Physics-
General
Easy
Question
Two blocks
and
are connected by a massless string (shown in figure). A force of 30 N is applied on block
. The distance travelled by centre of mass in 2 s starting from rest is
![](data:image/png;base64,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)
- 1 m
- 2 m
- 3 m
- None of these
The correct answer is: 2 m
The acceleration of centre of mass is
![a subscript C M end subscript equals fraction numerator F over denominator m subscript A end subscript plus m subscript B end subscript end fraction](data:image/png;base64,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)
![equals fraction numerator 30 over denominator 10 plus 20 end fraction equals 1 m s to the power of negative 2 end exponent](data:image/png;base64,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)
m
Related Questions to study
physics-
Three rods of the same mass are placed as shown in figure. What will be the coordinates of centre of mass of the system?
![](data:image/png;base64,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)
Three rods of the same mass are placed as shown in figure. What will be the coordinates of centre of mass of the system?
![](data:image/png;base64,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)
physics-General
maths-
If
then descending order of ![a comma b comma c](data:image/png;base64,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)
is
If
then descending order of ![a comma b comma c](data:image/png;base64,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)
is
maths-General
physics-
A disc is rolling (without slipping) on a horizontal surface
is its centre and
and
are two points equidistant from
. Let
,
and
be the magnitude of velocities of pints
and
respectively, then
![](data:image/png;base64,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)
A disc is rolling (without slipping) on a horizontal surface
is its centre and
and
are two points equidistant from
. Let
,
and
be the magnitude of velocities of pints
and
respectively, then
![](data:image/png;base64,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)
physics-General
Physics-
The acceleration of the center of mass of a uniform solid disc rolling down an inclined plane of angle
is
The acceleration of the center of mass of a uniform solid disc rolling down an inclined plane of angle
is
Physics-General
Physics-
A solid sphere of mass
rolls down an inclined plane without slipping, starting from rest at the top of an inclined plane. The linear speed of the sphere at the bottom of the inclined plane is
. The kinetic energy of the sphere at the bottom is
A solid sphere of mass
rolls down an inclined plane without slipping, starting from rest at the top of an inclined plane. The linear speed of the sphere at the bottom of the inclined plane is
. The kinetic energy of the sphere at the bottom is
Physics-General
Physics-
The moments of inertia of two freely rotating bodies
and
are
and
respectively.
and their angular momenta are equal. If
and
are their kinetic energies, then
The moments of inertia of two freely rotating bodies
and
are
and
respectively.
and their angular momenta are equal. If
and
are their kinetic energies, then
Physics-General
biology
Famous palaeonotologist/Palaeobotanist of India was:
Famous palaeonotologist/Palaeobotanist of India was:
biologyGeneral
physics-
A small object of uniform density roll up a curved surface with an initial velocity
. If reaches up to a maximum height of
with respect to the initial position. The object is
![](data:image/png;base64,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)
A small object of uniform density roll up a curved surface with an initial velocity
. If reaches up to a maximum height of
with respect to the initial position. The object is
![](data:image/png;base64,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)
physics-General
physics-
A uniform rod
of length
and mass
is free to rotate about point
. The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about
is
, the initial angular acceleration of the rod will be
![](data:image/png;base64,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)
A uniform rod
of length
and mass
is free to rotate about point
. The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about
is
, the initial angular acceleration of the rod will be
![](data:image/png;base64,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)
physics-General
physics-
A particle of mass
moves in the
plane with a velocity
along the straight line
. If the angular momentum of the particle with respect to origin
is
when it is at
and
when it is at
, then
![](data:image/png;base64,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)
A particle of mass
moves in the
plane with a velocity
along the straight line
. If the angular momentum of the particle with respect to origin
is
when it is at
and
when it is at
, then
![](data:image/png;base64,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)
physics-General
maths-
Assertion (A): If the system of equations
have non zero solution then ![lambda equals 5](data:image/png;base64,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)
Reason (R): If the system of equations
has a non zero solution then
is singular
Assertion (A): If the system of equations
have non zero solution then ![lambda equals 5](data:image/png;base64,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)
Reason (R): If the system of equations
has a non zero solution then
is singular
maths-General
physics-
Consider a body, shown in figure, consisting of two identical balls, each of mass
connected by a light rigid rod. If an impulse
is impared to the body at one of its ends, what would be its angular velocity?
![](data:image/png;base64,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)
Consider a body, shown in figure, consisting of two identical balls, each of mass
connected by a light rigid rod. If an impulse
is impared to the body at one of its ends, what would be its angular velocity?
