Maths-
General
Easy
Question
Let
is given by![f left parenthesis x right parenthesis equals 4 x cubed minus 3 x text then end text f to the power of negative 1 end exponent left parenthesis x right parenthesis text is given by end text](data:image/png;base64,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)
Hint:
In this question, we have to find inverse of function f(x)
. Firstly, we will assume x to be cos
and y to be cos 3
. Then, we will find f(x) for x = cos
and later find the value of
from that equation. Now, finding inverse of f(y). Further, replacing y with x to get the required inverse of f(x).
The correct answer is: ![cos invisible function application open square brackets 1 third cos to the power of negative 1 end exponent invisible function application x close square brackets](data:image/png;base64,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)
Related Questions to study
Maths-
If ![f left parenthesis x right parenthesis equals fraction numerator 10 to the power of x minus 10 to the power of negative x end exponent over denominator 10 to the power of x plus 10 to the power of negative x end exponent end fraction text then end text f to the power of negative 1 end exponent left parenthesis x right parenthesis equals](data:image/png;base64,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)
If ![f left parenthesis x right parenthesis equals fraction numerator 10 to the power of x minus 10 to the power of negative x end exponent over denominator 10 to the power of x plus 10 to the power of negative x end exponent end fraction text then end text f to the power of negative 1 end exponent left parenthesis x right parenthesis equals](data:image/png;base64,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)
Maths-General
Maths-
If
,then the inverse function of ![f left parenthesis x right parenthesis text is end text](data:image/png;base64,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)
If
,then the inverse function of ![f left parenthesis x right parenthesis text is end text](data:image/png;base64,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)
Maths-General
maths-
If
observe the following
![text l) end text delta f equals 2.11](data:image/png;base64,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)
![text II) end text d f equals 2.1](data:image/png;base64,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)
![text III) Relative error in end text x text is end text 1](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMYAAAAQCAYAAABN/ABvAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAOJ5y/mQAAA2ZJREFUeNrtWjFoVEEQ/RxyBEkjIYgcIgQJIuGaEEK4QgISrghyCBYpLOQghUgQEUQkhaSRFCnEJlgECcEmhGCRRkSCXCGIpAghCKlERAIWQUSOwDqDL7B89//M7P+e33MHHtze7g6zs/N2dvYuivKVR4SbUZAgQX6TFqEa3BCkW8V4fjdMeCPUz9jH+DVCf4625r32IMXxS152DBJmCVudIEaEQB9W6r8OcnTKUV8DMf57YiwTprX6shBjBvWGRn+J8KODjgrBH8QrFrIQY4zwyoMY3x3jpggfQZolQo/QhiuEt4Q24QOh5rjGGcGa3hMuxPprjvQrsVO7NrbjLPoOCIfCPpZJwg7WvwN/RAr9kj07al8j7GEdm9B5nDQTDs859GnsGCC8RvwYj0OvY8Qow9Ea/RMOMo0SduHoEtLegtCGFcJFfL5B2FY4w+67S3gY639MuOdhp3ZtBkHdhE+lfaMI1CG0h9AeU+iQEoNJMU84Z/l6UxhjfOictto894mHHe8SiF84YkQ4qST6yzg597Chtqyhz5bPHgsrOeyREqMC2+I2DHjYqV2bSanV0vpWkTHiGWRdoUNKjHGBr5Okbh0GlwW3jCQ7OFOc6iZi2Kg7xnyLnShRQiYynpsqHctpegSfL+GK5mOndo7x3MwDRwYoK/Vn8aFG70v4lK+mfZ52NKJfPxNMFZ0Y2qtUf8KLlEmAxIZZ1BaHCfM0QTeN6xPLIuGOp53aOb7EkB5WRSDGbdhVzRibvYSnuBoOdlPxzXfVB7Hv+En1pIeti9DXk1PG4DT9CdeEfUdxKbVTO6fbM0YN174F5Wmfpv8+apdCEuMWCjKt/uexOmNJ8ELh0iW5brUR6FLb1vGK4vrxUmqndo4vMVYdxWjDkZX/JjG4RnuBw6EXBXRfDoGsqXE6TgyfH/giOKYFR7GcR+E7gTa/fDwT6Nq1go6L5zkUthVrzFbKKeWyjcfyc+SMo09qp3aOLzFGoPvoVa6Kdq0gxOCr80aMCPw4sJxDIDdRExaOGJq/hLjkKk5Te5NbqBW2o+T3eFuqSKdtFMqchfjJ9Ys1Zhxt6TpP4PXjTEowHmendo7JsJmTOCDa0N3IGhA5EaOMzFVJuDHUPe0w8ONGyh5J6rw/JuFPhEGCxGQeLzhBgvzT8hNIYniYZwdsqQAAALB0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bXRleHQ+JiN4QTA7SUlJKSYjeEEwO1JlbGF0aXZlJiN4QTA7ZXJyb3ImI3hBMDtpbiYjeEEwOzwvbXRleHQ+PG1pPng8L21pPjxtdGV4dD4mI3hBMDtpcyYjeEEwOzwvbXRleHQ+PG1uPjE8L21uPjwvbWF0aD5GfSPLAAAAAElFTkSuQmCC)
The true statements are
If
observe the following
![text l) end text delta f equals 2.11](data:image/png;base64,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)
![text II) end text d f equals 2.1](data:image/png;base64,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)
![text III) Relative error in end text x text is end text 1](data:image/png;base64,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)
The true statements are
maths-General
Maths-
Statement I :
is one - one
Statement II :
are two functions such that ![g o f equals I subscript A text and end text fog equals I subscript B comma text then end text f equals](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOEAAAASCAYAAACttbnNAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAANvpXuIwAABMNJREFUeNrtW1FkXEEUHStWVJWIiFhVIiIqaomIqIhQFRERISr6tZZ+9Cvyk4+KqCqVj6qoUhURESEiKipKVUVVhaiIWBH6EVVRy6qIFbG8zrTn2elk3tvZ92Zmd5M9XDqvs3PfnLl35t47L4SYR4RKI6miiouDirLpfioZyB6VGgM6siClnOEocvWdSk6xfznAFvfOJbNpbWAv95NKHO2bBnS0UNmtAGNVMaJDQxyZggnuM2XuhDZsWitGqCwb1jFsQYctJ3RIZcEE906Zc2PDpskVKjNU0lROqaxSeUllUujXQGWOygn6LVCpFfpMS36nG7p0DFHZonJG5YDKbQ8jGEXIyOa8SeW6ZKxeKjsYi/VNKBiRIwiPQSopjJfCu8rQTWUb76aqtxy4V+HAbQ9Q+VqA/zEqP9BnXmKXxawlsW3TNXiZSfybyQRylGGuXx3CkATygWvYHWa4PmsCoWOKxDsFFkPEivBuQbHEhRYJxPrie45ijje4fptCvzY4SjsXrqyGOAm7YCjueO1od0v0suc9aDdjTk4RRl8q7lVPwiSVDczVi3/G1z4citnmAyrPA66lCCs2PUXlqeQ5OxmauPYMnJNHM/rx2FfcXcKA6YxpHjOCU0cktk+h35zH4gR1wlWchOLJ+FZ4Ng+DsxnGmeDezwmXFPhfk/B/FHAtZTBu0+xl6yUvdyK005IjnrV/C/2yhh3QpA4nYK5yJOEmjBMeU4kKz6J4ziONCMWWE5ri3o9nFV6ZrTZKONSRdxq36Q4qnz3CoU8B+oltEyGRqg4VTGFnzxXISQotXE5zYcbrd2caDKtcuA8zD0dxTjqc0LhNs6rPokeSOy8UMFYk/caFUFb8nQmo6JiQhM4iXiNHqNVwEp4S+b2Z6ZMwG0KvTu6nOUPLIjy36YQZFBd16rBm00NEXnpdRELsoh/JsXhMp7iEmWHWI0fRiUI6mlGsKLR7HWsMR5kusbJaHzInFKuhw8h9eLyXFGvqDDqhF/dusSaCk4OFh3eKGPesyM3EkeTGSUNOaNymWYXzF8lfQsZhAOxispfr515WusWCGAzikSRBHjDshIV0bCJ8PsL8/JLtJDefJ/hNLMDCMcP7gN9GwNOXEE7YiY3ErdzeQlt09AGkCY3QyzbLLZzMNrk/EAoXB1ydYRlz9Kuo7hRZ2BKft4Cfu2iz6ueCJie0YdN/d9xD7EbbmEhasjP1kPy9FTPghGSsjEcirRN+OtiO5V6ZsJDons84zLC/YT5bcKTH2JSCLFwr+Ve9PIUDxkm4y/pB8Mzeb8/HiJPYIN15dHqc8qa45wsXUaQoU9z/qzhhH3gPk8d1gvcc+BrS5IQ2bPoc2kmwrwMayPmysE00walqufCtEr6q0Q12Kn60qK9LKD4sSfos2zhNDMCKTbN87hXJ3we6u0lbkeO8wK79rISEvSP5S2s3hM5cAqdbx7q5G9G6R5RiCnzhIopogF+HOKmAD55LadNXkXieIKTYIPmvNIoBy8FGSkjYGPEuC/ddcCdkFd5dkv9sbdyy/lmhKPKGyn2uHSOV+SdtpbbpigsZmBHKLq0fkv8/q6vCTLGmH7lhB/LT1iotlwt++Qa7rkhVKTKKDCKOHMK30SolavgDghG8XeyyFBcAAAEadEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPmc8L21pPjxtaT5vPC9taT48bWk+ZjwvbWk+PG1vPj08L21vPjxtc3ViPjxtaT5JPC9taT48bWk+QTwvbWk+PC9tc3ViPjxtdGV4dD4mI3hBMDthbmQmI3hBMDs8L210ZXh0PjxtaT5mb2c8L21pPjxtbz49PC9tbz48bXN1Yj48bWk+STwvbWk+PG1pPkI8L21pPjwvbXN1Yj48bW8+LDwvbW8+PG10ZXh0PiYjeEEwO3RoZW4mI3hBMDs8L210ZXh0PjxtaT5mPC9taT48bW8+PTwvbW8+PC9tYXRoPj/uizkAAAAASUVORK5CYII=)
![g to the power of negative 1 end exponent](data:image/png;base64,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)
Staatement III : ![f left parenthesis x right parenthesis equals sec squared invisible function application x minus tan squared invisible function application x g left parenthesis x right parenthesis equals cosec squared invisible function application x minus cot squared invisible function application x comma text then end text f equals g](data:image/png;base64,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)
Which of the above statement/s is/are true.
