Maths-
General
Easy
Question
Assertion If
then
Reason If
is a homogeneous function in
of degree '
' then
- Both A and R true, but
is the correct explanation of A - Both A and
are true, but
is not the correct explanation of ![A](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAANCAYAAACdKY9CAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAIdJREFUeNpjYMAPChhIAOFA/AuIWYhRLAjEl4B4NxAHEKNhJhBHAnE8EE8hpNgSiLdA2eJAfBefYpB7zwCxLJLYOSDWwKWhHohL0MRagTgLm2INqGnowB6IN2HTcBiI/+PAGMGbBsQT8PhtORB7wTiS0DDnwaMhGdnAVUDsQyCopYH4FgM5AACEKxqdNkqvogAAAEl0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+QTwvbWk+PC9tYXRoPkHiA+IAAAAASUVORK5CYII=)
- A is true, but
is false - A is false, but
is true
Hint:
We are given two statements. First is an assertion and second is the reason. We have to find which of the state is true. And if both are true, we have to find if second statement is correct explanation of first.
The correct answer is: Both A and
are true, but
is not the correct explanation of ![A](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAANCAYAAACdKY9CAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAIdJREFUeNpjYMAPChhIAOFA/AuIWYhRLAjEl4B4NxAHEKNhJhBHAnE8EE8hpNgSiLdA2eJAfBefYpB7zwCxLJLYOSDWwKWhHohL0MRagTgLm2INqGnowB6IN2HTcBiI/+PAGMGbBsQT8PhtORB7wTiS0DDnwaMhGdnAVUDsQyCopYH4FgM5AACEKxqdNkqvogAAAEl0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+QTwvbWk+PC9tYXRoPkHiA+IAAAAASUVORK5CYII=)
We will check both the statements one by one.
A: The given function is ![u equals log open parentheses fraction numerator x squared plus y squared over denominator x minus y end fraction close parentheses](data:image/png;base64,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)
We have to find the value of ![x squared u subscript x x end subscript plus 2 x y u subscript x y end subscript plus y squared u subscript y y end subscript](data:image/png;base64,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)
We will first simplify the given function and find it's degree. The function should be homogeneous for further operations. Hence, we need to simplify it.
![L e t space z space equals e to the power of u
s o comma space z space equals space fraction numerator x squared plus y squared over denominator x minus y end fraction
space space space space space space z space equals space fraction numerator x squared open parentheses 1 space plus space begin display style y squared over x squared end style close parentheses over denominator x open parentheses 1 space minus begin display style y over x end style close parentheses end fraction
space space space space space space space space space equals x f open parentheses y over x close parentheses
S o comma space t h e space d e g r e e space o f space t h e space f u n c t i o n space i s space 1.
n space equals space 1](data:image/png;base64,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)
z= f(u)
So, xuxx + 2xyuxy + yuyy = g(u)[g'(u) - 1] ...(1)
![g left parenthesis u right parenthesis space equals space n fraction numerator f left parenthesis u right parenthesis over denominator f apostrophe left parenthesis u right parenthesis end fraction](data:image/png;base64,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)
We will find all the values.
![z space equals space f left parenthesis u right parenthesis
f left parenthesis u right parenthesis space equals space e to the power of u
f apostrophe left parenthesis u right parenthesis space equals space e to the power of u
n space equals space 1
g left parenthesis u right parenthesis space equals left parenthesis 1 right parenthesis space e to the power of u over e to the power of u
g left parenthesis u right parenthesis equals 1
S o comma space t h e space d e r i v a t i v e space o f space t h e space a b o v e space f u n c t i o n space w i l l space b e space
g apostrophe left parenthesis u right parenthesis space equals space 0](data:image/png;base64,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Substituting the values in equation (1) we get,
x2uxx + 2xyuxy + y2uyy = 1(0 - 1)
= -1
So, the first statement is true.
R: The second statement is directly the property of homogeneous equation of degree n and function of x and y. So, the second statement is true.
Now, if we see the first statement has z as function of f(u). It cannot be directly found from the second statement. We have to make the changes to find the value for the first statement.
Both the statements are true but, R is not correct explanation of A.
For such questions, we should know the formulas related to homogeneous equation. Before solving the equation, we have to see if the given function is a homegenous function. A homegenous function has same degree for all its terms.
Related Questions to study
physics-
Two blocks of Nass
and
ane connected a heavy string placed on rough horizontal plane, the 4 kg block is Pulled with a constant force F. The co-efficient of friction between the blocks and the ground is
, what is the value of F, So that the tension in the spring is constant throughout during the motion of the blocks? ![open parentheses g equals 10 text end text m s to the power of negative 2 end exponent close parentheses](data:image/png;base64,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)
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)
Two blocks of Nass
and
ane connected a heavy string placed on rough horizontal plane, the 4 kg block is Pulled with a constant force F. The co-efficient of friction between the blocks and the ground is
, what is the value of F, So that the tension in the spring is constant throughout during the motion of the blocks? ![open parentheses g equals 10 text end text m s to the power of negative 2 end exponent close parentheses](data:image/png;base64,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)
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Vct3BzeR0rGwfYOMjjICfnEuOgkSRCHk2/rHabgJTPZi2PXDqD7a0UEoc5lMpV1BoiaNpSLkXNaMTnyRoaPa+YaasDdhVJDhFINisclrb8xbgAZpSSnooaiTwcFUhNKZMl1IoZFNOHSCUSSBwcmHSwL8l87pvNmvfl//Xz4CCBg8QhkmIrs+WmOJ7dnrDvn/V1gAKJPAQ1tWKYLU4pIUERSHHExsYwPRtGzFOFrXAXudVLuH1jCV9c38b1m6u4u7YulSmDpC2OwsR7CE7MY3Y0gOmIAyH3oPHofTyeRxxkYrziOVvEE2oUUNpfwf7Nz3H783/B73//Bf7bp7fw1c1trGyncZApo1BroaFeUyuHen4HifUlrH59BVe+uo6bIuru6BpN6X2k925jd/lLXP79P+Of/p9/xG9/+xk+/eoG/nTzLm7eTWHzsGKiSG25vnkrw5qNkAfp1qXMFcRLz+IwmcfqRhXJjAhsKTxOp1VSb1zd0xUjPbq3TpjN5oDTYYdLzmW3v4Axck9UZ8nRRTOw1+Xb1NmUmQNkDrawu3UXG+t3cVfS+l351LSxYVaR39iQv93dkN/Jz5vb2NpPYi9XR6baRa2pe2T2zvw6QIFEHoMWDzHMdi88I3OIzZ/HzMIMTkx4MOvJw5paxs6ty1ha2sKtrSq2yx7YoxOYPzuP6akoYgEX/Noo9C3497K1pgXop454zLUMWsVD5ItVZGtOlCxRBOLjmJ2fwOR4BPGIH0GfE25pPKxiFOrJbWR317F/kMJ2vo3DdgAOfxQT43GMT45jdCyGaMiNQCcHe2EX+UIZmUoX1bY0RG4nwgEnXI4Hdh1ng0EehhYPSxftShG1dAqlZBKFehul0Bg6wYhZkdsrZXIQTH36YmQuIOVQJz5I2dagkvyqfzrDvZ+lrD5sssFDuff3rtx+E12tM+UiijldZ0m7q3UAuFS9e8cNp2/eAzmKSD7pIqIOB6y6OWZDyujuEtKbyyJ+stjJtpDV2cleP8LhIIJBP/xuK9wQZ7iaRC2XRCJdQ7Ig5VknF1AgEaKoGRfDabPDFpqBb+ZNTJ88h7OnpvHmjBOjnW3Ut65ga+sAK4dd7FRDcIWiOLsQxHjU1RMpcope7OV7YvohdFyHbmZbRSObQDmTRL7lRdV/Au65H+PtDz/Ez//tO/jovZM4vziKmRE/Ih4b7I0qavtbyGxtIiEeUNIaRTV+CpNz83jr9ALOnruA0+fexIlTJ3FORN/JcBNejxcWbwzeUBxTYxEsTvgQ8jlgk9ZIG4If8CTklUWHUkvJ6NSlMRFhIWI8l8ihZnPBcfIEfNOT8Ps88GrXmDn2h9ArgSpMhk/UG8+k0YKm1BWdeaozTZtomNRGywzm7q29dK97TyOjOomhWTNdMNViFvlMCqnDJFLpLNK5InKlCkpVOVdHvi/Ht83kBfmeflfP1T8VOYpoIdEZkL2NxN1+P1y2FmzpVVT313GQqeGw5kXdPYbRqTmcOLmA+YVZzE7FMBl1IOaqwtkqiVhuIFfsoCoC6XWaEECBRL4D9RLF+9Cd+sXDcPuD8PoC8Ht9CPssCEkFsjQKKOdySKeyYlQLyObFoNbEKLd7M3W+d5NgvibiqFlBu5pFNX+IhDQ8e6kmygjAHplAdGYOM7NTmJ+MYzwWQCTogc/tgFOXHWg3US9kUcpmUCjXUWo50HAE4ZFniIqnFI7GEYqOIBwKI+a3IeJqimeuIzt6q3q73U4EvdqloTP5zB0R8gD9QtGVFqNdQreaQqmoY+AayFTt6DoDGBmPIBr1SZm0mzW9BvM5n52okHuQf7tyD912A6hl0MxtIrlzB3dX17CysoH1zX2pM1I/NSJUa6Pe6o+BEqejW8+jUdhHRic7bO1gY3MPe4kUMvkMUoltJDbXsL22jLWVFSyt3MXq+ha2dCKDTnIo1lHQcSl6rv7dHBd0hmqj0UClUjGDkXUzad3oWzf/fvXQMmKH1S6OntMpzl4XtkYO7Uoe5VoLlbYdLZvX2MWQ2MJQKIRQOIxwJIxIRH4X8MLvtMEthVd83kGpfy2gQCJPgJi/TlOMcAutjg1Nqw9dVxThWBQzk35EfS04mllUUmJc725hdXUPuwkRSroNQku9zt5ZnrZiaczGzL6oF9EsHKCU2sHmTh53ExZULCJ0YiMYmxnH2IgIHK8TARFGbofdDGLVSLJFPd56HY1arbcEgLZjxlDIMQ7dRNMLp8sLl0tFlQ1epxgO7bswG+daYTeDYS2mkrxORoE8DRqBEaFRy0sZ3UexWBJxZEOuG4LNG8JU3IORgAMep5ZJKdHPXEn0T9hfWqBdOkD1cAW7azdx++YSrt9Yw+21HWzp+MBC1YzN0wUqWxoFatXl+ENUDu9gf3PdTLpYvnOA3VQehWoZhfQuUptL2Lp9FTevXMVXl27g6o1VLK9vY/Mgi0S+atZzqrelnh4jhaSRr4FAUlGUTqWQPDxEKikCty+S2rqemxzz6sxe1a5ZsX26W4HYODsapktVhXJbZHtXx7apE+x0w+X2wOMLwheKIRgXJzQ+gtGQC1GPFR4H5Pv9U74GUCCRx6DGQWqQipRqHvV8CsVSHbm6ByX7BCLTJ3D63DwWJ1wYceRgzW1gZ3kZl/+0LEb0EPtZNaC6m3/vbE9OX45o2Ea71qpZ1HLbyCfEiG/lsXJgQ8UagF8E2sRkBBG/C0453Ca3q10dete90L/8Xz/0Y5EGxNIW77ClXQ8ts3aMtBPomAUidVNNG+wOSbogn1gAa/97ei5CHopZeFSn9UiZKqdRS2+jUKog1/Gi7BqDKxDFbNCGUa8FHlHsKtp7pfM5IM5Lp1FCM7+L0s4tbK/cxNLN27hx6w5u393HdjInAqmG4r0IkhzfrKCR20F+W0TQ2gqWdeuSuykc5Guoy3PVignkd29j9/bXuPmnr/DZp5fx1ZUl3BTBta57MuZqyNe60HVhj1NFUdGjAsgIpGIRiYMEtre2sbO9LSIpaaa9V8pl1MSx0i5KPbbXnXjcrYEu22Izi/A61JEUe3d/I2RdmLfnCuoGzXaXD67QKHwj84iNT2NuxIPJsBVBtwV2HTfxmkCBRB6DKhsxEK0yioltJO/exWGqJN5xAM2R04gsvoPT5y/i7fMn8OZiGAvRFtzlbaTXrmPjzhbu7OSwo/tEVaURUXqa4wnoV8D+mkfNchaV5B6y2xvY3k5gM6Feuhg49YbcDtil3lvlOyqOjIduvq6iRzz3UAiBSAg+UVCuZhHdQhq5Ug3JShsl3fyzUUVLPkvlLkpVF+xuHwIhP/wBr3hT9ie/ZfLaoZ2xEE+8o2M0snnsbxeQL0mZdfvhG40hHA0i6BRxpF0aOqL6mSPm20Q4m1JVq2iLQMqlC9jfL6PcdMEWjCM4PoGR8RGMRYKI+t3wuaxw2pvynTJa9QzSu5vYXr2Lg8MSsk03mr5ReKMTGB2JY2IsjNG4G0FXC91SBoWdPeQKTRS7XtMlY3c6pV5ZYNaBPUYVRQeXqyjQgfMapU6nU7hz5w6+/vprEYGf4fPPPsONGzewubGBVCqFarVqxJF+71ij9y/J/KOfOq5S3oMO4Nb3YRPh1DusIb/riPV3SMkKwmIPmIkvAa8Vbsnv51OWjyYUSOQhaAVQlaHecU0ERA6pzbvYurWGg2QRBXsIlpnziJz4ERZO/RgX33kH7797Bu+ejWExkIc3dwspETN3NtPYFGOdKYq3eu+830XvGCN2jEAS77xaRjWXQfHwELnkPjK6joc0SKmCbrPwzQhVT1qpIZAK73QhNCYNxOQEYn6p4K0irJk9pDJ5bIuXnC3mUBbxVS2L4CpYka0FzeBsndkWjwfg9zj7d9MXbIQY+vWj20BXxFGzrouOVnB3x4JSXURIKIDJ6aCUIY/47HKsls/nFX0wY4+q6NQLqJcLSKbb2M2GYY+fwcI77+Pdf/0RPvzgbbx3ZganJiIYDzkQcjWl6cujWTvE/tY21lcSSJcdQGha6vSbmDlxHqfnFnH+jdM499ZJnDgxgcmgE6FWHW53BK74PEJxEVEiusb9VkjVMm3vcUHFgd1uh8/ng8frQbFYxN31dfzpq6/w//7DP+DXv/o1fv+73+Ha1avYEKcwnU4bkXT8xydpGRyUQy2/+qGf2pWoA++1oDakvOZQrxVQFEcym+ugWOlHnbSbWMd2HqO8/qFQIJFHIAKlI5WlXUS7lhZhkkPioIp8WfxmhweeWBi+SBj+YBSR0VmMzZzA9NwcTkwFcCJch6tVQCFXMNuRlKriZffP+qQM6q7Z4d8bgCschy8aRdTVQKBxYCJK+9sJbOxkkS41xdOR+5Kaq3GkAVabE87wGPyj04iNxDAWdiLurALFBLJ7W/L9PewdSONWsaIRWYD/xNuYnZvG4mQIUxG3WaKgdyfPHjXSZrwTOTKoB61JvenHRgvMn7pSLypo5DNSFhPSiLRQco/AEhpFIBzGSMiDsNtuxrHpwH/tstVTmmn62qWrv1MP3lznMdd6KFomO9DNpLvNIso662z/EAd7OWRbbrRH5hGYnDXLWEyNRTEa1QiAB16X3UxesFtb5rsaGTar3+cqqOj0basbNk8Qbo9XnAOvOAtBE30N6MQHEUHudh3WrtQxq8vULRUZLo3eiiPzqCcY1B59To1WaJm3yjvR9/zYd/ycGVzb6XLBJs/R7rTFWSrjUJywzc1NrK2u4ebNm7jy9df405df4SsRT9evX8famjiJBwdmYLd20R1f5PnF+dTxnfViGoX0ARJ7O0jsrpvu1s31DbM7wXauhXTNamKlaq5eYpa9FGihycMxnoWui1KSSpQVL6uGTA5iSMUi2h3w+h1wuaSRt7vgCGhf9Rzik/M4MRPHuUnxUp1NtKQBqVaqqDeapoKZ0/Y/nwg52GJzwRmMwz8+i+isLj7pxJQzC2T3cbi1g/X1A+ylyyi0u6ibKcwPXEHElcUTgjM0gqCIq1jEh5ivC2cthZp2Ge4e4CBZRkb3jhs/hdj5dzE3P4X5UT/GA3Z4HX1r8FQ3/QTIPZpBok3d7VfslPys4xyYXk7S96/RAW3wdMyJ/tyRBvNRqAw3KxNXRJykUshJOcpXmqgG4rD4w1IvnPBaOnBI/dFzmb39tGyaJNdrt+T3bZN6O/A/TQEblEkVSBWpmxkUkgfY3zzA1lYW2Y4XtqlFBCfGEY8EENeuEYcKk55A6/WO6PV0XE1vMHJLJ1LojNMH64+2hg6nmfVkdzrgtFvhtHbNLCaROHIbIvT0n/7tPIrB5bpaxuV59f025T3ru9Z3M5wXLzIpbbkHFUs2m9gK+dT7U/Gzt7dnRNLVK1fx2Wef4Y+//wO+/OJLXL92zYikffl7LpczkaWOnGswoPvYjFOSZx1MgKmX0iimE0js72JHxOH2nTVsbWxjZz+DvXwD2brFjNd8HbH9z0L/Z3IM0YpZr9dNX7l6P2p41Dvz+32Ij4xgdGzMVPynQ4/X7rWKfGTRKCVx91YCO7vSgPjjcI2PIzI9jlG/HRGxmHaHCAwd/CcNgrOWgL2WxmF3BGX7KPzBECZGApge9Ypx7d3HQ+9G/yYGW7dpsLSyqIpXs347g5RoIUREgM3MiUCawEgrjYAItkrDgpJU3ErLDk/AB2/QJ56x3Iucprdm0f3zNcSIFUTglatN1KUxsJsZRdJI1bWhsqJj98ERnUBkchqToxGMhtwIiffvkpM99F6fAjWYaow1j9JpMTi7uyakrxGF6alp+CSf1CCXxZMviQerXizTi006IFffvW5enE6mkE5J+T1MmqnfY+NjmJ0VcR6LwSliQbFI2elq9EUalax43Yebe0jUHCj6xuDyeeBzdOHpVoFmAZVSFgd37uJg+xDZqpRZRwTt0CSiPjtiHhHrdi2vIjmkPKgm+Ta9Emix6FpFcr9yzdz+DjL7+8hYfCjZvehI2WkXymiJSGsHx+CcPYF4NIh4wCmOitWU454G03OJsDLjpipoVvNIrW8jlcij6hlDJyD3H4phIuoRB6ELWycvjWcG2cMMDkR8JVMt2KdPIySOyljUZ2bnRdy9qjvMQGysrCwjkUgY4eXxuOHzes0XVBxVK5V77/5h+fI8k17X1Emxm1sbmziUe8xms+Zvg8HZOqNNRZAek0mLiJB6q8sCNHRmrAppTQOR1xdI+my9aOEPtRzPA3EE6vJ8mX0UN28hWWgi0Y2hYdXZvA5xHkUoNvNmte1irYtiN4CqbQRurx8TIRiH8Ug+1nPEIpn6mmrDVwOtoGrIby8t4cb1G6ZSqyEfGxvF2XPn8Mabb4rhtT6lZ6O1QPeUyqLb2EMpuY4//t11XL+SR3PmLAJvvoOpH1/EhVEHToqBVPuLdhX11F3Ulv8JieXL+IfUGdy1X8D43Dx+dGESn5yPwi21Sw3lQ+uY1rxOHagnYamvI7u7jP/2X1Zx644YoKkTCF44i4kzY5hOXQY2buHmRgNbJS9K7glMvP0uTr91DmfH3JgOORB02WCXFkHHZbTTy0gf7GJ1p4SNwxbSFZs0dh6Egi5pNGy9CJjbbxqGQCSKkZAXIfG6PQ4b5F+51957+761ZCBgNY9WVlbw5edfYEu8NI0kvPX225iampI87O2pRV4O2php/SiXymajzlxOtwlJmrr07rvv4uNPPsapU6dEzPrNcRYU0S4fiPC5g82ldawvbSNpl4Zm8pSUKy9iXivCzibc9ro0tHns3byF7eUtpCoiogIL6My+h4XZSVyYDmNeWh7dszAWdJvuuG/XU60tck2LOCeVBA6Xr2Lj8udYuXQJa4hhzzMrAqkNd8uCkCeAyMUPMPHBR1IXPFgMWBB3a4M9KL+mosq5KmjXMyK2tnHnt/8fbl9exl3LSRSi5+GZu4D3L87ho1MeeBsrKEo9XL91F5c+38XN1RYiH/4E8x+9j1MzMSzEXJj0dh84/330narY0PE82k2lkZaAvL8xca50nR2v1yN2SbvZ9OlePPomtGtN83ttdRXb29um60zrqdZXRfPC5LfcpNpUve9wJIJYLIpYNCZ2JIqI2gxxRMcnxhGLx/vPJs6gnPvo0UStcIjc2mXs/u7/xM29Jm7Y30EjOIdRuf8PTgYw5sqhll5DvuFD3jqLivusONqjeG8eiPkfJeJfXSiQjjnPTyDpOIU8us1DlDOb+OpXX+LG5QQqY+fgOPseRi++h7cmnTgXABxaaVpVNDIbaK79Fsk71/CPufO463gDo9PTeO/0CD44FTRrCj2dQFoRgdRGa+osQm+9jbm3FnHRvQFf4gaufnEbt9YyuFvwojz7EeIX3sdPLkTw5qwP40EHXGJ2dUuS2so/Y2fjLq4m3VgtR1FwjOHtE2GzXYr2oNlMV4E8gLwj3THdHYiIgfPB63bAJ963Q9cOEL5vLXlQIK2KIVaBtLK8bCJ+wWBQvGrPU+YNeV6Y7p9+VEDzzS158/4H7+Pjj0UgnT5tBvWaBrO9h2b+Du7cWMPNrzdx9bJ45FYHHOMR0x1ll+Jkt/T2Dex2aihIw5s7zKLctKHuiqEbm0N4bAGzM/M4f2IC5xdGcHo6BKco8m+XBa0tDwikFRFIlz7DyldfYqXhxY54+NV8S+qNFW5XWATSJ5j6+F/j3dkgzsXtGPeL0Jf76Z1Wz9WRc7XRblVQzyeQvvqP2Lx+FZeTEWx3Z9GKn8KPPnwDn7wTRzB/BeXNm7izcoivrlexdODHmZ+8j7c+uYC5sSDGfXZEpH707vCbDATSf/3Nb0zXlG6EqtFth8Nh7JPdoTNEX26kRe2iRosymYyJDpnuMsn3R6HHD5I+h9bdQCCAubk5cXbewkkR0dNi71Qo6Qy5o8cDAum3/wduJW1Y8v0ZIDZ9YXEOf/lWFHOBAuq5FWQKFhyWIkjWp8QxCOHcnFUcx9dPILGL7Zjz/LrY1PCJ2ZMfO60uatmseJ1VtOxO1GFDtdmBvS3X6lRRqxRQyiWRTx4isZcwK11nPfNwjc5gYjyK6bgPowG7CT1/m/7vum2zjkujnDKe7eH2FpZu7mMnVUfZIZ67CBd3OITRoA1eWxMluVY5k0Yxl0Oi2DaLUrosOlS7v76R3n2zhnbmLgopOc9hCbuHBSRSObNmTSl7KEZ7D/t7u9jb3cHe9iZ2dnawvZvCfjKPbLGOSseGtt1l7lujZN/HlmuDN+hiU0O8u7NrQvnNpnjj0SjC4bA0xG54dHE2MbhMLz5pNMMt798ujZ4ZqG3tTXfWtbE0wjczM2MiBve62DpldKWsFnXhRSl7paqUD+0+Cnng0vVl7HoOXWhUG5SuCJsy6pUamlKeOk4f4IvDp5MbJO/HokGMRryIBt1y7Ye1Pr1Cd6+LLaVdbLtIHySQsUVR8U6ZaGfY2UXE1ULL4kSxJY23qH+vRxf/c5rxQxrP6J9JTyYFU5LYDlsrLz/XUWq7Ue84xYGxIuDuiINRRSklwi4jz1h3o+EchXdsDifPzmJ+OmLGNvnlGo575/0manNUbK6urJrxPHURIg67XeyS3yTtWtZIi84ie1llXwWvvvNqtWbqpyYjgPsVXX/WpDZWkz6PfmoZcbvdxsGJx0cwOTVpysjI6Gi/PnvMMUePB7vYriNZsSHlXoQ1NCHPEcfZmRACXjs0+GWx+2G1i1Pr9CPgcyASsIiAZxcbOWY8vwiSelLimXbqaFVzyKxewd7aKu4mO9ipepG3xTA2PYbZqSCC9jrszRKahQLSIjDSORFOs+cQmj+FsdEoZqJeTPh1nIUaHXOBB+hfq12T62RQzewgv38bO2u38ekXu1hLWNGMLcJ/8g3MnD+D907IuSwpZG58id2l21i/m8CNnA8Z1zROXDiNE6cXMTc7gdnxGEacdbj2/ojk+nVcWUni2t0S1lMtON12MWK9NY7u13e5MasuExuELzaJkbmTmD5zzuxLdCJiQ9wjjYHO2Okd+cQMBKyJIK2s4IvPvzCzZDTfLly4gImJCRFQrafMH/Is0QZR33+5UhHRU0Rex52k06hUqw/vYmvrNg2HSOou5zspbG/mUG510HU7eguTmsW42lLvdJJDWcrfHSQ295Cr2VHxTKE9eQFTkzM4NT2Kk9pVNRHCpDgRKqy+XQ60hD4QQep3sa1+fRUrzrNIRd9A3JLDSDsFf0Mjqj5sdWdw8u0LOPfmSZycG8NMxI24CKh79U9P2W6Kw1NAK3UL2d1V3NpqSt22IFNzIiiCbTTmNlv1qJDSzarhFoEYHJH7jmBM7tXvtsEl4kK7sh+GvlONIP3mV7826wvpz34RJNodFQwFjcAwIkLf10sq+xoFUmflttgRrZMDB1PrrN7/QCg9+KnCKhIRgWi61SYwMz1txNH0zLQRGQERTWp/1eYePR4SQfL/BNbx81g8OY+fXYxBzLmUWZ2hB9Sb4gyLcLbZHCKS0BNO/TO9LlAgHXOej0AaIN/R9TGaFdSTq8jub2Brr4TtdBvJqksc4SiiIyIobA04REi1a01pXBqoNOyILCwiPjNldtePeh0IivZ4uC3UKjcQSDlUcgcoHOig1k3cWE5jN2dFKzgJ7+QCRhfmcXYujFGneEEbN5DZuIO97X0sHXZx2A1jZH4RE3Nz4tGNY0YFkqsJ5/7nSG/Iu7mbwdJOBVvZFuwOq7yj3iwcg7kpHWQptyGa0O6PwT9xCtEFEWWLJ3Bxyo3psDYIvRDz07zKBwXSYAySRqp0jMInn3yChcUF45k+1UnJM0Wnn+ssK+1mSWcySCaTJo90sPbFixe/LZA6FXQaBRR1GYu0fCddQq3ZQdsu55Ey1e07FzZrHZ1WHrs3bmB7eROpihMF/wI6cz/C4syEGYOkXVUTsV4E6bvHIB3icOUKNi9/gZWvr2HF8w6y4+9jPlDBrP0QkcY+lu/kcX3fgfCpNzF9/jzmT8yJEIuY8UIuKbti8M0dygOgVcujtn8Lmd11cUTE8SnYkas74PXYEPHJvVgc4jN44fbrkh5xhEQAxHX5AqnPLkc/qtq7yW8xEEi//vtf4drVa2KnmkZAzEr91LE7vehNf6r/yyj7cl2nCKRkKoXLf7qE5eXb2N7eMfbTRIlErKqAcjnlvblcRhi53C4EA0HEYjHER0fFxo5hcmISo2JrI9GI6W7TY4+mOFJaqItAyq5dwo4IpCUVSIGfwDJ2TgTSAn5uBJKI/K6UWynCnY4V7Y5NhLUIYbHfKrBfNyiQjjnPVyD1jLNu99GpJsX7SCGVKiCZqSJbkt85XKZrwWnrQveZ0vhKuy1uhk28rLEYwrEQ/F4xLjpFuL9WyrfvQn+rtbGBdqOCRrmASj6FvDRU+8ky8roGh0un6scQEMM0FveL2JJrZ/ZQzSSQy2Sxl20i13LBGxtFMCaGPBJCLORHwFpFd/sS0rsbWE83sSUNQEaOC3qsCLhUHvXuSBdJ6wnBmlw/jXrHgaZ4+t3wGUTGF/HBaT8WR11wi7D6QQJpWQTSF19gf3/fNBA///nPcfb8WeO1sha+PLQLVfNJ80ijCLu7u2ZlZe0Ofeutt4xA0vEl2jVkBJIuf9Guo16ro1ato1oR8aI75ct5etko/+02YLVVpUylsfHlV1i7sor9khvZ0Fl0Tv4rnF8YxbvTHkxG3WarHI9L11/SSJY5wQP0yuj9CNIVbKhAunJDBNKPkZ/+Vzg7acXpUB4TnV2sX1vBlRuHKEVOwzlzAWMi8M+fmcabJ2JmVW+nlHO7pY2ujhksZ5BZ+Rr78qzbNQ9SnSCq9iBCbgviHrmq1WkEksvsyxVGUOpVyO+BX7vupE7rGL5HNZoDgfSrv/97Y5fUBk1PTeHUmTMYFXHhDwbg6AukF1709SXLddVOJg4O8