![](data:image/png;base64,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)
physics-General
physics-
A binary star consists of two stars
(mass 2.2
) and B (mass 11
), where
is the mass of the sun. They are separated by distance
and are rotating about their centre of mass, which is stationary. The ratio of the total angular momentum of the binary star to the angular momentum of star
about the centre of mass is
A binary star consists of two stars
(mass 2.2
) and B (mass 11
), where
is the mass of the sun. They are separated by distance
and are rotating about their centre of mass, which is stationary. The ratio of the total angular momentum of the binary star to the angular momentum of star
about the centre of mass is
physics-General
physics-
A force of- F
acts on
, the origin of the coordinate system. The torque about the point 1, -(a) is
![](data:image/png;base64,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)
A force of- F
acts on
, the origin of the coordinate system. The torque about the point 1, -(a) is
![](data:image/png;base64,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)
physics-General
Maths-
The area of the region bounded by y=|x-1| and y=1 in sq. units is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAR4AAADtCAYAAABpuBrVAAAgAElEQVR4nO2dV5fbVpa2XxAEQIAECYI5FItVSmP3dE/PxVzP/5wfNe4LTytYgSzmHEES+bvQd06zJEu2ElPtZy2utluWBBbBF/vs8G4hDMMQBEEQByRy7AsgCOLhQcJDEMTBIeEhCOLgkPAQBHFwSHgIgjg4JDwEQRwcEh6CIA4OCQ9BEAeHhIcgiINDwkMQxMEh4SEI4uCQ8BAEcXBIeAiCODgkPARBHBwSHoIgDg4JD0EQB4eEhyCIg0PCQxDEwSHhIQji4JDwEARxcEh4CII4OCQ8BEEcHBIegiAODgkPQRAHJ3rsCzg3wjBEEAQIggAAIAgCIpEIBEHg/04QP5IgCPDhHs79++8c7kESni/E8zxYloXNZoMgCCDLMlRVhSRJiEajiEQiiEQokCR+DL7vw7ZtOI7DBSgSiUAURUSjUUiSBFEUT/4eJOH5Qmzbxng8xmAwgOM4SCaTME0Tuq4jFotBkiTIsnwWTx3ivAjDEI7jYLVaYblcwrZtAIAkSVAUBaqqIh6PIxaLkfBcGrZtYzKZ4N27d9hut8hms3BdF77vQ9d1aJqGaDQKURSPfanEhREEAWzbxmw2w3A4hGVZiEQiiMViSCQSMAwD0WgUsiwf+1L/EBKeL8TzPGw2G8xmM6xWK/i+DwBwHAfZbBaCIEBV1SNfJXGJsHtvMpmg3W5jtVpBURQYhgFRFKFpGnzf/yj/c4qQ8Hwh+8llFv1sNhtMp1PsdjvEYjEYhnHsyyQuCHbP2baN5XKJfr+Pd+/eYbFYIJ1OIxqNwjRNAOdT3CDh+UIikQhkWUY8HsdqtYJlWTzn4/s+MpkM8vn8WYS7xOkThiE8z4PjOFiv15jNZuj3+zziAYBSqQRRFHmB4xzEh4TnCxFFEaqqIpVKYbVaYb1eYzKZIAgCaJqG6XSK1WoFWZZ5hevUE33EaRGGIRcP3/ex2+2wWq0wGo0wHA4xHo+xWCyw3W7heR4ikQgURYEsyxBFkYTnEpFlGel0Gq7rIggCWJYFz/OwWq0wHo/5zRGJRKBp2llUGIjThEU7q9UKvV4PrVYL7XYbi8UCkUgEyWQShmEglUohkUjwto5zuN9IeL4QWZZhmiZUVYUoilgsFvy8vV6vMRgMoOs6fN9HLpdDJpOBJEnHvmzizAiCAL7vY7vdYjabodls4vXr1xiNRtjtdjAMA+l0GldXVygUCkilUiQ8l4wkSdB1HfF4HEEQoNvtwjAMzOdzeJ6H8