Physics-
General
Easy
Question
Two tuning forks A & B produce notes of frequencies 256 Hz & 262 Hz respectively. An unknown note sounded at the same time as A produces beats . When the same note is sounded with B, beat frequency is twice as large . The unknown frequency could be :
- 268 Hz
- 260 Hz
- 250 Hz
- 242 Hz
The correct answer is: 250 Hz
Related Questions to study
physics-
In Quincke’s tube a detector detects minimum intensity. Now one of the tube is displaced by 5 cm. During displacement detector detects maximum intensity 10 times, then finally a minimum intensity (when displacement is complete). The wavelength of sound is:
In Quincke’s tube a detector detects minimum intensity. Now one of the tube is displaced by 5 cm. During displacement detector detects maximum intensity 10 times, then finally a minimum intensity (when displacement is complete). The wavelength of sound is:
physics-General
physics-
A person standing at a distance of 6 m from a source of sound receives sound wave in two ways, one directly from the source and other after reflection from a rigid boundary as shown in the figure. The maximum wavelength for which, the person will receive maximum sound intensity, is
![](data:image/png;base64,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)
A person standing at a distance of 6 m from a source of sound receives sound wave in two ways, one directly from the source and other after reflection from a rigid boundary as shown in the figure. The maximum wavelength for which, the person will receive maximum sound intensity, is
![](data:image/png;base64,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)
physics-General
physics-
How many times more intense is 90 dB sound than 40 dB sound?
How many times more intense is 90 dB sound than 40 dB sound?
physics-General
physics-
A wave pulse on a string has the dimension shown in figure. The waves speed is v = 1 cm/s. If point O is a free end. The shape of wave at time t = 3 s is :
![](data:image/png;base64,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)
A wave pulse on a string has the dimension shown in figure. The waves speed is v = 1 cm/s. If point O is a free end. The shape of wave at time t = 3 s is :
![](data:image/png;base64,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)
physics-General
physics-
A pulse shown here is reflected from the rigid wall A and then from free end B. The shape of the string after these 2 reflection will be
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAS0AAAChCAYAAACS5un5AAAgAElEQVR4nO3deVzU9b7H8dcMIMMIg7K4IYuKx61UMI1jmpqpRzMr09LSUnOJND0Ht8zcr4fczs1LGbbYUU+ZaWa5ZanHDVNRcQF3QaQQEJAdZvv97h/dmWsdTYphGf08H48e2WNmfvyMmfd8189Xo6qqihBCOAltdd+AEEL8HhJaQginIqElhHAqElpCCKcioSWEcCoSWkIIpyKhJYRwKq7VfQNCVCez2YzFYqGsrAwvLy9cXeUjUdNJS0vct1RVpaioiC+//JI9e/ZgMpmq+5ZEOcjXirgvlZSUcO3aNRYvXszJkycZMWIEiqJU922JcpDQEvcVq9VKSUkJx48fZ8mSJRw9ehQ/Pz9cXFyQHW3OQUJL3DcURSE/P58NGzbwwQcfkJiYiKIoaLVaSktLq/v27nm2LwWNRlOh60hoiXueoihYLBauXLnCJ598wsaNGykpKeHxxx8nISEBq9Va4Q+SuDOTyUR6ejqnT58mIiICX19fXFxc/vD1ZCBe3NMURcFkMnH27FnefPNNVq5cSU5ODv3792fx4sU0bNhQAqsSKYrCzZs3+eijj/joo4/Izc2t8NihtLTEPUtVVXJzczl06BDz58/n6tWr+Pn5MWbMGEaNGkXt2rVliUMlUhSFjIwM/vnPf/LBBx/w2GOPYTAY0Gor1laS35i4J5WVlZGWlsamTZtYtWoVOTk5tGvXjtGjR/Pkk0/i4eFhH88SjmcymcjKyuKjjz7in//8J23atCEyMhJ/f38JLSF+TVEUzpw5wzvvvMOOHTsAGDBgAJGRkYSFheHm5oZGo5ElDpUoMzOTlStXsmrVKoKCgli8eDHt2rXDzc2twteW0BL3DNtyhri4OBYuXEhSUhKenp6MGzeOYcOGUa9ePXtgicphsVi4ceMGn3zyCWvWrCE4OJjY2FhatmzpsK7477qKo6YshXAkRVGwWq3k5OSwdetW5s6dS3FxMQ0bNmTu3Ln07dsXT09Ped9WMrPZTF5eHmvXruXjjz/G39+fDz74gBYtWjj0y6LcoWWbNlYUhVq1aslYgKgxTCYTFy9e5MMPP+SLL77AYrHQq1cvJk6cSFhYGDqdTgKrCly/fp3Vq1cTExND+/btmTt3LqGhoQ5v3ZYrtKxWKz/99BPr16/nxx9/ZNKkSYSEhEhwiWqlqioFBQUcPnyYFStWcOLECdzc3Bg5ciRDhw6ldevWuLi4yPvUQVRVpaysjMTERHQ6HUFBQXh6emK1WsnKyuLjjz9m7dq1tGjRgjfeeIOHHnoIV1dXh39hlDu0bty4wTfffMPp06d57rnnCAwMlDeDqDa29VefffYZ//jHP0hLSyMkJISZM2fSv39/vL295f3pYKqqkpOTw4gRIwgJCWH27Nm0a9eOwsJCVq1axccff4xer2flypWEhoZSq1atSrkPGYgXTkVVVSwWCykpKcTGxrJu3TqsViuPPfYYkydPpmPHjuj1eukOVhKLxUJGRgaenp6UlZWRlZXFxo0b+Z//+R9atmzJu+++S9OmTSt1/ZuElnAaFosFo9FIQkICH374IVu3bsXDw4P+/fszfvx4WrRogYeHR3Xf5j1NVVWsVitGo5H8/Hw+++wzYmNjad68OXPmzKF169aVPkMroSWcRnFxMV9//TUxMTGcO3eOBg0aEBUVxbPPPoufn590B6tQaWkpe/bsYfPmzfj4+LB06VI6dOhQJUtKJLREjVdWVkZGRgYfffQRX3zxBTdv3qRDhw5MmTKFLl264OXlVaENuOL3y87O5siRI7Rs2ZIFCxbQtm3bKlsDJ6ElaixVVTEajVy+fJl//OMfbN26FUVReOSRR5gzZw7t2rVDq9XK+FU1UBQFb29v5s2bZ1/pfqffg61LaTKZcHNzq/CMooSWqJFUVaWkpITt27fz7rvvEh8fT2hoKIMGDWL06NH4+vpKYFUjPz8/hg8fTqtWre4aQiaTiStXrnDo0CF69+5No0aNKjRQL6ElahRVVTGbzVy/fp0NGzawevVqrl+/Tnh4OOPGjaNv377UqVNHqjNUM4PBQEBAwG8uNLe1lH/88Ueio6PJy8uje/fuFf7Z8psXNYZtOUNWVhbR0dGsW7cOk8lE165dWbZsGaGhoTI7WENoNJq7TnwoikJBQQHTp0/n22+/ZcSIERgMBqlcKu4deXl5JCUlMWvWLJKSkjAYDDz//PNERUXh5+cnrSsnUlZWxvXr1/nrX/9KQkICgwcPZsKECdStW1dK0wjnZzKZyM7OZuvWrbz//vtcu3aNpk2bMnz4cIYOHWofvxI1n617f+XKFZYuXcqJEyfo0qUL06ZNo2nTplKaRjg/VVVJT09n6dKlfPPNN+Tm5tKzZ08mTJhA586d0el0ElhOxGKxkJ6ezqJFi9iyZQuDBw8mKiqK0NBQhy1LkdAS1cI2BZ6YmMisWbM4duwY7u7ujB07lsjISBo1aiTbcZxMWVkZ+fn5TJo0idOnT/P0008zefJkQkJCcHFxqfrSNEI4gm3NTkFBAQcOHGDGjBlcu3YNX19f/va3v/Hyyy9jMBhksagTsf1O09PTmT59OnFxcTz++OPMmDGDkJAQh2+cltASVcpisZCWlsa//vUvVq9eTW5uLn/+85+ZMGEC3bp1w8vLS7qDTsZkMpGcnMzChQvZv38//fr1Y/LkyTRp0qRSvnwktESVKSoqIjExkRUrVnDgwAFKSkoYPHgwI0aM4KGHHpJSyE7Gtg4rJyeHRYsWcejQIR5//HGmT59Os2bNHDLofjsSWqJKKIrCzp07WbBgAefPn6devXpERUXx0ksv0aBBAwkrJ6SqKoWFhbz11lt89dVXPPvss8ybN4/g4GApTSOcl8ViITMzk88//5zY2FhycnIICwtj4sSJ/OUvf5Ha7U7KbDaTk5PDmjVrOHDgAE899RRTp06lcePGld69l9ASlcJqtWI2m7l48SJr1qxh9erVaLVaunfvzuTJkwkPD5fV7U6suLiYbdu2sXfvXjp16sSMGTNo2bIl7u7ulf6zJbREpSgpKWH//v0sX76cw4cP4+XlxZgxYxg5ciSNGjWS2UEnl52dzcmTJ+nbty+RkZG0bNmyyn6nElrCoWzdhs2bNxMbG8v169cJCAhg6tSp9OvXz37CsHQJnZurqyvh4eG89tpr9oWjdytNYzQaAfDw8KhQF1JCSziEbbNzZmYm7777Lp988gmlpaWEhYWxcOFCIiIiHLrAUFSv+vXr8/TTT9OkSZO7dgnNZjOpqals3ryZZ555huDgYAktUb1UVcVkMrF//35iYmLYu3cv9erVY9iwYYwdO5agoCAJrHuMTqfD09OzXJUeUlNTmTt3LhkZGfTv399+6PMfJaElKsRsNlNQUMD27dtZuXIliYmJNG7cmFdffZWBAwdSv379SluvI6rP3UrTqKqKoihcu3aN6Ohodu7cSf/+/R2yeFhCS/xhqqpSXFzM8uXLeffddykpKaF169a8//77PPjgg+j1+uq+RVFNVFXl5s2bvP766xw8eJB27doxduxYGjVqJKElqkdBQQEXL15k0aJF7N+/n1q1ajFgwABmzJhBUFBQlUx9i5pJURSuXLnCvHnzOH78OG3atGHhwoW0b9/eIWu4JLTE72K1WiksLGTXrl28//77nDp1Ch8fH4YMGcKIESNo0qSJjF3dx2yTMcuXL2fr1q2EhYUxc+ZMIiIiHLZKXkJLlJuqquTn57N8+XLWr19PamqqfbNzjx498PLyksC6z5WUlDBr1ix27NhBhw4dmDNnDg8//LBD13BJaIm7UhQFs9nM5cuXiY6OZteuXaiqyqBBg4iKiqJ58+bUrl1bAus+l52dzbx589ixYwetW7fmrbfeokOHDg4fKihXaNlmAlRVtS8Us1qt9mlsebPeuxRFobS0lJMnTzJnzhwOHjyIwWDgpZdeYtq0afj6+srq9vucoigUFRWxZMkS1q1bR0hICDNmzKB79+6Vkg13DS2r1UpOTg6XLl2isLAQi8XCqVOn0Ol0BAUF4evrK1Pa9yhFUbh+/TpbtmwhNjaWtLQ02rZty9ixY3nmmWeoU6eO1L4S3Lhxg3feeYeNGzfSpk0b5s2bR6dOnSqtMfMfoWVb2VxQUEBCQgLHjh3jwoULXLhwgbS0NMxmM7GxsWzZsoWAgABCQ0Pp2LEj4eHheHl5yazRPaK0tJQrV67w4Ycfsm3bNvLy8ujRowevvPIK3bt3R6fTSQv7PqcoCnl5eaxcuZK1a9fSpk0bpkyZQkREBDqdrtJ+7n+ElqIo3Lhxg2XLlvHZZ5+Rn5+PyWSydw1VVeXcuXOcP38ejUaDq6sr/v7+9OnTh6ioKFq3bl1pNyuqhqqqnDhxglmzZnH06FF0Oh3Dhw9n/PjxNGnSRPYOCuDnXlhMTAyffPIJgYGBTJ8+nUcffbTShwt+EVo3b97k5MmTzJ07l3PnzqGqKq1ataJt27Y0btyYL7/8kpSUFJYtW4Zer+fo0aPEx8eTkZHBxo0bOXXqFFOmTKFXr154e3vLWIeTsVqt5Ofns2vXLv7+979z5coVQkJCGDduHC+88AKenp7yOxXAz1Vot23bxpYtWwgODmb+/Pk8/PDDVXM2paqqqtVqVcvKytSNGzeqDzzwgOrp6am2bt1afeutt9TTp0+rRUVFanx8vNqlSxfVy8tLPXjwoGo0GlWLxaKeOXNGjY6OVsPDw1W9Xq/6+fmpK1asUPPz81XhHKxWq2o0GtVLly6pb7/9ttqgQQO1Tp06ardu3dRt27appaWlqqIo1X2bDmcymdSIiAi1fv366tKlS9WCgoLqvqUazWq1qsnJyaq3t7fq4+OjduzYUe3Tp4+6bds21WKxlOv1Vqu1wu8lV/i5MP2pU6d4//33uXr1KkFBQcycOZMnnngCvV6Poii37Q5otVpatGhBcHAwXbp0YcGCBRw4cID33nuPkJAQ+vbtW/mpKyrMaDRy8uRJYmJi2LlzJwBDhgxhwoQJNGvWjFq1akl3UPyCqqoEBgYyadIkOnXqdNcJGVVVuXbtGnXr1q3wej5XgPz8fD799FOSkpLw9fUlOjqarl274u3tDfwcaja2H2Zb6uDm5oarqysPP/wwM2bMIDMzk6tXr/LFF18QHh6Or6+vHGdeQymKQn5+PgcPHiQ6OpqUlBR0Oh1/+9vfeO655wgMDJSwErfl4+PD008/Tbt27e466F5aWkpcXBxbt25l4sSJ1K5du0KzzlrbPqF169ah1WpZtGgRvXr1om7duuW+iC28IiIimD9/PhqNhri4OA4ePGgv/CVqFtv41apVqxg9ejQJCQk0btyYlStXMmHCBIKCgiSwxB3VqVOH4ODgu64WsFqtnDt3jlmzZpGQkIDRaERRlAr9bG1RURFffvkl+fn5PPzww0RERPzhdVdubm506dKF8PBw8vLy2LVrF4WFhRW6QeFYqqpiNps5ceIEkydP5u2330ar1fLCCy+wfPlyunfvLuvuhENYrVb279/PlClTOH/+PGFhYdSvX7/CPS/X/Px89u3bR61atejatSv16tX7w003FxcXdDodQ4YMISkpiR9++IGCggIaNGhQoZsUjmGxWCgrKyMuLo6YmBj279+Pt7c3r7zyCsOGDSMoKMjhpwGL+1NpaSlHjhxh/vz5JCUl0atXL0aPHo2Pj0+Fr+2anJxMZmYmQUFBtGnTpsKLBm3jW4GBgSQmJlJQUFDhSoXCMYqLi1m7di2LFi0iOzubwMBAli1bRo8ePdDr9dIdFA5z7Ngx3nzzTRITE/nzn/9MTEwMfn5+Drm2a1ZWFoqi4OfnR926dSv8xtVoNHh5edGgQQNOnDjBG2+8QcOGDeUDUQMUFBRw+vRpzGYzPXv2ZNq0aYSHh9/Xm521Wi2KopCdnU1qauovwts22fTr/77Tn3/PY5Vxzcpma3z8ViPEZDJx9uxZFi1axLlz5+jevTuxsbH2A00cwbWoqAgAvV7vkKX3tkF5T09PVFUlLi4OV1fX+/ZDUZP4+/vj5eXFE088wdixY3nwwQer+5aqnVarxWAwsGPHDs6fP4+7uztarfa2/2g0GnuRgDs9/luvvdNjd3tOea5rW/T7R8OuPI+pqkpmZuYdB9LNZjMpKSn813/9F8ePH6dbt27893//t8MbLa4eHh5oNBqMRiNms7nCF1T/b+9iaWkpWq2WV199ldatW8vWjxpAVVX8/f3p3LkzBoOhum+n2tlaDDqdjvPnz3PhwoXbtgbu9r693eO/9RpHX+/Xj//e1tydXnO759g+27dz4cIFoqOj2bt3L3369GHu3Lk0btzY4Z97V19fXzQaDdnZ2eTl5VX4gur/1Q3PysrC1dWVgQMH8tBDD0k1gBrC1hKWL5CfJ47efPNNsrOz7ftrFUWxl2G69d+//nN5nvN7rnG35zviGn/0cdt/W61WFEX5j61cRqOR1NRUli5dyr///W86derE7NmzCQ0NrZzSNE2bNsXDw4OUlBSSk5Pp1q1bhfaXWa1Wzp8/T0pKCgEBAfj7+8vx56JGcnFxkV0bv4PtOLCwsDAAewGFjIwMlixZwrZt22jVqhVr167Fx8en0r4YtT4+PnTt2hWTyURcXByZmZlYLJY/fEGz2cznn3+O2WwmIiICLy8vB96uEKKmsC1MX7ZsGV999RU9e/Zk1apVGAyGSm3Jaz08PHjqqacwGAzExcVVaNVqaWkpCQkJ7N+/Hy8vL3r27CljJ0JUM1u5bFv3zhEsFgs5OTnExMSwefNmOnfuzPTp02nWrFmlL07Wuru7ExYWRu/evcnKymL69OlcunQJq9X6uy926dIl5s6dS0FBAe3bt6dPnz7SNRSimlmtVpKTk0lKSsJsNjtk3WRhYSFffvklW7ZsoVmzZqxYsYIHH3ywSsZKtRqNBj8/P0aOHEloaChXr15l3LhxHD582N7i+q2/pKqqlJSUcPr0ad5++21Onz5NQEAAgwYNokGDBlJ/SYhqVlhYyIYNG4iKiuLixYsOWSWQk5PD5cuX6dmzJ6tXr6Zhw4ZVVhhBCz9P+Xbr1o2XXnoJb29vTp8+zfz58/n+++/56aefKC0txWw2/2JWwWQyUVpayvXr19m9ezfz5s2zlzUZOHAgvXv3tq9pEUJUD6vVSnp6OmvWrOHkyZNs2rTJIaHl4uJCixYtmDFjBoGBgb/ZOLHlRVZWFmVlZRVu6bnC/0+DDx06FE9PTxYvXszRo0eZNGkSf/rTn2jbti0NGzaksLAQq9XKTz/9RH5+PvHx8SQkJJCUlERGRgbBwcG8+OKLDB8+nDp16lToxoQQFWPrBe3cuZO0tDSsViuffvopEydOrPC2rfr16zNw4MByVQMxGo0cPXqUPXv28PLLLxMYGFihcS97e06j0eDr68vgwYMJCQlhxYoVxMXFERcXx9GjR/Hy8iI3NxeLxcK8efNQFIWbN29iNBpxd3ene/fujB8/no4dO1K3bl2poSVENVNVlcLCQtasWWMfiM/IyOCrr75i6NChFRpv1uv19lp5dwotVVXtB6TMnj3bftZARXtfv0gWrVaLl5cXjz32GOHh4ezcuZPVq1dz5swZ8vLyKC0txWq1kpaWhru7OzqdjrCwMJ577jleeOEFOaFFiBpEURS++OILUlNT7V0ys9nMp59+St++fSs8SXa3z7qiKCQnJzN27FiSkpKIiopyyB7EOzaHPD09efLJJ+nZsydpaWkcPHiQFStWkJqaypQpUwgLCyM4OJhGjRqh1+txd3eXwBKihrAtSdi4cSMajYYWLVqQnJyMxWLhypUrxMfHM2DAgEr7+cXFxRw/fpzZs2eTlZXFX//6V0aOHImnp2eFc+KOkefq6oper8fPz482bdrQuXNn/Pz8cHNzo1evXvTr14/27dtTr149PD09ZZuOEDWIyWTiu+++Iz09nebNm/Piiy/i5eWF1WolKyuLffv2YTKZHLZuy0ZRFMrKyjhx4gR///vfuXz5MoMHDyYyMpKAgACHTM5J0ghxD7p58yZ79uxBVVUmTpxI7969adWqFaqqUlZWxsmTJzl//nyFdr/cjsVi4dKlS8ycOZMffviByMhIJk+eTL169Ry2/Mmho+Xp6encuHGDkpISLBbLL1Lctlvc1iKz7VvSaDTodDoMBgO+vr4YDAYpZSNEBSiKQnx8PAcOHCA4OJjHH38cb29v2rdvT3x8PCaTiaSkJI4cOUKTJk0cVq22uLiYlJQURo8eTU5ODpGRkYwaNYq6des6dL2mQ0MrPj6euLg4Tp06xaFDh7DV6tJqtXh4eBAQEEBAQAAajYbi4mJycnLIzc2lbt26NG/enK5du9K1a1c6duyIm5ubLEwV4ndSFIWioiKOHj3K9evXmT17Nt7e3uh0Onr06MHXX39Neno6hYWFfPvtt/zlL3+p8DiToihYrVZOnDjBnDlzSE1NZfjw4UyaNMmhLSwbh4ZWnz596NatG+np6SxcuJB169ahqiq1a9emb9++vPLKKzRr1sweWrm5uVy4cIE1a9Zw8OBBfvjhB9avX8/YsWMZOnSoQ+pJC3E/MZvNXLhwgR07dtCmTRsiIiLs51ZGREQQHh5OVlYWRqOR/fv3k56eTqNGjSoULEajkWPHjrFgwQLOnj3LmDFjeOWVVyp03sRvcegVdTod3t7e/OlPf+Kxxx6zL4FwcXGhSZMmdOrUiWbNmtG0aVMefPBBHn30UYYOHcqyZcvo3r27/bihd955h02bNjnkuCEh7heqqmIymXjvvffIyclh0KBB+Pv72wPJ29ubUaNG4ebmZj/zcsOGDZSUlPyhVeq2dVgpKSnMmTOH8+fPM3LkSMaPH++wQffbcXgMajQaXF1dqV27tn0ZxK1jWb9+rpeXFx06dCAmJoYePXpgsVi4fPkya9eu5ezZsw4fKBTiXqUoCj/99BPffPMN/v7+dOrU6RdrsfR6PY8++ij+/v5oNBoURWHLli3k5OT8odBSFIVr164RGRnJ0aNHGTp0KFOnTsXf379SKz1U2uyhbaDd5rdaTC4uLjRu3Ji2bdvi4eGBVqslMTGRnTt3UlxcXFm3KMQ9JT8/n2XLlqGqKuHh4fYzAMxms/0fgH79+uHh4YGiKGRkZLBp06bf3aMxmUwkJycza9Ysrl27xquvvsrYsWMxGAyVvvypSvba3C3Fba0zX19f3N3dKSsro7S0lAMHDjB06NDfddq1EPcjVVVJSEjg4MGDaLVaVFVl9+7d//E8o9GITqfDzc3NXhp948aNDBs2DB8fn3Jvv8vPz2f79u0kJiby1FNPMXHixCqr9FAloVXeI45ufZ5tb6N0D4X4bbbKK9u3b7dv2dm8eTM7duy47XNNJhMlJSXAz5+zq1ev8vXXX9sLJpRHXl4eKSkpjBkzhlGjRuHn51dlC8xrzK5m2/9MW0i5ubkRGBiIu7t7Nd+ZEDWb2Wzm7NmzJCQkoNfrmTp16m9+blRV5fDhw3z99deYzWYKCgo4cOAA/fr1K3do6XQ6evbsaW+h/dbso9VqpaSkhJs3b1KnTh1q165dodnKSg2tWw93vFOf2fZYfn4+Fy9epKysDIB69erRv39/vL29K/MWhXB6paWl7Nu3j0uXLvHAAw/w2muv3fVshu+++46TJ0+SnJyMyWTi0KFDnDp1ikaNGpWrV9SgQQN69epl39p3J7byON9//z27d+/m9ddfp1mzZhUKrSrbxvPrgXlbWJnNZjIzM3nvvffYvXs3iqJgMBgYMGAAvXv3lnLNQtxFTk4OmzZtwmKxMHTo0HIFQps2bejUqRPu7u5YLBZ+/PFHkpOTy12O2dXV9a5FEm4NrPnz55OcnOyQWcVKa2ndOj5lNpu5cuUKly5dIjAwEPj5L5Sens6+ffvYs2cPx44do7i4GE9PT5555hlef/116tevX1m3J4TTU1UVs9lMWloax48fp0mTJkRERJRrMNxgMNCqVSu+/fZbiouLMRqNHD58mGeeeYb69evf9Rp3G6e2Wq0YjUZ27drFggULKCgo4PXXX6/c0jQVdWtt+ZKSErZv387Bgwft+5ysVitlZWUUFRVhtVpRVZX69evzxhtv8MQTT9CgQYPKujUh7hklJSWsX78ek8lEz54971r62KZWrVp069aNVatWkZ2dDcDevXs5d+6cvbhfRdi6rFOmTMFoNDJ16lSee+45h5SmqZKWloeHB127dmXIkCH2rTm2ej9nzpyxDyIWFhayYMEC/vWvf/H888/z5JNPEhISIoPxQvyKqqpYLBYSEhLYtWsX/v7+PPLII+VeJ+Xi4kLTpk1/8dnKzc1l8eLFhIaGEhAQ8Ie6cra9j9999x1LliyhVq1aREZG8vLLLzusSGiVDMTXqlWLdu3a8fTTT/+idrytz3vu3Dl27tzJZ599xqVLlzh+/DhpaWlcvHiR2bNn06hRI6nXJQT/PxZsMpk4c+YMS5Ys4caNG9SpU8fee3Fzc8PV1fW2La5bX//jjz9isVjszzOZTBw5coQPP/yQiRMn2suml/ezZ+sS7t27l+XLl5ORkcHMmTN5/vnn8fLyctiWnkptadn+srb9h7d7joeHB+3ataNFixaEhIQwc+ZM0tPTyc7OZv369XTr1o2BAwdKKWch+Lklc+PGDWJiYvj+++9JTU0Ffl7sOXfuXD7//HM6dOjApEmTbntQsu3177zzDv/+97/Jzc1Fr9fbH9dqtaxdu5akpCRGjhxJr169fvH4b7Ftwo6KisLFxYXZs2czcOBAh3QJb1VpoXXrbKGqqnc8/FWr1aLVau0VUTds2EBmZiZms5ni4mJiY2Pp06ePlHMWgp+/6A0GA2PGjGHw4MG/+JzZTtUyGAx37NrZXj9u3DiGDBnyH7P6tufodDp8fX3L1UW0Wq2Ulpaye/duZs+ejVarZezYsQwePBi9Xl+zS9Pc6tYxrTttmP41nU5Hhw4d2LVrF3GKPBsAAAO1SURBVPBz2KWmpnLz5k3ZyiMEP3/J6/V6QkJCKvT6Jk2aOOR+bJUe9u3bR3R0NFlZWUybNo1Ro0bdtqXnCFXS0iovjUbzH1UUbSkuhKhZbIH1ww8/MGfOHIqKinjrrbd48cUXy92l/CMqdXS7PCvib2W1WiksLPxFc9fFxQUPDw/pGgpRg9gG8+Pj45k9ezaZmZmMHz/evn+xMkvTVNlAfHm6h0ajkfj4eHvAaTQa2rRpI11DIWoYW9279957j/z8fCZOnMjw4cPx9vau9AZGpYWWxWLBZDLZu4m/1VW8dar03LlzWCwWdDodrVq1Ytq0aQ6ffRBCVExubi6bN29Gr9czbNgwxowZQ+3atavkc+rQ0FIUxb6fMC8vD6PRaO8aGo1GSkpK7AdWaDQa+6xiUVERu3btIiYmhoyMDLRaLcHBwbz22muEh4ej0+kceZtCiAoqLCykqKiIcePGMWjQIAwGQ5U1LBwaWrY6PSkpKXz66af2bp5tq0FCQgJhYWF07twZDw8PioqK2L17N8eOHSMjI4OCggLc3Nxo2LAh06dP59lnn6V27dqOvEUhhAMYDAYGDx7Mk08+WeU9IYeG1nfffceRI0e4du0a3t7ePPLII/bHbIPq58+fJzU1Fa1Wi6IolJSU4OPjg5+fHz4+PoSEhPDCCy8QEhJSaVOmQoiK8fPz44EHHsDLy6vKj/pzaGgNGDCAAQMGOPKSQogayMXFxX40WVWTDX1CCKdS7tCyde9cXFxk87IQ96lbc6C8Zz84WrnSx7anycfHh3r16uHm5iZLEIS4D7m6ulKvXj18fHyqrXuoUcux18ZWI+fixYsUFhYSFhZWJeebCSFqDtu2naNHj6LX62nevDkGg6HKB+LLFVpCCFFTSFNJCOFUJLSEEE5FQksI4VQktIQQTkVCSwjhVCS0hBBORUJLCOFUJLSEEE5FQksI4VQktIQQTkVCSwjhVCS0hBBORUJLCOFUJLSEEE5FQksI4VQktIQQTkVCSwjhVCS0hBBORUJLCOFUJLSEEE5FQksI4VQktIQQTkVCSwjhVCS0hBBORUJLCOFUJLSEEE5FQksI4VQktIQQTkVCSwjhVCS0hBBORUJLCOFUJLSEEE5FQksI4VQktIQQTkVCSwjhVCS0hBBORUJLCOFUJLSEEE5FQksI4VQktIQQTkVCSwjhVCS0hBBORUJLCOFUJLSEEE5FQksI4VQktIQQTkVCSwjhVCS0hBBORUJLCOFUJLSEEE5FQksI4VT+F9nx/ljbKI3sAAAAAElFTkSuQmCC)
A pulse shown here is reflected from the rigid wall A and then from free end B. The shape of the string after these 2 reflection will be
![](data:image/png;base64,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)
physics-General
physics-
A block of mass 1 kg is hanging vertically from a string of length 1 m and mass/length = 0.001 Kg/m. A small pulse is generated at its lower end. The pulse reaches the top end in approximately
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)
A block of mass 1 kg is hanging vertically from a string of length 1 m and mass/length = 0.001 Kg/m. A small pulse is generated at its lower end. The pulse reaches the top end in approximately
![](data:image/png;base64,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)
physics-General
physics-
Figure shown the shape of part of a long string in which transverse waves are produced by attaching one end of the string to tuning fork of frequency 250 Hz. What is the velocity of the waves?
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HVauXw4cMolUp+/etfD7pBwzNRq9UsXboUk8nE8ePH5aPqzkSSJAoLC7FYLERHR6NQKNBqtUyaNInt27f3Ovbg4+PDiBEj8PLyQqVSodFoiIqKYvbs2cTGxsqPs9vtVFVV8dVXX/Hpp5/S3NwsT3s2NTVx/PhxysvLqamp4csvv6SgoEAuc7d37152795NfX39Gdu+Y8cOnE4nkydPJiws7Dxfsf6l0Wi48cYbcTqdfP311xdN7+Ci3qxdXFxMbm4uiYmJTJo0adDfIvxQRkYGoaGhHDx4kEWLFjF69OgzPrazs5Oamhrsdru83dZdF6K9vZ3GxkaSk5NPC0N3AVq3EydOYLFYmDNnjrw12Gw2k5uby9tvv80tt9zC7t27efPNN/njH/+ITqfj1Vdfpbi4mIULF1JZWUlNTQ0lJSX885//lMvbFRYWMnHiRO69916ioqJOa3dzczPffPMNkZGRjB07dsDXFJwrpVLJxIkTSUxMZO/evVxzzTVEREQMdLMu2EXdMzh69ChGo5GxY8cSHR090M35RaKjo0lLS6Ompoa8vLyzPrarqwuz2Yy3t7e8x0KhUODr64skSWecJZAkCYvFwueff86jjz7K5s2bOXr0qLzGoaSkhNdee42MjAxGjx7N5ZdfjtFoJCcnB39/f8LDw2ltbUWSJG677TZ+97vfYTabef/990lLS+P2229nypQpFBUVUVxc/JPrHzt2jMbGRjIyMkhMTOyDV61/KBQKdDodCxcupKam5ozjMkPNRRsGkiRx+PBhtFot48ePH3IFKrRaLdOmTcPpdFJQUHDWRS4ulwuXy4VarZa//d3ThsBZ36hqtZqEhAQWLFiAy+Xi7bffJjc3F7vdTnFxMfn5+UyZMgVfX19SU1P505/+xMyZM4mIiCAmJoagoCCGDx9OWloaEydOJCkpCYvFQnJyMmPHjmXChAkoFApqamp+cu39+/ej1WoZN25cv29E6guzZs1CoVCQn5//i6eBB6OLNgzMZjPl5eXExsYyfPjwgW7OeRkzZgxBQUGUlJScdVbBx8cHHx8fuTArnAqI+vp6tFotERERvY6XuMcWxo4dy6pVq7jzzjsxGo0UFhZit9tpamqivb1dfrxWq2XhwoWMHDkSLy8vlEqlXPna/fu8vb3x8fGR93toNBqUSuVPwszpdJKVlUVUVBSxsbEDviz8fIwePZrQ0FDy8vJoaGgY6OZcsIs2DFpaWujq6mLUqFE/uVcdKuLj40lMTKS2tpaKioozPs7X15eYmBhcLpdcLt7pdFJUVERCQgIxMTE/O3jq7okkJSXh7e2NUqnEy8sLm83GoUOH5MVLLpeL9vb2C5pflySJxsZGioqKGDNmzJAZOPyxoKAg0tLSqK+vp7q6eqCbc8Eu2jDo7OzE29ubxMRE/P39B7o558XPz49hw4ZhtVopLS094+M0Gg2TJk0iMDCQqqoq7HY7FouFnJwcZs2aJR8W0tTURFVVFZ2dndjtdlpbW+UDZ6xWK21tbSQlJZGSkoKXlxdJSUn4+vqyceNG8vPzKSsro7S0lOrqarlkvdRLefsf//+PN125XC6+//57urq65HYPVenp6XR1dVFTUzPkNy8Nvb7ZOZIkicjIyAs6nGUwiIuLQ61WnzUM4NTahPr6erKyskhLS6Oqqoqqqir++7//m6CgIAA++eQTDh06xKpVq0hJSeHjjz9GoVAwZ84cTCYT//73v1m0aBFjxoxBoVCQkpLC0qVLeemll1i+fDnJyckEBQXxxz/+ES8vL7nr73Q6cTgcOBwOuru7USgUOJ1O7HY7XV1dSJKEy+XC4XCgVqtxuVwUFBSgUqlISEhAp9N5/HX0lMTERPmWzG63D5rNb+fjog0D4KIIA3cXv7S09KyHyAYEBHDdddcRGRnJG2+8QWhoKO+//z6BgYHy/XtGRgYpKSmkpKSgVqsJCAjg22+/paSkhJEjR/LAAw8QEREhT/FFRUXxhz/8gfT0dL799lt8fHxYuXIlsbGxVFdXYzAYmD17Nkajkbq6Opqampg3bx5KpZKqqiosFgsKhYLp06ejUqmorq4mISEBl8tFfn4+kZGR6PX6ITXl+2MxMTEYDAZqampoaWk5r9O7BouLOgxiY2OH5Cj1DwUHBxMcHExLS4t8ZuCZGAwG5s6dy4wZM+R7/h9+0EaOHMmIESPk8yyXLFnC4sWLUSgU8sKjHxd68fX1Zd68ecycOROFQiEPHMbGxhIZGYnT6USpVKLRaIiMjCQ1NVVew6BQKEhMTJQf4x4klCSJ0tJSIiMjh/yBuBEREfj7+9PQ0EBra6sIg/4gSRInT57kwIED1NXVoVarGTVqFJdddtkZz8mLiYkZ8icXBQQEEBISwvfff4/RaDxrGCgUCjQazRkHC3+8qMd98O3ZnOl3umcSfvxvP54V6G0hkcvloqKiQj5AZyjz9vYmJCSEqqoqOjo6Bro5F2TQDyC6XC5aWlp4+umn2bhxI4mJiSxevJiZM2eSnZ3NX//6Vw4cONDrz0ZFRXksDJxOJy0tLRw5cgSLxeKxwSODwUBISAgWi0WeKfAUi8VCYWEhNTU1Hltv717/UF9fT3R0tEfXfxiNRnJzcz36uikUCrmH1Nra6rHr9IdBHwZGo5GNGzeybds2Fi5cyPjx4xk5ciTjxo1j0aJFADzzzDPk5+ef9nMKhYLQ0FCPvdlsNhtHjhzhj3/8I/X19R4rU+bl5YW/vz9Op/O0OX9PaG5u5plnnmHr1q3yeoW+5j5yzmq1EhkZ6dH9Ivn5+TzxxBPk5uZ67BoAoaGh8lFtQ9mgDgOHw0F5eTmbNm1i3LhxTJgwQR5w0mq1pKamMnPmTMrKynjvvfdO+1mVSoVWq/XYend3/YADBw54tGegVCrx9vZGoVDQ1dXlkWu4ufciVFZWemx5rXudgiRJ+Pv7e3SxUUtLC9nZ2R4vce5e9m2xWDx6HU8b1GMGZrOZ7OxsKisrmTJlyk++RbRaLUlJSQQGBrJ161YeeOAB+UhtpVJJXV2dfFBrX7NYLNTW1uJyuSgrK5MH4TzBvYCqoqLCY88HoLy8HLPZTEtLC8XFxR45S8Jut1NQUCAvkDp58qTHem+1tbXYbLbTDuz1hNbWVjo7O+WTtwebwMBAQkJCfvb9OajDwGQykZ+fj0qlIjo6uteS5nq9nrCwMAoLC6moqGDMmDHAqXvTTZs2sWvXLo+0zW63U1tbi8Ph4OWXX8bPz89jJddLS0tpaGhg48aNfPPNNx65BkBbWxu1tbXs2bOHxsZGj8yZu8daHA4HH3zwAbt27fJYiFZVVdHe3s67777Lvn37PHINOBWi1dXVbNmyhcLCQo9d53zNmzeP5cuX/2y4D+owcDqdmEwmeUqrNxqNhoCAAJxO52mjuVqtls7OTmpraz3WttbWVlwuF01NTXI7PaGzsxObzUZLS4tHB9wsFgtWq5XOzk4aGho88iF1DwhLkkRnZycul8tjr1trayt2u522tjaPjk2YzWa6urowGo0ee79diPb29nMb0/L4AW4XoLGxUfrLX/4iBQUFSZ9//nmvp+EWFRVJK1askJKTk6Xy8nLJ5XKd8ynMF6Kjo0PatGmT5OvrK504ccKjJylv3rxZmjNnjvTMM8947BqSJEn5+fnS9OnTpYceekhqb2/3yDXMZrP07rvvSt7e3lJOTo5HDzT99NNPpZSUFOnjjz/22DUkSZJ27twpzZkzR3rkkUc8eh1PG9QDiP7+/kyePBmFQkF5eXmv6dbR0YHRaCQlJYW4uLghvZrtTLRaLUqlcsgPUMGpnoF7wPWHuxuHMq1Wi0Kh8NgMTH8Z1H8JjUbD8OHDmTdvHlu2bPnJTjmn00lZWRlms5l169ZdlEEAyKXJhvqiFjgVBp2dnfj4+KDRaC6Kv5l7l6d7H8ZQNajDQKFQEBERwf33348kSbz44ovk5+fT0dFBVVUVn3zyCXv27OHuu+9mzpw5/do2lUpFQEAAo0aN8vgqOp1Oh1qt9vgUmbe3NwkJCYSHh3tsUM89xvLDPROe4u/vT0pKisd3rep0Ory9vTGbzUO69zaoBxDh1LfiuHHjWL9+PRUVFXz77bdYrVZ8fHwICwtj1apVxMfHy1OK/dmuKVOm8OKLLxIdHe3R+n06nQ6tVuvxMAgPD+dPf/oTfn5+HhuodDqdNDc3ExQU5PGah+PGjePJJ58kJibGo9fR6XTodDosFgsmk8kjU7L9YdCHgbt6zsSJE0lOTqaxsRGz2YyPjw8hISEEBAQMSCFNlUpFSEgIISEhHr+WTqdDr9dTVlaGxWLx2JZfnU7HqFGjPPK73dzVlsPCws664Mi9UtHPz++cbyccDgdOp1Puqvv5+ZGWltZnbT8Tg8GAn58fdXV1GI3GM+6VGewGfRj8kL+/v0e6fA6HQ56GCggIOOcPm91ux2g0EhYW5tF734CAABISEjh27BiVlZWMHDnSY9fyJEmSsFqtFBUVcdVVV/U63ed0OjEajRw4cACr1YokSaSmpjJs2LCz/l1cLpc8z2+329Hr9Vx22WX9cvuo1+uJiIigqKiImpoaUlNTPX5NTxjUYwb9oaOjg2PHjrFjxw52797NgQMHfraeXVdXFyUlJWRmZvLWW295/BCNgIAARowYgcPh+MkejKHEvVCrrq6OiRMn9jrWYjQa+fLLL8nMzCQoKAiLxcLrr79OSUnJWYvCVlZWsnXrVnbv3s2ePXs4dOhQv92/azQakpKSkCRpSP99hlTPoK9JPRWU33//fWbNmkV0dDTbtm2jrKyMFStWnPG+uaOjg82bN/PBBx/Q3d3NPffc49E19lqtVi4EcvToUZYsWeKxa3mSe3m5SqViwoQJPwkDSZIoLi7m/fff584772TevHk4nU527NjBli1bCA4O7rWepSRJZGZmsnjxYkaOHIler8fLy+u8x5GkXorI9PZvP+SuHZmbmytXdBpqLumegdVq5fnnnycxMZEFCxYwc+ZM5s2bx7/+9a+zrjEPCQnh+uuv/9lDXN2lvnqrAeiuFeh+jJskSfLRZz8UFhZGREQEe/fuHbI1+k0mE0ePHiU8PJyEhISffGBsNhsnT56kvLxcPjRGpVIxadIk9u/fT1FR0U9+p9SzkvGzzz6TD0LV6XQEBAScFjbuZdDuqkytra10d3fLt3q1tbV0dnbS3NxMRUUFTU1N2Gw2TCYTNTU18tLmM00dxsTEEBUVJZ9mPRRd0mFQUlJCWVkZ0dHRBAcHo1QqCQoKwmAw8Omnn57x51QqlXyf2Bv3B7q1tZXi4mKam5vlD7DdbqehoYGWlhasVisNDQ2UlZVht9vlBTl5eXm0tbWddvsRHBzM6NGj5Q+Lp7ZMe1JnZydFRUVMmDCh10HftrY2iouLUSqVp43IJycn09bW1utsitPp5OjRo3R0dPDYY4+xYMECHnvsMblMnPsxtbW1PPzww7z44ovccccdPPHEExQWFlJSUsJf/vIXrr32Wj777DMefPBBMjIyuOOOOzhx4gQffPABN954I/Pnz2fDhg1nvFWJiooiNTWVpqYmTpw40UevWP+6pMOgtLQUq9Uqr/CDUyPQ7o1P56u2tpZXXnmFJ554gi1btrB8+XI2btyI2WzmueeeY+7cuaxfv57169ezdOlSrrvuOp566ikOHTrE2rVrWbZsGddee+1ph64GBQUxbdo0rFYru3fvHnKHfbq/mcvKys4YBhaLhfr6ery8vE6rmOzj44PZbO71zEm1Ws2MGTPYvn07Bw8e5LbbbuM///kPTz75pFxevrm5mVtvvZX58+fz+9//nnvuuYcDBw7wwQcf4OvrS3x8PBUVFZSWlvLkk0+yadMmcnJy2LBhA4mJibzzzjusXLmSrVu3nvF94ePjQ2JiIiqVyqObojzpkg4Do9GIj4/PaaPUKpUKlUp11sNCz8ZqtbJp0yZKSkq49957uf766xk1ahRPPvkkdrudOXPm4OXlRXNzM1deeSUvv/wyCxYs4M0336SkpJ5CIVkAABFUSURBVISnnnqKjRs30tLSwtGjR+ns7AROrWtISEggOjqaLVu2DLlbhYaGBr766iskSZJrNP6Y1FN2XaPRnBYWLpcLu91+xuesUqnQ6XQkJyfz4IMPsnr1asrKyvj666+xWq3k5+dTWlrKjBkzMBgMTJw4kccff5wbbriB8PBwUlJS0Ol0zJo1i7CwMH71q1/JvUX3az5+/Hi8vLzOeH6Fu95jWFgYO3bskP9uQ8klHQZOpxO1Wn3aG1OSJBwOx3mvMy8vL6e4uJiYmBhiYmKIjY3l/vvv57XXXsPX15eIiAh8fHxISkpi2LBhjBgxgoyMDKxWK0lJSURERDBp0iT8/f2pqqqSvw0VCgXBwcFMnTqV/fv3U1FRMaQCoaKigt27d5OamkpaWlqvYaBWq+US7D/s+bS1tZ12juSZqNVqgoKCuPzyy0lMTCQvLw+bzUZxcTEOh0Mu5qrX68nIyGDEiBFotVq5EKx7r4S3t7dcH1KtVqNWq+VCOWc7PCYhIYGMjAzq6urYv3//+b9YA+SSDgNfX1+53r+bzWbDbDaf96q1lpYWmpqa5OKgWq2W+Ph4Zs+ejUajkasGu99wGo0GnU6HUqmUeyje3t6o1Wp5EY1bYGAgV111FV1dXWRmZg6Zpa+dnZ3k5OTQ3NzM0qVL8fX17XVk3r18uLu7m8bGRvnfKyoqiIqKOufDcwMDA4mNjZWvo1KpaGtrIycnB5vNJr/+7qPj+0pgYCDp6el4e3uzdevWPvu9/eWSDoPk5GQUCgXt7e3ywJDZbKa9vf1nZwrORKvVYrPZKCoqOm3Aq7u7G5PJdEEbWby9vUlLS2P8+PF88cUXQ6YrWlVVxb59+wgJCWHBggVnfJxer2fcuHFERERw8uRJ4NTrdvz4ccaMGUN8fDxwagygoKBAXpTU3t6O2WzG6XTKm9e6u7vJyMjA29ubMWPGoNVqef3118nJyaGyspKCggKqq6v7dH+ERqNh2LBhpKWlsXPnThobG4fUQO8lHQYpKSkMGzaMpqYm2trasFqtNDY24nA4mDlzJnBqdeLhw4epr68/7VvafX/7Y5GRkURERHD48GG2bNlCfn4+hYWFHDt27Iw/8+M3jPtxP36se7Zj5cqV5ObmUlxcjNVq7YuXwmOcTie5ublUVFRw1VVXnfXodbVazYgRI1i8eDFZWVkcPnyYb775BqVSyZVXXklYWBiSJJGXl8drr70m/6327t3Lyy+/zKeffkpmZiYHDx5k3LhxpKeno9VqSUlJYdmyZRw+fJj169fzwgsvkJmZiSRJ2Gw2eZFZbW2tPNvT1dVFa2srHR0d8kyG2Wymubn5rL2JqKgoli5ditlsZufOnUPqVu6SDgN/f3/WrFmDyWQiOzub48ePc+LECRYsWCCXT7NYLLzyyiscPXpU7j04HA7MZjMmkwmtViu/ieBUGFxxxRX4+Pjw6quv8s9//pONGzfS1NSEVqultbUVrVaL1WrFZDJhNptpa2vD19cXo9GI0+mkvr4epVKJzWbDYrGcFhY6nY5rr72W6OhoPv74YxobGwf1ttmGhgYOHjyIXq/n6quv/tlv4sjISG644Qb0ej07duzgyJEj3H777aSlpeHt7Y0kSfJsg/t16e7u5uDBg3z55Zfs3r1brpzt3jdiMBh46KGHWLFiBQA1NTWMHj2aqKgoOjs7MZlMzJ8/X15bUFlZycSJE4mKiqKtrY2Ojg5MJhOTJ0/GYrFgNpvP+Jrr9XomTpzIhAkTeOeddzAajUOmdzD0lkn1sfnz5+Pt7c3Bgwfp7u5m4sSJTJ8+XV43r1QqGTt27GknBdtsNsrKytDr9UyfPp2DBw8SGBiIv78/KpWKK6+8koiICL744gvq6+tJSkpiwYIFKJVKiouLmTFjBnq9nvr6egIDA7FYLCxatIiqqiqsVivHjx9n+vTp+Pr60tTURHx8vFyP0N07WLNmDS+99BILFiwgODh4UO6U6+7uZvv27Rw7dozLL7/8nNbsK5VKIiMjueuuu+ju7katVp82s6BUKpk6dSpTp06V/+26665j4cKFSJLUa0VstVpNXFwcDz30EE6nE4VCIYeSwWDgd7/73WmPnzx5MpMnTz7t39atW3fOzzs0NJSVK1eyatUqtm/fzjXXXHPWw28GDU+WURoo/VH2bCC5XC6pra1NysjIkK6++mrpyJEjktPpHOhmncblckkFBQXSNddcIy1btkwqKCgY6Cb1q5aWFumaa66RJkyYIOXm5nq0vFtfuaRvE4YqhUKBv78/d9xxB3l5eWzdutXjpy39Uu6q0WVlZVxxxRWMGDFioJvUr/z8/HjooYcoLy/ntddeo66ubqCb9LNEGAxh11xzDTNnzmTz5s1s27ZtUK1K3Lx5Mzt27ODyyy+XT766lKjVatLS0li7di1btmxh7969va6gHExEGAxhOp2O++67j7CwMN58881Bsww2Ozubf/7zn8THx3PdddcRGho60E3qd+5Tv+666y7i4+N57rnnyMrKGtSzCyIMhjCFQkFKSgpr167FZrPx0ksvcfz48QFrj9PppLq6mv/3//4fkiTx29/+ljFjxgxIJarBIjIykocffhiFQsELL7zAoUOHBu3sjwiDIc7b25vZs2dz4403Ul1dzYYNG8jLy+v3dtjtdsrKynjkkUcoLi5m7dq1ZGRkDI1RdA9SKpX86le/4vbbb8doNMqBMBinG1WPPvroo335C93VbLKysjh58iQnT56Uy1B58lSbH/r666+pqalh/vz5Hi+GORjodDr5WPA9e/ZQVFREXFwckZGR/XJ9q9VKQUEBGzZs4Ntvv2X16tXcdNNNhISEXBSl0C+URqMhOjoahULBgQMHyM3NJSoqisjIyEHVa+rzMDAajXz88cd89NFHHDlyhCNHjhAdHU1SUpJHzu7rzaUWBnBqvjw+Ph6FQsGOHTvIy8sjIiKC0NBQeT+EJ7S3t3P48GFeeuklDh48yKpVq1i7di3BwcEiCH5Ap9PJBV327dvHoUOH5II1/fW5+Dl9GgbuI9S//fZbeVdYamoqs2fPJjAwsN/eHJdiGMCpQBg2bBh+fn5kZmaya9cuYmJi8Pf3lw9i6SsOh4PGxkZ27drFs88+S2lpKb/97W/5/e9/f8aNSJc6X19fhg0bRmBgILt372bHjh0EBwcTGBgob1YbSH0aBs3Nzezbtw9/f38WL17MpEmTmDRpEn5+fvKbQ+pZD97Z2SnvunN/c3V3d2M2m+VSYCaTie7ubry8vE7bkKJUKlGpVGd8w12qYQCn3nAjR45k1KhRbNu2ja1bt2Kz2YiIiJB3Q17Im87lcmEymaioqGDjxo28/vrrKBQKHnroIW655RaP9kIuBj4+PiQnJzNq1CgOHDjARx99RHt7u7zK1L2deiD0aRhkZ2fz1FNPsXXrVvLy8vD19SU6Olquey/11KvLzs7m888/Z8eOHXR3dxMXF4dSqeTEiRNs3rxZHnd47733+P7770lNTaWzs5M333yTL774goCAAMLCws44BnEphwGcukeNj4/nqquuorGxkbfffpv9+/ejVCoJDw+XawMqFIpz+uBKkoTT6aS7u5vW1lY2b97ME088QVZWFldccQWPPvoo06dPFyFwjjQaDbGxscyfPx+73c6bb77Jtm3bUCgUREZG4uXlJf9t+vM17dMw8Pb2Jjk5mdDQUPbv388LL7yAwWAgNTUVHx8furq6eP/999mxYwerV68mLi6OW265BUmSCA4O5umnn2bLli00NjbidDrp7OzknXfeoaamhry8PGJjY9m+fTs7d+4kNTWVuLi4XttxqYcBnBrF9vPzY/78+cydO5fvv/+e119/nU8++YSamhrUajVhYWE/e78qSRJms5msrCw2btzIgw8+yOeff87UqVN58sknWblyJeHh4SIIfiGFQoGfnx/Tp0/n+uuvp7y8nFdffZWPPvqI8vJyeQ+Kpw7M6U2fblQKDg5m9uzZTJs2jZtvvpnnnnuO559/ngkTJjBt2jRycnI4duwYM2fOJC4uDoPBwIoVK/Dx8SEqKoqrr76a8vJyZsyYwfLly6mpqaGlpYX9+/eTmZmJl5cXwcHB/OUvf6G2trYvm35RUigUaDQaxo4dy4YNG9i5cyfvvfceH374IW+99RYBAQGMGzeOyZMnExcXh5+fHz4+PlitVtrb26msrOTw4cPk5OTQ1taGRqNh/PjxrF+/nqlTpxIUFDRoBr+GIvfCpISEBP76179y7bXXyr3f999/Xz7Lc9KkSSQnJ6PX6xk+fDhxcXEeOd+z1zD49NNP+d///V9aWlp6/SGVSsWNN97ImjVrTqtN764f6C5Rde+997Jt2zb279/PmDFjOHHihHz8lFqtJiAggPvvvx+VSoXBYECv1+Pj44PBYMBgMGAymQgPDyc3N1cegAwLC8PhcJy2j7+qqopNmzbJdQv37dtHfX09GzZsYPr06T+7j/5ip9VqCQkJYeHChaSnp1NfX8/x48c5ePAglZWVbNq0ia6uLpxOJ8HBwZjNZux2O76+voSEhDB9+nTS09OZMGECwcHBhIWFDYoBr4uFSqUiKCiIWbNmMWrUKBobG8nNzeW7776jtLSUjz/+GJPJhNPpZNWqVaxbt84jqzp7DYNx48Zx9913n7FwhkKhIDk5+ayHc6pUKuLi4pgyZQo2m03+ADc2NsoVgNRqNeHh4dhsNpRKpby11N3ldJes+uG9k/sN+MNVXHa7ndLSUqqrq4FTpcdsNhvl5eVER0ef9SSeS4mfnx9+fn7ExMSQmprKr3/9a4xGo1y23V0SzB3qPj4+BAUFERQURGBgIAaDQQSAB+l0OuLj44mJiWHEiBHMnTsXo9GI0WjEbDbT3d1NUlKSx7ar9xoGSUlJJCUlXdAvlnrODrBarQwfPhydTkdERARdXV3s2rWLOXPmEBQUhMvlorKykoSEhPO+VkhICOvWrcNkMgHw6quvkpeXx6pVq5g2bdpptQiEUyHsPrfyhz0m98EuP9zvL/Q/d0/ZvXbETeqpfuWp8Zk+GzNwuVycPHmSoqIieYHRiRMnCAgIYMqUKej1etLS0khKSmLv3r28+OKLDB8+HJfLRXJysjzl2N3dLZ9C5HQ65e6r+8gqdxfWXTpbrVZjMBiYNGmS3JYvv/yS2tpaxo8fz7hx4/rqKV70RAAMbp6eXeizMJAkiaKiIt555x1SUlIICwujoaGBO+64g9jYWNRqNYmJidx888288sorZGZmsn//fkaMGMH8+fNxOBxYLBYiIyNxOBx0dHRgtVpRKBTEx8dTU1NDREQERqORhIQE7HY7HR0dBAUF9dVTEIRLWp+FgVKpZMqUKQQEBNDS0kJQUBBjxozB399f/sbRarXMnz+ftLQ0SktLcTgcpKWlYTAY6OjoYOzYsfJYhNlsRqfTcdNNNyFJEhaLhe7uboYNG8ZDDz2EWq0WYwGC0If6LAwUCgWhoaE/O8qpUqmIiIj4yTmF7nvYH/vxqbvuQqWCIPQtcZMoCAIgwkAQhB4iDARBAEQYCILQQ4SBIAjARXqi0ujRo+X13oIgnBuFNFhLtV6Auro6bDYboaGhg/LYMUEYjC7KMBAE4ZcTYwaCIAAiDARB6CHCQBAEQISBIAg9RBgIggCIMBAEoYcIA0EQABEGgiD0EGEgCAIgwkAQhB4iDARBAEQYCILQQ4SBIAiACANBEHqIMBAEARBhIAhCDxEGgiAAIgwEQeghwkAQBECEgSAIPUQYCIIAiDAQBKGHCANBEAARBoIg9BBhIAgCIMJAEIQeIgwEQQBEGAiC0EOEgSAIgAgDQRB6iDAQBAEQYSAIQg8RBoIgACIMBEHoIcJAEARAhIEgCD1EGAiCAIgwEAShhwgDQRAAEQaCIPQQYSAIAiDCQBCEHiIMBEEARBgIgtDj/wN8t7jkGpxBzAAAAABJRU5ErkJggg==)
Figure shown the shape of part of a long string in which transverse waves are produced by attaching one end of the string to tuning fork of frequency 250 Hz. What is the velocity of the waves?