Omnn5rp++t31s2sNbWp2u3t9/nNoGvtCteB2VH51OhRONLrHg3pZq7hCPwBvxFQRzdyNOB+BGn7t/+7CCQ7lvz/uhdBOrGAn12Mm0ku9yaMmI9eBsvrei2hQDrmPF+BNEC+K4a1226hLSKiWRfjWquKx11BudZG2+qGxemBw639+mpYXL0NY+W6ZoNOqVzfXb/0Gj2xojO8urpXmqTBXmlmSXwxqDqF3xhlEW3d/vojLbN+i1zHppsx9qI8Vos0WJUciuJxp1NZJKwxFL2TsIQncDLmwIQZcCgnMtfUJQ3a4lFnUUstIZXOYzvnwXZ5Al33JD55K4aTM+JJO7URM195Yr4pkJZNF5s2wjpW4X/8xf+E8+Ll6zEmf35QHpHvi5YtzQPtblHxqrMMl27dwvr6Xak/b5hI34MC6X5Z1aQ/3mtS+qjg1rGAJdH9h1j+7e9w87Ob2C6ICIm8hc75v8K7p2L4aNqKkYANHhHej855U9ilDtXRKCWQuC0C6esvRSDdxLLrXRTn/g3eOBPDm5NdLLhSyF77FLc+v4wbhVEcuk/AM30aF949iw9+vIgxrwMBizT+tqYYDnFEsgfY+MPvcefaMg7cEyKqZmGNT0kj6cKMR55BxYupew6pW044XCKORDD4g354XboxtM0sPPkwkXRPIP3d3+PWzVtikxxYELGm71NnfKnw0CjqC40g6bWEgS3U66tA+t3vfmdm2ul4Ke1a1TGD2lWmkaIJuVftQtPIlxmLFo+bsVPaRajfV9uqSZ/DPMsRRiNDtXwvgrRlIkh23H5QIL0Tx2zYZeKf+iRH+2leDBykfcwZNMDPdpD2MKo4xBCIALE51FA64ZZk158dLri84kGJt+WVawYDXvhFSPQEUs94PtnV+9fQfYH0OnYHHCL0VOypcTWbK/ZFlzFK/WP0HpwmDC6f/QGydksNtlYG9fw+Npf3sHvYQsU9AsfYDOJzY5gfcSPs7oXOTRJh5/J44Qm44JPvdVsN1FoulLphwB3BzJgH0WBvVeSnfZVqjO+vg5Q2UQldS0WN7JtvvWWMsObPwNAyvfg0eP/a1amNeqFYNJuWZjJZ030yvA6SKasiHO6dQ4X7N5KUTd2SwdqWv1WQ29hAcusAuaodZRHpnfGzmBkJYCFiQcCt53hUoZKGXIS+LtjarudRTu8huX0Xu+sb2NpKYLcRRNkVRzDkRzggZdpjhVtngZb2cZirmZQv11Brd9G02OT5xOHQ7dt1hp0IOF0GI7+5htT2Jg6LVSTyJSQzORR0cPbhfn8Cw66U2W3sbm9je3sXO4kiEtqN3pRyLc9q9zh79Vzu9sGn0Heq73PZzNhMmgHwKi4mJyeNczDoYrv3Dl9CUnSzWo0YqgOjdVW7Aefn53H69GmcOXvGzF5cXFw0ZWBiatKUAx1Lpd1vg/vXZ9V0NFExKAK+U0ezKqI4l0BmZx07S9exlW5ivxVDw6ZbrngxFvWKXXIavaqO7SOL5WtEr5QQ8likxkitMZ5yRz9taFs9cPrCCETiCEeCxkAH3CKMxPjqVH5zrEm9KvrdPHCN75v0LO16b/2jyj6quU1sSkOyupHDfrJkGr9Op4VaQxxojU5p5EaS/k6jSK1KXY7piMgUA+pwwx/xIzQaFAEoHrQa1GdoMPR+9frk6KD5MSgTkj2PwZS0++XuG0nzVs+hKzVL/mp9UTOr0U27imwL7BoRMpFSLQO9cz0c7ZbuCaRmRQRSNolCLot8SYRPvTf7qlnMoJQrmE1k83UnLL4Y4tPjiEft8NtyaOe3sHdnBVe/XsXSqu7qXzJb81RbKmJscPvE2fGI2CkfilhawtaVz3D1s9/jj3/4A/7QT/rzH//wO3z6h9/jX/7lc/z299dw6dY27hwWkRahVNU7fcQjDKqMeTfyXnVBRRVp6jTo714Gel0VbzqzTqf5q8jRiJYKo/c/+AD/9q/+Cn/1s5/hz//8p/hA/v/c+fOYEGHnFSdKn8eUkZd0798PKWdiF1Ug1QoZFEUMZipAvtJBraRbjWRRLuSQyleRKetium20Nb/6336dYQTpmKOV9flHkB5AT6Vhd00a0Rl4zPZBxKjXpfZS0Aub1bPL0qbogO8UNlbEmz4soCwGuSpCqK7jjPL6tyyy2YyktFklV1fLTekqymnxqus21O0h2INxhKK9pQX8rv6z9S/1pKghfVgESUP05y9cMB4rORroOjg6UFujCTpQW7vcHh5BehxaQrRp0XFD8ilCqFqoiSB3whEcg0+3zJmcwVzcjfGABW7H43ZH759DRFK7UUer3pCGXYq3xQWrJwz/2BxGpqYxOz2CyXjIDKDW9U+166thC8DmiYjIH0FkZMws9jc5EsZI1Iewzwavow1ru4aSrhieKaNi86Pri8AdiSEajYjACptFESMR+QwHEQr6EfR54ZG67nGI+AoF4AmJ86ALI0rd94oG1McYPMkggqTdyvou1U7oGB61R2Yws7s3mPllRV4Ggk3vUZfc0Pqo0dwZyWtdy0gHYOtgcr3XwfiiQZfa0Y4YPQLd4qbVQFueVSOJrbbY6+C4lKF5jE5MYHIijqmxECJ+t+nydZiu06e3d68aFEjHnBcukHoKSS2g/CvGQgyGBlfkp77h6B31UjAX1/FENXTbFdRLBSS2DpDNZFGs11Aol5GXBlDFUVEFUua+OErKu0ulcshUxTO3SuPijyIkDcRI1Iuw29qbwfY9no0C6fjwbATSgF596OpE+I4DDm8IgfgEYuMTGBmJYjxkl3KlS0d8R7nSMq3j8EQnWSwO2Jx+uAMxBEcmMDo9i6mZScxMxDAWDSAS0AHULjg9ATj8cXO9kYkps07P1MQopkalPIfdCHoAly5B0Kgge5hHriDXCU8gMDGHsYVFzM/NYWFmWsTCjIiFKUxPTWB6YgzjIxFEHUBQRJ1HhJEjGIEtEEHQaUXQfrwE0oNod1lvTaOYWctI71PvcbAUgd7ng8LoKNzzk/Pgvaq9FmfW6YNL7FtwbFYEtpShyXFMjkWlDPkR8DrgFsFr12c+To/5nOAg7WPOixmkfVyQGt1toNsqoltPopDYNANWV25vYyvXRrLpQNUunnDIj5B6SmaslHjw8k0d8K2z7+y6yvHoFCbEo5qdjGA8JsZEvPj7C+09HQMB++AgbW0wdBzGL/7mlzhz5kz/SPKy0YU8dVFDHaStA4t1JtvDB2k/CYPjOsZr101RdSJB16KzPHWMkjZCPVHx3fSiHdptp2K710XVQUccFFh0zJ5GcTWCq01gf8KBbobb7k1e6A207kd6rTr+qCQ+RNbMFl27cYCdvRqcItwCIoQi4zFE3A4ErNpFKFfu6oSJppnhWS+KA3H7FjLJHHLBaTTGTsE1fRKnYw4s+LpmxW59HH1yFRH3Bmnf0kHaTpw4cQJvvPUWJicmzFpI9wZpvwQ0HzXpRrODfdT0XtRWqig6fkLoOzDP2ytD5pmlPErxkNKpi7uJGJJntms5kgKpkSPNyFfo6b83UqQJeZUQ46az6hwRuELTmDh1AacuvoVzF07izPw4FuI+RD12s8idTb0phwcOXxj+2CTiU7qGknjb43GMxYKI+Jym60C3SKGxIE+Hlhg1r3bYne7+RAZdPdoFr8sGl+qkJ7a+Uv5U3DhccLq9cPv88AWDCATE4/d74PM44XbqBAU5xu6CzemV6wXgC8gxwQCCAR8CPje8ugGzrmdTL6CZ2UNpbwN7mRp2mmHU3aMIxDRSFMV0JIBQKGxSOCyCKTaO2Pg4JidHEY+EEPR64HdL3ZDncDst0rAev8Z0IIB08LhO1NBokX5qNOmoRLaeKfq8OgHG7oTd5YHLF4DXHxDR74XfK2VDCoYu3aACSR+d9q4HBRJ5hRCXSL3qgUAKz2P6jY/w5p/9JT7+6Z/jp3/+IX760Rt47/wCTs9NY252DjPzp7Bw+g2c/dGHuPjRR3j/4ilcPDmCxVEvQtIA6MJ66n0R8vRouelFKr6dnrJYfeO73y8pnVYTzUIGlcQGspu3sZVIYq3QRbLSQVVnLzS7Oiz8AfRG64Cu+9RuodJ1oW4NSCPrQ9DvQixolca1V+2OG6+cCCLPHAok8uphRJJ4gnY3nN4w/JFRREcnMT41i+m5eczNL5gZK/NzM5ibmcT05BgmRmIYEe9Yx3EEPLqXlQ129ab6pyTklaE/eFxXr+8UD1DZX8LOylXcuvo1/vTV17h09Qau3biJGzdu4Ob167hx/SauXbuNG0vb2C5ZUPTGYQ1GEPB5EXNa4H0ggvQ0mo+Qow4FEnmFUbOtYzR04GoQ3nAcYRFKY1MzmJydxvS0Dl4dwXg8hJguU+C0wmnTAZmUReRVRUS/OA52j0+cBx981hLc5bvIb9/C2s2ruHRJRNLX13BNRNGNmzdxU9MNEUc313F7bR8HdRtqgRE4glERSB6ERRx5pLqwxpBXEQok8gqjs4jEdFvtsDp1McgAvOL5hqIxs2hdLBZBNKxrOHnh1/EZ/XEhNPbkVcREd3RQt8sHhz8GT2Qco7EgJoNd+CxltEppZA4TSOwf4CAhn4kkDlNZpHMl5Is1lOtyDrcfrkjUjIHyu90isADdnIJ1hryKUCCR14DBAMXeytv3V+i+v0q3rpJtoydMXnFMPXAF4QzPIDB1Dovn3sA7F8/iwulpLE5GMRp0m5Xw7TrrzeExXdS+yChiE9OYmpvB9JSupxQ0m+v6XLpqPesMeXWhQCKvBw8ZtPqt1D+UkFcSKeO9CFIYzsg8wnPv4OwHP8Gf/ewv8ZM//xh/9sGb+OCNRZybn8L0xASmZhYxc+I8Tp2/iLd+9CP8+KN38fbZaZwc9WBMF5u096JSetonh7WMHB8okAgh5HVCp7Hb7GanfrsvAl9Up/HPYGJmHjM6gWFxEYuL8jk3jdmpMUyMRRGPBhDyOuB36KKpOh1ctNb3Ch0x3kSODxRIx5z7U1VpeI4+zKPjyiuVc4OIqVl8Und7c8LmDsGrsz3HpzExO4vZOUn97rRYwAWv3QKr7h03+G73aSNHPVgDyHGCAumYowLpG8vg6z+Dn/tpcBzTy069fBjkh/U4Lh7zCqP16N4igf2WXHKtn3evYD3SZ9UxSTYXHC4v3Lq4ZDCEoFkgsr//2mAhyv6yF7rL+0PPNZQG70r+c+/ne+nB90zIEeaZWGj1KHRLBaYXm9SF061GNJktCPT3Zpfw+6ltdhXvbXnB9HKS5o3ZxVySWe6/X19a7ZbJG9afl5u0Hun2C6YembqkkZVBpKSXN5p/yvB3j3+S59PnVEVohItuSTJI+v/aSGi4SN/Jw77/8GTelXmPvfI++K7WhVar+U2bxcT0A5OWr+fBM9mLTTclrNdqptDfOx2dg+dMb88cfff5YgFrK2tmP7Zyfy823WTzzNmzuPDGG2b5fM0b8uLRyqt7seXyeaytruLSV18hlUyZzTH/+3/37yR/LpgNhrWR1n/Ii0cjeZpPuVwOiUQCO9s7WF5exsbGhsmfDz/8ECdOnjR5xnr0ZKgNyufy+K+/+Y2xS7qlx9z8PM6dO4ex8TEEA4F7e7Gx3JPvxUBqSBnSmcm6Xcyzjkz+YIGknlVSjMrSrVtms8dmU0SS/MPw6fNH37F6YdVqDYeHCezv7RuhqsZpZGQEJ0+dxJmz58w0dt28krw4tPhrxVIvulavIZfNYWtrEyu3l6WepCVPnHj74tuYnJpCW/KGjcTLQ+uRRowqlQoKhTyymSz2Dw6QTqdx+vRpk0+6o79uVtuS+sas+m7UKdONs3//u98Zx0AFaCQaxeTkpBGag53y6UiT702/HlptVlM/T0ldDYVCRng/K36QQNKvqkelq63+3//Xf8H6nTuoVKvm96rkyPNH37UaH41CaNIuAqcYJzVGc3NzWFhcNAVGhRR58Wje1ES0ZrNZs4v/oTgThULBRP4C0uC6pKFge3sEkHqkzp7Wn0FEvCk/z0odWlw8gbGxUdOoa36S70ZtTlXaAm0btre2zM/aJuiGsPo30z6IMKUjTb4PD8oWFeMfffwR/vqv/xrT09Nwezz9v/xwfrBAUmNy+fJl/O3/8r/2unjKFeMNa/cPeXEYoSRJ+2LVAKm3G4/HMTo6ZsYS0LC/HDRPtI6oN10sFlEUcaSNhToW2rVj4bYmRwqtR6Yu9etLLKZ1aMREPTSM/7zGOrxqqABqSLnf2901kTh1EvS9mi4QDRux2JMfiJYnFdkaEPjpX/wF/uY//A3mFxbg9Xr7R/xwnolA+loE0v/2t3+L5dvLIpDK9yoCed5o1t23NKaroP/utZtNC4rP5zP/r4ODyYukly8qkDR6N4jwNSXpIFUzENhUvW/mIXkZPDwPtD55vB74vD4T+bhv0763yXwNuP8eO522OAUl4xA0pcxrNyYhz4aeI6PlTSNIP/2Ln+IXv/wlFkQgeY6SQFJP+NatW/jV3/0d1tfXUa1U9dYZOn3B9N62/leyU969vn+NUBijzqx4eUh2aH3QuvJgGvyeHC2+WVV0Svo3l9EgT46Wc43EmRmBpsD3yjtLPXkmaHmSOmm3O8xEip/9dz/vdbG53f0Dfjg/fJC2eMcHBwe4cf06UqmUiSjpKWlMXjKSB8ZA/bDsJT8QUwv6/zGNrPmRdeO4oHXImEj97P+OPBlays1aS/crASHPEK2R6sDYML/QmyEZDodNROlZ8YMFkqIiSYWR8RbYIBNCCCHkBaHjblUYPetI7zMRSIQQQgghrxIcSU0IIYQQMgQFEiGEEELIEBRIhBBCCCFDUCARQgghhAxBgUQIIYQQMgQFEiGEEELIEBRIhBBCCCFDUCARQgghhAxBgUQIIYQQMgQFEiGEEELIEBRIhBBCCCFDUCARQgghhAxBgUQIIYQQMgQFEiGEEELIEBRIhBBCCCFDUCARQgghhAxBgUQIIYQQMgQFEiGEEELIEBRIhBBCCCFDUCARQgghhAxBgUQIIYQQMgQFEiGEEELIEBRIhBBCCCFDUCARQgghhAxBgUQIIYQQMgQFEiGEEELIEBRIhBBCCCFDUCARQgghhAxBgUQIIYQQMgQFEiGEEELIEBRIhBBCCCFDUCARQgghhAxBgUQIIYQQMgQFEiGEEELIEBRIhBBCCCFDUCARQgghhAxBgUQIIYQQMgQFEiGEEELIEBRIhBBCCCFDUCARQgghhAxBgUQIIYQQMgQFEiGEEELIEBRIhBBCCCFDUCARQgghhAxBgUQIIYQQMgQFEiGEEELIEBRIhBBCCCFDUCARQgghhAxBgUQIIYQQMgQFEiGEEELIEBRIhBBCCCFDUCARQgghhAxBgUQIIYQQMgQFEiGEEELIEBRIhBBCCCFDUCARQgghhHwD4P8HPaWI5SElzhoAAAAASUVORK5CYII=)
physics-General
physics-
A plate of mass
is placed on a horizontal frictionless surface and a body of mass
is placed on this plate, The coefficient of dynamic friction between this body and the plate is
. If a force
. is applied to the body of mass in along the horizonal direction the acceleration of the plate will be ……
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)
A plate of mass
is placed on a horizontal frictionless surface and a body of mass
is placed on this plate, The coefficient of dynamic friction between this body and the plate is
. If a force
. is applied to the body of mass in along the horizonal direction the acceleration of the plate will be ……
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)
physics-General
physics-
Three forces are acting simultaneously on a particle mowing with velocity
. These forces are represcaled in magnitude and dircction by the three sidcs of a triangle
. The particle will now move with velocity…..
