Maths-
General
Easy
Question
The minimum and maximum values of
are
![1 half comma 3 over 2](data:image/png;base64,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)
![1 half comma space 1](data:image/png;base64,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)
![1 comma 3 over 2](data:image/png;base64,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)
- 1,2
Hint:
In this question, we have to find the maximum and minimum value of the given equation. For that first we will simplify the trigonometric function, later assuming the possible range of the trigonometric function obtained we can find the maximum and minimum value.
The correct answer is: ![1 half comma space 1](data:image/png;base64,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)
Related Questions to study
physics-
Figure shows a network of eight resistors, each equal to 2
, connected to a 3V battery of negligible internal resistance. The current
in the circuit is
![](data:image/png;base64,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)
Figure shows a network of eight resistors, each equal to 2
, connected to a 3V battery of negligible internal resistance. The current
in the circuit is
![](data:image/png;base64,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)
physics-General
physics-
The equivalent resistance between
in the given circuit is
![](data:image/png;base64,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)
The equivalent resistance between
in the given circuit is
![](data:image/png;base64,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)
physics-General
chemistry-
Which of the following is/are the rate determining step(s) of the given reaction?
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)
Which of the following is/are the rate determining step(s) of the given reaction?
![](data:image/png;base64,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)
chemistry-General
Maths-
Maximum value of ![fraction numerator 1 over denominator square root of 7 sin space x plus square root of 29 cos space x plus 7 end fraction](data:image/png;base64,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)
Maximum value of ![fraction numerator 1 over denominator square root of 7 sin space x plus square root of 29 cos space x plus 7 end fraction](data:image/png;base64,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)
Maths-General
Maths-
