Chemistry-
General
Easy
Question
In which of the following cases, the nitration will take place at meta-position?
I) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/906314/1/1188862/Picture84.png)
II) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/906314/1/1188862/Picture85.png)
III) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/906314/1/1188862/Picture86.png)
IV) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/906314/1/1188862/Picture87.png)
- II and IV
- I,II and III
- II and III
- I only
The correct answer is: I,II and III
Related Questions to study
Chemistry-
The correct order of decreasing basicity of the following compounds is:
I) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655588/1/1188847/Picture52.png)
II) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655588/1/1188847/Picture53.png)
III) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655588/1/1188847/Picture54.png)
IV) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655588/1/1188847/Picture55.png)
The correct order of decreasing basicity of the following compounds is:
I) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655588/1/1188847/Picture52.png)
II) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655588/1/1188847/Picture53.png)
III) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655588/1/1188847/Picture54.png)
IV) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655588/1/1188847/Picture55.png)
Chemistry-General
Chemistry-
Phenol . gives two polymers on condensation with formaldehyde:
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655569/1/1188831/Picture38.png)
X and Y are :
Phenol . gives two polymers on condensation with formaldehyde:
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655569/1/1188831/Picture38.png)
X and Y are :
Chemistry-General
Chemistry-
X and Yare:
X and Yare:
Chemistry-General
Chemistry-
Chemistry-General
Maths-
Simplify : 2m-3 =17
Simplify : 2m-3 =17
Maths-General
Physics-
In the figure is shown Young’s double slit experiment. Q is the position of the first bright fringe on the right side of O. P is the 11th fringe on the other side, as measured from Q. If the wavelength of the light used is
, then
will be equal to
![](data:image/png;base64,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)
In the figure is shown Young’s double slit experiment. Q is the position of the first bright fringe on the right side of O. P is the 11th fringe on the other side, as measured from Q. If the wavelength of the light used is
, then
will be equal to
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAM4AAAByCAYAAAAbF+7KAAAb8klEQVR4nO2deVhTV/rHvwk3rGEx7IQlyBIwgIISBVFRNqUi7lsf62BdWn20zqM+Mzp2bLW1dtymrhWrolNbq1idutQFEbEKqIyCCAqCIItsAYkQCdv5/eHD/TVDdSSAEDif57lP4NzLOe893G/OPe97Fg4hhIBCobQLbncbQKFoIlQ4FIoaUOFQKGpAhUOhqAEVDoWiBlQ4FIoaUOFQehUpKSlISEjo8nKocCi9isePHyMrK6vLy6HCoVDUgAqHQlEDKhwKRQ2ocCgUNaDCoVDUgAqHQlEDKhwKRQ2ocCgUNWC624CuQi6XY/r06X94Ljo6Gvb29u/YIkpvotcKp7GxEZmZmdiwYYNK+ubNm1FXV9dNVlF6C71WOACgra0NkUikkqanp9dN1lB6E7SPQ6GoARUOhaIGVDgUihpQ4VAoakCFQ6GoQa/2qlEor2PXrl1IS0sDANjZ2eGDDz5o44F9E7TFofQ5Vq9ejdTUVEydOhXjx49HTU0N9u3bh9ra2rfOgwqH0qvIzc3Fnj17MGnSJCQnJ7c5/+uvvyIrKwvr1q1DWFgYIiIiEBERAblcjuLi4rcuh76qUXoV58+fR2ZmJh49egQAOHXqlMr548ePY8aMGbCzswMAcLlcGBgYQEtLC01NTW9dDm1xKL2O1+0jUF5ejkePHmHw4MHQ0tJiry0tLUVVVRWEQuFbl0FbHEqvIjw8HDU1NXBxccEnn3yico5hGGhra+P58+esuB4+fIirV68iODgYJiYmb10OFQ6lV+Hk5IRly5bh448/bnNOIBAgKCgI3377LSorKwEAiYmJyMvLw8KFC9tVDn1Vo/Qpli1bBktLS5w6dQpnz56Fr68v7OzscPbs2XZ51TrU4uzbtw+lpaUqaR4eHpgyZUpHsqVQugxjY2N89dVXKmmDBw9Geno6mpub3zqfDgknOjoafn5+0NfXBwAUFRUhOzubCoeiUYhEonYFP4FO6OMEBwejX79+AIC0tDSkpKR0NEsKpcejcX2cjRs3wsPDA0FBQYiLi+tucyh9FI3yql24cAHff/89kpOT8fDhQxw5cgTBwcHdbRalD6JRwikuLsbw4cPB4/EglUohlUpfey2Hw0FFRQUmTJjQ5hyXq3ENLaWHoVHCCQ8Px44dO/Dhhx9iw4YNcHBwAMP88S0IBALU1NS8YwuBFy9eoLi4mPXQWFpawtTUFBwO553bQuk6NOqr19raGmlpafDy8sKcOXPw9OlTyOVy5OTkvJVIysvL8fDhQ1RXV792WEZHuXTpEmbOnIkVK1Zg3rx52LZtGxQKRZeURek+NEY4KSkpePr0KQBg1qxZMDQ0hEwmg0wmw6+//orc3Nz/mUdJSQliY2Oxd+9eXLp0CSUlJZ1qY0NDA+RyOWbMmIELFy5g7dq1qKmpadfgQYpmoDGvatnZ2Th48CCsra1RVVUFX19fiEQi9OvXDxKJBDo6OirXv3z5Ev/4xz/a5NPaYl25cgXx8fEYOHAghg0bhv79+3fYxhcvXqCwsBD/+c9/8Pnnn6OoqAjh4eF0SapeiMYI57333oOWlhYUCgWcnJwQHh4OU1NTAACPx2tzvUKhwO7du/GnP/1JJf3u3bv48ssvweVycf/+faSnpyMlJQVOTk4IDQ2Fi4sLO3K2vdTW1kKhUGDQoEEQCoUoKCiAXC7vstdCSvehMcIRCASYPXt2m/THjx8jPj4eQqEQQqFQZYSrkZER3nvvPZXrr169CgAQi8VwdXWFn58fsrOzkZKSgi+++AIikQjTpk3DgAED/lCQb0Imk6G6uhqrVq2Cs7MzFAoFCgoK0NTU1KZFpGg2GiOc12Fra4uFCxeCx+OBz+e36285HA6EQiGsrKzg7e2N/Px8XLt2DStWrIBYLMYHH3yAoUOHvnV+rS2Og4MDnj9/jsTEREybNg3a2trtvS1KD0djnAOvQ1dXFzY2NjA3N3+ta/p/oaWlBRMTEwwcOBCLFy/G8ePH4e3tjSVLlmDKlCm4cuXK/8yjvr4eGRkZ+Omnn2BmZgZ7e3sMGjQIYWFh7W65KD0fjRdOZ8LhcMDj8SAQCDB//nzcuXMHU6ZMwaZNmxAREYHz58+jrq7uD71kurq6WLx4MRoaGlBTUwO5XI61a9e2a3IURXOgwvkfzJ49G2fOnMH8+fNx9OhRzJs3D8eOHUNOTg5qa2tpx7+PovF9nHeBrq4uIiMjERQUhOTkZPz000+Ij4/HoEGD4OvrC1dXV9bDR+kbUOG0Az6fj+DgYIwYMQKnTp3CF198geTkZEgkEgwePBgeHh6wtbXtbjMp7wAqHDVQKpXIyclBaGgoJk6ciMzMTFy5cgW//fYbxGIx/P39IRKJ1I4HUXo+VDjtpLGxET///DOeP3+OBQsWwM3NDSNGjEBubi7S0tKQnp6OpKQkODo6Ijw8HK6urtSr1gvpsHDWr1/PuoFfvHgBHx+fDhvVU2lqakJCQgJSUlIwffp0uLi4sKOenZ2dIRKJ4O/vj6ysLNy5cwfr16+Hs7MzJk2ahCFDhnSz9ZTOpEPCOXHiBF6+fKmSZmxs3CGDejKZmZm4cOECwsLC4O/v3yZuxDAMrK2tYWlpicGDB6O0tBRXrlzB2rVrIRQKMXfuXIwcObKbrKccOnQI3333HTuS/p///KfaEyE7JJzOGBipKRQVFSEmJgY2NjYIDQ194xAaLpcLY2NjGBsbo3///pg7dy5iY2Px+eefQ19fH8uWLUNQUBCdUPcO2blzJ65du4adO3fC2dkZt27dwpw5c5CamgobG5t259cpfRylUgmlUgkOhwNtbW3o6OigsbER9fX1IISAx+NBT08PhBA29sEwDHR1dcHhcKBQKNiJX3w+HxwOBw0NDVAqlQBebXjL4/HYcoBXG+Pq6uqiqakJ9fX1aGlpAY/HY/N88eLFa+2tra1FS0sLuFyuiu06OjrQ1tZmy261vampCbGxsaisrMTHH38MDoeDlpYWcDgc9n64XC709PTYPBsaGgAA+vr6MDAwwMyZMzFu3DicO3cOX331FbZu3YpFixbB39+fvb/21lFrORwOB7q6uu2uI7lcDuDVyAldXV1wuVy8fPmSDfDy+fy3riM9PT00NzdDoVCwaTo6Oip1xOFwoK+vz9re2NgIAOzazb8vp9XOxsZGKJVK1vb/VUctLS1t/t+pqal48OABlixZwnYlgoODIZVKkZ6erpZwQDqBHTt2EIlEQnx9fcn27dsJIYTExsaSwMBAIpFIyIoVKwghhJSVlZFRo0YRiURCFi5cSB4/fkxkMhmZOnUqkUgkRCKRkJycHFJTU0O2bt3Kpp07d44QQsjevXuJp6cnGTRoEPnss88IIYRcuXKFBAcHE4lEQpYvX06qqqoIIYS4ubkRJycnkpCQoHIMGTKEODs7k5ycHNLQ0EC2bdvG2n748GFCCCExMTHEz8+PSCQS8sknn5Cff/6ZDBs2jAQEBBCJREL+/Oc/k8LCQlJbW0v8/f2JRCIho0ePJllZWaSyspKsW7eOtT0lJYW0tLSQnTt3EolEQoYMGULWr19Pzp07RyZNmkRsbW2Jnp4emTJlCpHL5aSsrIz4+voSiURCFixYQHJyckhVVRWZPn26Sh1VV1eTjRs3EolEQnx8fMiFCxcIIYTs27ePeHl5kYEDB5K///3vhBBC4uPjSUhICJFIJOSvf/0rqa6uJoQQNr+pU6eSrKwsUlFRQZYuXcqmP3r0iDQ0NJDt27ezdRQTE0MIIeTw4cNsHbX+f+/du8fW0fLly8nTp09JbW0tGTFiBJFIJGTUqFEkMzOTlJaWkjVr1rDlpKWlEUII2bVrF1tHW7ZsIYQQcurUKTJ69GgikUjIp59+SlpaWkhlZSVbR/PnzyfZ2dmkqqqKzJw5k2zatIns2bOHfTabm5vJwYMHyerVq4lMJlN5boOCgkh8fLxazzyHkN4Z+pbJZBg6dCgOHDigkr5y5UocOXIE7u7ub5XP9evXER0djUWLFiEgIKBTbVQqlUhOTkZsbCwUCgW8vLxYV7a5uXmnltVXOHr0KORyObsErkKhwJYtW8AwDNasWcNeV1BQwAa0zczM2l0OdUe/gaysLGzfvh1z587tdNEAgI6ODkaNGoVRo0bh9u3buHjxIg4dOgQ7Ozt4eXnB09MTQqGQxoM6AMMwMDIyQnFxMaqrq9GvXz8UFhZi9erVWLRokVqiAahwXsvDhw/xzTffYPjw4Rg7dmyXl+fr6wtfX188ePAAN2/eREJCAhITE+Hi4oKRI0fC0dGRxoPUQFtbG8OHD8fevXuxdu1aWFhYoKysDC4uLliwYIHa+XZIOBs2bGDXAWhFKpV2yKCeQEVFBXbt2gU7OzssWrTonU5Ck0gkEIvFKCwsZDu1W7duhYuLC0JCQuDl5UVXzGknAwcOxPz585GZmQng1STGadOmdagl75BwTp8+jYiICHYCWV5eHhISEjRaOEqlEgcOHACXy0VUVFS7J8d1BgzDwNHREfb29ggICEBeXh5u3bqFTZs2wdbWFpMmTYK/v/87t0tT0dbWhr+/f6fWWYdf1QYNGsSuHa2tra3Ra0crlUocO3YM+fn5WLp0KaytrbvVHi0tLVhZWcHKygoeHh6YMGEC4uLisGXLFvD5fERFRWHkyJG0D9QN0Ajc77h9+zbi4uIwadIkiMXiHvVKZGRkhP79+yMqKgoHDx7EuHHj8PXXXyM8PBznzp2ja7e9Y6hw8GofyLS0NOzduxehoaEICgpSexp2V8Pj8WBiYoJZs2bh5MmTWLJkCbZv347Jkyfj+PHjqK6upuu4vQN65tPxjikvL8eZM2fg6emJiIiIHiua/8bAwAATJkxAWFgYrl+/jkOHDiE2NpYVv6mpKYyMjLrbzF6JZjwhXYhcLsfZs2dRXl6OVatWaeQaATo6OggODkZwcDB+++03nDx5ElevXoVUKsWwYcMgEolgZmZG+0KdSJ8WTlNTEy5fvoy0tDTMmTMHdnZ23W1ShwkICEBAQADu3r2LuLg4HDp0CDY2NhgwYACGDBkCW1tbjWlRezJ9ugZv3LiBM2fOICoqCr6+vt1tTqfi7e0NDw8P5ObmIjExESkpKUhJSYFYLMbw4cPh5ubWo5wfmkafFU5OTg62b9+OKVOm9NqYCI/Hg5ubG5ydnVFcXIz09HRkZGRgx44dcHBwQEhICAYPHtzdZmokfVI4MpkM33zzDUaNGoXJkyf3+qEsDMPAwcEBDg4OGDp0KPLz83Hz5k3s2LEDJiYmmDp1Kvz8/OgrXDvQqJrauXMn9u/fD11dXfztb39DZGTkG68vLCxss+h6WVkZvv76a3YYhoGBQVea3OOwsLCAhYUF3N3dUV5ejmvXrmHXrl3YvXs35s2bh+HDh/e5OlEHjRHOtWvX8MMPPyAhIQFyuRwrV658o3AEAgEqKirapO/YsQPPnj3DX/7yFxgaGnalyT0aQ0NDGBoawsHBARMmTEBCQgI2b96Mbdu24aOPPkJYWBjdnuQNaEwAtKysDN7e3uDxeBCJRIiNjX3j9RwOB0ZGRipHUlISbty4gblz54LH46GxsfEPZwz2JRiGgZmZGaZOnYpz585h+fLliI6OxsSJE/H999+jrq6OnalJ+X80psUJDAxEdHQ0Zs+ejc2bN8PJyandfZO6ujro6elh165dEIlE7Hu/UCiErq5um6OveZ20tbUxduxYjB07FgkJCYiJicGPP/6ICRMmICQkBKampjA0NKRrJUCDhGNhYYG4uDjs2bMHERER+Pe//w1LS0tUVlaCYRjY2NiovFo0NjYiPj5eJQ8DAwNERkbC2toa5eXlyM3NxfXr1yGTyWBubg5zc3OYmZmx/QAjIyP2lab16Cv73AQGBiIwMBC3bt3CqVOnsGbNGgwZMgSDBw+Gu7s7zMzM+rQzQSPuPC0tDXw+HyKRCHPmzMGRI0fw7NkzAMCdO3dQVVWF8ePHw9nZmf0buVyO6dOnY8SIESp5paSkIDExEaGhoQBejVNTKBQoKipCYWEhioqK8PTpUyQlJYFhGBgYGEBfXx/6+vrg8/kwMTGBQCCAQCCAqakpBAKBRo42eFukUil8fHyQlZWF8+fP49ixY7C2toanpye8vb0hEon6ZAukEcJ58uQJLl++DIFAgBcvXkAqlUIikcDKygpcLhe3b9/+w28/c3NzrFq1SiVt5cqVKr9zOBwYGBhALBZDLBaz6c3NzaioqEBZWRlKS0tRVlbG/gyAXbUFePWKY2VlBUtLS/bTwsKi17RODMPA09MT7u7uePLkCW7evIm7d+8iOTkZLi4u8PPzg6enZ3eb+U7RCOGMHj0ahBDIZDIAQGRkJMzNzVFdXY3c3Fw4ODjA0tKyU8v8/VyYgQMHAngllrq6OlRVVUEmk6Gqqor9uaamBiUlJVAoFFAoFGhqaoJAIICtrS3s7OxgZ2cHoVAIgUDQqXa+SxiGgYuLC1xcXFBYWIj79+/j7t27+Pbbb2FlZYXQ0FD4+Pj0+rgYoCHCMTY2xqRJk1TSlEolbty4gcuXLyMgIAByubzL3accDgd8Ph98Ph/29vZselNTE168eKFy1NTUoLKyEhUVFbhx4wYqKyshk8nAMAz69++vcgiFQo172Fq/DHx9fZGfn4/k5GRER0eDx+NhxowZkEqlvToe1GHhLFu2jB11W19fjzFjxnTYqLeBx+MhICAAgwYNgoGBQbdMcW6FYRj069ePnQkLvGqdGhoaUF9fzx4vX75ERUUFCgoKUFBQgFu3brE7U9vb20MsFsPNzQ1isRhOTk4a0Xdqdaq4u7ujpKQEycnJ2LNnD/bv34/Zs2djzJgx0NfX724zO50OCScxMZFdXbKVd/XNyeVyYWJi0mMfrtZVL3V0dFTW0xaLxfDz80NzczNaWlrQ3NyMmpoa5OTkIDMzE0lJSThw4ADy8/NhaGgIDw8PeHp6sp+/b+l6Enw+H66urujfvz8iIyORmJiIvXv3Yvfu3YiKisL06dO728ROpUPC6c1NcVfB4XDAMIyKM4PP50MoFCIwMJBNUyqVePr0KTIyMpCRkYHDhw8jIyMDCoUC7u7uGDBgAPvp5OTELlerpaXFfnZHHIphGBgbGyMiIgIRERG4fPkydu/eja1bt+Kjjz7CtGnToKOjA4ZhNDpOphF9nL6Ijo4O2xH/ff9OJpMhOzsbjx49wqNHj3D+/HmUlZXBxMSEDera29tDJBJBIBC0CeryeLx3+sCGhIQgJCQESUlJOHLkCI4dO4aIiAiMHDkS9vb2MDQ01MgJdlQ4GoapqSn8/Pzg5+fHprXGoZ48eYK8vDykpqbi5MmTIITAwsICZmZmKgHe/w7sGhgYdHkw08/PD76+vkhPT8eJEyfw5ZdfwsfHB1KpFGKxmA0taApUOL0AfX19uLq6wtXVlU0jhKCyspIN6hYWFuLevXuQy+XQ0dFhg7oGBgYwMDBgg7m/D+x2tpeSYRj4+PjAy8sLOTk5uHjxIk6fPg0TExN4eXnBy8sLLi4unVpmV/FG4URHR2P69Ok9tgNOeT0cDodtZX6/S15dXR0qKirYoG5paSnKy8tRWFio8rfAqzDAfwd2TUxMOtw6MQwDd3d3uLu7Iy8vDzdv3sSdO3eQnJwMR0dH+Pv7QyKR9GgXPQMAlZWViI2NRWpqKlxdXfH+++/DxsYG+/btQ0hICJRKJaKjo7Fw4UJUVFTg2bNn8PX1pYLSQFpbGJFIxKY1Nzfj+fPnKgHdqqoq1NTUoKioCNnZ2VAoFKirq4OWlhasra3ZOI6trS1sbW3VHiXRGssqLi7G/fv3kZqaioMHD8LQ0BDh4eHw9vbuke5spqmpCUlJSUhKSsLs2bORlpaG3NxcWFhYsBcZGhoiODgYfD4f9+7dw4MHDzBgwAAqnF6ClpYWTE1NYWpqqpL+8uXLNoHd6upqVFRUoKioCPfu3UN5eTlkMhlsbGzg6OioEtgVCARv3W8RCoUQCoWQSqXIyclBamoqDhw4AD09PURGRiIgIKBHCYhpbGzEkydPwDAMwsLCMGzYMDAMo+LpqK6uxvHjx6FUKrF7927cvn0b+/btw759+zBy5EiN6tRR3h49PT3o6empfIk2NzdDqVSqBHbr6+vZoG5aWhp++eUXFBQUQEdHB87Ozuw4QLFYDEdHxze+6gkEAkilUnh4eGDcuHG4desWDh06hJiYGEybNg0TJ07sEW5sRldXF6NHj8Yvv/yCwMBAbNq0CcOGDVO5qKGhAYWFhRCLxfjwww/h5+eHyZMnw8nJiYqmj6GlpcU6Fn6Pm5sbmpubVQK7JSUlyMrKQlZWFo4dO4asrCyUlJTAzc2tTWC3dXtG4P8H3jo6OsLOzg4RERG4evUq9u/fj02bNmHp0qWYNWtWt7qxGQ6HA09PT8TFxeHSpUtYsmQJZsyYgcWLF7e5uHWvSB0dHfD5/D49H4OiCpfLBZfLVenQt7YyEydOZNNevnyJ+/fvIyMjA/fv38eJEyeQkZEBCwsLlaDugAED2DF8XC4XoaGhGDt2LG7evIm9e/eyAdWIiAiYm5u/VUB15cqViImJQWNjIxobG3H+/HmVoHN7YFpaWiCXy8EwDEJDQ1FfX4/ExER2Y9U/orm5Gb10B0RKF6OnpwepVAqpVMqmEUKQn5/PBnXj4+OxZ88e1NXVqczUdXBwgEgkwmeffYasrCz88MMPOHr0KCZOnIgxY8bAwcEBSqUSlZWVyMvLg42NDXR1dQG8mthYUVGB2NhYBAYG4vTp01ixYgVSU1PVug+mvr4ely5dQkFBAby8vHD9+nXY2Ni8djiNgYEBSkpKcPnyZYwfPx5mZmY94p2TorlwOBw4OjrC0dGR3f2OEIKamhrk5eWxx9mzZ5Gfn88GdD08PODg4IBjx47hX//6F0JDQ1FcXIxLly7hxx9/xMaNG9nW7unTp9DT02MHA1dWVsLJyUltmxl9fX14e3sjOTkZ2dnZsLGxweTJk2FsbIyJEyeyK8EEBQVBT08PEokE6enpuHnzJnx8fGBqakqFQ+l0OBwOTExM4OPjoxKHampqUpmtW1hYCD8/P9TW1iI7OxtxcXGora1FVVUVvvvuO1Y4paWlUCgUuHjxIu7du4czZ85g3bp1atvHAICLiwu2bdvW5uSnn37K/ty6iy+AP+z/UCjvAoZhIBKJVOJQLS0teP78OcrKypCTk4MHDx6AEKKy3Ul2djYaGhpQW1uLpqYmrFixQkWQ7bajQ3fRw6moqMDmzZtV0vLz87vJGkpXweVy2eFCgYGBKC4uRr9+/fD++++z1xQWFmL06NGIioqCtrZ2h8vstcIxMjLC8ePH26QvXbq0x85poXQcb29v6OrqYurUqZBIJADAjoIYMGBAp4gGADiEuscovYijR49CLperdC2amppQWVkJfX39Tttoq9e2OBRKKwzDwMrKqlPzpGF/CkUNqHAoFDWgwqFQ1IAKh0JRAyocCkUNqHAoFDWg7mhKr2LEiBEqQ226ChoApfQqWh/nrh54TFscSq/iXY3Up30cCkUNqHAoFDWgwqFQ1IAKh0JRg/8DGF+6SFQl6wkAAAAASUVORK5CYII=)
Physics-General
Physics-
When one of the slits of Young’s experiment is covered with a transparent sheet of thickness 4.8 mm, the central fringe shifts to a position originally occupied by the 30th bright fringe. What should be the thickness of the sheet if the central fringe has to shift to the position occupied by 20th bright fringe
When one of the slits of Young’s experiment is covered with a transparent sheet of thickness 4.8 mm, the central fringe shifts to a position originally occupied by the 30th bright fringe. What should be the thickness of the sheet if the central fringe has to shift to the position occupied by 20th bright fringe
Physics-General
Physics-
Figure here shows P and Q as two equally intense coherent sources emitting radiations of wavelength 20 m. The separation PQ is 5.0 m and phase of P is ahead of the phase of Q by 90o. A, B and C are three distant points of observation equidistant from the mid-point of PQ. The intensity of radiations at A, B, C will bear the ratio
![](data:image/png;base64,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)
Figure here shows P and Q as two equally intense coherent sources emitting radiations of wavelength 20 m. The separation PQ is 5.0 m and phase of P is ahead of the phase of Q by 90o. A, B and C are three distant points of observation equidistant from the mid-point of PQ. The intensity of radiations at A, B, C will bear the ratio
![](data:image/png;base64,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)
Physics-General
Maths-
Represent -7 + 3 on number line
When we add something to the given number, we don’t start counting the second number from zero. We count the places from the number itself. Any negative value means we move in left direction. Any positive value means we move in right direction.
