Maths-
General
Easy
Question
Using Simpson’s
rule, the value of
for the following data, is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAgEAAABhCAMAAAB4U4IgAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAMAUExURf///5ylpbW1vc7Wzmtra0pKUoyEjFpaWubv73MQWube5nN7e5yUlPf377W1ra2ctaVjOnNjnKVjEHOcWqUQWgAAAIyUlHuEe63v3kIZY4Tv3q3F3oTF3hAQEDExMVLv5qVjpVKt5hnv5hmt5nMxWlLO5qVjhFKM5hnO5hmM5qVa76XvY0Jr3kLvY6XeMUJarULeMaUxlKUZ76WcMUIZrUKcMaUxGUIp3kKtY3Na73PvY3PeMRBarRDeMXMxlHMZ73OcMRAZrRCcMe+cpRAZYxBr3hDvYxAp3hCtYxBrGd73xUJK3kLOY0II3kKMY86cpRBK3hDOYxAI3hCMYxBKGa2U5oSU5iEhGYxjY6UxWrXepaWcczoIEKWcUmtzc0JrGe8Qpe8ZEEJKGc4Qpc4ZEEJCQoSUvd7W1sXFvd73EK1jY+8Q5u9aEO/OEO+UEHMQKc4Q5s5aEM7OEM6UEHMQCHvvpWNjOnvFpWNjEO8xpe8ZMe9zpe8pY85zpc4pY84xpc4ZMe9Spe8IY85Spc4IY973lO/OtUIpEN73QggACKVrzqXOc6XvEEJrjELvEKUQpaUpzqWtEEIpjEKtEKUQKXNrznPOc3PvEBBrjBDvEHMQpXMpznOtEBApjBCtEBApQt73a+/OlKVKzqXOUqXOEEJKjELOEKUQhKUIzqWMEEIIjEKMEKUQCHNKznPOUnPOEBBKjBDOEHMQhHMIznOMEBAIjBCMEBAIQu/Oc+9z5u9ac+8x5u9aMe/OMVLvtVKtte+15u+UMSlrWu+UcxnvtRmttXMxKc7Oc85z5s5ac1LOtVKMtc615ghrWs6UcxnOtRmMte/OUu9S5u9aUs4x5s5aMc7OMVLvlFKtlO+U5s6UMSlKWu+UUhnvlBmtlHMxCM7OUs5S5s5aUlLOlFKMlM6U5ghKWs6UUhnOlBmMlEprWpzvpYRjOpzFpYRjEEIQOggpEHOle87OnM7Ozs7W73Nae0pKY7WllHuElFpzWt73/2tzWoyEnJyllP/v/wAAAJF+rwEAAAEAdFJOU////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////wBT9wclAAAACXBIWXMAABcRAAAXEQHKJvM/AAAQv0lEQVR4Xu1d0ZKrqtIOjAIVMblyvNLX8r9ad5R5gvMOedW52lVWKlOVPVN/I8RgItCZYdbZ62w/1KBxOihN0900zGbFihUrVqxYsWLFihUrVqxYsWLFihX/ZoiXPnXqnXyatFJMkYZe2EqfIWtznjZ1yj1LkdrkZfx3UlTKVvoMnNpMMhTJKcpXm0kG8stmkuH8bjPJQIvFJvsNCL5Eke9sJhl+gAOkzSQDKWwmGch7aXOpQOvUFLfLHJBeBiTnKZJcBsjkHHCubSYZDnVqGfC7OOD0J/QC6WUAs5lkSC8D+t/UC9TJKX4kf7sks5lkSM9TtN7aXCp49IDkLfbyT5EBASFKksvs/dcoBsr4A3pAvkTxv6kJ9r3NRPDxt834MCfUHyiFTRZ+8nucDBAD3VFcIc/B+hLDjs4ICTpiX/tf1gEnA0R/ILgylr9LBmA1QUE40t6JyAAhc1cRF0XXNA3s7WCvPOKMkdm9zLKMt/krppQhPQAIcU1I3gidoYCQqs7/+mn9aXMBCFJAGZWSGB74Z