl3dzc3cuy6VptVhEbCRx5cCBC7Lz8oba4yP71MtreWPX4LeeOWOD+0ppo1kB2YEG1ApPBz8zYHfNdhSEA4yAcHIz2oA43Rrb5dDsvszQXCTS3t2pj2leH4P8AwKQYPQ7TjpV3XIp21yQxx3jRPpc8ZMQcr5m5CgGOA2A3NdLtAJOBk9TS0AcrpNvPbanojCK8UPpzrdtIHI8z93t3k9xiTH/1xVnWNMuJNajkt0d4L6BrW4KtjyuQRIPQ7Qwz67K6GigDkZbK/SS5SKKcXw1CI2soz5a2wKZG7oF2hwV6k9uQarxWMjT2lxNYTtHDrVzK+6BiwjdZArYxkgllrtqKAOUs7fUYvESSqJZYXupTIJoXR4kO7B8wHa6dNqkZAI9DXTXX/HrN/uN/Kpaiuf8Aj1l/3D/KgDntA0R5PDumv/a2pJutYjtWVcD5BwPl6Vf/ALBf/oMap/39X/4mpfDn/IsaV/15w/8AoArSoAyP7Bf/AKDGqf8Af1f/AImj+wX/AOgxqn/f1f8A4mteigDI/sF/+gxqn/f1f/iaP7Bf/oMap/39X/4mteigDI/sF/8AoMap/wB/V/8AiaP7Bf8A6DGqf9/V/wDia16KAMj+wX/6DGqf9/V/+Jo/sF/+gxqn/f1f/ia16KAOV0PRXkF//wATXUl23sq/LKvPI5Py9a0/7Bf/AKDGqf8Af1f/AImjw/8Ad1L/AK/5v5itegDI/sF/+gxqn/f1f/iaP7Bf/oMap/39X/4mteigDI/sF/8AoMap/wB/V/8AiaP7Bf8A6DGqf9/V/wDia16KAMj+wX/6DGqf9/V/+Jo/sF/+gxqn/f1f/ia16KAMj+wX/wCgxqn/AH9X/wCJo/sF/wDoMap/39X/AOJrXooA5/UtDddLu2/tfU2xC5wZVwflP+zVe0sYbXS9N+067qEBuEjSNTMo3MQMKPlrd1X/AJBF7/1wf/0E1g6oT/wjmghY5pCLizkIjiZ8KrKWJwDgAUAaX9gv/wBBjVP+/q//ABNH9gv/ANBjVP8Av6v/AMTWsDkA+tLQBkf2C/8A0GNU/wC/q/8AxNH9gv8A9BjVP+/q/wDxNa9FAGR/YL/9BjVP+/q//E0f2C//AEGNU/7+r/8AE1r0UAZH9gv/ANBjVP8Av6v/AMTR/YL/APQY1T/v6v8A8TWvRQByuv6K8dpan+1dSfN7brhpV4zKoz93qK0/7Bf/AKDGqf8Af1f/AImjxH/x52n/AF/23/o5a16AMj+wX/6DGqf9/V/+Jo/sF/8AoMap/wB/V/8Aia16KAMj+wX/AOgxqn/f1f8A4mj+wX/6DGqf9/V/+JrXooAyP7Bf/oMap/39X/4mj+wX/wCgxqn/AH9X/wCJrXooAyP7Bf8A6DGqf9/V/wDiaiu9CcWc5/tfVDiNuDKvp/u1uVBe/wDHjcf9c2/lQBzWm2Mdt4f0x59Z1OMy28eyNHBJ+QHCqFJOK0LXS0vbZLi113UpYZBlXSZCD/47VH7ZFp+gaHcizmnvRaKkDpDJIseUXcX2A8cDjGTjjuRpeFoIrbREihFwVEjkyXERiaVixZn2HBUFicA0AL/YL/8AQY1T/v6v/wATR/YL/wDQY1T/AL+r/wDE1r0jMFUsxAUDJJ7UAZP9gv8A9BjVP+/q/wDxNH9gv/0GNU/7+r/8TV211K1vLRrq2mWWFSwLIc9CQen0pYtQt5LWO4MgiR41kxL8hUHpkHp1oAo/2C//AEGNU/7+r/8AE1zln4S1DUPEyatdXF3YR2zbY8yq1xOAf42UYCH+7z+FdyCCMg5B71GlzBJG0iTRsi/eYMCB+NAEtFRNdQLCJmmiER6OXG0/jSvPEjojyorSfcBYAt9PWgCSiomuYFYK00YJbaAWH3vT61U1fWYNHtTNKDIQVHloy7sFgucEjgE0AaFFR+fF53k+anm4zs3Ddj6VJQAUUUUAFFFFABRRRQAUUUUAFRXP/HrL/uH+VS1Fc/8AHrL/ALh/lQBS8Of8ixpX/XnD/wCgCtKs3w5/yLGlf9ecP/oArSoAKKKKACiiigAooooAKKKKAMjw/wDd1L/r/m/mK16yPD/3dS/6/wCb+YrXoAKKKKACiiigA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The carrier wave is given by c (t) = 2sin(8Ï€t) volts.
