Maths-
General
Easy
Question
The solution of
is
Hint:
In the question we have to integrate the given function.
The correct answer is: ![tan space fraction numerator y over denominator 2 x end fraction equals c minus fraction numerator 1 over denominator 2 x squared end fraction](data:image/png;base64,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)
Related Questions to study
physics-
For the given figure, calculate zero correction.
![](data:image/png;base64,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)
For the given figure, calculate zero correction.
![](data:image/png;base64,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)
physics-General
physics-
Three capacitors
are connected as shown in the figure to a battery of
volt. If the capacitor
breaks down electrically the change in total charge on the combination of capacitors is
![](data:image/png;base64,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)
Three capacitors
are connected as shown in the figure to a battery of
volt. If the capacitor
breaks down electrically the change in total charge on the combination of capacitors is
![](data:image/png;base64,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)
physics-General
physics-
The charge deposited on
capacitor the circuit is
![](data:image/png;base64,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)
The charge deposited on
capacitor the circuit is
![](data:image/png;base64,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)
physics-General
Maths-
If
then y satisfies
If
then y satisfies
Maths-General
physics-
In the figure, a proton moves a distance d in a uniform electric field E as shown in the figure. Does the electric field do a positive or negative work on the proton? Does the electric potential energy of the proton increase or decrease?
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)
In the figure, a proton moves a distance d in a uniform electric field E as shown in the figure. Does the electric field do a positive or negative work on the proton? Does the electric potential energy of the proton increase or decrease?
![](data:image/png;base64,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)
physics-General
maths-
Solution of
is
Solution of
is
maths-General
physics-
Two charges
and
are placed 30 cm apart, as shown in the figure. A third charge
is moved along the arc of a circle of radius 40 cm from C to D. The change in the potential energy of the system is
where k is
![](data:image/png;base64,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)
Two charges
and
are placed 30 cm apart, as shown in the figure. A third charge
