Maths-
General
Easy
Question
If (m+n) P2 = 56 and m–nP2 = 12 then (m, n) equals-
- (5, 1)
- (6, 2)
- (7, 3)
- (9, 6)
Hint:
The correct answer is: (6, 2)
![G i v e n space colon space P presuperscript left parenthesis m plus n right parenthesis end presuperscript subscript 2 equals space 56 space a n d space space P presuperscript m minus n end presuperscript subscript 2 space equals space 12
U sin g space f o r m u l a comma space e x p a n d space t h e space a b o v e space g i v e n space e q u a t i o n s
P presuperscript n subscript r space equals space space fraction numerator n factorial over denominator left parenthesis n minus r right parenthesis factorial end fraction
P presuperscript left parenthesis m plus n right parenthesis end presuperscript subscript 2 equals space 56
rightwards double arrow fraction numerator left parenthesis m plus n right parenthesis factorial over denominator left parenthesis m plus n minus 2 right parenthesis factorial end fraction equals space 56
rightwards double arrow fraction numerator left parenthesis m plus n right parenthesis space left parenthesis m plus n minus 1 right parenthesis space left parenthesis m plus n minus 2 right parenthesis factorial over denominator left parenthesis m plus n minus 2 right parenthesis factorial end fraction equals space 56
rightwards double arrow left parenthesis m plus n right parenthesis space left parenthesis m plus n minus 1 right parenthesis space equals space 56 space
L e t space m space plus space n space equals space t
rightwards double arrow left parenthesis t right parenthesis space left parenthesis t minus 1 right parenthesis space equals space 56 space
rightwards double arrow t squared space minus space t space minus 56 space equals space 0
O n space f a c t o r i z i n g space b y space s p l i t t i n g space o f space m i d d l e space t e r m s
rightwards double arrow left parenthesis t minus 8 right parenthesis left parenthesis t space plus space 7 right parenthesis space equals space 0
rightwards double arrow space t space equals space 8 comma space minus 7 space left parenthesis n e g a t i v e space v a l u e space c a n n o t space b e space t a k e n right parenthesis
rightwards double arrow space t space equals space 8
rightwards double arrow space m space plus space n space equals space 8 space........ space left parenthesis 1 right 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)
Similarly
![P presuperscript left parenthesis m minus n right parenthesis end presuperscript subscript 2 equals space 12
rightwards double arrow fraction numerator left parenthesis m minus n right parenthesis factorial over denominator left parenthesis m minus n minus 2 right parenthesis factorial end fraction equals space 56
rightwards double arrow fraction numerator left parenthesis m minus n right parenthesis space left parenthesis m minus n minus 1 right parenthesis space left parenthesis m minus n minus 2 right parenthesis factorial over denominator left parenthesis m minus n minus 2 right parenthesis factorial end fraction equals space 12
rightwards double arrow left parenthesis m minus n right parenthesis space left parenthesis m minus n minus 1 right parenthesis space equals space 12
L e t space m minus space n space equals space a