The minimum and maximum values of
are
The minimum and maximum values of
are
Maths-General
chemistry-
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/487150/1/939414/Picture72.png)
(A) and(C) are different compound s and rotate the plane-polarised light in the same direction, andboth are dextrorotatory. Both (A) and(C) do not show diastereomers, whichof the following statements are correct?
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/487150/1/939414/Picture72.png)
(A) and(C) are different compound s and rotate the plane-polarised light in the same direction, andboth are dextrorotatory. Both (A) and(C) do not show diastereomers, whichof the following statements are correct?
chemistry-General
chemistry-
Which of the following dienes and dienophiles could be used to synthesise the following compound (A) ?
![](data:image/png;base64,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)
Which of the following dienes and dienophiles could be used to synthesise the following compound (A) ?
![](data:image/png;base64,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)
chemistry-General
Maths-
16 sin ![x cos space x cos space 2 x cos space 4 x cos space 8 x element of](data:image/png;base64,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)
16 sin ![x cos space x cos space 2 x cos space 4 x cos space 8 x element of](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAN0AAAANCAYAAAAt+ms1AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAvZJREFUeNrtWk9kHFEYH1GrVpSoqqhaIiJWrCWqIqpCVQ+x1hJV1UPtJYeqXnuu0kNFVC8VOVWViqiqKlWxhx5CVFSsXnKoqh5yi6i1ltffk9/o6/Pmz86Odr8xP34yb1/mzfebee/7vvfNeF6ONDEPboCHYBfcBW9mRNsiqATbXwSfgEdgB3wPnsunrHy0wBvgKNtl8BN/kwytpy180a2DD8ETYAF8BG6nfI1pcBX8DP6i41X5svj3KIFfhGt4BjaFT6CO1R7hokgLDXAPXAZnubAj0eTqt/GAfXYa1aKQb+AtRyrSpij9t+YYdwLcokdQMR+oBBvjPHBJWvS1P/JYCX4uR0YG4i+67wNq8XGe0a2YZHLoE88a7dvgU+t/quABWKfhU+ALo/8iuA/OsD3D9pw1zk7ADc2CjSbmmGJK1FJglC5FLDoJWvR+7q71XB4PoMUeu550glwDV3h8xfBwJjYs4139iw7v9dr6TXupsYza6OMk9w3zQrVoj3/HaCvBz6XC6NllpP0JXhpAi4kfdCKJ8QG87B1X3k47+nVl7lTI+YeOfLbA303UBygySLBxjJPlqlAtFUeEVkK1lBhRx43xZxlFKwm1mOgaaa6LkbjHQYKMiRpEhRjmqoqtMXef6mNCD7uNE1xwk4K1bDvsV0K1bAbYtMC9YRItqUU6/z3TSogXOUjJW5m4zzw6CzZOczIUhWtRfXrvYdbS6bMvjhYTq0n3dNo7v+FkGeVm1RVW12Lk5TVHOrAZck7c8u2w26g336+843dBWbjfcSPRsGtpB2QdZe7tkmixq5c73t/V0UicAd9Zg+sN7POAG6xLvQ0K1m/1143+C8yVy8beYD+kmKDRDAnzkmx8y0iXhfsdd9FJ0NLgwlvgdUd4rMdeTqjFxnXvz3u6apTjLdCTuD6JeclKjo0qc/