8kAQXlTcVxPF+YAAoQyt5KypoV3otQv/1tB6QGyacnLILuGIcQxKfz1xSpFX/rXprlxiazaXJcxO9gLD/g8FIi3c+g60r+cVcXibPrbZECGodhfeNHOK86PEAcM2UjIlQFZS/tewGYvLGB/sZkQWDs+SVa1iGKG9ID3kZC4VHziSdlIMZbRT5pirEHa7fUHq9qX8TyI7X+WKP6ADMBQHFgvWLXIk48I2QIHNkAduaxUnuJvA9UL2NqRVefvTiZ8+AVFKcT4HbT7iZBsiM15geKAT8PntGoQ7Q7jDzgwCee9lBLBUh74BdscJUshAzSAA2xOQ1xUtMbIyWYQIFWHEMcI60JWypEB0RoDPQDR+xhAGRGKgIcDZi12aKu23wyqqqwjdigYRsdwgdUES3ZE6gExW6CYsdJnEVABLQimF7CYU/dhH9fbuMOoHxgZgHs7GrgyonyCfaeLljVXLV1WDUIEzoDSAzTqhDJgrgcMVwnuwxP+m6HBCFiE14o2juIvm91GlME2jvcHCNbcNIwAer5E8V4PANEMMmAy03Cd4AxYf4CWAck4wCFUnjptxHESII7vBQSvUB5JUkTqS/DGGeAiFS9y5dqHD0DKADEw3lxQglosytx7W2DoWpLd7HTKs2d7gadkAIrNYxxwqTJXBH9kcqCs6wI1h9IENURdxarWIDY6XGaV+5uUs8NBqibz1zLIAIRDAKq17Tq+xxQSowcAimOLMUT9eEYPCDQBBzEJe1rqTuix83e1aD1AHpE9VUwGyGaBEKhd/oFv+n+oXy63Yvi7/QvhD8CODTJHY/0SsLbApmguOFZDyIDH1y9U5VfP9zgZUMpusetcQHhcoJTNEiGRVW9e+ihr0IIdO8Rbx+kBlP9lHCFfBl4GYP0BsZHXRU0YxO6sb5jhjBsXoC1Kw9IIxwfsu2Wzhx1z7w88Ex/QtxhtBeMTLEnO6mPctA0BrQcUWAmL0AQf6/qTzzreOXC2wKDANAaEvItXBCkO7VjR1n1zQ1kHGgFqXMCiz6vXuLDCxAfQtgaD0LGnf9AfAA0AKQNiegDIAPP4MoOuf6jH4osu0CxQ4wKiMJpEjxnvJoH6EpmxA4dfIKpJBgZAb14SGBonb8WhxgWoUdSHFqzLKOIyoKSdKkFfcF4dWIPPegexMULQCfpF4AwRGQDv0Qhr6PqhZsGehTNRVMrPX6hxAdK1TMpXyTHdYkgPkE37CnRYrglBucoN1Y63jYAv/N03yh9gOkBxaTDiND422Hejc5FV3aRZfsEjhJIBghSXpjrmdcgiviKkB4h9cTlWFX/XhFSVw91tw4s6a3lAN8JYg8BYVQWk4YDggMC4wEhohFbXxoGmXjUKyqh4wDN4OIl4N0DAEqyLrM0wteQZGXKebigyTQk+5NVQH3493QugYoSEPF0yDbaNc3pIBgg9iA+4aKaV2RkuDbI4XRgNsRamF9haylkWCDWZEJABPTOPCg8LhKAXgGsDqaGMJCTndxgZUA6SnYo6+LATnokTRPy2F89Ei5eoXwrqAaXxm+C1Jg2kNfgEzskjew/o+QLY2vptcYIIy/Q5xGyB5/HxxNggDj8RK4wfG8Rhy01rmWNZBnwH6aPF07/dZ8YGcYiOCzyNA9JWxkPkv0cGoK1BNNLLgPSx3fIHZMBSi/0OQAbYnIv0MiB9tHh85PVZnNP3Asl56hmvMArlFjU2+H0UyfUA8ifMG/wDZIBY9gfUhx2lsQ2fKOX1E39kNl/SGyDLxo8oUbuZD38CFPyAIXhLkY0eCj7mlpLexl9zU3Q7ME7gI5amLZ7oeVkPUNZWTYYut5kk0KZ0q64GNQbRey/ZRXWFPUkF1drMIp4p/xV5kOJXwJVPD9BWebqk5w26599L2iIatSz3YiiJzadztpC0aCUn90qCBGU0GbGww08+XHpM8KTucbPTMULza4tHdMLGB3wbPzB3+N+qB9hcKvzTZo3h8QPWYHJ/ADruDI3ktsBvmzHyJ/gE03uF/wSfoGdcIL0MSE7xB/wBuBihJ0CSt9j06wcgI0UB/TAM13v7wR0YE54VyVz8O9cQ+eL6AQGk1wOwmqCQGW/t5Ia+4NydsNNznu0ifoqwHtBTKR+muwsaZPcwByxS3PQkNGIeHh3uKZHzP/8c4EpwCDYcJyhGirMaFYvFdoBdPwCKJgeU7wjJAaJo/365hjW1nZykgYboZduFpmIAAl5hQTPF31Sj5oEROx4IlQGEOID+yvM31bV3oRbCnaL1iFCM0FAozlXb3mJXhHzLObQKHmCqkB4wFHl+ybvWiegu90q98VYFAmRQPsGthDYJRXsP8dIVyPgAcryU0IJG/suPj3YYbSOziAJ6gFBV0ZfbYrZwwsCbyMzXgB4gsiobNj2r7ubhkSrIASHNPav4IIRsmql2+q6RW9GrUBz9PqAH1FV+2JakqW5xRLJRQylo2/jj/A8nP8UJ9NjthKBqKVr6AThrUOS3d0mr1uZcZMfw7ISTvxeATkT/6ba9hfGCyDldIlPTAjJgm421olnLXDAA4RXkgNCssWychgtC5O36mEM7EqehGYSBscGSmdDb042DBvvEsjHRyEtAxQjtzPoBuMl9uPkCQ9dO3c+lerM5F6RRwQ4qsDSOdkwBoOFO3LiVB/jNcDBiSMIaimVWzXzeGS/CHBD1B5TuzBlDug9GH4fqy3z1cVs/QNowVnhyb6QgKlbYArd+AGbeYDnwqmPSFlSZOU2CMnYQm4GZL2gX5rf46HB5F8o/NGEOiNsCujOwWQ3SUT0D1o+4LfBZPITyv3SBkFHEqrLXage86oBhAPQvXg3oGVvgPMYex4DRAz5lV3UqNw+6bY+GQaGbgfYATWBk2B50Qfg4vHliSOP+gL6zhC2GztULHhH3B/SzCXh9numZZPZsCfH4gF4d76N/SRNYnCQeIwT9yhT5d13xgQaWu3pCBkADwAQVovQAoY7ELnriCOdDq4VMXn3ok16NjMB8y1bE5wxNMzwsoIP9pgyYNVhRg2mRf1MGgKp293jAE4FyxP0Bbm2DJqS5entpvAtQfaJlQNkXXWDVrBtQa4kJ1Uy0HOFcgNimrfEMgK6o25t38aLomqK7e8b/jh4wgrrTnIBf4bWGrcGoHjCo7v4xWBPSt8+xOV7QcBwxRdVfJ0KyNhCIjpUBhKkGNcUft5YYvMvpLtpMrZx2SnL7AFYG0MxjEsRkAOiad3cMzZdtgRGDct0BPddTkUYO8FZKTAb0/GHqueyCs0hja4uLzFlLDlAfVca7lvj5BikDRMZVF1yKYgJKBpCK25yumKlpgq7dXjm454FJ74DI2GCfP3T6IAOCXBPRA/psVl1yLKnmAHr2vZeIHiB+dX/f/Sltw+tTyXAvUBaNW6GCdZdhuyXKP+//81Ag5gwBRN8TNS37EwBOBhSOwePIgA1YW9cHgI4iyAHh9QMWWpf+oW/IgP5X55ZnaJt3+UHaSrHW+38kwjJA1N29FkhVZIGycE/1yZqZprizuvv+6NcEnxkblO4aRV5gRofBTrvVz00GCMn/mmaQxjggODIksll1GcRkQPDtlqx7d9uKXmLyciraqsv0TOJlhPUA2d23qH6c9BlCeGzwo5nrEIWe4AgA+8r7LlE+QYu+PSLGJjGxwn3nKPiTDBCMk9PUjVk9wIugP4B1ozop9CjJxOK0a4ITlIMyQLa/9LOPFMeXIDRKsAUCixQF4wOoWe5BjCMihmTW6gmJm95fzOB8AdoaiuMK2JpdM9vZvnROi7sDyidoeX+uZvqAGR2mrut7kgFMkc2huaqIwowWUOXRY0P+gOuiHDLbAl8pqwfFbIGQHvCioMTwqqR+OqamOyP+gMCXIjd9EtEKNss1rxAjFETmLwjxzx3WigqFMn4Ob0D4Q0FrlbYXAB3Y+7ZQ8wZ3pnNKtX4AvEf3vVnhLGQH5ruYfC6TP8DjhgqNDQLvv9c1y7pcaC+OfaHkGJYqARkgiqN6r1ld6JUPNuP6AQYRazAgA+DBGCvYZVT9VKXGJ+asfq9DC8uFfIKyAYo1K1o9BJppdyBIfy25hrzyN3SUHlCMSyf0b0cMu2DGBTL3GaHSdcXQbvRns8qOY1mfIPOtLRGQAUDKQglNXtfDPsu66tjxwJ8F9ABgIwstosb1AzTKXVOFRrED8QEOxZEDWt0urvAr/AGfoFD2r8chUbNQ9cA7pUPMmd/mR80bJG2nfmU85Fe4ATEu0KvKOS1Nsx9YoVevf6kLI+gGoyscCrlsrITGBqGx1hqMgFSRtbYa6KWAFlcws/bLIgIyoGfvI0VW7KFw5ysbCQkkpb8JBeIDhG6tBexM29ikBm4fQG6ZH/GXMbR+ANEE9d9LqAFaGHlHWVEH/ysAKj5gs6WyKK4DOREgxgW2zaxdF8tjg47TaAlfnjfofd4fiBMMWoNfQWANkS8CuZ7gE0DoATM1YLRaF/6kOIYrJD4y9CxiPsHngVpJ6in8QJzge2oOiPsEhesNAAi1UNlDGzGN088XiI4LPI0fWEMk/foByWVAJE5Q9ANr7l4M1PZ9nCBZ8OnNgV5TFI30MuAjOQek59IfmDESlgHbgucPTur+orirUPUZjw7+ppcB6fWA9L1AfLz5WST/v8OxcYFyoEtOtH5wdUNxm0jgxQ+sIoPwdz2H9PX1EzIgdb8ilscFMkIkOcs9Ibsd0flbOsNFstt/7MlZn8FOdpDGr2D/GHP36ZzXcyq39CE1Lfgpu+lLcEUne8dS+thzflcwJ/n/3E/zTDK1cy/M0/igzmZTqIxAkY+5pcO1iA4BfQ6b3vU5vJiHw7nO4aBzi0T14Tzm3GSueY5nttgL7Gqm8cqYHDPmCKca7/qg8+/j0V41F7wYCY5kzP3OEQ41e71u5qdGwLnNeaFvuNvNBhhp2TNzRZ9AQa4X7vcR7qNOx+u35ktDdjzR5O5vtscxZ35tOr0dDMYntnfoy5qa3u094/HuMAJyS9+NB6gE+DTbdTfXFo/wHLbSlzDNMTdccj3qz+mrMW8P5tQD+HK68eGoM+bD5K7E9e7BeO/1Hmc3H+NX05nZ78/vdv3hOZoMYMzYC9fdHGZHjWsOPnV2PL0d9Mf1srngPrDJm4+7wzWjs77DtN19LOVXrFixYsWKFStWrFixYsWKFStWrFixYsWKFStWrFixYsWKFStWrFixYsWKFf/r2Gz+H1+xuOTPAZn7AAAAAElFTkSuQmCC)
- 55.5
- 11.1
- 5.05
- 4.975
The correct answer is: 5.05
![not stretchy integral subscript 1 end subscript superscript 3 end superscript f left parenthesis x right parenthesis d x equals fraction numerator 3 minus 1 over denominator 4 cross times 3 end fraction open curly brackets 2.1 plus 4 left parenthesis 2.4 plus 2.8 right parenthesis plus 2 left parenthesis 2.2 right parenthesis plus 3 close curly brackets](data:image/png;base64,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)
=
.