XgMSZIQBAFEUUQikeBRz34I/b0IggCe5/FOalEUz6KBjPg0LNKxbRur1QqTyQTdbpfndWKxGLLZLCqVCqrVKrLZLL/P6Kh1oeznbHRdRyaTQaVSgW3b2O12mE6nsCwLtm1D0zRkMhkkEokfIjz7DWWbzQYAEI/HkUgkoCjKWdyAxMewCtZ8PsdoNMJgMMBoNMJyuYTv+9A0DcViEdVqFYVCAclkEoqiIBo9n6/z+VzpCSLLMjKZDG5ubiAIAjqdDjqdDlarFW8urFarSKfT94TnewlCGIbYbrcYDoeYTCYAgFwuB1EUqXv6jPF9H5ZlYTgcotPpoNfr8YhaURT+sLu6uuLRzrk1rJLwfAMswXd9fQ1RFGHbNprNJkajEQBgOBxiOp0inU4jDEM+R/O9CIIA2+0Wg8EAzWaT/3/JZBK6rtNx68wIwxBhGMK2bSwWC142Hw6HsG0biqIgnU6jUCigVCqhUCggkUjwCuo5QcLzDYiiiHg8jnw+D9/3MRqNkEgkEI1G4bouFosFBoMB4vE4stksUqkUJEn67hHPYDDA27dvAbw/alWr1bPoXiX+BWtKZf06k8kEvV4P3W4Xi8UCoigilUqhWCyiVCohk8lA1/WzPVKT8HwDkUiEVxI8z+NPosViAQCwLOteJMJmar4XTHj6/T7evHkD4P1Ra7vdkvCcGWEYwnVdWJaF+XyOwWCAdruNdrsNAMjn87i+vkatVkO1WkUymTzr4zQJzzcgCALvFk2lUvzmcF0Xy+USruui3W7D930oigLTNHnU8z0IwxC73Q7j8ZjfoGx0gzgfwjCE7/t89GY4HKLf72M4HGI+n0PXdaTTadzc3KBeryObzULTtLMVHYCE55sQBIHnbFRVhWmauLq6gu/76Pf7mM/nmE6nCMMQpmmiXC4jlUohHo9zD5VvuXk+fEoC76Ms13Up4jkDWLGBHbGWyyWGwyG63S7G4zF2ux1vychmsygUCsjlctB1/WxGIz4FCc93QpIkpFIpXF1dIRqNIhqNYrfbYTAYwPM8/gSLx+MIwxCxWAyKonxzspk9LV3XhSAIZzOdTLyHDYCyyLXRaKDZbPJ+sFKphHK5jGKxiFQqBU3TzvqIxSDh+U5EIhHous7tCTzPQ6/Xg+/7WCwWGI/H6Pf7iMViEAQBpml+9yoXcV6wKhaLWofDIZrNJprNJjzPg2maKBQKvDs5Ho9/1+LEMSHh+U4IggBFUbgD4Xw+h2maiMfj8H0f6/UavV6PdxZLkgRN075Lvof1Bp2L3y7xHhbpsO7k0WiEyWSCxWIBTdOQTqdRq9V4v46qqmdXNv8UJDzfEZbzURQFqVSKP60GgwHCMESv14PjOBBFkVumsgjoR4xTEKcNa7lgjYLT6RSu60KWZaRSKeRyORSLReRyOV7FIuEhPglLCJZKJViWhWg0im63i06ng/F4jGg0ikqlAsdxjn2pxBFxHAfT6RR3d3dot9uYTCYIwxC6rnPRYcLDLHUv5eFEwvODiMViyOVy8DwPvu9jPp+j3W5juVxiMBhgMplguVxCVVX+JKN8z+XDksms5WI4HKLdbqPb7cKyLG7YXiqVkM/nYZomEokEJEm6qKIBCc8PQBAEyLKMZDLJ8zv9fh/dbher1YpXMDqdDgDAMAzE43ESnguHDfVuNhus12t0u110u130ej3MZjNEo1EYhoF8Po9KpcLtV1ge8FKiHYCE54chyzKfl7IsC8ViEf1+H6Io8j4f1vEMvI+QiMuGzWGxJsG7uzs0Gg10Oh1st1vep3Nzc4NKpQLDMC7WQpeE5wfAkszsXJ7NZlEsFlGpVCAIAr/5fN/nZfh0Og1N04596cQPhA31jsdjtFotNJtN9Pt9LBYLCILAfXaY3UUsFjsrq4sv4TLf1QmwX+FKJpPI5/Oo1WqIRCIYDAbYbDawbZvfbNlsli9mo3zP5cB6dVi0s1qtMBwO0Wq10Ov1YFkWFEVBPB5HLpdDNptFOp3mVheXUsX6EBKeHwxbuJbP5xEEARRFge/7aDQamM/nkCQJ+Xwe2WyWTyAzx8JLOtM/ZJiN6W63w3w+R6/XQ6PRwGQygSzLPJFcr9d5i8Uliw5AwnMQVFVFPp+HpmlQFAXT6RTv3r3DbDYDAPR6PeRyOd6AyEYuSHguAzaLxfyTe70ems0mNpsNarUaKpUK6vU6rq+vYZrmdxmlOXVIeA4Ay/fIsgzHcfign6IocF0Xs9kM3W4XsixDURT+Is4fdsRiNqbD4RCLxQK73Y4byZVKpY/GIi4dEp4Dwo5dmUwGV1dXcF0X6/UalmXh7u4OAPjOrnO0syQ+xvd9LJdLtFotvp7GcRwYhgFN01Aul5HP57k3N8vxXTokPAeG+TTX63UAwN3dHUajEWazGWzb5vM5dMy6DARBwHK5xLt37/Dq1SuMRiO+cTaXy/EKlmma0DTtbLZEfCskPAdEEARuGlapVHhzIfNmliQJo9EIi8WCD5hSkvk8CYIAYRjCsixMp1N0u13c3d1hu93CNE1eNi+VSjBNk3vsPBQezjs9EaLRKOLxOEzT5P08g8EA6/UaQRBgsVjwfA8Lv2kb6XnB3AQ3mw0mkwn6/T5fe8Qql/s7sdhyyIcECc+BEUURsVgMhmFwoWFuc0EQYD6f4+3bt3BdF7Zto1KpXNRU8kOAeTCxqfNWq4X5fA7XdaGqKrLZLGq1Gmq1GtLpNBRFeXDuBCQ8B0QQBEQiEb58LRKJYLFYoFAoYLFYYLFYYLVaod1uw/M8yLIMwzCQTCYfVBh+7jC7i3a7jWaziV6vh/V6jTAMuUVuuVxGqVR6UHmdfehuPjDMrCsSiUDTNH4TbjYbiKLIDaE8z0MymUQul+ObKZhYPbSb9BxgOZ0gCLBerzEajbib4HK5hKIoUFUVlUoFuVyOdyfLsszXTz8kSHiOCOvjqFar/N8ty8JgMIDrunxSmfk0x+PxB9Fcdo4w32vmsdPv99FoNNBut6EoCiqVCvL5PKrVKorF4kdugg/tYULCc0REUeQT7JIkYbfbodlswrIsLJdL6LrON1NIksRfJDynBxuJYCtq+v0+7u7u0Ov1UC6Xkclk8OTJE1xdXd0rnQMPT3QAEp6jwhoKWf5mNBohnU5DVVWs12us12sMBgMekquqilgs9iA6W88J1p3Mjsl3d3f3bEzZkblSqfBoZ39TBAkPcVDYDSeKIvfZLZVKmE6n3AZzOBxyc/hkMolUKnXkqyYYrBLleR4vCrx69Yonk5l96c3NDUqlEtLpNOLxOM/VPWRIeE6EaDSKZDKJq6srOI4DTdPQ6/UwGo2w3W6hqipKpRJKpdKxL5X4/wRBAEEQuI1ps9nEP/7xD0wmE2QyGZ7Xubq6QrlcvmfY/hCjnH1IeE4A1tGcSCRQLBbhui7v8WGjFGysYrVaQVEUxGIxXkkhDg/bh8Xm7ZirYLfbxXq9RiaTQaFQQL1eR6VS4c2gl7IX61sh4TkR9gdIPc/jYjOZTPjupcFgAMMw4Ps+8vk8fN8/9mU/WNje+ul0itFohE6ng+VyCQB8J1ahUODl80QiQVYne5DwnAjMID6RSPAKCZvhms1mcF0X3W4X0WgUrutCUZSL9eM9B1i/TrvdRqPRwGAwgOM4vDjA1g4zCxSKdO5DwnMiRCIRbgAmiiJ2ux0KhQJvJvR9H8PhEGEYIhKJIJPJwDAMeJ5Hx60DwhLKtm1jsVig0+ng3bt3mM/nEAQBhmEgk8mgWCxyG1P2gCDh+RckPCcEq3Qwn+ZCoYD5fI4wDDEajTCfz7HdbhGNRlEsFhGJRLDb7XhOiPp7fixsHxabxRqPx3wswnVdFAoFFItFPg7BbGyJjyHhOUHYxoFcLsdXHtu2zaecZVlGpVKBJElYLpfY7XZ8YwXx42BT55Zl8URyt9vFYDCALMu4ubnB9fU1rq+vkc/nSXQ+AwnPiSJJEkzThCAICIIAg8GAT69rmobBYABVVTGbzbDZbOB5HjUW/mA8z4NlWTyZ3O/3MZlMsFqtYBgGEokEqtUq6vU699cmfh8SnhOF+fYAwGaz4Tmd5XIJ3/e5cdhkMsFiseCWC2wIlfj+uK6L+XyOVqvFE8q+7/Nd52xNkWmaiEajlHv7DCQ8JwjbySUIAlRV5Td2rVZDEAS8omLbNsbjMS+567p+7Eu/OFgyeX8L6Js3b/D27Vtst1vE43FkMhlUq1VUKpV7FSwSnk9DwnPisA0V+Xwejx49QjQaxWQy4dYLrORu2/axL/UiYULPupNHoxEajQaazSY0TUO9Xke9XsfV1RX31yH+GBKeE4Udl6LRKHet2+123MvHsiysVissFgtsNhv4vs+fsHTc+n54nofNZsMbOJnQW5aFRCKBbDbLhSedTiMWiz3o4c8/CwnPGaBpGjKZDB8W9TwPs9kM/X6fm0+xI8F+PxDx7bB8WqfTQbPZxGg0QhAE0HUd2WwW5XKZz2LFYjGqZP1JHszd+eF5+5zO377v81mudDrNKyjMQnXfOtP3fTiOA9u2qaryDbBq4nK5RLvdxosXL7h3ciQSgWmayOVyfAcas7nwPO8i2xq+dxR38cITBAE8z4PneXyojzWB7UcKpwy7xiAIsNlsYNv2vffBRJQNLDKTcTZISnw5kUgEvu9jMBjgzZs3ePnyJbrdLjzPA/B+PxpLOC+Xy3vJ5FO/n74E1inPrFtlWf4uFrwXLzye52G9XmM+n2M+n3NT9fV6zb+455ATYU/RzWaDbreLt2/fotvtYjab8QbCzWaDu7s7/O///i8mkwlkWebCdA4CeyoIgsCPtKyK9ebNG0wmEwDv827L5ZKL/2AwgKZpF+UWwN5HGIa8mbVarSKfz/Mp+0gk8tXR3UULTxiGcByH76rqdDpot9vodDrc54YJzynDhFEQBDiOg+VyyYdHLcuCbdt8OeDbt29h2zb+7//+D9FolE+wX8oX4kfw4efPcmX7C/kmkwksy+KtDoqi8JEJXdfvmbZf0s86DEPouo7Hjx/DcRzIsszXLFPE8xl834dt21itVphMJuj1emg2m+h2u7Asi98