4eN5o1R8XpKz3QXkDo9dOUHoWOC7cxKiWTpiXOopOkZYlpaJcpZcsaO4kW19bC/CKl5+VfpOTI8f/xG5RVjTtTkkQ6AAABDHRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT54PC9taT48bWk+Y29zPC9taT48bW8+JiN4QTA7PC9tbz48bWk+eDwvbWk+PG1pPmNvczwvbWk+PG1vPiYjeEEwOzwvbW8+PG1uPjI8L21uPjxtaT54PC9taT48bWk+Y29zPC9taT48bW8+JiN4QTA7PC9tbz48bW4+NDwvbW4+PG1pPng8L21pPjxtaT5jb3M8L21pPjxtbz4mI3hBMDs8L21vPjxtbj44PC9tbj48bWk+eDwvbWk+PG1vPiYjeDIyMDg7PC9tbz48L21hdGg+0q1bpgAAAABJRU5ErkJggg==)
Maths-General
physics-
Five conductors are meeting at a point x as shown in the figure. What is the value of current in fifth conductor?
![](data:image/png;base64,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)
Five conductors are meeting at a point x as shown in the figure. What is the value of current in fifth conductor?
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oq/VUwZkmKYY9TZLRiTZDSR0JZEgnpMCSUJZFQXxIJ9SWRUAxDQlkSCfUlkVCWREJ9SSSUJZFQDENCWRIJeNgPMhgCyJL/pfEwBGAwGg/DQCOuSCCGUSkZDLUQZdbgrIUKDEYehoA87HHGBUzZw/jN0pZceeWm9oqFF7/pHMzH6fISgNFg3aK49Vh5hZtlJemmXNnFL4upnDRS9KpKfrbexJraATdLtfOqsLW7GPd7JrdCMK/EbM1vrvG+3W7HFToXrBNtkeWGX5hjrjjPWK4ULMRsNZCpDhxa5KL9We6ZWK6AXyFWq3MhZCEv27xaI18XTjC1jCLwte+pZYbJXht2XsKadxxz6VVCNLKGTue3Wf7yXqyfPEy0V6fiUrVR3kgzLrlRe7f2sA+R/GSwWc21jssBupeL8jXWgsHsrt0+s8jJX4lsTwXBw+HaO+oao2WrFj7GtW5e0sDcyttkLgg+ephaaogX41Q7qwBj68RtAz/8/CInfxlGjhss9MPtjTZTzY1jpdOa117EP7ey9q/gaOuTwV57jp4VSOq4V955kLdqWpW8XnjIBrupYpXJxUWm06xa1dZ7H1W59fRfFdOCsOjb6pVc0PESw44maW0ALUNYvcF87hrFemawBgSF4Yep821zlSt3Cl1drYTj6x6zaKA7uVlU3bPZm/SsAIXRW3UqFmB1K8LKxyys9hDCFqFcu52TlT73juAnVHuq2sR3LQuxVHnPL4rZ9ZufcwFvtdvOhr46MNjWu1GncRe9d7m2worpqn4TFj2eLu+yNmt2NhfePTXJHPlvC4mvjjziuvbUh6JmbKDbbAh0UCuPSkj04NPKx+px6Pi8cmjfAu7Jw1DoOHV8iMfgkTwMBXhYkQK6q4HH3ervnqHQ3tc0LwcBxDDyMAwUw5Bwv5uX1iXegpQ+kpwlycMQjFlyOicegLIkEsqSSChL4ug0dY1wcAr6OEYdRn3Jx8mygmIYAhCupPQx0IgrEtBhFPQx0IgrEhpxRUJ9SSTUl0RCfUkc0JekEVcUpMOQcE86DIWR1dN3Sf7SGH7dUY14hI7sRRAE8TReXv4FeAggvQOIh1QAAAAASUVORK5CYII=)
physics-General
physics-
The figure shows a network of currents. The magnitude of current is shown here. The current I will be
![](data:image/png;base64,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)
The figure shows a network of currents. The magnitude of current is shown here. The current I will be