Related Questions to study
maths-
A curve passes through the points given by the following table :
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/506990/1/977896/Picture4.png)
By Simpson’s rule, the area bounded by the curve, the x-axis and the lines x=1, x=4, is
A curve passes through the points given by the following table :
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/506990/1/977896/Picture4.png)
By Simpson’s rule, the area bounded by the curve, the x-axis and the lines x=1, x=4, is
maths-General
maths-
With the help of trapezoidal rule for numerical integration and the following table
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/508625/1/977890/Picture3.png)
the value of
is
With the help of trapezoidal rule for numerical integration and the following table
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/508625/1/977890/Picture3.png)
the value of
is
maths-General
maths-
A river is 80 metre wide. Its depth d metre and corresponding distance x metre from one bank is given below in table
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/508624/1/977888/Picture2.png)
Then approximate area of cross-section of river by Trapezoidal rule, is
A river is 80 metre wide. Its depth d metre and corresponding distance x metre from one bank is given below in table
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/508624/1/977888/Picture2.png)
Then approximate area of cross-section of river by Trapezoidal rule, is
maths-General
maths-
A curve passes through
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/508623/1/977887/Picture244.png)
Then area bounded by x=1 and x=4 by Trapezoidal rule, is
A curve passes through
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/508623/1/977887/Picture244.png)
Then area bounded by x=1 and x=4 by Trapezoidal rule, is
maths-General
maths-
A curve passes through the points given by the following table :
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/508622/1/977885/Picture31.png)
By Trapezoidal rule, the area bounded by the curve, the x-axis and the lines x=1, x=5, is
A curve passes through the points given by the following table :
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/508622/1/977885/Picture31.png)
By Trapezoidal rule, the area bounded by the curve, the x-axis and the lines x=1, x=5, is
maths-General
maths-
From the following table, using Trapezoidal rule, the area bounded by the curve, the x-axis and the lines x=7.47, x=7.52, is
![](data:image/png;base64,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)