Represent -7 + 3 on number line
Maths-General
When we add something to the given number, we don’t start counting the second number from zero. We count the places from the number itself. Any negative value means we move in left direction. Any positive value means we move in right direction.
Maths-
Statement-I: ![integral subscript blank superscript blank fraction numerator 1 over denominator 4 plus 5 s i n x end fraction d x equals 1 third l o g vertical line fraction numerator 2 t a n left parenthesis x divided by 2 right parenthesis plus 1 over denominator 2 t a n left parenthesis x divided by 2 right parenthesis plus 4 end fraction vertical line plus c](data:image/png;base64,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)
Statement-II: If 0<a<b, then ![integral subscript blank superscript blank fraction numerator d x over denominator a plus b s i n x end fraction equals fraction numerator 1 over denominator square root of b squared minus a squared end root end fraction l o g vertical line fraction numerator a t a n left parenthesis x divided by 2 right parenthesis plus b minus square root of b squared minus a squared end root over denominator a t a n left parenthesis x divided by 2 right parenthesis plus b plus square root of b squared minus a squared end root end fraction vertical line plus c](data:image/png;base64,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)
Statement-I: ![integral subscript blank superscript blank fraction numerator 1 over denominator 4 plus 5 s i n x end fraction d x equals 1 third l o g vertical line fraction numerator 2 t a n left parenthesis x divided by 2 right parenthesis plus 1 over denominator 2 t a n left parenthesis x divided by 2 right parenthesis plus 4 end fraction vertical line plus c](data:image/png;base64,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)
Statement-II: If 0<a<b, then ![integral subscript blank superscript blank fraction numerator d x over denominator a plus b s i n x end fraction equals fraction numerator 1 over denominator square root of b squared minus a squared end root end fraction l o g vertical line fraction numerator a t a n left parenthesis x divided by 2 right parenthesis plus b minus square root of b squared minus a squared end root over denominator a t a n left parenthesis x divided by 2 right parenthesis plus b plus square root of b squared minus a squared end root end fraction vertical line plus c](data:image/png;base64,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)
Maths-General
Maths-
Statement-I: ![integral subscript blank superscript blank fraction numerator 1 over denominator 5 plus 4 c o s x end fraction d x equals 2 over 3 t a n to the power of negative 1 end exponent left parenthesis fraction numerator 4 plus 5 t a n left parenthesis x divided by 2 right parenthesis over denominator 3 end fraction right parenthesis plus c](data:image/png;base64,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)
Statement-II: If a>0, a>b, then ![integral subscript blank superscript blank fraction numerator d x over denominator a plus b s i n x end fraction equals fraction numerator 2 over denominator square root of a squared minus b squared end root end fraction t a n to the power of negative 1 end exponent left parenthesis fraction numerator b plus a t a n left parenthesis x divided by 2 right parenthesis over denominator square root of a squared minus b squared end root end fraction right parenthesis plus c](data:image/png;base64,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)
Statement-I: ![integral subscript blank superscript blank fraction numerator 1 over denominator 5 plus 4 c o s x end fraction d x equals 2 over 3 t a n to the power of negative 1 end exponent left parenthesis fraction numerator 4 plus 5 t a n left parenthesis x divided by 2 right parenthesis over denominator 3 end fraction right parenthesis plus c](data:image/png;base64,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)
Statement-II: If a>0, a>b, then ![integral subscript blank superscript blank fraction numerator d x over denominator a plus b s i n x end fraction equals fraction numerator 2 over denominator square root of a squared minus b squared end root end fraction t a n to the power of negative 1 end exponent left parenthesis fraction numerator b plus a t a n left parenthesis x divided by 2 right parenthesis over denominator square root of a squared minus b squared end root end fraction right parenthesis plus c](data:image/png;base64,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)
