Maths-
General
Easy
Question
is equal to
- 0
- 2
- e
none of these
none of these
The correct answers are: 0, e
Let direction cosines of straight line be l, m, n
\ 4l + m + n = 0
l – 2m + n = 0
Þ
Þ ![fraction numerator l over denominator negative 1 end fraction equals fraction numerator m over denominator plus 1 end fraction equals fraction numerator n over denominator 3 end fraction](data:image/png;base64,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)
\ Equation of straight line is
.
Hence (c) is the correct choice.
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physics-
A bob of mass M is suspended by a massless string of length L. The horizontal velocity at position A is just sufficient to make it reach the point B. The angle at which the speed of the bob is half of that at A, satisfies
![](data:image/png;base64,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)
A bob of mass M is suspended by a massless string of length L. The horizontal velocity at position A is just sufficient to make it reach the point B. The angle at which the speed of the bob is half of that at A, satisfies
![](data:image/png;base64,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)
physics-General
Physics-
A piece of wire is bent in the shape of a parabola
-axis vertical) with a bead of mass
on it. The bead can side on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the
-axis with a constant acceleration
. The distance of the new equilibrium position of the bead, where the bead can stay at rest with respect to the wire, from the
-axis is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAVMAAACbCAMAAADoWYgrAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAMAUExURf///9bW1mtra/f374SclO/m75yUlBAZEISEjObe3lJaUrWc5oSc7+bWnIScxa0QWq1jEOalnGtaWubWc+Z75uZac+Yx5ubWMeZaMRlrWnsxWntjMebWUuZaUhlKWtbe3q1rlEqtWq2tWkoZra0Z70op3krvGUqtGa0xGUJrGa0plK3vGa2tGXta73sZ74TvnBApUoTv3nvvWnutWhBrGXsplHvvGXutGUIIUq3OWkpK3krOWq1KlEqMWq2MWkoI3krOGUqMGUJKGa0IlK3OGa2MGRAIUnvOWnuMWhBKGXsIlHvOGXuMGSkpIbVjWq0xWq1jMea95ualvZRjWuac5r3Fxc7Oxa2tnAAAAJylnLW9tUJCQrWttUpKWub3e+ZateYQtealEOYpEBlrjBkpjHsQKeZalOYQlOaEEOYIEBlKjBkIjHsQCDEQGdZa5tYQ5tbWENZaEGsQWmtjEBAhIXtzezoxOkIpY+/WvbXmra1rzkprjEopjK0pzq0QKXtrznspzoTOrYTO73tSpbXmjK1KzkpKjEoIjK0Izq0QCHtKznsIzoTOjITOzntShFLv71Kt71LvrVKtreZ7teYxtealMeYpMealc+Ypcxnv7xmt7xnvrRmtrRlrrRkprXsxKRlr7xnvaxmtaxkp7xnvKRmtKRAIGeb3xVLO71KM71LOrVKMreaEc+YIcxnO7xmM7xnOrRmMrRlK7xnOaxmMaxkI7xnOKRmMKVLvzlKtzlLvjFKtjOZ7lOYxlOaEMeYIMealUuYpUhnvzhmtzhnvjBmtjBlKrRkIrXsxCBlrzhnvShmtShkpzhnvCBmtCFLOzlKMzlLOjFKMjOaEUuYIUhnOzhmMzhnOjBmMjBlKzhnOShmMShkIzhnOCBmMCEoxGVIQGfda5vcQ5vfWEPdaEIwQWoxjELXv77XF77WUvbXvzq1r763va0pr70rva0prrbWMlK1K763vSkprzkrvSkpKrXtzpbXFlOb3EEpra+b3QnNzUt737973///3/wAAAFC+NDAAAAEAdFJOU////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////wBT9wclAAAACXBIWXMAABcRAAAXEQHKJvM/AAAOyUlEQVR4Xu2dXZKqOhCAIZiQyaMbyIrySIBEljBvE5Zxl+HeZglWWdZNB1DAH0BBMx6/maOCHEdjp7vT6XSCDx8+fPjwHmDF60cfboBVKt3dJh1sL44Ygos/3IbTbYxtm6KsTOpT1/hCKtgge/GHIUxM7G1SVkc3oPY6bNv1wxB7orW9o6Y6DIKolkTc3Fd3gUSgHFBaHX24AeHpNgwi3ShKstPMPuYMaWObM2UmBzluWt1UBx9uQXggUCBBVgHDvnjJAl5SroQOeKEwcY35pemXbWOUu8s+3IBbuUMiMKv6sLT6MiFWyUb2fCZ5SaLAGa9QaGZShYYs2TuD6ShrktqrVKx03VRSVA/KzN6oeBWYTKycRk12AU5R4ZTqv0rEmu58k9y2IS4EOlSH0jkBQSCgTTdwQFiG4IxyL5e6x/8sXDYW+wb8Fy6iWWN5cBkTjhNO4AwROLRmnoIDGygGz483UW7Mha22/tfga723d+HR6gdquxXCRIH+SVWZW7eVcOMkdFPYG7mzanYURGTWtDVi/0YMCipBlb+ZnK4MESP26EAQtWqBy8TQLzjPmT2Lft01I+B5Bl/Fb2373gbMZhz0RJQmMJIaDdP2S8jfru8bMeNH+jLrSUKH7B+X7zfq2puwfjQHkdMBQ2BT62YqOH47bQrULtITwT+1bJJMDYcP35fEzPfh3UgMSDM0Zy/xCDXGTJlsRr2nah8i2dLqwdsxxkwlcabnVxLqXZvUDowG7USEMjGnoFbwTf3gDeGDcqoKJCh49PMAQ2KZh+lsL/gXUWEay18Yo84BBhtFtjAWew5WaJopieeBB/zKg20CHowdyA/BY9vp909zorjR2sRPH1q0IiQVuP+JSTzZ6yHUOZ+KkL5ELjpd3X/rsmRBIKa//UfBZU9Zpn2LfEebUpbZVznkcWzmkvAx9JwJLiACuR6e850dSXtt2p+kz7fTZYvHECN59vxUNTd2pMjgPZQeBMrPEh9IPFn/RSmNYdql6L2U7Rb1/SLQThhHxtDEcjtj+O1e1FmbTpdTTA8gHsRF/zssqk+70cbfDFqzcPMQz6czh5H0J+rA7k+EpwH93h/MmcXlYklnv/v3aLYJYMp88rufBd02U1VGSYs8nixblFuNSrjTqR3wom3aTYORQhAVirIJMTwXKVo6J+wHjO6QU2vtD5qRC9ZhyQ+Ie+kFnKrDuDDREoStT8r7Km+6nMJ8apBnfc93cdbdNvUH3k8mmS6ntutbqdmK6uhp4OI1qvMaX8e3c5bwOFVOORHO5UWXwnmtOdjZiQbMUfjkfkOPbk+EemZkqpwqhhAEES7FvPZtzT03fCC3RhWuAz0NLo5ShXox1Tvs/lW4WDCgIXWa/+YpsTf17fHXkaKsfGrqCzl+WNPrs3fY/asclpyFSuOs+jn91nfb7Rb+CfsQ0mafxnF+JO392Tnl1Krr+n4BKA0dnFe/QH1gT9pfJWL29CCVozc4PUyQU/lUfdWnGPjueTF0xezwOkDFe/1zpJxiRdD3YAxoyZ6nB2Rw8/xJMP5dhcow6zqo4+SUG/2THbMqr4EXjKHg86Fwl2eGchtW9ZsqOrb5ME5OoyQV2c9Q6+/FchHVxMvVWXWLmO7nHqlPZVmydf34Km6ObyEIfYUgjoTQTo7EODlVPzpkw0I4Jj37TnxdSMThI/cM/yg5JTELXpyoV3gaQVk7M9UxoKP0KcnWz08S7HIW9/UF4tqvm0E9Qk4pTJOOYjNX9sUZvQk+j1hBm5JOCw3LqRndpPtysfF+szDOU2R7bm5wHIVRNtpB4t9L2f2952uyD51A5ICcYjQleWYxn/9sutcnpLXenRDqbTnFDFKgXs+lyS9v2MSqo+9v232sfchJsNCxKv0lFCYI2xFzsr0em+DlCEfrGXjrSdXw7pzUjRw0KSauscJLOeabwWHxy2l3/uv6VIlyonQsNXfifyWWiMvdyYpe1afqe2qTLhZDuZDy4hm4TFupR9f6fprBYuiJLBRD6Y5SvMToU6WeazYqzzzyCKHwjY+0Mrd52sruuyynFFbg+0LiqYXiSLftx/q4GP+inN7bpMvEUPopCZ7AkbK/9YElP2biX5BTbAZnni6zTP4pZlNt5VOIoEhES4kGq6PneSFPGt3ZpAFexJfydAylkBXLdt2dkySe+aeY3b1YEtPLPsRD8LWfFspFH9vLIyL9Ux/0/VPbpH452Lmf4RNZ0vCr/eZkU2DG9qyuPrVD/PvGl3gh37RjBjwiKZFGBDX69IsyykNYiXPYE9HRp6EQd/a0/XqXLLH409dKYfC+5KqZ2OAGpsojK6g4L+PSWisuQciwlBtRhjwEBctdctS+ecIeYC4hif14bX0Krk3Cg70tY1PMrk/x05OgRpLCbAmv/Xxuqs60iXmaZaW2/inVpX3nSutMc8xKkGdUwuCFlJC1wnVpTa99Ym3dT1pCIr/SZW6fKARIUXVtuo6z+UsBKE/FNMhhIFJ3Itwo0v33LqRiq62chgkkjXOTMWwlUIFkyCSxsheqBMQxcfW5ZQISypW7df8D21PwhHICbLJ7dfF18IuyH4dRO/vu6k50ivPl2jYEPS0sTuOHhvikXJ0tun4Yf6egMfoNaTX7yXfHL/7g5qVoVjcEqWpI3st+iWx67ucQyiFZM2Zuf/FuMrIZmxKfoiYNvXw5v+C1dPJ1+4s3mgfk250Znxhxi5kLdf2N6vVVJdMGLHREs9Qao3madObx/gvcfbDAkTXC2DmU4FHyygzdoFcdcpexMi6Y0fPUKp05LvUCA6Wsu64EwqqEuWVSMloeg7dX+gzurNfGZq0TEsuwnEuXzlp3Mdy9wECZQuGdVtyUkXXFZaDiWqWra5+tE4rE1gJIs8soEymd3Vl/nJdk8WqEXQ0ZO5hJYZieCNeU0lyvf9bKlogUCKfILMq7BbKWlwz0ZZwGyo4GZSwDGDxauYVht/nJYsSuENf3lkKUbF1Ak8IK527BgXuZ0Uy/JvWEahyYEgdUBMmPFdO6KPYaBvHlFeL6HohFqZ2YQk2RWYLpMxZcxv21xk8Ba9t3Id7huj4/cLZ1o21rs4TCkZWZ5gceR+4Htw8NDaI9s20KOmCW1pgx//Q1EyZhqZwGxYLisERpQsum9mA+akLcrTjCLANVPFN+p56rTV+Ub8rt+6/KaFjFI6kM+Kmc47jYcAo+9W+8oTKdSXm1q4Q8QuhtOGqQFCGC4pX++W+MXD+Prhv9x+C/K50hEnsW+F29RJnORgTre/K5am7ME0Pplxj4c7hYX9IU1n+Mecb7f38vxdzFT9UsFeXxdgY9eFb97u9R56CZWYRj9XhzyEXrKD6HOs7PhB9K7Kym2F+kbtNf4cXqQ25eMSSdm7rvR4rTXknfO3g0D+VPO6YnTvmn0aQtoi6Bm+0S76RJ5/jrVHbfEdEHder+sfkoPk/A8fWc5DSlSj9WdAQ/VL9TvomUHvWpRYkyzx+T1P0D/9vXpMg7OMlpgDIePNio9yPfaJffVj6/W9qVz7hH1wTeauNkcqzEVc8AqfsHMndvE4vJW+2LVtWdsYA+w2B41d3rkY778U2EP+pweEaz7kTBCKZa2MzNnd7/nXEp6emisrtxNgqHtLK6yCUA4NWdXfGevo/dFM5bQTJKVkjXuxbhWtCe9zn39O/H9vrkGTIXtusP0XMqXquL9dP/OGTb2wqtVqW41gaTcAUBJ8DpS1IjluZsr6OjwbAiNFFUcTHta7B/YdSeyX+N8zY9Lu/9ImzaDpDT6qFYIX0jP7/NWT2UdtJTaCYNAKIJsT6cur3+35KBen15QSa06uhGwgq91cipSyuGchFsdvTuweo1lHmXUOlFLrWp7JgabtC8cRUro282cOpxaT++TW9xdEjYOBdgROoFlojNtvGvp1zSpxxSWztwoimsM70NH8wR4goVr9nt7ZlcrIMWJqrvRX2RApEBsz6wPgr2oig2HpeEn4uLdv9AWHG+Ft/qQXPb/4FU2GtwYtg8aVneU8upIq7bHvYEBoukCALWXfLnbjlBO3NP3+WpeXfD1MLJ6cF+4AKSUJUmENRA7AvBqqsjRKPariS2/7IpPisEEtl6UG9MwcWwpfY2+uJ8KVruAylIgEtq/60CozGKW2upcmMltH4cfIWKMo3ScH+WdtKPoWDMFdWMqsf9e37qHpjFWY71Y2vjlwTaFLut5ZAO0h8rm7QMQoFWrZi9LLAdd7bDHZinSDOzIsoVSanBUAKkAnMpldWgtu35LPslYKZV/UIRTjO2ao48BPJQuNvPOhcYwc7rympYvm6FmCJXT+Es9Hew8moKtjOGUkLzTao2P2iTbsiKEGNMEcdFyuvyHnwDYoYVFAE5qA3oAelOcQW51Vht7FW4OhWmcBWvTiUpuHDuCRPvjrJqMp9jhJAzEWlh36wRWLtiNP1ySJxZ6b1WKzcKU2LtT0WcicIgLX5QmqiisEbJfk0QxyclhFdUqe0pzkqoFmhcZZpfDeWEpKtis7en7CvSEr5PpWGFJ2aw2zc2GjYUEVnZtGnqWWGxLs7uS1HSVOvAfaawadPUCmAOje02ZR4KUWOrPVXiNGq1Tyd3WqEqrbQP4QnM3TN1tSX3+IvX/+P0BA65bfKIc7CK9ROcR5HZHoNkhzz2eXqg8k85USozAQO1v2myfYosi0EyEDPWzry4/jCsAG8eBjJk+jB1UuF5HGMoRnBYumrPgCIArCfg6iIhFXFpWm7AK+DHAZjU1i8j2YVJNF9o2pQKq/DcgL04DvbrrYrdiMqfms6c2bfCmccjCJfXBw6n+9pJYf0fUAZt3IbivtZ09hGQ00OKmnF8iro5KHAA8WN/i2d5SCtP+gKK2UZNioNqhqYfRnDK6b1E6HwWAhVCPozmYvz0RNXn+xr2w00G5k0/TEaq3ziEgfWH2UjYTpDbu1vj/C3zbxaEZsIFpa4TnU34fbhN+J19D7hJx7Hqh5GM2IcjaUbaH8aRfLz517BA3f1/HuTtdNrfRcX+Biv/LG+zZPnDhw8TkW+bff86Ek92434rTCfP78McRJ+I4IcPH96AIPgfiu/gicDzJE4AAAAASUVORK5CYII=)
A piece of wire is bent in the shape of a parabola
-axis vertical) with a bead of mass
on it. The bead can side on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the
-axis with a constant acceleration
. The distance of the new equilibrium position of the bead, where the bead can stay at rest with respect to the wire, from the
-axis is
![](data:image/png;base64,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)
Physics-General
physics-
A point P moves in counter-clockwise direction on a circular path as shown in the figure. The movement of P is such that it sweeps out length
where
is in metre and t is in second. The radius of the path is 20 m. The acceleration of P when t =2s is nearly
![](data:image/png;base64,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)
A point P moves in counter-clockwise direction on a circular path as shown in the figure. The movement of P is such that it sweeps out length
where
is in metre and t is in second. The radius of the path is 20 m. The acceleration of P when t =2s is nearly
![](data:image/png;base64,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)
physics-General
maths-
The equation of the plane containing the line
where al + bm + cn is equal to
The equation of the plane containing the line
where al + bm + cn is equal to
maths-General
physics-
A small body of mass
slides down from the top of a hemisphere of radius
. The surface of block and hemisphere are frictionless. The height at which the body lose contact with the surface of the sphere is
![](data:image/png;base64,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)
A small body of mass
slides down from the top of a hemisphere of radius