(i) Sketch the amplitude modulated waveform
(ii) What is the modulation index?
Answer:It can be observed from the given modulating signal that the amplitude of the modulating signal, Am = 1 V
It is given that the carrier wave c (t) = 2sin(8Ï€t) volts
∴ Amplitude of the carrier wave, Ac = 2 V
Time period of the modulating signal Tm = 1 s
The angular frequency of the modulating signal is calculated as:
(t)m = 2Ï€/Tm
= 2Ï€ rad s-1 (as Tm = 1)……………….(i)
The angular frequency of the carrier signal is calculated as:
(t)m = 8Ï€ rad s-1 ……….(ii)
From equations (i) and (ii), we get:
(t)m = 4(t)c
The amplitude modulated waveform of the modulating signal is shown in the following figure.
![](data:image/png;base64,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)
(ii) Modulation index,
m = Am/Ac = 1/2 = 0.5
Question 7.For an amplitude modulated wave, the maximum amplitude is found to be 10V while the minimum amplitude is found to be 2V. Determine the modulation index, μ. What would be the value of μ if the minimum amplitude is zero volt?
Answer:Maximum amplitude, Amax = 10 V
Minimum amplitude, Amin = 2 V
Modulation index μ is given by the relation:
![](data:image/png;base64,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)
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⇒ μ = 8/12
∴ μ = 0.67
(b)
If Amin= 0
Then μ = Amax/Amax = 1
Question 8.Due to economic reasons, only the upper sideband of an AM wave is transmitted, but at the receiving station, there is a facility for generating the carrier. Show that if a device is available which can multiply two signals, then it is possible to recover the modulating signal at the receiver station.
Answer:Let ωc and ωs be the respective frequencies of the carrier and signal waves.
Signal received at the receiving station, V = V1cos(ωc + ωs)t
Instantaneous Voltage of the carrier wave, Vin = Vc cos ωct
V.Vin = V1.Vc{cos(ωc + ωs)t. cos ωct}
= ( V1.Vc)/2 {2cos(ωc + ωs)t. cosωct}
= ( V1.Vc)/2 [cos{(ωc + ωs)t + ωct} + cos {{(ωc + ωs)t - ωct }
= (V1.Vc)/2 [cos{(2ωc + ωs)t} + cos ωst ]
As the receiving centre allows only high frequency signals to pass through it. Obstructs the low frequency signal ωs Thus, at the receiving station, one can record the modulating signal (V1Vc/2).cosωst , which is the signal frequency.
Which of the following frequencies will be suitable for beyond-the horizon communication using sky waves?
A. 10 kHz
B. 10 MHz
C. 1 GHz
D. 1000 GHz
Answer:
10 MHz frequency will be suitable for beyond the horizon communication using skywaves.
10 KHz cannot be transmitted because the size of the antenna will be large for this apparently lower frequency.1 and 1000 GHz are very high frequency wave which will penetrate and so cannot be transmitted.
Question 2.
Frequencies in the UHF range normally propagate by means of:
A. Ground waves.
B. Sky waves.
C. Surface waves.
D. Space waves.
Answer:
The signals having Ultra High Frequency(UHF) can propagate through Space waves. These can neither travel along the trajectory of ground as shown in green nor can propagate by reflection in the ionosphere as shown in figure in red. The UHF signal propagates as shown in Blue in the figure.
Question 3.
Digital signals
(i) do not provide a continuous set of values,
(ii) represent values as discrete steps,
(iii) can utilize binary system, and
(iv) can utilize decimal as well as binary systems.