Statement I :
is one - one
Statement II :
are two functions such that ![g o f equals I subscript A text and end text fog equals I subscript B comma text then end text f equals](data:image/png;base64,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)
![g to the power of negative 1 end exponent](data:image/png;base64,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)
Staatement III : ![f left parenthesis x right parenthesis equals sec squared invisible function application x minus tan squared invisible function application x g left parenthesis x right parenthesis equals cosec squared invisible function application x minus cot squared invisible function application x comma text then end text f equals g](data:image/png;base64,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)
Which of the above statement/s is/are true.
Maths-General
physics-
A glass capillary sealed at the upper end is of length 0.11 m and internal diameter
m. The tube is immersed vertically into a liquid of surface tension
N/m. To what length has the capillary to be immersed so that the liquid level inside and outside the capillary becomes the same?
![](data:image/png;base64,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)
A glass capillary sealed at the upper end is of length 0.11 m and internal diameter
m. The tube is immersed vertically into a liquid of surface tension
N/m. To what length has the capillary to be immersed so that the liquid level inside and outside the capillary becomes the same?
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PfWDOOYRgkJSXhypUrqFWrFtq2bYt9+/ZBo9FAKBSiTZs2Nr2B3Guh+CkpKVCr1bC3t9eZ3k9OTsbHH38MADh37hzs7OwMmhIMwyA+Ph7Z2dkQCoXw8vLikjVdu3YNIpEIjRo14ia5nJ2dERsbi4EDB+LevXsl5Lm5uWHZsmXYtm0bBAIB5HI5OnbsCKVSydnulcXNmzfxySefwMXFBadOncKMGTOg0WiQnJyM3bt3Y8CAAZXav8rktVD8Zs2aITMzEwcPHkTv3r055daOYcnMzISvr69RI+IXX3yBffv2AQA6dOiAU6dO4f79+2jfvj3kcjkePHjAZTCmf15q3dzc9MpSq9UICAgA8K9//lVYLUVE6N+/P6KiotCqVSv07t0bz549AwDUrVvX5rMwvxZeHXb7S3b7G1a52a02hUKhXoXXaDQoLCzU+SgUCuzduxdTp04FUPSkEIlE6NmzJwoKCkpstWmIzMxMjBo1igszDg4ORnx8fInRvqJTfrP3IyMjA9WqVeOUHij6sdp67p5XWvHlcjk8PDzw+PFjALoznhcuXEBwcDCcnZ2RlZWl1149deoU7O3t4ebmxn0cHBxw4sQJrFy5EkuXLgVQFBHJbhzx8uVL1K9fn5NhaD9ZVoEGDhzI5czRhn1iTJo0CcOHDzf1FliMSCTiBggWlUpVItmtrfFKKz4A5OfnAyja5GHQoEHccXaKn2EYnVTgpOVvZ+PY5XI599E+zi7u0J40cnBw4JR55syZmD17NgAgLy+vzH4KhUI4OjoiPz8fXl5e8PPz42LxR40ahfXr15eZslwfZGF8zrZt2/D111/rJKUNCAjAhg0b8PHHH2PYsGEYOHBgiR+GLfDK2/hCoRBKpRI1atQA8G+CJtbmzs3N1ZnxZBgG33zzDXJycrB48WJERUVxozYRwdXVlZOl7bnRR1paGgDgnXfe4SaSyuLWrVvo27cvtwNLSEgIoqKiuJ3J9bXTtGlTZGZmIjIyEvv27UNERARcXV3Rrl07znwyF5VKhXPnziE4OBgFBQUgImzatAm9evXChAkTkJmZCZFIhDFjxnAZnm2FV37EZ2F3BREIBLh58yYGDhwIHx8fLhMBAMyYMQO9e/fGrFmzuO12WrZsiebNm6N58+Z46623sGrVKmRnZ2P9+vVITExEREQEoqKiuPWvHTp0wKNHjwD8G04skUjg5+dncAROS0tDSkoK94NKTEzEo0ePsHXrVjRp0kRvuAE7Irdo0QIZGRn47bff0K1bNy7cwRxIa5bb3t4e33zzDZYsWYIlS5agV69eAIp+pM2aNUOrVq1w584ds9t6XXnlR3zWLGGV6dChQ5g4cSKXY37r1q2QSqWws7PjRq3w8HDMmTNHr7zt27fj/Pnz6Nq1K8aOHYvnz58DADZv3gy5XI4OHTrAz88P27Ztw969exEWFobp06fr9KE0unbtisWLF2Pu3LkAilKABwYGwtPTE2vXrtVrLvXs2RPVq1dHUFAQBg8ejLp16yIvL4/bRcVUWI/XiRMnEBsbi1OnTiE8PLxEPZFIhOrVq0MikVS627UyeKWvWCQSYc6cOfjqq684j4hKpUKHDh1QvXp1qFQqZGdnw8HBgQsBlsvlGD58OJo3b67Xp8+aPwMGDEBwcDDUajXGjx8POzs75OfnY8GCBQCKfgjPnz/HyJEjER4eXur8ADu6JiYmYs+ePahWrRoWLlyInJwcLFy4kKvHKp8+OWlpaVi1ahXq1q0LoOj9JTc316x7xjAMjhw5ghEjRkChUKBr16566xUWFiI5ORmOjo4oLCw0q63XmVde8RcvXozly5dzNnzfvn3Rt29fg+eWNkM7bdo07n+NRoPGjRvjhx9+0Kl3/PhxPHz4EDVq1OBy4JQ22tvb20MqlSIiIgI7d+6Eo6Mjzpw5g9atWwMo2tc2JSUFHTt21NkAguXQoUPo168f6tSpAwBISkrC7du3uRidw4cPo0+fPqXOI+jj1q1bCA4OhkgkwokTJ9C9e/cSdbp27YobN25AIBDoLa/yVGiAhJn06NGD1q1bR5mZmeXajkajocjISGrTpg0FBgbS+fPnueP6CAoKogMHDtDcuXMJAAmFQi52XqlU0oMHD8jHx4cA0LBhw+jly5clZOCfNbk3btygq1ev0sSJE2ns2LFEVLQbe+3atembb76hnJwcnfNKi9UpK76n+LHp06fTpEmTbDJm57VQfCKisLAw+umnn8q1DaVSSdWqVaNnz55xx8pSiqCgIPrf//5H27Zt01H6Jk2aEBGRvb09ASCBQEAAaMiQISVkuLq6kqOjI3l5eREAWrx4MRER5efnU1xcHEmlUgJAsbGxOufxC1Es45U2dbS5fPkyAOssMikNkUiEFy9e6Bwz1JZUKsXIkSMhkUgwYMAANG3alJvEqlGjBhITE7nJIm9vb51zc3NzIRKJcP36dZ1JMyKCRCJB/fr1oVarMWDAgFL3w+Uxj9fGncnyqk21s/356KOPoFarcfPmTa4sISGBy3/57bffYsWKFVyZVCqFu7s74uPjdZReW6ZarUZiYiImTpzIx+FbmddmxH/VYVMEFufcuXMoLCzUGbFjY2MRHBwMoOgpEBMTo3fpolAoREZGBgoLC/ksC1bmtRvxX1VYxczOzkZgYCCCgoKgUqng5uaGatWq6eTyCQwMRHR0NGJiYhAdHc3tnKLNy5cvMWvWLHTr1g2HDx/m0whaGX7EtxIMw+Cvv/7C//3f/3Ezv61atcKePXtK5Ld3cHDAm2++WaY8FxcXDB48GB06dEBgYCCXgpDHOvCKb0WePHmCe/fucYvTb926hfT0dLM2drC3t0dISAhCQkLKoac8vKljRRo3bowRI0ZwZs/EiRP53UxeUWxuxNd2h1rTNUpEqFGjBtatW4eCggKIxWJ8//33ets1pY+lHXdwcLBKv20Vm1N8hmFw7do1+Pj46A0hsEQuEUEsFuOXX34BAFy6dAlZWVlo27Yt3NzcSij0yZMnoVar0aVLF51AMYZhUFhYiNOnT0MsFqNLly7c8bi4OKSlpeH69et8+nBLqIxZs8qmYcOGFBERYbGcoKAg2rx5c4njGo2G4uLiSCQSEQBatmwZKRQKrlylUtGlS5e4md69e/eSUqnkypVKJe3cuZMrv3r1KhER5eTkUNeuXbnjZaUR5ykbm7TxXVxcytVUyMvL49yZDMNg1qxZOpNXMTExXLQmwzDo37+/zvae7Goz9unQunVrpKen491338WJEyd0TDUe87BJxa8IWL89q5zaPzTtdbxsubbZwi6J1FZshmHg4uJS4jiPefCKXw64uLggKyuLCyX++eefuawOQFEmBnY5IgBcvXpVJzS4T58+OH/+PPf/06dP4e3tjcOHD9t0Lhxrwiu+hbCj759//gkHBwd07twZQNEI/9dffyEhIQH9+/cvUb9mzZrIzMzEw4cP8dZbb5WQGxYWhsTERCQlJcHPz487vnbtWrx48QJff/01srKyyvPSqjQ259WxNm5ubti3bx9GjRoFhUKBM2fOoGvXrjh69Chq1qypU5f+8epIpVJ07NgR7u7uOHfunE4Zi0gk4hanaMMGq/n5+ZW5mQRP2fAjvoXY29vj1q1byMzM5Gz3kydP6rXD2bCGXr164c6dOzh//jy6d++O1NRUo3L+a2OLywWtCa/4FpKbm4sRI0age/fuUKvVEIlE2LBhg96dzQEgPj4ekZGRXPnx48dLrAEo7UezZcsWDB06FNHR0fD19eVfci2AN3UspKCgAIGBgfj222/h7e2N4OBgjB49utT6TZo0Qe/evfH7778DKMp/z+beZGEYBjKZDOvWrYOjoyPGjx+PgwcPYvbs2Xj58iWePXsGf39/ODo6luu1VWV4xbcQ1kQJCQnhEkDt3bsXQqFQZ1E8a8PXq1cPe/fuRa9evSCRSHQSVcXExODevXtwdXXF3bt3MWvWLABF9nz//v1BRBAKhVzqEX1pQ3iMg1d8K1JYWIiDBw9yqcsPHz6Mrl27QiwWg2EYZGZmIjY2Ft7e3jh+/LjOuenp6Zg2bZrOcTYM4oMPPkBISAiSkpKQn58PPz8/CAQC3s63AN7GtyLnz5/Hxx9/zD0F3n33XURHR3Plq1atQnh4ODp16lTCFdmvXz8cP35c5yWXteE9PT1x+/ZtfPTRRwCApUuXYvPmzbw70wJ4xbcixWdrgX9nZCdPnowvv/wSDMPg6dOnXP5OFnYhOmvOODo6wt7eHi4uLnj27BlEIhG2bdsGIsKQIUPw5MmTV2798esEr/gWoh1+0K5dOy5nJwA8fvyYW2xeXEmLe30OHDiAkSNHAgB69OgBmUyG3NxcZGRkcCEM2vBKbxm84luAh4cHRo0aBYlEwr2IBgUF4dmzZ3j27JnOqL5q1SosWLCAi9vX3qiBZcWKFUhNTeXCmsVisU4Mj/aThE2byGMe/MutBQgEAm6nk++++w7Z2dnYsGEDfH199dafNGkSevfujZo1a+rdecXFxYULRCsO6xVasmQJtm7diqysLH51lwXwI74etEdSY0ZVgUAApVKJixcvllpHo9HAw8MD1apVQ//+/UsNNmPby8jIQPv27fH+++8DKDJt5s+fj6VLlyIxMREZGRk2meXYWvCKrweGYTB79mwcOXLE4A6KQJFSBwcHY+3atXrrEREEAgEiIyPx8ccf49y5c/jtt98wZswYbl8vbZlstoYLFy7g0KFDGDx4MDQaDQ4cOICcnJxSZ4V5jKdK3cHio7M5NnBERARmzpyJtLQ0uLu7l1k3Pz8fvXv3RkREBJYtW4YOHTpwZcuWLUNERARkMhn3Azl37hwuX77MvRBv3LiRU/z9+/dj5syZuH//PlJTU3HixAlOwX/55RckJydj0aJFqF27NpeSkH/BNZ8q9axkN0S4e/cu2rZti1atWpl0/vr163Hr1i1IpVLs3LkTtWvXLnORuFqtho+PDz7//HPONpfJZPj555/x3//+F0BRPv8pU6agWrVqCAsLQ7NmzbjcmoMGDYKLiwsuXbqEqVOnIiUlBbdu3cInn3yCTp064cyZMwCK4vMlEgn69u2LvLw8HDp0CH///TefZMoSKmB5Y4UyefJkql69Oo0ePZouXrxIx48fp+PHj9O5c+e4Oq1bt6avv/6a+1+pVNKuXbu4LMcshtJnh4eHEwCaMWMGdyw2NpZbE8tmSd65c6dOeePGjem9997jjrGZktmMy7169SK1Wk2hoaHUqVMnrp5areb+3r17N9WvX9+EO8OjTZUa8YkIq1atwqpVq/Drr7+iffv28Pb2hlKphFQqxZUrV1C/fn3k5uZyAV4JCQmIjo7G3LlzkZiYqCPPkCnB7sul7V2RSCQICAhAamoqNBoNXF1dua1IiQgNGjTA3bt3deSEhYXh0KFDUKvVEAgEeOONN7i9vrTRtu3z8vJ4U8cSKvuXVx4UH6nlcjm5u7uTnZ0dNxpv2bKF1q1bRwCodevWZrUTFBREO3bsKNGmWq0mLy8vYhiG4uPjSz1fKpVym10MGDCAANDChQuJiCgjI4Oys7NLPZfPj28ZVerllqX4SMhu16NQKNCoUSMAwIgRI5CQkAAiQmRkpNltsXvEarcpEAjw8uVLaDQa1KtXT+95UqkUHh4e8PT0xP3797F7924QEebPn48DBw7Ay8urRPpwHutRJRW/LO7du4fg4GDMnj1bJ+VHedGpUycwDIPNmzdzxx48eAAfHx/u/5CQEJw+fRoAsG7dOvTr1w9A0aZw3t7e3G6JpOWl0hfGwGM8VcrGN5bjx4+XOkNqTdq2bYtLly4BAMaNG4e0tDTMnTsXCoWC28WRDT1mlZvdHFogEECj0SAjI0PHfblw4UJs2LAB+fn5XI59HtOxOcWnf2Jl2L+tmTuTXTnVuXNnODg4cErPhjawAWwNGjTAgQMH0LdvXxARNm7ciHfeeQcAMGHCBMhkMixZsgRAURpCNkX4zJkzsXbtWs73rx0gx2MaNqf42opuTa8Iw9EfN9UAABoaSURBVDCIj4/H2LFjcfXqVZ0yjUaDd999F/PmzQNQ9M7Rp08f/PLLL1AqlRg0aBDEYjGICO7u7pg2bRrq1KkDLy8vtGnThpNz6NAhyGQy7mnAYz42p/jWRCgU6gSbJSQk4MyZM5z5AgBjxoyBv78/evfujYYNG+Lp06dYsmQJ/Pz88MUXX3Dnsk8MIoK3tzdGjBhRor0lS5Zg+vTpnNuVTxpbOoae5mYp/rp165Cbm2vTj1oHBwekp6dj165daNiwIZo2bYqgoCC89957OHToEACgf//+WLZsGbf/VWpqKubMmcOts/Xy8sKwYcNgZ2fHKX3xFVjaeTL79OkDhUKBCxcuIDExEdHR0fjhhx/4GVwtFAoFhgwZUiKnUXEYItMDWnr27Im0tDSbHnGEQiFu3boFiUSCtWvXctGWcrkcvXr1glgsxrFjxwAA0dHRkEql+Pnnn/Hjjz/qmCrp6enw9vbmlDw1NRVXr16Fv78/3n77bZ022TpqtRoRERH46quvEBYWxieW0iI3Nxc7duxA8+bNy65YsdMGVYvg4GDas2cPKRQKSkhI0FsnLS2N3nrrLW7iTPvz5ptvkkwm4+rm5ubSmDFjCAD5+/vTo0eP9Mr84osvCAC1b9++XK6rKmAo3MTm/PjWRK1WQygUYtmyZZgyZYreF87w8HDcuHGDM1nEYjG8vb3RoEEDREdHQyaT4enTpwCAKVOmcMmonj59qncLUODftb3s5BlPSQw5LnjFt5CMjAzMmzcP3bt359bXauPh4QHg38mnHj16ID09HbGxsVAqlQgMDERAQAAuX77MTWqxPyAvL68S8nr37g21Wo3ff/8dUqm0vC6rysMrvoWwI8v48eOxaNEinczGABAVFYUePXoAAIYPH85lUGPTiOfm5gIoejKEhIRwi1kaNWqEx48f68hq3rw52rZti4ULFyI9Pb1cr6uqY3V3JulxI+k7Zsr55sgxpj/GyjO2Xp8+feDh4QF7e3uIxWKkp6fD0dERhw4dQlpaGiQSCVdXrVajoKAAwL+zty9fvuTW5bLpRgCgRo0aSE1Nxa+//solqyI9PomQkBAkJiYaFc6Qk5ODNWvWYMKECQbrsty5cwehoaEl9tzNycnBl19+iblz5xotCyiKMK1duzYKCwv1ripTqVSoVq0at28wYL1JR7MUv1WrVnj27JmOV0cul6Nx48acJ0MbhmGwdetWzJgxg3v0FycrKwtz5szBtGnTSm2XYRisXLkSX331lcHVUXl5eejVqxe2bdvGHXv77bfx+++/w8fHh7uBJ06cwMCBA/XKM6ZPxQkPD8eZM2cgFArRpk0bZGRkQCaTYePGjVwMDlBkxiQmJiI0NBTZ2dnYtGkTl17k+fPnCA0NhUQigUgkwo4dO2Bvb49mzZqV2fZPP/0EuVxulGKoVCrUrVvX6OsCgLp16+LcuXMl3NgqlcqsjfQcHR1x+PDhUlfK0T+b6WnDMAwiIiKwdu1auLm5QalUws/PD1FRUSa1bZbiz5o1i5tBZFGr1Vzudn20adMGK1euLHU0KiwsRGhoqMG2u3TpAk9PT4OjmlKpRO3atXWO3bp1C926dcP27du5ncWDg4OxYsUKvfKM7ZM2rMIDwLx585Cfnw+JRIKzZ89i2bJl3IspwzBwdHREdnY2AOCHH37A3r17kZWVhQYNGmDdunWQy+UQCoXo1KmTUW0bdOHpwZQR1MnJCW3btrWKLKDoXhV32RrDe++9h8DAQNjZ2UGj0eg8SY3FLMXXHrmKU5pp0aBBAzRo0MCgbEOmTpMmTdCkSRPTOgxg8ODBYBgG0dHRXFpujUaDGjVqYOjQoWb3qSy0k8Z6e3vD1dW1xJfUs2dPCAQC5OfnQ6lUQqFQoHnz5ujTp4/J7ZmDtcM2yhsiwltvvaV3FxlTsLqNr+/iTbkhxmQ1MASrqM+ePcN3330HBwcHiMViLi4mMjIS1atXN/oHZOkXSkRo164d2rVrZ9I5/AqrkljrnlTJWB2GYZCYmIgdO3bg4sWL8Pf3x759+7B7925s2LABYWFh3NOjIhTMHPm80pcvVVLxAeDUqVP4+++/dVZXaTQavHjxAp07d4ZarcaLFy90FoTw2A5V0o9PRBg9ejR27dpVwmOQnZ2N7777DrGxsSa58vTBMIxZyZ3UajUePnyo46YzFT6plGWYNeLn5+dDo9GU+TgmIjg5OZX4gjQaDfLz8w2eKxAI9OaXNIayYu7Z/52dnS3e3VytVnOLQtgVVIZwdHTEjRs30Lp1awBAcnIyfHx8uBVZxuDs7KyTqMpUZDIZ1Gq13kjQ4j768oC9b2U5MUQikd6tjgoKCrgd44vj5ORk/D0xJwDI19dXb9BV8c+9e/dKnHvz5k2jzq1Vq5Y5XSsTOzs7un37NhEVZULQzlNjKrVq1TLqOsrzExYWZlbfQ0ND9crz9PQ0+36YwpkzZwxeW48ePfSe26NHD731RSIR5eTkGN0Hs8KStdeBlgYRwdPTs0RiU5VKhczMTIMjvkgkKnNewBzs7e0RFRWlN6bGVJRKJYKDgzFu3DiMGzcOOTk5Rp3n4OCAO3fucP7w+Ph4eHt7mzTiu7q6Yu3atdiyZYtOPn5jkUqlUCqVep+G2jPGQFHg3OrVqw0+HeVyOYYMGaKzp1dpsHmOyhrx7e3tuZ3htcnOzoZCodB7rre3t9Ejvlmmjr7gKWMRiURV4oVSLBZDJBLB3d0d9vb2qFatmtHnatf19fU1a+G7h4eH2csPS5s918eMGTMwZMgQg5mZ1Wq10XohFovN1gF9PwZzqLJenYqAiMxaBKI9upsy0mtTEYtPiAgBAQEltiM1dM7r4IrlXQM8pVKV5x94xeexSXjF57FJKkzxzXAe8fCUG2a93LLL5oyN+65Vq5ZFniBrYe6LZGmYO3Or7SHh97GqHMy66927d8eTJ0+MSi+iUCiwYcMGjB492mBdmUxW5qwu/TMbrC/+OiMjA25ubmUqko+Pj065TCaDUqk0ykWmVCqRlZXF9c3V1RUqlQo5OTkoLCxEdnY27OzsjJLFhkUDRYlh1Wq1zo+S/lmAYWixjXb9zMxMo56qnp6eJv9YCwoKyszHX9b3UhZEhIyMjFLLRCJRma5X9r6z/fLy8irfmdvyYvHixQZn9BYvXqz3XIlEQlevXjWpvfnz51O7du2Mqnv58mWDfevYsaNBOUeOHDFqVjY0NLRMOdr58QsKCsjBwcEouc+fPzfqerVZsWKFQblz5swxWW5OTg6JRKJSZTZq1KjM8/fv31+xM7flhUKhKHVWDvh3Ro9dxaRNbm4uJBKJSdndFAoF1Gq1USOVWq3WeRq5uLigfv36mDRpEiZMmICcnByIRCKjZEVFRenE6lSrVq3EiF88PWFxtmzZguXLl+PBgwcAiq6fDPjQiQguLi4muxwLCwvLXNJY1vdSFvRPlmh9/TbmHqhUKi5Wio0zKteZ2/LCnJvHUnz2sywlYMtMaUsoFHKpALWPsYpevKwstM0hd3d3vcFYplKeac/t7OzKJR8/wzAW9VskEpl037Wpsu5MhmFw4cIF+Pn5oVevXgCApk2bIjY21qqpwc0JG9CedeXT/1UOVVbxgaI89MOHD8eRI0fQpUsXjBw5Ev7+/pXdLZ5XgCqr+EQEHx8fLmXH22+/jfHjx8PNzY2fU+CpuorPUlhYCAD48ssvAbw+QVQ8lmFocKuSis8qd05ODo4ePYo+ffrgjz/+0Jl0M3bUL4+ng3ZsO/tia2o7pb1smiKnIp98FdHWvn37sGPHDrx48cLg4Ga2V+fu3bvIzc01e+0nwzBo0aKFUe7HW7duGcwQptFo0LRpU275GZud7MSJEzh58iQYhsGLFy+4WHg2/UhCQoLeSS+VSoWgoCCj48ZfvHiBuLg4gzOx9vb2nAsSAM6ePYvOnTvDzs4OSUlJSE1NNXhPnJ2dcf/+fb1tMQyDv//+G2lpaaXKUalUaNSoUZkLfe7cuYO8vDyd75d1W5qTuIphGDx+/BiPHj0yeraa/pnIa9GiRal18vPzcefOHRAR5s2bh+fPn+PIkSOGvzejPf7FaNu2LYlEInJxcTH54+zsTB4eHpSbm2tUW8HBwWRvb1+mTIZhKDo6mjtnxYoV9M477xARUWZmJgUEBHCbKbOsWbOGAOiVB4DbvLk0goKCaPPmzUREtGPHjlJlaX9cXV3JycmJm3gRCAQUGxtLRETTpk0jAOTu7k5ubm5lygBAb7/9tt5+DR8+vMy+AKA//vijzGtr2bIlicVinfMcHR0pMDCQnjx5QikpKZScnEzJycmUlJREWVlZZX+JRLRo0SKj7pF2e4aWoEZHRxMA8vDw0DluKD/+KzVzWx4YugGWoK34phAXF8cpPvvj1+6nSqUyKOPHH3+slJ3NMzIyCAAxDEMCgYAEAgEBoLlz51Z4XyyhStr42ryKL7JKpbLE32w/V69eDZFIxM3sloa1A+6MxdPTEwqFAnK5HAUFBSgoKIBcLseCBQsqpT/mUuUVvzLIz89HzZo14eTkhIcPH3LHyYgXPFahX+XdTtiZXPZjb2//2m0EaJOKb4wCWoJarcaTJ08gk8nQo0cP1KlTB/v27SvTo8QeY6fwjc3awGMeNqX4ffr0wcOHD8vd/HFycuL2CYiPj0dSUhJmz56Nbt26YeXKlahVq1aJcxiGwa5duzB58mTUqVMHBw4cKNc+2jyV+4pRsQCgmzdvWk2er68v/fDDD6WW79mzh5ydnXVCbf38/GjIkCHc/ywrV64kAFS3bl26du0aEZX9Yv7DDz+Qr6+v1a7F1hAueN3eSixgyZIlGDVqFHx9fa0ij2EYhIWFlZp+o1GjRnB3d0dQUBC6d+8OALh37x7u3LnDPXUKCwvRuXNn3Lt3D+7u7pg/fz7atGljcIaZYRgEBAQgLCzMKtdSFdC+Z4bun02N+NopBC1FezQubWQufvzy5cvUp0+fEmnwIiIiSKFQGJRnStvGUh7u3vJ0IRuS//PPP1NKSopBGRW+EIUqMVbG3t4e0dHRpe4fWxrW6LO2DKlUiq5du8LR0REXL14EAOzfv19nB5WKJCMjA9euXbN4p3p2O6iyZlr1ceHCBcjlcoNRAEqlEi1bttS7fvvkyZOws7PD1KlTsWbNGm47ptIwO2Th0aNHKCgoMFohNBoN3NzcjM7KpVQqkZCQYHDVT506dYzus0AgwIMHD+Do6Ai5XG6wvlqtRvXq1UvkkzQH7Uewh4cHrl+/DgBo0aIFEhMTK3UxfnR0NHr37m1xej6ZTIb27dvjyJEjJp03duxYpKamGvzhZWdn4+jRo+jcuTN3TK1W4+rVqxgwYAAUCgWSk5Ph5eVVfqZOy5YtCQCJxWKjPgCof//+RstPTk4uUz4AatCggUl99vDwMLnP8+fPN/XWmE1Zj/CcnBySSqWUmZlJBQUF3HG1Wk1ZWVkklUpJKpVSVlaWzv95eXlmt2kuFWnqXL16ldzd3U2WYbbiazQasz7WbsMU7O3tORu/vPpcXtStW5d7J9AOD2AHCPbDMAwxDGPSAvjXHXO+I7P9+AzDmPWxdhumQFqPv/Lqs7VRqVRwdnbGzp07kZeXB7VaDblcjv79+3PlAJCamgqNRoM33ngD3333HYgICxcuRGpqamV2v0Iw5zuqkhNYpPW+TsXe3Yv//6ojFApx/fp1NG/eXGeHmaysLABAzZo1ERcXB39/fzAMg8LCQi5Wf8qUKThx4kSl9f1VpkoqPsMw2LJlC4YOHVrpI7alMAyDhg0bQigUcgvbGYbhth4Si8WoX78+gKKZ6Tlz5mDAgAEAijI/FN/kmqeIKqn4ABAeHg4vLy+MGTOm1Dqv2+gvEAiwfv16KBQKrFq1qkT5n3/+iZCQEHh4eLx211bRVEnFp392Up86dSoEAgGWLFkCQP9GcAkJCRg8eDC++OKLyuiq0bCKvGfPHuTk5KB169YllNvZ2ZmL6nzdn3TljVl+fDJjQsfQOabKLKs+wzAgItSoUQNTp05F/fr1MXv2bDAMw2XmunjxIq5cuYLc3FxIpVKzE1lVFAzD4I8//kCdOnXQr18/vXXy8/MN5umx5n02l/KQaWobZik+wzA4e/YsMjIyDMZhFxYWokWLFgYnmhiGQVxcHKKjo8vM2qVUKlG3bl2EhoYalAcUZdvq3r07Dhw4ALVajcOHD6Np06b47bffcPz4cQwaNAiHDx8uU9arwPXr17Fx40bMmzcPjRs3xrVr19CyZUuu/PTp03jvvfcM5g0q7bujfyYE2eRb2vUTEhJw8+ZNi7OpGfvdaVNYWIg///zTpDY6depkcNLR7JCFHj164Nq1awZzRUqlUqxduxaffvqpQZnff/89vvjiizIz5GZnZ2PUqFFYvny5QXnav/qaNWviyZMn8PHxQV5eHrZv344PP/ywRL1XDSJCXFwcGjZsiM2bN+PDDz/E4MGDkZGRgcuXL0OtViMqKgpt2rTB6dOn0bFjR4PXou+7UyqV8Pb2xr1790rU37RpE6ZNm2bSpnH6MOW7Y8nKykLjxo2h0WiMSmyQnZ2NY8eOGQ7eq6gJA1MCr8qrD2KxmOLi4iySUdEolUry8fEhT09PcnFxIQcHBxIIBDRmzBgiIkpJSSGRSEQ+Pj4EgCIjI8uUVxH3uTJkmtqG2aaOtc8xZ3LLVOzs7FBQUGCRjIpGJBIhLS2t1PKaNWvqrOE1REXc58qQaWobr1Sa8PJGJpPBwcHB7FxAPFUHm9IAiURisdIrFApUr14dzs7OSE9Px+