. The surface of block and hemisphere are frictionless. The height at which the body lose contact with the surface of the sphere is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAXgAAACKCAMAAACXbqEyAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAMAUExURf////7+/vz8/KGhoTU1NTAwMJWVlXNzcxoaGoqKioKCgoGBgYuLiyIiImJiYnV1dUBAQOnp6ePj4+Tk5Ozs7ExMTGVlZXZ2djs7O9nZ2dfX19zc3N/f30dHR2ZmZtbW1t3d3efn5+jo6O7u7vDw8O/v7/Pz8/X19fT09Pf39/r6+v39/fn5+Xt7ezo6Oubm5ltbWz8/P97e3kZGRm1tbeHh4c/Pz7y8vKmpqZaWloCAgGdnZ1JSUhcXF1FRUerq6u3t7VRUVENDQ8XFxdTU1Li4uJycnFlZWT4+PiMjIwcHBwAAAAEBAXh4eHJycnFxcXBwcH9/f35+fnR0dHp6eikpKS8vL0hISIODg8PDw9jY2MLCwqOjo0FBQQ4ODgMDAxAQEB0dHSoqKjg4OElJSWBgYDw8PDQ0NDc3NyUlJQQEBDIyMjExMRkZGQwMDCEhIbKyssrKyuDg4NDQ0Kenp0JCQg0NDR4eHm9vb4eHh7u7u+Li4uvr64yMjBMTE/Ly8szMzJiYmCcnJxgYGAgICB8fH4iIiNvb26ampl1dXRYWFqurq9HR0URERGpqasbGxpubm25ubgkJCSwsLL29vbq6umtrayYmJgICAiQkJE9PT319fc7Oztra2omJiRQUFKKiopqammxsbD09PQoKCgUFBc3Nzfb29ldXV5eXl8fHx9LS0gYGBtXV1RISElBQUKysrAsLC8HBwRsbG19fX1ZWVlVVVRwcHKSkpOXl5WlpacvLy5+fn6+vr9PT08DAwKCgoFpaWvHx8WhoaLa2tp6enoaGhigoKLW1tfj4+I6Ojr+/v6ioqGFhYWNjY05OToSEhI2NjaWlpUVFRZSUlLm5uXl5eSAgIJKSkrOzszMzM5GRkZmZmcTExA8PD4WFhWRkZLS0tCsrK7CwsK2trXd3d3x8fMnJyZ2dncjIyLGxsbe3t/v7+5CQkK6urlNTU0pKShUVFVxcXF5eXi0tLZOTk6qqqhERETY2No+Pj1hYWDk5Ob6+vi4uLktLSwAAALnhSb4AAAEAdFJOU////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////wBT9wclAAAACXBIWXMAABcRAAAXEQHKJvM/AAALbklEQVR4Xu2dQZKzLBCGcwGuQFnVx/FGrFix4zochmLLFWD7dyNJTMaoMbSZ7x8ek4kaEuNL23QjOpdOp3MSyYsXU6glOizIHIyJ5udTuFqiw0L0MNA0Pe6vFytriQ4L0Q7LdOF5iX7QZOIPDLiuC88LCo9UwSvkbrrwzBSLfxK+W/wJ3Cy+Ll8uRfhu8dzcLP4ySY+vXfgzmFl8Vb4I310NN08WTy/d4s/gZvGke3kWi+/CczO3+Ko9hZPd1XBz9/HkY+gF6RbPz83i5/TGlZ9q8dNUX3DqFs8LgCzCL9CF52HQKoUobXZo3rPHZO4456weSoTZaQUMKkTnxVgQMUoZaYoG/5YHLYhRWBeTGuqnOh+BoifpSfAshLfSSH8FK0LU2YIoNSNcVLqL/xmgU7RFc++iQWOm1rR4F3xcTBaJslaKavChVTDRikziW5O62zkKDMGRihlFT8WNP6KxSuTk32foEG0u4kdVktvOWwAoiZ4jk+1i2L4AGJRXhGflafkqvje6S/8eOpJbFy6Q6D+suqCL4/9p8lV7ZTxKn23o7n43kCz5Cmc0nVx9RcjSO5dDXXwCP6fVVHtS1+/trAKBZLcGQ5PXqpPBu8HGwVJUvwyA1on8lXBd+k0Gkj2ji9FrqiMB207rLiq+MHkCgx10OdgGC5fq93cWGUilLMOqrU8YjFlspCi/rngBlqjS93b2FehkyCWnLWMvUKub0p6SGOEbh/XpVN1O55Ek98s+gVnTLor0eRSm+/qfaCPQKDHfrGI1BooXs6H7m0eKl8GY+z3ZlaozewAVMcKR3d/M0cXLvOFkCuCwcX0DSOhvsukZ1RVK/rHpe9vJgF/KW1cJmM7abvQTA5q7N1WZdwD7tvDF32TTPT2iMK9/28sUDlg8kjxmCt3dkJvBMO+I7mjx7/n4AoaWdIT99Ux2wObOHo4h9XKH8RY6CKzs+gv+JgqDSPl+q3rl4AdhSPZvu5tieUfl+wRQDtOGP5vHYq7qN7q41knvJFAPACXK/m/GlRDzeCB4n3Gocb2Bh9ufbGIhjqM7Fs1cORZOVgAwrhRpCDLGiHG9NlHGgL9L0xgdrBFQ9A4dFAHXUP8aGFxDia+mcTzU7aOwhKSyiT6EZYHKRixSvpfyBSyLRaayMiqcSdfvpS2enkdT1nQser/zkfD4cWxihZTOYh6GujjrLIU6CVdYOhQCvlJXMkR8h84fAr1DqmpcYSOVpSJUW4bWYNmBytIJLy2pLAmPbziqASzrLNWAwXdKbUnrnDj5PgCDG3P8UPdPhccmFpX/8g0QHFX6eRTd6+4fB9CS6uxBKKz8akAfciancxbQRPcGgKZfUn/VN8Co9kSTJ/9+pFOMA1L+e7FNoDFZp5k8mHH82L+3gvx8/tp5cKx1jO3qAjdF97rbHxI+Sr8mivJf6qIPOXopzzJ5PLzksc6tZw70xy9A8fwovtFFDxjSuHhxti7zkjBfbeRnPg0nK5AE2vwX+swS5gROXgZzRiOjxWhb+fc2Fj8p7ykxOpmEm0ThMUeuKxgZ7Og/6p+ZA95d6uyHYDj9BV9DWyThTwDkwoj245iVcZPvABjgYlCJjXX9nedxkvBoWb8icfqBxiNRgzx/wNM5wqODb9Wwtkb50cHFeOrXOpNThCcH/0t1Jzc/Gmzvzr6K4QzhIaIjrbvZBGjl4wtxFF/oOzhDeLSpxg6+UTg5QW6+hJRw5iXKJwg/oBdt62gaJVAViuaLCuBOvHSHX3h0NKJZBD/RKoGqgKnOZoj+tOiGX3jV3NE0tvjibOzkbMJpd+ZmFx5wp9p0jc0I9VIcHWWy4tPTUQNgK1QFP83Ns9/rJYy5Ycr6CGgvfAyHB9ncQXd4c+90twR+uG93gamTrDvHALmxcn+sDwFV21cCojsxumGitKx171pSnVfIrXo88cC8BfPJ2S8PQfichGkhg6OJ1XvFsVVvmXa1fSVA/usXjwDuTvOWlaKacj09aJmbBapoIjMzTzTy6x8mZZaW9RrHY9vaqlqxEkf/KPY/fMMhkHj8MnCN47VwzY4neDR5pAyF5GJgvaEOGXzdr6ZcRwuHpqN05l6eSN7xqeNYhxigwTN4eKSOjzeiZb2qcXzspRz42ljwj5XcliQyR0hz5+ClUC/AwOYpgAe2YQBacCau2FzxGPyNltUKFNg8C83lahKdY+f6cswGuQyepz61pbOAT0DgSKaiUEYIpmGrkc3gQX5yKc5rMBj46VsUx5AnmX1U8imMasTg2Qwe0FbqbFv8+HPoNiRrW6dTYEesTbWwtQYENJ+6P61pfCLkjsGDtP78GVq2tsxBCDyKFM8IfYoRmGh9IuQGNkuLcUxrX4NtK/4NLAP0B76m9e371eyGXMALr5JaijRJHu/nABqCR23jM60zjl9gvIHJrzJKYxteIOnIo4ETHFENNR9ssNWoxoig7sAzxrcb82Qpb9WeY3y8wqaVTR4+5QFbpldmqH2rtlCX013pftKrITF7LneAtO0rmAGBbk3/gmY3R1e+XNBcrmZuDGBEXPeFAbaoZtXXELjZdn6Zw8MPeWT0NGxxPH61fO1riOB/9R1zIXDGNJwWD8s51A0w/huXq+0G7YaxY5JR+EH5vJ6nqnI7iV8KiFan/xcBydfPr+1WD4r+xc5Gs7p4NEu+iAniaLeF/a0nwtHFs14BwvjdYPKqk58Iv/NWxRQa8J57YlRe+R3d5FraD9vYpn0/VwZeF8/YV4Not6ebHOSHA7otxy0khpHXxTPG8XudPEY3n5k8y/j4MGZeF88YTpZIfm+8CIAxzjJq46wVh/D405nG01R4LT6tdNc8oY3OWSySx/XaYxHeZcYuYYTV4rdTqDva+jFprX5MWqf8BeExB6k7wQNnArW3dZ2A+GqQosrrQSmH8Fqwneau8Maq7o2O8uGV8IlOZ6/AITwGNYzhHjvURNU92UEZvln+Yf4MXJW+YPGJOahhhsKa3ZEiTBZfBa/Qmm9YPHUY0LbZAMPpyiDNLgHcAm4Wf8Fp+kP/VPkbPh4zELYRNROs4SQZ6/67oJLwaGVFclosypcvOT+qGSTnAIOymyWc5DqqQNn9t78FQddGXC2eVpDJ46q0cdRwCI+/u+wBCzopQOEvQ3oRTnyOsqvnXR+YXM3N4mnNpsUDVQkJX2bagcJzhvFJJroeHV/qitbQpZf7A/nSuBaLryt2WHxKQMJD4x5KjZlf2QMetHU6BjVdccnCW8I/Wjz+oUqgA3PFx4MNFxcvra8gHzxvp3DKVisvGAMbbKTqvmwyNa5k8NNEf4pFqLXG1YjkZPM7hbAnrna0NLi0LjEg999v+R7HV+VJ+OJq1oQHL7LIra8/03wD4wt0RyX6Jx98xP2p6z2On4MHwXpUY/I47u6K24seM3OPQbnrfZ3n4G3hH5UvJybX43ig/2J7bY9bQcJzykIRg2AdEWtGX/dlE4rj0cfXT06UpY043rQ3+Isac9k4bZ/hSQZl5TRHj9ZP/P7wjvCLgQS6mlWL//wKY8xnfkzSc5NFneGB/ptBUvNdej2V9uwxiS5LOod5sadJaSnV1hZWXVEKP0nGMSNlneFA4tdLWfdlg2RGYWt1PWD9aJa0eYdV4VU9t/sA1uUN3fj1FXs/v/V6pe7KJrFW1zNW1gKv2NzCusWjq1lgtvI62+r1FXs/v/U6zd2XNpnOsU4vs4XnivzB1ia2hK/FHtnc6v+Uut+7dn+7UJV4mYHOqD+ztK4p7Bs4SP1de37eZhm13nU51GKd9qy6Goyd/qfTbHb3NJv9fFqP80vg2mFh1eIp3evwUCVeBhPsDhNV4mVqmc4RyGhXnlXiZbBIh4kq8QvKGZf+PPLcnNaY3u/PI8+i3esH/tmASvTn+8/77OJjix1FOot05TqdTqfT+RqXy39zjOnVHrSANQAAAABJRU5ErkJggg==)
physics-General
physics-
Average torque on a projectile of mass
, initial speed
and angles of projection
, between initial and final position
and
as shown in figure about the point of projection is
![](data:image/png;base64,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)
Average torque on a projectile of mass
, initial speed
and angles of projection
, between initial and final position
and
as shown in figure about the point of projection is
![](data:image/png;base64,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)
physics-General
physics-
A string of length
is fixed at one end and the string makes
rev/s around the vertical axis through, the fixed and as shown in the figure, then tension in the string is
![](data:image/png;base64,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)
A string of length
is fixed at one end and the string makes
rev/s around the vertical axis through, the fixed and as shown in the figure, then tension in the string is
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physics-General
physics-
A thin prism
with angle
and made from glass of refractive index 1.54 is combined with another thin prism
of refractive index 1.72 to produce dispersion without deviation. The angle of prism
will be
A thin prism
with angle