is moved along the arc of a circle of radius 40 cm from C to D. The change in the potential energy of the system is
where k is
![](data:image/png;base64,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)
physics-General
physics-
Figure shows three spherical and equipotential surfaces A, B and C round a point charge q. The potential difference
. If
and
be the distance between them. Then
![](data:image/png;base64,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)
Figure shows three spherical and equipotential surfaces A, B and C round a point charge q. The potential difference
. If
and
be the distance between them. Then
![](data:image/png;base64,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)
physics-General
physics-
Charges +q and –q are placed at points A and B respectively which are a distance
apart, C is the mid-point between A and B. The work done in moving a charge+
along the semicircle CRD is
![](data:image/png;base64,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)
Charges +q and –q are placed at points A and B respectively which are a distance
apart, C is the mid-point between A and B. The work done in moving a charge+
along the semicircle CRD is
![](data:image/png;base64,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)
physics-General
physics-
Consider three concentric shells of metal A, B and C are having radii a, b and c respectively as shown in the figure
Their surface charge densities are
respectively. Calculate the electric potential on the surface of shell A
![](data:image/png;base64,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)
Consider three concentric shells of metal A, B and C are having radii a, b and c respectively as shown in the figure
Their surface charge densities are
respectively. Calculate the electric potential on the surface of shell A
![](data:image/png;base64,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)
physics-General
physics-
Work required to set up the four charge configuration (as shown in the figure) is
![](data:image/png;base64,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)
Work required to set up the four charge configuration (as shown in the figure) is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJgAAACkCAYAAABreuf3AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAABJtSURBVHhe7Z17sE3lG8dfx92Ra3IO+SGJcimOEaKixhQml6F0MZpICekPlcgoQpOGiEw1pqZMSnIpxi1O1AxT7qnjEsf1uF9P7pf1W5/HWtpnn71pX959Dj2fmdfa691rb2ft97ue93mf93nXKuC4GEWxRJK3VRQrqMAUq6jAFKuowBSrxEVgq1atMhMnTvT2FOUf1IIpVlGB/Yf56aefzB133GEKFChgNm/eLFvq4knCBEYXygm0aNFCToLXf//9t/eukmhGjhxpWrZsaaZOnWoIhU6fPl3qGzVqJNu4QaA1Ujp27Ehw9prFp3nz5lKysrKc7Oxs+Tz7St6Qnp4u7cPWZ8KECVbaJCqBBbNy5Ur5A0MxYsQIORnE5YPAqFfsEnixU/w2qlmzprRBIIjLRptY7SL37t1rBg8ebNwTM6mpqVJHtzhz5kzTrFkz2VcSCyP+LVu2mJdfftmrudxOv/zyi5U2sSqwGTNmyLZ79+6yhSVLlsg27n29kgvXgOQoffr0MStWrJD3An//MWPGyNZGm1gV2OLFi41rek3JkiVlH+s1evToHHVKYqlTp45sXbdG2mPKlCmmWrVq1tokLgJLS0uTqyMYrghMLyaYMmvWLFOrVi3z6KOPekcoiebBBx80rv8lI8i3337bdOjQwaxZs8Zem7im0xo49jiU/De+g8nrwNGLkvfYbJOE5oMRzMOCZWdnaxeZT7DdJgkLtMKvv/6q/lc+Ah/svffeM24vY61NEiYwfLBhw4aZJk2aeDVKXvL999+bm266yUyePFnCFp06dfLeiTPSUVpmwIAB0s/7JVxQVrnx0Jx8xSpxF9jatWvNsWPHTEpKiqldu7ZXq/xXiYsPdubMGfPEE09IhkSrVq1Mly5dTIMGDUzBggXNW2+95R2l5BUbN2409evXN0WLFpU2Kly4sKlXr56ZP3++d4Q9YrZg27dvl4Dq008/bfr27SvD3aysLBn+rl+/Xk6iRIkSZvXq1aZMmTLep5REQQB8zpw5pn///pL7dfHiRWkXpuyI5hN4/fbbb02xYsW8T8SXmASG5apSpYr57rvvJPzAH4/ADh8+bHbu3Gk2bdokJ7NgwQJToUIFCVMoiYPeAxF98803Yr0ISxw5csTs2rXLZGRkyEX/ww8/mMaNG5vZs2d7n4ovBd0/Iuo+DKvVtGlT88ILL4jpTUpKku2lS5ekILizZ89K/fLly0VkTCsp9qFn6dWrl1m2bJlJTk4Wd4W2AWwKbXPhwgXpLull7rvvPpmTjDcx+WBkQT7//PPyx/JH+8KCQoUKidkl1lK6dGlTqVIlM2LECHlPsc+4ceNMu3btREC+oGgbREbbFC9eXNqlXLlypmLFiub111/3PhlfohYYo0V8qnPnzkm3yJYuky1Xhi86rhyEVr58eQm2coxiH9yWGjVqSLdIL0K7UM6fPy9tA/QsdJ233HKLWbdundTFm6gFhgnmj0M0hw4dktDEiRMnzMmTJ+WkTp06ZU6fPn1FcMDJceVwFWmxW/bs2SMX9759+8zRo0fFCPhtw5b28YXHcVg32jDeRC0wYlz8QVu3bhWHfv/+/eLcUzgh3jt+/PgV0XFCnAhWTYv9Qt4X2as7duwQI3DgwAExBDj5FNoHsdGj0E4YCxuj/JgEBuR7bdiwQUaMnAxi2717txSuHoR38OBBeV23bl35jGKfp556SgZWjCL//PNPs23bNmkbCqNIQklYOdqFcv/993ufjC8xhSk+/fRTcQ7bt29vqlatKk4j5hmzy9WBsLh6sHJ0qYsWLdLJ7gSBZWIdBAHvhg0bijNPPJJ6ehMsGiKjbRAc4SQbo8iYA60E6rhC7r33XnHk8bEQGN0ippirJDMz0/Ts2dOMHz/e+5SSCFh/2rZtWwmw4vAzosfXom1wZXxL9vHHH5tu3bp5n4ozCCwWXEfe6d27t+OOFJ3KlSs79erVc9LS0hz3hJyyZcs67kk5Q4cO9Y5WEo3bTTquJXNKlizppKSkOG5P41SoUMFJTk52XKvmzJs3zzvSDjELzIcTadmypeN2k1hEOak2bdo4GRkZ3hFKXoERGDt2rLRHkSJFnKZNmzqjRo1y3MGYd4Q94p5Nga/FggK6RSX/Ub16dZOenm7F3wpFTJF8RbkWMQmMech4341FubGIWmAE6lglPG3aNK9GUXITtcCwXK7DKLEtRQlH1AJbuHChxLuI2NuYw1JuDKIWmJ9uS3TYv6GGogQTlcD8OUZgMpv5SEUJRVQCw3qRSwSk4pCSqyihiEpgc+fOlclsH/XDlHBEJTAc/EC4r4HGw5RQRCwwUqVJyQmERLZg0SkKRCwwLFWovPpELOJUrj8iFhh3ZSGXOxjyitQPU4KJWGDhYl6sHFI/TAkmIoEhIBYHAAsEWF9XqlQp2SdLUgOuSjARCezHH38UIbGObtSoURIDY7FA69atxfEnfKEogUQkMHLsBw0aJFH8F198UerI9ebeEyxR11tjKsFEJLCPPvoo7O2YWC3EMilFCSRiJ19RIkEFplhFBaZYRQWmWEUFplhFBaZYRQWmWEUFplhFBaZYRQWmWEUFplhFBaZYRQWmWEUFplhFBaZYRQWmWEUFplhFBaZYRQWmWEUFplhFBaZYRQWmWEUFplhFBaZYRQWmWCUmgfG8yFdeecXbU5TcxCQwngGZqIcqKdcnUQls8+bN8jxotopyNSISGHeW7tSpk2nXrp0ZMWKEqVWrllgxRQlHRAKbNWuWmTlzplm9erWZMWOGmTBhgpk8ebJaMiUsEQns1ltvNQMGDLhyH7AqVarINjs7W7aKEkxEAuMB8EOHDjVTpkyRB40jNkW5GhEJjK6QJ9cfP37cLF261EydOtV7R1FCE5HABg4caDp27Gj69OljUlNTvVpFCU9EAitXrpw4+dxtmvvlf/3111KfkZEh+4oSTEQCe+2110yPHj3M+PHj5fbl+GPs02U+9thj3lGKEoATA0OGDHE2btzo7V0mMzPTqVatmren5DdoG9ooUURkwYIZPny4mTRpkrenKLmJSWCKci1UYIpVVGCKVVRgilVUYIpVVGCKVVRgilVUYIpVVGCKVVRgilVUYIpVVGCKVVRgilVUYIpVVGCKVVRgilVUYIpVVGCKVSISGMvW5s+f7+3lZN++faZXr17enqJcJmILxo1PHn74YVm6BidOnDBvvvmmqVmzplm4cKHUKYpPRAJ75JFHZGX34sWLTZcuXaSOtZHjxo2TO++0adNG6hTFJyKBNWnSxJw5c0ZeHzp0SLanT58WcZUuXdq0bt1a6hTFJyKBFStWzNSuXdvby8nFixfNPffc4+0pymUi9sHatm1rChUq5O39A+LT22kqwUQsMBx8//5ggXBrJ0UJJmKBIaSzZ896e5fhpihYNkUJJmKBAc5+IBcuXFALpoQkKoE9/vjjpmjRot6ekdCF+l9KKKISGPGwwoULe3tGb92khCUqgWGtGDWCxr+UqxGVwMD3uQi8qv+lhCNqgTFqxIphwcqUKePVKkpOYrJgWC/iYkA2xeeff26GDBlisrKyzKuvvirzlMeOHZP3lfwBbUaCQsLw7nQYFdyOcebMmc64ceOcUqVKOWlpaU6HDh2crl27Og0bNnTKlSsn9fPmzfM+oeQF/P5ly5Z1aG63t3EKFizolCxZ0hk6dKh3hD0K8M9lqUUOVgsL9r///c988MEHEuHnqR/UZ2Zmmq1bt5rffvvN/Pzzz+a5554zH374ofdJJRFgrVq0aCGveWhG1apVzcGDB822bdvM8uXLJeWqRIkSZsmSJdbCTDEJjLtNL1q0SJ5h5F4V5vz58+bkyZPmyJEj0k1yIhs3bpRnGyGyuXPn6oAggRAQJ3/vjTfeMJcuXTKnTp2SLJjdu3ebTZs2mT/++ENy+BAit6L3IwPxJGofbPv27eadd94Rq5SUlERXK9siRYrIVcFtzitUqGBSUlLkyqlRo4bp3LmznIxiHzKPz507J1nItAsGgLahlylfvrypXLmy9DyNGjWS29CTNGqDqAWG1apfv75JTk6Wq8MvpO0AGRecUPHixeWkEBtXULiUayW+4JL069dPLvzAgtgIkmOtaDuiALfffru4ODaIWmBfffWVPC+SZEOSDpkApyAwukoKguPKYVqJk+H1ypUrvW9QbLJ//37pObBOftvQJswb+0bANwBM9fF67dq1Uh9PohYYTjyCwWk8evSoCA0L5QuOrpDCiWGqERtXDg8yLVCggBbLhd/68OHD4g8jMr998JEpftsgOh/cnngTtcB4nB8i27Vrl4wafaH5hdEkJ+WfjH9CgwcPzmW2tcS/IByejrdz506xZjj3FARHHIxCG/ltAzZGklELjEUfv//+u9myZYuMFhk1Ug4cOCBXDoJj619FiA1wKhX78PDYZcuWmb/++utK+9A2iA2DwGvaiC3BcARpI+U9aoF16NBB/th169aJyIh5cbVg0RgGc0J79uy5ciK8pr/XMEViYIS/YsUK8asISWDNaCO6QdqH4gttx44dpn///t4n40tMcTBCFDxx7YEHHhCHkvAEfhmOJF2jb8k4GcQ3ffp0SfVREkOrVq1EWM2aNZPQBI48zY2P7McqcXMY8WPpbMTBYhIYNG/e3Kxfv17MK7Ev/khGKZwE/TwngdB47J+tobASGro+UqkIouJfkZRAmAKfCz+ZtilbtqwEwW1F8lF0zIwZM8ZJTk52XAvm3HzzzU5qaqpTunRpxxWbzH1NmzbNO1LJCz755BOZi3RHltJGtAulX79+jmsIvKPsELMF86FvJ3ti1apVYm4JwjZo0MB07dpVovlK3oNFwyfDWl3LYu3du1fiY6FWkEVC3ASm3FhMnDhR5jLT0tK8muiIehSpKP+GmATGCAVTSoyLrtGPdSn/Hfx2Rwe8DiaqLpIv69Onj9mwYYOpW7eu6dSpk+nWrZsMgZXrk2Bx4E/ffffd5s477/RqLi9PZAYHOP7JJ580FStWlDnp2267TeaZZ8yYIe/7RCww1Mp/RALb6NGjpQ6BQfCXK9cPfhv6YDwQD1kwPszCDBo0SMTF69mzZ8uSRV8TEyZMEMOTAwQWTHZ2tuOqMUehDjp27OjUrFnzyj40b97ccb/c21NuBGhP2j0Y2h3Z9OjRw6v5py7U8SEFxoF8ILD4QuO1q1zvSMfJysq68r5y4xBOYNTT3rS7D3qgLhQhnXzMnWupchTqFixYIO8HruT2u8VYh7PMm7377rvmpZde8mqU/Ai+GXpITU31aoysJqMuJJ7Q/hXul0jx2bRpU666f0tGRoYzduxYp2XLlk6hQoUk4s922LBh3hFKpBw9elRWCrGKKNYIPVaJ9g0GyQS6Q+np6eIyhXORIhLYl19+eaWLpPDliCvclwfijjydqVOnOp07d3bKly8vy9mKFi0q3+eX6tWre0cr0XLXXXfJ78rFWrt2bWfgwIHSTvEC3wtB8Z3oARHSduFcpIgEhjPnjh7lP/G/MNyXczWxZrJ3794iHObAEFWgoAIL70+aNMn7dN7C+VAC/YzrhTVr1sg8sP+7IjTmh9nSW9Br0HtEC4Ki/dEBvw+/E/9POCISWDDhvvyhhx6S+iJFilw50WuVpKSkkPXxLEzIXw1+PK5ORsUUPsNVer3RrFmzXOfuF34DLnRER2/y2WefOZmZmd4nI4fe62ouUkxzkSNHjgwZXMNh/+KLL2QFEQmITJhe6xYCJCMy98VSKltUqlRJ/uZw9OzZU5LzSF8BYkOuFeYKkn0fEvXq1Kkj6wzyI6Sm87exvRa0DTn8/P6cP2smIoGFvSQ05Ip/eUQdyWfFdvv27SXPa/jw4TlGFYGQe8QKYu6tP2fOHElwI2eMhQjBuCZcVhnnFUzwsozrmWeekX3ur/H+++/nEhg8++yz3qv8BxkTLHi+lsBY6YW4aA8yjRHJv804ZpqQRdd9+/aVAGv37t1DZl5EJTAaAsH48GP/25vQYckQHCuKsXAkvbGsjeREMi6XLl2a6xadiYSLx+02ZHEKTy8hHTyKnyhPYdqGCzkYXwCEnMh2ZdU3v3U0yYZYO7JifQgx+dNIOUBgeQmDAYbVJL/h/zRu3Nh7J/H4AUO2DGjwL/LBTxQRJBfiZ/F3k1TI63j5W9Fwff16lqFRAkMu15vACAW5VspJSUmROxwRFkq0oIKJycm/0cAfYY0BawfIY2fwgpPvWjR5wknILiCfwQAkP2UQa8JhAOnp6ZI9MGnSJON21eJXuENwWcxyPYgL8lt6ulowxSpqwRSrqMAUq6jAFKuowBSrqMAUixjzf1CiP2dNe9a8AAAAAElFTkSuQmCC)
physics-General
physics-
The points resembling equal potentials are
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)
The points resembling equal potentials are
![](data:image/png;base64,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)
physics-General
physics-
In the following diagram the work done in moving a point charge from point P to point A, B and C is respectively as
then
![](data:image/png;base64,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)
In the following diagram the work done in moving a point charge from point P to point A, B and C is respectively as
then
![](data:image/png;base64,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)
physics-General
physics-
Three charges
and
are placed at the vertices of an isosceles right angle triangle as in the figure. The net electrostatic potential energy is zero if
is equal to
![](data:image/png;base64,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)
Three charges
and
are placed at the vertices of an isosceles right angle triangle as in the figure. The net electrostatic potential energy is zero if
is equal to
![](data:image/png;base64,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)
physics-General
physics-
A hollow conducting sphere is placed in an electric field produced by a point charge placed at P as shown in figure.
be the potentials at points A, B and C respectively. Then
![](data:image/png;base64,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)
A hollow conducting sphere is placed in an electric field produced by a point charge placed at P as shown in figure.
be the potentials at points A, B and C respectively. Then
![](data:image/png;base64,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)
physics-General