Maths-
General
Easy
Question
The value of the integral
dx is :
- 3/2
- 5/2
- 3
- 5
Hint:
The correct answer is: 5/2
Given, ![not stretchy integral subscript e to the power of negative 1 end exponent end subscript superscript e to the power of 2 end exponent end superscript open vertical bar fraction numerator log subscript e end subscript invisible function application blank x over denominator x end fraction close vertical bar](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFoAAAAtCAYAAAAuj3x7AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAeOiuv/QAAA3NJREFUeNrtWkFkXEEYHiv2UBEiKqqq5BBRsbeKFRElImrFXqJ6qIpSVVGrSk89VC/VQw9VvURFVS0VFSsiVORQOYSqVVW9VFXlEL3EqqoI23/s9xhjXu2bN/+bzev8fLLz3j+Z93/vn3/+N/MLka3cJLQIPwgVEYRNHhGKhCnCXqCDX/oIf5R2O8e2erVtifA4wcO0A9HJ5QKhAa8ORDPJKGEdcVoEotPLQ2QX3wnjyvVtkC0cEC2zls+EQ/ydj+lbJrzHmvCVsGhp/DXYpcsD3Muc6CfKwDXCc21QFbZET4C06CWOo13W9MZwfQrtEcKrFMZ/IAwrbfnSnnJ49CCI24cnrRIKyv1TWto2C52000u/v2rIw2V7Tbu2Qrju0MvmlEV8hrDFFTo28bEhPeMWSFUNvmTw2hUGoluGOF/EdVV+wjlcTue3hGlCkzDEQXQFna4SzuD3jjZYN1PJBdFx+odd6qUhuoZxSlyL4Q4GiNKygkFnwjB9hUeP/h3znLZETyJsyfBxmYPoAXTY7kL3NuEbXkrbQIirGK1nGVXCG0OoKxvWGRuiR5D/nyD0I5NxHjqq6LDsKdfU759HNnEO7RLak5reRcI7ZAoFLGa72ud/N2npScKGRqwMpS9dE30fHRZ7hOjI0C+YOZ/gDHH57x70dvGSWgnS0iJmymlDnzpenjOiX6NDxRPRLmXYkJbZpqXObWuiw9gxJLoBL44IbRhmpm1a6tw2GdOOYlbwXid6gfBR+QSvGXRs01KntvVD+SBvO1wO0lKnts1CeTPHRNumpU5tW4ByPedEe7ftBpSfBaJ5bVtW9jgC0Yy21aFcDUTz2rYB5ZkMH6Z9zGFF9AGUB4JH89lWwIfKUa9Mr7wSPQTF/UA0r21zUGwEonltizZbXgSieW2L9qHvBKJ5bcsihw5Ei84ZoVQ862jQsjCfO/73RMs93F8OB92KGTgLom1LutiJHhU8u3Ztjx5tU9LFQrQsqZ3G7yUozeeIaJuSLuf23sPFdXwRypPlZkZvOMsYnbSky7m9MlbJ4/gronOsI4/kSxb/1GaTJUuik5Z0OSe6D2TL09+7olOZEydxhSa97tE2JV3eUtd/1T8n8fisibYt6fJCNFehCTfRaUq6vNjGVWjCSXTaki4vtnHlneEoSxOuQpNAtEG4Ck1yLX8BLlB3NZ6SYEUAAAFVdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1zdWJzdXA+PG1vPiYjeDIyMkI7PC9tbz48bXN1cD48bWk+ZTwvbWk+PG1yb3c+PG1vPi08L21vPjxtbj4xPC9tbj48L21yb3c+PC9tc3VwPjxtc3VwPjxtaT5lPC9taT48bW4+MjwvbW4+PC9tc3VwPjwvbXN1YnN1cD48bWZlbmNlZCBjbG9zZT0ifCIgb3Blbj0ifCIgc2VwYXJhdG9ycz0ifCI+PG1mcmFjPjxtcm93Pjxtc3ViPjxtaT5sb2c8L21pPjxtaT5lPC9taT48L21zdWI+PG1vPiYjeDIwNjE7PC9tbz48bWk+eDwvbWk+PC9tcm93PjxtaT54PC9taT48L21mcmFjPjwvbWZlbmNlZD48L21hdGg+F95DvAAAAABJRU5ErkJggg==)
Let, I =
i.e. ![open curly brackets fraction numerator negative log x over denominator x end fraction space comma space e to the power of negative 1 end exponent less or equal than x less or equal than 0 comma space close curly brackets
open curly brackets fraction numerator log x over denominator x end fraction comma 0 space less or equal than x less or equal than 2 close curly brackets](data:image/png;base64,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)
![I space equals space integral subscript e to the power of negative 1 end exponent end subscript superscript e to the power of 0 end superscript fraction numerator negative log x over denominator x end fraction d x space plus space integral subscript e to the power of 0 end subscript superscript e squared end superscript fraction numerator log x over denominator x end fraction d x
P u t comma space log space x space equals space t
T a k i n g space d i f f e r e n t i a t i o n space b o t h space s i d e s comma
1 over x d x space equals space d t](data:image/png;base64,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![I space equals space integral negative t d t space plus space integral t d t
I space equals space fraction numerator negative t squared over denominator 2 end fraction space plus space t squared over 2