rightwards double arrow left parenthesis a right parenthesis space left parenthesis a minus 1 right parenthesis space equals space 12 space
rightwards double arrow a squared space minus space a space minus 12 space equals space 0
O n space f a c t o r i z i n g space b y space s p l i t t i n g space o f space m i d d l e space t e r m s
rightwards double arrow left parenthesis a minus 4 right parenthesis left parenthesis a space plus space 3 right parenthesis space equals space 0
rightwards double arrow space a space equals space 4 comma space minus 3 space left parenthesis n e g a t i v e space v a l u e space c a n n o t space b e space t a k e n right parenthesis
rightwards double arrow space a space equals space 4
rightwards double arrow space m space minus space n space equals space 4 space........ space left parenthesis 2 right 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)
Adding (1) and (2), we get
![2 m space equals space 12
rightwards double arrow space m space equals space 6](data:image/png;base64,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)
Substituting m= 6 in (2), we get
![6 minus n space equals space 4
rightwards double arrow n equals 2](data:image/png;base64,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)
Thus, If
and
then (m, n) equals- (6,2)
Related Questions to study
physics-
A thin uniform annular disc (see figure) of mass
has outer radius
and inner radius
. The work required to take a unit mass from point
on its axis to infinity is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALMAAACJCAYAAABn9Qk4AAAgAElEQVR4nO2dd3Ab153HPwRAgg0sINh77zSbercly7IpF1mO28U+XxInTr3kLrnJTXLnu5mcM5m7ZHxnO/H57MR2EjmOrGLFliUrkiVZkiVKIsXeKwg2ECBAEIUoe38ouxElSqYkNlH4zGBYsNh9i/3u2/d+71d8BEEQ8OJlESCb7wbc6rz++uts2rRpvpvhBa+YvSwivGL2smjwitnLosErZi+LBq+YvSwavGL2smjwitnLosErZi+LBq+YvSwaFPPdgPmkq6uL8+fPX/X9mJgYsrOziYiImMNWeblRbmsxm81mTp48ybFjx1AoFDz88MP4+/sDYDAY+PDDDwG48847efjhh1EqlfPZXC+fw20t5ujoaDIzM9mzZw9RUVGUl5cTHBwMwNjYGKGhoRw5coTf/va35ObmUlxcjI+Pzzy32svVuK3FHBkZSXZ2NqGhodx///0sWbKEwMBA6f309HSMRiNvvvkmTU1N3HHHHZPEbDKZMBgMWK1Wenp6SEpKmo/T8PIXbusJoNVqRavVMjIywrp16/D19ZXec7lc6PV6+vv7kcvlhISETPpsS0sLH3/8MW1tbXg8Ht59912OHDmC1WrF61U7P9zWYh4YGKCurg6ZTEZoaKjU0w4MDFBfX89HH31EdXU1eXl5LF++HJns4tc1OjrKb37zG9588018fX0pKytj7969fPnLX6a6uhq73T7PZ3Z7clsPM/r6+qiursZkMvG9732PzZs34+fnR3d3N4cPH8bpdPKFL3yBp59+epJFY+fOnUxMTPCNb3yD9evXMzg4yIkTJ/jv//5vfvrTn/Lzn/+cjIyMeTyz25PbWswdHR309/fz4osvsnTpUs6fP8/o6Ch33HEHDzzwACkpKajV6iusGEePHiUyMhKNRoPD4cDlchEQEEBBQQG7d+/GbDbP0xnd3ty2Yu7r66Ojo4OgoCDKyspITU0lKioKt9uNXC5HqVTi5+eHXC6/4rNKpRK9Xk9bWxtyuZzR0VEGBgYYGhrC19dXGo54mVtuWzF3dXXR29tLQkICycnJ+Pr6EhYWNq3PPvjgg7z11lt88MEH9Pf343K5aGlpobGxkYcffti7yDJP3JZidrlcVFVV0dnZycaNGyeZ46bDqlWr6O/v54MPPuCdd95BEAScTifl5eU8/fTTaDSaWWq5l2tx24m5tbWVhoYGPv74Y/r6+nA6nddtIw4PD+fee+9FpVLxu9/9joaGBp555hnWrFlDcXExfn5+U35OEASsVisBAQHeocgscNuJub6+nqNHj2K320lOTmZ8fJy2trbrXvCIj4/nscceY3x8HLvdzo9+9KNrbu/xeDCbzezatYuKigo0Go1X0DPMbSdmtVrN6tWrWb16NQB+fn6EhobO+nEnJiZoaGjgO9/5DgkJCaxevfq6hzders1tJ+a1a9fOy3HHxsY4ceIEDoeD6upqCgsLvWKeYbzPuTnCbDbz6aef4vF4uHDhAiaTab6btOjwinmOsFgsnDp1Co/Hw8mTJzEYDPPdpEWHV8xzgMViobu7G7vdjiAIGI1GBgcHsdls8920RYVXzHOA0WikoaEBl8sFXDTRtbW1MTIyMs8tW1x4xTwH6PV6zp49y8TEBAAOh4Pa2loGBwfnuWWLC6+Y5wC9Xk9VVRVutxu4KOYLFy54xTzDeMU8y0xMTKDX69HpdJP+393dzdDQEE6nc55atvjwinmW0ev19PT0XBE76HK5GBwcZHR0dJ5atvjwinmW6evro66uThovi8hkMjo6Oujt7Z2nli0+vGKeZVpbWzl16pQ0XhaxWCzU19fT3d09Ty1bfHjFPItcGhR7OYIg0NLSQk9Pzzy0bHHiFfMsMjQ0xMDAwBW9ssj4+Dh6vd4bZjVDeMU8i3R2dtLR0QGASqUiJiYGHx8fkpKSCA8PB0Cn03nHzTPEbec1N5e0t7czNDTEsmXLKCkpYWRkhB07drB9+3YAzpw5w+joKF1dXeTn5191PwaDAbPZTHR0NAEBAcBfc35YrdYpPxMVFUVkZOSkXCCLHa+YZ5GQkBBWrVpFcXEx5eXlHDhwgD/84Q9UVFSQmZnJ0aNH0Wq113QF1ev1fPLJJ/T19bF9+3bi4+OBi0OUo0ePUltbi1wuJyoqipCQECkIQC6Xk5+fT3l5OdHR0bdFIIBXzLPIli1b2LJlC0ql8govuYiICJ588kkmJibweDxTft7hcHDs2DF++ctfIggCd999tyRmhUKB1Wrl8OHD+Pv788ADDxAdHY3T6cRkMvHHP/6RHTt28IMf/ICKioo5CUCYb7xinkWmkzX0WvGCra2tvP/++5w+fZqlS5dOej88PJyHHnqI48ePExISwuOPPy4lnhEEgU2bNvF3f/d3HD58mPz8fIqLi2/+hBY4i//Zc4tit9vZsWMHmZmZPP3001Nuo9PpMJvNJCQkkJ6ePuk9jUZzW42XwSvmBcuLL75Ifn4+d911lzTpu5zz588TFxdHQUGBtFwuCAJjY2P85Cc/obe3l5SUFCIjI+ey6fOGd5ixwPB4POzZs4eEhASWLFmCQqG4ak7o48ePo9PpaG5uZu/evVitVlpbW/nzn/8spT+4//77vWL2MvdMTEzQ1tbGwMAA69atIzExEb1eP+W2ol+HaAnRarVotVr27dtHXl4eTzzxBOvXryc5Ofmq4/LFhlfMCwS3201/fz+vv/46ycnJDA0NMT4+zuDgIDqdDpPJRE1NDTabjeLiYs6ePYvL5WLFihVs2rQJuVxOUFAQe/fuJSYmhscff/yKnNKLHa+YFwgul0taQElISKChoQFAyhc9NjZGTU0N4+PjFBUVcfDgQdRqNStXrmT58uUAhIaGsmLFCj777DNMJhPBwcG3hX1ZxCvmBYJMJkOj0VxhuQgICEClUqFUKomNjSU2NhaLxcLx48fZsmULycnJ0rbR0dHcfffdvPXWWzQ0NKBWqwkKCprrU5k3vGJeIPj6+hIfHy8tiohotVoaGxsxmUysWbOG6OhoPvnkE8bHx0lMTCQ4OFhKwxscHExRURFhYWHs3r2bmJgY0tPT8ff3R6FY/Jd68Z/hIkAmk+HxeOjs7OSPf/wjv/jFL3A6nTQ0NNDQ0EBAQAARERHSsvYzzzzDa6+9htVqZdu2baxYsYLo6Oj5Po1ZxyvmBY5KpeLuu+8mJycHtVpNdHQ0//Iv/wKAv78/wcHBk6wVKpWKJ554gri4OICr2qgXI14xL3CCg4Mlrzs/Pz9yc3MnvR8YGCgV4oSLw5WcnBwSEhIQBAGlUnnbCNor5hlgYmKC/v7+ayZ1MZvN6HS66y6rJo6FRS79fSp8fHzw9/efJPDbBR/hNi9aNzExwcjICBaLBb1ej8ViwWAwYDKZJqUB8Hg8jI6OMjo6OsnLra6ujtbWVh555JFrTrJsNhvNzc0cPHiQhx56iNjY2Enby2QyAgMDiYmJmfQ5X19fQkNDJctEdHQ0/v7+REdH3xaTuuthUX8bExMTmM1mrFYro6OjWK1WzGYz4+PjjI2NMTY2ht1ux+1243a7cblceDwe6eel97kgCFL406W2W5lMhkKhQK1WX9PN0mq1MjQ0hI+PDzKZTHpdit1up6+vb9L/xO0VCgUymQxfX198fHzw9fWVcksHBgYSFBREWFgYfn5+REVFIZfLbztno1tezB6PB5vNhsViwWQyMTo6KgnYarVKme0tFgt2u136W3xfJpMRFRVFaGgo0dHRhIaGEhkZeUXJNJlMRkREhGQ1EHn99dd55513+OEPf3jNdhoMBkJCQti5cyfPPfccy5cvnzSWdbvdWCwWtFrtpM+JT47h4WFpqGK1Wunr60MQBIKCgqRhhUqlkgoNyeVyQkND8ff3JzAwkLCwMMLCwggODiYkJISgoKBFVwf8lhKzIAiSIC0WiyRWvV6PXq+nt7cXrVbL4OCgNH6Ni4tDrVaTkJBAdHQ0cXFxaDQaoqOjiY6O/twx6Fwhiu96nOhtNht9fX0YDAbp/K1WKzU1NTidTtra2nC73URERJCQkEBCQgJRUVHExsai0WgIDg4mMDCQwMBAgoOD8ff3v6VXDBe0mD0eD06nU3pZrVa6urqoq6ujtraW+vp6+vv7CQ0NJSUlhfz8fDZt2kRGRgaJiYnTLoV2qxIQEPC5lWDFWMHa2lpqa2s5duwYra2tdHZ2kp+fT2ZmJnl5eRQVFZGamopKpUKhUODr64uvr++UdRAXKgtWzG63m5GREc6cOcOZM2c4ffo0dXV1REVFUVpaypIlS/jiF79Ieno6ISEh+Pj4SONL8XcvF013mZmZpKen88ADDyAIgvQ6d+4cDQ0NVFVV8fbbbzMyMkJqaiolJSUsXbqUZcuWERsbe8uMuxeUmAcGBqipqeHMmTOcPXsWnU5HTk4O2dnZPPvss2RmZkrjQPHlrYj6+fj4+EzZw5aWllJQUMD999+P3W7HYDDQ2dlJW1sbBw4c4MUXXyQkJISlS5eyatUqCgsLr7C2LCTmVcwOh4PW1laOHTtGdXU1Y2NjqNVqEhMTefTRR4mPj5fGkaGhodIj0MvMIHYIoqtobGwsKSkplJWVYTKZMJlMDAwM0NnZyZ49e3jjjTdQqVQUFxdTVlZGeXn5ghqGzLkyxsbG6OjooKqqivr6elwuFxERERQVFREREUF0dDQxMTHExMSgVqvnunm3NaIl5NK5hmhB6evrY2hoiJGREQwGAzt37uQPf/gDubm5LFmyhIyMjHmfTM+JmF0uF52dndTU1NDZ2YnFYgEgLCyMuLg48vLySElJQa1WL9jxmSAIjI+PYzQaJ6XbGhkZwWaz0dXVNeXnFArFvF/kmyEkJISQkBBycnJwOp0YDAa6urpob2+nra0NnU7H3r17CQoKIjU1lYKCAlJTU+clumXWxOzxeLBYLLS2ttLR0YFWq2VgYACPx0NCQgIlJSUUFhZKaarmGtE2fbkNenx8XDL5XZ6G1ul0YrfbJ60Anj9/nuHhYXbv3j3lcWQyGX5+frhcLs6ePYvH42H//v20tbWh0WgICAggMDBQGkKJdbfDw8NRKpULaiLr6+srmTSXLl3K2NgYDQ0NnDlzhp6eHvR6PV1dXcTHx5ORkUFOTs6c2rNnfDlbjJjo7u6mo6ODmpoaOjo6SE9PZ8OGDRQXF8+ZgF0ul2STHhsbw2azSSIdGxuTFldMJtOk7cxmM2NjY5PE7OPjQ1hY2BWz+9raWpqamnjkkUeuOL7T6ZRWIcXHdFNTEyUlJajV6kli1mg0KBQKydstMjJSWvAICAiQFkXE10Iaq8LFRaHq6mqOHj1Ke3s7KSkplJaWkpSUREJCAmq1etZ76xkTs9gT9/f3c/bsWQ4ePIhOp2P79u3cc889xMXFzeoQwu1243A4mJiYwG6343A4MBqN9PT0SDeWmKRwdHSU8PBwYmNjpQUV8W9xvB4TEzOt4YG4Avjxxx9f8Z5Wq8VoNBIWFoZCoWDfvn1885vf5MCBAxQVFdHS0kJzczNjY2MIgoDD4aCmpgaAlpYWTCYTGo2G2NhYoqKiSE9Pl17iIoefnx9KpRKlUrkgJscej4f+/n4++OADduzYQWRkJBs3bmTFihUkJSURFBQ0a+2ckb2KNuF9+/axa9culEolzz77LPfcc89M7H5KRFupx+PB7XYzPDxMXV0dDQ0NVFdXc/78eUwmExkZGeTl5XHHHXdw3333kZubS2Rk5JyM6U6cOCFZAL70pS9JpdOcTic9PT38/ve/p7q6moceeojvfe97U+6jp6eH9vZ2enp6uHDhAn/605+orq4mMTGRwsJCcnNzKSgooKCggMTERMnOLv6ca2QyGfHx8Tz77LN85Stf4fjx47zxxht88MEHbNq0iYqKikntnEluqmcWE47s2LGDffv2kZyczLZt2ygrKyMgIGBa6alulMHBQU6dOsWhQ4c4ffo0NptNWhzIy8sjPz+fxMREKWRIXM2Sy+Uz+kVeq2euqqrif/7nf9izZw9qtRqPx0NXVxfZ2dlSIvIlS5bw7W9/m4qKiin3LzpBiY5QTqcTl8tFR0cHTU1NtLW10draKi1dr1q1inXr1rF+/for/Ejmg4mJCWw2G1VVVezZs4fe3l42bNjAE088MePWqhvumcfHxzl58iS//vWvSUtL4+tf/zo5OTlERUXN2uy9urqac+fOUVlZycDAALGxsRQUFLB161YiIyOlR29QUBBBQUHzPoFKTU0lJSVFGovDxQ6gvb0dQRCQyWSkpaVd4XB/KeINeDkhISFkZWVhs9km+ai0tLRw/Phx/vd//5esrCxKSkpYsmQJmZmZ8xLc6ufnh5+fH0uWLCE1NZWmpiY+/fRTvvnNb7J161a2b98+Y8PP6xazw+GgqamJPXv2YDabqaioIC8vj7S0NFQq1YyKZ3x8nLq6Os6dO8eFCxfw9fVFo9Fwxx13cM8990jRyuJEaiHN/OFiCJNGoyEwMHBS4XfRT9rX15fIyMgrglinw+UO+KITVlZWFkuWLGFwcBCtVotOp+PVV19FLpeTlZVFeXk5xcXF10yjOxuIHYxarSY2NlaKX/zXf/1Xtm/fTm5u7k1HxFyXmAcHB/nss8+orq5GpVKxZMkSVq1ahUqlmrElZbfbjU6n49y5c9TU1OBwOAgICCAzM5PExEQSExNJSkoiKipqwWfqkcvlREdHk5ycLE3sLiUiIoKoqKgZiQrx8fEhICCApKQkkpKSgIsT0N7eXnp6ehgcHMRsNrN//372799PYWEhK1euJDo6ek5t+yqVisLCQlJSUoiJieHs2bO89957FBUVsXr16hu6sUWmLeaOjg5Onz5Ne3s7MTExbNq0ibS0tBs+8OW43W5aW1upq6ujp6eH0dFRBEEgPT2d/Px8cnJyruumaW5u5vz588hkMhITE4mLiyM2NhY/P7857cETExMpKCigvr5+0mKLTCYjKytLEt5sILp9rlixApPJRFtbG/X19TQ3N1NbW0tXVxfJyckUFRWRkpIyZ7GCPj4+hISEsHbtWtLS0vjoo49obW1lYmKCZcuWkZGRcUOd4+eK2ePx0NzczMmTJxkcHKSkpIS77rprxmLMXC6XNGOvr6+nra0NlUrF6tWrWbly5Q3bpPv6+ti9ezfNzc1kZWVRWFhIeno6arWa8PBw1Go1arWakJCQWe3hExISKCws5L333pskZl9fX/Ly8khNTZ21Y19KaGgoZWVllJaWYrPZOHnyJAcOHJB8wHNzc8nOziYxMXHOnngymYykpCSeffZZjhw5wunTpzl8+DAOh4Pc3NzrNuFdc2uPx0NHRwc7d+5EJpOxefNmysvLb+oERNxuN2azmY6ODo4dO8bJkycpKCjgmWeeoaCg4KYtIeIK1c9+9jP279/PwYMHsdlsaDQacnJyKCoqorCwkMzMTMLDwwkKCiI4OFiK3JgpK4BGoyElJeWKnkahUJCWlnZTj9UbwcfHh8DAQDZu3MjGjRupqalh586dvPvuuxQUFLB27VpSU1PnPHPohg0biIiI4KOPPmLv3r34+vqSmZl5fddBuAput1sYGhoSnnvuOeHVV18Venp6rrbpdTMxMSFotVphx44dwoYNG4R/+qd/Eurq6gS73T5jxxCPU1lZKaxdu1YICgoSZDKZAAiAoFQqhaCgICE4OFhISEgQHnjgAeE//uM/hI8//ljo6uoSDAaDYLFYBKfTec1j/N///Z+wcePGa27z0UcfCQkJCdKxASEkJET47W9/O5One1PU1dUJP/rRj4TNmzcLL730kmA0GgWn0yl4PJ45bYdOpxPeeOMN4Tvf+Y6g1Wqv6/hXFfPIyIjw1FNPCa+99prQ398/YyfldDqFkydPCt/4xjeERx55RKitrRVsNpvgdrtnZP9THa+zs1NYv369EBYWNknQ4svHx0eQy+VCSEiIoNFohMjISKG8vFx4/vnnhYaGhmvufzpirqysFCoqKiYdc/Xq1cKhQ4dm8lRvCrfbLdhsNqGmpkb47ne/K9x5551CVVXVjHcwn4fH4xGGh4eFP/7xj8KTTz4pjI6OTlsb8ueff/75y3vrrq4uXn75ZXJycnjggQeIioqaEWuFzWZj9+7dHDx4kNLSUr7xjW+QmJg4q/ZgmUxGcHAwmzZtQq/XMzQ0hNVqvaIojiAI0lK4+LuY8DsqKuqq+6+qqqKuro6nnnrqqtu4XC4MBgMnT57E5XLh7+/Ptm3bWL9+veRYNN/4+PigUCgIDw+nqKiIpKQkXnnlFZRK5aSSbXPRDqVSKS34vPrqqyxfvpzAwMDP1cgVY+bu7m4OHTqEQqHgwQcflMLWbxaDwcCOHTswGAzcc889FBcXz1n+M4VCQWJiIv/4j/9ISkoKf/jDH2hsbJyUFwMuCtrf358tW7ZQUVHB0qVLZ8TaIPprizeQIAjccccdxMbG3vS+Zxo/Pz/i4uIIDg4mLCyMjz/+GJPJxIYNG0hJSZmTNsjlciIjI1m7di1arZa33nqLJ554goSEhGt+blJ3Oz4+Tk1NDTU1NWzdupX4+PgZEbLRaGTnzp24XC7Wr1/P8uXL5yWRX1ZWFo8//jhf+9rXWL58+RWTTLlcjsfjwePxEB8fT1pa2oysZgYEBBATEyMtKgUEBBAbG7tg/ZxlMhlhYWGsWLGCzZs3Mzw8zPHjx+e0aL1CoSA2NpZt27bR1NRETU3NpIWnqZg0zKiuruazzz4jISGB++6776aHFsJfPMF27tyJwWBgzZo1lJaWzutFDA8Pl7zkxDwVogOQr68vCQkJWCwW+vr60Ov1+Pj4EBkZedWbejrDDB8fHywWCydOnKCvr4+cnBweeeSRObdkXC9yuZyEhAR8fHxob2/HYDCg0WhQqVTT3ofZbGZgYACFQnHdJj+5XE5ERARms5nz58+j0WiIiYm5qi6lYcbo6CjV1dWYzWaefPLJGXHTczgcHD9+nOrqarZv305+fv6CyIEWGxvL/fffLy3CHD58WMpstH37dsbHxzl37hyNjY2cOXOGjRs3kpubS0lJyQ1/LyqVipUrV3LmzBnKy8tvmTQIcrmcFStW4HA4qKys5OjRozz00EPTNp0ODg6ye/dulEolMTExk1xapztfePDBBzl79iw1NTXSAthUSFemoaGBgYEB0tPTJ2Vjv1FcLhd9fX28+eabPPTQQ+Tn5y+oLO6hoaFs3ryZ0NBQJiYmOHHiBHa7nQcffJC8vDwOHTrEvn37qKmp4cSJE5SVlfHMM8+QlJREcnLydUdQiAtBv/zlL1m5cuUtFd8oCtpgMPDZZ5+RnZ1NSUnJtD//8ccfc/LkSfz9/cnOzqasrIyioiIyMzMJCQmRUpsFBwdPubSuUqlYu3Yt58+fp76+/tpi9ng8nD9/HrfbLdXHuFlGR0c5duwYHo+HtWvX3vTFczqdmM1mLBYLLpdLyrN2uXOTmJ7r8skdXBxGiNHIYqrXNWvW8OKLL/Lcc89RW1uLwWDA19eXhx9+mHvvvZfTp0/zy1/+klOnTnHw4EHuvPNOvvKVr1BUVIRarZ52jo7AwEBKSkooLi5m6dKlt1zxnMDAQJYsWcLw8DBvvfUWhYWF03pKZWZmsm3bNgYGBmhoaODUqVNUVlaiVCpxuVyST0ZZWRm5ubloNBr8/f0lF2JxaLJ27VoOHTpES0sL69evn1L0CrgogM7OTiIiIsjJyZmRkx8YGGDPnj1897vfva4x1tXo7e3lV7/6Fe+99x49PT3k5+fz7LPP8tRTT00ag7/22mu89tprtLW1XZEvIikpidWrV/PMM8+wbNkyydc5NzeXffv28dxzz+Hv7y9ZHQICAli/fj0rVqygpaWFH//4xxw+fJj9+/ezceNGvvnNbwIXe66pbp7LiY2N5aOPPsLPzw9BEKb1mYVEfHw86enp7Nq1i56eHmk8/Xls27aNI0eO0NzcLCWmFOcplZWVXLhwQfpOYmNjWb58OevWrWPp0qXk5uZK9V4SEhIwGo10dnaSlZV1xXF8BEEQzp49y86dO8nJyeHpp5++aZuvxWLhk08+4ec//zkffvjhTdmRBUHAarWyY8cO8vLySEhIoLu7m7fffpuqqip++MMfsm3bNmn7kZERfv3rX/P666+TmZnJq6++Ku2jurqaF154Ablczj/8wz/w6KOPTjqOyWQiICDgCmckQRBwuVyMjY3R3d3NL37xC44cOSJl5zSbzURERNz4F3YLYbfbGR0dJTQ0dNq2Z0EQGBoawmw2T1n0/tLvWi6XS0WJxICKu+++mx/84AecOXOGxsZGycpyOQqAoaEhKWfCTCxeGI1GtFotWVlZN70gIibP3rp1K8HBwQQEBBAZGUl/fz/Dw8P09vZO2j48PJywsDDp8SXact1uN5GRkVRWVrJ79+4rUgOIAatXa4Ovry9qtZrg4GD+7d/+jccff5z6+npaWloYHBy84fO71ZiYmGB4eBidTkdhYeG0Tbd2ux2z2Tzle8JlwU5ixxEYGEhWVhb5+flS0K8gCBgMhin3o4CLvZlCobiuDJTXYnx8HIPBQGJi4ozsT/QLFgkICCA4OJiIiAjKysombet2u+ns7ASgoKBg0j78/f2l1LcOh+OG2uLn50dqairR0dEUFRVhNBqxWq03tK9bEZvNxoULF/jVr37FD37wg2lZp3p7exkbG2NgYOCK9A1iSJvH4yEyMpKCggJKSkrIyMggMjKSsLAwkpKSCA8PJyIiAo/Hg9FonPI4Crh414iJrGcCl8vFxMTErExyDAYDtbW1tLS0SLPiS9FqtXR2dhIUFERmZiaCIEhJWo4fP86pU6coLCykuLj4ptohpoJd6LbimcZqteJ0OlEqlZSXl08rYuXMmTNS2WRfX18UCgVKpVLKr5GWlkZMTAxRUVEkJCSQkpJCbGzsFdYvcTJ4+Q0hooCLF8bj8dxwb3XFTv9iILfZbDOyP5GOjg4OHDjAwYMHMV/IjqUAABIkSURBVJlMrF27lpGRkUk3TXNzs5Rs5t1330Uul2Oz2ejs7GR0dJS8vDwqKipmzGpzu+FyubDb7dNe+BKv2djYGPn5+SQnJxMfH49Go5EmlCkpKcTFxX1uL2+32wGuup0CLvoONDY2XnVMc70EBgYSHh5ObW3tjOxPZHh4mPb2dkwmE11dXXR0dKBUKvn+978vmYmqq6txOBz4+Phw/PhxJiYmpPzEP/nJT6ioqCA9PX3OY+AWC1arleHhYZKTk6e1QqzX68nJyZGyuRYUFJCZmXlDE+aRkRFkMtlVAzYUAFFRUTidzquORa4Xccl4z549WK3WaXk8TQexhFh3dzfvvPMOr7zyCr/5zW949tlnUavV2Gw2Tpw4QXx8PH//93/PypUrMRqN7N27ly9/+cusW7dOmpTON2LydKfTKY3nL7cOWK3WK9KBiSgUCikJzFym9BXrexcXF0/ruEuXLmXp0qUzcuzh4WFkMtlV1ywUcDFOzel0Mjw8LJWuvRlUKpUUXVFTU0NpaemMCcjPz4/MzEyefvppBEHgN7/5DTqdjtDQUGnR46677iI7Oxu4WGpMzONx7NgxUlNT591bzel00tXVxYULFxgYGJASgpeWlk4aJ9bX11NdXY3RaJQEDxdn/+Hh4WRkZJCenk54ePic5MfweDzodDouXLjACy+8MKcZlARBoKurC4VCcVVPRhlcDO1JTEyUEh3OBFFRUVRUVPDrX/9ayvo5kwQEBEhFdPLz81EoFDQ2NjI6OkpERIR094rOQ1/4whc4fPjwgjCjnThxgldeeYULFy5gNpvZvXs3Tz75JD/+8Y8nbWe323n//ff58Y9/zI4dO4C/Jt55+eWXue+++3jhhRdob2+fk3YPDAzQ3t6ORqMhOzt7Tp8IRqOR9