Maths-General
Maths-
Statement-I: ![integral subscript blank superscript blank fraction numerator 1 over denominator 3 plus 2 c o s x end fraction d x equals fraction numerator 2 over denominator square root of 5 end fraction t a n to the power of negative 1 end exponent left parenthesis fraction numerator 1 over denominator square root of 5 end fraction t a n x over 2 right parenthesis plus c](data:image/png;base64,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)
Statement-II: If a>b then ![integral subscript blank superscript blank fraction numerator d x over denominator a plus b c o s x end fraction equals fraction numerator 2 over denominator square root of a squared minus b squared end root end fraction t a n to the power of negative 1 end exponent left parenthesis square root of fraction numerator a minus b over denominator a plus b end fraction end root t a n x over 2 right parenthesis plus c](data:image/png;base64,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)
Statement-I: ![integral subscript blank superscript blank fraction numerator 1 over denominator 3 plus 2 c o s x end fraction d x equals fraction numerator 2 over denominator square root of 5 end fraction t a n to the power of negative 1 end exponent left parenthesis fraction numerator 1 over denominator square root of 5 end fraction t a n x over 2 right parenthesis plus c](data:image/png;base64,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)
Statement-II: If a>b then ![integral subscript blank superscript blank fraction numerator d x over denominator a plus b c o s x end fraction equals fraction numerator 2 over denominator square root of a squared minus b squared end root end fraction t a n to the power of negative 1 end exponent left parenthesis square root of fraction numerator a minus b over denominator a plus b end fraction end root t a n x over 2 right parenthesis plus c](data:image/png;base64,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)
Maths-General
Maths-
Statement-I: ![integral subscript blank superscript blank fraction numerator 1 over denominator 3 plus 4 c o s x end fraction d x equals fraction numerator 1 over denominator square root of 7 end fraction l o g vertical line fraction numerator square root of 7 plus t a n left parenthesis x divided by 2 right parenthesis over denominator square root of 7 minus t a n left parenthesis x divided by 2 right parenthesis end fraction vertical line plus c](data:image/png;base64,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)
Statement-II: If a<b then ![integral subscript blank superscript blank fraction numerator d x over denominator a plus b c o s x end fraction equals fraction numerator 1 over denominator square root of b squared minus a squared end root end fraction l o g vertical line fraction numerator square root of b plus a end root plus square root of b minus a end root t a n left parenthesis x divided by 2 right parenthesis over denominator square root of b plus a end root minus square root of b minus a end root t a n left parenthesis x divided by 2 right parenthesis end fraction vertical line plus c](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAdUAAAAyCAYAAAAKj0F5AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAbSkFbcgAADiRJREFUeNrtXQ+IFscVfxyHiIhE9LgeJihyiBwiB81hrQlSKiIiIsXQHKE0ckGkSJAQMHA5TAghYkCDCYWgIiJGEHMJ9jCCBCsixbSYI/0nDUFKKKkcGLFixF5ynef3Pm47N7M7s9/OfrN7vx889Pbbndl98+fNe/PeGyIAAOqO+YqmKkTgTRy8AQAAAAx4VtElsAG8AQAAAFrHJ4peABvAm5z4jaL9BZbXr+hqjuf2y7sAAAC0DYsVfSv/AuCNL1Yr+kPBZR5R9FzOZ6/KOwGR476iDrChbVihaETROFhROHYp+gh9H7xpQYj1F1hel6KbBr6uU3RW0V1FD2UuMAneHyu6UicGL1R0TNEt+fCzNeh0vYq+wNzbVpxUtJPgiBECvF+4HX2/drzppXwmVB/0B6hjWBbQOi4rGqSG4xijT+oeNNx7RYRrLXBB0deKlit6UdG/FG2p+DdtU3Qac28UgFAtFssUTSiaG7DvT1W0n5TBm5D4haJTges4oGh3geV1iJba5Xj/UsvChmXP/joM0C3SmX+t6An5P68kFlXoG3gVdFjRHUUPRNN+T9HexD1DlgZ7Q34DIFSrgleosX9lwz7RHF5X9I2MCdbeegK1WYfU1bR0jcvE2Y5+UgZvKBBv9tH/h9ns9SyHn39ZUbei49Qwc98WYaUrUU8b6s87R7LWecyTLw8M19Yq+rQOA/SqNFJnovGqhA4ZFDvk/wsSnXObdu916XBN7BDhC0CoVgmfK9qU8vsZRV/JpLxQxsVBTw3Np83GZFHbrOuMYeyV1U/K4A0F5I3td5dyzogAZYG6Xu5