I space equals space minus 1 half left parenthesis right enclose log x right parenthesis squared end enclose subscript e to the power of negative 1 end exponent end subscript superscript e to the power of 0 end superscript space plus space 1 half right enclose left parenthesis log x right parenthesis squared end enclose subscript e to the power of 0 end subscript superscript e squared end superscript
I space equals space minus 1 half open square brackets left parenthesis log space 0 right parenthesis squared space minus space left parenthesis log space e to the power of negative 1 end exponent right parenthesis squared close square brackets space plus space 1 half open square brackets left parenthesis log space e squared right parenthesis squared space minus space left parenthesis log space e to the power of 0 right parenthesis squared close square brackets space
I space equals negative space 1 half left parenthesis negative 1 right parenthesis space space plus space 1 half open square brackets 2 left parenthesis log space e squared right parenthesis close square brackets
I space equals space 1 half space plus space 1 half left parenthesis 4 right parenthesis
I space equals space 1 half space plus space 2 space equals space 5 over 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Related Questions to study
Maths-
Assertion : Let
be a function defined by f(x) =
. Then f is many-one function.
Reason : If either
or
domain of f, then y = f(x) is one-one function.</span
Assertion : Let
be a function defined by f(x) =
. Then f is many-one function.
Reason : If either
or
domain of f, then y = f(x) is one-one function.</span
Maths-General
Maths-
Assertion : Fundamental period of
.
Reason : If the period of f(x) is
and the period of g(x) is
, then the fundamental period of f(x) + g(x) is the L.C.M. of
and T
Assertion : Fundamental period of
.
Reason : If the period of f(x) is
and the period of g(x) is
, then the fundamental period of f(x) + g(x) is the L.C.M. of
and T
Maths-General
Maths-
Function
f(x) = 2x + 1 is-
Function
f(x) = 2x + 1 is-
Maths-General
maths-
If f(x) is an even function and
Exist for all 'X' then f'(1)+f'(-1) is-
If f(x) is an even function and
Exist for all 'X' then f'(1)+f'(-1) is-
maths-General
physics-
In two separate collisions, the coefficient of restitutions and are in the ratio 3:1.In the first collision the relative velocity of approach is twice the relative velocity of separation ,then the ratio between relative velocity of approach and the relative velocity of separation in the second collision is
In two separate collisions, the coefficient of restitutions and are in the ratio 3:1.In the first collision the relative velocity of approach is twice the relative velocity of separation ,then the ratio between relative velocity of approach and the relative velocity of separation in the second collision is
physics-General
Maths-
Suppose
for
. If g(x) is the function whose graph is the reflection of the graph of f(x) with respect to the line y = x, then g(x) equals–
Suppose
for
. If g(x) is the function whose graph is the reflection of the graph of f(x) with respect to the line y = x, then g(x) equals–
Maths-General
Maths-
A spotlight installed in the ground shines on a wall. A woman stands between the light and the wall casting a shadow on the wall. How are the rate at which she walks away from the light and rate at which her shadow grows related ?