spy4+DHZ0dF0XYRhCFEWIogjP87Db7dDr9bBYLPj0uiiKZMfwBzChYBGL7/t8MJcdydl9wgSJPdDYdpBLy+vsiyebObu+vsZut+Nd8t8isBcvPJFIBLIsIx6PwzAM5HI57HY7RKNRbDYb7iJ3TPb//v1/3g93PyQSicDzPMznc/T7fYxGIz4wutvtIIoiEokETNPke7ku6Un8PdkXG/aQYiVzANxylm11/ZTh/iX9fPffi67rKBQKSCaTPNr5Vi5aeJjHTTKZRKlU4kZbtVoN6/UajuMc/WbZP0Z9mGva39W0D9tKsd1u0Wq18Msvv/AnkaIo0DQNuVwO9Xod//Zv/4ZKpQJVVY/+Xk8NlhAOggC2bcO2bcznc3S7Xbx8+RK9Xg+CIKBWq+H29pbbl7IcB/D+M9pP8F/iz1hRFOTzeVxfX8MwjHsLKb+WixYe4P2wpa7rUBQFmUwGtm3DcRweSh8blvhlIrOfCGbJuw8/YGaVul6v8c9//hOTyQTNZhOr1QqqqsIwDJRKJTx69Ah///vf8eTJE2iaxr17LvHL8TUw4WHGa9vtFpPJBMlkErvdjld06vU6fv75Z9zc3NyLfNgxdz/fcezo+UfAclrxeByqqvKREMrxfAZ21GJPqP0v3rErPftP2u12C9u2+Q511rej6/q9HUwMQRCw2Wwwm8343i0mSMyTmeV4gH/tfXIc5ywS6odk/3NwHAeCIPAZLFEUYZom79UJw5C7AcTjcWiaxh9s+0Zul8anovKv5eKFBzjdEQLWl8NMpabTKZ+70jQNtVoNNzc3SCaTv3szx2Kxj8JeJqxsoLHRaPDq3XQ6xWKx4F+uh8j+w2b/vmAJZFaMCIKAuwfKsoz1eo1Wq3Wvb4fNz11fX8M0TUiSdG9fFvFpHoTwnCr7DX+tVou/LMtCKpWCbdswDAPpdPqTycz9Ixrwr1Kw53l8Nxf7M9mcEZv5oi/Ie/aPtYqiQNd1mKaJTCbDm+bW6zXG4zFGoxFarRZc10WtVuN5NTaiwra9Ep+HhOeIsCes4zjYbDY8sTmdTvmWAhbWf+r374uOKIo8x6PrOoIgQK/Xg+M4fL0uazbct954aDDBZrvO95tI2TYITdNQKpW4+f52u4VlWXxFMdt1xlYObTYbKIoC3/dJeP4EJDxHZP8Jy5KWkiTxL4XneX9q5IEJD3MtrNfrSKfTmM1maDab3C61UCjwLQisv2dffB6KCLGcDttbxuxjHceBqqpIJpO8ipNKpeC6LjabDTdas20blmUhl8txG4z9ERzijyHhOSJsl1YqlUIul8N4POYrbgH86QoU++8URUE2m8WjR49gmiYajQZ+++03zGYzXl7/61//imKxyI8EH1YoLt3AShAE+L6P1WqFXq+HVquFXq+H6XSK5XIJSZL41Hm9XodpmtzyNJVK8arOarVCKpVCKpWCKIo0E/eFkPAcESY8yWQStm0jnU7fm4P5s3kYdtNLkoR0Os1narbbLTRNu+fpU6vVUKvVeGfzfoR16U/sSCQCURQRhiFWqxWi0Shvq5AkiU/8V6tVlMtlFAoFmKbJiwCxWIx3Li8WC2iaBsMwuBg91KPr10DCc0RY+VtVVSQSCW4Q/qU3MBMLlptgHdrT6RSVSgWbzQapVAq+72M2m0GWZaiqyo8J6/Uai8UClmVdbKmdNZOyZPFut0O/38d4PIZlWZAkCYVCAdlsFtVqFcViEbqu88bLaDTKLWfj8Tgcx0E8Hoeu6zAMA8lkkgsT8ceQ8BwRVknRNA2u6/LGNFYe/1QD4ef+vFgsxqsyxWIRNzc3vHHQsiy8fv0ag8EAiUQCiUQCjuOg2+2i0WhgNBrBtu1vHgA8RZiFLDPNj0QimM/nGI/HcF0XuVwOxWIRjx49QqVSQbFYhKZp/CjKvI0WiwVvY9A0DaZpIp/PI5VKkQHbF0A/pSPzYav9/ojE/rDin2l2ZO6DTHzy+Txub28RhiHm8zl2ux0ajQYkSYJhGEilUnAcB81mE69evUKv1+NzXpfCfjSoqioymQy3KN3tdtjtdnz+Kp/Po16vo1QqIZlM8kFI1uPDGjw3mw2vagG4179zaYL9oyDhOSJMWFirPltVY1kWRFGEZVn8xRLBn4tG9vtRZFmGYRi4vr6GIAhot9totVpYLpdcxGRZ5hFXLpeDJElwXfeijgsf9jiJosjN1NjPwDAMvpomnU5D13VuYbrb7bBYLDCfzzEcDnF3d4c3b95gvV5ju93yaiTzrfm9LnPiY0h4jojneVitVuj3+7i7u8Nvv/2GRqOBfr8PRVH4FoliscinzffHIH4P9kWLRqNIpVKo1WrQNA2RSIR7EHmex0vBhmGgXC7jL3/5ywHf+WHYjyJd1+W+TMPhkEcs2WwWlUoFtVoN2Wz23vGKJaFfvXqF58+f482bN+j1emi323BdF+VymY+71Go15PN5fkQjPg8JzxEJggCWZXFDqU6nww2n2K8tl0ssFouPPJY/BTsaiKLIzcd1Xcd6vcbz58+59QMTJ5