vZ2QkJCyMzMnHIb+fPPP/+8j48PdrsdrVaL1WrljjvuuOmDBwQEEBUVxc6dO4mJiZHq180E4+PjHDlyhBMnTvC3f/u3FBQU0NzczPPPP09MTAz3338/6enp0vY+Pj74+fnxu9/9DqVSSXJy8rxkH/V4PIyMjFBdXc2mTZvYtGkT5eXl5ObmYrfbOXDgAGlpaSQnJ6NQKIiMjMThcGC1WiktLeVb3/oWRUVFlJaWUlFRweDgIIcOHZKcmGYTl8vFwYMHOXXqFF//+tfn/Ol24MABTCYT5eXlV63jIj0nioqKqK+vp76+nqGhoWtGV0wHuVxObGws3/72t3nvvfcIDw+ntLT0ugXtdDppamripz/9qWQsT01NJS8vj23btpGWlsa///u/88knn1BdXU1QUBAvv/wyNpuNrVu3AheHJqtWrQLgzTff5PDhwzz33HM88cQTN3WON4LL5WLNmjVSlk+4OGHu6+tj165d9Pf3S1HcgYGB2Gw2QkNDWbZs2aQbMCIigszMTI4ePTpjE/drcezYMVpaWlizZs2MuTxMF6fTycGDBykqKpq0dnA5kpjDw8MpLy/HZDKxa9cuvva1r910I5RKJatWrUKr1XLkyBF8fX0pLi6+Lnu2uC6/ZcsWaXEiMjJS8u5TKBSsWLGCxMRESZwhISGTemZx0vDCCy9IF36uLwj8NV/E5dmXlEql5PxUUFAgfT+i1UapVFJYWDhpX01NTdLNO9t1RsSMUnFxcWzYsGHOJ9Dvv/8+wcHBFBYWXrOTlcQsk8nIy8ujv7+fI0eOUFtbe8UXeL2IURX33nsvu3bt4vjx4zgcDoqLi6dtpxR7+L/5m7+56jZTrdNPxWOPPTat7WYLMcz/csSilWvWrJHG/wCdnZ309PTg8XjQ6/VUVlZitVppbGzk3Llz6HQ6Nm/ePGs2c7fbzenTpzl37hwREREsX758Tgv0uFwutFotH330Effeey85OTnXnHROeickJISioiL6+/vZv38/arWamJiYm54pR0VFsWXLFvbv38+JEycYHx+ntLR0znMzLEQ8Hg/d3d3odDqefvrpSR6GNTU1GAwGVCoVDQ0NOBwO2tvb2bt3L8XFxWzdupX77rtPstzMFOKq6cmTJ6msrCQqKooVK1ZcdeI1G7jdbvR6PXv37iU2NpbS0tLPtU1fMR1NTU3l7rvvxmw28+GHH6LX6ydl4rlRkpOTeeSRR4iNjeXo0aN88skndHZ2Sq6AtysjIyP09/ejVqtZu3at9H+n00lVVRW+vr6UlJRIlWUdDgeDg4N873vf41vf+taknnwmmJiYoLe3l2PHjrF7925iY2O555575lTI4kT5xIkTNDU18eSTT05vwjlV/gGXyyV0dXUJjz76qLB7925haGhoxvJa2O124cCBA8JXv/pV4Z//+Z+FxsZGwWQyzVrejIWM3W4XDh06JOzevVuw2WyT3tNqtcKWLVuEr371q0JTU5MgCIJgsViE/fv3C8HBwcLbb78tGAyGGWuLy+USzGazUFtbK/znf/6nsHHjRuHIkSOCxWKZsWNMB7fbLej1euH9998XnnrqKaG3t1dwuVzT+uw1MxoZjUbhwQcfFN59911hZGRkxhosCBcv1n/9138JxcXFwiuvvCIMDw/Pefac+cTj8QinTp0SKisrp0y08uGHHwpLly4VXnjhhUnvj4yMCEVFRZNEPhNt0el0wuuvvy488MADwve//33BaDTOSwdjNBqF3//+98KXvvQlob6+/ro+O2USGPirbbasrIx33nmHrq4uNBrNjDmhBwUFkZ+fz7p16zh06BAvvfQSJpOJuLi4GXNFXcicOHFCWgDw9/fHx8dHKg+hUCj4/e9/j9Vq5a677qKgoECyfgh/iVDZsWMHxcXFpKam3pS34/DwMG+++SYvv/wyJpOJZ555hscee4yQkJA5r3yr0+l45513aGpq4ktf+hJ5eXnX1YbPLQPhdDppb2/nww8/ZGJigg0bNrBs2bKbbjj8NYuQTqejo6ODo0eP0t3dTUZGBvfeey9FRUULti7gjSD8JSH4Sy+9hMvlkooAyWQyacLz5z//mZSUFD744AMCAwPZtm0bDz/8sJRd3+Vy0dLSQkVFhRRlvnXrVvLy8qbdDrfbTXNzMx9++CHnz58nLS2NlStXkp2dTXR09LykgqiqqmLfvn0EBASwZcsWMjIyrntNYlo1TTweD21tbZw6dYr29naSkpK4//77b3ph5VJsNhttbW20tLTQ0dEh5VooLS1l2bJlJCQkLIhqSjeDy+WisbGR/fv3SxE0Ys8j/MWC0NPTQ2hoKHq9Hn9/fzIzM1m9erW0Kiv8JRfJz372M/R6PTExMWzcuPFznXkcDgf9/f1UV1dz9uxZjEYjCQkJpKWlkZOTQ2pq6pwH2QqCIBkaGhsbSUxMZNWqVWRmZt5QJ3ZdBXo6OzuprKykpaUFX19fVq5cyZIlS2Y0V9z4+DidnZ1S0nGbzYbD4SA4OJi0tDTy8/NJSUmZkSDZuUasCnB5lVcR4S/Vsy4tIKRUKqfMMdHW1sb4+Dgej4eYmJgpZ/tWq5Wuri6amppob2/HaDTi5+eHv78/8fHxFBQUkJWVNS8pIKxWKxcuXODw4cN4PB7p6TBd19KpuO5qU2NjY9TU1HDkyBHgYsRzeXk5qampM5pcz+l0otfrqampobq6Gr1ej5+fH8HBwYSHhxMdHU1KSgopKSnzVuV1oeF2u7FYLPT09NDV1YVWq5UKdjqdTsLDw6UycomJifNSA8Zut9Pb20tVVRWtra3Y7XbWrVs3I4lxbqh0mmgH/NOf/sTp06fJzMwkLy+P7OxsYmNjZyVj5MjICLW1tXz22We0t7cjl8ul+iaRkZGEhoZOegUEBMx72bDZRoxnNJvNmM1mRkdH0ev1aLVaenp6sFqtpKenU15ePu+JGsW5UUtLCw0NDfT09JCVlcWjjz5KaGjojEw2b6oOoMfjQavV8sYbb9DR0UFBQQGrVq2Syi3MVjmBsbExmpubOX78OMePH2dwcJCUlBQp21BKSoo0kRFL9YplexdaRarp4Ha7pXp6NpsNu92O1WpFq9XS3d0tFeIZHBxEoVCwcuVK1q1bR3Fx8bxnkRKDPrq7u/n000+pqakhOjqaxx577KbjMC9nxsoNNzQ08Lvf/Y7a2lpKS0t55JFHSE5OlsrgzpaIPB4PJpNJyl4qvsbGxoiNjSUzM5P8/Hzy8/PJy8uTJl3iuFQul09KFiP+PVeI4+RLX5f/T8zXUV9fT2NjI62trVKV1qKiIvLy8qTX56V9natzEoOae3p6eP/99zl8+DAFBQV88YtfnHERi8xo7Wyn00lLSwu7du1i//79JCUl8cUvfpGNGzfOarJq8eK73W7pp8FgkKqY1tfXU1tbS11dHQqFQqrZERMTI9UvFJ2qSkpK5tQ0NTIyglarZWhoiL6+PnQ6HTqdTiocr9VqcTqdpKamUlBQQH5+PllZWVJUilhx9tLXfDM2NkZlZSVvv/021dXVbN68mSeeeIKsrCwpsctsMGNiFpmYmMBkMqHT6aSJ4sDAAHfeeSf33nsvGRkZc1LNSHw02+126SU+poeGhjCZTBiNRgYGBqRUBHAxmthut5OUlHTVHNJpaWmEhYV9rnCGh4cZHByUooovpbe3l5GREfz9/YmIiCAsLEyKkFGr1URERBAaGopGo5HcQ8VClmKevIUgXBHR/n3gwAE+/fRTlEolGzZsYMWKFURGRhIeHj7r133GxSwilj4Q81g0NTXR2tpKSEgIpaWllJWV3bSL6Y3gdruxWq04HA4cDgfj4+NSBh246EPscrkwmUxXDfcyGo3YbLYrMvFcTlBQECqVasqeKDQ0lMDAwEkCFX8Xg1v9/PwICAhY0AtHLS0tfPbZZ5w7dw6bzUZSUhLZ2dkkJyeTmJg4Y5UXpsOsiflSxsfHaWtro62tTbKzjo+Po1AopBJm6enpCyJqWkQ0aU2F0WiUap9cC7HE7lSLPaKT/q1mcbHZbPT29kpzE7vdTlBQEGFhYcTFxZGZmUlqauq8uCTMiZgvZWBggObmZlpbW6VoWzFZXlxcnFQud6bK8Hq5OdxuN4ODg5LtWqfTMT4+jtvtxuVyER8fLxXEjIyMnNdV2jkXs4jb7cZoNFJVVUVVVZWU0OXSMWNUVBQxMTGo1Wo0Gg2+vr63pGntVmJiYgK9Xo/RaESv19Pf38/IyAgGg4GRkRGcTifx8fGUlJRQWlqKRqNZME+XeRPz5VitVimurbq6Gq1WK8XyiT12eHg4ISEhqFQqgoODCQwMXDBf5K2Ix+PBarVisVgwm82MjY1hMBjo7e1Fp9NJpYgTExMpLi6mrKxMqmG+EFkwYr4cs9lMXV0dn376KQ0NDZw/f15Khp6dnS05x6hUKim3nZ+fn2T6WUgz/flGNFc6nU4cDgdOpxOXyyXl4GtsbKShoYGGhgaMRiMlJSXk5+dTUlLCsmXLbpks/wtWzFPR0NDAmTNnOHv2LOfOnaO9vR21Wk1GRgbFxcWUlJSQlZVFUlLSpAtwuw1NLr+kY2NjaLVaGhoaqKyspLGxkfb2drRaLenp6SxdupRly5axYsWKeYlanyluKTE7nU4mJiak1/j4OP39/fT19UmTyp6eHkwmEyEhIZKjf3Z2Nn5+fuTn50upwxZTpnuj0YhOp2NwcFCyX3d3d0t+GmNjYwQHB5Oamio90eLj40lISCAwMFB6qolPtluVW0rMlyOm4bXb7VgsFsbHx7HZbFgsFgwGA6Ojo9hsNgYGBnC73fT19eFwONDr9djtdqlORlBQEBkZGfj6+pKeno5KpSIuLm5BCF4skSyuFFosFrq6urBYLPT29mI0GqWqByEhIYSHhxMUFIRGo5E8DMPDw1GpVAQGBk7yV7lVfVWuxi0t5qshLoyIiyMmk0nKuO50OhkbG5vksCNWshL9IMQMnVfLV52UlDSlA4+Pjw8ZGRlTmqccDge9vb1TFuURCz9O5eN86aKKaLMW630EBQVJCytBQUH4+/sTHByMUqlEpVLh7+9PUFAQAQEBt3xgw3RYlGKeDh6PB4vFgtFoxOFwMDQ0hNvtZnh4WCpCc7UVQNEBaCquljrh8spXl3ItnwqVSiVZb8LCwvD390ej0aBUKqVe2GvRuchtK+abQUwweTmCINDZ2TllD6tUKomLi5uyh1SpVHO67LtY8YrZy6LBa4z1smjwitnLosErZi+LBq+YvSwavGL2smjwitnLosErZi+LBq+YvSwavGL2smjwitnLosErZi+Lhv8HZku65UQ6DdYAAAAASUVORK5CYII=)
A thin uniform annular disc (see figure) of mass
has outer radius
and inner radius
. The work required to take a unit mass from point
on its axis to infinity is
![](data:image/png;base64,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)
physics-General
physics-
The two bodies of mass
and
respectively are tied to the ends of a massless string, which passes over a light and frictionless pulley. The masses are initially at rest and the released. Then acceleration of the centre of mass of the system is
![](data:image/png;base64,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)
The two bodies of mass
and
respectively are tied to the ends of a massless string, which passes over a light and frictionless pulley. The masses are initially at rest and the released. Then acceleration of the centre of mass of the system is
![](data:image/png;base64,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)
physics-General
maths-
If
to
terms,
terms,
, then ![x colon y](data:image/png;base64,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)
If
to
terms,
terms,
, then ![x colon y](data:image/png;base64,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)
maths-General
Maths-
The coefficient of
in
is
The coefficient of
in
is
Maths-General
maths-
maths-General
chemistry-
Compounds (A) and (B) are – ![](data:image/png;base64,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)