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)
A spotlight installed in the ground shines on a wall. A woman stands between the light and the wall casting a shadow on the wall. How are the rate at which she walks away from the light and rate at which her shadow grows related ?
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)
Maths-General
physics-
If reaction is R and coefficient of friction is
, what is work done against friction in moving a body by distance d?
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)
If reaction is R and coefficient of friction is
, what is work done against friction in moving a body by distance d?
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)
physics-General
physics-
The force
acting on a particle moving in a straight line is shown in figure. What is the work done by the force on the particle in the 1st meter of the trajectory
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)
The force
acting on a particle moving in a straight line is shown in figure. What is the work done by the force on the particle in the 1st meter of the trajectory
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAM0AAADSCAYAAADpPEQnAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAABrQSURBVHhe7Z0JcBRFF8dbIMidgHJfViCABSgRELE4/EDlKOUyXKJcIkgZDuUoDrUKueUWFEQOYzhUlBu5w+mBIMEClEMEhIpaiECCoqLut/+2O06W3c1Odo6emfermpqZ3s3uZnf+069fv37vNp8fRhBExOQTe4IgIoREQxA6IdEQhE5INAShExINQejENaI5cuSIOCIIc3GFaNauXcsSExNJOIQluGKeJj4+np09e5a1bNmS7dixQ7QShDk4vqdBL3Pu3Dl+vHPnTuptCNNxfE9TtWpVFhsby44ePcrKlCnDateuzdLS0sSjBGE8ju5pUlNTWf78+dmIESP4+YoVK9gnn3zCTpw4wc8JwgwcLZrx48fzXiUmJoafV6tWjU2fPp2lpKTwc4IwA0ebZ1evXmVxcXHsvffeY927d+fOgLvuuiu7nSDMwNE9TShhkGAIM3HFPA1BWAmJhiB0QqIhCJ2QaAhCJyQagtAJiYYgdEKiIQidkGgIQickGoLQCYmGIHRCoiEInZBoCEInJBqC0AmJhiB0QqIhCJ24IhtN4CI0uzh16hQbNWqUOLsVrCxt2rQpa9eunWghnAj1NAZSoUIFNnbsWFaqVCm2Zs0a1qBBA36OrXfv3uzMmTOsffv2XDjXr18Xf0U4DeVE88MPP7DbbrstxzZp0iTxqNoUK1aM1a9fnycuBK1ateLn2NC7rF69mg0fPpzt37+fjRs3jj+HcB7KiWbmzJni6D+SkpLEkfPp1q0b3yMBCOFMlBINepl169YxDLO0W40aNcQz3ENCQoI4IpyGUqJBL3P69GnWr18/tn79etHqHnBTGDp0KD9+5ZVX+J5wIP47uRJkZGTAi5dj69ixoy8rK0s8IzQrV67kzz979qxosZd58+bxz9OkSRP+P2DDsfy/du3aJZ5JOBFlepry5ctzU+zQoUPMf9HxNnigevbsyY+dyIABA7K9Z0hsCCcA6N+/vyt7Us/wr3bUAz2MvDvndmdWtafx3wBEy3+cPHkyu8cJ9jihPsp5zyRw337wwQf8+Pjx43zvBuDU8Jtr/Pjzzz/ne8JZKCsaAJNNXmBu4tKlS+KIcCJKi0ZSuXJlceRsEAXwxhtv8MlN0KlTJ74nnIXSosFFhruyU2K1EHsGISQnJ/NzhNHgXG7Fixfnj6H39I9teE9KOA9lAjZxB0ZFsxdffJFfTDL4ccqUKblObqoSsAmRQwzhqFmzJh+vEQ6GuwMUYN26ddlepYSEBN/w4cMjmqMBqnnPCHdDSwMIQieOcAQQhEqQaAhCJyQagtAJjWlMpmvXruzChQusYMGCosV9oAw9vJ9egURjIosWLWLPPvssu/POO13tZsZcWqNGjdjOnTtFi8uBaJyOqi5n/4XEP5fblwIkJSX5/D2p78aNG6LF3dCYxiR+//13lp6ezvLly8cKFSokWt3JyJEj2Z9//sl2794tWtyNkqJJTU11/A+wbds2fiGtWrWKPfDAA6LVnTRs2JAVLlyYLVy4ULS4G+VEgzv0oEGDWN++fUWLM5k2bRq/kLwSlIkxTVpamjhzN8qJ5qWXXmKZmZl8Pf3atWtFq7OA8A8cOMBatGghWtxPnz592LVr19iRI0dEi3tRSjQ//vgjmzNnDs919s8///DgTSeyadMmdvPmTTZ48GDR4n6wLB3jt3feeUe0uBelRIMMLWXKlOEh9G3btmUXL150ZG8ze/Zsbpo1a9aMlSxZ0hN3X1CrVi3HWgd6UEY06GWQSAO+fvQ0sbGxfMJs9OjR4hnOQGua4X+6evUq37zAE088wc6fP8//bzejjGjgLZs7dy6/W0kwMQjPjJN+BC+aZhKY07jhrVy5UrS4FDFfoxRxcXG+Xr16ibPcUWlyExl0ihUrJs58vg4dOnhqnU/FihV9devWFWfuRDnvmZOBafbpp5/mWJ4Nk9NLa3xat27Nvv76a/5duBUSjYHAcwSvH+aZvArM0r///ptt2LBBtLgPEo2BLF68mHv+3B4BEI577rmHB6cuWbJEtLgPEo1BwBw5fPgwe/zxx0XLv2zZssXVpkowmjdvzvbu3SvO3AeJxiCCmWbw+rVp08ZzmTSfeeYZ9ttvv7n2/ybRGEQw08xrPYwEed2w6M6t0QEkGgMIZZq5fUlAODC2+eijj8SZuyDRGEAor1m5cuXYZ5995knHQI8ePdjPP//ME0C6DRKNASxYsICH/QQTB9q82OM899xzPDoAa6PcBokmSmCaHT161FXFdI0ANwpM6i5btky0uAcSTZS8/fbb3DSTVc6I/4BD4Ntvv3VdwCqJJkpgmt1xxx05Ak0l6IXgcj5x4oRo8RaIDsANxW3RASSaKMAdFILo0KGDaMkJ5mkwuen2UPlQVK1alZUqVcp1rmcSTRQgrxmZZuHBuiIUsXLTnBWJJgowngllmgG4nBH1i71Xkemd3BQdQKLJIzDNTp8+zbp16yZabgUepM2bN4cUlRfAIkJ8D25KW0uiySPz58/HAr7sUoFEaOrXr8+2b98uzpwPiSaPIPQdOZq93ItESv/+/Xl6J7d4EUk0eQCm2ZkzZ3hFgNyALe/VwE1Jly5deHqnpUuXihZnQ6LJA9I0y81rBldz48aNPbc0IBCMaVCg98MPPxQtzoZEkwdgmlWqVCnXtf9e72G0IMzou+++c8WcFYlGJ9I0g8mRG14M1AyFTO+0evVq0eJclBRNhQoVWHx8vDhTixkzZnDTLJLkGZifgcvZyzkDJHFxcaxs2bJ8sZ7ToUpoOkFoCEAmSUIfvXr1YsuXL2fXr193dC9M5pkOYI9///33YSc0idCMGTOGp3dC7R4nQ6LRwaxZs/h+4MCBfE/oAx60okWLOr74E4lGBzADq1SpErEJ6PWlAcFo0qSJ49M7kWgiJC+mGf7Gy0sDgjFgwACWlZXl6PIjJJoIIdPMGLCaMyYmhi/ecyokmghZsWIFq169ui7vHFzOcLViI/6jdu3abN26deLMeZBoIgDmFaqyoV6OHuBWvXLlCqtXr55oIQBKDeI7dWp6J1vnaeCvP3nypDgLD8LLQ2H2PA1ms2GeoXiulxeUGQUcJEWKFGHjx49nY8eOFa3OwVbRnDp1iuf9xXJYAM9K6dKl+TE4duwYX+iF52BpcSjMFk3FihV5JvxIBU7kDryQJUqU4L+x44Bo7CYhIYFXMguGXzA+v/0rzoJjZiU0f+/CX3vq1KmiRR/p6eniiNCSnJzsy5cvn+/GjRuixTnYPqaBiSZ7k2CgqhiSM9jFhAkT+B52uF4Q3JmYmMjriRI5wbIKJCVxYr5n20WTlpbG99qSewDjB4B2mEZ2gTUgNWrUyNNYBqIhgoMYPiQlQXISp2G7aNavX8/32t4ESRgyMjLEmX1gDPPTTz+F7AWJ6MAYFgniHYcw02whKyuLjxdQEfnQoUN8mzdvXsjxTSjMGtP06dOHvy7GNXll8uTJUf29m9m7dy//fnft2iVanIGtosEAX4qmY8eOfMM5Bv96MEs0pUuX9tWqVUucEWZQqFAh35NPPinOnIGt5pk0zfbt28dX9GHz33XYQw89xNvtBKbZpUuXPF2p2QruvfdetnXrVnHmDGwTDbxmWMUXOF7Aqs37779fnNnH1KlTeQYV/11QtBBmgFi+y5cvOyo6wDbRhPKawVOFzW42btzIY6SijRsbPXo0RTmHAWmw8ufP76g1NraJRmaSt3MOJhTSNEM1r2jA3XPKlCm0niYMiM/DTfL9998XLepjuWgQOgOX8po1a1hCQgI7dOgQN9VUgkwza4G1gfROTpnXslw0r732Gtu5cydfV1GnTh32+uuvKzEnowUOirp160ZtmuHvcSd1chIJKxg1ahTfp6Sk8L3yCC+aozHS5XzkyBH+Wn4bW7QQVlCuXDlfo0aNxJna2DamURWEq2Ng2rlzZ9FCWMEjjzzCDh8+7IispCSaAFASAmYjrba0lmHDhrGbN286IukGiUbDV199xTIzM/kPSFgLJjmR3gnJ5VWHRKPBaNMM3qDChQt7vmpApCCAE04i1SHRaIBp5h+MGubtgmhgo1P1gMhA8Sekd1J9XotEIzh48CA3zaKd0CTyTqdOnViBAgXY9OnTRYuakGgEEydONNxrhnwFkydPphKDOoATRvUAThKNYMeOHdymNnoiEhN3lMEmcpDBFOmyVI7XI9H4gWn266+/0gpNBUDaWhR/WrZsmWhRDxKNHzNMMyJvYH4M+QPeffdd0aIeJBo/ZplmAFHOtDRAH4hLPH78uLJeR8+LBoIxyzTD0gCsp6GlAfqAiYb0Tps2bRItauF50cC9efvtt5NpphAo/lSyZEk2d+5c0aIWnhfNnj172P/+9z9TTDNaGpB3mjVrxr744gtxphaeFg26f9jNQ4YMES3GAtEg6SFVd9ZPcnIyu3HjhpIBnJ4WDbp/mGZmZr+haOm88fDDD7OCBQuyJUuWiBZ18LRozDTNiOhp0KAB+/jjj8WZOnhWNGabZkT0IIATCU5US+/kWdFYYZrR0oDoQHonRAfIzEWqEFQ0yBYjwxgwkMUHnzRpEj+3gxEjRhhersIK04yWBkQHfhu4n5cvXy5a1CCHaJBKqWnTpuzatWusQ4cOotUYIESIT25I5RQMhIdrn4cNtS5ffvllw4SL9FFkmjmDpKQk9dI7iQQbHCQgT01NFWfGk5GRkV0VANvJkyfFIzlBNQFUR9M+jjYkSg/2+fRmo/GbZDzxthVVuPw3H1MqtHkFVFzAbzt//nzRYj/ZosHFDNFYgRQNhAExBCPYZ4GIgolNr2hiYmIs+1+J6EH1BtwwVYGbZzDLMJnUu3dvnFoCysehbGCbNm0izrCJ9KWIEUPCwbyCorbIejJ48GDRQqhO69at2YEDB8SZAkA5MHlwGOyujxoyuCujJwJ4DtqgfLThro/H8feBJlUoxNtm/51fQPxcS6ieQNa0gakn0dPTICFd0aJFxRnhBGQCx61bt4oWe+FXL4oo4YIPBBco2vGBpWi0YxLtGEOaTnit3MDzgByn4HzixIm8TRJKNKiWhufjs0n0iMZq02zWrFm+K1euiDMirxQpUsTXqVMncWYv/OrFBZfbRSpFA2Rb4IUOAURie+JvJegxcI5NK4RwF3bge0cqGvk8q8rVyUGs08rjqcijjz7qi42NFWf2EtXkpv+fEEf/4h+wsf3794uzyChfvjwvbQHat28f8XwMqg3oZcaMGbxStFWV1mh+xjiwxgZTISqsTVIiIgADfH8vw48x4RhqDida/LYxe+yxx8SZ+VBMm3G0bduWp3dClQm7UUI0ADVK/OMjfoxZYMQchQPBfHrAmvO//vqL37GsAlloUPKblgZED25ASIW1efNm0WIfXDRw4x47dow32MlTTz3FXdEglJkneyHkx9IDYs2sNM0kEAz1OMbQp08