and made from glass of refractive index 1.54 is combined with another thin prism
of refractive index 1.72 to produce dispersion without deviation. The angle of prism
will be
physics-General
physics-
A triangular prism of glass is shown in the figure. A ray incident normally to one face is totally reflected, if
. The index of refraction of glass is
![](data:image/png;base64,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)
A triangular prism of glass is shown in the figure. A ray incident normally to one face is totally reflected, if
. The index of refraction of glass is
![](data:image/png;base64,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)
physics-General
physics-
Which of the following diagrams, shows correctly the dispersion of white light by a prism
Which of the following diagrams, shows correctly the dispersion of white light by a prism
physics-General
physics-
A ray of light incident normally on an isosceles right angled prism travels as shown in the figure. The least value of the refractive index of the prism must be
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9/pk+fLh5qF8kRDnXkTx9vyHsoLS2NjRs3cuDAAWbOnEmJEiVQKpVGPZRM1WdpWFenpWm6sEajQaFQ0K5dO8qUKUNERASxsbGMGTNGfBmWiFU4zJHfUHx6FAoF58+fZ+PGjQQFBdG0adMcz1NN9cNW2zvp4wVBQCqV8vHHHzN37lwSExPp0aMHsbGxWZ5fRCQ7nGbOqouTSF6fprl58yYzZ86kevXq9O3bVy9Uc81UY2F7mMWG8pUqVYrw8HA++ugjOnTowIYNG7K4R4qImMLh51kz719KpVISEhL49ddfuXjxItHR0RmuEM1czpSZaihsrIytzeLM7epG2e7du1OhQgVCQkI4d+4cw4cPx8PDI7tfnYiIc7gbpjcdtVotBw4cYNu2bUyYMIF33nnHoN+vsTpMtWNp2Fqz2FS8IAg0a9aM9evX8/fffxMYGMiLFy+MPpuIiA6nuJFfFyeTybh+/Trz5s3D39+f1q1bZzmfao5gLAnnZPXYUsHqPguCQLly5Vi1ahXFihWjRYsWHDp0SLzryQD79+/H19eXGzduOLorDsfhWzc6pFIpjx8/ZurUqXh5eTF06FBSUlKyFZC9563ZtW9JmbS0NEaMGIG/vz9t27Zl/vz5GQ4lvO28ePGC0NBQatSogbe3t6O743AcvnWji0tJSWH16tUcOHCAXbt2mZynGqrDnvPWzGFzPhsrk5aWRps2bahcuTJDhw7lypUrjB8/noIFCxp81reJsLAwKleuTJ8+fShQoICju+NwHD5n1cWdO3eOZcuWERkZSbVq1bL1UsrtEdOaOi1ZHU7/WaPRUL16daKjo3n+/Dnt27fn/Pnzb7VZvGjRIo4dO8bIkSPFy9b/Pw73DZZKpdy9e5fx48fTtm1bvvvuO70paGp7J/NnQ3WbG87JvNVYPzPHmzOPdXFxYdq0aTRu3Jivv/6adevWkZKSYrDuN5mTJ08SHh5Ot27dqF69uqO74zTY9YjckydPMhyRk0gkxMfHExYWxpUrV9i9e7d+RTg9pm7TtzZsizqM1WnO7f+m0lxcXPjrr78YNmwYnTt3ZtCgQRQqVChLuTeR5ORkvvvuOypUqMDPP/9M0aJFHd0lp8GhThFarZYtW7awdetWpk+frn+1hq1MXFuPmObUmV1b5qSlpaXRuHFjoqOj+ffffwkODubmzZsGD9q/aYSHhyOTyejTp48o1Ew47A4miUTCtWvXmDt3LlFRUdSuXTvDxdy2EKi5ZWxZpyWmr6k0tVqNt7c3v/76K2XKlKFDhw5s3rz5jTaLV69ezc6dO+nVqxdVq1Z1dHecDodcRSqRSHj48CGDBw+madOmdOnShaSkJKP5LVmlNbdMbq4eZ171tdYbSqvVIggCQ4YMoXLlygwYMIAbN27Qo0ePN27UOX/+PFOnTsXX15emTZs6ujtOiV3nrHFxccjlclJTU/npp584ePAg+/fvx8PDw+QVKobibDEHtaaMva+N0X12cXHh0qVLhIeHU6FCBYYPH0758uWzPE9eRKlU0rdvXwB++eUXSpYs6eAeOSd2n7PK5XJ27tzJ5s2bWbBgAZ6enlm+qObMA03t2Zoqk9vz1pyYvqbS0tLSePfdd1m4cCEAQUFBbN++/Y24AjUqKoq7d+8SFBQkCtUEdhWrXC7nypUrTJ48mXHjxtGwYUOjfr/WbIfo4pxp3mrLtLS0NFxcXAgLC6Np06aMHDmSefPm8fTpU/Iq0dHRbNy4kY4dO/Lhhx86ujtOjV3N4CtXrtCjRw/Kli3L0qVLsyyWGOtKduarueXeBLNYd3pHKpVy+PBh5s+fT+3atQkODqZSpUpZnseZiY2NpW/fvtSoUYPx48eTL18+R3fJqbGrWHv16sXu3bvZs2cPxYoVM0ssxuLNLetsAs0ctjYNXu/H3r9/n9mzZ5OUlERAQABNmzbNct2rM5KSkkJYWBiPHj3Sn64SMY3dzGCJRMLWrVtZvny53n3MXDPWUF5zTFND+Rw9b80ctjYNQKVSUbp0aUaPHk3lypX55ZdfmDNnTp64AnXhwoX6O5ZFoZqHXf8Eu7u7Ex8fj0ajwcXFRX/vr6HRzlC8OXHm1pfT7Z3sylhSX07SVCqV3mp55513WLNmDY8fPyYgIICKFStm+T04A3v37mX16