aIZrkPZp9xCdUt9j5834dlWeh0Ovjll1/4TjJN01AsFlGv11GpVGCaJu9xYliWhXa7jX/84x/49ddfMRqNMB6PEYlEeG8PKwiwQWTijyHhOQHY0YjZd7AO5EKhwPt6vjR3wI4VbDNFJpPhx4nVagXgfTVruVxy4alUKhd3TGDWtyxBLMsyYrEY4vE4TNNEqVRCpVJBPp/ny/j2j5rs6CpJEm8uZNXIbDZ7Lwql/M6fh4TniLDjEztKGYaBSqWC1WoFSZJQLBZxfX2NXC6HeDz+0ZfiS9A0DdVqFT///DMGgwFs20aj0cBsNkMkEuEreC/tmLBardBut9FsNtFut3m0wkZSisUi8vk878f58OebSCRwe3uLIAhQr9e51WwkEoFhGMjn88jn81y8ZVk+0js9L0h4jgizvpBlGaZpcmtJluCNxWL3SuzfYr4Uj8dRq9UgCAJisRhevHiBt2/f8h3tT58+heu63/kdHp/NZoN2u43nz5+j0+lguVzy/BfLyRQKBaRSKZ5sZ7DZrUePHqFQKHCzNdbrJEkSP84qisIjKuKPIeE5ImxWi81r/UhUVUU+n4coirBtG61WC47jYLVaYTgcot/vo9PpYLvdci/nc69ubbdbPjbCRkdYoyCLdrLZLFKp1CcjPfb5UO7m+0LC8wBgT+dEIgEA/ElfLpcxm83gOA7evXuH3W4HRVH4+MS5wnIttm1jMBjwVUAA+CjE1dUV706mpr/DQz/xBwJroBNFEYVCAdVqFaPRiC+pe/nyJV68eMEnrz/cx37KVS5W+maCw3qdmFvgYrGA53nI5/NQVRXlchm3t7colUrQdZ2SwkeAhOeBwMrwLJ9ULBZRq9UQBAE/ajGHws1mw4WHNSWeOh92fu/bVEQiESQSCb4poVAooFQqIZvN8p4d4rCQ8DwgWEt/PB7nyVK2qpcNSzJPGlZFYzmOUy+zsx1YbN/VfD7nHeCpVArlchk3NzeoVqvIZrPcJ/nSbUBOFRKeBwjznGEzRtvtFt1ul0/Jsy9nJpNBKpXiIwSn+iUNw5AvNFwul2g0Gnj9+jW63S4kSUK1WsXTp0/x+PFjPHnyBIZh3DP/Jw4PCc8DRJZlLiqSJGE4HHJx0TQNV1dXuL29xdXVFQqFAnK5HBKJxMkKz/622OFwyG0rXNeFoih49OgR/vrXv+LRo0eoVqv3tnIQx4GE5wHCOqVZvieXy6FQKGC5XPJOZ1ZSZ93U8Xj82Jf9Sdj0PduewXqTMpkMdF1HrVbD9fU1KpUKstnsR2MRxOEh4XngiKKIdDrN7TMWiwVWqxXevHkD13X5IOUpC89yuUS73cbr169xd3eHXq+HIAiQyWSQz+d5IpntAKdd8seHhOeBw0Y16vU6BEHAu3fv0Gq1uH8Ps0tlDnun0t/D8jqu62IymeDu7g7Pnz/ne8SY1QezMTVNkyeUL9Ho7Nwg4XngSJKEZDKJcrnMrT37/T622y2m0ykGgwE6nQ6CIIAsyx/tmz90zocJBrO68DwPo9EIr1+/xrt379Dr9bjpfblc5nkq1p18Dq0BDwESngcOswRl2xSm0ym63S5msxmCIMBgMMCvv/6KRqPBTc+ZleqxYSV0tjGi2+1it9shkUggm83i+voatVoNmUyG/JBPDBKeBw6bF2P9PGyUghnAj0YjzOdz+L6PzWbDvWyCIDjqcWXfkpT17wRBgEQiwRPi19fXqFar3Nzrz9jHEoeBhOeBw+w/WV8LS8Yul0u+laLX6/FtmbZtw3Vd3tF86OoQ60j2PA+O43CLClVVYZom4vE4stksn0czTfOLVgURh4GEh+BfSkVRkE6nUalU+Grf9XoNy7KwXq+5j42iKIjFYlyw9mejftT1fbh2eLlcYjwec6sKVVVRrVbx+PFj3N7eolAo0ADoCUOfCsFhM03lchmRSITnfPr9PjzP455B+XyeV4lUVeXl6R8pPEEQ8B3zlmWh1+vh9evXeP36NVzXRb1ex3/8x3/gp59+wu3tLXK5HInOCUOfDMERBOHexonVaoVGowFN0xCGITKZDK6urnjuJJvNwjCMH25+xdYOW5aF6XSK6XTKu5PZfNn19TWePXuGn376CaVSCYlEgoTnhKFPhuAw3x4WvWSzWeAGpzcAAA75SURBVG6YNZ/PEYvFuHl6NBpFOp3mHtGHYDweY7FYYLfbwXEcxGIxFItFRCIR1Ot17rFjmib3myZOExIegsOSr8w+g/X3zOdz7tM8Ho8RBAHvaC4UCgf5gnueh8Vigbu7O7x48QKj0QgAUCwWYRgGbm5u7pmvUzL5tCHhIX6XfSP67XYLURTRarV4eV2WZT6GkEqleB7me8OqWMw7+bfffsM///lPbLdblMtlVKtV/jIMg7cGACDhOWFIeIiPYKtxWGmaVZImkwl6vR7m8zlUVYVhGPB9H7qu8z6g75lgZrmdIAiw2+3QbDbRarUwHo+5oyKzMc3n80gkEjR1fiaQ8BC/C2ssTKfT3EK03W4DeD+U+fbtW9i2jbdv30JRFADvoxPg+4xRsKMScxH0PI+X0G3bRiKRuLcpgpX5Ka9zHpDwEJ9k3yB+uVzyEvpwOMRwOMRkMuEL7wB8NHz5oRfy5/hQrNi/s85ktvlUVVVeeWO7wAzDoDmsM4OEh/hd2HGLiUk6nebL66bTKVarFcbjMTabDd/Vpaoq36r5tZs1WVey7/twXRe73Y6vdE6n03zBYbVaRaFQgGEY/IhFIxHnAwkP8VlYiV3XdZTLZTx79oxPhm+3W6zXa8RiMWSzWRSLRaRSqXsC9KV/F/tzt9stF7d2u839kwuFAp4+fYqnT5+iUqnwtcPs9xPnAQkP8afQNA3lchlhGHJ7jM1mgyAIkEql8OTJEzx79gyFQgHpdPreyuU/k/NhorHb7TCbzTCbzTAcDtFsNhEEAcbjMXK5HG5vb/GXv/wFjx8/RjqdRiwW+9FvnfgBkPAQfwib48pkMnw8Yjqd8p4eNg1erVZRq9VQKpVgmia3GP0j4WFHpDAMucVFu92GIAjY7XZYLBZQFIV3TbNtEYqiUHfymUKfGvGnEEWRdy5ns1lUKhW+l4sldS3Lwna7hSAI0HUdqVTqi/4ONgTKpuInkwl830cul0Mmk+G+yZlMBvF4nCpYZwwJD/GHsNI2Ozbpuo5CoYB6vQ4AfAlgp9PhHs6lUumL/x7m+TMcDvHq1Su0Wi2oqsqrVyyaYsc44nwh4SG+CFEU+bjE1dUVwjBEq9VCv99Hv9+HIAjIZDLI5XIQRRHRaBRhGPLXPux45bour2Dd3d3hzZs3ePHiBQaDAWq1Gp4+fYonT56gWq0ik8n88KFU4sdDwkN8EayxMJVKoVQq8a5iFvXMZjN0Oh0kEglMp1MAgOM4H3k1A/9KKDPvZNu20e/38fLlSzSbTazXaz5pXiwWUSwWKdq5EEh4iC+Cldf38zfr9RrD4RCz2Qyr1QrNZhO73Q6SJGG73WKxWPBenP1eG5YbYiZfbBC00+mg0WhAFEVu8mWaJtLpNN8BT5w3JDzEF8OsRlnOZz6fI5vNYjKZ8DL4dDqF4zhYrVaYz+e89L4vPPvdyezF+nh2ux3S6TQ0TUMikYCu69wXiPp1zh8SHuKLYZEK27VumiYKhQJmsxnfc2VZFjabDa9SsQ2lLFphRyt2DGNezqx6VqlUUKlUcH19DdM0oWka/72nsOGC+DZIeIivhvX3GIaBarUK27bh+z7m8zlWqxUcx0E6nebmXKqqQlVVBEEAy7Iwn8/5azqdYrlcIhaL8X1YNzc3ePbsGUqlEh9EZX8vcd6Q8BDfRDQaRTKZRKVSQRiG2G63aDab8DwPAJDJZPDTTz/h0aNHME0TqVQKQRBgOp2i0+mg0+lgMBig1+thNBohkUjg559/xn/+53/iyZMn3N+ZKlmXBQkP8U1EIhFomgbg/fFpMpkgm80imUzC8zzoug7DMJDL5VAqlZDL5SAIAgaDARzHubeni3n8PHv2DP/+7/+O29tb3ihICeXLgoTnjNmfHmccet/V702wX19fY71eY71eQ5ZlLBYLdLtdnr+RZRmWZWE8HqPf78OyLG46VigUcHNzg1wuh2QySZHOhULCc8ZIksQTtuzLz5K4h5xh2p/lqlQqmM/nCIIAo9GIdyKzPh5VVaHrOiaTCVqtFhqNBqLRKB49eoTHjx+jXq+jUqkgn8+T6Fwwn707t9vtvVInVRNOg/1JblZBYts9LcvCZDLBcDjkCdkf/bmx67Ftm/szq6rK+3iWyyUmkwmCIIAkSUgmk2i1Wmg2m2i324jH46hWq5AkCYqiwPd9LBYLOI7zp6fbiR8Hi6Kj0SiPpr91O+tnhee3337jniubzYYnDKmqcHxEUcRut8ObN2/Qbre5IVer1cIvv/yC5XIJWZYP8qVl9wNrAByNRhgMBhiPxxiNRlgul4hEInBdl9uWDodDtFotTCYTbLdb3N3dQVVVrFYraJoGTdP4tggSnuPAeqai0Sji8TgMw0AymUQikYCmaYjFYl/dRS6En/lU/+d//gfj8RidTgej0Qjb7fb9byLhOSrsCeS6Lu/0HY1GEAQBuVwO5XIZqVTqYH0v7H7wfR+2bfNtn+x/HceBIAj85mU5ntFohNVqhWg0imw2y61V94+QJDzHgwmPqqoolUp4/PgxdwjI5XJ8V/3X8NmIp9FooNPp4PXr19wFDgB5254IzASdNd8BQK/Xw3Q65eHwoa+HjT+w7RDsBYBvAmUbKVzX5b/Oup2ZhzPtxTou7LNkD4zb21uey9M0DfF4HKlU6qs7yT8rPKlUCrvdDqvVivdohGFIwnMCsN3m2+2Wz0jt++Ac0/ycicaH4rE/of7hrzPB+r0pduLw7H8GmqZxZ8lEIoFYLMYN4b6WzwrPf/3Xf2G9XnNzb/ZUpSfRcWFHLdu20W638csvv+DVq1cQBAHPnj3D3/72N1xdXfHz9zG+yF97j5DonA7ss5BlmbdK5HI5GIYBXdd5Du5r+Kzw/P3vf+chMQudiePDIoXtdotff/0Vy+USvV4PgiDgyZMn+O///