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)
Three forces are acting simultaneously on a particle mowing with velocity
. These forces are represcaled in magnitude and dircction by the three sidcs of a triangle
. The particle will now move with velocity…..
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)
physics-General
physics-
A body of 2 kg has an initial speed 5 m/s. A force act
it for some time in the directive of motion. The force
-me time (t) graph is shown in figure. The final speed of the body is
![](data:image/png;base64,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)
A body of 2 kg has an initial speed 5 m/s. A force act
it for some time in the directive of motion. The force
-me time (t) graph is shown in figure. The final speed of the body is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZcAAAEECAYAAADklHngAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAF9OSURBVHhe7b13l5xZct75pPemsry3AAq2Lbo102PIcZqhdCSukUhK+kN79An0Dfgt5CgdUbtnz54VyRUlURTNcGZ6ONMz7dHwQDmUzcpK731uPDcz0Wg0gAa6E0BmIX6NtysrXb33NfHcuDcirqUlQFEURVF6iLXzU1EURVF6hoqLoiiK0nNUXBRFUZSeo+KiKIqi9BwVF0VRFKXnqLgoiqIoPUfFRVEURek5Ki6KoihKz9EkSuUeeCnU0ayXUcmnkN6+g1gih6OKEy1fBL7IKEaGQxgOehD02OGwWNofU5QvhVxvjQqa1RzK+SR27qSRyFngn1tAeCSCsMcGr8MCu15mA4l6Lso9yM3eaqDVLIq4xBDfuIyNj97FB+99gPc/uYUrWzHsJgvIVhpoaJdE+aqwX9usolVJo5LewfbN67jy8Q2s76dxWKijWGvpdTbAqOei3AMvhQaajTKqhSyy+/tIpPJI1hxoeULwhiIYGgoi7Hcj4LZrj1L5inTEpZpHpZDB/n4WqYIFvqkZBIdCCLptcMtFptfZYKLiotxHSzqUTXFg6qhXKqjVG6g15e622eWfA3a7iIrNKpsFes8rXxm51ugtN+V6q1TqqDUssLlcsDvkOrNaIP/0OhtQVFyUh0CRkUuj/U9o3+VGUvSGV3rKp9cZLzkzlSf/02tssFFxURRFUXqOTugriqIoPUfFRVEURek5Ki6KoihKz1FxURRFUXqOiouiKIrSc1RcFEVRlJ6j4qIoiqL0HBUXRVEUpeeouCiKoig9RzP0HwMeomajYUpSWK1W+aGFKRRFUR6Fei6PQUOEJZ/Po1gomMeqx4qiKI9GxeUxKJfL2N/fRzQaNSJTq9VUYBRFUR6BistjkMvlcOvWLaytrSEej6NYLKoHoyiK8ghUXB5Bs9k0WzKZxHvvvof333sPd7a2kEqlUK1WVVwURVEegorLQ6BwcPgrnU7jYH/fiAo9l/W1dRya4bGCER5FURTl86i4PAQKB4e/trfvYHNzE4VCAalEEmu3b2Nnewdp8V44NKYoiqJ8HhWXh2DEpVDExtoGbt+6bYQmk83izp072NvdRTKZQLVS6bxbURRFuZfeikurvf56s9kwvfoHb3xd3se3tz/1ENrL7JpNDH1LvpMG33zePH//5/lc+2835T0N+Rvm73S/43PvfzScU8mKmGyI17K5sWEixkqlEmKxmIkaix8dmYl+k/+iKIqifIYeJVGK8W7U0awVUSvlkclXUSzL7/J8Wwj4kwuvO2BzuOHx++EPB+B1WOB8YD5iQ8SkjlqlhnKxgka9LN9URaFsQ63lhi/sh9fnhtthhV1esTRraNYrKBcKyGXyKLecaDl88DhbcMl7LA4XLDYXbHY73HbA9ogcSO4r51oSiQRu3byF//qnf4oPPvgANRGbingqTqcT586dw8U33pDtIhYXFxEMhTSxUlEU5R5svy90Hn95qE8iBs2qGPZ8Aod3tnCws4fDXBWZQgVF6fGXCnnZCigWqyITNjQ9ATjtFrjv953kexq1MiqloklazOYr4kUURLgySBzEcBRNIVsHyvIdLZsDdhvggIhLtYhyOo7U3jbi2SoSdREU1EU9ayIWIlTVBqp1CyxWEST5uw9z2egdcX4lenBg5lc++eQT7O3tyXe1XyNulwsejweBYACBQAAhFRdFUZTP0JthMRpWblaLaEMV+TtXcXD9A6zvp7BTsKIIGnoRgXoRzUISuWwWR4UGCrX2xz+lhXpVhCidQiYWQzKRRqreQsXuFK/DglpyE7Gbv8bVy9dw6cY+NqJ5pEvi5Ugz+P2WcgGW+DbyIjLRcgvZpg1VEYRaPoNC8gipoxji+RLSDYjsPBgO3XE4jEmTnMhPy7406nXj0bD0C39mMhkjODs7O8bD4WcURVGUT+nZnIvFaoPFLiIiP+vxOyjs3MBhXgy8LQJHaBxDwxGMhT0IuehpNFERYal9xibTKyijWkgjIyIQ208gniyKsLjl8xH4xDtw1dOoRa/hzo3LuHbtFm5sHWI3WRZPxoqmxQmnyIy3nIWlVkHB5kLN7YPV6YS9IZ5PLoZ8/ADReAb7maZ4Me2/ej/duRbOrXATXwd+v98Ii91uh9frlb8C5MW7SYqwJFMplIql9ocVRVEUQ4/EhZ6LzcynWDm/UYijntpHvm5H1RWBNzKGkbExTIwNYyQSQsjnhsdmga3zaUNLrH01iVL2EEeHR9g7zCOea8Hm8cEfCss2Cr/LCkcljvzebeyt3cD6+jbWDzI4EBErNx1wWh0IogGXeDlNtxsWbxBOjwcee028phTKmQPxSBLYPiiiVPt8jgpFg/MqhXwe+VzOzL2MjIxgamrKzLVwKGx0dBThoSG45fv5Ot/LiX2KkqIoitKmZ55LG+nnW6wcHZONppqT+XU0G1U07U5Y/CPwjM5jbGwcy0NWDLvbnzI0ykBuG7nkLvaTWezmXcg2whhxOxAxb3DBHpyGf2QGE84cAoU1JHdv4ubGHi7vFJAuN2G12WET78khHoaD8yqyLza7Q4RJPI5AE5ZWHkfbMWxfP0Su2B6T60YzcLir0okIq1aqcLpcmJycxKuvv4ZXXn3VeC9DIiqnT5/Gyy+9hNXTq4gMD5shsQRLwognoyiKorTpsbgYH0aMvE1EpoVGKYNicg/Jg3XsR6PYTVcRrwfQdAYx7LWKR9H+jKFWQi2xjezRHuLZIhItL8rOIQQcts5Oyv/do/BE5jA3F8H0cBPO0j7id9Zw+8YW7sRLSNbFFxLvxS5/3y5v7+6LK+CB22cXsamisH+A+PoO4qUKcvL6vSNzFBib1WYm6ufm5nD+wgVcvHgR586fE28ljGERk5MnT+LlV17GK6+8Yh7Tk7HJ3+BnFUVRlDa9iRa7S93MmSQu/xz7e7u4Y51EUQSmmbqF+GEM+/EqDgohWOxeTA3Rs+h8TGgUEsjeeh+7+0nsFD3IB5cRnJjG6Qk7PA6+sYHUThT5TBGBlUl4R4JAPo/KYQL5eAblyCSsoigT6U1k3SEchuYw5HUj4mrC56ygUsgjcZDC/s0jFPIV+F5Zhjvig180gV/PaC/Oqbg9buOhcChsbn4eMzMzqNXruHXzJsLhIbz08stYPrGCpeVlI0DT09MYGRmG1+sz8zKKoijKU/BcCDvxZnjM6YbT64XX54HH7YDLJoLCxMZGO6nxXhr1GgrpnIhHAWXOtouht3mcxuh3aTXle21uuEcWMDK/gpXlcSwMNxAoi5Bdvo7Ll7ewX24gb7V3PBLuCF0YBho4YZc/6qhm0CrGkShXkZR31OUt3V3h33I4HGbSPhgMGpHh3Ap/d7lcZvN4Pea1SCRiQpA5XOb2eGBjTLSiKIpi6LG4UAgsHRHwwDs8j/GlC1i58DrOnz+H8ydmsDLmxoin9RmvhTSaTZQqdREWZvHL62KrRV/aX3kXTsJbUGuG4RHPZPHsKZw7N4WlsSbK1z/E+q8+wPVkBXs1q7ynKxr8Ag7T2czfdKACS7OEQqWBgmjY44xmNepM6hRBlH1kRn5dPBld00VRFOXh9FZcpOdPj4UeAOc67C7p8fuG4Q9NY3hkEpPjw5gacWHIz/d1PtNFDDWTFM1mjPb97+Hvne8XL8ThHUZwfAlTi0tYnh/GciAJW2Yd73y8j8vrWRREpEQPOt8h/2vJZ83WMhtlqsmn+fITcne3PtcIRVEUhfRQXNizZ12vmomgqrO+FzfxFWAPwu0LIxQKIDLkRMDHoarOxzq0h6REkOxWU56lxRpizEXpWv9W3Qyd0WOo1sS7sbhg9U0iNL6A2cU5nF10YcxTwJ2NOHZ2s6iKt8HyM50Pyya/yd9oWmR/RJxc8nec3I2vog/quSiKojyQHomLGNmWGHNTWyyNXD6HVKaAdCqDXLaIQoWFWJywOV3wuO1wucSD6HyyC+t++fxe+LxuOMTraYo4sLYYC1ECFTQrWRQzCaQTSSRTWaQKNRSbbtiCE4jMLGHlzAksL44jgipc9bJ8RsRO/gr/D9Tk/yJO8kdrdi/gDCLssCMsvz+qzpiiKIry5eid5yIi0KqzyKRsdg9argAcliZsjaqZqzCGXtwEM7/+AIPO/BRfJIJAOASf2wl7XT5XKpq5GEahtUS4GvIcPZJKtY5qtYl60wqLMwDv8DRGl85i8dQqzi6NYHHEjZDTBpfVAisngERsWJamIX+44R0SQRrFsKudP/O5aR1FURTlK9Mzz8X81+JEvB2e8QVEFlYxPRLAuN8Kn73tQ3AO5GEDSYws845OIDA6hqDfDU+jBGs5i5p4ROb7Gw2Tbe8Nh8X7ccMlKmUT4bFaxSPyDsMzcRqzp1/F179+Bq+ensBMwIEgR+REXFrlEhoV8X6kuZahUbgmZjDmcbbFRZVFURSl5/RIXMRCs5y+MyhexBKWv/EP8LV/+Hv44bdexjdPj2FJPImwS7yI9jsfjIiLbXQOgfFpDIf8GLGW4K2lUWo0UYYbVvcwJk6dw5mvvYnzq0tYmQiLQNjhZgiYxQW7J4zQ7DIWvv4WTp87jdUhN8bdgFs8qnquhGqeQ2MOeKamMLQ0jyGPC375sxpArCiK0nt6tJ5LL+DsfRapaBR7GzEcxipouEMYv7CKibEwRrgOS/uNj4UJh7Y0US+kUNq/jfhRHAcFCw59J+EaXcDX5hwQ/Xksbly/gf/wB38An8+H7/3g+1heXsbwyIhJurw3D0dRFEVp07s5l68MZz9CCATHMD87hpV58V6CLcT30zg4yIn38vAhtQdhscq7KylUC3EclaxIWEbRCi1gZW4Er8w74Hd13qgoiqL0nD4SF8LcmAACw8MYnRzF6GgIPoYnd5wrTu0/mZvVRMsq3oU3DFd4HOGRcUxFfJhk2X91OBRFUZ4afSYugogBnGH5N42RqTmsLo1ifswLjmA9cs7mc8g7nSG4Q5MYn5rGwtwY5iYC4rFwYWRFURTladJ/4mKxiQPjhM3lgZs1vnwu+Fw2M9/yxM6G1SH/+D0e+Lh5nHDa2qtWKoqiKE+P/hMXwnwYU0bGCitzVb70pDm/h5/vfI9sOv+uKIry9OlPcVEURVEGGhUXRVEUpeeouCiKoig9R8VFURRF6TkqLoqiKErPUXFRFEVReo6Ki6IoitJzVFwURVGUnqPioiiKovQcFRdFURSl56i4KIqiKD1HxUVRFEXpOSouiqIoSs9RcVEURVF6joqLoiiK0nNUXBRFUZSeo+KiKIqi9BwVF0VRFKXnqLgoiqIoPUfFRVEURek5Ki6KoihKz3kBxKXV+akoiqI8K461uLRqZTTKBZRLJRQrNZTqLTRUaxRFUZ46x1dcWnXU8ikU4odIJpJIZEvIVIBqo/O6oiiK8tQ4puLSEm0RbyW2g9jmLWxv72E7lkW02EJJxUVRFOWpc0zFpQCU9xBdv4LrH1/ClWubuLWXbotLs/MWRVEU5alxPMWllkElvYmdW1dw7dIVXL21g41oFslyC1UVF0VRlKfOMRMXKkcF+WQO27cyyGcrsNoBh8cCm9OCZgto6YS+oijKU+cYiYsIS6sEVI+QThawF3egDg8CIS+CIRd8HhtsFkD+PTEWa+dT/LzFYn63Wq3m8YtGS9S52Wyi0WigXq+jcRw2aQs3tovtUxTlq2ORm+l43E3NOpq5KKqHN7GVc2Et5UL1xk9QTOwjPnQKloXXMb76Kt6csmHR3/nMY7KxsYF/+6/+NXx+P374ox9ieWUFkUik8+qLAy+USrmMSqWCSrWKlhjjrrx2L6JBkdv799dqs8Fut8PlcsHpdMImvyuK8uU5BuIiu9+solHJIx/dxtGta4jaxhB3T6J17ccoRTcR8y2hNf8qRlZfx5tzbpwMdj7aIZ/PI5vNoiYGs2EMJl0UeUEODY3O2u01/Mkf/RE8Xi++/vWvY2ZuFkPhIdjstrb3IrvQkv+cDiciwxF45X3HjXqthkKxiHg8jlQqhUK+IM+24HA45BiYh4OH7Dgv/+4tYLXaRFycCA8NYWZmxoiMoihfjsEXl1ZN/uVQzUexv7GDqx9uoxScgGNyHI2rP0F2dwv7rjm05l7F6NnX8bXlMM4MSy+183Fy8+YNXLl8BYl4AmXpmXeHvHho+JgG9ZNLl+AQY7OwsIBwOAyPx2NeM5a1Y6DozXzjm9/E/MJ855uPD5l0Gnt7e1hbWzM/c9mciKkDgWBgoHv5HAqrSqeiXK6YYT62ZX5+Ht/+zd/A8PCwOa8v4vCnonxVBl9cmiU0K0lU0newcWsPv3w3jlZwCEOTAZSv/wLJvR3s2WeB2Vcwcf4NfO3sBC5MuuCRj3YnnN5++2381V/8Je7cuYN8Liceif0zwzs0PplMxogJvRL21mmE2gIkb5A300ixt/vP/49/jldefbX9wWMEj83lTz7BJRHZ3d1d1Ks1jIyMmDa73C5zbMyFNCiXk5w7q9WCcqmMRCKBo9gRsnLu6a2srKzgez/4PpaWluDz+cxwmaIoT8YxEJcimmXxOFKbWL99gL/9IAeIsRuKWJG7/ivE9g+wb5uBRcRl8sKbeOvlWbw05wNHxrr97T//H3+OP/njP8ba7dtmeMzOnvh9vdVu7/X+w9X9vSk/FxcX8S//5b/E17/xlnnuuEDhvPTxx/jF3/4CH330EY6OjozI0gifOXMG/oDfGOBBu5S4z+w0bK5vYH19HbHYIQKBABbkPL70yitYXV3F3NycERidg1GUJ+MYiEtF/mVQze5hb/cQV26mUGoyoquG1NV3ENsTcRHPxTL7MiZf+jv4xitzeHnej5B8tGsufvqTn+B/isBsbW0hJ71Xu016qne1xYJavYZCPg+rxWp66TRKtnuGxAjFZVYM0b/4F/8Cr1183Tx3HKCw5AsF/OqXv8TbP/sZbt26jVqtZozua6+/htcvXjTDgezxm0tpUC4nOXf0QI9iMXwswnn50ifGI5uansLQ0JAZJmPgxht/502Miod2dxhUUZTH4hjMudTlXxn1UhrZdBbRoxzKDaBSKeDo/R9jb2sb2/Y5NMVzGT//Bt46M353WKyrHzdvtOdcOLfCaKi7cyngeLsV8UQclz+5bOYYOB5v5ly8YmzkNfMlcgSb8j8a2W+aOZcF873HgYIIy87ODj54/33jvaRSafj9fpw8eRIvvfwSzp0/j2DwvgiJAYJzbFevXsWtGzcROzzE9My00UcO/3HO5eKbbxgh5RCg2+1WgVGUx2TwxcUgTZBmsJfdbLZgddhRL2ex/7P/gk0xGmv2eVSmX8Lw6it4Y9qF5UDnYx26+Rr0PrqHozuhz+GQ69ev4//8j38Ir8+L3/zOd7C4tGQMDz2Y7vsIDU93Pua4ED04wK9//WsTjp3LZhEIBDE1NYnFxSXTyx8Wo8vw3UE1upxPY6cinUqZ6tnh8BBS6TR+/vbPUCyWpK1TRkiXlpcQkXOuEWSK8njYfl/oPB5gxH0QI28RA8fQYYYS2+wuOGwWuIfGEJ5ewsTMDKbHhjDhA9z32X4aRgoFheH+jc/T6HCuwSveytlz5zA9PY1QKPTA9x63ni29Fg6HcVhwYmISKydOyLaCKenh04OjsWWbBzmiiueN8yo8p6FOJKDH4zb5PIyMY5g5vRaGog+ykCrKs+RY3yXe2dOYfuWbOPfyBby8PI7VMBB0dF58Ajj+3mQWd71hDA7FhvMOx8LpewBsF705tjUWi5lIsVqtbnrxy8vLZtiPnhsn9btRc4MK959iwqE95rdwuHN4ZBivv/EGTojHwsz92GEM29vbODw8NHNyx/W8K0ovOcbiIv6L3Qmb02161y67DQ5prfY5vxgaT861rK+tY3dnV3r2DjOfNDo2ZuYeGFHF3j4ZZGHpQk/k3o2Cw2uGcy2vvvqq8Vg42X/71i3syc+qiK6iKI9Gba3yOdhbZw/9xvXrxqjSS5manr5b8obCk81kUSwWzXsHuSfPeTpO6rO9DEvmYz5HRkZHcfrsGYyJqNKTo+fC48EIM75PUZSHo+KifAYKBSe5WeLl6rVriIpBnZmdNTk8HDo6OorhyuXLeP/9941nUywU0WK56QGFQ3+cV2IFhvffew8729tGNHkcOOw3Pj6O+fk5TE5Ootlo4mD/ADdv3kL8KN75BkVRHoSKi3IXGlQaW3olTJQ8jEZNTTFm4TNEl/MRiUQSt8S4XrlyxRhl09NvDe4iORTSqLTz5s2bJhydj3kMut4LJ/onp6YwKwLL4UC2l94LJ/rp6XTfpyjKZ1FxUe7CIS722jmJfxg9NMmjzL5nr310ZNRESrE8zsHBAXZFWBKJOKq1qgnhHlTq0kbWTaNHQrFMi2AwWKMrGpyD4bDgnIjL+MS4SaKlqOzu7phJ/lKpZN6nKMpnUXFR7sJefFoMLY0s81uGIxEsMjJsZNh4LZzotjvscDodJjSX4ddWhoB3Pj+IMEmWwQmshmzaZGvnLt0Lnx8SgaEHx3Bst8djxPf6tWtmeIxCpB6MonwWFRflLhzySSYSZt4hfnRkhoJOrZ66m4FPcRkSwWGZGyYVToxPGG9mkCPGHCIsxjOZnzdh1nzMpRPosdxLe/5lwgjM6NioEeLtO9sixHKs4uLBye+DHNigKL1GxUUxMBqKiZLsiZv5hGzW1NY6feasyQMhNLgLYoTfuHgR3/rWt+S102YBNYrOoEIvhBUX3njzTXzz29/Coogm51nuFxcKaHgobOaeuOxCMBQyQ4g3b9w05YO4JhCHFRVFaaPiohijyGrQnMQ/ih/J73UxnizzMmXCcDn8RWhgaVQn5Hn24Fn6hfkgg+y5cEiMlQbYVnpqfOxwcgG0z7fJtF+8OM5Brawsm5+cd2HhSwYCMESbIq0oioqLItAgxmJH2N3dM2ubcAGwleXlu3kt9/bi+ZgGmYJDj2WQhYVw/81c0mO2ia/zuJw5exYXLlwwgsLouTtbWyb/pZv7oygvOiouigm9PYweYH9/z0zoj4yM4uTqKvyB+yp8CjS8ZhORGXRh6cJ2UDS5fVGb+DpFiGHJk9NTeO2118xQmamsfeWKqaysCZaKouLywmOGxDIZE36cSqZMoiCHwpg02Z1r6cIJa/bMmWDJSWxmtdPrGeSJ7G74dSqZNG3qDm09qk0UGHo6XPfl9TcumgXT0umMeC93TA4MvT8KjE7wKy8yKi4vOBQK5q3QY2H1X05as4YYh35oQO+F4bac7Odyx8xmX1u7jaIY40EOw6XXxnkTrt/y3rvvmkg55q58UZvo5TBEmXM1DAiYnZs1x29zcxObGxvGg9HhMeVFRsXlBYYGlPMELMbIHjuNJSepR5jXIl7L/UNELPPCCsG3b902C2ztbrcz9FsDLC6fZujfwtUrV+Uxh7UqX+h1dL0XRpZNTEyYyDqW7GdgxP7+PvZko2CrwCgvKiouLzBdw8qhnGqlinAobFbajAy1J/Lvp9VqmgXDWMBxb3cPyWRq4Jce4BAYhwWj0YO7JV2Ytf84beqKLyPITpw4Ydb54RLZ9AZZTZoiw+9TlBcRFZcXFK68aeZaRCg4R2CzWhEZjpjqx4wWeyCczHY6jVfjlx773YWz7vNwBgkuVe1wOE2SpM/HxcA6i589Qd0BHgfOU5kM/skJ851MRt3a3DSixaE3RXnRUHF5QckXCmauJZFMGu+DyZBcq6W9VvxnJ/K7sKfOIbPFpUWcPHUSXO544DP0nQ6Tcb+0tIRTp05hdLRdQ81ifbI28TMTk5Nm/oW5MvQK6QntiAeTlGPM3xXlRULF5QUlEY/jRieznImRLMpIYbk/QuxemOOxtLyMt956C9/9/vdx/qWXxMsJmucHFY/Ha9bI/+Y3v4nvSZu4+qRfhNZ4ZE8IRYUixcl9en8cQmSAwMbGhpmLUZQXCRWXF5TDwxhu3bxpetTsrTPqiRFijxIKeijM72A0GSf+GYrLnI9B9lzsdpuZMxkbHzel9fmYE/Vfpk0UJAoM17/hEBmPFSsuX7t6FfvixdTkWGuBS+VFQcXlBYKT1IxeKpXLpurx5sammVmgUeUWEsOofHUYPXZqddV4QRSpa1eumiWSY0dHZv5F81+UFwEVlxcIhhJzeGZNDB0jvjg5zyrHoyMjpsfOeYMvgvMzDD8uFYt3F9UaZGPJfTdtKrFNpfZaLl9x8TMeR3qBrFU2N88lC0awubmFd375S3PcBz3CTlEeBxWXFwQas3qjjkQ8gY8++gjxRNyEznKjwLjc7s47Hw6/g3M0LHDJEGbmcQy6oWzUG8hlc3fbZKoO1L561QEW9OTw4ap4MOfOnzfH6t1fv2tqkHGorKoejHLMUXF5QaCHQU8jFjs0y/nSoLLEy8z0DELBkFnX5Ivgd0QPorhx7ToufXwJW9IbZzb7IBvJSrViEh6ZFPqxiO7+3r7xzL7q3Eg3wXJsfMyU6Gf9MQoOE1Cvy/FjuZlaTSPIlOOLissLAI0/hYW950OzhHHUzLXMzc2ZiWyvz/tYEV/8nnQ6ZZIut1gF+ChmAgIGeQ19el7JZMIs28zSLQwbrlW/ujfGuRaKCYcbGYm3srIiXuKUqV+2vr6OAzkH2UzWJHEqynFExeUFgAY0n8ubdeKPYkfG8A0NRcToTSAUDj32miw0uPV6w6ybX5Uevxk+Yg9/gEd32CYmlLI9pk3yuFcRXV2BCYnAMIOfk/yMKKMos54Z84wYrqwlYpTjiIrLCwC9FpYkuXPnjumZM9mPuRhDQ2GT1/K4eSo0lhzq4VLADF8Ohb582G6/wLYzr2V4RNo0NiaPfT1tE8WENdt4zDk8Njk5Yf4mhWVHvCVO8LMqs6IcN1RcjjnshdN4cQL/zp0t8WByJhN95cSKKXnyuMJCaCiZaLm4uIST8h0MX6bhtA6wuNCzYOmWpaXluxn6TldvV9e0yjHmcaKneIJ/Q/4eo/ZYMJRDjJx/0RL9ynFDxeUYQ2PFOZFsNtOOhpLeMosyrp5eNZn2jBB7EmGgwR0ZHZHPLoFDPIw043dw4bBBhUmgNPacE1k9fdrMQT2tkjYUc0aPcYiMYpNhBv/OthEYepSNHg3HKUo/oOJyjDEVf8WAxY/iptwL516YNc6JfHogHP4RK9p59xdDg0sDycx8fp6lX47DsBiH+hiOzTbx8dNqE7+TGfzzCwsmB8YlXhMXaGNwBAWGuUOKclxQcTnG0GthZBjLv7NnPDY+gSXpoXeXL/4y9bOUrw7nrF6/eNEMLzabLayvreHGtWumA6AFLpXjglqXYwwXAGNiIMu+FwtFzExP48RKe0jmy8BhNgYHMJGSHhEz2hnpxBUYBxXOSXG+g3NRbBMfP+3oLVNBeWICc/PzZt7KbneYYcurV66YeRhFOQ6ouBxDKAIcAmMmONdrYaQYjSgjxBYXF9rDYV8Cfm97IawdU5eMOTPsabOszKDSznNJYtu0acOsw8JQ66c9uc7huMmpSZw+cxoLS4vm733wwQemUjUDMJ7231eUp42KyzGEhonJeqZESyYDq9XWDh8eGzPFKZ8kQuxe+L1cFvn27dum0i9FxmSzD7AhZKViDh3e6ixzzNDgSvnpVy/mkCQTLFldem52FiOjo+b4Mlz8ow8/NJ6MCowyyKi4HEPYG2dkGJfZpfHn2iIsP8KJ+C/rtRAaXA4ddZdGTiTacwSDvIZ+vdEwSxHzeLFN6XQGdTl+z8KwmwTLUMgMjbFEPwWGniFrvzEHhh6MZvArg4qKyzGE9b64CiINJgWBVXm5Nj4jxb4KjHZij9thd5gQXq4Xz1DmQY4WI/TsKLpsk80mt8Qzag6PG+dfhjsVlJeXlozg8NxxiI6eIefNNINfGURUXI4Z9CRSqSRisZjxMkweh4gL18Z/1CqTjwON4d3FwqbuXSys84YBhKLy6WJhk888vNqEQvv9JpFzbmEB47IffI5e59raOuJHR8aDedrDdIrSa1RcjhmcY9nfP0A6lUaz0UQwEDRZ55xzYa/4q0CDy6Gb5eUlnD592gy1mSRKy+BeRhRHVi5mxQImUY6PtZMon2WYNsWMosb5Fya3Mg+GRS25wBi9mHQqZaL0dA5GGSRUXI4ZnJzeWN8wHoxZG196wixSSYP5VaG4dOcIZjuJmFxw7Fn18p8GFBd6YKw2wKHD8FDYiPCzbhMFhjXOlleWceHCBXi8HjOpzwn+XQoM14CRc6oog4KKyzGg26Pl5C/zJDhez543S71PTXP54pB5/atCg8uhNQoMDTKHc+w220CLC4/TvW160nprvYRCR8/pzJkzZh1+h9NhClxubW62Kyjncjo8pgwMKi7HBE76cgEwZuMz0oieytTkFKbEy/iqE/nKs8UrYvfmm2/g4uuvm6USuMDY7Zu3jCej3osyKKi4HAPYm+WwCRe7SiQSpjfOGlaca+FP9oh7AT2kSrlietAM3+VEs8nQH+C5AB47hmt32/QsMvS/CJvdjoX5BTMHxGAMrjfDCX6u/MmfnH9RlH5HxeUYQGO4v7eH999/D+VKGUtLS+KxTJs5FxqqXkERYY7Ljes38MmlT7C1dceEPQ9yEiUNNY/d9WvXcOnSJTHee+3E0Oc9/GSxIMIaZG9cxNLKstmnGzeu4/InnxgRVJR+R8VlwOE8S7FUNOvAc212lmJZWFzE+OQ4/AF/T6OeaHCZ+c85nZs3bhijXBGjN8hJlEw45eqcLB558/p1xA6P+iYyixWaucCYCTQQD5ReI6PH1mRfGWquKP1Mn4qL3Nhyc/MG/3TrvPS4fO7zsnVeOi50h3RYtp0Jk9w410JjxCExTk73crKdxzCfz5mxf0alZdIpI258flBp1BtmSCwmAnNwEDWP+6VNHM6MRCIme5/LJDAfhwVIb4gIch1+lq5RlH6l/8SlVUezWkA5e4T04S52tmWLpnFUaqFYN7LzhbSqJdRycWTjB4hFD7B/mEA0mUc6X0W1fnyibUxxykzGZHJzNUO3x91ZrncUfn/AGKdeigu/y+VyIxAImugqihc9o8GNFZMbwGY1x42Gm94BHz+vaLH7Mcfb7TYh3/PzCyY4gxWtY4cxbK5vmMANDksqSj9i+32h87gPaKIhwlLNJ0UYDk1F371oAke5GnINpzFkTocVNqsF8u8hNFGTz+fj+2aRrFgii0S+hmJNRMfqgNtlg8v+ZJrKoSAWE2T+A5Pc2Ju8a1h7aLyfhLYXkTeFFllJl94E9+n0mTNmVcXuWvC9hH+Tk/iEQzbj4xMms9ysaNnD4bdnCeerqpWKOY8MrWa+C0OSea77pU126STYHXaTFEtPNZlIolRpiwrn1Oit0otlW+h1HctNOlKsA8fHZFCvtxcJixiMPhnTEI+iURKPJY507ACHe/s4iCVxmKkhiyFYQ/M4cWoOJ5ZGMex1wGu3QP7dA5vBC6+MzO4Womvr2E/mkKg6UHGPwT88icmJcSxNBjDif7LoKU5g/4c/+ANjUL/3g+9jWQSG9bqeZZmQ++FNdngYxc0bN/GLv/2FMSynVk/h3LlzRgCZu9HrG5CXCgsrcu2TqtzsZgXHPjPET0rX+6NQ85jSe6EX02uv76vCfeM8C3NerrB6czRqzseJkyewwmWTTVWBjsfF3R7ckcrPwQHt7rwexXR0ZNR450p/0z/i0qwAlSOkjw6xv3uInd0YjhIpFCt5HERrOEz7sPyNr+H8W6/gxKgPY14r5N+nQzKthmx5uQtj2L6+iZuX7uAoX0bB5oUlPIPQ+CxmpqewMunHqP/JevT9Ji7spbKgIbO3ucDUL0VcWBvrR3/vt8x8S9c4Pg04zk9DxwgxDh/x71BY+skQPwk8lmwPN94KbA/Paz+KZalcMkNizHv5+KOP8Mknn2B4mEUv50xGvzkXLMXDc9Ent/VXha3gOeJ112w14XQ48cqrr+LiGxfbb1D6lv4Rl0YRKNxB7EB6Zztp7B6VkC/m4bHGsfb+TXz4y30M/9Y/wtnf/m28sRDGStiOiNjPtkmTJjRrQPUAzdw1fPzhPn79YQ4Vmx2uoQgCE/MYmZwRz2UM88MuhD1PZjj6TVzKlYpZEvfWrZsmQuzq5Ss4c/YMfu+f/lMzZMdTOqjGXnk05ZIIjHgwP//5z/Hf/ut/NcNkrB/nlWuzWxPtOJ17XssUfgZasK02ad8/+O1/iN/53d/tvEPpV/pIXKpAMYF8oYhUoY58w4a6POeqJbDz9l/i8l/8FaKv/A68v/l7eGtlGGdGHBh3oz33Ij2aVr2E+uFlFG78Of7mSgk/2Z/E8MIylk8uYGV2HFMjQQx5nfC6bHjCKZe+ExeuMLm+sXF3WVz27C5ceAnf/7s/MAZGOb5weIiT+EyY5fln2LRdevM875yXaXsufGP7/QNL97