Physics-
General
Easy
Question
A (nonrotating) star collapses onto itself from an initial radius Ri with its mass remaining unchanged. Which curve in figure best gives the gravitational acceleration ag on the surface of the star as a function of the radius of the star during the collapse?
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKwAAACCCAYAAADblyOeAAAPRUlEQVR4nO3da1BU5R8H8O+yLLusyGVBXW6KmSBiyqig0UpJacqEGXgpDUvCSwTolIQ6QL6gkTIwmVp0KhUD1PCWGTRJYqCpyJBX8IIMIkjiguiictnl/F847j+M617YPYff51XrnvOcnzPfHp/znOc5y2MYhgEhLGFm7AII6QsKLGEVCixhFQosYRUKLGEVCixhFQosYRWdA1tdXa2POgjpFZ0Cm5eXB5lMBqVSqa96COmW1oF9+PAhli1bhps3b+LTTz/VZ02EdEnrwKampqKyshIikQjbtm3DlStX9FkXIZ0y//eHGzduYPv27XB1dUVpaSk2bdoEoVDY6Yn37t3D1KlT8fDhQ1RWVqKxsbFfCiYDW4ceNiUlBX5+fli5ciXq6uqQk5PT5Yn29vZITU2FpaUlvv32W4MXSgjwTA/75ZdfAgB2796Nuro61NfXd3niqlWrNN+HhoaiubnZgGUS8kSHHvbChQtITk7GG2+8AXd3925PFIlE3X4mxBA6BHbNmjWYMWMGxGIxWlpaAAAMw0ClUqGkpIR6UWJ0HQI7ZcoULF++HOHh4aipqUF2djauX7+OFStWQCwWY8GCBdiyZQva29uNVS8Z4DqMYZOTk1FdXQ2pVAqVSgWGYdDW1oYbN25gzJgxeP311yEUCmFmRk90iXF0SB6Px4OrqysEAgEsLS0hFothY2MDNzc3HD58GFVVVXjzzTeNVSshPT84aG1txYMHD8Dn8zFjxgw8fvy4P+oipFO9+rd94sSJqK2txd9//43169fTQwJiNOY9HbBnzx60tbVBJpOhra0NFhYWNIVFjKbHHvadd96Bl5cXsrOzceXKFURERFBgidH02MMKBAIsWLCgP2ohpEc0P6VH9GDF8CiwelJZWQkfHx/cv3/f2KVwGgVWT9zc3BAeHo5FixbRk0ADosDq0apVqzBs2DCsX7/e2KVwFgVWz9LS0lBQUIA9e/YYuxRO6nGWgPSNUCjE/v374e/vD3d3d0ycONHYJXEK9bAG4OjoiMzMTLz99tuoq6szdjmcQoE1EF9fX8TFxWHevHloa2szdjmcQYHtRltbG3R53/OSJUswadIkREVF6bGqgY0C243PPvsMhw4d0qmNr776Cjdu3MDWrVu1bkOhUGDp0qVIS0vTqRYuoMB2IzY2Fs7OzmhoaNC6DT6fj71792LLli0oLCzUqg0HBwfY2NjQ0AIU2G7Z2Njgr7/+QmxsrE7tSCQS7Nu3D++//z6qqqr6dK5KpUJ9fT14PJ5ONXAFBbYHkZGRmD9/PpqamnRqx8vLC8nJyQgODu71IvgjR44gJSUFOTk5+Pnnn3W6PlfQPGwPzM3N4eXlBV9fXxQVFcHKykrrtubOnYvz588jLCwMu3fv7vbYpqYmxMfHo7i4GHw+H3l5eVpfl0uoh+0FZ2dnrF69Gnfv3u3ymPr6eixdurTHt+AkJCSgtbUVSUlJ3R537NgxDB48GHw+H8CTYQWhwPba8uXLkZ6ejl9++aXT7+3t7WFnZ9fjjRGPx0N6ejr27NnT7augmpqaaOVXJyiwfRAaGopdu3Z1OTf79MZIpVJ1O061srLCwYMHERUVhatXr3Z6zNSpU3Hp0iXk5eWBYRgoFAqd5oS5ggLbB6NGjcLWrVvxySefdBmeS5cuYfr06XBwcOh23nTkyJH47rvvEBIS0mlP+txzz2Hnzp2IiYnBBx98AFtbWzAMQ7uWGR1UV1czvr6+ujTBSqGhoUxmZuZ//vzjjz9mIiIimNbWVub8+fOMlZUVc/fu3W7b+vrrr5nAwEBGrVYbqlxOoR5WC9u3b8eIESOwY8eO/3w3evRoCAQCjB8/Hj4+PigrK+u2LVpD2zcUWC08neqSy+UoLy/v8jiBQIAhQ4b02B6toe09CqyWbG1tcebMGVy9ehVHjx7V/PnT7TENDQ0wNzeHh4dHj209XUMbHx+PkpISg9XMBfTgQAdmZmbw8PDA4sWLIZPJEBQUhC1btsDa2hpKpRI7duzo9SPVf6+hPXHiBIYOHWrg6llKlwHwQL3pelZ7ezsTHx/P5OXl6dxWeno6M23aNKa1tVUPlXEPDQn0gMfj4d1338WmTZugUql0aovW0HaPAqsn7u7uyM3NRXR0NORyuU6T/PpYQ8tVFFg94vF4SExMxPXr11FZWan1+wn0sYaWqyiweiaRSLB582bs2LEDwcHBWodWlzW0XMZjdPi3q6amBsHBwThz5ow+a+KM48eP459//sHQoUMREBCgVRuHDh1CYmIiCgsLYWlpqecK2Yd6WAN65ZVXMGHCBKxfvx7V1dWaX+bpi7lz5yIoKAhhYWEGqJB9KLAG5unpidOnT6OyshJTpkzpcnVWd3q7hnYgoMD2E5lMhtTUVIjFYiQkJHT7K5PP6u0a2oGAAtuP/P394ezsDA8PD6SmpuLatWu9vinrzRragYAzj2YZhkFGRgZaWlpQVVWFyMhIk3y8aWZmhsWLFwN4Mt964MABHD9+HBYWFj2e++81tCdPnoSNjY2hyzU5nOlhT506hV9//RXh4eEYPXo0K5brrVmzBrm5ucjLy8Ps2bNx+fLlHs8JCAjAsmXLBux7aDkT2AkTJuDzzz9HRUUFysrKWDN3aWNjg8DAQGzcuBFisRgymQw//PBDt+cM5DW0nAmsUCjEvn37cO3aNbz66qvGLqfPvL29MXLkSMjlclhaWiIjIwMRERG4fft2p8c/XUPb03ZxruFMYHfu3Im6ujrMmjXL2KXoZPz48Vi0aBECAwMxfPhwPHr0CPPmzUNubm6H44RCIQ4cOICEhIQBtYaWMzddEokEP/30EywtLVFVVYXy8nL89ttvrA2wRCLB2rVroVarsWTJEly8eBE1NTU4e/Ys1q5dCzc3N0ilUmRlZQ2oNbScCexbb72FIUOGYPDgwRg7diyKiorw4osvGrssnfH5fMyZMwdz5sxBbW0tVCoVxGIxJk2ahGnTpmHDhg2IiYlBSEgIjh07BoFAYOySDcrk1hIolUpER0frrT2uUqlUaGxsxOPHj3Hq1CnY2dlBrVbjhRdewLhx45CSkmLsEg3C5AJbV1eHYcOG6a29gcjJyQk1NTXGLsMgTG5IYG9v36v5SDYrKyvDrVu3MHPmTADAhQsXsHXrVsyePRtBQUEAgLCwMDQ3NyMrKwsAcPnyZRw9ehQzZ87E2LFjATxZDSYWi+Hr69uhfU4PC3TZX0N7uv6rsrKSOX78uGZPVlFRESOTyZjU1FTNMWvXrmWio6M1nxUKBVNSUsI0Njb2e71sY3I9rKljGAbt7e3g8/mor6+HXC7HkCFDsHLlSgBAVlYWzp07Bw8PD0ilUnh6euL777+Hs7Ozpo2NGzd2aNPe3h729vb9+vdgK87MwxqCWq1GbW2t5vM333wDR0dHnDhxAgBgaWkJGxsb+Pj4aI5Zt24d9u7dC6lUCuDJohUPDw+d3itL/s/kbrqMRa1Wo6KiAiKRCK6urgCePH3y9PTUPE1qaGjAoEGDIBQKjVnqgDZge1iFQoGDBw9qfjK+sLAQ7733HkpLSzXHnDt3rsOjT4lEQmE1sgET2Fu3buH06dOaz1988QUOHz6MR48eAXiyCCUmJgYHDx5EQUGBscokPdHljs2UZwnKy8uZO3fuMAzDMPfv32fGjx/PJCUldXpsWVkZExUVxTAMwxw5coRxdXXttzpJ33Cmh1UqlZr/3r9/PxYuXKhZmW9tbY3z5893+fNFGRkZmhunwMBAXLp0yfAFE61wIrAxMTEYN24cHjx4AAAICQlBcXExpk2b1qvz7927p9ljxePxIBKJdH7lEDEMVgZ26dKlCAkJ0XyOi4vDzZs3YW1trVV7EydOxLZt29DU1KTZakM/5GaaTD6wCoUCaWlp+P333zV/tnjxYuzatUvzWde9TaGhobCzs4Obmxt8fX3h6Oio+bkhYlpM8kmXWq3G48ePYWVlBYVCgYsXL+Kll17SfP/aa6/p9XoWFhYoKCjAtWvX4OLionVPTQzPJAPL5/Nx9+5dWFlZYcyYMZDL5Qa/prm5uWZRCTFdJjskGDlypLFLICbIZANLtFdbW8vZLeAmOSQgupk5cyby8/Ph4OBg1DqUSiUyMjKQn58Pb29vODg4oLa2FpGRkVqvTqMelhjM4MGDMWPGDGRnZyM6OhrLly+HSqWCt7e3Zs68ryiwxKCeXSwUFBSE6upqrbem05CA6KSxsRFJSUloamqCi4sLVq9eDZFI1OXx+fn5cHR0hLe3t1bX0zmwarWaNa8FGihaW1tRXV2tWYlmaLNmzcJHH32E0tJS/Pjjj0hPT8fkyZM7HLN//37k5ORAKpXi5MmTsLW11epaOgW2ra0NUqkUCxcu1KUZomdisRgrV67s98fLZmZmKC0txYoVK/Dnn3922GUREhKCc+fO4ezZs3BxcdH+IsZeLkbYrb29nUlJSWEEAgHD5/OZuLg4pqWlRfN9VVUVA4BRKpVMc3MzM2HCBGb16tVaX4/GsBzQ0NCg+V0wHo8HOzu7futd79+/Dx8fHxw7dgxSqRTPP/98h++f7uhobm6GlZUVdu/ejcmTJ8PPzw/z58/v8/X4GzZs2KCXyonRlJeXw8fHB5cvX4ZEIsG6detw9OhRBAQE9OpFyboQiUQYPnw4hg8fDolE0uE7pVKJP/74A2KxGIMGDcKIESPg5OSE0aNHIzc3FyKRCKNGjerT/1w6bUIkpsPPzw9hYWEIDw9HS0sLXFxcEBUVhYSEBGOXplc0D8tBT3tVbSfnTRmNYTmmubkZcrkcrq6u+PDDD41djt7RkIAj/Pz8MGbMGM0cbH5+foex4ZUrV+Dh4cH6nRQ0JOAQPz8/yOVyVFVVYfPmzR2+S0xMhEKhMFJl+kNDAo6xtrZGVlYWpk+fDl9fX8hkMgBPdgZzAfWwHNDa2orbt29rHpFPnToV8fHxWLBgAYqLi3Hnzh34+/tTD0tMQ2lpKTIzMwEAt2/fhpOTE2JjY/Hyyy+jpaUFQqEQAoEAXLhdocByQGcrn/h8foeNm4Z+gNBfaEhAWIUCOwA0NjbCy8sLFRUVxi5FZzQPS1iFeljCKhRYwioUWMIqFFjCKhRYwioUWMIqFFjCKhRYwioUWMIqFFjCKhRYwioUWMIqFFjCKhRYwioUWMIqFFjCKhRYwioUWMIqFFjCKhRYwioUWMIqFFjCKhRYwioUWMIqFFjCKhRYwir/A10CDm0CEaJCAAAAAElFTkSuQmCC)
- a
- b
- c
- d
The correct answer is: b
Related Questions to study
physics-
Inside a charged thin conducting spherical shell of radius R, a point charge +Q is placed as shown in figure. The potential of the shell would be