fHrxpd3QAFw3u8pgzCTZf8s033/A95jcksi09PZ3vAf4W4SkgnHkl3wMxbcGYNm0aT6wQCmnTNmzYkO8jxWrTjDCevn378rCqRYsWiRabgDcArl8car1XQOtelltgG7xc0pum3dAWCJ4b+LxgSFd0MDCnE+jWzs17lpKSwh/3m0qihXAqlSpV8iUmJooze8i+aiGGYHM1dqGdvJRI97TeMBr/+McXFxcnzqwDsW1+88zn75lFCxEtzz//vK9AgQKWxA2GItsR4P8wfJyAMHwVgCtaC8y6Ll26cGeBnpLpcPuiwlb37t1Fi3Ug3xnW0lDeM+MYNGgQd+jYmd4ph/cMHqYzZ85w4UQaD2YFGP8gRg0bnAV6WLBgAc+h1bNnT9FCOBl4VjE/iKUmdpFDNPAurV69mme7X7t2rWi1n5kzZ/KCS2PGjBEtkYPEDMihZYfbFy5nBBvqTYCOC0JPb+o14AG1Nb2TMNMcTagxDezefPny+QYOHChanAH+F2wUfhOc7du38+/nwIEDosVacvQ0bsOJptn69etZQkICP1Y5c76dyPROb775pmixFleLxk7TLK9gchf5CyCcxYsXh5zP8jr16tVj27ZtE2fW4lrRwGuGzPMoEmQn8J5FGrj55Zdf8nSs8BzK/AUYYxK3gigW3FDs8Ey6VjQqmGb4QRs3bhxxCieUA/ePv/gxEoyAOXPm8D2RE/yu/vEqW7hwoWixDleLBl4rO00zPUsDcNfEEon69evzc/Q2uJsivMno9FVuAPF88fHx2UG+VuJK0eBixcXWo0cP0WIPegI14VYPnFiWc1LkEAgOemOkd9JzczIE4UVzNIEu5/Hjx/NzFcJXEO+WW8iHjP0LtwULK/I6+L3x3SxdulS0WIMre5qUlBRumqlQijySpQH4vPPmzcMN7JYN7YAcAreCSfiyZctaPq5xnWjQVSMUyG7TLFIQroRlF7169RItOdE6BFQKbVIFzNkgttBKXCcapK7FHbpfv36iRV0ggnHjxomz4BQvXpwX0cUYDc8l4eQE+ev++OMPa4s/+S8wx6Md01SvXt3nN83EI/aCsUzr1q1Djq3wmbVbsDVIgc8J9Twvg/ROXbt2FWfm46qeJjMzk5tmoUwdq8E8zZYtW0JOwPm//xybdDdrCXxOqOd5mUaNGvHv2SpcJRrMzeCisjK9LmE/qCqB9E5WFX9ylWg2btzIqlSpooTXDMjJVb1LAwh9IKcEogNQ3t4KXCWaixcv8owlqgBXM1I4qSJit4LvuW7dumzDhg2iJXqQiCVU1htXiYZMM++CUoMXLlwwLL0TRAMhBuu9XCWaqlWr8gkvwnsg0BU3TaNi0XDzXbVqFXv11Vf5BKp2JfNt/jeCG9PRYN0MghsrVarEqlWrJloJr4EaNkhda6R3EZPlmDyNiYnhN2TU/3SFaM6fP88nAAG+NMKbXL58mU/+wuIwCsgDEejIgIOJZkyeKy0afAGoDoDFZKBy5cqsRYsWPAEIQQSC8QycAnqiy8OB+bXmzZvzjLFwa6MCX1xcnLpjGmRkgbK1WeKRshZtdqbvIdQFF7RRgkGuBqSLSkxMZGfPnuVBoXh9Dnoa1UDaWXy0YNlYkDoXjwUrOUgQRrFmzZqQGVuVEw0qnEEUSJMbCggmt+cQhFkoNabBGAbmF8jKygo5dsHArEKFCvw43PMIwgyUGtOkpaXxPTxh4YSgzfMsSw+qBoSNZcpYoiDXxBDuQCnRYEYXoHZnbsgaNpFmerEarPl/6623eO4yO4HnB6JFXRdsEDEEbTawGpDzQL4vPoNZZSFzA4N6fAajcFVEgErA07dv3z5xZg8QBzxAstgWgIhh2potHCyYQ845WP+YNsBnsKOoFsSLAshGopRoMA8DIillKC8EJ2XPtBr0dsgxgHGfvHjlJLCZOQeQ9BDzGnJmHnsUIsbqUzxmJUOHDhVHxqGUaDBxCfDlhrsTah+jBVmhQUpe1B2S40N8V7Nnz+bHZoL3Cax6UKJECb638veSAg1XjjIvKCUa/LgTJ07kx+HuhPIxmamFCE640iS1a9cWR9YAp4iVThuYZehlzLhJKDemQaIEmBDJycl8ABcI2vAYEoXjLkroA0WG8f1aVeUad3s4AdDryWkCK0BaLJS/N2U6AvM0qoHkeXKSE8VtMYmJzf9jO25SU/4PKoDvFXVVrUrMgd8J/7/c8N74DGaDmqza7xzHeH+jUFI0EnzBCJuRokFYjRVfupGoJBrciFJTU8WZNcjfEILBd4HPYDb4vrUZST0lGjegimhw4doZrycrc5v9XeCmEHhjMFo0NE/jATCpCDc+5o7sAlEc/ouXlSpVSrSYA5xETz/9dPakKjY5PSHPo4VEYyLw4IBLly7xvR1AMKNGjeIOFomcrbd6hh7C1VudWy8Qjb8zyLFBrECeRwuJxiTgMZLBp/v37+d3OKvXAUEUMiIAn0XeaXGMyUazKkjz1Y3+95HeTylSzMxb5bUzFb/yCBcCDxJ+3lCbmeMbOGy074UxBcZUdmH0mMYVOQIIwkrIPCMInZBoCEInJBqC0AmJhiB0QqIhCJ2QaAglQAj/hAkTrC9vngdINDaBCT/tjDzWm1g9Qx+I1asqtSDh+O7du/nqXRTuVRkSjQ3g4rjvvvtYRkYGP8fFingphLvYydatW1nTpk0tSbwRCLJX7tixg3Xu3Jl1796dxcfHW1oSUBd8ipOwDMyMY12QNnQdIDIXs/h2g8+HyyLw80lQfDcmJiZ7tt/MrWDBgr6xY8eKd1YHigiwEJhfyMiyZ8+eHLnbVAMxcjCRQmXTQdoss8YeKKY0cuRIHruGgsOoD6Nc+UUuHcISEANlxSIsI8CiMatXyA4bNoz3MG3btg2ZR1kFaExjEBjYB+Y0wDnu2ngM4xZEGyclJYlHc4LHtQNx+XpyfCFfK5LBOv4GjgWA18ExNhzLttxeDwPzOXPmiDPzeeGFF3hJlfT0dLZp0ya1K9oJ8RBRoF0Lj2Ms8UWPIpdpy/NgXzfW68ulwPLOrn09jHXka8kcCeHW+MuKC9gwRsLfyvfG36MNEc65vR7acnsvr0KiMQAMnrUXphSKFrTDPAsEA24pEuwBQutlOLs2hF+G+8vnBQMikyLUXvDy82EvkUuQg71euMe8DplnBtCuXTueY8x/gfEFZ8gpFpg6CO3BgEMgMEsoFmq1bNmSHyO1q0QuGoMJEwqsjKxTpw4/1ibmi42N5ftWrVrxPZDOiGCvF+4xr0OiMRBZHSAzM5PvzeKXX34RR8YQ7vWMfi83QKIxkIMHD/K93YnPjcTsRBhOhERjICgV4h8zsOnTp4uW//CPacSRM5CeNtScJHJCookS6WaGSxfm2YMPPsjPMZGJTbp027Rpk51KKBTnzp0TR8GRF3I0ZGVliaPwr3dS5F2mqgxBEA4BIo/gK4SnSxbVhdcMbXD9aj1V0vOFvRZ4uKTrFxu8VTKUBRsew3Owad3J2tfWIr1k2PB8eMHwetKjhtfDeW6vh8+BvyFuhcJoogQ9zN13353DU4WATDgD4FXTgp6oWrVqOZL2oScKrOaGSF9ZFQ7Iu33g84IlgA9ME4X3xFhL+3p4/YoVK4Z9PXjqhgwZQknmg0CisRCYazVr1uSmj1k5x4wANwKUPnSTQ8NISDQWgzEQkuapKhz5+fxmndJBpXZCjgCLgcnmH0/waGeYcSoB0w6mIwkmPNTT2AQ8V7g4VeptML6ysryfUyHREIQuGPs/p3oBU/qO/igAAAAASUVORK5CYII=)
physics-General
physics-
The pointer reading
load graph for a spring balance is as given in the figure. The spring constant is
![](data:image/png;base64,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)
The pointer reading
load graph for a spring balance is as given in the figure. The spring constant is
![](data:image/png;base64,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)
physics-General
physics-
The force acting on a body moving along
-axis varies with the position of the particle as shown in the fig
![](data:image/png;base64,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)
The body is in stable equilibrium at
The force acting on a body moving along