m/87W9/O1hV68Nr+x6QAB2X/dwaq2jJsgxZlhGNRr/ZJeCzwmOa5lf/wcRhWC6XSKfT/OljmiZqtRqePHly7EsjiE9CyZozZj+By/gwoUsQpwgJzxnDnPv2k7LMUIvl4wjiFKGRiSPyYfnZ8zy+RRMA9yxm5+lzKzMzEWTvab9Euz/aQVXShwcJzxEJgoAvxmP+NJPJBKvVCgCg6zqy2SxSqRQSicRXb+g8BmEYci/m+XwOy7J4v1E0GkUqlUIul0M6nb7ntUM8DEh4jkgQBNhut5hOpxgMBmg2m3j58iW63S4AoFKp4NmzZ7i+vkahUOAL9c5FeDabDfr9PhqNBgaDAVarFTabDWKxGK6urvDzzz9D0zQSngcICc8RYRsa5vM5ut0u3r17h+fPn+Pu7g6CIGC1WvESpqIoiMfj3Pvm1GFra5bLJQaDARqNBqbTKebzOVRVhe/7KJVKlIt6oJDwHBG2wG4ymWAwGGA2m3FDLEEQ+EbNfr8PXdeRTqe/eDvnMWEDhiyXw96v67pYr9dwHIeqbw8UEp4jEYYhfN/nNhbj8Ri+76NcLuP6+hoA+KK78XgM0zRRLpfP5ou678dcLpd56Z9ZrbCW+3NJlBPfFxKeI+L7Pp+1mk6nCIIAhUIBxWIRwPuBz8FggOl0itlsxr+05wDbv6XrOnK5HBzHwXK5xHA4xG63+2jFDfGwIOE5ImEYwnEc7HY7bLdbSJIETdOQyWQAvN9JzkZWdrsdXNc9qy8qszrVdR3JZBLxeByyLHObDOLhQsJzAnw4kf17E93nJDgMFvUoisJNo5jHDvGwIeE5Msx/hpXImZkW8N7Rb9+8/dwa7di173vsACArXYKE55iwDl5WMmfVnvF4DOD9TvIwDPmvn1u0wBokmX0uezF3QtZQ6Pv+R9syiMuGhOdIsGhAlmXenzOfz9Hv9zGZTACA50KY49u3+J8cA8dxsFgs0Ov1cHd3h1arhU6ng81mA8MwsFwuYVkWdrsdt1s4p/dHfD0kPEckEolAVVWkUikYhoHVaoV+v8/dBBOJBIrFItLpNJLJJGKx2Nl8MVnifD6fo9frodVqodvtYjQa8cZCFv3Yts2jv3N5f8S3cV5JgwuDCU86nUYul+MG7a7rwnEcSJLEt3AahoFYLHYW4xIA7k3K27YNx3EAvN8FxmbOBEHg/w3lfB4WFPEcEVEUEY/Hkcvl4LouIpEIJElCPp9HJBJBJpPB9fU1qtUqstksNE07G+FhFS22IZQJaTKZRBiGuLq6QqlUQiKRgCRJZ5c4J74NEp4jIooiNE1DLpdDLBZDJpNBrVbjO7I0TYNhGEilUtB1ne8RPwcEQUAsFkMul+Ni+ujRI744wDAMFItFmKbJIzk6Zj0cSHiOyP7GTV3Xkc/neZWHJZ/ZnBN7nUtkwEYm0uk0dF3n78vzPIRhyPt7WFKZ/R7iYUDCc0RYQlUUxYu0hrjk90Z8G+fx+CQI4qIg4SEI4uCQ8BAEcXBIeAiCODgkPARBHBwSHoIgDg4JD0EQB4eEhyCIg0PCQxDEwSHhIQji4JDwEARxcEh4CII4OCQ8BEEcHBIegiAODgkPQRAHh4SHIIiDQ8JDEMTBIeEhCOLgkPAQBHFwSHgIgjg4JDwEQRwcEh6CIA4OCQ9BEAeHhIcgiINDwkMQxMEh4SEI4uCQ8BAEcXBIeAiCODgkPARBHJzosS+A+D6EYXjsSyCIPw1FPBcAiQ5xblDEc+ZEIhHIsoxYLAZBECBJEiKRCARBOPalEcQnIeE5YwRBgCzLSKVSyOfzEAQByWQSsiyT8BAnDQnPGSMIAmKxGLLZLGq1GgRBQCaTQSwWO/alEcRnIeE5Y5jw5HI51Go1AEA2m+XHLoI4VUh4zphIJAJN01AqleB5HgCgWCxC0zQSHuKkIeE5YwRBgKZpKJfLUFUVAJBOp0l4iJNHCKkWe7aEYQjP8+A4DhzHAQBIkgRFURCNRkl8iJOFhIcgiINDDYQEQRwcEh6CIA4OCQ9BEAeHhIcgiINDwkMQxMEh4SEI4uCQ8BAEcXBIeAiCODgkPARBHBwSHoIgDg4JD0EQB4eEhyCIg0PCQxDEwSHhIQji4JDwEARxcEh4CII4OCQ8BEEcHBIegiAODgkPQRAHh4SHIIiDQ8JDEMTBIeEhCOLgkPAQBHFwSHgIgjg4JDwEQRwcEh6CIA4OCQ9BEAfn/wE1iaxKChz8SgAAAABJRU5ErkJggg==)
For such questions, we should know area of different shapes.
The area of the region bounded by y=|x-1| and y=1 in sq. units is
![](data:image/png;base64,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)
Maths-General
For such questions, we should know area of different shapes.