Maths-
General
Easy
Question
What is the LC M of 9 and 18:
- 1
- 9
- 18
- 6
The correct answer is: 18
![](data:image/png;base64,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)
LCM of 9,18 = 3 × 3 × 2 = 18
Related Questions to study
Maths-
Find the GCF of 9 and 16 :
Find the GCF of 9 and 16 :
Maths-General
Chemistry-
The correct statement about the following disaccharide is:
I) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655636/1/1188918/Picture321.png)
II) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655636/1/1188918/Picture322.png)
The correct statement about the following disaccharide is:
I) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655636/1/1188918/Picture321.png)
II) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655636/1/1188918/Picture322.png)
Chemistry-General
Chemistry-
A carbonyl compound P, which gives positive iodoform test, undergoes reaction with MeMgBr followed by dehydration to give an olefin Q. Ozonolysis of Q leads to a dicarbonyl compound R, which undergoes intramolecular aldol reaction to give predominantly S.
![table row cell P fraction numerator 1. M e M g B r over denominator 2. H to the power of plus end exponent comma H subscript 2 end subscript O end fraction Q fraction numerator 1. O subscript 3 end subscript over denominator 2. Z n comma H subscript 2 end subscript O end fraction R fraction numerator 1. O H to the power of minus end exponent over denominator 2. capital delta end fraction S end cell row cell 3. H subscript 2 end subscript S O subscript 4 end subscript comma capital delta end cell end table](data:image/png;base64,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)
The structures of the products Q and R, respectively, are:
A carbonyl compound P, which gives positive iodoform test, undergoes reaction with MeMgBr followed by dehydration to give an olefin Q. Ozonolysis of Q leads to a dicarbonyl compound R, which undergoes intramolecular aldol reaction to give predominantly S.
![table row cell P fraction numerator 1. M e M g B r over denominator 2. H to the power of plus end exponent comma H subscript 2 end subscript O end fraction Q fraction numerator 1. O subscript 3 end subscript over denominator 2. Z n comma H subscript 2 end subscript O end fraction R fraction numerator 1. O H to the power of minus end exponent over denominator 2. capital delta end fraction S end cell row cell 3. H subscript 2 end subscript S O subscript 4 end subscript comma capital delta end cell end table](data:image/png;base64,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)
The structures of the products Q and R, respectively, are:
Chemistry-General
Chemistry-
Consider the following reactions I and II,
I) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655007/1/1188868/Picture105.png)
II) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655007/1/1188868/Picture106.png)
Products 'X' and 'Y' are respectively:
Consider the following reactions I and II,
I) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655007/1/1188868/Picture105.png)
II) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655007/1/1188868/Picture106.png)
Products 'X' and 'Y' are respectively:
Chemistry-General
Chemistry-
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/655564/1/1188862/Picture84.png)
II) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655564/1/1188862/Picture85.png)
III) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655564/1/1188862/Picture86.png)
IV) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655564/1/1188862/Picture87.png)
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/655564/1/1188862/Picture84.png)
II) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655564/1/1188862/Picture85.png)
III) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655564/1/1188862/Picture86.png)
IV) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655564/1/1188862/Picture87.png)
Chemistry-General
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,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=)
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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)
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,iVBORw0KGgoAAAANSUhEUgAAAVMAAAAnCAYAAACyj6sXAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAZpE86XgAACIdJREFUeNrtXXFkHUkYH88TFRGiIipOqaiqU+FU1YkKVVERUeJEnVOl6tSpKv2joqpC9I+qqqMiIuqEqDpVVU5FVZxyKuJUlXOq6lSJqoqIkJtPfiv75s3sm53dfTu77/vxkbeZ3Z1vdua338x8335CMBiMIuFnKVMpXq9fypLDeVOoC4PBYBQOh6T8mfI1p6Wcdjx3CXViMMR+KRNSlrkpuF0VfC/lgZQvUjagy+mc67QESzItdEv5V0rFUffvpLzgfuSGLikzUj6ikR9oHkSRcF/KOSlbzH/crgqeSxmX0oHfB0Fm45qyfY5T5WZMx6NwFWSVRPcXIFXuRzHxVMp7Kfuk/CLlg5ThEujFZMrtaoO9UlY0x09J+S3je9+UciHF61VglXYn1J14YCrj/lC68TkMpX6S8g3+prfVbh70jBZq13Xl9zXoGcgVhbCuh2ZyyyAl9fzLUnqkzEpZk7IKklINmQFNfc4ayOwG/mfCOGaZSXQnHJXyjMk0HpbQIaqhjsKDntFK7XrUMNVekDKqOf5Yyh2xvTxWMZRbAHESkR5DuV4QV3uoHK1fthnq9QpkHOCMlLsNdIk7PTfp3oa6MZlaohMKLfKgZ7Rou+6S8lJsb86oeKOxOMdBlGHMSTmpHHsrttcFVawqs77NiLoNSbmFv49bWIpx11+jdBcwsphMLTEKhaZ50DNasF3JsvxdygnN/yqYmqtYhDUXxnOFdOncr5pzq5prbjao4x+wbJdF46W3OO5QUbo3ItMtC2m58XkdCp3hQc9osXbdBzLpM/z/CEhSxZqoXQrTEecRw2zvqOZ41DSfcBGk1sjv0+QO5aI7T/MdsACFhnnQM1qoXQ/AimuPKDOO6buKT8pvmiK/0pw7a7jmrMbyNE2zA7/QW0LvvhSGyR3KRfeA+HkDKgaWodABHvSMErSrTb16YERUG5S7LfQuS+Q2uCv0ewKEFwZtTul23HXHTa5RZD0+AumRX+hfEdN8W3coW90F6nTTMzL1ejzTzuKmKNcOPpMpk2kUHlsaD7RrrnMxItekexgztE5KfqhPlDIPRf2GlOm4btOoG9cMkyfNHu9HWNEzKepOiOMV0