effw6GYSCRSLiJo7IwNM7Y0DhUqdiU4lsDsViMw4cPQyQSoXbt2ggICEB8fDyGDh2KmJgYg+ezmc4CAgJQr1497uPt7Y2dO3e+FubXq0Jpg4Qxg4fZ8fhkpCfE2HrWatec9kw5RyAQoEWLFrC3t8ewYcMwdOhQeHp6okmTJrh8+bJRMnx8fPDVV1/ppNJTKBQmL+AwhdKusbK+R2u0xQ4igwYNgkQigUKhwN69e41a82G24jMMg++//x6XLl3Su6OHQqHAihUrSu2ERqPB2LFjkZ+fb1ROlry8PMyYMcNgoiWGYbB7927s27evzG1kgKJNzcLDwzFp0iSD7RcnPT0dH330EZd/kojw8uVL/P3331i6dCmWLVumdzMyIoKbmxuGDh2qV672l56dnY0JEyZYFCWqVCpRo0YNfPPNN3rLGYbB3bt3sWjRIr33Kz8/Hx988AEGDhxoVvvTpk1DWlqaUfky8/LyMHLkSG59sjG4uLiga9eusLe3h1KpNHp3GYu2AmKYou0u9dnNxtjSAoEAQqHQqLpCodDoL7+sfhVv31SFUqvVWLduHWbNmoWgoCAAwJUrVxATE4PJkycjKSkJL1++xOzZs7FixYoSW9WY6t0y5jrKwphrNPQ9WjLSs3KN1QdTZ5V9fX2xePHiEsfLzatjq6ZOQUEBJBIJNm/eDHd3d6jVapw4cQLBwcH4/PPP8fTpUzg7O6NatWp49OgR/Pz8TOpLeVEVTR1LsMjUsWY9a7VbHnMM2tjb24NhGCxcuBASiQQZGRlYsWIFNzPt7++P3NxcjB492qCpVZGUFddkyfnlQUW09Urtevg6kJiYiP/85z+4ffu2zuJsdpRSqVRISUnB0KFDrbKbIU/5wCu+Cfz1119o0qQJcnNz4ezsrFPGjlJ5eXlITEyEg4MD75N/heH9+EZy5coVNGnSBECRJyElJaVEncePH2PatGno06cPzp49a1IoAU/FUu4vt5aeY21M6YN2XaVSyYXyqtVqVKtWrYQblt39vKCgAE5OTty2RJXV/4qU9Sq2VxYWxeqMGDEC//vf/wzuTp2VlYWZM2di/vz5JslXKBQIDg6GTCYroWQKhQJBQUG4dOmSyf0ePHgwDh06VMJcYcnJyTEutLWSWL16NWbOnIlhw4Zhw4YNaNKkCa5fv27WYpqffvoJ48aNMyrkWKlUwt/fH7dv3zan2wCAX3/9FZ999pnRIc7sj4XNLWotLFL8a9euISUlxWAGrMLCQjRs2BAhISEmyddoNPjzzz+hVqtLjBRqtRqurq7o0qWLyf2OjIwsM3OXUqlEhw4drJJBrTxITU3Fl19+iY0bN6JRo0a4f/8+ZDKZWS/TSUlJuHHjhlGLTDQaDRwdHU2aYCpOcnIyrl27ZvSiFlbxe/bsaXGKQ214U8dKdSsKtk979uzBiBEj8M0338De3h5DhgwxeVcSWzZ1yt2Pb+k51saUPrwK/S0NmUwGd3f3MrNIGKKir+9Vup+8V+c1g2EYxMTEICEhAcOHD6/s7ry2vHYLUSrjcfkqPaIBYOTIkYiJicHly5dfub69Llh1AkuhUCAuLq7UgCSNRgOJRIK6deua3QbDMJBKpUhJSTHKpiUiiEQio3LiExFiY2O5l2m1Wg1fX19Ur17d7P6WB/Xr1+cmx3ilNw+rjvgxMTFo1KhRqW41hUKBVq1a4erVqxa1s337dgwbNswo951SqYSPjw+ePXtmsK5KpYKvry+ysrIgEomgUCgQERHxSu3hqj3CW2u0VyqVyM7ONhj8JxaLLc6hX1ymVCo1e4bbkj69dqYOj/U5evQoevbsabBes2bNcOvWLaMU1ZgfZG5uLjw9PS3arJrtk6nwis8DlUqF/Pz8MpXV0dERV69eRbt27cr0pyuVStSpUweJiYkG2yUi5Obmmv3kIiIIhcJSJyLLgld8HqNRKpVITEws892KNT8CAwMrsGemwys+T5XDmCeISV6dgoIC9OvXDyqVivcm8LxyFBYWYteuXQbzhwImKr5AIMBbb72lN3aGh6eyUSqVRgfq8aYOT5XDGFOHD1ngqXIYY43wis9jk/CKz2OT8IrPY5Pwis9jk/CKz2OT8IrPY5Pwis9jk/CKz2OT8IrPY5Pwis9jk/CKz2OT8IrPY5P8P8bVxCeOEZ9TAAAAAElFTkSuQmCC)
physics-General
physics-
Water flows through a frictionless duct with a cross-section varying as shown in fig. . Pressure p at points along the axis is represented by: A resume water to be non-viscour
![](data:image/png;base64,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)
Water flows through a frictionless duct with a cross-section varying as shown in fig. . Pressure p at points along the axis is represented by: A resume water to be non-viscour
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAPcAAABcCAYAAACyVyN+AAADtElEQVR4nO3d23KrMAyFYYfp+z8y6VWmDE1igXyQl/7vdpPQTbyQEQ55PJ/PZwEgZ5v9BwDog3ADogg3IIpwA6IINyCKcAOiCDcginADon5qG7DGBYjl8XiYtqNyA6IINyCKcAOiCDcginADogg3IIpwA6IINyCKcAOiCDcgqrr8FMAc1mWmn1C5AVGEGxBFuAFR1WvubSP/SvZ9n/0nYJBquBkM63udoPksc6FbnsAr1IQ8F8KdCCHPhXAnRMhzoFsmytII3fe97Ptetm2jcSroUfuVz+MqmfMZvjYgem8f4fU9X2PZ7lvV3bbtUlU+vj/VfD7vCrVquHn66druTr0J+nyEGyZXq/j5tS8EfRzCDTNPwI/vcUbg+yDcgbRqSq0WFgLfB+H+gls9/4M36lhcbZ7iP2+4l7rPze2a6+525lvv94zPss5bWJcK9x2eLrH3vUazzFQ+/dvopln0Y6nAPC2/MujvnpUVP3DPPezaayz7VDymWXDNja8I+to8AZeflre4/bOy4/+9ZYORhtmfVk3Ld8fUU1xlK/eoTrl3iWsmLS5RLMev5SWO5f17fqaeyi0Z7lbVmltpmC31tPzdNSVhBIyV+1tTxrI6qee1Xqvrm9otIk4YmCHFtHxmyFYN+JV+QOuvy47gPdF7jo93H9b3SxHu2aIFfNayUo+Rja7ox8O6Hp9wDxAt3GejlpVirOHhbrlabaXBZwn4p21qlbbXstcVKzz+ULkHil7BoUXmVthK3xTKvvIN8YUKN9bjvdZf6YQ+g2fmHCrcK1TCrNNyT4hX/hrtykKFO7qswS7FF+KMxysC0698RvlwqADX9F6IQic+tpTd8juLHaJU7RGrqqz7nn0sMpDplvfSaplihMHM8ltY3Q73lS+MvPNu29Y/UDdjUHoWq5zNDhOhXlvoafnstcKz9z8LoY5Ddlp+fkTQrMGWaZBHaqDCJ3Tl7kW9636nx0C1jkm2ctfcnTYrDuC7x4JQ65Kp3Fmvjz2YgseXtnIf9XqEryqCrU8m3EcM2u8Idg6S4VbSegkpwc7jVrhbPYmlxe9ljXoIYOvXWgPWMogEOxeZhho+owexLhpq+IhqnRePwRBGsHMzVW4ehbMmgp2bKdwMEmA8z/V2KUzLAVmEGwjIW7VLIdxAOC2CXQrhBkJpFexSCDcgi0UswGQtq/URlRuYqFewSzFU7p47B9APlRsQRbgBUYQbEEW4AVGEGxBFuAFRhBsQRbgBUYQbEEW4AVGEGxBFuAFRv8Wjd1jcbv9VAAAAAElFTkSuQmCC)
physics-General
physics-
A cubical block of wood 10 cm on a side floats at the interface between oil and water with its lower surface horizontal and 4 cm below the interface. The density of oil is
. The mass of block is
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)
A cubical block of wood 10 cm on a side floats at the interface between oil and water with its lower surface horizontal and 4 cm below the interface. The density of oil is
. The mass of block is
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)
physics-General
physics-
Water flows through a frictionless duct with a cross-section varying as shown in fig. Pressure p at points along the axis is represented by