tW0b9+eZs2aObo7eQa7msGDBg3iyJEjNGvWTD93TX8k7E0wi3Nan7VpEsnr63AuXrzIihUrkEgkdO/enUaNGmXpjyO5ffs2I0aMwNPTkylTppA/f35HdynPYFexvnz5ko0bNzJv3jw8PT0ZPnw4jRo1QqVS6V3prBWdsXhbiTgvzGMFQcDd3Z24uDiWLl3KyZMnadu2Lf7+/k4hiqSkJCIjI/nvv/+IiIjIcwtijsauWzdpaWl07NiRyMhI3NzcCAsLY/ny5ajValxdXQHjc0pj80Rr91bNmXeaas9Y2Bb15SQtNTWVIkWK0Lt3b7788ks2btzI5MmTuXfvnpH/FfsRHR3Ntm3b6NChgyhUK7DryPrs2TPkcjmurq7ExcWxfv16NmzYQOXKlRk+fDhVqlTR3w6hIy+OtLldnzlpUunrv8OnT59m/fr1+nntBx98kKVv9uDIkSP8+OOPeHl5sWLFCipXruyQfuRlHOLIr1KpKFq0KMHBwQwZMoR79+4RFBTEnj17cHd3RyaTZSljqJ7s4gzF28ORIjfqszRN51f88ccfExISQsGCBRk+fDirVq2ym9eTWq3m6tWrzJ8/n5CQEK5evYq3tzdeXl52af9Nw64j6/Pnz/V7gLrVTN2iyJIlSzh16hS+vr4EBATg6emZYZTNyWhqKC63HClsPZdNH2dNmiAIKBQKEhIS2LRpE7t27eKzzz6jV69euXavUWpqKqdOnWLJkiWcOXOGBw8e8PjxYwAGDx5MZGRkrrT7puPQ86yCIOh9XsPCwggICGDr1q106dKF8+fP4+7uniG/OaOksXhz9mmN5cuunLV7rIbqM1W/NWm67Z38+fPzww8/0Lt3by5cuEBYWJjNbwwUBIHHjx8TExPD4cOHkcvleHl56YVaokQJ3n//fZu2+TbhsJFVh655mUyGIAgcPnyYOXPm6I/QtW3bFrVaneGsqz3msebks+e8Nbv6zUnTWTK3bt1i9erVxMbG0r9/f5o3b55h6pETkpKSePDggX5VOiQkBK1Wi7u7O3fv3mXJkiU0aNDAJm29bTj0KlL4v7/+utsMmzRpwpQpU/Dz8yMyMpKhQ4cSHx+Pm5tbhi+doXrMiTMUb20+e85bM9dpaRqgt2QqVKhAcHAwjRs3ZsSIEUybNo1Xr15hCzw8PKhSpQr58uVj3bp1eHl5sWnTJpo3b07hwoV57733bNLO24jDboowlCYIAhqNhnLlytGnTx+GDh3K33//TYcOHTh9+jTu7u5Gv5Cm4uxpFuemQDPnsSQt/WeVSkWhQoX4/vvvGTRoEHv37mXkyJE8efIEW6BUKlmzZg0xMTGEhYVRrFgxPDw8KF68OJ6enjZp423EKa4iTZ+m++uvUCho1aoVUVFRVK5cmV69erF8+XLkcrnelM7JaKqLM3e12JJyuTlvtbQ9Y581Gg2urq589tlnjBs3DpVKRUBAAKdPnzY6LTCXEydOMHPmTAYOHKifo1aoUMFh20ZvCnads8bHx2eYs5pqWrdaLJFISEhIYNu2bcyaNYu6desyduxYSpcurV8tzsmqsLF4W8xjc9u10ZL2TOVzcXHh+fPnbNiwgRUrVjBy5Eh++OEHvaOKJTx48IDevXtTtmxZZs2apY+PjY3lzp07fP755xbXKfIah4oVshcsvF58UqvVHDp0iAkTJqBSqZg+fTofffQRSqVSv0Vhqg5z4m0hWHu4MlraB2PbO+nDMpmM5ORkDh48yNy5c2nevDmjRo2y6A13L1++JCIighMnThATE5NB7MnJyXrvKhHrcLhYwTzBSqVSBEHg1q1bzJ8/nwMHDtCjRw+6deuGQqHQrxbndD/WULw1q8/2Fqi57Zsqo1voe/DgAdOmTSMtLY0ZM2ZQpkyZLH3JjFqtZt26dQwaNIht27ZRv359g/03NQ0SMY1TiBXME6zuP1qtVhMTE8Po0aOpXbs2kZGRlC1bVu+Z4yxmcW4L0pL2LemXRCIhKSmJRYsWsWXLFqZPn06LFi30LoyGiI2Nxc/Pj759+9KnTx+j+USsx65iffHihf4ib2NYMsqeOnWKsLAwXr16RWRkJA0bNkSlUjnULHa0QDPHmTvCZk6TSqUolUr++OMPwsPD6d27N4MGDTK4H5uQkEBQUBAeHh4sXrw4S7qIbXCIWME8UZpK042y8fHxzJ07l/Xr19OtWzd69uxJ/vz59S91yqlZbAsT2FCcI81iS/64aLVabty4wfjx4yldujTz5s3L4FmmVCqZOnUqGzdu5ODBg+Lb3nIRh4kVci5YeC1amUxGTEwMISEh1KlTh6lTp/LOO++QlpZmsi5bm8W2FqQt27DWXNd9VqlUTJkyhePHj7NgwQLq1auHVqtlz549fPvtt2zfvp1PP/00S39FbIfDX6Zsal/UnD1TQRBQq9W0bt2a7du3o1ar6dixI3v37tUvaOTEh9hYvLUOFNmFc8MLypTfcHb90P3r6urK8OHD6dy5M//73/9YtmwZr169YsSIEfz888+iUO2AQ0fW9FgzyhqKl0qlzJgxg5kzZ9K9e3d69+5NoUKFLL6JwpK8jhwxza3T0pHUWJogCJw7d47Ro0ejUqmoUaMG69aty9K2iO1xuG+wjuw8m8yN12q1hIaGsnDhQhYvXkxgYCD37t2z2E3RVF5nGjHNrdMajydDaRKJhBo1avDNN99w48YNnjx5QmxsLCK5j9P4BuvSLTWLDcUrlUqaN2/O4cOH8fDwoF27dsTExJCammpRPab6nBOf3pyEc1KHLQQrlUo5e/YsU6ZMYc6cOXzyySc0adKELVu2mLSORHKOXc3ghISEbLdudNjCLJZIJLi6ujJnzhzCwsLo3r07ISEheHl52XV7xxnM4pwuMMH/7b9+//33NG3alNDQUFQqFQcOHCA8PJyuXbsyZMgQmx23E8mIQ8SqI7umbTWPVSgUHDp0iODgYCpWrEhERATlypXT/+Gw9TzWXqLOybzVmjS1Ws3IkSN5+PAha9eu1e9py2Qy7t+/z5gxY/D09GTSpEmUKVNG9FayMQ5fDc5JurlllEoljRo14vDhw/oXE69evZqEhARkMlmOzWJD80dz8jhy3mpN2tq1a4mJieGXX35BpVLp0zQaDaVLl2bmzJkUKFAAPz8//vzzT/1et4htcOjIqiMnZrElo69UKsXFxYUlS5YwdOhQvvvuOwYPHqx/nYduxdicNszpj7V7trk9Cpuqz9gK+4ULF+jUqRNjx47F19c3y