![](data:image/png;base64,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)
Inside a charged thin conducting spherical shell of radius R, a point charge +Q is placed as shown in figure. The potential of the shell would be
![](data:image/png;base64,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)
physics-General
physics-
A spherical hole of radius R2 is excavated from the asteroid of mass M as shown in the figure. The gravitational acceleration at a point on the surface of the asteroid just above the excavation is
![](data:image/png;base64,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)
A spherical hole of radius R2 is excavated from the asteroid of mass M as shown in the figure. The gravitational acceleration at a point on the surface of the asteroid just above the excavation is
![](data:image/png;base64,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)
physics-General
physics-
Net charge on the outer surface of conducting sphere is
Net charge on the outer surface of conducting sphere is
physics-General
maths-
where
are the co-factors of the elements
for
are the direction cosines of of three mutually perpendicular lines then
and
are
where
are the co-factors of the elements
for
are the direction cosines of of three mutually perpendicular lines then
and
are
maths-General
maths-
The point collinear with A(0,1,-2),B(3,l,-1) and C(m-3,-4) is
The point collinear with A(0,1,-2),B(3,l,-1) and C(m-3,-4) is
maths-General
maths-
The shortest distance between any two opposite edges of the tetrahedron formed by planes x+y=0,y+z=0,z+x=0,x+y+z=a is constant, equal to ___
The shortest distance between any two opposite edges of the tetrahedron formed by planes x+y=0,y+z=0,z+x=0,x+y+z=a is constant, equal to ___
maths-General
maths-
In a three dimensional coordinate system P,Q and R are images of a point
in the x-y the y-z and z-x planes, respectly. If G is the centroid of triangle P Q R then area of triangle AOG is (O is origin)
In a three dimensional coordinate system P,Q and R are images of a point
in the x-y the y-z and z-x planes, respectly. If G is the centroid of triangle P Q R then area of triangle AOG is (O is origin)
maths-General
maths-
The angle between the planes 2x-y+z=6,x+y+2z=7 is
The angle between the planes 2x-y+z=6,x+y+2z=7 is
maths-General
maths-
‘L’ is a line in the space given by the Equation
and
is a plane in the space given by the Equation x + y + z=1 then
‘L’ is a line in the space given by the Equation
and
is a plane in the space given by the Equation x + y + z=1 then
maths-General
maths-
The intercepts made by a plane, P , on the co-ordinate axes are a, b, c. The co-ordinate axes are rotated about the origin by an angle q. The plane P now makes the intercepts a¢ , b¢ , c¢ on the (new) co-ordinate axes. Which of the following statements is true?