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOgAAABiCAYAAABagp/GAAAFWUlEQVR4nO3cS0hUfRzG8Wd834huiyRBIgyRCKEQOxMZaaGbxFZBbqLcxn9auAiCiGACyaCNYdMQBA1EKzcToaFGCV2gywzNLhIhCNx2WQQxi/MuokXO+DaDl/9vznw/cDY+R/iBPMz/osbCMAwFwKQG3wMAWB4FBQyjoIBhFBQwjIIChlFQwDAKChhGQQHDKChgGAUFDKOggGEUFDCMggKGUVDAMAoKGEZBAcMoKGAYBQUMo6CAYRUV9PPnz4rFYjyr8LS3t+vZs2dr/XNFRFRU0G3btkmSwjD841mK/O/5lStXdPLkSV2/fr0kB5aK8V/91t/CwoISiYS2bNmi27dvq7m52fdIMIo9qAdtbW2anp7Wvn37FASBHj586HskGMUnqGeTk5NyzunMmTO6du2a73FgTFWfoEsPPMhXnp84cUK5XE7z8/M6dOiQPn78WPJ9qF9VFdTCIUsU86amJk1MTGhwcFBBEOj+/fsl34v6xBLXmOfPn8s5p97eXo2Pj/seB55xSGRMT0+P8vm8fvz4oYMHD+rdu3e+R4JHFX2Cfvr0Sa2trSXLtqX7LPLVz2OxmMbHx3X+/Hmh/rDENa5QKMg5pz179iiVSmnr1q2+R8I6YolrXEdHh169eqXGxkYFQaCnT5/6Hgnr6J9kMpn0PQT+rr+/X01NTRoaGlIYhurp6fE9EtZBVUtcC3sy8l+/G93V1aVMJqOdO3cK0cU9aA3m379/1+HDhxUEgbLZbMl7iA4OiWrY1NSUnHM6ffq0RkdHfY+DNcAhUQ0bGBhQPp/XwsKC+vr69OHDB98jYZVV9An6/v17dXZ2mt2Tkf/y+8/XhoaGhGhgiRshL168kHNOR48eVSqV8j0OVgFL3Ajp7u5WPp/Xz58/FY/H9ebNG98jYYUoaMRs2LBBd+/e1blz53TkyBHdunXL90hYAe5BI5wXCgUlEgm1trZq//79gm0XL14s+Rp70Dpw+fJlFYtF32Pgf9y4caPs3TcFBQyIxWJlC8oeFDCsooLOzc2Z+R8+5ORRzJfDEhcwgCUuUIMoKGDYv9W8bO2ej5w8Snk57EEBA9iDAjWIggKGVVTQbDbr/Z6InDzK+XLYgwIGsAcFahAFBQzjHpSc3EheDntQwAD2oEANoqCAYRUVNJPJeL8nIiePcr4c9qCAAcvtQas6xYV9T5488T0CVhEFjYhv377JOafHjx8rCALf46BKfX19Zb/OPWgE8tnZWTnnNDAwoC9fvgjRwR60xo2MjGhsbEzpdFqDg4O+x8EqY4lboxYXF+WcU7FYVC6X0+7du32PhDXAPWgNymazOnDggDo7OzU1NUU5oyyswL1798Jyr0r64yFf+/zSpUthS0tLODk5WfI+ooc9aI2Yn5+Xc07bt29XOp3Wjh07fI+EdcAStwY8ePBAQRDo+PHjmpiYoJx1hEMi44aHhzU7O6tHjx7p2LFjvsfBOuMe1HDe1dWlvXv3KpfLadOmTUL9qWqJG4bhHw/52uR37txRQ0ODzp49q0wmQznrGEtcQ4rFopxzKhQKev36teLxuO+R4BmHREa8fPlSQRBo48aNevv2LeWEpAoLOjY25v3v5aKcb968Wb29vbpw4YJSqVTJe6hf3IN69PXrVyUSCS0uLiqdTqu9vd33SDCGJa4nMzMzisfj2rVrl+bm5ignyuKQyIORkRHdvHlT6XRap06d8j0ODKuooFevXlUymVzrWepGd3e3crmcWlpafI8C49iDAoaxBwUMo6CAYRQUMIyCAoZRUMAwCgoYRkEBwygoYBgFBQyjoIBhFBQwjIIChlFQwDAKChhGQQHD/gMrch19arvMmQAAAABJRU5ErkJggg==)
Water flows through a frictionless duct with a cross-section varying as shown in fig. Pressure p at points along the axis is represented by
![](data:image/png;base64,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)
physics-General
physics-
The diagram shows a cup of tea seen from above. The tea has been stirred and is now rotating without turbulence. A graph showing the speed v with which the liquid is crossing points at a distance X from O along a radius XO would look like
![](data:image/png;base64,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)
The diagram shows a cup of tea seen from above. The tea has been stirred and is now rotating without turbulence. A graph showing the speed v with which the liquid is crossing points at a distance X from O along a radius XO would look like
![](data:image/png;base64,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)
physics-General
maths-
maths-General
Maths-
Maths-General
physics-
A small spherical solid ball is dropped from a great height in a viscous liquid. Its journey in the liquid is best described in the diagram given below by the
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)
A small spherical solid ball is dropped from a great height in a viscous liquid. Its journey in the liquid is best described in the diagram given below by the
![](data:image/png;base64,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)
physics-General
physics-
Two communicating vessels contain mercury. The diameter of one vessel is n times larger than the diameter of the other. A column of water of height h is poured into the left vessel. The mercury level will rise in the right-hand vessel (s = relative density of mercury and
= density of water) by
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAWYAAACkCAYAAACkcYQdAAALqUlEQVR4nO3d72tb5f/H8df54h/QO95wtjZrpnf0Rudkw1JLOsYyBh0dlukUJAPpSGA3nb9WZrRT2oFWhhVFWHanq8OxMoeuE9vYjYBl4hS9Z2a2VvCeuaN3z+fGvjnktGma33mneT6g5JzrnJxzslx97eo7VxLHdV1XAAAz/q/ZFwAA8COYAcAYghkAjCGYAcAYghkAjCGYAcAYghkAjCGYAcAYghkAjCGYAcAYghkAjCGYAcAYghkAjCGYAcAYghkAjCGYAcAYghkAjCGYAcCYhgez4zgteWzAEvq6HfV4LhgxA4AxBDMAGEMwA4AxBDMAGEMwA4AxBDMAGEMwA4AxTQnmeDwux3G8n2QyqUQi4WtLJBJKJpO+tng8rkwm42s7duyYJGlwcLAZDwUAas5xXdet9iCZTEaBQKC0EzqOanDKhh8bsIS+bkc9nouqR8zZbJbRKgDUUNXBPDU1pUwmo3feeaes+9WynBGPx6t9GABgRlWljGw2q+3btyubzaqjo0P//PPP5ieklAFUjb5uh7lSxtTUlLeczWbLHjUDANarOJiz2awuXLig8+fPS5IWFxf18ccfl3RfZmUAwMYqLmVMTU0pEAhoeHjYG8onk0klk8miI2dKGUD16Ot21OO5eKjSO/b29ioUCvnaQqGQOjo6qr4oAGhnFZcy1oZyTm9vb0n3r0c5AwC2gpq8waScoTylDKB69HU7zM3KAADUHp+VAQDGUMoAWhB93Q5KGQDQBghmADCmacHMdDkAKIwaM9CC6Ot2UGOug8nJSe3YscPXdvfuXTmOo9nZ2U33LSQWiykWi9X0OgG0j7afLjcyMqJ0Oq27d+96bcvLy5KkRCLh23dhYUGjo6MVPmoAKJFbA+UcpkanrOmxg8Gge/HiRW89Go260Wh03fEkuTdv3nRd13XT6bQryfvJ3T8cDvvao9Go7/6F2vOvIbcdKIY+Ykc9nguC2X0QxOFw2FsPBoNe8OaC+ObNm24wGCx4rlyg5h+vUPBOTEz41vP/MwgGg/yyoWT0FTvq8VwwK0PSSy+9pPn5eUnSrVu3JEk9PT2KRqOamZmRJM3MzGj//v3efdy8Yv/u3bslyVcOyXfr1i2l02mdPHnSaxsdHV1XKrl48WJVjwPA1lDxx35W6/Tp0zp9+vS69kgksq7NLfCKZ6G2SvX390t6EKCpVMoL4IGBAZ06dUqSdOPGDV+Qzs7O6ujRo2Wdx3Ec33o4HK7msgFsUW0/KyMnGo0qlUppYWFBAwMDkh6MhNPptDfizQ/wo0ePKp1Oy3VdpdPpks7hPigdeT/Xr1+v2+MB0LraflZGzsDAgD7//HPNz897pYmenh6Fw2FFIpGCo9uenh5J0ldffeVrDwQCvrJGf3+/gsGgJicnq7pGAG2iFoXqcg5To1PW5diSfC8Cuq7rTkxM+GZd5ORmbej/Z1hIctPptOu6/hkb+S/4KW9Wxtpta18MBIqp5+8RylOP54J3/gEtiL5uR8Pf+ReLxer257elWRkAYEnREfOOHTs0Pj6uF198sfhBGDEDDUVft6Mez0XRYHYcR+l02nuRqxYXRjAD1aOv29HQUkbujRbLy8teyaBWZQ2LszIAwIoNR8y5N1BEo1FNT09rdnZWp06d0h9//LH+IIyYgYair9vR0BHz0tKSwuGwpqena3pCAEBxGwbzjRs3fG+PXlpa8n1WRLWYlQEAhW1Yylj7wt+BAwe0d+9e3wfx5O9LKQNoHPq6HQ0rZeR/wlrO/Py8+vr6anpyAMB6BYM5lUr5Phsi97kP27Ztq8lJmZUBABvjLdlAC6Kv28GXsQJAGyCYAcAYvloKAIyhxgy0IPq6HdSYAaAN8NVSAGAMpQygBdHX7aCUAQBtgFkZAGAMpQygBdHX7aCUAQBtgFkZAGAMpQygBdHX7aCUAQBtgFkZAGAMpQygBdHX7aCUAQBtgFkZAGAMpQygBdHX7aCUAQBtgFkZAGBMzUsZ2WxWHR0dJe1ba/x5h3ZBX7fDVCljampqXVs2m9Xc3FxVFwQA7a7iYA6FQr6ZENlsVseOHVMgENj0vszKAICNVVXKOHz4sLLZrJLJpIaHhyVJV65cKX5CShlA1ejrdtTjuagqmO/cuaOdO3d664uLiwqFQsVPSDADVaOv22GqxixJvb293kh5eHh401DOx6wMACis6lkZuVFzKaNliREzUAv0dTvMlTJyEomEIpFIaSckmIGq0dftMFfKyCk1lHOYlQEAG6vJiLmsEzJiBqpGX7fD7IgZAFA7BDMAGPNQM076ww8/6MKFCzp//rzXdu7cOf399986c+aM1zY2NqZt27YpGo16baOjoxoaGtLQ0JDXdujQIcXj8cZcPGDEf//95y3n/ym92XK5baVsq+a2FtsasbxRWz00pca89kW9XPtGbaUu79y5k7ob2oLjOPr333+9dYK5ecEcCoWoMQPAVkcwA4AxBDMAGEMwA4AxBDMAGEMwA4AxBDMAGEMwA4AxBDMAGEMwA4AxBDMAGEMwA4AxBDMAGEMwA4AxBDMAGEMwA4AxBDMAGEMwA4AxBDOAoo4cOaKHH35Y586dK7j9jTfe0COPPKJPPvmkwVe2dRHMADY1ODiod999d137vXv3lEgkFAqFtLKy0oQr25oIZgCbeu655xQIBHTlyhVf+7Vr1xSJRNTd3b3uPo8++qg6OzvV2dmpt956y7dtYGBAV69eVSAQ0Pbt2732np4eBYNBBYNBXbt2TZL0+OOP66effvL2+eKLL/Tqq6966+FwWN98842efPJJPfXUUxofH9f4+LjvfLFYTIlEovJ/gAYjmAGU5JVXXtHs7Kyv7b333tPhw4fX7dvX16e3335bq6urWl1d1dLSkq5everb58SJE8pkMvrzzz8lSaFQSK+//rrS6bTS6bQ+/PDDkq/ttdde0++//67ffvtNBw8e1JdffultW11dVSqV0r59+8p5uE1FMAMoyYkTJ7S4uKgff/xRkjQ3N6fBwUHt2bPHt9/y8rLu3bunWCzmtb388su6dOmSb7/8mvXt27d1//59HT9+3GtbWFgo+drOnj3rLT/99NPq6urS9evXJUnfffed+vr61NnZWfLxmo1gBlCySCSiy5cvS5I++OADvfDCCxvum1/KeP/99zc99mOPPVaz6xwZGdHc3Jwk6fLlyzp06FDNjt0IDzX7AmrNcZxmXwKwZT3//PMaGhrSs88+q0wmo+Hh4Q33/euvv+S6riStuy3k/v37BdsrCez9+/fro48+0s8//6yVlRUdOHCg6Lmt2VLBfOfOHS+YHccpe3ntbaXbqrktd9tmbZUsl7Ot0Ho5baVsq2S/cpX6S1tsv0LbSmkrtl7OtkbYs2ePAoGAjh8/rrGxsYL77N69W93d3ZqenlY0Gi3puM8884wk6bPPPtPo6Kgkae/evfr+++/V3d2tr7/+Wrt27dLKyorOnj2r/v7+osfr7OxUV1eXxsbGdOTIkTIeoQ2UMgCU5c0335QkDQ0NbbhPKpXSmTNnvFJGV1eXPv3006LHTSaTmpiY8GZlTE5OSpLi8bhmZmb0xBNPaN++fSW/KDgyMqKVlRUdPHiwxEdmh+M2+L9dx3GUTCa9UefaUWglI91aLa+9ZcS8+bZC6+W0lbKtkv3K1eoj5nKWy20rZVs1t7XYVmj522+/1cmTJ/XLL7+UtP9myxu1hUKhmv/1wogZwJZ0+/btlixjSAQzgC3q0qVL2rVrV7MvoyJb6sU/AMj59ddfW2omRj5GzABgDMEMAMYQzABgDMEMAMYQzABgDMEMAMYQzABgDMEMAMYQzABgDMEMAMYQzABgDMEMAMYQzABgDMEMAMY05RtMWvWj+ABgrXpkWlM+j5lvsgaAjTU8mBktA0Bx1JgBwBiCGQCMIZgBwBiCGQCMIZgBwBiCGQCMIZgBwBiCGQCMIZgBwBiCGQCMIZgBwBiCGQCMIZgBwBiCGQCMIZgBwJj/Ad9EiEG62cEEAAAAAElFTkSuQmCC)
Two communicating vessels contain mercury. The diameter of one vessel is n times larger than the diameter of the other. A column of water of height h is poured into the left vessel. The mercury level will rise in the right-hand vessel (s = relative density of mercury and
= density of water) by
![](data:image/png;base64,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)
physics-General
physics-
There are two identical small holes of area of cross-section a on the opposite sides of a tank containing a liquid of density
. The difference in height between the holes is h. Tank is resting on a smooth horizontal surface. Horizontal force which will has to be applied on the tank to keep it in equilibrium is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOkAAACiCAYAAACkqOpMAAAOUElEQVR4nO3df0xV9f8H8OdFQhDHDwkp4Sp4EV1ScFuANGiXX441t6S2ZtIWtP4xLEGzf5ojmtlM270W0eoPuDRkzT8UnZk/iHvTckI1rsQmSujVAeVuyQWlYCF8/uh7+QbC5cflnvM+5z4f213j9L6XF0eeO+e87useNGNjY2MgImH5yV0AEbnHkBIJjiElEhxDSiQ4hpRIcAwpkeAYUiLBMaREgmNIiQTHkBIJjiElEhxDSiQ4hpRIcAwpkeAYUiLBMaREgpM1pENDQ6ipqYHBYMDu3btx6dIlDA0NyVkS+ZDe3l60tLRg586deOaZZ7Br1y65S5qSRq47M9jtdnzwwQc4ceIE/vzzT/j7+2PVqlXQarXQ6/XIycnBxo0b5SiNVO727ds4cuQIjh07hgsXLiA+Ph5paWlobm6GRqNBVVUVDAaD3GWOkzykQ0NDOHXqFA4cOICOjg4YDAYkJyfj7t276OvrQ19fHxwOB+x2O0JDQ1FZWSnUDiPlGhkZwa5du1BZWYkNGzYgJiYGOp0OixcvHl9js9lgsVhQWFiIgwcPIigoSMaK/yVpSO12Oz766CPU1dUhNjYW+fn5CAwMnHZ9e3s7vv76a+zduxc7d+6UqkxSofb2dhQWFiI0NBQpKSkICQmZdu3w8DAsFgtu3bqF1tZWLF++XMJKHyTpNandbkdlZSWio6ORl5fnNqAAkJiYiJKSErz//vs4efKkRFWS2nR1dSEzMxM6nQ45OTluAwoAixcvRkpKClauXInq6mqJqpye5Ke7J06cwL59+/DTTz8hNzcX6enpMz7n6tWrOHfuHNra2vDoo49KUCWpyYYNG7Bs2TKkpaXNuLavrw/fffcdOjo68Oabb2L//v0SVOieLI0ju92Ojz/+GKdPn4ZGo0FeXh7Cw8PdPsdqtWLdunX47LPPJKqS1GD79u34+eefkZ+fP+Paa9eu4fjx43jsscfQ1NSEpUuXSlDhzGTr7rrs27cPBw8eRGFhIR5++OFp1/X396OyshIOhwOhoaESVkhKdePGDSQkJKCsrAzBwcFu1zY3N+PSpUv48ssvsWnTJokqnJ1F77777rtyFpCZmYnAwEBUV1fjySefnHZdYGAgBgYGMDg4iIyMDAkrJKXavXs3QkJCsGbNGrfrLl68iDt37uDs2bOzOiWWmuxHUpetW7fit99+c/t2S09PD06dOoXu7m4JKyMlunr1KpKSklBaWur2bRS73Y6jR4+ira0Nq1atkrDC2RNmLPC9996D1WrF33//Pe2a6OhoaDQaNDc3S1gZKZHZbEZ6errbgI6OjsJisaCqqkrYgAIChTQ+Ph4vvPACrly54nadTqfj2zE0o8OHDyMhIcHtGqvViry8PBQWFkpU1fwIE1IAePHFF9HV1eV2jVarRWNjo0QVkRJ9//33WLRoEVasWOF23ZUrV7B9+3aJqpo/oUKak5MDu93uds3KlSvx448/4v79+xJVRUpz/PhxrF692u2a33//HeHh4UhKSpKoqvkTKqQREREIDg5Gf3//tGsCAgIQFBSEzs5OCSsjJfnmm29mnCoaGBiAVquVqCLPCBVSAFi7di0cDofbNTP9AxBFRUW5/f+Dg4MzrhGFcCENCQnB8PCw3GUQCUO4kAYEBMhdApFQhAspEU3EkBIJjiElEhxDSiQ4hpRIcAwpkeAUG9JPP/0UGo1m/GG1WmE2mydsM5vNsFqtE7ZVVFTAbrdP2FZcXAwAE7ZlZWUBAOLi4sa36fV6AEBWVtb4NtcdJYqLiyc83+l0oqKiYsI2m80Gk8k0YVtDQwMaGhombDOZTLDZbBO2lZWVwel0TthWUFAAAAgPD3+gRr1eP74tLi4OAFBQUDDh+QBQVlY2YZvdbn+gRin2ratGT/atq8aenh7v/vJJTJjPk7o8//zz8Pf3x/r166dd88UXX+Dbb7/FunXrJKyMlCIxMREZGRlu74fV2tqK4OBgHD58WMLK5kexR1IiX8GQEglOFSGdfH3C61Pfuz41mUze/SWTEa9JSXV4TUpEkmJIiQTHkBIJTrEh5TADm0WT9y2HGSTCxhF5io0jIpIUQ0okOH+5C5js6NGjM64pLy9HR0eHBNUQyW9BjqROpxMmkwlWq3UhXm7OOHHEJhInjqbhCmdtbS2MRiM2b968kLW51dHRwcYRTUltjaN5ne66wnno0CEAQE1NjaQBJfIlcz7ddTqdiIuLQ0VFBZxOJ5xO5wOnTt542Gw2b/z8Qpt8ijzfx9mzZ+X+UcgDcw5pWFgY+vr6YDQax7dZLBaMjY159ZGcnLygP7gSlJeXu90nfX19iI2NnXHfbdy4Ue4fhTww78ZRaWkpxsbGYDQakZWVJXnTiBNHGqSnp8NutyMoKMgnm0WT9y0njmZgMpmQnJwMg8Hg0etw4mh2XJcdTqdz/OyG/qW2xtGCDTOUlpZ6HFCaPVfTDsD4kYXUiRNHCuR0OmE2m1FTUwPg356Amt8n9HUMqQKZzeYJ70sbDAYcO3aMR1OVUkVIfW3i6IcffoDBYBhv/mg0Ghw6dAjPPfccJ45UiB9VUziNRgPB/gllx8YREUmKISUSHENKJDjFhpQTR/x42uR9y4kjibBxNDdsHD2IjSMikhRDSiQ4hlTheKqrfqoIqZonjjzhS00kThxJiI0j8hQbR0QkKYaUSHAMqULl5+fjq6++krsMkoBiQ+orE0fTOXPmDGJiYtzuI7U3izhxJBM2jmZ2/fp16HQ6vv0yDTaOSHYtLS3Q6XT48MMPx48kPPVVL4ZUgW7duoWuri4A/w4z7N+/H2azWeaqyFsYUgVqamrCtm3b8Pbbb8tdCklAFSH1tYmjM2fOYOvWreNfNzU1ITs7+4F1nDhSBzaOFGaqplF8fDz27t2LLVu2yFiZONg4Ilm5mkYu169fR1dXF1JTU2WsiryJIVWY8+fPT/gDTL29vQCA1atXy1USedm8/j4pyaeqqmrC1xkZGXy/VOUUeyT19Ymj2VB7s2jyvuXEkUTYOCJPsXFEQvH0aEviY0iJBKeKkKp5mGGme/C6avX1e/BymEFCvCadG42G992djNekRCQphpRIcAwpkeAUG1JfGWaYqlnkevh6s2jyvuUwg0TYOJobNo4exMYREUmKISUSHEOqQDabbcrtdrsdTqdT4mrI21QRUl+bONq2bRsuXLgw3vzRaDTIzs5GbW3tlDX6QhOJE0cSYuNoZk6nE3FxcbBYLNDr9WhtbUVBQQEsFgtiY2PlLk92amsc8UPfChQWFoaioqLxo1BWVhaKiooY0P/T3t4+q3WFhYUefy/XrVSLioo8fq3pqOJ01xeVl5dPuP7csWOHjNX4rqKiIly+fBl6vd5r9z5mSBUqLCwMpaWlAMCjqMyMRiMMBgOKi4u9ElbFhpQTRxp0dnYiLCwM1dXVPtksmrxvXTW6vqfL5LWuR319/ZTb5/NwNa5sNhuKi4tRXFy8YJ12No4UzmazITk5We4yFKmwsHDBGkcmkwllZWVITk7GK6+8gqKiIoSFhS3Iayv2SOprpjsa/PeIqdFoEBkZKXepPsdkMqG2thZGoxEWiwWlpaULFlCA3V3FKC8vR3l5udxlKMJc3oLxlNVqBQBYLJYFDeZ/MaREHkhOTobBYPDq91DF6a6vTRzxY2viTBx56+j5X2wckeqobeJIFUdSIjVjSIkEx5ASCU6xIeXEEZtFk/ct73EkETaOyFNsHBGRpBhSIsExpESCU0VIOXHEJhLvcSQhNo7IU2wcEZGkGFIiwTGkRIJTZEgdDgcnjtgsemDfcuJIIrNpHNXV1aGurg5paWkSVkZKERERgVdffRVLly6ddg0bR14WGBjIv3lCUxoZGYHT6XQbUKVRZEj9/PzgcDjkLoMEdPr0aaxdu1buMhaUIkMaExODxsbG8a85zMDrU9cww5EjRxAfH++NXzvZKPKa1OFwoKGhAd3d3RJWRqJrbGzESy+9hNdeew2BgYFu1/Ka1MsiIyMRHh6OyspKuUshQVy7dg0lJSXIzc2dMaBKo8iQAkB6ejr27NmD8+fPy10Kyay+vh5ZWVlISEhQ5aiocCFta2vDbM7Ao6OjkZubi5ycHBiNRoyMjEhQHYni3r17+OSTT5CQkIADBw4gOzsbTz311KyfPzo6Cj8/4X79pyTczbEzMzPxxx9/zGptYmIiQkNDUV9fjz179kCv1+OJJ57AyMgIRkZGMDQ0hOHhYS9XTFIZGBhAT08Pent78ddff+Hxxx9HVlYWVqxYMa/Xctf3EIlwIY2IiJhTQ0ir1UKr1SI7Oxu9vb24efMm/Pz8xh89PT3QarVerJikEhkZCZ1Oh5CQECxZssSj17p37x7WrFmzQJV5l5AhHRoamvPzlixZMmXrPSkpaSHKIpX59ddf8fTTT8tdxqwId1Kem5uLGzduyF0GqVh7ezvWr1+vmCaTcCFNSUnBP//8g87OTrlLIRW6e/cuzp07h3feeUfuUmZNuJACwFtvvQWbzSZ3GaQyAwMDOHnyJN544w08++yzcpcza8JNHLmkpqYiMDAQOTk5cpdCCjc2NobW1lZcvHgRr7/+OioqKuQuaU6EDemdO3ewZcsWtLS0YNOmTYrpxJE4bt++DZvNhsuXLyM1NRU7duzA5s2b5S5rzoQNqcvnn3+OqqoqdHd3Y/ny5QgJCcH9+/cxOjqK0dHRCQPi5NuGh4cxODiI/v5+DAwMYNmyZXj55ZdRUlKi6KF74UPqcvPmTfzyyy+w2+146KGH4O/vP/7fRYsWyV0eCSA4OBhRUVF45JFHEBUVhYCAALlLWhCKCSmRrxKyu0tE/48hJRIcQ0okOIaUSHAMKZHgGFIiwTGkRIJjSIkEx5ASCY4hJRIcQ0okOIaUSHAMKZHg/gecNQ9fuh6JswAAAABJRU5ErkJggg==)
There are two identical small holes of area of cross-section a on the opposite sides of a tank containing a liquid of density
. The difference in height between the holes is h. Tank is resting on a smooth horizontal surface. Horizontal force which will has to be applied on the tank to keep it in equilibrium is
![](data:image/png;base64,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)
physics-General
physics-
A cylinder containing water up to a height of 25 cm has a hole of cross-section
in its bottom. It is counterpoised in a balance. What is the initial change in the balancing weight when water begins to flow out
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)
A cylinder containing water up to a height of 25 cm has a hole of cross-section
in its bottom. It is counterpoised in a balance. What is the initial change in the balancing weight when water begins to flow out
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)
physics-General