bIgJsXuI+3t+cY6k/zxzpa7ZdS2bz8xx5t0pjgXTkKsdzjWgruib+IR0qiU0ygBgb6rIqglCtLeYbrq0SDasz5Tnu+32GsX43QJsNymSexAlFmwP3k3byhgLy5oZBA3Uth79tp6FM1laTlsfJlPp950jf/Vk2y1+jhgOTCQ+rPmi3SUc+UuFv+NowwDrE9GHCRVnFjVO1TNwQqrMHvaJtMN+e0n57S9GhDMvNfctkdjejjfJk/bkkmkcSl8nN/JunzjrzxvZ+LuXws/cMz3YaypzMaBefOdInjIa17I8VbUy5p/JC9XXpEDsq+v790rl0rEnRvvdIwyEmCkI1VrwqgoNjLT/TfmOHkCdTnrX1fd/9Ktc208NTbJN7UXXGwBsKxJs1lvnMpZy0b9Ovp5l/feZIWxiNCctFoPam3FML8+8Z6chV9fRlT7mTFrPLccP1ZszUQTK7dAMQqjGBs8z8QNN7XD9R9CWlmzdtff8lMoc8tNpmE4Yxdr2EftJO3lAg3vD7nchZju3bTNcvkt386jNHDjvybaVotPMy7quFo9K4dOSVFX3/bTRzr4FoOj5SXymdk4Zlc/GfCOZfCNX4+cFaygfy/3cVvZZxPzuz7DBoABzCEML7l8PvkuErIzIpl9FP2sUbCsSbd8gc6uJSDn/bkOWb9eu2kBqfOdI1jKZb5uhOB37tlner9HzCXmGTVN1ED9z4f6PpzCDsgTYmnXCzZqY4r3WQLRYtF4BQjYkfRxV9J5PShMMCeJQaDisb5O8lcm1HoHfkcIv3ZQ7hPb5TMtbK6Cft4g0F4g172R7LWc4omR2gTNdNzkW+c6RrGM2Yh9Lm6kUc7XzSPBrpTsUnqG7pOLxA4FyWP6OGt9vcxEp0lGZ6AjPYjX4T5vigwqNqR1yVkcLOhw+PKfpe0YfklquV4xi3ivDgBfM45Qtv8cGwaCMjMu5ulVBnHXnTJwrBFM3c88wq5zaZE17YrjO/VrcwR/oIQBfnLp80hdHOIxvl5S5g7geARygrhZ3vpHBFntlTET52lVjXbOVNq+WESKjfCnwS6kcrVJ+Rl0MqPwBooKwUdr6TwoA88ziaCLwpEHzwQAxpAXkfdWfA8TNVJkO5st+ibwHAI3Amrr0GjYD3jjiEgbcY2DvTZE6bJ5PDBNlTZbYyyLejecAboBShOl/GMpviObSITeMLXR48QtM5f4H4Ok2eYHOgNeip33ggsTk4mQLzNM30UGRHmcsiQDuFOExjksz7Z2g/AIhTqLJA5XClN2W8834z51N2Cjs9Teb8uAAwW6GntjwgwjGJ5XJfEiMyCE3l9UCoAkBlhCqbww/nfbHzUtmGkjQrUDnaJviaj/d6ijj+23SEGP+te8xzvtlFhvLueQ5ytAsIlD1HThUwB5JlDpggR1OvCXek8AVY+ES5EoP5t1zoad5sLv5574OmCgBxa6oD5B7WY5TIk5SdWBkAZgv0dG4cz2jK1sWhG0lTr2+qTAhVAIhTqHKSjNG8L7VIKrqF9gGAR+B9lKRbPwe8nzcsRjmD10pN+JrCcFjQDkGoAkBlhCpbnW7kfalNUtE5tA8APIKezo09eNmlvun110xpN6w9t0AWp81UmfzvWXl2PYQqAFRGqDI4y9abMv55bLNlap3Lg7+Uik6gfWY95hIcHximdG5Pi2b6UFawthyxrK3+U+7jJOScrWyC7OkOIVQBoDyh6oMnqBEex1ujHE435Ppg8xzVl2vC5DLytdYVbLX4I9hQKFZRemamoiaF+QRvd/AGQjUK1ClGtax8rXXFIUVvgQ25wfurnJWsGY/KHoRXKf1kjqImhWfJ7mE82wHeQKiWikvyYktrwLSy8rXWFX+nxgHPQH6NiJ2c7onF5LxoqmVMCp8oegFNAN7kBB/0XmTuX9ORci7YL+9SaaH6gOyB6UWATbFsYmYHDt5nGvcU4D5M43ytw1LfN/Jtl8icySYrp6Nrnleuj/fQJuVdk/ldhywd9Q3ysM+XhGWKviW3A4TT2mpK+HlVLAdA9vhrFYul7RaDneBNDoQ4pYZT3z6X81mfU2oexMbMFRT+dJoxWb0vFAGr51QtUqhy2V+JYGvWd9DwfVk5HV3zvA5L55mT8k5cT3fiby7zvQgH1u4C+0GHrDavt9nCMVsEPB+I8VHK77PZzwC8cRNi/QWWxwrJTQNf2XOWveHvJhQsk+D1OU81CvDB3esTEylPPFsD1TVIM4PmWePbHEiocn7VPu3aAmlE3cSQltPRNc8rd8as1I6bRLCT3PtppP3id4qej1ALq4OADw22xthOZ5ntfgZV5k0v5TOh+qA/QB2sbIwYrl8WmTBf/u6TugcN97oefN52jIiQGpPJ5i+yWgjZodcaGLvUQcPIk6vxvuH6XE2oZuV09Mnz+oxM1lmLkouykGFeL4qwX7DJ9z+KflRgmeulrWPBA6onlln6axNF+BlMgTdtAWfoOhW4jgOiXBW5iL1J7genL7UsbF6kOM53zQTv5V1T9CtFH4uwWR2wPt20kpZYvNUBbcuvulbTDrNyOvrmb+2R+y8lVmA69oi5Y3Wk/cIllMbHTNYjK9DlkXxfbAK+SLxCjS0IG3z8DIoQqq36UFSNNxSIN/s0RWKvZzn8PG9p8dbTcRm/t0VYJXGBGjHYOvL6g7DWeayABa8+b0eLTmHKcWmk0JPehPb3OvI3w7kOaFt+1Zc0U0RWTkfXPK+6FvuFLFbI8M28j3DQYuaIAW9Lv7DBx0y2QiwhPZF8W2wCvmh8LosiG1z9DIoSqq36UFSNNxSQN7bfXco5IwL0uCwq+b4lIsDmJe5jxcrmE5LHH8TXbLuWzObnOTRz2w6ghmdt0vQyIgImhFA9TDOz3MwRYdCjaaI3MrQ2lzyvOnh1pm+680R+Tjoxa7GcYSdG8y+H0jyV8rurmaxHeBfLaUexCfhWYLKCrBINK81j29XPoKiFbas+FFXjDQXkzQ2DBupaDn/bTkOZt7U5aDJjLvTxB/Hdn2XZcI3sqf8eQoSaTQXvi1DiznHKILCKGtCj0pGajkPN/KymdHJpOR1d87wmMSBCN9lZu+Rbk9e4zJORtdEyyg6lcTWTnc9YeBQFF/NXbAI+L3pF25gyLHw4UcehDD65+BmYxlwev4Y8PhSt1Fln3tjez6Uc2zZbp6HMrNPJfPxBfMJoWMvmLciNKfdAqFowLCurEemwtwKZg7jcrSJYJ6UT2OrJyunokue1eQbtpHT0lZqGPCoCWcfpDJNUSJhi9XY5aKGuZrKyUq65mL/KEvCh8aoIDl74fKb9xg4hT6Y86+pnUNTCtggfiqrxhgLxZg2Z/QBcykn7Nv16mvmXyN0fxBZGY8JyEahpYW4w/3qgCyxoq7YzoP3mEkpTppksC67mr7rlVOWwoB9oeo+LM199mWFhcPUzKEqoFuFDUTXeUCDeDJL5kBOXcmzfZrp+kezmVx9/kGFHvq0UjXZexn2VcVQCZieaK/p/U8Pbr4m5sspPC6XJayZzmajLNjFWHdwOH8j/31X0Wsb9rn4GRQnVInwoqsYbCsSbd8gc6uJSDn/bkOWb9eu2kBoffxDXMJpuWRC7ZG3bTTOT7QBAdGBTzneJQcn7z3/OeKZsM5nL5FmmiTEmHJX26xSNJcu87eNnUIRQLcKHomq8oUC8YS/bYznLGSWzA5Tpusm5yNcfxDWMZozct2Qqk/wBAP5L08nF33ZY0ZdtJstCu0yMMeAxRd8r+pDccrX6+BkUhbJ8KOrOmz7RSqdo5p5nVjmm84DTrjO/Vie0dV9/EFcB6GqVqlyaQmB24/eK/ir/dzmVpmwzWRbaaWKMAVdkEtpTkfftAm+C86bVckIk1G8FPgn1AaDt+Lms6H9K2XF8ROWbybLQThNjDBgQwfE4ujJ4UyA4CiCGtIC8j7oTzQFUDeycxKFCLgkd2mEmy0K7TIyxYDu6MHgDAEA8OCor+udr8j0I0wIAAADahm4Rqji4GQAAAAAKwC6wAAAAAACKQSdYAAAA4I//AQWr+sK9FYIqAAADSXRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtc3Vic3VwPjxtbz4mI3gyMjJCOzwvbW8+PG1yb3cvPjxtcm93Lz48L21zdWJzdXA+PG1mcmFjPjxtcm93PjxtaT5kPC9taT48bWk+eDwvbWk+PC9tcm93Pjxtcm93PjxtaT5hPC9taT48bW8+KzwvbW8+PG1pPmI8L21pPjxtaT5jPC9taT48bWk+bzwvbWk+PG1pPnM8L21pPjxtaT54PC9taT48L21yb3c+PC9tZnJhYz48bW8+PTwvbW8+PG1mcmFjPjxtbj4xPC9tbj48bXNxcnQ+PG1zdXA+PG1pPmI8L21pPjxtbj4yPC9tbj48L21zdXA+PG1vPi08L21vPjxtc3VwPjxtaT5hPC9taT48bW4+MjwvbW4+PC9tc3VwPjwvbXNxcnQ+PC9tZnJhYz48bWk+bDwvbWk+PG1pPm88L21pPjxtaT5nPC9taT48bW8+fDwvbW8+PG1mcmFjPjxtcm93Pjxtc3FydD48bWk+YjwvbWk+PG1vPis8L21vPjxtaT5hPC9taT48L21zcXJ0Pjxtbz4rPC9tbz48bXNxcnQ+PG1pPmI8L21pPjxtbz4tPC9tbz48bWk+YTwvbWk+PC9tc3FydD48bWk+dDwvbWk+PG1pPmE8L21pPjxtaT5uPC9taT48bW8+KDwvbW8+PG1pPng8L21pPjxtbz4vPC9tbz48bW4+MjwvbW4+PG1vPik8L21vPjwvbXJvdz48bXJvdz48bXNxcnQ+PG1pPmI8L21pPjxtbz4rPC9tbz48bWk+YTwvbWk+PC9tc3FydD48bW8+LTwvbW8+PG1zcXJ0PjxtaT5iPC9taT48bW8+LTwvbW8+PG1pPmE8L21pPjwvbXNxcnQ+PG1pPnQ8L21pPjxtaT5hPC9taT48bWk+bjwvbWk+PG1vPig8L21vPjxtaT54PC9taT48bW8+LzwvbW8+PG1uPjI8L21uPjxtbz4pPC9tbz48L21yb3c+PC9tZnJhYz48bW8+fDwvbW8+PG1vPis8L21vPjxtaT5jPC9taT48L21hdGg+0S8AUQAAAABJRU5ErkJggg==)
Statement-I: ![integral subscript blank superscript blank fraction numerator 1 over denominator 3 plus 4 c o s x end fraction d x equals fraction numerator 1 over denominator square root of 7 end fraction l o g vertical line fraction numerator square root of 7 plus t a n left parenthesis x divided by 2 right parenthesis over denominator square root of 7 minus t a n left parenthesis x divided by 2 right parenthesis end fraction vertical line plus c](data:image/png;base64,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)
Statement-II: If a<b then ![integral subscript blank superscript blank fraction numerator d x over denominator a plus b c o s x end fraction equals fraction numerator 1 over denominator square root of b squared minus a squared end root end fraction l o g vertical line fraction numerator square root of b plus a end root plus square root of b minus a end root t a n left parenthesis x divided by 2 right parenthesis over denominator square root of b plus a end root minus square root of b minus a end root t a n left parenthesis x divided by 2 right parenthesis end fraction vertical line plus c](data:image/png;base64,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)
Maths-General
Maths-
I: ![integral subscript blank superscript blank fraction numerator 1 over denominator 3 plus 4 c o s x end fraction d x equals fraction numerator 1 over denominator square root of 7 end fraction l o g left square bracket fraction numerator square root of 7 plus t a n left parenthesis x divided by 2 right parenthesis over denominator square root of 7 minus t a n left parenthesis x divided by 2 right parenthesis end fraction right square bracket plus c](data:image/png;base64,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)
II:
Which of the following is true
I: ![integral subscript blank superscript blank fraction numerator 1 over denominator 3 plus 4 c o s x end fraction d x equals fraction numerator 1 over denominator square root of 7 end fraction l o g left square bracket fraction numerator square root of 7 plus t a n left parenthesis x divided by 2 right parenthesis over denominator square root of 7 minus t a n left parenthesis x divided by 2 right parenthesis end fraction right square bracket plus c](data:image/png;base64,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)
II:
Which of the following is true
Maths-General
Maths-
I:![not stretchy integral subscript blank superscript blank fraction numerator left parenthesis 1 plus x right parenthesis e to the power of x end exponent over denominator s e c to the power of 2 end exponent left parenthesis x e to the power of x end exponent right parenthesis end fraction d x equals blank l o g blank vertical line t a n fraction numerator x over denominator 2 end fraction vertical line plus s e c x plus C](data:image/png;base64,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)
II:
Which of the following is true
I:![not stretchy integral subscript blank superscript blank fraction numerator left parenthesis 1 plus x right parenthesis e to the power of x end exponent over denominator s e c to the power of 2 end exponent left parenthesis x e to the power of x end exponent right parenthesis end fraction d x equals blank l o g blank vertical line t a n fraction numerator x over denominator 2 end fraction vertical line plus s e c x plus C](data:image/png;base64,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)
II:
Which of the following is true
Maths-General