Compounds (A) and (B) are – ![](data:image/png;base64,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)
chemistry-General
Maths-
Maths-General
maths-
A triangle is inscribed in a circle. The vertices of the triangle divide the circle into three arcs of length 3, 4 and 5 units. Then area of the triangle is equal to:
A triangle is inscribed in a circle. The vertices of the triangle divide the circle into three arcs of length 3, 4 and 5 units. Then area of the triangle is equal to:
maths-General
Maths-
If one root of the equation
is reciprocal of the one of the roots of equation
then
If one root of the equation
is reciprocal of the one of the roots of equation
then
Maths-General
Maths-
If the quadratic equation
and
have a common root then
is equal to
If the quadratic equation
and
have a common root then
is equal to
Maths-General
physics-
Two blocks of masses 10 kg and 4 kg are connected by a spring of negligible mass and placed on frictionless horizontal surface. An impulsive force gives a velocity of 14
to the heavier block in the direction of the lighter block. The velocity of centre of mass of the system at that very moment is
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)
Two blocks of masses 10 kg and 4 kg are connected by a spring of negligible mass and placed on frictionless horizontal surface. An impulsive force gives a velocity of 14
to the heavier block in the direction of the lighter block. The velocity of centre of mass of the system at that very moment is
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)
physics-General
Maths-
In a Δabc if b+c=3a then
has the value equal to –
In a Δabc if b+c=3a then
has the value equal to –
Maths-General
Maths-
In a
simplifies to
In a
simplifies to
Maths-General
Maths-
In a triangle ABC, a: b: c = 4: 5: 6. Then 3A + B equals to :
In a triangle ABC, a: b: c = 4: 5: 6. Then 3A + B equals to :
Maths-General
physics-
A bullet of mass
is fired with a velocity of 50
at an angle
with the horizontal. At the highest point of its trajectory, it collides had on with a bob of massless string of length
m and gets embedded in the bob. After the collision, the string moves to an angle of 120
. What is the angle ![theta ?](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAANCAYAAACkTj4ZAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAANVJREFUeNpjYMAE1kC8DoifAvFBIDZHkvMD4sNA/AOIPwHxbCAWx2IGWBPIECYoXxSI7yLJbwJiSyR5D6jBGOACEEujie0AYj0G3OAHuoALEM/HonA5EHvhMATkujXogiD/BmFRDPKqGxZxWyBeDMQ86BLXgPg/DoweoAZAvBAprOCACRoLxIqDAlgQm19BNu7FIm6KLQyA4A+ukIdFOzqoB+JEBhIADzTqkQHI6eeAmI2BRHAFiPOgbA0gPg7EPjjU/sdnkB7UVb+A+BI0OzCQYxBFAABjSyrUJ4reUwAAAFl0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+JiN4M0I4OzwvbWk+PG1vPj88L21vPjwvbWF0aD684/g2AAAAAElFTkSuQmCC)
![](data:image/png;base64,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)
A bullet of mass
is fired with a velocity of 50
at an angle
with the horizontal. At the highest point of its trajectory, it collides had on with a bob of massless string of length
m and gets embedded in the bob. After the collision, the string moves to an angle of 120
. What is the angle ![theta ?](data:image/png;base64,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)
![](data:image/png;base64,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)
physics-General