From the following table, using Trapezoidal rule, the area bounded by the curve, the x-axis and the lines x=7.47, x=7.52, is
![](data:image/png;base64,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)
maths-General
maths-
In the group (G={0,1,2,3,4},+5) the inverse of
is
In the group (G={0,1,2,3,4},+5) the inverse of
is
maths-General
Maths-
If (G,×) is a group such that
for all
then G is
If (G,×) is a group such that
for all
then G is
Maths-General
maths-
In any group the number of improper subgroups is
In any group the number of improper subgroups is
maths-General
maths-
Shaded region is represented by
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6UEYSUI86v+xM0KGm8xjBuKkNiNFa+OZUJqjhHiJT2NjG/ejzD095+ASAjTF4ofpIACqKiJLGVnOAaIKxG39I3PrB2rkOtvVCeJnidPVSiD8JHY6A2FJEZc6zvZ7ix4XkmKpXH7IbEZPJx0azILwPUTyAhQ2Sn8caVptcv/eGwoGnoflMFgH7NmiBkPBJEep15oh2jGKQvtQW31T6G0DKkLXOC0apQhwrOPLR1fK0Ax3cjVQ7u4ISIZ0K/aUImNShuJgPR49S44VkeZ2jmoqp6xDguftXhtG/B6QfO8yLCgiClHHGiPKbB6Wm8I+5msqmbvrJT6AmwFg4AMY1laPp6HJGlBjZ+h6xfI4IGUcVxmvp71T/qqenbCkc0Lm31CEP/4AtRkB67W31fuuXeemHOXmgUlR2s56b+L80z6PWMOAjZzRrKwW94G8Z47WTgJapb+CDT6uXV5R8muwCg440SjKG991Pd9iiJ9aNr792Nf+E+3RZA4PG3c9BA2B5B44cQlhAvaLYLh8Ht9XDMB+BsBYrzqAHaoSFVgGs/uE8Por9C6QKARXRDmBjWgFPN1VLd24l3buCQeOy84Ds0y40jsBxBdIaiuHFCnijHOcaHJQQy1NA+B7/TxeSh9QnAuuiy5oHa/BdIDYodb5QQTkOYA5qLZeYKDhhqWtzIkBdYyLAzhmVtGCnCWp4oR4Zhgdei5KsEL8gHDM3PQjNb1Rhvg+htRf07XgpZzkTlFA0h/PABPPAFtBot/K3V5Qv6D8e3A2hgFct09END6EXZM+SMDc5wmMeaNxlZse1ZlhcvqwPHdpEcRusF2bV5+8F+gWyGzcTPCBrE5V6xZ9M3FSr9iUV66XSjCL+q0A4sqDD7e4ON2AmiIkHLEcYZG5zhUoXQk6H8EFUsSrXcTn3PhaXY2QW2/faD/QaGQ6UHbOMxU0YQjoXP5mK8Uwi9nGlCLYUP2I0bIMYKll1smxDGgszs6IYgYwxbQpoePZyNDKe73Y00tAPb5VvD0lupYUHV27Z6l+HvqA/zjA25IHtRtt619aZxeCh20/qFq1xjPeyNF5KfmS4AiGE383p6/YGW2HIJI7qbrCrg2w26ngn2bfl4fHyob6Ne0E8X+jUrH4QcISC6rKx1FcpvHn7BV1xhcoRQosgccaask2uhmVqeleDLAWSUBdKIW15Y7ULLDb0lwQoUDiaX1Pf5uSrulHNHjARVPIFHjsZwIyfbKxKkOUJB5N6SZQizCwDb90l1dzsnkYqRxcHPVZLY//zxshNlHa9JHMhDEE1GbCOj6HKE2Q0FkDc2aD8voll1k66TDsULIFVjZk198wvOl/1EWUcMo4QiE3RYK8UvVcohIwgpg+yFaSaqJ4Yvxm2yn0u/Y9wmpCcA3A/pSA4kUTRe4pbFbxwhGbofRje0LNNMVM8Mj6M8XpPkCA2O14YJnpJO0wAiwrbaZQMQlh6wPfL79exEOR4yFREmNzRuihPK+BEmmRcmN0ROlmu6seHAfri6U04iwrI6BCQDZjKavnCCDrBwQ2UIyzc2HJdhcWMDDZIrUY5Q9ARCyLQ0JYSpNtTOkmdY3NhwXIb5xoYkQ0iCgkg3NDMZRTetjgQhR2glGeb9Guqw9aHPsFlydC8UREm0LCgVZd9IhjB7oSPE+W7mdlg/9DvlHB8UCSaExs0JFkuZ9OSFBpBWzrB5VIbs1/BY7ZBNRlFkpMgL5iFFMMohYj/PwgDifLe8seGgDG3K5g3AWJQlYVKQWSBBX2WyPUBwVRsW/RrqoPUhx2t0uDpqKhGMblggjFFKaINclrMfKss4XhN1TD9Uv0ZWIIwlOUnE1sZ9DS5kACHlAFmWsPVzI8dkyBPldV2Y/DC7oUAZsEgwJrQFFN0QZlKW2/uGu2aF9Bia9t6IIjkbl2glcClycXPuEwF6jsWJsuuQ9eHThGjyJPJYF2Zo5YfZEyFsZ3toZ5PluZ05/IhlucvDhgxQAig0JqO3RihjoMwNM0H7VeiG63HAIzIcaj4uIn5GkBCc4sYLM8YSpMkKcirKnh/s6UGUAzKM4zUOkDIaxFI4ostcj39ukjamohc6QvZrVg0KdLz6sOjXKIJUICkRFMmo6HVGzyPKEWpXZeIIdx6wPZ4fvrwAYPDEr4AY/U8JDyuCplSUdx6wPRxDnCjjUAuEqS40iGYbjFD2Q0mblS2KI9ybYfNo/cMh8ETZCGY/dITGLzrjk6ITar3tEwlajrC9N6IcrT7s+uKNKJJ8KSpyVFSSNA+MXugIta9JGe70a6iDlWVvUBygokjQsPkCJlKKoxJFbU1FhHJq5rs7Y8PBGPLGhliWzQ/lTFnGJ9lG5of8WhtrZ0n57fVrqGMxLK5DuTYIoZUvKnqSbxkBGkHa/jwfx6oPbbwGZhElhKsK0f/czO1W0gpIP4CkTHf7NdSh/FA3NjhESRgKgpRTLAGuKRrA7IaWIezVzOGHYlhMbbiiaFbKISraILSvKOxkUoYvZ6ICw+P0DzVeUwJM9J49kZEDBMKSItdA2pOyDGEvZ6I6UH3oM1HFY6ZAwWC4JYmgATSEWoogkxS2dym/T2YOP1BZbouR1ySCyADX/giJXcEvEcwIneCrBgU6DkN7wNYQRi90P1QkKyVc2RudIFOQNqeUGym+nr/sOAw5E1WyQiuEigqVCGlGFcKGLs9y70TZdZj6sLhvuBRRiCLp0TYQTZGgUYS4A+UAX5wou47ih5qxwYvymiK1RpgoJi/0hZKSNpZE8PNXURyFoV+HkunIC0U/FBgRXPkiuUWMkSK3pmKWn7469CD9w/JEWVGW08gIaWuJoCAawrSTcmS+n06IeZD60G/YVJSOPktIPCJBX6wUKUrcVLIcixs2d3SMslz2azzekaNL+BJF98BUkJ23ZQj7w0xUbzPEqfh060LxONA/kM+wmSwnspJvGUZGhaIDSmlbZfLHGTbfZhju9+62fPzTadeKfg3Nw5MMnpuHQtERE27lhoz+9C7q9+vDqrkNehj330k3bNohJzMESqxEPuaFgrjGSPFrk2f1xxk2368Pw4w+/D8tyZphc8eM4B5FwXOABcVVdagfgPbHGTa/wXCT49BwGvd/KbtTjp5oB52CLVdyQmuOBUZbY1Jun50ou77RPxzCepeKMxf8Q/mJsh1yTDK4ckpwGEV6W0c0cauc3Z8L2XfKcjeWbX1o/uMnmYurvrtSv+YzmY8Ky64S1cQPm2ovKMAN8T/A/+FlaOGHTPyFAPF+TxTRd1r+26nrAl/N8lrzfZyTeYh/XMQPvjraSxWbMLrPTTO67Qf+D7Bk6qvC1tX948Oft+dvwKlg/kNN5hCvNFd13T+ZB0v/SSEZ01HadWlsXpLoljvq6tH6BX+jLswfY68+UztzDrAPn07on6hd0Dv8qlRkY0X4rNQwR31pyuZuO2XiFzRUY5yIoO0D6gNG/05DqHo4y0byjMJeyakaVCyjsA9d7Ctdju+0KZwA8UeJEwxmWltjsIT+SgmagmFkmoq7xhkbPtd3+oc/jCDVLYvdhB09kAQscssYtyAjQRmFDbTPV/o11PvnKT9DQ0C1qOPOYWOiswVo3LIr2re+y+rJxtcqzpcH/MP/sl57U1O9+L2HTmCFMS4EyBNRBUWTtkX45DpUqeyHA9/r9smVl5+vrkeBlg/uYnSQYrRRJCiIvt0fLgAUSgwHvmFrevzbAZh3hX5ObFzEUgn77GbRCqPAMVKC0qbljA2fKzHky7tut3k18drv0xCsQIuCSLyC6HFWdkO3L/VrqFgfDrNuhfjtDK1aFDkpE5FZlDkmlW6oTXf6NZwKUZMjbhX90OZKGx5fq0V/tFpVi5GFeKxhap2Sz8obPTUo0zwvC9/RtVVkaLNqagLOX6/Bq8UyJGOIixhT0QshbEY3fEJxr4Zhj1BkaDNCjr9lvuY/aFUtphDNCDIpYCuljZ4vAEwsqpxCe6tYHwasG6xdOYTQMYnVYuLniwgqYVxJ63b7NcTHGWP9Y1b0w2Fp6v5QrwFRtWhAYutiobC4SIor9vo1/WNZmr2h0tS3GfQuhSOJ1WJ+aMpCshgZOE84Q4S9fk3TtHyxgH8qlBgeURNHxcAkkonLZBYlhP7F/njNxLekdI+dgZyD3G/zSlNd9SSTq0WDREsJI8jYP++eKHfsudR6VcJGh/ZDaPBRMcHLHplM7NbJ3X4NzoU/6rbff1PywRlCHBUzNrIcJWMoYO7e2DD0S9/zvfzPOgFDFehIsQyFMVgS4avjNVEHrw9dulhAQAYJoTALnoJ9ebwm6gx+SKV+ThkKswD76gWAQmdhyKt/rBZFKSFUtLGvXYcqdRqGsZ+T+SlOZguEL14AKHSO+tDV2TVUhkjMQmH+IMrXi/NwJj+kdFNEArjmx8gbFGzmTfPQ6a0dStozKvnSsEZkQ1Wn95qdRKwWiUsOKHaKPOHjNZ3fCYPUUlVx2LXVS3eGJr4jKjRNg47kVM3r91GcQOjnsFo0ZpZQzC/8QZQ+vRqGLybjO6KoStdJ+ocz5EvPetJr7/ldmacRnMvunF0DZGTjNfmVSLxTMBjDSXe3tU0cuuHL+PgCw9swHmfY9evyfk4EaEEp3VY5+RvcTF1lDXU9IhoanDPr48ChxElX8sZf8qbB/2cN1s+J/JSE2YMofFWoNsJfVz38jax6y2Vfx/dbDiOKOV8GiTVn9EOKBVrgPDDt/Rr54dR88CLnMLWNIKpFCffQNbNeEaV3idrrCJvf8abB/0LtUqUTF8GM4zViCE/1SyOdLhgvrCNDVVXzQ32cgVdWJr2O8LR+CAFTnLKTELs4cQhfLegKwNU9EFmLQtVstLEh35drL1A+sR9CqZ9DjOlBFHvBr9Tf0YNmCQ/eGlsrzC2mpkLTxK/O7IeUV4vEmCYOQZPrKbTgy6L7phPWblnAkGV46m2QbJpP7YdQuvpXzERVP514pPcmm1ZnyD++j/0/uHFZ4zmrB2yHqtoM+m9eaqm3YJqmuql++vny/+K/x2HuUN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)
maths-General
maths-
For the following shaded area, the linear constraints except
and
, are
![](data:image/png;base64,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)
For the following shaded area, the linear constraints except
and
, are
![](data:image/png;base64,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)
maths-General
maths-
The minimum value of objective function c=2x+2y in the given feasible region, is
![](data:image/png;base64,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)
The minimum value of objective function c=2x+2y in the given feasible region, is
![](data:image/png;base64,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)
maths-General
maths-
In a test of Mathematics, there are two types of questions to be answered–short answered and long answered. The relevant data is given below
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/506870/1/977679/Picture283.png)
The total marks is 100. Students can solve all the questions. To secure maximum marks, a student solves x short answered and y long answered questions in three hours, then the linear constraints except
, are
In a test of Mathematics, there are two types of questions to be answered–short answered and long answered. The relevant data is given below
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/506870/1/977679/Picture283.png)
The total marks is 100. Students can solve all the questions. To secure maximum marks, a student solves x short answered and y long answered questions in three hours, then the linear constraints except
, are
maths-General
maths-
The feasible region for the following constraints
in the diagram shown is
![](data:image/png;base64,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)
The feasible region for the following constraints
in the diagram shown is
![](data:image/png;base64,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)
maths-General
maths-
Shaded region is represented by
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)
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)
maths-General