Which of the above statements are true?
A. (i) and (ii) only
B. (ii) and (iii) only
C. (i), (ii) and (iii) but not (iv)
D. All of (i), (ii), (iii) and (iv).
Answer:
Digital signal obviously use the binary signals i.e 0 and 1 only and no other signal other than these. It is also a signal that represents discontinuous values and it cannot utilize decimal values (0 to 9) which are continuous.
Question 4.
Is it necessary for a transmitting antenna to be at the same height as that of the receiving antenna for line-of-sight communication? A TV transmitting antenna is 81m tall. How much service area can it cover if the receiving antenna is at the ground level?
Answer:
No, it is not necessary for a transmitting antenna and the receiving antenna to be at the same height. Because in this specific case of transmission there is no physical obstruction between the transmitter and the receiver.
(b) Height of the given antenna, h = 81 m
Radius of earth, R = 6.4 × 106 m
For range, d = (2Rh)1/2, the service area of the antenna is given by the relation:
A = π d2
= π (2Rh)
= 3.14 × 2 × 6.4 × 106 × 81 m2
= 3255.55 × 106 m2
~ 3256 km2
[As 1km = 103 m , so 1km2 = 106 m2]
Question 5.
A carrier wave of peak voltage 12V is used to transmit a message signal. What should be the peak voltage of the modulating signal in order to have a modulation index of 75%?
Answer:
Amplitude of the carrier wave, Ac = 12 V
Modulation index, m = 75% = 0.75 (unitless as a ratio)
Amplitude of the modulating wave = Am
We know for modulation index:
m = Am/Ac
⇒ Am = mAc
⇒ Am = (0.75 × 12) V = 9V
Question 6.
A modulating signal is a square wave, as shown in Fig. 15.14.
The carrier wave is given by c (t) = 2sin(8Ï€t) volts.
(i) Sketch the amplitude modulated waveform
(ii) What is the modulation index?
Answer:
It can be observed from the given modulating signal that the amplitude of the modulating signal, Am = 1 V
It is given that the carrier wave c (t) = 2sin(8Ï€t) volts
∴ Amplitude of the carrier wave, Ac = 2 V
Time period of the modulating signal Tm = 1 s
The angular frequency of the modulating signal is calculated as:
(t)m = 2Ï€/Tm
= 2Ï€ rad s-1 (as Tm = 1)……………….(i)
The angular frequency of the carrier signal is calculated as:
(t)m = 8Ï€ rad s-1 ……….(ii)
From equations (i) and (ii), we get:
(t)m = 4(t)c
The amplitude modulated waveform of the modulating signal is shown in the following figure.
(ii) Modulation index,
m = Am/Ac = 1/2 = 0.5
Question 7.
For an amplitude modulated wave, the maximum amplitude is found to be 10V while the minimum amplitude is found to be 2V. Determine the modulation index, μ. What would be the value of μ if the minimum amplitude is zero volt?
Answer:
Maximum amplitude, Amax = 10 V
Minimum amplitude, Amin = 2 V
Modulation index μ is given by the relation:
⇒ μ = 8/12
∴ μ = 0.67
(b)
If Amin= 0
Then μ = Amax/Amax = 1
Question 8.
Due to economic reasons, only the upper sideband of an AM wave is transmitted, but at the receiving station, there is a facility for generating the carrier. Show that if a device is available which can multiply two signals, then it is possible to recover the modulating signal at the receiver station.
Answer:
Let ωc and ωs be the respective frequencies of the carrier and signal waves.
Signal received at the receiving station, V = V1cos(ωc + ωs)t
Instantaneous Voltage of the carrier wave, Vin = Vc cos ωct
V.Vin = V1.Vc{cos(ωc + ωs)t. cos ωct}
= ( V1.Vc)/2 {2cos(ωc + ωs)t. cosωct}
= ( V1.Vc)/2 [cos{(ωc + ωs)t + ωct} + cos {{(ωc + ωs)t - ωct }
= (V1.Vc)/2 [cos{(2ωc + ωs)t} + cos ωst ]
As the receiving centre allows only high frequency signals to pass through it. Obstructs the low frequency signal ωs Thus, at the receiving station, one can record the modulating signal (V1Vc/2).cosωst , which is the signal frequency.