aSdpTFY9vb28fO9rYZDvzRb/0I/+Sf/bPOG5R+pY+GxUQgKuL6ysOG3QYLx7z5fDmJg7/5Y1z/s/8H15Z+G+WL/xhvLkawep+4MMKssv0BMu/9Ef56rYGf5pYxsrCKkyeXcGZpAnNjAQz7HHB27r0n4ebNm/j3//bfwef34fs/+AGWV1ZMBM/ziipidBiHRK5evYpSsYhTq6tmroUZ3U97n1h+xAyLyfmiuA7yfAsxQy6cLO4Mi7E9/TosZpB9rMm+soNB79Ui++nxes0c271DlIMeeG+55y7lfNja7TWTQHrl8mV869vfxu/8nnou/U5fRYvxRrFwASoxkDa5tiyoiEOTwcH6LjZupmFdOofJs6cwP+zGsNsKt9jR9iXYyWNpNtCAFXWbfE89g8zWGvZub+IgU0aq4UTTG4ZX1MXzhPaXE9gffPAh3G6XMeSMkGJk1rOGbeTQAFdM5M12sH8gxtCF1y++brLyGab6ND0pBg1wnoel4DfEcyrJvtCb62tj/AXQC9iWHjFrd7FNhIaaIt2PbeJcl/FcZF8/eP99ZOXapCCyHhmvSXowXYE0i7oN6Mb9727sAGSyGRO1yQhQziuePXe2c0SUfqV/xIVGUTYjMPzZqqFZzqCSiYpLnMWdlBfhk6tYPDmDcb8TAYcFnJY3ppT/k61lsaJld8MuRtblaKGZOUIlnzFhzBWbHzYRl1H5bNj9WQPMaCG62wzr5Xg2L2D2Co/kZzKZxNqt27j08ceo1+qml0gDz4W4WMere8FzUSc+xxub29OAvWuGZ2+Jgd/b3TMhtEyWfOXVV8yE/tMUFsKbnMLCbUcEjjf++MTEU4lMe1YwMGJjfR23uHaKHFMGQwxFIkao+7FN3Q5GN1Of54AReyz1w3kXXntd74U/B3Xrijvbweuea9ocyb3JgAYmlJ45q+LS7/RXnstd4yheCPNdsnEUDrdxkLfhyH8CU0vzWJoIIuy0wcVcl867qSzmP6t4PA4PnP4R+MMjGAk2EPIB1ZYbtaZX3uHHdMSN0eBnI6lYyuTnb/8c7/761/hQPJQrV66I+32l44ZfMcNP22LQjaDEE9Jr3MR1+Uz7PZdxWVx1DlPt7e1iQowtF+Z6GrDHunb7dntfRBCZyDi/MG+G6Wjgnzb0XGjQ7mxtISnCGpa/zxudPebnNUT4VSmKuPB80iNjmPXk5BQmxifEE/CaBMt+g+JCY8vzz+sxHB4ynjSvha7HZTpnA7514WMOW6YSSdP5YyeQawmpuPQ/fdjdbEkXvYx6KY9SoYx0xQlbeAJzZ0RcJoYRslvgkmvvc6ZMvBarCIsjMIzAyAzGppewcmoBJ0+NY2LYA6+liWahgmb18xVv6YFcv34dH3zwAX4tAvPeu+/iXdnee+89IzgUFxoeeins4V669DHel9f4Ot/bfT+FhmPhTwtGzLDHSoHj/cf1Wmjcn4WwEN7oXNCK801chCwUDpsEv3uNwaDBvIlAkEs3j5rjGeAaNfKc5eFZus8VHmvuX1i8lW7WPr0Wl/v4RYp9hnubdUybeNzoM3FptSfmc3GkE+ICJzI4KDhQd/gwMeqGX1SlWa2jIT2ZZqM9qdxsymc432I2+b0hW0u8GqcP7kgEkfFhDEfE2/G54ZOe6IMyXKrVmhkeyUlPsNsjND9luzfBjj0o875cXl5rv4ev8/133yfv6TVsG70WiiCHBbgPHLahl8SlcZ1i4J8FNFxc5phJmgwemJ6ZeerzPE8bHjsK5YkTK2bpZg4vct6in9tEcYkMRbC4uGgqCoTDIi6dMOQXgkGPhHtB6J9oMSZB1vIoJA+QONiRHnoM++kajlpDCA6FMD8RhNPDsXA/xgKAxyFCI95Kg3JhtcHnkmZUisjGU6hYXGg6nXC3tlEUodrYsyNTjsDpm8SF1WHMTX62p//OL9/BT3/yE1OrqZAvSG/2U7+IJoaGneVVGGgQCgZNuRPTu6UB6hw9ChuX//3d3/tdXHjppfaTPYKnaG93B9ev3cCHH35ohqc4NHDx4usmO5v78izgflBAOebPNUYoLGY1yu6xGEB4LFnSptsmzlvQE+znNvE8cL+5cR+7Q2HHVVza0WKc97xk5j6//tZb+N//8T/qvKr0K32U51JGM7+H2J3b2Lh1G9fXothONZB3jyDoc2B6yA7ryDkERuZxZqSKkKuJSsMmQiJC4XBiMiQeS+YQO5/cQBIeVEJj8NsLIj11FBtBWFyj8AdHsTjpw2jos8aYOQOctE+lU6hWqu2gAnmeB8ZqtSAaPTTDYy4RrBMnT5rikIySat/MHQMk4sJx71dee830JnsJvSZGBl27ehXRgygCInDcD4rY5ORE513PBl4u914yNGqDKixdTJvaD+62ZdDbdJxQcRlM+kdcajk0Elexef0KPv74Jj64HsVOogKL1yM3eg0OMfKuEz/E9OpFfHMqi1FnBdmyFXlLCBa3F6cmG2hGb+OTv/gZdpt+5CdOIeR2IRLwIzw+ifDYGCLDQxj1ipdz34QNe4A04Bxm6yImUwxOu8QJF5L6T//xD02v9jvf/Y4ZjuBCTuzdMmmtY5qMQWKuQa8nt3lz/Y8/+zOTzMkliznPwpDoufl2GfZnCY9R95Jhe7vboGKEpbMRtqXfPQDuK89D13Ph/nIb5PPwKFRcBpP+8lwKh0jGDrF/EMdeLI9MqQarwy43U930Ku2jpxEam8VSIAePpYpCxYoSvLA43JiONGHJRbF35SpiNQ9y/hkEPB4MBX0IDgXFa/HD63XBLXbjSQeRmFPwb/7VvzaT2X/3Rz80Q1EM/3za0IBQ9Lj64x//5z8yUWJnz50zkTInT500RRaf1ZBYF+4PjRovGxo0I7B9bowfBdvR7VjwMTsG3Pq2TbKPPP7FUskYXR5/j9vTztDnUF6fBiJ8FVRcBpP+EZcnoVVBs95AtW5Bo8XxZhtcTgtsIjio5lGo2lFseOB2O+BxiQH8inbieZV/odFjhNq63Fh/8T//wiTMffNb38JLL79kkiaftQHkpcLABYbvtnN+PCZSibkVg9pr5jFmFB6DJPiYniA7EfRA+7FNPAfMb+IcINfTZxh4JDJs9tuEIt8zX3hcUHEZTAazy2lxwGpvZyK7XVzPwtrOSbA6AVcIHp8fIT/riH11YXmesDe9tbWFDz/8yBg6ZiaPjY8Z4/c8etbsMdOLe+edd/A3f/M3Jh+INz6fH1SKxRJui+H65S9+gb/58Y/FiK2ZoA4e+36E4lKpVo03yzwshsYz8ZdLXXc9SkXpBwbU9LJH2c3m5Zhz+5n2/zlMY4PDTk/GPDmQsBfN3jSHwmhAWBlgcWnxuZWeITRc7DHTAF+7dg27O7uDv4a+GOrD6KEpY8+5NVZAYDHIvhUX2bhv3SoRBRH3arXSFpbO3J+i9AODKy4cspCNPXr+9/nn278OImZMvVg0JWVYP4zZ8IxE4wQ+S+o/q6TJzyHiQiFpNhvtjdWoB7ynTIPMNrA9PO6mTX1spHlJM/GTw2BMoByVzgY92W7ZF0XpF/Rq7DNo6Fh5mDXNWJIkm82YuR7WEOMKfDQkz3oSvwtDtBlEMD09Y7LDR0fH2vMtA2zUOLcSiQxhZmYWCwuLGBqKdNrUnz0TdqYccv55Hhg1yCTae+e9+nGeSHkxUXHpMyguTNrkODrreHF4jPXDWCAyEAjeNSLPA/aMmSh69uxZsxogh+k4XDfIPWaXy2nyks6dP2faNDMzYzxDsy5Kn3JXXObnjbjQq32hMvSVgUCvxj6jVq2ZMjQs0EfPxSFicvrMGUxMjJvKAM/TgFDUOAyzfGIFZ2SfZqW3P+jlXxwOpxHuEydOGtFkfbF+NtQ81qwUQW+WpXgYEs85uKcduagoT4qKSx/RqDfMJD6HxDhxnk6lzRK2J0+dMobE4Xi+BoR/m7169pojwxH4A4Nd+oUwp4XGOTzUbtMgVHjm8ea8C0WQnY9uXo6Ki9JPqLj0EeVKGelMGtHDQ1OFmQZjZHQEc3OzZgK3H4weI5U4VMftOIS+tifz221iYdJBaBP3j/vLiDFGtvEx2zDo50I5Xqi49BH0WjjXwnXxOe/CqsNT09Pw+wNGWJ53z5TGi/vFEFiKH/d30AWGRplLRTM5NJ1Om/b1c5u6wsJzwCRKerjMNaIwqrgo/YSKSx9BgxE9OMCBGA3CSWZWP+6X4Q4ar+4+UgC5Wicj2wbZqNFQU1jYpt2dHbMeDw11v8Jjzf3jsWfW+s72NlLJpPFiKJSK0i+ouPQBNAosQcK8lqPYkXgERfi8XqysrGDiGSxf/LhwP/f39szKm1wsbX193fT6B9mocVhpe3sHn1y6ZNrExNCyeC/93CYjLokE1tfWZN9FXMSLNEsGyD6r96L0CyoufQANHIfDuBAYPQPmXrB2GZPkGBXULwaD+5Ho5N+sra2bEiTc90E2aDTUrN+2tSltur1mHleqtb4VFx5rblXZbw5LUgjZhmajwRc771KU54+KSx/QLfNyeBg1wzRT01OYnW2H+ZJ+igKy22xwOpxmbRuHfbCXOCbcf7vdBofTAafLZaKw+Fy/tov7xc7HyPAwTpw4YRIpGY7Ma0UjxpR+QsWlD+CYPydn+dPusJukPk7kP69M/IdBw8WEvampSTMXRO+KobCDbNB4jLkePY85DTVDkh3O/g2v5n5xn4ciESwuLZmgD4aGP+8cKEW5H70anyOfmWuRjdVuOQxGQ8d13fvNWHB/uG7/qdXTZhVMVmk22ewDbNRY8YDDj6fPsE0XMDU5CberfxNDu+LC5ba53yxkygXk2A4VF6Wf0KvxOcKQV85bcOlihsDSQHCFSyZMMq+l34wFDRsLZ7IcjQk2mJwwiXz9aogfBzPEJB7YwsKCGWbi434vpcJ9czOZVTwuCgu9ln4IVVeUe1FxeY5w0aed7R0RmAPzO4c3xqUnyl5pPxo3Gi/WEutm6NOwHZ8M/SEj7FzKuh+SVR8FjzevDx57zhHxsQqL0m+ouDwHutFVhWIRW5ubiMWOzHDYxOSk2dgT7VfobdVrNROhVG/UBzpSjHD/2Sa2hzk7g5AUyv3j/tLbZQiyZugr/YiKy3OAhqBULpm5FibvlUpF4w1MTk6YMXQOj/UjNF5cnIrhuoeHh8ikM8awDbJRo5h0573YJj7u5zZxvyjuDP7Y2dkx+8zw9X5e4Ex5MVFxeQ7QoMWih+31WsSY2e3tcX8KC0WmX4dluFBYd50ZLg18IMJ4HPJcmO3O5aSZ8U7h7OeqA9wvs8yxHPtPuMzxzZtm9UwuLqdJlEo/oeLyHGDPmEmI169fN14K1+TgYmABf6Cvx86bYrjYU7518xauXL5iSo9waGaQe8wUEorkzRs3pE2XTXAFh5r61kjLftFzYR20bRFEigw9F87fqeei9BMqLs8YGq1SsWR6yesiMIy+WlpaEs9ltK/nWgj33dQWi0bbtcUSCbMGfas1uEaNQs8hJgoMS7+wtli9VhcvrU89l87Phuw3hZGeFz1hCj+FR1H6BRWXZwQN811DFj3AYezQ9PrpsZhEuKFw3861dKFXxWxwVg+gII6PjZt9tvTxqo1fhFnmeHgYs3PzJimRUXB8rq+XOZZjzsCPCxcu4MTJk2YBt+46NBo1pvQLKi7PCIoLh1tYQ2xrc8sUfAwE/MYwMNOd0WIMLe1nGPLK9WWWlpewurpqkj0HfyVKh5nrWl5Zwerp0+Z8OF39W3WA+0VB535yhVIKIufrmMza7yHUyouFisszwgyHiaeyt7tnJmFp1JaWl8VIjMLv95nf+x0atqFw23NZWFrE2DgN8WCv3W48l0jELMhGb2xYvJh+TgzlflFE/NIZocBw3+m1GG+rT/dZeTFRcXlGMKoqm8masf29vT0EgkGTET4cGZae6GBkuXMf6WHRoHE4LxgKHYskSr/fb0SlLfT9v3QzxZxDYxQVeo4UFk2kVPoNFZdnACdduVpgPBE3+RTMpeAE/srKCVMIkpWGBwW7GDIGHnAYhsMzg+y1EBpkGmcaabZpEDwAesHczER+s3k3SozPKUq/oOLylOENzxwERlYd7B8gJyLDEirjE+MmBNnr88JqG5zTwKAEemGcP6JoDnr4K8/PvW3i43430jzmHGJlODKj97r7rSj9hIrLU4aGip4KE91YVp+9zZmZGVNdOBAMDNRY+d22xGJmeI8rIFJg+t0YPwoaZRrobpv4uJ/bxP1inguXNt7c2DAh4RQZzdBX+g0Vl6cMb3je/BQWzrW43S689NJLpqT+oMG2HB5EceP6DVy6dMlktR+HJEqem+tXr+LSRx+ZZZxZmqdf28QqCfRUuLjcr955x2Tpc5857DoIXpfy4qDi8hShgWJPOH4UN8NiFTHELO9y8uQJMyk+aLA9LI/CHvOtGzeMURv0HjOTQI/Ea1lfX8eNGzeNB1Ot9HH5F9nqrIcmYsJqAixdw5VMKZKDfB6U44eKy1OERR4Po1EzJFbIF+D1+kzi4eTUlJk8HkTyxQISyYSp5JzJZAd+rJ+G2gRbxNmmmDwuoFHv78rIHEZlYAXXdHG53Ca6TaPFlH5DxeUpQq+F67VwlUmxVpiZm8Hk9JTJoxhEaLzGRhnltoLTp09jZmbwkygZ8TYmgs+wcCYlcriynxcL47HmMee83esXL+LsubOms8IQas3QV/oJFZenCCsIc54lJyJDg7C0uGgm8gcVGlwurXvu3Dm89vprJgl00Jc5ppAwKfT8hQt4/fXXMTM7Ix5B/65Hz/3iPrM6wusXX8eZs2fNNcX8I83QV/oJFZenACPCKCz0WBhRxaKCwXDI1BAbxLmWLuwVM/lzXIwZe87D0pZBzwznkBJzjRgWTmEJhcKmTf0MBYYJlEz85L5T4LtDY4rSL+jV+BRgNA8jkDiGX6lWTC4L64dxbXwOXwwqFBEaMq7vz8AE3wBks38RNMimTaGgKcrp9bZrdPVzm7hv3G/uJzc+HuRzoBxPVFyeAsVCAZubm8Zz4c3PHubE+PhAC0sXGjIKCieU+90IPw7GUNs6ber0/vu9TQw2YHQYAxGYoMvH9JY1DFnpJ1Rcekj35mZZ/e2tO2auhQUGJyfayxf3+3DL48AEQ3pmzG/hAlXMuxhkeM7ubVO/Vx3g/jJCj1FtR7EjpJIpIzCa46L0GyouPYS9R/Ymj+JxE37MRac41MIJV3ov7BUPMjRejIBjeDUzwzmvxF7zIAsMjXImnTE5I7udbPd+rzrAfU6nU9je3m5XFZDOjK5EqfQbKi49hIZ2d2cHu9s75jHnWlg9mPMt/kBg4MWF4kkD/PHHH+NXv/oVbt26hUJn7fZBhR7LnTt38OEHH+BXv3zHZL6XSsW+NdQUPV5bh9FDXLn8CdbWbpvhV3MedGhM6SNUXHoIs9Vv37qNO1tbcHs9Zr2NEdkoLMdhwpWGi1Wd29nsN0yYNY3zIBu0WrVmAi/W1tZw4/p18ThjqJT71xvjsaaIUADpOXJZZg7n6bCY0m+ouPQQ3uRXr1wxPWEOhS0sLBjPpd+XL35caLzKIqAc+uN8ElfTbA54b5keCgWSbeKQX7ncHl7q1xZZ5D+b1Qa3y41gMAS/P2DyXgY9ak85fqi4fAm6hqd7M3OMnmP1HLePJxJmmIiZ3hQYhu065MY/DnBYj+06deoUzp0/j7n5+YFPouSSxsxxWT29ahIpJ6cm4HL3d4a+qSog5+HM2TMmkZUh7jwPxyF6Tzk+qLh8Ce69fdnLZbQOly/e2NgwvXhO3jM6zCxBS+MrN/1xgMaLSwH/na99Db/5ne8YgeGQH58fVGiUV06s4OtvvYXvfO+78viEyXbvW3GxirhQEKcm8fIrrxhRpOAzqXKQz4Ny/FBx+ZJ0e4gc/6a4sFLw2u3bJoN9YXHRCIy54Y+J10LY5oCICYWTvf3w0NDAh1fTINO77LbJeJp9XnWA+8xrK3Jfhr56LUo/oeLyZZB7mB4Kt0q5bCZVd3Z3cHCwj9GRESwvL5syIlwb/7hBw0tjxt69u1PgcZCNGvefw0w01mzTIC3dzKPePfYqLEq/oeLypbC0haVSQTaXM6GgXFeDv3O4ghP53Sq1itJr6C0zCCGdyZjACnZwNFpM6TdUXL4E7CWyGCUXaaKwHBxETe4Bo3fGxycwMjpiqiAPSg/4STDZ7KWSGQo8Dkvr0iBXa1UT6dctpdLPbeL+UlwY2Xawt2euP0a6cdGzQT8XyvFCxeVLQHFpMLNbeo6MEGORSofDaTyWsbFRM7xid9jp4BwrmPvBbHBmhXOdGq5K2e/G+ItoZ7u3l6Fmm/o9Q5/7xTX006mUCXnnfvM6ZIg4z4P6Lkq/oOLypWjf4KlkEvsH+yIwB6ZK8Nnz5zAUiRzb8W+GWHPd/PfefQ8/f/ttXL923fSaB1lc6LFsrm/g3V/9Gm//7GcmMIOFR/u5TTURRC7lsLW5eVdc7pZ/6VNRVPoPdlT436OR1/m+L3Fdqbg8CR3RqFZryOVypueeTCTM+PeoeCwnT5400VTHFXouXN749u3buHr1KnZ2dkzbB1lcuqVUWMrm6tUrpm5avw/38Tbn0Bg9LHZy+JjDtIryxVAo6uKxV00likpFHsul8/mrne+T60o6Muy4VCtVVOUaa3RefRxUXB4T3rrWjrhksxkccG18MbQ86ENhFqecvLtE7rFF2s95JJvdZhJD7bZ2pNgg+2nce7bJbrPJZodlAObJnA6HKS20urraDnsfGdEkSuUxMN0StBoiFoUc0rEkUvEsio0m6p1XP6UlwiLiI+/LHSXkfSnkRIHK5pXHQ8XlMeEt271xk4mkKeDICDHe0HPzc0ZYjuME/r2w/WPjo2a9+TPnzmJmdhYerqE/wO1m6DFX1jx56hTOnjtnqiq4+jgYg+eA4eBM0F1cXjbngEOyxzWA5DhAT5g2g/N5HIbtrVfcFK+1Ll5s2xOpVikTD6bVqKKWF5GIx5CMJ5As11FoMaJVOljm//ciz1la8v+afC6Pknxub/sI0UQJZRGjx2mBXo2Pwz1HnRPALKnPkvP0YHwBP06unjIRYscdCunS4hK+9vWv4zvf/a4plzLwGfreTob+N97Cd7//PZOhzzDyfhYXJkwy2ZNJnyOsuC37S8FRcelPGHxx/do13Lx+A7s7u2aOjEOZXx1+RwmVYgapRAKH0RQSiTxqYvw/Twu1kngre7uIbmwjehBHxu5CXa4jl02uqc67PkV8ermvnS4LPL46WrUUtj6+jY0rO0iWavJXxRbK9igvRq/Gx6DrtbAHwsWZqPqcyOZqjCMjw5iV3iMzpY87PAZBaSe9tKmpKdN7Zs+fzw8qNNTs+dNjYZv4uN8z9LlvPO6c3+smfh7nnCqKZvd8cGJ50C63Wq1uKm/fvHED77/3Hn79zq/wwfvvm7lLPl8Ub+bL0KxmUYrexv7tT3D98mV8dG0TV7YSOEhXUPqMdokMNI5Qzh7gMJbA7lEZsZzNRLgGvFbYeTxrBZTTUSSiuzjYP8DBUQaJXB3FpgsWuxtuSwOe1DpKh5tYj5dxkG+av/EoD8b2+0LnsfIQEiImH3/0kREXDj8wx4Cl2tljpLAsr6yYMW8TfXHMN8KbvXvDP+g9g7bd26YHvd6PG4dW7v2d3Pv7cdoYNMIO3eHhoTHGHAo8c/asafP9x6GfNsJ7JB4/wvWr18zS53dk29vfv5ufxIASwmuPHYTu58ijOzgtNIox5Hc+wdbaOm5sHGE9CeRaLAsUEtFwwS2qYb6hWQEKm0hG97C5lxdhcKPijGB+NoLJkBPOVhHFdAKJmIiL7Fcyk0O2Ip3plhMtm1s8mxbspRQa25eRqjZwxzUPq8ONkMsGj3g98u+BWKQxn7ZGeSDscfz7f/cHZsx0embanHT2Fjkkwaq0q6dPm4n83ri6/c39F7y5eAb8EhqUNnE/ebvSoDJisVIpm/L7DqfDeGBdwT8OmLbygbSX8xRchG/t9prp7XM49rvf+64xxoyY61d4PugF37p5Ez/+q782EYmJRMK0jcOanOtjRQ8Ob3YL3bI2IT1SLo/u/IKlFBrpNaSv/xiXru/hwx0bdqwnMbywih99YxknpgJi/DviUs2gsfdzbGwd4IMdN6JYgH9sEd97LYKFURGe3B6298q4c1CDtZmSHbeg5hqHIzAl+xPBTKAEf/Y6Uu/+Kd5NhvC3/t/C2RMz+PpKADMhuxGxB6Hi8hjcloviP/3hfzL5LKGhEDxuD4JyAbDUOS+Mcdl4ob8I4qI8P4zBbbbX0C9IrzcjHjQjx7jiKT1qDtMagZH3DvpN3TVXbAdDYWmUo9GoSVrmUg/nL5w30Zv1Pr7nuH8O6YSyoO1Pf/JTrK+tmQXe2DlgZ5QCw2HYociQERYuozA9PY3pqSkjPBxqd3eiAB9EM7OBwo2/wEfX9/HujhN3bGcxtriK//Xb81ie8MFlbR/HZimB4tU/xa3NKN5PjCLhewmRuVP4++edmA5G0Tq6io/XgMvbHgx50iJsFBexaf45+IPjWB6uYKR6HeVP/jP+et2B/zfzG3j53DK+/8oYFsc88DsfPLui4vIYbG1u4f/7kz/B9s62CVllkUNeGDz5HBrjBWBufD2UylOE1xgNk1k/KJU2QysUlWAoaOZeaLBoiI7btchOW7fkUKFQlN60dOxGRu4ej36F+0fPhcmu77zzjqlsUZT95z7zNW5t78YOj9iU8YlxnF49jVOrq1hZWbm7HhQ7DXzv5yjsobH517h0K4Z397y4YzmNycUT+EffEo8o8Gm18nr+EIlf/t+4sRHFpfI8chNfw9jyWfzWiQamXeto7b+Dn16y4JdrQ5geKWN01AWrf0Y8lzk51mNYGaliuHUTrbX/gj/7qIp/f+08Xnn1tHhICzgxKwLperD4qbg8BryJmZW+vX3HFKqUg2YuGtNbpNva6S0qylNFDAwTWTlBzIijZDJhhk44jMIOj0t6yVw76DhdizRONFFc8ZQiw433HIel+x0KAveVycYffvgh4kdxM390r8nlY6vVJu1xmFVruT7P6dOnTWj8zMyM8WjYaXhguH/hALgj4rIWx7u7Ii5WEZeFFfzOt8Yx4v3U4Ney+9j78R/ixuYhrjaXUZr7JqZOvYQfLdYw6d4CYh/iZ29v46e/zqEV8CEwNYnh+VOYnF7E9NgI5oJVBOu3ge0/w39/J4N/88sFvHTxHH70vVM4NT+EYY/YwM7fuhcVl8eAY76cTGTPgz9ZHoS1xXiz86DqIVSeBTRWvNZoYNmL70YsMpiExtbMu/Ca7LzvOHF/z30Q2tcVF+bEffzxx6YSBM8b970rkBQOjnywozosQsIhv8XFRSwsLpghd5aT4nvo4XyOwj5ad36MT24fGc9lSzyXqYUTIi5jGPF9Glxczezizl/+R1zfOMQNywnUFr6F6dMv44eLDUz44kBmHR/95Fd45+2r2KoGURtexPjJcyZE/9TCOBYCDQRqG8Den+PPfp7Ev/7ZJM6/cR4//MEZrC5ERMgcDww7VnF5DOjGMlKMvQ4KjSlvLs/dPXAvwiG0tCeL2YOyyn0u5svcJDwOLD0y2IfANKjTvk6HodGJQmq/4TnSFgvuVxv24pumc1MTkeFrHArrTuabd/GnbDxnbbHht/Acyblqts9V/932nfbJzlo754A7av57wK6a/Zf2dd//6eHh+2Uz7eSnnx+8Vzgntra2ZuZcWDLpYH/f2A8OY3Iyf3Z2ziRhz87Mmlw5DrMzd4yvdzsN3XP7OSguW3+NT9YSeHffh23bWUwtnsA/+dYIQpxw6UBx2fmrtrhcwwqq89/GlIjLj5aASV8RyKWRzCQQje0heusydg4yuFOZgGX4FKaXT+Hbp/1YDoqXtPM/8N9+nsK/eXsaL70hnsv3TxtxUc9F6QENtOoN1OXGbcIGi40lYHC8kqVMp+FeY95HGIP6BPvVkk6QCFGNhrZzvhxyvvqwZZ/FiKD87HRkHo20zQyXMWucQipCa7c+NDz2ecCE67/6y7/CtWvXTCg1BZ+T+LPipSyJl8Klw+cX5hEIBDufeEyKHBb7MS7dPMCvt+xYa5zEyPwJ/G+/MYuFEY+c8Tb13AFib/9fuLEZxaXKAvKTX8f4iZfw909aMOXJo5U8QtruRlJEr3rjL7F767Z4QkEkXacQWbiAf/DmMM6PRYG1P8V/f7eIf/fxKl557Qx+9BtLODkbxJDrwavtap6L8nhUs6ik9xHb25ab5QDbhxkkSy1UbT64HBY4BlphWKCvjHI+i8R+HOl0HnXpNVI52azn27QaaqU8svEkMskccqUaGhyDt1kfkFXdplWvoF5Io3C0i6P9HdzZjWE3nkeiQOFkb9om3k7HO+grypwgQCIaQyKRRbbSRIXBYCIYdu7v/Ttcz6CejeFQvIH9vUPsH6SQyJZQqIrQsMcvIvOwY/QsYQVrFkTl5PzJUyfx2sWLeF228+fO3V0S3ePxPjQq7KE0xOso7SF2EMPmdhx3DkrIVSzwcol1nwdhd2cuuFGFNbeJQrmGo1oQRcc4XN4QTo40EWzuorn3K3xyK4q/vSrXWSqGivRhyo5RuELTsm/jWJlwYtiaQmv7A6zHbbiO85hbmMapuRBG/U44H6LkKi7KFyB3dyOPQvpIbvpDxA6PcCSGLp7MiitdRq5QZ4EuOLxO01Pqpx7jYyG9e+naoZSJIRk9wMZGHLFsHY6xCJxuBzhtTHF5Ls1q1UTUj5A5jGJ/O2bqOuXqIuRhvxxyOz5fIpWDEHU0KjmTFJeU83UUS+AoU0C2ZkPN5odPzpPf3S062v7U80VclGZZ9lnERHr1sYM4UkURFThgdbjMsJBTei72z3kx4q3IOcvFD3B4JG1MFZDK11Btiocmn/MGPHA5RZTknc+7mRxSr9fqpsDo7NycWfeJk/VMZWAwxt3AoCc9Ibx2GyKmogbFugstewihSATTcxMYDXvvioul1YCtkURRLqdE2Y1qyw+3y4OFSReG3CLoObm2cjYcldxyfdjhC4bhDU1heGwS42NDmIlY4a0mkLh1FTsFHxJjr2BxYQwr4yJgHpt0LB+83youyqNplqQbI4b3KImDwxwy+QLyRRayyyAVS4nxyqEuF6NtKASfqAtD3p/3zfxEiGGr52PIRLexf2cb125nECs5MLQ8iYDPCbfYawrmc2lTvYh6ahNR2a/19Rj2U3UULW4EJyMIeBxGXD67X9IRaObFAxMvJxFHdD8lnYASyi0LWq4AHP4IwgH5vIfDY/0gLiIsDRGWcgrF1AE2b+1JDzyLmi8svWZpo98Lv7TTLeJiEwPW3l8KKEOQK8gdbCO+Lz33TBEZMbBVuGFzeeGVz4VC8pMemnn388VqsZr5E0Z+RYYjJoWBv3frwT10TuWL4Gfs0v1xhuEOjmFkfBJzsxOYnY5g2H9Phr5F/FV7HRUR3oI4O426DS6HHePTITnGHD5zyHeE4BahiwyFEY6MY3h0AhPjw5gYkevFVUMlm8TujW0krMNwnXoJi9NhTIecCMgN/7AO5UAPZijPAI7zsxCexQ6rOwBPeMT0jsI+Ozz1DJqJHek15nFQEA2SjtRgzeDV0awVUCpmTPWFeFy8sUQO+VwRFWmzNMeYsmcP/2oNjWoWmWwGiUQaCdm3TJrCXkG18ZB1NRpVtArSQ01GpTNwhGi6glRDDG5wWAxGGCNBF/wue9tQdz7yPGk166aYYv4oijhX1UyVcYQArCIugaDflDDxiPfxGSFscTImJ30C8cqiUezsppEqWNCw+eBh7tlQACG/G275TD8IC3G5XWboi8LCoTF6Kk88BPYgrCIKrmF4h2cxNb+EkycWcGJxDOMhtwjrPefYKv6bbxy+yBQmRocwFbYi4hSPp1BBouJEPTCD8MQ0FmfGMDU5jTF5PDkxholhD4a9dVhqeeRKDaRcC3AML5rs/5mIEz4RlkfNiam4KI+mZRNT54bTE0JwWHpHUzMYZwbxyBBGvBb4WjlTHylbEVPN+35gkJ0Vz6BWyaFQKiJbrkkbWqhXeDOJ6HQijbrbM4UGVISlWkwjW6ogU26gVBGxq3GIktF5D9mnRl28sAzK6SSyIpapUh25lks6BUH4/AGEpTfrcUlvnhbhuVtdBoeUUMklkdw/wO76HuKlFsr+Idg4FCaWyWZKvjPOrQsbLsegnkerdIRUKo1YsoxcWcTF6obL55N2euETUeI8QA/Md0+gkFBgGFL8pYa/HoocJKsHTm8YwaERjI5FMDYcRNBtN9n5nyJHwkbPZARjY8OYHvVixG+Ra72GfMmKumsI3tAwRobDGI4MYSgs3kvIJx6uDW5rDa1qCdWmFY2RFQQml7AQ8WDMa4M4wCouylfAIr0jRxi+8BjGpicxNTeD6dlZ6dmI2zwSxljYCa/T8um8xHM3Wo9Js4G69JpL+SwKcpOVLE40xTPzusTVl5vmIeWSngmtVg3VfAqFbBq5pg1Vhxd2l1t68eIt0k48ZN8YFl4vV8UbKItoVlATz6Aqz5UrjKaSz5mJ/C85BNNzquI1ZlHMHCG2G8XWRgL5llV6xj40ynJekglks0XkRfTpEX/ab5FHjZIYvCwqtaqZR6hyNUWuyMkoRitVSdopbRyUS/GrwnaaEPrO8Nrn281npIPoCiEyOoKJqWGMjgbMfGKjWkeLId3iBdkcItBy/buNt8hPSQdLeoxN8ZRtLhGb+RWMzs5j3ONEUF4X5+iRx1jFRXk0Vhssdg8cbukVej3ibkvvVy4up1ue8waktyg9nYAbYhPgEKP8qIutf2jIDVNCnhPd6TJKVekhS2/ZE/LIzcVxevaQP82ReHZtogml0S0iE89Lz7yMpt0Bh5+9cjnmDLHlDX/Pvt1LyyJ3vNMv54WeihchVx3O8hHi67ewvbWLnUwVafHOTGjyg77gmSF/vCltK6dRysZxlMxiJy5CWM7DXo0ivnkN6zduYG3nCLvJEjL02u6qi5yNllMMqRi7oTAiETfcjRQqiX0c7h1g5yBtSs6XxSAqn8Vid8m1FEIgMiIiI55K2IewuB/2zjCppZvLZgSKP22iOeIZyT0eiLCOIj2j9lwWO19fdF/ohL7yaNjLZW/XXIByw7ZKqBVzyGXE+GWbKDT9GFkSb2YqiLB0Vb6oN9MXNIvSu0/jKJpBSsSlynY5WIajgfRBEfWWC0Or8wiGvPCLFbY/k16wGHzxpiz1PKqFJHa3MkhmanAO20QIa6jkxBOpys0uIh+aG0NQBMcvn/rMfsl+tkxnwM7OO+yNAmqpQxyub+CoZEXWNw2fdAzCbptZIOpRQxpPnWoS1cwB4tE9rO8WsX5kx9CYE6PuHBI3ryMalfMj11bd7oXL40FQ9rkd8sqNfWJne/jMXkMzu49MKolooiLi6UBDPjMS8SAgHQXtPd+D8VCc8k86UXIdcTKfARMPFgq55q12ERcOifvh8flNIIhX3J3HvW5UXJQnQK6qYgKVLIcsCsi0fKiGZjEzNYppvwNOeXkQbuZmZh/F6Cb2jopidBsoWVqoV8uo53KI7WRRajjgWZiB3y+9Y2sLjs+FwT4FWk20arIPiTvI761hI9FCvC7H1FVDmetrHGaRL0oPXnqSvvERMQyyb2IV7j3epsdpE2Ph9MLtC8EfCIpXaUfEk0e56cZeNoBhsQ7jYfHSnGJ4n6e6lBOoZWJIHCXFo3IhapnFmQureG11DKP1AzkWRRyUPKjDBbfLjdEA91lay86OxS7tlF64OwBfUNoY8cLjEqtXbohoNU30lX8qIsdAPiN/6jm2sk/hMaRn0j6cX4h5b+f9naceBxV25bFpNcqoFBiGXES1YYEtFEFwZhZhn/Qu5XXpLA8EzUIWlWQMRfHA8tUqcqUq8iKW+WQGxYI8VyqKR1NELi/eQoPVCJ7+EIsZ6hIPpZ5NohzbR75SQrbZEg+xhHwqh0JW9qtQQK5YRCZbRrEkPfb7d0t6plYOfXhD8EWmMbq4ipXzq3jzzVksTLjQiGdRyxbBKgvPdVyMf5qVEBiFKFeNRUTCwf2dPY3FhbO4cHoCJ6YcsInAFMVDLmREdO+Oi4l5kx61xSHXnG8IobElTJ1+FafOruLERBAT9grc5TSK9ToK8u7n2MoXHhUX5fGoi1EqxJGX3mHWEkYjOIfRsTGcGnfA7+Aa2xVjMAaBlrj6FpcfTjvgbBZEbNJiwNJIiYeQE2EpiGHPMNO7UEVdDOAzs8MiDi2nD/AE4bHW4KomUcqmkM1kkBVRzxcLIohlEZmKiR5rfmE3UuTe7YI9PITAUBhjQR8C0sO3c3jksbqsTwn+abuIiuyL1SUiIr/ba1URPQZ/yy9ejvP7xRtxw2V3wsEJek7UPxQf7O4QPKEQghE/QiEXfHYrszeU54iKi/JoWg0TmZM/3MLO2k2srW1hbesA2wdHOIzuIxXdxu5hGrupBko1scID0FW0MKEwNI5wZASjkRBGQm4EfU64RG1sFkYasQS6HQ7Hsxs66g5pWaU37hqewchwBJNDPgwFXfC6HcbA2q1tI+uwW2BvVdAqiaclnkwyJ2JTraFaLaGUEzFKxJGIHSIel5+pClIlF2yeEMYnQ2J4uajYPXkjzwu7B1YRUZcvaFZMHGqlUM4nsJfLI51tmWE8byCAYJDDYQ00qnnUykV5rYh8JoVKOopkXK7BeAJJ+T2Zr6EmwuzsCGmQkXXyZ553M19ktHCl8mhEWBrpdWzcvI0bN3exm6wgW5M+idsLj8eNgPQWHaNnMTq1gFfm3BgJiEHu8zu6WSmIoRIvoFxHpVZCrZlBLnmI2E4MV95LoGAbwcr/8h2sLE1iQQwfe8FPPzSZw2IN2bc8qqUCcuUWqo2SPH+E6MYeNq4dIV4QYRiewtLXzmJpzIbJahx7WQ+OagHMTEhvHXkUKfipLNLFBqqeAOxOGwKWAqrWCMquWcyM+jAZ6cy5PM/z1Mqjnhfx29/F5q19bGzm4Dh5BuGZUQxFP0K5WEfUtQx/MIDxkAOjHjk24qpF8w6EGjEMNQ6wlvMh3vAi5GN5GK4/b5f2+uALhjAxM4yQx2HCbZXng3ouyhdAb0Q2q/SqOVHskZvX5zH1qVxidKW/DVOGn+FJYqwGoadocbjNvIQ/HMHQ8ChGRiYwPjGDqZk5LK4sYXl5BrPDfkS87QilZ2OEeRzF4Luk9x0Qwzg8gpHRMYzKvk1Mz2JucRGLS3OYnxvD+JAHAeYWteqm9D6H7tql9LmxCGfN5H1UxZOsNcW82obESIcxMS6GWDwBhzlvzxmLS9oagjc0irHxUczP0INpoSkeWM0WhiMo52SM5Uf8JijBZmmizorc9aapgEyPul6vircm76+3YLGLYAaC4rUMIRQOwGs3RU2U54h6LsqjqRfRyB8gdpjA/mFOetRcR4Ri0zGGIjj2oXmEh8ewELEj4JbnB0Fh7sLLv4x6OY98Jo/YbglVMXyRU7NmqIxDK88vUIFzWOKNZHJIxQooVEQUxGMMTYUQsJXhyMWxn3MhVfdjfMQFj0X2PRVDltFlxaZ4KuJVun0Yko6AN+CHMxiEx2Ez2dsPS8R8djD0WkSwlEMxlUA2kULK6kXF6oG7VobTJV5aaBheuZ481ipQKaEg3lyy5ETQkkYYCWxl7EhWuRKnG16feNI+P9z0qN0sc8NhxM6fUp4LKi7Ko+GcS71ieoiVKnvJ0ruUK6YtIPI/8VosDhbhE+PmsJj1XQYPMeLM2JeecbUiPX9x6J1e1n+6p/LAc4OeiAh6tYFGq328HU4mejI1vYR81YZK0wWvqU7L+bGCtEHOlXgtVYu0weE0htbhZPgu52zoaz7vNnXhUKB4X7UK6lXOG9VNFKIJp5bryeFyiufYhK1Vk2Mg56bO+nXM0amJ4FSQLoiA8nePeGPyXhaCtHcm/21y4vqjjS8uKi6KMoiwxlarKYJjFbFvVw0Wm9p5vt0BaLRsJlBgUASfEYdcwrnJaD5RB7s8107cbUfssU0taas4zGaoslHjPEwLVofdBF6omPQXKi6KMrDw1m0XdnyQYTV3trwwMEZXdtgYo8646gPbJNvd5zvvp4Aq/YeKi6IoitJzdMpLURRF6TkqLoqiKErPUXFRFEVReo6Ki6IoitJzVFwURVGUnqPioiiKovQcFRdFURSl56i4KIqiKD1HxUVRFEXpOSouiqIoSs9RcVEURVF6joqLoiiK0nNUXBRFUZSeo+KiKIqi9BwVF0VRFKXnqLgoiqIoPUfFRVEURek5Ki6KoihKz1FxURRFUXqOiouiKIrSc1RcFEVRlJ6j4qIoiqL0HBUXRVEUpccA/z8mSgh2kY/wtgAAAABJRU5ErkJggg==)
physics-General
physics-
A force (F) varies with time (t) as shown in fig. Average force aver a complete cycle is
![](data:image/png;base64,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)
A force (F) varies with time (t) as shown in fig. Average force aver a complete cycle is
![](data:image/png;base64,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)
physics-General
physics-
Fig shows the displacement of a particle going along X axis as a function of time. The force acting an the particle is zero in the region
![](data:image/png;base64,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)
Fig shows the displacement of a particle going along X axis as a function of time. The force acting an the particle is zero in the region
![](data:image/png;base64,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)
physics-General
physics-
A body of mass 6kg is hanging from another body af mass 10kg as shown in fig. This condition is being pulled up by a spring with an acceleration of
. the tension
is
,
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)
A body of mass 6kg is hanging from another body af mass 10kg as shown in fig. This condition is being pulled up by a spring with an acceleration of
. the tension
is
,
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)
physics-General
physics-
A granophyre record is revolving with an angular velocity
. A coin is placed at a distance r from the center of the record. The coefficient of static is. The coin will revolve if
A granophyre record is revolving with an angular velocity
. A coin is placed at a distance r from the center of the record. The coefficient of static is. The coin will revolve if
physics-General
Maths-
We need to remember different formulas for this type of questions.
Maths-General
We need to remember different formulas for this type of questions.
physics-
Two masses
and M/2 are joincd togcther by means of light inexcusable string passed aver z, fictiodess pullcy as shown in fig. Whcn the bigger mass is rekasod, the small ane will ascend with an acceleration
![](data:image/png;base64,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)
Two masses
and M/2 are joincd togcther by means of light inexcusable string passed aver z, fictiodess pullcy as shown in fig. Whcn the bigger mass is rekasod, the small ane will ascend with an acceleration
![](data:image/png;base64,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)
physics-General
physics-
A particle of mass
is initially at rest.
force acts on it whose magnitude changes with time. The force time graph is shown below,The velocity of the particle after
is
![](data:image/png;base64,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)
A particle of mass
is initially at rest.
force acts on it whose magnitude changes with time. The force time graph is shown below,The velocity of the particle after
is
![](data:image/png;base64,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)
physics-General
physics-
A solid sphere of mass
is resting inside a cube as shown in the figure. The cube is moving with a velocity
Here
is the time in scond. All surfaces are smooth. The sphene is at rest with respect to the cube. what is the total force exerted by the sphene on the cube (g=10ms-2) )
![](data:image/png;base64,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)
A solid sphere of mass
is resting inside a cube as shown in the figure. The cube is moving with a velocity
Here
is the time in scond. All surfaces are smooth. The sphene is at rest with respect to the cube. what is the total force exerted by the sphene on the cube (g=10ms-2) )
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)
physics-General
chemistry-
Oxygen has an oxidation state of +2 in the compound
Oxygen has an oxidation state of +2 in the compound
chemistry-General
physics-
Three Forces
and
together kccp a body in equilhcium. If
along the positive
along the positive Y. axis, then the third force
is
Three Forces
and
together kccp a body in equilhcium. If
along the positive
along the positive Y. axis, then the third force
is
physics-General
physics-
The Figure shows the Position-time (x-1) graph of one dimensional motion of a body of mass 0.4 kg. The magnitude of each impulse is
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)
The Figure shows the Position-time (x-1) graph of one dimensional motion of a body of mass 0.4 kg. The magnitude of each impulse is
![](data:image/png;base64,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)
physics-General