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAUgAAAEnCAMAAAD8aCqOAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAALiUExURf////7+/vf39+jo6O/v7/r6+vz8/NjY2I6OjrCwsOTk5Pv7+/Pz87+/v2lpaZeXl9zc3Onp6bKysmdnZ5iYmLOzs2hoaLGxsdra2uLi4qenp2RkZI+Pj9HR0fX19dvb27S0tIiIiF5eXnl5ec/Pz+7u7sDAwOHh4fDw8NPT07y8vMXFxe3t7ZmZmXFxcWBgYFZWVlxcXGtra4eHh8vLy+Pj40JCQqampufn587OznR0dDg4OCAgIE5OTsTExKGhoXBwcFhYWFVVVWNjY4yMjH19fSQkJCYmJq+vrzMzMw8PDyEhIZ2dnfHx8czMzIqKiltbW1NTU3Jycra2tubm5n5+fiMjIwYGBjAwMJubm+vr6x4eHk9PT01NTXZ2dvj4+P39/aKiol1dXVBQUIGBgd7e3r29vREREQEBASIiIpCQkDs7O6Ojo76+vuzs7Le3t1RUVD09PSwsLC0tLfb29kFBQcrKyi8vL6CgoF9fX7q6uqysrEdHR8jIyOXl5URERMLCwmVlZZKSktnZ2fn5+bu7u0tLSzk5OfT09ExMTPLy8kZGRouLi9TU1NLS0lFRURgYGFpaWtDQ0MHBwTc3N4SEhEhISHp6eikpKTY2NhYWFt3d3ZaWlj8/P+Dg4IWFhXt7ewkJCRQUFDU1NRcXF7m5uRMTE1JSUkBAQImJiYaGhhUVFW1tbR8fH62trTo6OqWlpcPDw9bW1mZmZt/f32JiYkVFRbi4uD4+PqmpqRwcHHd3d5WVlScnJ4KCgpGRkdfX156ennNzc4CAgGxsbLW1terq6pqammpqanh4eKurq83NzZSUlHV1dW5ubnx8fFlZWaioqH9/f6qqqpOTk29vb9XV1Y2NjZycnKSkpJ+fn2FhYcfHx8bGxoODg1dXV0NDQ66urklJScnJyTExMTIyMhkZGUpKSjw8PCsrKy4uLioqKiUlJSgoKDQ0NBISEgQEBB0dHQ0NDRoaGgwMDAAAALlkId4AAAD2dFJOU///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////AEo/IKkAAAAJcEhZcwAAFxEAABcRAcom8z8AAA7vSURBVHhe7Z3LgesqDIZPKyy0pAl2bGgj4ypYUQVlsKQMGjoSkPgRnLET8phYX+beiZM5iaP8kgCD+McwDMMwDMMwDMMwDMMwDMMwDPOFANQ7zEN4kXy9yzwAuCDZkB1gQ3YCEhuyC9mQnG4ehxXZCYyRgg3ZAc+K7EPO2hwjH4djZCc8tyP7wM2fTnDW7gRn7U5w1u4EZ+1O5KzNinwcVmQneDyyEzlrs2s/DrcjO8FdxE5wF7ETnLU7wT2bTnBfuxPcjuwEtyM7gYYUpt5n7ga8Eyom05IkGHclVXwsOdbvNV5GpVSILU1CsHJpMxP1YF09YEa8DGTIlnObOAxXaSgNw2m4Mi+Dri3QkvHKWwHQjj96aUgQg7JDbEaCgwMSFRmv2j/g7OkHDbmwmAuDkNameshMMFGFK18Fp6wKeunaIO3gTNCBFXkNRsl4lT3QkNElu1QkoA2NF4Nl327Q7GsDRUm7UCQYRVHT6YFHMBs42zYLhsmFIlGLCv/U2FPgJvw1Rsemo6IhF4pEy+Y/FYPmdHON02LNkHNFgjyhZ4P3kn27hRvahkQBzhXpxc9JYza3ejgp7idecUORw3QpEyRV7KiwTa5FfZS5YFYUuYyRILROkHHhRFmHmbHm2ssY6ZU+j22AxHTDvr1gTZGLGAlJj3Y1euAW0JKNisRutro03L3C3k29z1TWY+Ssr51Ow9jeBGwBcVNyDgpvpWfjxXR4zcy65EY2x4KPjE8hrizYnq+Ix2xd7xG8Wn4Oyk6FIDgFPwh4GYIUETXJpnwAtCNdZjBkSTbkA9CgLlkwW5K7KvdCfl3yMhiyKFvyTtCvw7l9w5a8G7oQO7YTUZPs3fdx8etC9e7xAWYTlK8vfl3g3H0PaEcxt2Pu9gXW5C4oPi70iHDu3k1ph9eDCTnjcC96K6hHe+XXGdbkLmicomlHpMTJesDcAlXX9utMbU+yd/8KgLDrdkTQu1mTv9PO1zO4j7OBRjv8Gu7j/Erx63qwDmecX9jg1xnULfdxboD2uZ1nRsz6FTEG/fr3+HgGNRnnkyOZCvr1jfbjEm5PrkF+vVmPBI1XSo+wMafs0yNBGSdKIdjBZ8yuK2yEcndA89dDJkc8e8dcHZcXfO61/zeDft0eN7sJJFrwqXhZ/BnwMdyzDrMYcjYJ7cAA0LjZfdNrncAgGVCS9fi4AKrRyaDEfWsHAf91itRqOrpz+5SECI/kC/oiMEwe3ZA57arw2NVqL+yDr/D3cTnt3pGwZ3ip1cGvLWZDXi9r3wtqEi1ZD46IdxEt2cEvqZ8uj6tJSDFgA6ZHO5C8+7A9HJ9iFM65LmUTsG900PYkQBJB9qs9UXL3AUVJfi17rinCOGkPmHFoGVJHPRLk3Ye7joPxsadfF1CTaMkjiRKAliH1XyuYLXkkQ2a/foZ0PPa7j6NJyMvinrN29VB9nKdOk0BN2mNoMuvxick1e/cRDJn9+pmNFEDv/vo+DuRpUs9t7NFMg+8fVTPiBZOfAOPkd4+Z58tcLwhgpWVeD74QtGMI1xWvn4BP2O++543mdTE+FCC/dq8Ryp25G+R1Nd+PA+2oXrcoE9C793eeQOnndBSmUPG28x2Pt8VJ0oM3zhteqUcCvXu/Jo3Szz9DjHBlMB9SVMouq4zm6bb1fgvaKeCFdswNVruzPQnGPl+R4ILKpbW8o0uoetHAAGd/TqttDgB3x7S9B6GVJvssCVLbZ3/XaMehFMQ0tENCbqqVZwp41voU1kYYwdA1rtfakc6JWkE73tUL/eyyk17Y4ScbEkSu0ohfXpzGRKdCwPDePGvU4zvsmL9dbAXVgw34YJ+ctdFxLZVbJVuEskGCsVP9QdIhYSe3eRrk14/OprgPzDh7rnd7ZduFAXtBIzbJlBjplc45xWCfeXxTHwfpndYN36ZCrepdpfNyy3yzbYx+9uUz8AZQ92hIMKEkNh9L7smgrWyi6pfXBQpznnmPHgnIuXvbu0MaXjHLoCiSnDwba2bIfwIdncKnumoB0bQU8cY5tZhxNno3YK5pl47vS1Wkq41/TD9jYAYMnHgK+NwslSNoR/XeLbsgbc04XqxV8+3KDUXSg2QsPJM4cyPIeux92XUfFOA3WZI0stTBMyiKRHueY+Q4HQ8NOAgphVSnebTO06TeqkeC9hbaEidftKNQboij0TBr0zmhQC82c2oYBj1ojf+fRBmgaQCfsGlC7nf/eh4Qh5ud3F5UReLb1XbkJcNRtpPJITIMahRgnk6xewTmGZQ4+cuZQDy9ZBCtKvKf0LSWAySGw/IEbQdXd0ZAk14q0mc9Puny9W5ofLLd7ZogX7OIrCqSdh4U3tDAaXn837+kLtvHGHu2L9kxfood6SveMD65vQ/0CKb2nyi5aX0aLt8ehLGcP96v2ztirvyolel+cyvo2UCq/RMaj7RqklTk5MKgE7k3iG2Oz/Hrwtbc/XxG4V8GyyuTg/IM2fHjKiWQd9/S5PJTfQKfWQuOvPvWt2vSS4fwR8CY5hvDp9aKwlYQefcKGNWF7Hy1OL9ufvU55N70U25eSmycXb8x5ZnPnBGWLenMyk0oFQI+7ddv+LPH/8FJtBHdEJeb2vhGI/U1UwiovOuetPmM/kwDABkVnnQbuhaFplR2CT6S9xKj267LQPh2MeCtIuhHnMEuNd0QWralgkiyPoMP52cE7VLx3pGKNYB2oo3lRJc/Ihd2oE8dCtkG5TbeFXtiFrWl6fXyDV+2/Jxf+3KA3x19RcFiu3KKovXo0uzxgVeRe1uOitxcY2ifElpqQeeN/9VYNmdnxKKXPd/Ovwo5mBQS7Xyt8uIt8n+81V8OOz54Sh8YJktvi4zUuqWIjvSik65vWb4cGmucp7nyNP42CVWJz5WHP4Taa121lH/JBK8GIG+cFYpSfZgoP2N0tMHNiIFfv8Cw/jmi/E2Pnwu1y7uvk7sfyjMfqccNUBTFk/8E/856/Kt2vIhyV2/gOWQ7flTE3ol31Dx/e6Qkv/6sUb39mBQxfWOkfKMcih3/sB4JbG/mPuP7REnx8UOuwj0GRkqhYp3v+wZKnvn7dkRoIhV1dN6RdGr7sR79dbJ3vWfySunPfIUeMxgpo8L0/eJP9F16zBRRYu58pX/Dx/avH+E8ulYPXwF9ed+lx4JJOem8TJPFr78nPo7QxsTUpnzJZyvtxy/UI0HDwWjKl4iS9PhN+XoBRsqIkfLpH7Dm66+1I0KZNKfvevwUvjNfz6GC2XXI9ylDGfiiUPz6C/rXv3AZyKAVPPWxfhi6lvkF4z2boPSNkTLJ/pPWQNJsiq/N10uA6tpjsOzfQqf6h2/q2L8FoCFfpHdGoGkp9LLvHpV/ITRFHulc7QjTNb3qu9aRvgEgQwba/qOrIQ1tWoCufSBF5jCZK5F3/NA0BzKK1KeY9F/BO8zaKCBqU/b53FStQNFcqHp8FOpsLNq5q48laZU9tnuOpMYJ6OKUvDt8eqqecaTgeAUtOOhwHYL8+huuuz4AFfzaXDNhjWLHenBUaNSL0vcDpix+fWg9ZkhPDww05Hx9eD0WfKL9v+7UFNtxAty9JV2udnXwPDODeo33TD3PejxO73oDlL73D4EVPdYDpuDT3t2SjufX3tDyxvkHBpeWoz8u2l3p+2h+DZCC1oOeVdgCZ0+lbN0IXfzObcpttsz96yP5dd7aA/12VsLTy1YpVDAybNxxG/2a7Lhdv3+fZLXADy4HO/nYaAU7NHb0oyKacUubEv3aHmqcAnwsVRF9mNTXoQKpERVVDyeQKDHy/eLeVY/16Bj48FPKA00rOPh4kg6N2TIFRsrfNwJBOx5s3IzqBSVDJQkmGqMHHTitmjmasvHNuS00L+VoevyHKduKmLP2+MkBm4wGtdqWJP2jm0NCVEn1cP0ZSGpQVLdhWhHY5w1TMFCu1f+u6bttSfxujtifSepUCm+P9YPRqXPtaKeGRTN9xCeVqxFcPZ/HzQ44/oiKLA1vPzZXvBgCgPdoyPWMgaJsXtEhv37jerL3gTEyhzOMi+eI6NRpUFZhS3JRCnWOp4tjSx/Ofn20+EiQgLIi0ZBVfrQ3ggo0L8LqUi1+BbrMOK9GcMh8XcEmY25HerRAMVpuoufZpiYOt3dJoP7LNH0D1QU9ph1Jf1TDljZnLwHvEjXpueGXovS5o3NO36hH9XHVAF8HbeUnxNhbwebjpYLnWAp1FbrMWCfxH9ivM9jyGYbTpQqvUaMKfdThN8sAzSDF9J3717f1++14Q4WqLiZwk7ohfsv0sZK+DW2GvHGskmlDOwxheDi0X3eC0vdX7x75MsCoZ+8ndRTC03c4OwagFCeaHgArsg8QOEZ2gQ3ZCYyRbMgesCI7wYbsBGftTrAiO8GG7AQbshccI/vAiuwEZ+1OsCI7wYbsA02qYkN2wIjLPAHmfsCnYDuXZTkmLuYCN/WIuRPweX+scOx5Fh0AEiRSt7Fl7sXLbEeqblMfYe4CjMv1ltwRp+r2hWrxHWyF0pMgQ7Jfd4BmTte7zCOgIVmRPUDXvlrejeRydYvicrn8M7OCj6GlSJl3DZ4nc9p6nNP7Gk1FemcHrfV8/Zh3+qesSGEaNGOko6USPgUdJs7shRry8kemRUORAOJEWoRk7WSEzamgbGBJrjAuHBsBqcp4kJouBpc6yDhZ08zMaMXI877KMK5gzjU0pEm/L985KjfakWCsvoxmUMUCB7Syni3ZZKUdSZjp8jGIdG0HglWcbpq0YmTBy2Gyss4rTctxkh14OL3JqiJB6ElBB0hDXvxgwol9u8lajPTS6kmj0YvB0sLHpH5y2QxmCSmy3p0AZLhRqYBN9NNJD3jDXzxa1KKpSLSjnadnqZUQUgpsSc66O8wZE8N1jDRiXvwLG5G6/pUXK3Wujk5DkUCVHKjyYR5Ky49IWyqRIEZrvjbRoJW1TfgZbKB6LfU6rVdjZQcfhkvFB2akpUgqsVSoW+OAGOcQQIq/lcs4JM2sncfHM5cH6h2EU02TtXYks5Nm1mb2w4rsxI3RH2YPrMhOtPvazG5YkZ3grN0JVmQnOGt3ghXZCY6RnfCRF4d0wSeeid8J1iPDMAzDMAzDMAzDMAzDMAzDMAzDMH+Jf//+A3nuylPLXT5UAAAAAElFTkSuQmCC)
physics-General
physics-
The equivalent resistance between the terminals
in the following circuit is
![](data:image/png;base64,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)
The equivalent resistance between the terminals
in the following circuit is
![](data:image/png;base64,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)
physics-General
physics-
The equivalent resistance between points A and B of an infinite network of resistances, each of 1
, connected as shown is
![](data:image/png;base64,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)
The equivalent resistance between points A and B of an infinite network of resistances, each of 1
, connected as shown is
![](data:image/png;base64,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)
physics-General
Maths-
The period of
is
The period of
is
Maths-General
Maths-
The period of
is
The period of
is
Maths-General
Maths-
Period of tan 4x+sec 4x is
Period of tan 4x+sec 4x is
Maths-General