-axis varies with the position of the particle as shown in the fig
![](data:image/png;base64,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)
The body is in stable equilibrium at
physics-General
physics-
A frictionless track
ends in a circular loop of radius
. A body slides down the track from point
which is it
height
. Maximum value of
for the body to successfully complete the loop is
![](data:image/png;base64,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)
A frictionless track
ends in a circular loop of radius
. A body slides down the track from point
which is it
height
. Maximum value of
for the body to successfully complete the loop is
![](data:image/png;base64,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)
physics-General
physics-
Velocity-time graph of a particle of mass 2 kg moving in a straight line is as shown in figure. Work done by all forces on the particle is
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)
Velocity-time graph of a particle of mass 2 kg moving in a straight line is as shown in figure. Work done by all forces on the particle is
![](data:image/png;base64,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)
physics-General
Maths-
Domain of definition of the function
, is
Domain of definition of the function
, is
Maths-General
physics-
If
represent the work done in moving a particle from A to B along three different paths 1, 2 and 3 respectively(as shown)in the gravitational field of a point mass m. Find the correct relation between ![w subscript 1 end subscript comma w subscript 2 end subscript a n d blank w subscript 3 end subscript](data:image/png;base64,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)
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)
If
represent the work done in moving a particle from A to B along three different paths 1, 2 and 3 respectively(as shown)in the gravitational field of a point mass m. Find the correct relation between ![w subscript 1 end subscript comma w subscript 2 end subscript a n d blank w subscript 3 end subscript](data:image/png;base64,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)
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)
physics-General