![](data:image/png;base64,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)
physics-General
physics-
The equation of a wave travelling along the positive x-axis, as shown in figure at t = 0 is given by
![](data:image/png;base64,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)
The equation of a wave travelling along the positive x-axis, as shown in figure at t = 0 is given by
![](data:image/png;base64,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)
physics-General
physics-
An enclosed ideal gas is taken through a cycle as shown in the figure. Then
![](data:image/png;base64,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)
An enclosed ideal gas is taken through a cycle as shown in the figure. Then
![](data:image/png;base64,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)
physics-General
physics-
Two moles of monoatomic gas is expanded from (P0 , V0 ) to (P0 , 2V0 ) under isobaric condition. Let DQ1 , be the heat given to the gas, DW1 the work done by the gas and DU1 the change in internal energy. Now the monoatomic gas is replaced by a diatomic gas. Other conditions remaining the same. The corresponding values in this case are
,
,
respectively, then
Two moles of monoatomic gas is expanded from (P0 , V0 ) to (P0 , 2V0 ) under isobaric condition. Let DQ1 , be the heat given to the gas, DW1 the work done by the gas and DU1 the change in internal energy. Now the monoatomic gas is replaced by a diatomic gas. Other conditions remaining the same. The corresponding values in this case are
,
,
respectively, then
physics-General
physics-
A student records
for a thermodynamic cycle
. Certain entries are missing. Find correct entry in following options.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAARIAAAC+CAYAAAD5noACAAAgAElEQVR4nOy9d3gV153w/7lzu3Slq94lVEEFZBC9F4MN2Ca2gRiXxB0Hl7jt+rUdJ944ydp5HTvvZvfxxqxNXNYxxnQEmGoQAQmLJoGEACGBKOoSqrfOzO8P/2YioQK2CgLu53n4A0kzc86cM99zzrdqZFmW8eDBg4ceIFzrBnjw4OH6xyNIPHjw0GM8gsSDBw89xiNIPHjw0GM8gsSDBw89xiNIPHjw0GN0nf3QYxH24OHGQaPR9Pkz2gkSWZbJzMwkOzubyspKJEnq8wZ48OChd1EEhyAIGAwGlixZQmpqKlqtts+e2UGQHD16lE2bNnHq1CkkSUIQbt7TjyRJyLKMLMsIgnBTvQtJktTxv5H6LcuyukBqNBr1342Gn58foaGhWCwWqqurkSSp/wQJgCiKuN1uJEnCZDJhMpluyBd9JSRJwmaz0draiizLGI1GvL29b5p30djYiNPpxMvLS+339d53WZZxOp00NzcjyzJeXl4YjcY+/cCuBaIoYrfbKSwsxGAw4HA4+vyZHQSJLMtcvHgRLy8v3n33XcaPH39DrUhXiyiK7Nu3j6effhqTycQrr7zCwoULr3Wz+o17772XoqIiRo4cyR//+Ef8/PyudZN6jCRJ7Nmzh3feeYeLFy/y3HPPcd9996HX669103oVt9vN//7v//Lhhx/idDr7RefZqSAB0Ol0hIeHk5CQcMNJ7KvB5XJx+vRptFotgiAQFBREQkLCdb8qXy1eXl5oNBp8fHyIj4/H39//uu+7KIqcPn0ag8GAVqslKCiIuLg4TCbTtW5ar+JwOAgKCkKn0+F0OvvlmZ1abeCf50etVntTCpK2+qG27+J6/5iulrYKO0EQbpi+t91dt+3bjYSy+PUnN9+ZxYMHD72OR5B48OChx3gEiQcPHnqMR5B48OChx3SpbPXQu4iiSFNTEzabjZCQEARB6FZ5KUkSLS0tOBwORFHsYMJTrtVqtRiNRgRBQK/Xq4q2/lCMSpKE3W7HZrMhimIHT+i2bTQYDOh0OnQ63Q9S4MuyjCiKOJ1OGhsbsdvtaDQaBEHAZDLh4+Oj3kuxUHh7e/diL79HkiTVP6OpqQmn06kq4L28vPDy8lLbYbPZMBgMGI3GK46DLMvY7XaqqqoICwvDYDBcl0ptjyDpJxwOB59++ilHjhzh3XffJSAgoNsJY7fbOXLkCAUFBRQWFmK329UPVafTYbFY0Ov1CIJAWFgYFouF2NhY4uPjiYyMRKfr+6F1Op2cOHGCQ4cOcerUKerq6tQ2arVazGYzJpMJnU5HUFAQPj4+xMTEkJCQwKBBg64oTGRZprm5meLiYvLy8ti3bx/V1dX4+flhsVgIDQ1l6NChREVFAVBaWorVauW2227r1X5KksSlS5c4ceIEhw8fZu/evdjtdgICAjCbzQwaNIjk5GRCQkLQarXk5OQwYcIEhg4desVxEEWR/fv38/bbb/Pee++RmprqESQeuqampoZPPvmExsZGdu7cyd13343BYOjy7w0GAykpKWi1WvLy8vjqq69wuVwkJCQwffp0wsLC8PLyorGxkYKCAo4cOYLL5WLUqFHMnDmTqVOnEhwc3KeTUq/XExcXhyRJFBQUsGbNGpqamvD19eXee+8lNDQUX19fVRgcPHiQ1tZWMjIyuP3225k0aRLh4eEddlCyLON2uykrK2PDhg1s376diooKkpOTmTJlCgkJCRgMBsrLy9m/fz+rV6+mtraWuro6HnnkkV7rnyRJuN1uTp48ydq1a9m1axcOh4PExESmTJnCoEGDEEWR8+fPk5WVRVlZGY2NjVy4cIFBgwaRmpra7f1lWaa1tZU1a9Zw8OBBPv/8c37/+99fl17EHkHST+zatYsTJ04AsHLlSmbOnElAQECXf6+s4v7+/oSEhLBy5UrsdjsZGRn827/9G1arVfUVqKmpYc+ePSxdupTPP/+cHTt28C//8i88+uijGI3GPuuTVqvFz8+PjIwMANauXUt9fT0BAQH8+te/Jjw8HI1GgyzLNDQ0sH//fv72t7+xcuVKdu7cybPPPsujjz5KYGBgu/uKosiJEydYunQpy5cvJzExkV/96lcMHz6cmJiYdj4S5eXlbNmyhT/96U+UlZXR0NDQa/1zu90cO3aM9957jy1btjBjxgweeughxowZQ0hIiPqxi6LImTNnWLVqFe+++y5arZba2torepTKsszx48fJycmhqamJdevW8fTTTxMdHe0RJB7aI0kSra2trF+/Hvh+chYUFJCXl8fUqVOv6DgkCAIxMTGYTCaampowGo2YzeZ2q3hAQAC33347VqsVURTZs2cP//3f/83EiRNJTk7ucxdwjUZDeHi4usNS9AZt+2a1Wpk+fToRERG0tLSwZcsWPvnkE5KSkpg7d656rSRJVFVV8emnn7Jy5Uo1PGHOnDmqfqUtoaGhLFy4EJPJxL//+7/jcDh6HGyqCIDKykree+89tm7dSmxsLI8//jiTJ09W48/a6oBiY2N59NFH8fb25s9//jP19fXdRs8rup+dO3dy9uxZRFGkoqKCNWvW8NRTT2E2m390+68FHqtNH6OcgYuLi7nvvvvQaDRcuHCBnTt34nA4rrhqaTQaVYmq/P/y1Ur5cMeNG8fkyZMBKCkpITMzE7fb3Tcdu4y2nq+Xt09RjhqNRlJSUpg7dy6iKHLy5El27NjRbhfhdDrZu3cvK1asoL6+nieeeILJkyerbu2dPddisTBz5kzuu+8+XC5Xr8SXiKLI6tWrWbNmDVqtloULFzJu3DhVQLbto0ajQafTERgYyEMPPcStt97KpUuXum2DLMtcuHCBAwcOMGLECMxmMw6Hg5UrV1JTU9Ojtl8LPIKkj3E6naxevZqQkBDeeecdEhISsNlsZGdnk5+f36sBVVqtFr1er6Y+KC8vH1BJqmRZRqPRYDKZ1DZeunQJl8ul/k1VVRXbtm2jurqaiIgIZs+ejdVqveJW38/PjylTpuDn54fNZutROxXdyP/+7/9it9tJS0tj2rRpeHl5dXudIAhYLBYWLVpEU1NTt212u90cPHiQmpoann76ae644w60Wi1nzpxh586dPWr/tcAjSPqYkydPkp+fz7333oufnx+PP/44Op2Oo0ePkp2d3e4j6gmyLHP+/HmKioqQZRmtVktycvKAitxWTNoHDhxQd1rR0dHttvE1NTXk5eUhiiKJiYkEBARclQVKq9WSkpLC9OnTe9xnSZIoLS2lpKQEgMjISOLi4q5oZVLMwaNGjWLChAndtqOuro6cnByGDh3KkCFDWLx4MV5eXtTU1LBt2zYaGhquq8RiA2eW3YC43W5yc3MxmUxMnDgRnU7H7NmzSUhI4NKlS2RnZ1NeXt4rE6alpYVdu3aRk5ODJEkkJydzxx13DKgQeZvNxr59+9i1axdarZbU1FSmTZuGj48PgHrcycvLQ5IkYmJirtonRInQHj58OL6+vj1SVrrdbv7+97/jcDjQ6/WEhYURGBh4VffUaDRYLBbmzZvX5buXZZkTJ06Qn5/PpEmTiI6OZuzYsUybNg1RFCkoKGDfvn29tsj0Bx5lax8hiiLnzp3j0KFDTJs2jbCwMARBIDw8nAULFvDOO++Qm5tLfn4+YWFhVxXKLkkSp0+fZsOGDfj7+wPfC5Dq6moqKir46quvqK6uZtq0aTz99NOqabU/UY4r69evV/07WlpaqKmpoaamhq+++ory8nJGjx7Nk08+SUZGBoIgqCbfgoICnE4ngiAQGRl5xeNEW3rL0qHkLXG73Xh5eREREfGDIoS7yyqnmHzz8/OxWCykp6djNBqRJInHH3+cLVu2cO7cOXbt2sXo0aP71OrWm3gESR+h7EZqamr42c9+hp+fHxqNBqvVysyZM/nyyy8pKytj586djBo1ioiIiCveU5IkiouLWb16NYGBgapg2b9/v5rJLTY2lp/+9KfMmDGjWz+VvkKWZerr69mwYQPh4eHIssyZM2fIycmhsbERURQJDw9nxowZzJkzR13plRSIdXV1wPdCwWw2X5MQf0mSuHjxIqIootfre9WColilDh8+zKhRo4iKilKVtxkZGYwfP549e/awd+9e7rnnHoKCgnrt2X2JR5D0EY2NjeTm5hIREaE6LilHmKioKCZPnsxnn33Gxo0bue+++1Sfi+4QBIHhw4fz/PPPYzabkWVZdYDKzs7mm2++ob6+no8++oji4mJ++ctfEhIS0q8CRaPREBoaygsvvKAeWZqamrhw4QKHDx9m3bp1VFVVsXr1ahoaGnj88ccZOnSo6tqvXNP2fv2NRqMhICCAs2fP9vq9nU4neXl51NfXM2nSJLRarZoKUa/Xs2jRInJycjh27BgHDx4kPT0dk8k0oHRdneERJH2Akq7y8OHDJCUlkZ2d3c486nA40Ol0mM1mSktL2bFjByNHjkSv13f74QiCQGhoKMOHD28Xx+F2u5k5cyZTpkzhT3/6EwcOHODUqVNUVVXxl7/8pd8FiZeXF2lpaerxC75fiWfNmsWdd97Jm2++ye7duzl37hzV1dX88Y9/JCYmBq1WS0xMDPD9O1TijPobQRBISUkhPz8fURR7NeepzWZjw4YNuN1uLly4QHV1dbtxbGxsJDQ0lOLiYnbv3s2sWbOIj4/3CJKbDVmWaWlpIS8vj7KyMkRRpLy8vJ2AkCQJh8NBcHAwTU1NfP311zz99NP4+vr+qBgZrVZLQECAakJ87bXXOH36NCtWrGDq1Kk88sgj19xTUhAErFYrY8aM4d///d/55S9/SV5eHhs3bmTixIk88sgjWCwWBg0apH40JSUlqst9f7d16NChrFy5ksbGRkpLS3G5XOh0uh/9HpWjW3V1NVu2bCE6Oprly5d3CA2QJAlvb2/0ej1ZWVkcP36cmJiYfomd6gkDu3XXIbIsU1NTw5YtW1iwYAEvv/xylwrDjz/+mN/+9recOXOGzMxMfvrTn/6oCaOYHc1mM5MnTyYjI4OSkhJsNhs7d+7s1fiTnqBE/Q4ePJgFCxZw7NgxXC4X2dnZ3Hffffj4+BAUFERsbCxlZWWcPHmShoaGq1Yaty010ZMIaEEQGD16NAaDgebmZs6dO8f58+fVXdPVtEMUxXZKV0WZvHLlSmJiYli2bBmDBg3q9PqcnBz+9V//laKiIjZs2MD48eOvKpL4WjKw90vXIbIsU1hYyKlTp5g8eTK+vr4YDIZO/2VkZBATE4PD4eCDDz6gsbGxx883m82EhISo2v6BOPksFgvR0dGdmkcVRaxOp6O4uJji4uKrSmAsyzIul4tz585RVVXVI5O6VqslIyODxMREADX6+GrNsQ6Hg6KiIlpaWtSfSZJETU0NmZmZzJ07l+jo6C7nRUJCAuPGjUOj0bB161bOnz8/4H1KPIKkF1FWxM2bNxMdHU1GRka7/BuX/xs8eDDDhg1Dr9dz8OBBDh06pBbluvy+V4MkSTQ1NVFTU4MoihiNRsaOHdsXXe0RyirvdrsxGAzccsstqvk7ODiY2bNnExMTQ0tLC5988glnz57F7XZ3+x4cDgeFhYXs2bOHxsbGHglQxfv28ccfJyAggDNnzrB+/XrOnTuHy+Xqsh2SJKnK1D179mC329XfiaLI1q1baW1tVSO/u5oXwcHBjB49moCAAKqqqvjmm2/6razEj8UjSHoRSZJU68TYsWNVk29XWCwWxo8fj7+/P5IksW7dOmw2W7sJoxR1UlbDriaTEmG7ZcsWDhw4gCRJTJw4kbvuuqtfdiVt86V0hdKXnTt38vXXX+N0OhkxYgRz587FYrEAYDKZmDRpEg8++CCBgYFs2bKF999/n5MnT3YZN6RE0a5bt474+HgSExN7pJxUMsvfddddPPzwwxiNRjZt2sSyZcs4c+ZMl/0URZGsrCw2b97MjBkz1Ohuxbq2evVqhgwZwpAhQ7o9wur1etLS0lRrX2Zm5oAvoevRkfQCSnXC5uZm3nvvPaqqqhgyZAhut7vTiFVl5yKKopoVS5ZlduzYwc6dO9WtvUajwel0kp+fT3NzM6IocvHiRfbt20d4eDjBwcFotVqampo4dOgQ69ev59ChQ1RWVjJ58mR+/etfExIS0mf9bpu97NSpU6oQbGlp4bvvviMsLIyIiAh0Oh3Nzc0UFRWxcuVKDh06RHFxMWPGjOH5558nISGhXemPwMBAHn74YQICAvjkk0/IzMyktLSUkSNHMmfOHJKSkjCZTDQ0NFBTU8OpU6c4cOAAM2bMYPjw4b3ie6K049lnnyU4OJjly5ezYsUK8vLymDhxIrNnz1YVw/X19apvyOnTp7n//vtJTExEo9Hgdrux2WysXbuWgwcP8swzz6jZ1ToTJoouxWKx4Ovrq+Z6+eKLL/jlL3+J0Wi8Jv5BV8IjSHoBm83G7t27+fLLL9m0aRMajYYvv/wSm83G9OnT2+WuUKirq2Pnzp2sWrWKS5cuodFoKCsr4ze/+Q0FBQXMmjWLlpYWcnJy2LBhg7q13bt3L0VFRRiNRjWcXSlDabPZiIiI4LnnnmP+/Pmqf0Zf4XA4OH78OHv27GHjxo3U1tai0WioqKhgyZIl7VIeuFwumpqaaGlpISQkhMcee4yFCxe2O9YoKGbghx9+mClTprBixQo+++wzcnNz+frrr7FYLGrxp9DQUKZPn84DDzzA0KFDe/UjMxgMxMXFsWTJEqZOncqXX37J6tWr2b9/P5999playlQURRISEpgyZQpPPfUU8fHxaLVa1VP3iy++YP369Vy6dIlNmzZhsViYM2cOgwcPbvc8xeS9f/9+1q1bR1FREfC9Z/AHH3xAbW0td955J9OmTRtw5mCPIOkFtFotkZGRPPLII9x///0IgoBOp8PPz69L3xCdTkd8fDxPPvkkjzzyCKIotssB6ufnh9Vq5dZbb2XSpElqPWbFGnF5OoHg4GCsVquaw7U/atoq5/lJkyYxevTodud4xWKhtFGWZTVRk5LD1WQydes74+XlRXJyMq+88gpLlizh2LFjqu+JRqMhNTWV0aNHY7FYMBqNPTLPdoVGo8HX15dRo0aRlpbGiy++SGFhIRcuXKC2thaTycQtt9zC0KFD1Xa0TflgtVqZM2cOM2bMQBRFdDqdWnO4s2cJgkBwcDB33nkns2bNUo9zWq0Wk8nUpzvMnuARJL2AyWQiPT0d+KcOo6vcHMrP/Pz8GDlyZLtr2v7+h9Dds/oSvV5PZGTkVbn3Q+e5VLpDEUZ6vR4fHx/CwsJUZbTy0fVHWkJBEFSLiq+vL7Gxse3a0bYtbdFqtQwaNIiYmJirmhfw/S4oOTmZIUOGdNmWgWiJ8wiSXuDyJDdd/e5qr+nJ8/sb5UO6GotCb/Tz8l1Wf/e9bVa0q2lHd8meukIJYuzufgMNjyDpJX7MAA/USfFj6I++DJT39WN3jH19zbVkYGlsPHjwcF3S6Y5E8RK02WxcunRpwGmI+wOlGJIStetwOKivr7/uVoofi91uR5ZlbDYbDQ0N12WJhMuRJEk1o4uiSGtrK01NTe0cx24EXC4Xra2t/RrwqJHbHMYkSeJ3v/sd77//Pna7nejo6B5nm7pekSSJxsZGzpw5g0ajISIigqCgoJvmXZw4cYLW1lasVqsaY3I9912Z5kraBafTqY7pjbZQKu74FRUVGI1GVqxYwaxZs/o0W16XOhKlVseN9pJ/CEqpTMVjtaKi4lo3qd9QrBJNTU0cP378Wjen11Cc6OD7mjgVFRXXtYDsDCWxdn96wnYpSARBUEsS3owo2/rq6moEQcDf379D0p0bmfLycjVe50ZatVtbW6mvr0cURaxWKz4+PjekIGlqaurVYmFXolNBIggCvr6+fPjhhwPSi64/cLvd7Nq1i0WLFmE0GnnzzTd5+OGHb7hJ1xWTJ0/m6NGjTJ48maVLl14xbuh6QJIktm3bxuuvv05ZWRmvvvoqjz322IB0Oe8JLpeLDz/8kPfee6/f9D+dChIlDsBoNGKxWK5J3sxrjcvlwmAwqE5RBoPhhly9usJgMKDRaDAajXh7e98QfRdFUS1wpXiKenl53XC7bofD0e/pGW++rYYHDx56HY8g8eDBQ4/xCBIPHjz0GI8g8eDBQ4/pt1gbJVKyu9/3lMvvPxADnxTb/pU8RRVfAIWr8Sztj8A5D+1RxqltJPDVvuO2Y9yb43stUjL2iyBpaGjAZDKploDLUVLwtbS0dPoB6fV6vL29cTqd2Gy2Do42yt94eXm1yzrV3NzcIdelcq9r4akpyzJlZWXIskxkZGS3ZkdRFKmvr6epqQmj0XhFnx5RFGlqauoyHaFipVCSIXnoOUp6y5qaGlwuFyaTidDQUMxm81UJBYfDQXV1NS6XC39/f3x9fbu0kEqShM1mw+FwdOloplgWrwV9KkgUL8I1a9aQlpbG8OHDu3TTVbKBlZSUqMmLdTodCQkJJCUlMXLkSGpra9m9ezdlZWVqLIhWqyUuLo4hQ4aQnp7eTpAUFxdTVFRESUkJbrcbPz8/0tLSGDdu3FUXp+4tXC4XJSUl/P73vycoKIjXXnut0yQ1imt+UVERe/bsoa6uDqvVSmhoKBkZGaSkpHQqgOx2O0eOHKG4uJjy8nI1SbHRaCQ2NpaYmBji4+OJjIzsj+7e0CgLX3FxMdu2bSM3N5fm5masVivjx4/nzjvvJDIyslPzqyRJuN1uKisryc7OJj8/H0EQCAwMJCkpiTFjxuDn59dpGsby8nLy8/M5e/asWv5UqU44ZMgQIiIiGDZsWH+8gg70qSCRJImzZ8+yZs0asrOz+fOf/9ypIFGydoeHh3PgwAGWLl1KXV0d4eHhvPXWW4SEhCAIAt7e3vj6+nL48GG+/fZbmpub8fb25u233yYkJKTDyw8JCaGiooJ//OMfFBYWMn/+fCZNmnTFinZ9QXV1NW+99RZr164lPT1dzW/aWQrGL7/8ks2bNxMWFsbtt9+OKIqsWrWKNWvW8OqrrzJu3LgOk1Sv1xMeHs7FixfZsWMHBw8exOl0Mnz4cN566y0iIyNvKs/cvkJxPc/NzeW9997j4sWLWCwWysrKKC8vZ926dRw/fpy33noLX1/fDuPkcrnIz8/nb3/7G0VFRcyaNYvk5GSKiop44403WLhwIU888QTBwcHtrlOSYYWEhHD48GGWL1/O+fPnMRqNvPDCC0RERBAaGoogCNekOmGfChKn08mOHTvUOqYvvvgiSUlJnWZ5MpvNpKWlodVq2bdvH9u2bcPtdhMbG6vWxfXz82PmzJl4eXlx9uxZDhw4gMFgYOjQoURGRnYQUhEREXh7e7N8+XJaW1u5//77SU9P79PgpcuRJAmXy8VXX32llhVQYnjaoiRN3rx5Mx9++CEjR47kueeeY/DgwRiNRqKionj99ddZunQpVquV5OTkdttgg8FAUlIS4eHhlJaWcvz4cZqbmxkzZgy33nprv2UTu9GRJIn6+npWrFhBRkYGTzzxBFarlXPnzvHZZ5+xe/duVqxYQUJCAk899ZSaj1Y5stfV1fH73/+e8vJyHnvsMX7yk58QGBjItGnTsNlsLFu2jKCgIB566CGMRmOHpNhjx44lMDCQgwcPUlpaiq+vLw8++CCxsbFqqsmrrb/Tm/Sp1ebChQvs2LGD8vJyqqqqWLFiRZf1SRQ9R1xcHJMmTUKj0dDQ0MB3332H2+1WPwKTycTEiRMZM2aMusUvLS3t9PnKR1NdXc3w4cNJS0vrVyEC3+su9u3bx+rVq0lLS+v2bysrK/nwww8RRZGZM2cydOhQvL290el0jBgxgnvvvZdvvvmGTz75hPr6+g7XC4KgCh2LxYJGoyExMVEt0O0RIj1HFEXWrl3L/fffzwsvvMCcOXOYOHEiCxYs4O233yY5OZnGxkZWrVpFdXV1u2slSWLDhg1s27aNhIQEFi1aRGhoKAaDAT8/P7Ui4ieffMKePXs66LuUDHHBwcH4+/uj0XxfsD0wMLDd+F6Lce4TQaJs/woKCigvL8dkMiHLMp988gm1tbVdKos0Gg3e3t4MHTqU6OhoXC4XmZmZ7Yo4K27bEydOJDg4GLfbzf79+zvdzrndbhoaGqitrWXcuHHXJKaiqqqKpUuXMmXKFDIyMrpUpsmyzO7duzl69CgxMTGkpKS02xabzWbGjRuHLMts376dwsLCLrewbXceN1ocyUBgwoQJZGRkYLFY1A9Yp9MxePBgXn75ZcxmMyaTqZ0eTslp89e//hWj0ciQIUPaHX00Gg3+/v6MGzeOEydOkJmZ2WnQ3eWWoWtxTO+MPhMkNTU15OXlcddddzFx4kQEQaC6uppVq1Z1G94sCIJagU6WZfbt29ehZKFGo2HkyJEEBATgdrvZvHkzzc3NHQpLud1utm7ditVqZcKECf0aeyDLMna7na+//hqXy8WCBQvUidcVBw4cwOVyERUV1a7WC3yfdV6pi1tcXMyRI0ew2Wyd3mcgTKwbFYPBQEpKSodavIowCQkJwWq1ctttt7UrsyFJEqWlpZw7d05Vjl4+FwwGA6NGjVIXxxMnTvRbv3pKn3xZLpeLo0ePUltby/Tp01mwYIG6e1AqvHcnTKKjoxk5ciTe3t5qBTqlHIOCYtqVJIm6ujqysrI66B5aWlpYu3Yto0aNIjQ0tF8/MIfDwdatW8nNzWXx4sXExMQAXX/ksixz7NgxZFlGr9d3Wq7Ay8tLzWBeWlrar2HiHv5JV2PocrnYtm0bw4YN46GHHmq3G5RlmcOHD+N2uxEEoUMtH/h+sVCO35WVldTV1fVZH3qbPhEkLS0tHDhwgMDAQFJTU7n11ltJTU1FlmWKi4vVj74rjEYj48ePZ9CgQciyTGZmJk1NTaqQUAZFkiSMRiN2u53t27d3WKFPnDjB0aNHufXWW/tVN+J2uzl37hzffPMNI0aMYOzYsZ0KBgVF0VpcXAz8swzD5ZjNZqKiopBlmYsXL7YrUu3h2kCSaU0AACAASURBVKC4ODQ0NJCVlcWFCxd4/fXXO1gRJUlqJ0g6G19BEAgJCSEgIID6+noaGxsHdL3ftvS6IJFlmerqao4fP86kSZMwm80EBwfz0EMPodPpaGxsZNOmTTQ0NHT5knQ6HRkZGQwePBhBEDh16hQHDx5Us3Y5HA6OHj1KSkoKGRkZSJLEkSNHOH36dLt7bty4kfDwcIYPH95vysa2NXjNZjN33333FUPwJUni/Pnz2Gw2dDqdWujqcpTiSpIkUVlZSWtra192xcNVYLfbKSkpYdmyZbzxxhtq8avOvKxPnz6NKIoYDAb8/f07vZ/iMNna2kpDQ0OnFr6BSK8KEkWhtG/fPvz9/UlPT1fPjrfffrtaD/fQoUMcPny460b9/w46Y8aMwWq14nQ6Wbt2rZq0t6SkhNLSUqZOncqiRYsQBIELFy7wj3/8Q62pW19fT1ZWFrNnz1ZLK/YHysqzf/9+5s+fr9aH7Q4lG5ssy6oGv6trFBfo2tradkpoD/3PpUuXWLNmDf/xH//BX//6V7W28e9+9zuysrJwOp3q3ypjDHQrSBQkSaKhoeG6GeNeFSSyLHPp0iUyMzOZO3cuVqsV+N49OyAggEcffRRBECguLubbb7/t1t6t0WiYOnUqQUFBuN1udu7cSW1tLS6Xi8OHD9Pa2sqoUaO47bbbCA4Oprq6mpycHNVNPDs7m0uXLjF//vx+S8wkyzLNzc0sW7aMqVOnMnz48G6rzndHVzokxR/Bbrd36Q7voX8wm82MHTuWBx98kIceeojIyEiam5vZvHkz77333o/O8avsQJxO53Uzxr0uSLZu3YpWq2X8+PHtPmBBEFiwYAHx8fHY7XYOHjzIiRMnun1RSUlJjBo1Cp1OR11dHdnZ2bS0tJCXl0dgYCAREREEBwczd+5cZFnm1KlTFBYWYrfbyczMJDk5uYP1oy9pbW3lzTffVLX2DoeDpqYmGhsbaWlpweFwtCuF0NraqrqytzXrKX4fl+N2u2lublbN5P3tE+OhPUajkbi4OEaNGsUzzzzD559/Tnp6OoIg8N1337F+/fpOg/I6qxiooBRbV3ymrpcx7rUvTKmF8/HHH7NgwYIOqd4Uz9SHH34YQRA4duwYubm53e5KjEYjd999N0ajkdbWVnbu3ElpaSmFhYUMHTqUoKAgzGYzCxYsQKfTcebMGQ4fPkxJSQm5ubncfvvt7bwD+5qsrCw++ugjzpw5w//5P/+Hp59+mqeeeoqnnnqKZ555hk2bNqnZ+V999VWeeeYZsrKycLlcak5UURS7NOva7XaqqqoQBIGYmBgsFku/9MtD1yi1iQMCAsjIyGDZsmUEBgZSXV2tKlcVrFZrt2OsxFnV1dVhMBiuOgBwIJj7e81F3ul0snnzZgwGA7Nmzerw8Sqeq3PmzGHp0qVcvHiRXbt2MWXKFBITEztvnE7H9OnTCQ0NpbS0lLy8PPbs2UNVVRUpKSnqh5SSkqLGKxw4cICamhrcbjeTJ0/uV9+RS5cuYbVaycvL6zC4yi5EyfCdk5ODj48PM2fOBCAyMhKr1UplZaUaEXq5pcdut1NeXo5er2f8+PGEhYVdsU0DYZLdLAiCQFJSErfeeitffPEFXl5e6s5DEASGDRvGli1b1AXhckRRpLi4GFmWGTJkCLGxsVccv4GSmL3XBMmlS5dYvnw5Tz75ZKfKTWU7FxYWxt13381f//pX9uzZw4kTJ4iLi+uymrvVamXevHn853/+J2VlZaxatQqr1UpUVJT6Er28vJg1axZFRUXk5uaSl5dHeno6AQEB/fqik5OTWbJkiWpdaovL5SIrK4vs7GxCQkJYuHAhISEhpKSkoNPp0Ol0TJ06lRUrVlBXV0ddXR1hYWHqO1FMxOfPnycgIIBbbrlF1UEpmv3OtsuhoaF933EPwD8Xy2HDhuHj46POa/j+g58xYwb/9V//RWtrKxcvXuxwvdvtpqioCPh+cYyLiwM65qZp+zwloPVa02uCJCcnB5vNxq233qoGD3WGxWJh5syZbNy4kRMnTrB3714mTJigbvs645577uHjjz+murqaxsZGHnvsMaKjo9XfG41GJkyYwGeffUZxcTE+Pj68+OKLeHl59Vb3rophw4ap/jKXY7PZcLvd5ObmEhYWxpIlSxg0aBA6nU6tPn/HHXewdu1aqqqquHDhQjsh4Ha71ZilESNGtAtTP3/+PBcvXlTN3PBPwT1kyBDPrqQfURThwcHB3HLLLerPlR1Jeno63333HWVlZR2udbvdHDlyBLPZTHJyMgEBAciyTGtrKydOnCA0NLTdnNBoNCQnJ3f7vfUXPRZlyrluy5Yt3HnnnVd0A9fpdKSmpjJt2jQAvvnmG86fP99t3EhycjLjxo1DkiQsFgtpaWntzGdarZbExERGjBiBKIrExMSQnp7e73EmSgkPJYFQ238Gg0EVGkp5C4PBoCZY0mg0aqRueXk5xcXF7XY2jY2NbNu2DV9fX2bMmEFsbCzw/U7n7bff5k9/+hMnT55U811otVomTZrk2ZH0Mkr8VktLixrJDf+M8t6/fz9bt25l9uzZHQSJ2Wzmqaeewmw2c+bMGTXvjhLOUVpaytGjRxk8eDCzZs3CZDIhiiLbt2/nN7/5DZ9//jkOhwNZltW0GhMmTLgxBIkSF+B0OpkyZcoVt1mCIBAWFsbkyZOJiIigtLSUnTt3dql01Wg0eHl5cd9996HVaomOjlaPAwparZaoqCg1anjMmDFERERcV/V4lPrCzz//PFarlczMTDWbmizLbN68mdWrVzN79mweeOABfHx8kGWZyspK1q1bx65du9i4cSNOp5OysjICAgL4wx/+oB5/PPQcJYbsySef5NVXXyUzM5P6+nrVSfLrr7/m5ZdfJiIighdeeIGAgAD1WsWfatq0aSxevJhjx46xbt06WltbVZ+R3/72txiNRp544gkyMjLQ6/WIokhmZiZZWVmsWLGCgoICampqaGpqYtGiRYwfP35ABO71+GjjdDrJysoiLy+PV1555aoL8yhRwHq9nvXr1/P44493+nfKAEyaNIn4+HgSEhI6BDwp5tBbbrmFtLQ0xo8fr4ZZDxS0Wq1abEpJDXA5er2e0aNH89prr/HBBx/w1FNPMWbMGFpbWzlw4ACLFi1i8eLFREVFqX0LCQlh1qxZZGZm8tVXX1FUVITL5eLll1/uNtrYww9Ho9Fw/vx5Dhw4gNPpZOvWrURGRhIREUFzczOCIPDkk08yd+5cwsPDOzU4WK1WnnzySYxGIx9++CE7duxg8ODB5OXlodVqeffdd5k5c6aqaBcEgYULF7J+/XrOnz/P66+/TlxcHElJSfz85z8fMIXteyxIlNwZ6enpP7po8ZWyOgmCQHBwMK+88go+Pj6dKlEFQSA9PZ3XXnuNW265ZcDZ33U6HT/5yU9ISUnBarV2KejMZjNz585lwoQJZGVlsXfvXgwGA8uWLSMxMbFDciKDwcAf//hHxo0bR0FBAYMGDWLhwoVX5VHr4YczfPhwPv30U/Ly8igoKCAkJISkpCTS09NJTEy84kKq1+uJjo7mlVde4d5772Xr1q0UFxdz//33M2/evA7u9TqdjhkzZvD3v/+drVu34na7mTJlCtOnT8fX17c/unxV9FiQ+Pj4MGHChC41y1eDsuvoDi8vLxYtWtRtli/FIjQQV2FBEEhNTSU5ORmg2/5qNBp8fX2ZPXs2t912mxoR3FXfg4ODeeyxx5AkCY1G02WSbQ89RxAExo0bx6hRo9ScqVqt9gcnj9JqtSQlJREXF6da3DqbtxqNBkEQmDJlCuPHj1f//2M9pvuKHremq0jG3kbJ/tUdXQ3GQOCHvqcf0hfFfOyh71HGsac7XuU+VzNuvfXMvsSz9/XgwUOP8QgSDx489BiPIPHgwUOP8QgSDx489JguBUnbtIY3I51ZoW7WdwHXf9+v9/ZfLT2xnvaETlXGSkqAyspKSktLb0p/BFEUqa6uVjOu1dbWdlk/50ZEqcPc2NjImTNnqK+vv+5NypIkUV5errq219TUcPbs2QFtDfkxuFwuNQK+v+hSkDgcDj744AO+/vrr634C/RgkSaK6uhpRFLHb7Sxfvpzs7Oxr3ax+4+LFi8iyTFFREa+//voNUR9HySesjOuqVavIzc0dsC4DPxZJkjhz5gytra395hbQ7Y7k4MGDN22FNqXIl+KtW1hYSFFR0U3zLpRgsurqar799lvg+s9tomz7FS/qoqIiTp48ed3363Lazt1rKkjgeyenCRMmtMuJcTMhSRIVFRXs3r0brVbLiBEjVBf1m4FNmzZx6dIlwsLCGD9+/HXvLavoDS5evMihQ4doaWlRx/RG25GIosjJkycpKCjot2d2KkgEQcBisfDYY48xadKkG+5FXw1KIqJ9+/ZhMBi49957eeCBB67rj+mHcOzYMRoaGkhNTeU3v/mNmgryekYURXbv3s25c+dwuVzMmzePBx544Ioe09cbTqeTTz/9lLNnz2K32/vlmZ0KEiUpTmBgIFFRUTetIFEiKwVBwM/Pr13U7Y2OsgMxm81EREQQEBBw3fddFEWCgoLU/B1+fn5ERERgNpuvddN6FYfD0W1Jk77g5jPHePDgodfxCBIPHjz0mH5R6TY2Nqo1OrraHis1X9qmF1T+VomSvNwEKYqiWki8rROOEtp9vSsIrycUS4Hdbu+Ql0Y5KndWGkSxpLjdbmpqatQUCkpej87GT7EqKjWBLq8doyRhHggpCG8W+lyQSJLEhg0bGDJkSJcJh5TavWfPnqWoqAin06nmpfT39yc5OZmYmBhSUlJUfY0kSdTU1JCfn09RURHV1dXIsoy3tzfx8fEkJSWRmpp6wynSBiput5vCwkI2btzYobi5Xq8nNTWVOXPm4OPj0+53Sp2f3bt3c/jwYcxmM35+fowfP56RI0fi4+PTQfg4nU619Mj58+fV0pgajYagoCDi4uJITU1l0KBBN4T/y/VAnwoSURQ5f/48q1evJjIyknfeeafLVULZsZw6dYpVq1Zhs9kIDw/nF7/4BSaTqVOBoNPpMJvNSJLEypUruXDhArNnz2bIkCEeAdLPOBwOli1bxmeffdahuLmPjw+//e1v2/1McXrcu3cvX331FYWFhdxxxx1YrVYOHjzIP/7xDx5//HHmzJmDl5dXuzmj0WgwGo0YjUaOHz/O119/jSzLhISE8POf/5y0tLQBkcf0ZqJPBYnT6WT79u0cOXKEnJwcnn/+eeLi4joMsCAIDB06lKSkJCwWC4cOHeL48eOkpaWxaNEiBg0a1GFiaDQaAgICGDduHCkpKZw/f56NGzdy991393uFvZsdWZbJz8/nu+++Y8qUKR2EeFxcHHfeeWe78iCiKJKTk8P777/PpUuXeOWVV5gxYwZ6vZ5bb72V3/3ud/y///f/iIyMZPTo0e0cq/R6PYMHDyY+Pp6hQ4eyceNGbDYb0dHRLFiwgIyMjJvWkfJa0aeCpLKykm+//ZaKigpcLhcrVqzgpZdeQq/Xd/jItVoter2e0NBQYmJiKCoqIjY2Fl9fX7WMQ1uUSaLsStLS0jh48CCJiYlqmQcPfY8kSdhsNjZs2MC0adP42c9+hslkUn+vVAEIDAxUx0Qp9vXNN9/w3Xff8eyzzzJlyhT12BMXF8fs2bN59913efvtt/nggw+IjIxsVztXSSk5aNAgfHx8cDgcWK1WIiMjPdnirgF9umTn5eVx7Ngx4PvJ8/HHH9PY2NhldKKSu1XRo+j1erXuS3coyjW9Xu9RsPYzkiSxf/9+SktL+dnPfkZycjJxcXHqv9jYWEJCQjp83CdOnGDXrl1qGZO2iYx1Oh3Dhw8nJiaGnTt3kpmZ2e2cUXYfipLdQ//TJ4JEFEWqqqrIz89n/vz5TJkyBZ1OR2VlJatWreo2Y7yH64vW1lY2b97M2bNnycrKoqCggAsXLqh6ks4SVivhB+fPnycqKqpD2UmNRkNMTAwRERFIksSXX37Zr33y8MPpM0FSWFhIXV0dt99+O/Pnz8fPzw+n08mKFStobm6+afJD3MjIssyxY8fYs2cPubm5PPPMM8ycOZN/+Zd/Yd26dZSVlakm2rY4HA7Ky8tpbGzEy8urUwW8t7c3gwYNwmQyceLECbXCnIeBSZ8IktbWVg4dOoSfnx8pKSnMnDmT1NRUBEHg1KlT7N27t19zJXjoG5TyoGlpaUydOpX4+Hiam5tZt24dL7zwAq+99hq5ubmqOV/h0qVLnDx5Ui3ncDnKLiY6OhovLy8cDgfnzp370XWTPPQ9va6VkiRJPdYopSX1ej333Xcf+/fvp6GhgczMTCZOnDjgquF5+GFoNBpGjhxJXFwcFy9epLi4mGPHjvHtt99y5MgRNmzYgN1u59VXXyUjI0PVkzQ3N3P+/HkkScJqtXaZWEipSChJEmfPniUuLs6jAxmg9OqORJIkHA4H+/fvx9fXlxEjRgDfB4DNmzePuLg4nE4nBw8eJC8vrzcf7eEaIAgCXl5eREZGMnLkSBYuXMirr77KX/7yFxYvXozZbGb79u0sXbqUmpoa9TolWRRAQEDAFX1+JEmirKzMo1sbwPSqIJFlmdbWVjIzM7n99tvVAtaCIBAYGMgjjzyCVqulpKSEXbt2dXp+9nB90bbym8FgwGq1MmrUKJ5//nkeeughXC4XGzZs4MSJE+2Os21zAl/NHLjcyc3DwKLXBcmWLVuw2WxMnz693ZZVEAQeeOABteBybm4up0+f9px7b0AEQSA2NpY77rhD1Zvk5uZ2mhujM58ihZaWFnUXcqOF+t9o9JogUQK2Pv30U+67774O/hxK/odHHnkEQRA4duwY3333nRonoTboR5YAlWW5nU+Bh2uLIAhkZGQwbdo0tFotp06dUsfaYDDg4+ODRqPBZrN1OLIou5SqqipsNhs6nY5hw4Z5HM0GML0mSERRJCsrC5fLxW233dapG7zJZOInP/kJkZGR1NbWkpWVRUVFhfo3SgyFciS6WiRJora2FrPZPKAqtN/MaDQavL29SUhIUMdTOcJYLBZiY2PRaDRUV1fjcDg6XC+KIuXl5djtdqKjo0lPT7+iorW7AvMe+pZeEyT19fV8/vnnPP7441it1i7NemFhYcybNw+NRsPu3bspKipSEw0r7tRBQUEAanqAK52hnU4neXl5eHl5eSxBAwgl3F+WZdLS0lSlqp+fH2lpaVgsFioqKrDZbB2uq6uro7KyElEUmT59OkajUR3XzuaETqfDarV6on2vEb0iSGRZ5rvvvqOxsZHbbrut28hLi8XCrFmziIyMpLS0lH379qkOahqNBpPJhK+vL1qtlrNnz9LU1NSlIFHyWDQ1NXHs2DECAwPbTTgPfY/yUV8+RpIkUVdXR3FxMRaLhWHDhqmCxGAwkJycTHJyMrW1tdTW1nZQxJaVlVFZWYnJZGLSpEnqPZubm9U6O231a2azmUGDBnmivq8RPRYksixjs9n45ptvmDNnDr6+vt1+yHq9nvT0dKZPnw7AN998w4ULFxBFUd0Ojxw5ksGDB5Ofn09OTk4HPUrbZ9fU1PDRRx8hCAJ33nmn5xzdj0iSRENDA9XV1e2czpQ5kZWVRW5uLvPnzyc9PV0dG41GQ3x8PJMnT8ZkMpGfn99uVyKKInl5eZSUlDB16lRGjx6NRqNR3fFffPFFtm3b1m5e+Pv7M3bsWM/4XyN6/Nbdbje5ubnU19czduxYbDZbt16rsixjsVgYPXo0a9eupbi4mN27dxMbG6tmtRo/fjwLFizgk08+4T/+4z8wmUzMmjWrnSu1y+WisLCQ//7v/+bQoUP84he/YNy4cZ7UAf1ITU0NH3/8MdnZ2YwePZq7776b8PBw7HY7GzduZOXKldx66608+OCDWK3WdguMxWJh0aJFnD59muXLlzNhwgRSUlKA7+vNrFu3juDgYJ599llCQ0PRaDQ0NTWxe/dudu/ejZeXFxkZGWpek4ULFzJjxgyPw9o1oseCxG63s3nzZo4ePcqvf/3rqz5a1NXV4Xa7sdvtfPHFF9x///1qvgp/f3+ef/55fH19+Z//+R+WLFlCamoqY8aMISEhgZqaGnbs2MHJkycZNmwYb775JnPnzsVsNnuONf2Eklqxvr6erKwsdu7cyfvvv69+yKGhoSxZsoT7778fPz+/Dh+4VqslOTmZ3/zmNzz//PP89Kc/Zdq0acTFxZGVlYVOp+Pf/u3fmDRpknpcUZwcV6xYwaZNmzCbzTQ2NjJ9+nReeuklj37sGtJjQeJyuZg0aRKDBg1SjydXg1LxTMnn2Ral/MMvfvELHnzwQfbs2UNWVhbl5eVUVlai1+uZMmUKv//970lNTcVkMnnSB/QzSlrDJUuWEBcXx/79+2lubiYmJoa4uDgyMjIYPnw4JpOp012CkjIiISGBL774guzsbHJycigrK+Phhx/m9ttvx8fHp924mkwm5s6dqyZFUnyTZs6c6dGNXWN6LEgCAgK48847e6Mt7VAsOF5eXixYsIAFCxb0+jM89AydTkdcXBxLlixhyZIlP+oeBoOB4OBg5s2bx7x587r9W61WS3h4OIsXL2bx4sU/6nke+gaPQsGDBw89xiNIPHjw0GM8gsSDBw89plMdiaKRVxLX3IwRum63W3V4Ut6H2+2+aRR6St8lSUIUxRui76IoqnE9irJf6duNhDJ3+/O77VLZKooiFRUVlJaW3pS+GW63m4qKClWg1tTUUFJSct1/TFeL3W5Xs72fPXuW+vr6677vSq5YxXmutraWM2fO3HBu9S6Xi9ra2n7N36KR24gtSZL43e9+x5///Gfsdjs6ne6mrQ+jJN9RJp3RaOxQqOlGprW1FZvNhpeXl2pavZ773rY0qJLbxGQyodPpbihvWGWnpfhoGY1GVqxYwaxZs7rMRNcbdPoG2x5pbuasVMq2XqPR4Ha7O5SivJFRBKjdbr+h5oAypopH7I12rFFwu939Om6dChIlhd7s2bOJj4+/KXckbrebkpIS1q9fjyAITJs2jREjRlzXq/IP4bPPPqO8vJzExETmzJmDyWS6rvuu7EhKS0vZsWMHTU1NTJ06lfT09BvyaHP48GFycnL67ZldChKTycRjjz3GrFmzbsr4BZfLxdatW9m4cSNGo5F77rmHxYsXX9cf0w9h+/btVFRUMGTIEN544w0CAgKu+76LosiWLVvIy8vDZrNx11138cQTT9xw2dccDgcffPAB+fn5/Zai8ubbanjw4KHX8QgSDx489BiPIPHgwUOP8QgSDx489BiPIPHgwUOP6RdPnObmZgwGQ7e5XDtD8ZUTRRGXy0VjY6PqKOfr66vmuhgI5mkl0bFSUS4sLOyK7WobinC5O3Pb0hqX30cxZSrPUwpTKRnkOnvHyjWKD8Xlz2r7vN6yzij9a21t5cKFC8TExKjJq7pDqdjY2NiITqfDx8dHHeeu2iaKYpdu4cp1N2OoR3/Rp4JEGbht27YxZMgQBg8efFVehG0FSEVFBQUFBRQXF3Px4kVcLhd6vR5/f38GDx5MRkaG+tFeC4GifCyNjY1kZ2ezdetWhg4dyqOPPqomtO4KSZIoLCwkJyeng7ObVqslJSWFcePGYbFYOjyvsrKSPXv2cOTIEby9vYmIiCA9PZ2hQ4d2muTH6XRy+vRp8vPzqampUR0ONRoNPj4+REVFkZSURExMTK94ekqShMvl4vTp0+zcuZODBw/yzjvvXFGQuN1uKisrycrKoqioCKPRSFhYGMOHD2fYsGGdemdKkkReXh4nT56kurpadcRS3BiSkpKIiooiNja2x/3y0Dl9KkgkSaK8vJzly5cTGxvLm2++eVWTVEkqvGnTJtWPIzY2lpiYGIKDg2lpaWHHjh2sXr2aqKgoZs6cyU9/+lN8fX37VZgoSY5zc3NZuXIlu3fv5syZMzz77LNXtfo1Njby8ccf89VXX3Ww9wcGBvKrX/2K8ePHt3ue0+kkNzeXTz/9lNLSUhYuXIifnx9HjhxhzZo1/PznP+euu+7CZDK1u58gCJjNZnx8fNi6dSvr16/H4XBgtVp55pln1HIRvbEbkWWZ8vJyMjMz2bBhA4cPH0ar1XZav6btNaIosnfvXj766CMaGhqYNm0awcHB5OTk8Pe//52XXnqJ2bNnd9g1KUmwzGYz2dnZbN++HbvdTmBgIG+99RY+Pj7XvUPdQKdPBYnb7Wb37t3k5eWRk5PDs88+qw5od9vvqqoqPv30U7788ktuueUWnnzySeLi4vD398dgMOB2uxk1ahS7d+/mD3/4A4cOHeLs2bM888wzhIWF9VtciNPppKCggIKCAurr6zl37twVk18rSJJEfn4+BQUFJCYmdvCuHDZsGJMnT27nLKVc8/7771NRUcFzzz3HvHnz0Ol0pKWl8eabb/Lhhx8SHR3NyJEj263eer2euLg4YmJisFgsZGZm0tLSQlBQEHfddRdDhw7ttffS0tLC9u3bqamp4cKFC1RWVhIUFNSty7bb7ebMmTP8+te/xm6388orrzB16lR8fHwYPnw4ixcv5i9/+QsREREMHTq03YKk0WhITk4mPj4em83G4cOHKS4uJjQ0lAULFqhz7kZy9R9o9Kkgqa6uZtu2bZw7dw5RFFm1ahVLlizpUleirPDr1q3jz3/+M6mpqbz88sskJyer1yhn+cGDBxMdHY1er+fFF1/ko48+wul08sYbb6jlIPsag8HAsGHDSExMJC0tjdzcXJqbm694nSRJtLS08I9//IOJEyeqCZLbYjQasVgs7XZYzc3NbNq0iT179vDiiy9y2223qUeFxMRE7rnnHt58803++te/8qtf/YrExMQO70Gr1ZKQkKDmQg0KCiIyMrIX3sY/8fLy4p577qG1tZXz589TUFBwxWscDgf/9V//RXFxMQsXLmTmzJn4+PggCAJJSUm88cYbPPnkk7zzzjv83//7f4mJNhsUGQAAEJBJREFUielwD51OR1RUFKGhoZSWlpKamvqD9XIefhx9cg5QzvFHjx7lxIkTCIKAKIosXbpULYbVGaIokp+fz7Jly2hoaGDhwoUMHjxYLTStTAglYbS3tzcLFy7k7rvvprGxkRUrVrBy5cput9C9iVLQy2q1MnbsWHx8fK7qOlEUOXjwIMXFxUyaNEk9soWEhBAaGkpoaCh+fn7tVl1Zlrl48SLr1q1Dr9eTmpqqlnjQaDTo9XoGDx5MUlISa9eu5eDBg12uwIpwUt5jbx8HBUHA19cXf39/EhMTr5jdXZZlLly4wN/+9jcsFgujRo3CbDaj1WrVvo0fPx4/Pz/27NnD9u3bO1Uaw/eCsu11HvqHPhMkDQ0N5OfnM2PGDLXA0blz58jMzGxXIa0tzc3NZGZmUlhYSHx8PMnJyZjN5i4nulJQ66WXXsJisVBZWcm6des4efJkX3SrSwRBQK/XX3VMUlNTE1u3bqWkpITq6mrOnDlDXV1dt1tvRcF6+vRpoqKiOliFNBoNUVFRJCYmYrPZyMzMpLW19ZpaKpRM8d29F+U4m52dTUtLC1arlVtuuaXdNYrAHjZsGFVVVeTm5lJTU+Oxwgwg+kSQuN1uCgsLqaioYM6cOcyfP5+AgADcbjcrVqygqampgzCRZZnGxkZV0MTHx6s1gLvtgCAQHR3N1KlTAcjJyeHYsWNdCqtrjSRJagTqgQMHeOaZZ3jwwQd54403WLVqFSdPnsTlcnW4zm63U1hYiNvtxsvLq4PyUKPREBAQoFpdjh8/3mWFwv7mSjorWZY5evQosiyj1+s7FNNSBFJKSopazvPixYseQTKA6BNB0traSm5uLhaLhfT0dGbPns3gwYPV486BAwc6FSQXLlygpKQEWZYJCQm5qqOCRqPBbDYza9YsNBoNNTU1nDp16pqvxl0hiiItLS1ERUWRkpKCwWCgoKCAjz76iOeee44//vGPHDlypEOKS5vNxtGjR9Vdy+UfprJqh4eH4+PjQ2Vl5YARJFdClmWOHTsGfL8wtK2oCP88giUlJallWuvq6gbsYnEz0uvKVqV49NGjR7n33nvx8fFBr9ezcOFCDh06RENDAxs2bGDs2LFqnWAlc1V+fj4ulwutVktQUBDe3t5X9UytVkt8fDwWiwWn00lJSQmNjY0DMqOZVqtl2LBh/OEPf6C6upry8nIOHTrExo0bKSkpYfXq1TQ0NPDyyy8zZswYtFqtmoTn9OnTyLKMt7d3B/OugrJbaWxspLa2ltDQ0AGdBkKWZVUpC98rmTurH60UTQO4dOkSDQ0NA3KhuFnp1R2J4m154MABDAYDo0aNQqPRYDAYuPfeewkPD1f9II4ePdruOrfbzalTp1QnKX9//6vygoR/rsaK41Z5efmA3ZEIgoC/vz/JyclMnjyZhQsX8tJLL/Gf//mfzJ8/H1EU2bFjB3//+9+pqqpq55zX3NyMJEn4+vpeUcgqO7zrYdV2OBy4/r/2zj6mrfKL49/evmEB6UqrOLCEgSssTM1whlBGMkKYQyXMVRuJkSy+xcRF1LlscUMxi4nvM2bxD2OILkbnHySKcRgzQRTQoC66RnQUBiKTl62lFC7Q9ra/P8jzWNbC+OVCWeF8kv6x0Oze5/a53+ec85xzHr8fCoUCer0eiYmJURcAtuiMj49jYmLimvx91yvLKiRsW/Pzzz9HeXk5NmzYMHcRQYDJZEJNTQ0EQUBPTw9aWlrmRd6ZJcNvbJF06GjE66RSKBRITU1FUVER6uvrsW/fPszOzqK5uXnRWM/VxhsMBhfdIbvWCN/av5r4+Xy+uHHb1gvLbpG0t7fD5XKhrKyMb18yH3ffvn0wGo3wer3o6urChQsX+KRhmZds1fF4PJienl7ytWdnZ+HxeADM1bnEU9crpVIJjUaDjIwM2Gw2pKSkYGRkBE6nkz8D9qKxZ7mQu+Lz+fjqHi/nIYffoyAIUcfGOtoDWHMNm9cCyyYkLH37gw8+gM1mi9i2ZbsKzCpxOBzo6uqCz+fje/5Wq5XHBC5durTkZsvMmmFHKKSnp0ckc8UDKpUKt9xyC/bs2YNQKIS+vj54vV4Acy8Yc2f8fn/U7NlQKAS32w2v1wuNRoPNmzfHxTNg3dxZLOhKK4qlz//zzz9QKBS48cYbYTQa40Ik1wvLNsv8fj86OzvhcrlQUVERdVdBrVajsrISaWlpGB0dRVtbG0ZHRwHMrcp33nknz7IcGxvjL9HVCAQCfJIZjUZYLJYlx1euJRQKBVJSUpCXl8fzL5iLl5CQgM2bN0OpVMLj8URk0IZCIUxOTvJzW3Jzc2EymRYVkvCK39WCjc1sNnMh9Hg8Ee6NJEno7++HQqGAxWJBTk7OVYPIJDSxY9mExOv14qOPPkJNTQ1SU1MjJjDLBcjMzERFRQVCoRBaWlp4gJUFIUtKSqBQKDAwMDAvZrIQLMDrcDigVCpRXFzM60zieSIplUrcfPPNXBB1Oh0KCwuhVqvhcrkigo3swKehoSGEQiEUFxfPE1OW+BWOIAjXxMouCAKsViuAudSBwcHBeULCLJK+vj6o1Wps3boV2dnZEASBjytaawSDwRDTcaxnlkVIQqEQzp49i7GxMVRUVCy6UiQnJ+Ouu+7Cxo0b0d/fj87OTp6glpSUhMrKSmRnZ6O3txfnz5/n7spC1w0EAnA6nWhra8PGjRtRVVWFTZs2LcewYg6LDXV3d+OGG25ATk4O3+bVarXYunUrsrKyMDY2BrfbHSEkw8PDGBgYQGJiIi+5Z+7C8PBwxEqvVqthsVhWdXuYxX0qKiqQnJyMyclJ9Pb2RgiJKIpwOp0wGo28VgiYs4T/+uuvefE0ZmllZ2evukiuF2QLCWtC09TUhJ07d0Kv1/OAKWvaE/5RKpXIz8+H1WpFIBDA6dOnMTw8DEmSoFarUVRUhPvvvx+CIOCLL77A0NAQ/H4/b1rDPuygI6/Xi3feeQeBQAB2ux27d++OuVvD7ufK+4smgJIkQRRFTExM8AOa2Bm009PT+Pnnn9HZ2YnKykoUFBTwoKIgCMjIyMCuXbswPT3NK43Zc/X7/ejr60NPTw9KSkqQn58PpVKJQCCAb775BgcOHMDXX389rw9JQkICduzYsaKBy/BnEs1yAOZe/OzsbFRVVUEURfzxxx/8N2dj+/HHHzE+Po5bb70VhYWF/P9uaGhAbW0tOjs7+fcBwGQyIS8vb8XGRcxHtpCwArTR0VGUlpbybmYLfSRJgslkgtVqhcFgQHd3N9rb2+H3+7l7U11dDbvdjt9//x1vvvkmxsfH54kJm1wejwcvvvgiOjo6cODAATz11FNITU2N+SokSRKGhoYwMzMDYC5m4/f7owYNXS4X6uvrYbPZcOLECfz9998QRRFTU1P45JNPUF9fj+LiYjzyyCMRxW4pKSl48MEHsWPHDnz22Wf4888/+bUGBwdx8uRJGAwGPProo7zyd3p6GqdOncJXX32FL7/8Ev/++y8/07i6uhqlpaUrJiSSJMHlcvH8Fyb+0bZ3dTodjh49ipycHHz77bfo7u7mQeX+/n688MILSEtLw/79+3nlryiK+Pjjj/HDDz+goaEBMzMzuHz5MkRRxP79+7Fly5a4CDavBWTPIEmS0NLSgtHRUTQ0NCAxMXFJP97FixeRlJQEj8eDxsZGPPDAA3xr02w249VXX0VlZSXefvttVFVVYc+ePSgoKEBmZib6+/t5NmgwGMT7778Pq9UKjUYT84kTDAbh8/nQ1NQEURSRlJSE5uZm6HQ6PPbYY8jIyIio4r106RJ++eUX/Prrr3jvvfeQnJwMv9+PqakpPP7443jyySejPkdmzT333HM4cuQInn76adx3333IyclBY2Mj3G43Dh06hPLycl75qlKpUFhYiKamJrS2tuLEiRNwuVy44447cOTIkXnd15YTv98Pp9MJh8MBQRDg9/vxxBNP4NChQ7BarRFWo0qlwqZNm/DKK6/g2WefxfPPP4+qqiro9Xo0NjYiGAzi9ddfR2lpKXfFEhISUFBQgLNnz6K9vR319fWYnJzE9u3bYbPZombIEiuDbCGZmppCVlYWAoEAgsHgkn84s9mM6upqHoQN385kfTp37dqFsrIytLa24tixY3j55Zd5i4AtW7bg8OHD2L17N3/pYj1pmO8+MDCAbdu2oaGhgQeOBUGA2+3G9ddfz4N+bFfp6NGjMJvN+O233zA5OYmsrCxkZmaiuLgYRUVFC/ZOZc9q+/bt+PDDD9Hc3IzW1lacOXMG5eXleOONN2AwGOY9C51OB7vdjomJCfz0009wOp249957sXfv3hUTERb49Xq9eOaZZ1BbWwsA/LkMDg7CYrFEjE2hUKCgoACffvopTp8+jba2NkxMTODuu+9GTU1NRDsJpVKJgwcPQqPR4Ny5c7hw4QL27t3L4y1kjcQO2UKi1+ths9kWjAksBZY8Ff5vNlkEQUBJSQmOHz+Ow4cPo6OjA6IoYmRkhB/wvVpbmKyNQW5uboT/H37/4bBq5YMHD3LxZUlYGo2G99JY7JqCIOCmm27CQw89xC05QRCg1WojAqcsc7a2tpaLtVqtXra2igvdo8lkQmpqatS/LxbcValUSE9Px8MPP4zq6mpeERztftl16urquLuk1WrjfscuHpEtJItlWS4HLCiYn5+Pl156CcePH8eZM2fgcrnw7rvvIi8vD7fddhv/bqxh7tj/g1KplJV5y4RWq9VCq9Uu6fuxzvSVMy9Y0+alQFmu1wZxY/upVCrcfvvtqKur402Rz58/j9deew1dXV2YnZ2NiwI1gliLxI2Us1qcvLw8mM1mFBUVobW1Fd999x3q6upgt9txzz338F0b8o8JInbEjZAwBEFAUlIStm3bBovFArvdDofDge7ubpw8eRKCICA3NxclJSXXZD8SgliLxJ2QAP/V7ej1eqSkpCA9PR07d+7k3cNYcI4giNgQl0ISTrQGw7E614YgiDniXkgAEg6CWG0oIrkA8dJZjCCuZDXmblSLJLzg7spu5uuF8JoQ9jwCgcC6sXzY2Fl9zFoYOyuOBP5rTcDGtpZYqJ5pJVnQtQkEAjh37tyq1K9cC7Dxsxepp6cHbW1tcf8yLRXW79XlcqGjoyNmx6CuJMFgEA6HgzcG7+3txffff7/mAvM+nw+9vb0xdfkVoTBzIxgM4tixY3jrrbf4ae7r9RT3YDAIURQxNjYGADAYDOuqCOzixYuYmZlBYmIijEbjqndSWw7Y2dKXL1+GJEnYsGHDmqzJCQaD8Hq9UCqVEEURp06dQllZ2YoeYRphkeh0OqSlpUEURbjdbrjd7hW7eDzAVqupqakl95BdKyQkJECSJIyMjKz2rSwrLH1/rf+maWlpkCQpJovAPCFh1ZeiKMLn863L2AhBrBWuu+46SJKErKysFbe65rk2AHjzoYW6WREEER+wUhGVSrXiVkmEkBAEQfy/rK0oE0EQqwIJCUEQsiEhIQhCNiQkBEHIhoSEIAjZkJAQBCEbEhKCIGRDQkIQhGxISAiCkA0JCUEQsiEhIQhCNiQkBEHIhoSEIAjZkJAQBCEbEhKCIGRDQkIQhGxISAiCkA0JCUEQsiEhIQhCNiQkBEHIhoSEIAjZkJAQBCEbEhKCIGRDQkIQhGxISAiCkA0JCUEQsiEhIQhCNv8DbyyUsnF1JJwAAAAASUVORK5CYII=)
A student records
for a thermodynamic cycle
. Certain entries are missing. Find correct entry in following options.
![](data:image/png;base64,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)
physics-General
physics-
Figure shows the pressure P versus volume V graphs for two different gas sample at a given temperature. MA and MB are masses of two samples, nA and nB are numbers of moles. Which of the following must be incorrect.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANAAAADPCAYAAACEJF86AAAgAElEQVR4nO3deXDU9f3H8ed37yO7m2OzmzskISSBkHAYYiUcIiBY603VH6OtlvY3reP87Ezb38zvaJ1fZ379OXUGOzq/4k9R1LZaAyIIwg+FIRxqSIRgLhBCgBCSsElIyLVJNru/P/jtCoIXu9ndwPsxs0MO8t1PYF/7uT9fxefz+RBCXBNVpAsgxEQmARIiCBIgIYIgARIiCBIgIYIgARIiCBIgIYIgARIiCBIgIYIgARIiCBIgIYKg+fIXRkdHcblc9PX1MTY2BoBKpcJkMmGz2bDZbF97QbfbzcDAAIqiYLPZUKvV41NyIaLAFQFSFIWBgQE2bdrEvn37KC4uJj8/n5MnTzI0NMScOXNYunQper0eRVGuuOCJEyd48cUXmTJlCo8++igWiyUsv4gQkXBFE06j0ZCZmYnD4eDw4cOkpKRw8803U1ZWRmNjI7/97W/57LPPGB4evuJiPT09vP/++2zcuJH//u//5vjx4wwNDYXlFxEiEq7aB9LpdMTExGCxWLDb7TidTubNm8cjjzyCy+WivLycCxcuXPYzXq+XQ4cOUV5eTktLC8eOHeOFF16gra0N2TEhrlffehBBpVJhtVqxWq20tbUxOjoa+J7X66Wrq4vnnnuO2tpaADweDxs2bGDPnj0MDg6GvuRCRIFvHaCOjg4OHz5Mf38/s2bNwmw2B743OjrK3r17qa+vx+12A+Dz+ejr6+PNN9+kpaUl9CUXIgpcMYhwqdHRUT799FM0Gg3t7e3U1dWxcuVK7r//fkwmU+Dveb1eXC4XQ0NDGAwGdDodiqLQ19dHV1cXfX194/6LCBEJXxugsbExTCYTHo+H1NRUvve975GZmUlsbOwVI3A+nw+r1UpmZiY9PT1kZmZSW1uLwWAY119AiEj62gAZDAYKCgpYvnw5MTExX3shlUrFTTfdxE033cSWLVvIzc3ltttu48CBA1cd7hbievC1Afq21Go1aWlp/OY3v6Grq4stW7ag0WhYsWIF8fHx3zj5KsREddUAeb1ehoeHGRoaYmho6BuHoTUaDaWlpZjNZgYGBoCLE7JWq5V7770XrVYbVCF9Ph8ul4vt27eTnJzMkiVLgrqeEKFyxSicx+Ph5MmTtLS0kJKSQnt7O2fPnmVkZOSrL6JSkZCQgMFguKy5pigKcXFx39j8+yb+AP3973/no48+CupaQoTSFTWQz+dDURRuvfVW5s6di06nw2QyBdbFRYLP52NwcJDe3t7L5p+EiLQrAqTVasnKyiIrKysS5flK/hpQp9NFuCRCfGHCbGfw98NUqglTZHEDmDCvRq1Wi6Io0oQTUWXCBEin0+Hz+b52MEOIcJswAfIPhV9tG4UQkTIhAqQoSmDwQGogEU0mRIDgYhNOpVIxOjoa0SF1IS41oQKkVqvxeDx4PJ5IF0cIYIIESFEU9Ho9Go2G0dFRacaJqDEhAgRgNBrR6XS43e7Apj0hIm1CBEhRFIxGI1arlcHBwSvOYxAiUsISoNHRUbq7uzl27Ng11x6KomC32xkZGZEdriJqhCVAg4ODbNu2jd/97ndBvfgdDgejo6P09PSEsHRCXLuwBGhoaIjPP/+cysrKoM6JS09Px+v1yiElImqEJUBer5ehoaGvPM3028rJyUGr1VJXVxfC0glx7cIWILfbHXSAEhMTiY2Npb6+PoSlE+LahSVAiqKg0WjweDxBnVIaGxtLcnIyzc3N9Pf34/V6Q1hKIb67sARIpVJhNBqDngC1Wq2kp6fjdrs5ceKErEgQERe2ABkMBtxud1A1kNFoJDU1Fa1WS319vaxIEBEXlgCp1WqMRmPQAVIUBafTSVxcHA0NDRIgEXETqgYCcDqdxMfHU1tbKwESERfWPpDb7Q664x8fH09eXh41NTUMDQ3JQIKIqLA24TweD6Ojo0HVQjabjblz59LR0cHRo0dlYamIqLAFyGKx4PP56O/vD2pDnNlspqioiNjYWPbu3SsLS0VEhSVAOp0Op9MJ8I2nnH4TRVEwm82UlJRw+PBhXC5XqIopxHcWthooLi4Oo9FIa2tr0AeDGI1Gvve979HS0iLr4kREhXUlQkJCAmfPng06QAaDgbKyMvr6+jhy5IhsbxARE7YNdRqNhuTkZFpaWoLu+Ov1eoqLi7FardTU1EgzTkRM2AKk1WrJycmhvb096P08KpUKi8VCWVkZzc3NfP755yEqpRDfTdgCpNPpyM3N5fz583R3d4fkmrfeeitut5uPPvoo6AlaIa5FWGugKVOmcP78ebq6uoK+nqIoFBUVER8fz6FDh2hra5MQibALaw2Un5/P8PAwbW1tQe1M9UtNTWXKlCm4XC4aGhpkVYIIu7D3gfR6Pc3NzSGZADWZTNxyyy34fD4+/PBDObFUhF3YAqRSqbDZbEyePJnTp0+HrB80Y8YM0tLS2LZtGwMDA1ILibAK+7lwM2fOpLu7m7Nnz4bkeunp6cyfP5/Ozk4+/PDDwE2OhQiHiARoZGQkZOcaGI1GZsyYQWpqKu+++65MqoqwCmuAFEVh8uTJGI1GampqQrKSWq1Wk5WVxZw5c9i3bx+tra2yT0iETdhroIyMDBITE2lpaQnZ0LPdbue+++6jp6eHbdu2ycGLImzCHqC4uDgKCgro6+vj6NGjIen0m0wmCgsLmTNnDjt27ODYsWMhKKkQ3ywih8vPnDkTvV5PZWVlyEbNzGYzq1atwuVyceDAgZDMMwnxTSISoClTppCcnMzOnTsZGRkJSTPOYDCwaNEisrKyqKys5NSpUyEoqRBfLyIBcjgcFBcXc/LkSY4ePRqSTr9arSYxMZHHH38cl8vFzp07ZWJVjLuIBMhmszFt2jS0Wi0VFRUMDg6G7Nrz5s1j0qRJvP/++7S3t8vEqhhXEQmQSqUiNTWVjIwM9u3bF9LJz+TkZJYsWcKFCxd4++23ZUhbjKuI3aEuKSmJwsJCKisrOX/+fEibW/PmzWPu3Lm89NJLnDp1KugdsEJ8lYgFKDY2luXLl3PhwgX27NlDb29vyK5tt9u54447sFgs/M///E9Itk8IcTURC5DRaKSoqIisrCy2b99OR0dHyK6t1+uZMmUKt99+O9u2baOuri6k/Swh/CIWIJVKhdlsZunSpbS0tNDY2BjSDn9CQgI/+tGPUBSF1157jZaWFtlwJ0IuonfpNhqNLFmyhL6+Pg4ePBjSwQStVktSUhK/+MUvqK2tZfv27XI7FBFyEQ2QTqejtLSUlJQUqqqqOHHiREivbzAYuO+++0hNTeWDDz6goaEhpNcXIqIBUqlUWK1WHnzwQbq7u9m+fXtIm3FqtRqn08mqVavo7+/nlVde4cKFCzI3JEImogGCi1scFi1ahN1u54MPPsDlcoX0Ba5SqSgrK6OkpIQ9e/ZQUVEhw9oiZCIeIIDs7GxmzJhBR0cHH330Ucj7Kk6nk3vvvZf4+Hj+67/+i3Pnzkl/SIREVARIr9ezaNEi4uLiePPNN8dl9UBxcTH/9E//REtLC3/+859pb28P+XOIG09UBEhRFIqLi1m+fDkHDhygtrY25NsRjEYjN910Ew8//DDvvfcelZWVsv1bBC0qAgQX7zy3aNEikpOTeeedd0K+q1SlUpGQkMBjjz2Gw+Hgtddeo6amRppyIihREyCNRkNWVhZ33HEHFRUVnDlzhtHR0ZA+h16vJycnh6eeeoqOjg7WrVtHW1tbSJ9D3FiiJkBwcfXAypUruXDhAlu3bg3Z2XGX0mq13HHHHXz/+9+nurqal156ibGxMVmlIK5JVAVIpVLhcDj46U9/yo4dO6ioqBiXORuNRsPjjz/OggUL+Pvf/87mzZtlrZy4JlEVIEVRMBgM3HPPPZjNZrZt28bJkyfH5XkcDgf/8A//QE5ODn/4wx+or6+XQxnFdxZVAYIv+kL33XcfTU1NvPfeeyE7N+FSOp2OqVOn8tRTTzEyMsKzzz7LkSNHZJJVfCdRFyC42JRbtmwZOTk5/PWvf6WpqWlcRsusViulpaX88pe/pKamhldeeYWzZ8/KUh/xrUVlgAAmTZrEHXfcwfDwMC+99NK49VFsNhuPPPIIP/7xj9m9ezfPPfcc/f39MqggvpWoDZCiKMydO5fly5fz1ltvUV9fP24hUhSFVatWsXz5cvbs2cPq1avp7++Xmkh8o6gNEFwc1l6xYgXp6emsWbOG1tbWcakZFEUhMTGRVatWsWDBAsrLy3n++edDvrBVXH+iOkB6vZ5Jkybx0EMPUVVVxf79+8ft3Gv/wfePPfYY06ZNY+3atWzcuFGOxhJfK6oDBBcPH1m5ciVpaWn85S9/oaamZtwOTNRoNBQUFPD000+TmprK6tWr2bhxI729vdInElcV9QFSq9XEx8fzL//yL/T09LBu3bpxPWVHp9ORnZ3N888/j9VqZfXq1bz88su43W4JkbhC1AcILoaopKSEu+++myNHjvC3v/1tXJtV/hsiv/DCC+Tm5vLqq6+yevVqent7pTknLjMhAqQoCjExMTz44IMUFxfzxhtvsHv37nEdldPr9RQWFvKb3/yGGTNm8Je//IUXXniB1tZWWcEtAiZEgPyysrJYsWIFRqORP/3pT+N+Nzqz2cwtt9zCP//zP1NUVMQbb7zB3/72N06fPi1HBgtgggVIq9UyZ84cnnzySfbs2cO6detwuVzj2jfx10TPPvss8+fP5+WXX+ZPf/oT7e3teDwe6Rfd4CZUgAAsFgsLFy7kZz/7GevXr2fHjh3jfjMttVpNcnIyzzzzDA8//DC7d+/miSeeoLGxUZpzN7gJFyCVSkVcXBy/+MUvyM7O5vXXX6eiomLc7wWkVquJi4vj5z//OU8++SRdXV088cQTVFRUhPRcbzGxTLgAwcVRsoyMDH7961+j0+lYs2YN1dXV4z5CpigKycnJ3HXXXfzyl79Ep9Pxn//5n2zYsIEzZ87ICN0NaEIGCL5YK/fII4/Q3t7OM888w5kzZ8LSuXc4HCxfvpzf//73+Hw+/vznP/PKK68EBhekX3TjmLABgosd/Lvvvpuf/OQn1NTU8Mc//pHOzs6w1AQxMTGUlpaybt065syZw+uvv86vfvUrmpqaGB4elhDdINRPP/3006G8YGtrK7t27cLpdLJgwQIMBkMoL38FrVZLWloaKpWKtWvXYjKZyMrKwmq1juvzwhfzUzfffDPx8fHs3r2bt956i7S0NBwOByaTadzLICJrwgfIP+mZnZ1NX18fW7duxefzkZ2djcViGdfnhouDGkajkUmTJjF16lSamprYunUrLS0tJCUlER8fj1qtHvdyiMiY8AGCiyNkRqORKVOm8Nlnn/HJJ5/g9XrJycnBZDKhKMq4Pr+iKJjNZpKTk5k6dSpdXV1UVVVRU1ODTqfDbrej0+kkSNeh6yJAcDFECQkJ5OXlUV1dza5du7DZbGRnZ6PT6VCpxr+7p9VqSU5O5uabb8ZisbBz504+/PBDxsbGSEtLQ6vVotFoxj3QInyumwD5OZ1OUlJS+PTTT/nrX/9KWloa2dnZGI3GsDy/oigYjUamT5/OzTffTFtbG8899xx1dXXExcUxadIktFptWMoixt91FyCAxMRE8vLy+Oyzz9i8eTM2m420tLSw9In8FEUhNjaW0tJSbrrpJg4dOsTmzZv55JNPcDgcOJ1O1Gq11EYT3HUZIK1WS2xsLHl5eZw4cYKKigpGRkbCNjrnp9FoMJvNZGZmMmvWLOx2O0ePHmXnzp00NTWRkJCAyWRCr9eHrUwitK7LAMHFOaLU1FRyc3NpbGyksrKS4eFhMjMzMZvNYekTwcWaSKfTkZSURF5eHtOmTaOzs5OqqiqqqqoYGxtDr9djMpmkfzQBXbcBgosDC2lpaRQWFtLc3Mx7771Hf38/06ZNw2AwhH1UzGAwkJKSwvz588nLy6O+vp5NmzZRU1NDQkICsbGxqNVqVCqVBGmCuK4D5JeQkEBxcTFut5uXXnqJkydPUlBQgN1uD/sLVVGUwOTvsmXLyMvLo66ujtWrV3P06FESEhJISkpCp9OFtVzi2twQAVIUBZPJxNSpU0lOTg7cYCsjI4OUlJSIzM+oVCo0Gg3JycnccsstlJaWUl1dzYYNG9i1axcqlQqz2YzJZJL5oyh2QwQILjbnTCYTubm52O12Dh48SGVlJQaDgfT0dDQaTdj6RX7+/pHFYiE9PZ3i4mLsdjsul4udO3dSUVFBU1MTY2Nj6HQ6jEajhCnK3DABgovv+gaDgby8PBwOBwcOHGDnzp1otVqcTid6vR6NRhP2cvmbdU6nk8LCQmbOnInFYqG2tpaDBw+yb98+WlpaUKlUeDweFEVBo9FImKLADRUg+OLFOnnyZPLz8/n888959dVX6e/vJycnB6vVGpEQ+Wm1WuLj45kxYwY/+MEPyMzMpKWlha1bt7J582ZqamoYGBggLi4OvV6Pz+cL1Jwy8BB+N1yA/Pw385o/fz4Gg4E333yT6upqHA4HWVlZYW/Ofdmli2SXLVvGkiVLMJvNHD16lI0bN1JeXk5DQwMqlYr4+HiMRmPEy3wjumEDBBf7RQaDgfz8fKZNm8aBAwf44IMP6O3tJTs7G71eH9FmkqIoqNVqdDpdYCTxtttuo6ysjLGxMerq6tixYwcbN27k0KFDDA8Po9FoMBqNMqcUJpFrq0QJjUaDw+Fg0aJFxMTE8NZbb1FeXs6xY8d4+OGHKSoqIi4uLqIvRv+d+wwGAw6Hg0mTJlFcXEx9fT1VVVU0NDRQV1dHbW0tDoeDgoICpk2bRn5+Pk6nE5vNhtlsnlCBcrvdtLe309vby+joaGDUUq/XYzabiY2NjYrf6YaugS6l1+vJyMiguLiY0dFRtmzZQmVlJRaLhYSEhEBtFOn/MPhiqVJubi5z585l7ty5zJ49G0VRaGxs5NNPP6WqqoqPPvqIpqYmBgYG8Hq9DA4OBracq1SqqB6EGBwc5MMPP2TNmjW88847tLa2cvr0aaqrqzl8+DBDQ0NYrdaIDfz4SYAu4T/xp6SkhJkzZ/LJJ5+wceNGTp48SW5uLlarNWpCBF808Ww2G5mZmSxcuJAVK1Ywf/587HY7nZ2dVFRU8NZbb7F+/XoOHDgQCJS/RhsbG8Pr9Qa2oCuKEhW/n16vx263U1dXx/79+9mwYQPLli1jxowZdHZ28h//8R+cPXuW4uJibDZbxMp5wzfhrkav11NaWsratWt54403eOedd7j33nv58Y9/zEMPPURmZmbUbknwb6XIy8tj5cqVDAwMcOLECT7++GNqamrYu3cvb7/9NiMjIzgcDqZPn05RURH5+fmkp6eTkZGBzWaL6Lu6n1arxWKxBObLFEUhPj6eRYsWcejQIcrLywP3j4pU6CP/rxSF/CNgSUlJPPbYY5SWlvL++++zbds2Pv74Y+655x6WLl1KRkZGVLxbX0qlUqHT6QJLgWw2G3a7nYKCAi5cuEBnZyft7e0cP36c48ePc/r0ad5//302bdoEgMlkIikpiczMTDIzM8nIyMDpdGKxWLBarcTExIR1b5X/39f/p1qtxuv1jtt9or4rCdDXUKvVOJ1O4uLiyMvLY/bs2Wzfvp23336b2tpali5dyqxZswJ9pGjknzw2GAwkJiaSk5ODx+NhYGCA3t5eenp6OHXqFM3NzTQ3N9PW1kZ3dzdnz55l3759ge3ysbGxJCYmkpSUREJCAhaLJfCIiYkhJiYGvV6PTqcL7LxVq9VXPK7FyMgIhw8fxmQy0dPTQ21tLXV1ddx5550RrX1AAvSt6HQ6UlJSeOihhygrK2Pnzp28+uqrfPLJJyxevJgHH3yQ9PR0LBZL1DbtLqXRaLDZbNhsNjIyMigqKgJgbGyMnp4eurq66OrqoqOjg2PHjgUe1dXVjIyMBHbdmkymwJ9mszmwUdA/QnZpyCwWS2Ap0tVqlktrGJPJdFm/ZmRkhC1btqDX62lsbOTo0aN4PB4eeOABrFYrXq83YnNgEqDvKC0tjUcffZTbb7+d9evXs2bNGrZu3cr999/Pj370o8A7YrQ17b4N/7kSCQkJV3zP5/PR19fH2bNnOXv2LC6Xi3PnznHu3Dk6Ojro6Ojg4MGDuFwuenp6GBgYuOzwfUVRUKlUgQ2E/hpKo9FcVltZrVYWL17MU089FXjumJgY/vVf/xWTyURfXx/79u3jmWee4R//8R959tlnWb58edialV8mAboGiqJgt9t55JFHWLZsGeXl5Wzfvp2NGzeycuVKbr/9drKysoiJiYl0UUPGfwZeTk4OmZmZjI2NBUbw/B9f+jWv14vb7aavry/w6O/vZ2BgALfbjcfjuexn/J+r1WoKCgrQ6/VXvWmA2WymrKwMm83Gfffdx7p16ygqKmLy5MkR+FeRAF0zfzMoJiYmMNBQUVEROIlnypQpLFiwgJkzZwZWe0/EWulSKpUKlUr1rZupVwvXpcPmV3uoVCr0ev1XBsh/Dl9GRgZqtRqfzyd9oIlMrVYHOtbTp0/n008/ZcuWLTQ2NlJTU8PkyZNZuHAhBQUFpKenExsbO6HmxoLxXQN3qbGxMfr7+wMrEc6cOYPFYsHr9dLV1cXevXuJi4vj7rvvJi4ubhxK/+1IgEJEq9WSmJjIsmXLWLhwIfX19WzZsoXy8nJ27NjB5MmTmTdvHnfeeSdZWVkYjcbLOtXicsPDwxw5coTTp09js9l48cUXyczMZHh4mPr6ek6dOsXjjz/O97//feLj4yNWTsUX4lPQKysr+bd/+zeKior493//d2JjY0N5+QnD6/Xi8XhwuVxs2rSJzZs3c/DgQbxeL6Wlpdxzzz0sWbKEtLS0qJi0jDaDg4O4XK7AQf3+cyLUanVgVM+/CTKi6xQlQOPH5/MFmiJ9fX2cOHGCLVu2sH//fjo6OjAYDNxyyy3cddddFBQUkJaWhl6vlxoJAgMRV3t5RtM6PnnrG0f+naOxsbHExsZit9vJzc3lrrvu4vDhw1RWVnLkyBHq6uqIj49nypQpzJw5k6KiIlJSUkhISIj4O+x46O/vp6amhvj4eKZOnXrVv+PvP0U7CVAY+fs9/vOz77zzTo4ePcrevXuprq5m7969fPzxxyQmJjJ79mxmz56N0+kkISEBq9WK2WzGaDRO+EC1trby2muvkZyczO9+97sJ/SYhAYoA/7bySZMmMWnSJJYsWUJ/fz91dXVUVVWxa9cuXn75ZdasWUN6ejo5OTnMmDGDOXPmMG3atMBE5KUTkBPh3RouNmsrKyvZv38/BoOBn//85zgcjqhpkn1XEqAooFKpsFgszJkzh1mzZvH4448HbpFSVVVFXV0da9eu5ZlnnsFms1FSUkJxcTF5eXnk5OQE7oUU7S9Cn8/H4OAg9fX1TJ8+nfr6erZt28YPf/jDCTvpLAGKEv7+kn/XpdFoJCEhgXnz5tHX10dPTw/Nzc1UVlbS0NDA//7v//Luu+8yOjqKwWAgIyODwsJCCgsLycjIIDY2NjDRGy3NPo/HQ3V1Nenp6cyfP5/nn3+e9evXc+edd0bF7tJrIQGKQv4w+Ydrk5KS8Hq9FBYWUlZWRldXF2fOnKGlpYUzZ87Q2tpKd3c3e/bsYffu3Zdte7bb7SQmJgYedrsdq9UaWKGt1+sxGAxhuQHY2NgY1dXVzJ07l4yMDO6//35++9vf0tDQwJw5cybkLTElQBOEfwmL0WgkJSWF6dOn4/P58Hg89Pb20tnZSUdHB0eOHOHzzz+nqamJuro63G43Pp8PnU6HwWDAaDQSExMTCFRSUhLJyckkJSVhMpnQarWX9au+/LG/w//lFdX+j7VabWApzqU8Hg89PT00NjYyf/58AAoKCjCZTKxfv57JkydLgER4+Qcj7HY7drud/Px8FixYEPh+f38/HR0dnDlzJlBjnT59mra2Nmpra2lvb+f8+fN4PB7UajVms5m4uLjANgWj0YjBYLji80v3+/ibnf7P7XY7CxcuJCMj47KyDgwMsGvXLgYGBnj33Xcxm8309/eTlpbG/v37OXHiBKmpqROuGScBuo75702UlpZ2xUrpS1dMnzt3jvb2djo6Oujs7KS/v/+yldPDw8OcP3+e9vZ2RkZGLluF/eXrpaenk5ube0WAenp62LdvH7///e8Do24jIyPcc889PPDAA1RXV0f8fINrIQG6jl06MPFVvF4vTqeT/Px8RkdHL9tm4F+OdOnj0tXUV1tVbTKZSE1Nvew5RkdH6e3tJS4uDqfTSUxMTGBT3tSpUyksLKSiooKlS5dKgMTE8uUzFEJtZGSE06dPs3XrVhITEwOb7BRFwefzMTo6Sn5+Prt37+aDDz4gOTn5qhv6otXEmH0TE5bH46GioiJw1sK5c+fwer3Axdrv+PHjAOTm5tLc3Ex1dXXgZ91uN729vXR3dwceg4ODgZ+PBlIDiXFlMpn4yU9+ctXvabVaSkpKKCkpuer3jx8/zu7du+np6QmsyJ41axbz5s2LmnkjCZCIWllZWRw/fpzy8nLq6+vxer3ExMSwePFinnzySQoLCyN+iMu4BGhkZIS2tjaqqqowm83j8RTiBuA/I2Hx4sV0dHTQ1NTEhQsX2LRpE01NTTz44IP84Ac/ICkpKWJBCnmA/BNpn332GX/4wx8i/g4hJr7h4WEGBgZQq9UMDw/T3d3Nxx9/TFdXF2azmQceeOD6CVBCQgJ33XUXXV1dV90MJcR3MTIyQk9PD4ODg5w7dy4weWyz2cjKyiInJyeir7OQ70i9dE5AiGD4fD4aGxt5/vnnef311xkeHkatVpOTk8MTTzzBo48+itVqjehWjpAHSIhQaWho4MUXX+TIkSP09vYCMGvWLFatWkVWVlbgbhmRJAESUauzsxOXy8Xg4GDgaw6Hg8TExKg5GkwCJEQQZB5IRAX/Ojz/+7l/DZ9KpQqcbjQ6OorP5wvcN1YmUoX4f3V1dTQ0NOB2u4GLe4UKCwuxWq2MjY3R3NZe6a4AAAJNSURBVNzMwYMHGRoaIikpibKysqhYjSBr4URUyM7OBmDt2rVs3boVh8MR2GCnVqtJSUmhu7ubqqoq0tPTMRgMEQ8PSIBElLBarcyePZuMjAwaGxuBy+8dZDab8Xq9lJSUkJGRETWnuUqARFRQFIWUlBR++MMf0traSm1tbWD0zev1MjAwwKlTpygoKMBisUS4tF+QAImoYbVaKSkpITc3lw0bNtDR0QFc3BJRV1dHamrqFZv1Ik0CJKKKxWJhxYoV1NfXB5pyw8PD7N69m1tvvZXExMQIl/ByEiARVUwmE3fffTfDw8NUV1fjcrkYGRnh3LlzxMfHj9vO2WsVHT0xIf6fVqtl8uTJlJaWcvDgQWpra1GpVGRlZWEymaJi5O1SUgOJqOJfbf3www/T39/PO++8w/bt21m8eHFU7i2TAImoNHPmTJxOJ1u2bGFgYICsrKwrDmuMBhIgEZXi4uKYO3cuaWlpzJs3L2rvPiF9IBGVNBoNt912G263m9mzZ0d828JXkdXYImoNDAwwNjaG0WiM2qMBJEBCBCE6G5ZCTBASICGCIAESIggSICGCIAESIggSICGCIAESIggSICGCIAESIggSICGCIAESIggSICGCIAESIggSICGCIAESIggSICGCIAESIggSICGCIAESIggSICGCIAESIggSICGCIAESIggSICGCIAESIggSICGCIAESIggSICGCIAESIggSICGCIAESIggSICGCIAESIggSICGCIAESIggSICGCIAESIggSICGCIAESIgj/ByCCfIAM1y7ZAAAAAElFTkSuQmCC)
Figure shows the pressure P versus volume V graphs for two different gas sample at a given temperature. MA and MB are masses of two samples, nA and nB are numbers of moles. Which of the following must be incorrect.
![](data:image/png;base64,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)
physics-General
physics-
An ideal gas expands in such a way that PV2 = constant throughout the process.
An ideal gas expands in such a way that PV2 = constant throughout the process.
physics-General
physics-
A process is shown in the diagram. Which of the following curves may represent the same process ?
![](data:image/png;base64,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)
A process is shown in the diagram. Which of the following curves may represent the same process ?
![](data:image/png;base64,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)
physics-General
physics-
A resistance coil connected to an external battery is placed inside an adiabatic cylinder fitted with a frictionless piston and containing an ideal gas. A current i flows through the coil which has a resistance R. At what speed must the piston move upward in order that the temperature of the gas remains unchanged? Neglect atmospheric pressure.
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)
A resistance coil connected to an external battery is placed inside an adiabatic cylinder fitted with a frictionless piston and containing an ideal gas. A current i flows through the coil which has a resistance R. At what speed must the piston move upward in order that the temperature of the gas remains unchanged? Neglect atmospheric pressure.
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)
physics-General