The intercepts made by a plane, P , on the co-ordinate axes are a, b, c. The co-ordinate axes are rotated about the origin by an angle q. The plane P now makes the intercepts a¢ , b¢ , c¢ on the (new) co-ordinate axes. Which of the following statements is true?
maths-General
maths-
A ray of light is sent through the point P (1, 2, 3) and is reflected on the XY plane. If the reflected ray passes through the point Q (3, 2, 5) then the equation of the reflected ray is
A ray of light is sent through the point P (1, 2, 3) and is reflected on the XY plane. If the reflected ray passes through the point Q (3, 2, 5) then the equation of the reflected ray is
maths-General
maths-
The length of the rectangular field in 100m If its perimeter is 300m then what is its breadth?
The length of the rectangular field in 100m If its perimeter is 300m then what is its breadth?
maths-General
maths-
The side of a square field is 65m What is the length of the fence required all around it ?
The side of a square field is 65m What is the length of the fence required all around it ?
maths-General
maths-
The dimensions of a cuboid are in the ratio 6 : 4 : 3 If the length is 42 cm, then its volume in litres
The dimensions of a cuboid are in the ratio 6 : 4 : 3 If the length is 42 cm, then its volume in litres
maths-General
maths-
If AC = 28 cm, BC = 7 cm,
BAX = x0, then area of the shaded portion is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHoAAACdCAYAAAB7GGzeAAAaxklEQVR4nO2dZ0BUxxqGn4VVwBaNKLKAq4INu0hRih1bbInRRE001mjEnmJsMeXGxGuLvWtujL3EJBp7QZBi7AIKRkCNYqHD7rLszv2BoIkNZXfPUp5fumc4857znu+UmflmZEIIQQlFHgupBZRgGkqMLiaUGF1MKDG6mFBidDGhxOhiQonRxYQSo4sJJUYXE0qMLiaUGF1MKDG6mFBidDGhxOhiQonRxYQSo4sJJUYXE4q80dmaTFTqbPRSC5GYom100i7Gujnj6jaSPYlSi5GWImy0nrv7dnAiSSCSj7F7751iHdVF12jdDX7bdYrXO3encekMTu3ew02d1KKko8garbu2i1/O2OLp34MWteVoTu/il5ji63QRNTqbyzt3c1l/n/2zJrM9zhIL7UV+3XWRbKmlSUTRNDojmG17rtNo4n7ORlzh3JHpeFplc23PZkIzpBYnDbKiN4A/k19HNibgt3RkNp2Y8+cyyn7ejNG7UxBA+e4ruLi8p9QiTU4RNLqEp1E0b90lPEGJ0cWEIm/0ubNnpJZgFhRpoyMuX2bQwP6kpaVJLUVyirTRkyeMJSU5ma9nzZRaiuQUWaMjIyKIuHwZgP1/7CM9PV1iRdJSZI1esmghAI6OTiQnJbF+7RqJFUlLkfyOvhYTQ/vWPjg7u7Bl5y78WnoiL1WKkyHhVKhQQWp5klAkI3rp4h8AGDNuPLa2Vfhg6DBSU1JYu2qlxMqko8hF9I34OFp7t8TB0ZGjgcHI5XKSk5Lw8XIH4GRIOBUrVZJYpekpchG9bMli9Ho9HwWMQy6XA1CxUiWGjhhJeno6q1cul1ihNBSpiL7999/4tfKksq0tJ4JDKV26dN621NRUfDxbkJ2dzcnQcF5/vbKESk1PkYrolcuXotVqGfXRmH+YDFChQgWGfziazMxMVixdKpFC6SgyEX3v3j18vNwpX64cJ0PCsbaxeaJMeno6Pl7uqFVqAkPCqFKligRKpaHIRPSalSvQqNWM+HD0U00GKFeuHKNGj0GtVrHs4Zt5caFIRHRyUhKtPNwobWVFUOhpypYt+8yymZkZ+Hp5kpaWSuCpMOyqVTOhUukoEhG9fu0aMjMzGTp85HNNBihTpiyjA8aSlZXF4oetZ8WBQh/RaWlpeHu2QOj1BIX9+ZyWLzUxvy9jY4iORn2HMHtQW5ISEzkWdAoHB0eTapaCQh/RP/24ntSUFAYNGfrc5k39rU18vUxFt146fvpmB2MCxqHValm8cIEJ1UpHoTZapcpk1fLl2NiUYciw4c8tq0+6S2J5OxyVCiom36Nf/wHYKxRs3byJ+Lg4EymWjkJt9KaNG0lMfMDAQYNe2AAir92RjrK9zPp8N5qOHbGysiJg3AR0Oh2LFs43kWIJEYUUtVot3Js1FrVrOImEhISHv2aL2OVvika1aoi6tWoJv2EjRN96NUTd2q3ErCC1EDq1SEtTC93D0hqNRnh7tBA1He3FX9euSXUoJqHQRvT2rVu4m5DAO/0HUrVq1Ye/WqIc/APzB9bGUiOoUrclNavY0nrGaiZ5WYGFFeXKWeXdxkqXLs3YCRPR6/UsnD9XqkMxDVJfaa9CVlaW8PZoIZyrO4hbN28+sV13b5cY01wpajvZifp9Voq47GfvS6vVCr9WnkKpsBNXr14xomppKZQRvWf3Lm7evEGfvv1QODj8c2PmJdYGfEVsv41sCGiCPmQO4+cGk/SMnFm5XM74iZMBWDivCEe11Ffay5KdnS3a+rYSNR3tRVxs7L+2JorN7yuFUmEn6rz1nZj3bg2hVNgJpcJR9FgQ9dx9tvP1FkqFnYiMiDDuAUhEoTP61192C6XCTowP+Mig+92ze5dQKuzEiCGDDbpfc6FQGa3T6YR/u9ZGeZ7qdDrRsW3Ovi9eOG/QfZsDheoZffjgQa5ERdH1je7Url3HoPu2sLBgwuSPAZj33zkG3bdZIPWVll/0er3o3qWTUCrsxOVLl4xWR1f/9kKpsBNnz/xplDqkotBEdOCJ41w4f472Hf1xbdDAKHXIZDImTHoY1XO+N0odUlFojF60IKeZcszYcUatp31Hf5o0bcaJ48c4HR5m1LpMSaEwOiw0hPCwUHx8/WjW3M2odclkssee1UUnqguF0bldiWMnTDRJfa3btKW5mxvBJ08ScirYJHUaG7M3+vy5s5w4fgwPTy88PL1MUqdMJmPSx58BOc9qUbjHZgCFwOjcaA4YP8Gk9bby8cHD04uw0BCCAgNNWrcxMGujIyMiOHhgP02aNsPH18+kdctkMiZ+/AkAc+fMLvRRbdZG56a+Bowbj0wmM3n9Xi1b0crHh7NnznDs6BGT129QpP6QfxYx0dFCqbATnTu0FXq9XjIdp8PDhVJhJ97o7C+pjoJithGdl/o6VppozsWtRQvatG3HxQvnOXTggGQ6CozUV9rTiI+LFTUd7UU7X2+Rnf2cUQMm4tzZM3l3F51O9+I/MEPMMqKXL12Sk/o6dhyWlpZSy6FJ02Z08PcnMiKCP/b+LrWcV8LsBvDfuX0b35YeVLO3z0tkNwcuX7pEt04dcKldh/2Hj5rFBfgymF1E56a+Pp7Ibg40aNiQzl27ERN9ld9+3SO1nJfGrCL6/v17eHu6U6lSpScS2c2BK1GRdGrflpq1anHw6AmzuhBfhFlF9JqVK9Go1U9NZDcH6tarT/eevbj+11/8smun1HJeCrOJ6NzU1zJlyjwzkd0ciImJpmMbPxydnDhyIohSpUpJLSlfmE1E56a+Pi+R3RxwcalNrzff4kZ8PDu3b5VaTr4xi4jOTX2VyWQEh/35whxnqYm9fp12ft7Y2ys4ejLYLB8z/8YsIjo39XVYPhLZzYEaNWvSp28/bt26ydbNm6SWky8kj2iVKhMfTw80GjVBYX/y2muvSSkn39y4EU8b75bYVqnC8aAQrK2tpZb0XCSP6M0/b+TBg/sMHjqs0JgM4ORUnX7v9ifhzh02bfyf1HJeiKQRrdFo8GvlSWpKKkFhhW+St79v3aK1txcVK1bkxKlQbGzKSC3pmUga0Tu2bSXhzp18JbKbIwoHB/oPfJ979+7xvw0bpJbzXCSLaK1WS1ufVty9m8DJ0NOP5TgXLu4mJODb0oOyZcsRGBJmti+TkkV0burrPxPZCx9V7ex4b9BgEhMfsGGd+U7+LklE63Q6Orb1Iz4ujuPBIYV++qf79+/h4+mBlbUVJ0PCKV++vNSSnkCSiN73+2/8de0ab73dt9CbDGBrW4XBQ4aSkpzMutWrpJbzVEwe0UIIunRsx5WoKI6dPIWyRg1TVm80khIT8fZsgaWlJSdDwnmtYkWpJf0Dk0f04YMHiIqMpGfvN4uMyQCVXn+dIcNHkJaWxupVK6SW8wQmjWghBL3e6Mr5c2c5eOyEwXOcpSYlORkfL3f0ej0nQ8Kp9PrrUkvKw6QRfTLwBOfPnTVKIrs58FrFigwb8SEZGRmsWGZek7+bNKL7vtmLsNAQ9h44bLQcZ6nJ7YnL0mRxMjQMW1vzmPzdZBEdGnKKsNAQoyaymwPly5dn5KjRqNUqli9ZLLWcR5hqXPHAd/oKpcJOnPnztKmqlIz09HTRrKGrqFOzuki4c0dqOUIIE43rPnf2DIEnjpskkd0cKFu2LB9+NAaNRsOSRWaypIMprqahg98TSoWdCDkVbIrqzILMzAzRoklD4aJ0fOo0lqbG6BEdGRHBoQMHcPfwxNOrpbGrMxtsbMowOmAsWq02LytUSoxudF7qq4kT2c2Bdwe8h121amzZ9DM3bsRLqsWoRl+LieG3Pb/QpGkzfP1aG7Mqs8Ta2poxY8eTnZ3NogXSLulgVKNzU1+lSmQ3B/q+8y4KhQPbt24m9vp1yXQYzegb8XHs2rGd+q6utO/ob6xqzB4rKyuzmPzdaEbnrvoqdSK7OfDW231xql6d3Tt3EBMTLYmGfBmty8pElZlBZmYGmapM1Fm655a//fffbNuyGWdnFzp37WYQoYWZUqVKMW7CJIQQz5/8Xaf5x3nW6LLRqHL/r+H5Z/0FvPgLTCUOTWoinBV2Dyc5txNKhULUd39TfHvwjnha/v8X06cKpcJO7Ni21dCfg4UWrVYr2vi0FEqFnYiKfNrk7zpxe10fUSf3HDvVFQHrV4lBLtWEUmEnajgPFJsfvHr9+Wsw0V4Qczo4iBqNRood1+NEzKkF4t161YRzj0Xi+r9mnrh7966oU0spvD3dhVarfXVlRZBdO3cIpcJOjBw25Bkl1OLapqHCy8lO1PQIEHvjI8Tad1xFw07TxKG/C3Yu8/mMliO3BPRZZCSnkPwgGZWuNE6Nm1DlX4n/uau+fhQwtlDlD5uC7j164lK7Dn/s/Z3Lly49pYQVtd6Zx8JRjbG+uY3J/j2Zd68H8zfMor19Ac9lvi4HbYSY38lBKBX2wlnpIGoq7EStRj3Ft4duiscDOikxUdR3qSk83ZoKtVpdoCuwqPL7r3uEUmEnhg5+79mFVEFiprdCKBUOot3nx0SSAebHeam3blmVfqyMusnV8z/Tv2I4K8Z9yb7UR9tzU19HfTQGKyurgl2BRZTOXbtRr359Dh04wPlzZ58soL/DgZlT2KnzopWznGs/juWTLdfJLmC9+TQ6i+xsQJvM7evRREdd5Xa6ACHQPxy2kJaWxto1q7C1taXfO/0LKKvoYmFhwcSPPwVg/r+XdMi+xaGZ7zHxdzsm/Pgz61Z+RstydzkwYySzjyYUzOwXB71KHJzY6B9v3TWq1xRufv3EN3tjRe4rwtLFPwilwk6sWLqk4PeZIo5erxfdOnUUSoWdOB0e/vDXNLH9g5oPz3F10X3+BRH6tZ+o7fDwvDs2EJP3q165ToN0UyYkJIimDeuLxq51RXp6uiF2WeQ5fOigUCrsRP9+fUxSn0FaxqZ99glJiYkMGPie2eYemRtt27WnabPmBAUGsnql8YcHF9jojIwMDh3MmSNzzaqVnDh+rMCiigNCCJo1bw7kLOmg1z9jTUUDUWCjZ82YnidSq9UyaMC7LFuyqNDPb21MYq9f5+3ePVm3ZjUAmRkZLFuyyKh1Fmi4b1ZWFg3qOKPVagH4YOgwDh44wM0b8fj4+jH5089o2qy5wcQWdrRaLdu3buGbL2eRnp5GjZq1sLKy4kpUJGXKlOHSlRgsLIzTz1SgvX7/7X/QarV538z29gr2Hz6KTCbjZOAJer3RlUULF+RdCMWZazExdOnYnimfTCY9PQ2Azdt34O7hAUBmZqZRB/2/stE6nY6fflwPQEf/Tnm/ly1bFgsLCxwcHChXrhxzv59NW99W7N65o1jezjMzM1i0cAFd/dsTE30VT6+WlC1XDuCJyeiWLlpotHP0ykYvXfwDarWaUqVK0b5jxye2V6xUiYNHT6BQOHDzxg3GB3xEv7d6E3H5coEEFxZ0Oh0/rl+Hj6cHc7+fjUajoZaLC5u27XjqzMDlK1QgLS2NVcuXGUXPKxkthGDF0pzbjF/rNpQu/fTmTnuFAg+vnCWMGjRsRFhoCF392zNqxDDi4+JeUbJ5o9VqOXL4EG909mfG1CmkpqYw6IMhANjb2z/zGfzBkGEAzJ87B52uQD3PT+WVjP7pxw15z5ku+RxYsOCHxbi5uwM5ifAd2vjyxfRp3Lt371UkmB1qtZotmzbi1aIZQ94fSGREzp1r8iefMvnTKS/8+46dOlGhQgVUKhVzZn9rcH0vbbQQgvmPLeVXJp8NJJZyOS1beQPg2qAh2dnZrF+7mjY+LVk4by53bt9+WSlmQWpqKt9+/RXNG7ny6eRJPLh/n4YNGzF2wiSAl0qdfX9wTuSvW7PK4FH90kbv2b2LxMTEAlXaqXMXNm/PmQZZrVIxf+4cvFo0o99bvQvFwp86nY4jhw4yYshg3Bo3ZMWyJahUKuzs7ACYMm0G1apVe+n9tm7bFsiZf+3bb74yqOaXNjpXgN0rHMjjVHw49UPXN7ozctRHyOVyQkNO0adXD97o7M/qlSu4m5BgVm/qly9d4psvv8DbswVDBr3Hgf1/oNNlY2NjQ8jps9SoWctgdf24bq1BP0tfyuijhw/n3WLr1K1nEAHW1tZMmTYdZxcX5HI5PXr2Iioygq9nzcSjeRNaNGnEF9OncfVKlEHqexmysrIICgxk4by5dOnYjm6dOrBqxXLu3L6NwsGB7/47D3uFAmtrmwJf+I9TqlQpsrKy+M9XXxpsny81PmXWzGkA+LZuY/DOC5lMhoWFBT8sXU7KwP4cP3qEWs7OxF6/zvq1q1m/djWVK9tSz7U+rg0aUrduPRo0bISzi4tBplHW6/XEx8Vx6eIFrlyJIjLiMqEhIaSlPhpZYW+voFOXLqxfu4aO/p3p925/Fv9g+AyMBo0ace7MGX76cT1Tpk03yPHl2+jw0JC8TINPp0w1ygHmkvudOX7Sx6SlpTH104+pXl3Jgwf3CQoM/MeioJaWlji71Ka+qysuLrWxsrbGycmJyra2zxxPnpaaSmxsLGq1irjYWKIiI4mKikSjVj9RtlOXrqQkJxNyKpgPhg7D3dOT9WuNO3Fc06bNiIqIQK1W89WsmXz1zeNv4To0KjU6ASDDsrQ1cp2aLJ1AyOSUtrF6qqn5Nnr61M/z/t2wUaNXPoiXwdraOq/DZPDQYQz6YAjO1R2orlTiUrsOx48eQafTcfVKVIFv7dXs7blz+zb2CgWfTZ3OjM+nkJKSzJdf/4cVy5aYdB1puVzOyA9Hs3DBPDZt/Imp02c+miZatYfxTUazL0OArAxe03+n//leTPwlhWwrd6Yc3M1I5ycbZPL1jL586SJRkREGPZhXITdCK1euzNoN/6Pqw7fcXb/+zlt9+wLg6dWSN/u8DUC9+vUZ8N772NjYIJfLGf7hKBwdnQAYOnwE7w0aDMC0mbM4HhQCgKOjEz179ZZ8BOvoseMAyNZqmTVj2qMNNr2Zt/Mz3MvLsKjaiff71KXD4HeoYVOXwet/ZPhTTIaHRmen3CI68gq3UrLQZWmeGJs0/fOcD/7SZjrgz9bWlsqVbQHwa9OGocNHAtCsuRvfzP4ee4UCGxsbpk6fSS1nZwC8ff1o1LgJgFlOqm5lZZXXRrFtyxbUKlXeNpuGo/jyIzds7v7KnG+X8N3UTVgOms3HfpWeGbkWe2f2xqe5G/6d2+PXvDmeTb2ZcUKTVyAmJpozf54GoFo1+2KfR2VKcl94s7O1fPvN149tKU39Ed8yoklprm/6hk36AXw1sSXPez22mLQ6HJteyzkWFUvY1gAa2yQQFniZrIcFUpKS8wqrVJlm9V1b1JHJZHk9XDu2bSErK+vRRqtGDB3WhrKUomnfD2jxgo8gC1UpT96f2AOljZzKbsP57usRuJZT5Rnt5u7O3gOHUSgcuHf3LpDTrluC8cnMzMxrNHl3wMAnPrP02Xr0CLJ1Ol4UfhZYV6bK6xZ5/63SZTo/jPOm3GOFXBs0YOee31Aqc+bufLt3T1SPPTNKMCxZWRo+njie9LQ05HI502bOYuqML/5RJjtyPgM//QMV2Zz5rh+zAjXP2FsOclTRREVn80bjh2+ZWbGEn5HRyEvJ468o1ezt2bZ7DyOGDObc2TOFYq2nwsrunTtJTU1FWaMGK9eso269+k+UkdefwJ6/8j8vjMVruig2fr2Y0/ezyUoIY/24AYxfdoK/n9J5UrVqVTZv38nwkR/mPS927dheMlTIAOh0OnZu3w7k9Ih5+/ryy2/7nmryqyBfMqEdU1d8T59mc5CXrkLj3pNZMWcgtZ6xPLK1tTVTZ3xBm7btGTVyGAcP7OfC+fMGEVOcmTxhHDHR0VhaWjJm3HgCxk0w6Le83GfSRo6OvsetvzOxsXfEtkz+FsD29vXl1737mTR+bF7X4oH9f9D7YWNFCS8mLTWVc2dzEu1ioqNp2cqbGbO+or6rq8HrsgCwsKmCk7My3ybnoqxRg607dzNj1ldYWVlxOjwMXy8P9Hp9yWfYc8g9N927dubSxQtUrFiJhUuW8fPW7UYxGQwwgN/CwoIhw4ZzJDCIHj17oVarEEJwLSaGfb//VmL4Y+j1erZs2khGejqQ07w5dsJEjgedomev3kZtjDLYaHEHB0d+WLqcfQeP4Ne6DRqNhlEjhhF4/Lihqii0pD7s6vzz9Gk+nTwJmUzGO/0HcDwohImTPzHJ+hsGTwuo7+rKho2bWLBoCXXq1iMx8QEAE8aO4VpMjKGrM3v+2LuXDm18AcjSaOjWvQdHA4OZPWduXqeMKTBKF41MJqPXm2/Rs/ebnAoOYsO6tRz4Y19ehv/hQwdp0LChMao2C44fO0pwUE6f+dEjh4Gc7MmxEyZKNo21UfviZDIZrbx9aOXtw82bN1i/ZjX/27CeC+fPMeyDQQBcvHCBW7duGlOG0RFCcDo8jBvxORO7rlyeM+a9br16tO/gz1tv98XZxUVKicY1+nEcHZ2YNnMWo8YE8PNPP7F188/ciI8nKjICH093rK2t0el0XL50qVC8wKkyM9m2ZTP3799HrVLRp1cPIGe8V/eevRg8ZCiNmzSVWOUjTN67XrmyLQHjxhMwbjx/XbvGlk0/s3XzJpKScoYQd+vUIa95df8f+/KG0EpJ7oUXHX2VK1GRAGzdsomtW3JWgy9Tpgy+fq1p274DHfz9zWbBlMeRdBhFLWdnpkybzidTPuf8uXMEB53kVPBJwkJyRnvs2Lolr+zK5Uu5eCGnBU6lUpGZmWEUTRqNhuCgk3k9dJMnjCM8LBSAbVs255Wr7+pK6zbtaNOuHW4t3J9ImDM3JF0o/FmoVJmcCg7m+NGjRFy+RPTVKyQnJz9RztLSEp1OR9dubxAXF8flSxdp174Dzd1a8N/vZ9OylTf9+g/gP19+QWpqKrP/O4/lixcRFRVJt+49SEpKIvhkILXr1CErK4u42NhnanJ0dKKFhwctW3nTpm07gw7vNQVmafS/0ev1xERf5cL588Re/4vY2Fhir1/n1s2bebf8gpI73Lh8hQrUrFmTFu4euLl74OzigpNTdbMcbvQyFAqjn0daWho34uPRarPQaDTciI8nLe3RWGy1Ws2tmzcRQlC9upLSVo+6V197rSIOjo7UqFGTKlWrFulhUoXe6BLyh2QrwpdgWkqMLiaUGF1MKDG6mFBidDGhxOhiQonRxYQSo4sJJUYXE/4PAbJECy5V3RsAAAAASUVORK5CYII=)
If AC = 28 cm, BC = 7 cm,
BAX = x0, then area of the shaded portion is
![](data:image/png;base64,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)
maths-General