PJk2oHKfS7pYHdZEPcNa5696JK0azN02XLUQafLQVihdLxNM6VegFVKVir5m4Zdo1YV67XRcYrLD9ZE20C6vZpy82J7h9+V+Gx1zzqctHQbVidQuadsaHkJ2hxYYV0KYbl0Jzw/iw+dJIGvHzrxlkzHULl55i0vMVqiZ9MsXYq8rHNepPsJPlfQOuk5j2ecXvaH87jZr8xbuYOWXGhzgpZcaB2bNjRozS4cwugaXugDrim6BNYcrfN9hc5zhilwOwb4p4i2KQOZMvIn0w70NVreIXc0Wm7psjlxWuzE5DPyA60jku/hGfzdKXbiwtUQxbjhhWk5VyeFGm7ZhWl/WOd5Ub97TLvOz0GcVcglsb1pOspkymSaYvkOjK9J9Edau6ZvK1i5jc4bBiyjuZgwWFkUjqhuQsQNL/QFqi43QYph7EM5tW0mDdfbw2TKZJpi+SnMDp3wBDc7npKSLG6W4Hux833JsLW6ZmjrOOGFeTxT0UCXCqbs6pR+l6j3LPlPo6MpVDNq8HC/K/44sSFH1+sGfbLLdbB8xsU7+YWXG/qFPmTRFI5IsA0v9GWar+picrtxLceWKVumScsfFglcwSpYd9rk55Mr6OPDOkdsUzhinPBCX6DqMiLqv7oUvCQmE7QNkymTqWt5CqR46Fqp3bjRR34+uWLUQCxBWocw4oQX+oQ7ii5Doj5iiF7ur0VtdA6R7ryhbc4ymTKZplieZkFvXCs1hBs94ueTK9pBIv2hh0ohfx9Ebdhh3PBCn6CGUFZFbVqcXpS5qpzXiZd9f2hJ5AHOPVZCMuVUz/mRKWEZM6Mq+t5FYf4ATQ1+wI3mmM9yRw/IhHwoKQpmUNSGHbqEF/oEXQjlAF4iG7AITJ+AJOv0HcqRJU5Re5+EOSy1qGTKqZ6zIdM4oJRNtH9BS58rIobvdvAd08tNaIDhDBshi40V3+LhfcAgLOM1kD65Jt3OYZnhWxEdSWXz3DnVc/6pnl25wcuXZbN8TDtggWRJpmmiTPHwaYJ2z0+J2g9+0ODP8rsOtH5K0XmBP+lhkM6BhP2BUz3nn+rZlRu2fB0cVLG9Gd/nHszlrNY6eMMhX3zJeLDR5tVXWMRPYJlm0R841XM9sk717MINXo73dWF2fE4LNKV45tgIWZEpvbHfYV1ETd9LUGPIbdP1Fjlu3hXkXfDGw36d1rmc6jm7L+27csO6b4Ngv8j+a1FteNvt9YhMiUinRXS+HTWG3DZdL8ElLW8R0QPdaN30ZEl04lTP+jGcRQ6opNyQOwbFjjvJBSgwkuH9ppSpS5ZkuoGHTtPAS6I+NDMAdZhGobNqDLltul5CUePm4zyTsFwsiV6c6rm5qZ6TckOumECFH+Pt+DemJVnhkOaBZhVTG6CKt/EEBoBuk2IMb/qRiLUmNYbcNl1vgGbFzeeJLlhhL4XZ37NIunCqZzPSTvXswg1e4QY6/o9ovC8iWx8yuldfwgZL0sAnhD7enbAH06BFjQWrxnzHSdcbIE7cfNHRgWddVHCq5+anek6DG3JFFYRKazdX0JDNnA7mketlvcHUZgUvF3X6Nhvxu9HxIsbNiwzb2Wdwqud8Uj378G3dwqOZlim5z/zToMyMZjqkpuGNk663qHHzSZdz3haw3pzq2Z9Uz4WzTMtMpg/xBq1AhkCkpyLOIefv15qOqcaQ26brLXLcvC1oujuGQUjtPIjBW8QsDZzq2Q7NSPXMZOpRg43BOqJF/FW8dQ9rygXfbqVyi4YOpcaQ26TrLXrcvC0GMBDXIYvCMp2Dp32RUz3nm+qZyZTBYGjBqZ4ZDAbDE3CqZ0/xP6r4GMbEaJriAAACaXRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtc3Vic3VwPjxtbz4mI3gyMjJCOzwvbW8+PG1yb3cvPjxtcm93Lz48L21zdWJzdXA+PG1mcmFjPjxtbj4xPC9tbj48bXJvdz48bW4+NDwvbW4+PG1vPis8L21vPjxtbj41PC9tbj48bWk+czwvbWk+PG1pPmk8L21pPjxtaT5uPC9taT48bWk+eDwvbWk+PC9tcm93PjwvbWZyYWM+PG1pPmQ8L21pPjxtaT54PC9taT48bW8+PTwvbW8+PG1mcmFjPjxtbj4xPC9tbj48bW4+MzwvbW4+PC9tZnJhYz48bWk+bDwvbWk+PG1pPm88L21pPjxtaT5nPC9taT48bW8+fDwvbW8+PG1mcmFjPjxtcm93Pjxtbj4yPC9tbj48bWk+dDwvbWk+PG1pPmE8L21pPjxtaT5uPC9taT48bW8+KDwvbW8+PG1pPng8L21pPjxtbz4vPC9tbz48bW4+MjwvbW4+PG1vPik8L21vPjxtbz4rPC9tbz48bW4+MTwvbW4+PC9tcm93Pjxtcm93Pjxtbj4yPC9tbj48bWk+dDwvbWk+PG1pPmE8L21pPjxtaT5uPC9taT48bW8+KDwvbW8+PG1pPng8L21pPjxtbz4vPC9tbz48bW4+MjwvbW4+PG1vPik8L21vPjxtbz4rPC9tbz48bW4+NDwvbW4+PC9tcm93PjwvbWZyYWM+PG1vPnw8L21vPjxtbz4rPC9tbz48bWk+YzwvbWk+PC9tYXRoPsPmAY8AAAAASUVORK5CYII=)
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