+q6ILz2etJoNKxbt45FixYREhKCv79/BicKEetxCrHqsNYsttRcVigUnDp1isGDB+Pq6srIkSP54IMP8PDw0N9YYW3bttruMSePPeaxEomEV69e4e/vT926dRk1alSGK3YM1SOTyTh9+jTTpk2jVq1aDB06lOLFi2d5PhHLcJqtG7DeLLZ020epVPLBBx+wZ88e6tatS1BQEHPnzuXx48e4uLgYdFi3ZFXYWgeK3F49tmblWK1WM378eP2WmEajybYetVpNvXr1mD59Oo8fP8bf3599+/bpPcpErMOpRlYd9jKLdavF69evZ+jQoTRr1oxBgwbh4+ODVCrNMoKYasPa0dOcfLYehc2tz9XVld9++42xY8eyatUq/a0Ppkzm9GlyuZyUlBRmz57Nnj17GDp0KG3btnWKV3nkRewq1sTERLO3bsC61WBr0hQKBVeuXGHMmDE8fPiQwMBAvvzySwoVKqRfSDG3DWuEZm253BCoDldXVy5fvoy/vz/9+/enffv2RuszVbfOSvnjjz9YtWoVjRs3pmfPnqJZbAUOESuYN3pml8+WaXK5HK1WS2RkJEuXLuXrr7+mV69eVK5cGaVSaXDxyRnmtsiJXWQAABTOSURBVLkRlslkJCYmEhAQoH/vq0QiyfI7sOSPQb58+bh8+TLTp09HLpfTq1cvGjRoIO7JWoDDxAq2EWx26ZaaxTKZjN27dzN27FgqVqxI//79qV27Nq6urmaPsjkRrDn5cjoKm8ovkby+02rkyJGcOXOG5cuX4+3tbdT0Nbde3d3BcXFxzJgxg0uXLhEUFISvr69oFpuJQ8WqIydzVHPSrZnH3r59m8jISE6fPo2fnx/+/v4UL16clJQUs9uw5zw2uzzm1pc/f37WrFlDWFgYM2fO5JNPPrGovuzmsS4uLqhUKjZs2MDu3bv54osv6Nq1K8WKFctSTiQjTiFWcD6z2MXFBaVSyaJFi1iwYAENGzakX79+1KxZE5VKZXDD31rBmhuX2/NWhULBtWvXCAwMpFOnTnTu3Fk/0lpanykxS6VSFAoFx48fZ9myZXh5edGjRw9q165t8uqYtx2nESs4n2ClUilSqZRDhw4xY8YMtFot/v7+tGjRAnd3d/3BgOzqcTaz2Ng89eXLl/To0YOSJUsSHh6Ou7u7wX3nnApW99nDw4ObN28yd+5c7t27x48//oivr6/oRGEEpxKrDmc0ix89esScOXP4448/aNKkCf369aNs2bKkpqZavXhkKN5RgnVxceGnn37i0KFDzJ49m6pVq2ZYUMrOvLUmTavV6r8Xy5cv5++//6ZVq1Z06dKFokWLZin3tuOUYgXnEiy8/jKnpqbqXekqVKhA3759+fjjj0lLS8vWq8dUvL3MYkNpgiDg6enJpk2b+OWXXxg1ahQtWrTQm7+2MrNNmcVyuRyJRMJff/3Fxo0bKVOmDMHBwVSpUiXL873N2FWsL1++tHip3haizS6PuWk6s/jMmTMsXryYq1ev0q5dOzp16kTBggVJTU01u35nGWkVCgVXr16lT58++Pr68uOPP+Li4pJlTp7booXXi1sXLlxgyZIl3Llzh759+9KyZUtcXFwQcYBYLXGKSI+zjLQ6s/jZs2csXryY9evXU7t2bUaMGEHFihUNmsWm6rd2BDUnX3ZhqVRKUlISgYGBuLu7ExERgbe3t9GL5mwxkpv6LAgC7u7uPHnyhMWLF3PmzBnatWtHly5dxFsTcZBYwfzFpPQ4i2Dh/1aLd+zYwZIlS3Bzc6N37940a9YMQRAM+sFaIlhD8bYwl9N/9vDwYNy4cezatYsJEyZQv359tFqtTefDlgoWXjuo6A61b9u2jQoVKjB48OC33uvJYWLVYWnzziRYnVl87do1li9fzt69e2ndujV9+vShcOHCTmsWC4JAgQIF2LlzJxMmTKBnz560adMGqVRq9GK53BCsqTISiQQ3NzfOnTvHqlWrePDgASNGjKBhw4ZvrdeTw8UKuTPKmkrP3AdLRkFDaQqFgvj4eNasWcOyZcvw8fEhLCwMHx8fi1wVjcXbQrDpPysUCm7cuEG/fv1o0KAB/fr1I1++fNkuklkaTh9nLC27Mm5ubty/f5/ffvuNw4cPExgYaPUb7vI6TiFWyJ0R1lA+uVzOwIEDOXnyJAChoaH4+voaPGFjiWDlcjlpaWkcPXqURYsW8fTpU4KDg2ndujVSqTTHZrEtTGB4PWKpVCp69epFcnIyEydOpFKlSmbPU61pM6ejrFwuJykpib1797Jlyxbef/99fvrpp7duP9Zp3EVM3WxoLL+l+eRyOVFRUfz5558EBwfz/fff07dvXw4ePGhxG4bOcMpkMj799FMiIiL49NNPGTVqFKNHj+bFixe4ubkZrMPaq2PMzZc5XLBgQVatWsXdu3cJDAykYsWKGf5Q5fTqmOzC1twWqVarcXNzo3Xr1oSGhnLv3j06duzIpUuXrLLK8ipOI1Ydhv7TdHPD9D+6L03mazJlMlmGn8x5pk+fTs+ePfnuu+8IDg6mTp067Nq1y+SXyNw0rVaLWq2mTJky9O/fn59++okjR44QFBTEpUuXcHd3N/tgu7VXoJqK9/DwYO/evURHR9OlSxf9Ylh2z2VOu5YchDcmflNlBEFAq9VSo0YNQkJC8PHxoU2bNkRHRxu9judNw+nECmT4z5NIJGzevJly5crh4+NDhQoViIyM1ItYl08mk7Fu3ToaNmxIlSpVqFy5Mo0bN+b27dt64T5//pyEhAR8fHzQarVIpVJ8fHw4d+5chnZN9cmcNJVKhbu7O+3atWP+/PkUK1aMLl26sHz5cgRBMDgVMHc0NZTXnHy6eerkyZN59913+eabb/THAo3VYeubKtLnMRVvql6VSkWpUqUIDAykb9++TJ06lfDw8LdihHVKsQL6mxoWLVrEwIED6dSpEzt27KB79+6Eh4fz008/kZKSoh9p586di7+/P/Xq1WP58uVs27YNjUZDo0aNOH78OIIgUKRIEerUqcOiRYvQaDQkJiayePFimjdvrm/XVoLVXX/y3nvvMX78eLp27cpPP/1EaGgoiYmJKBQKs+vPqVkslUpRqVRERkaiVCrp1q0bhQsXRq1W58rVMebWYYm5nD6s0WjInz8/vr6+REREcObMGTp16sTjx4+zPP+bhNMsMGVGIpFw4sQJ/Pz8aNq0KatXr9anhYaGMm3aNH777Tc6duzI/v376d69O40aNWLy5MmUKlUKgMuXL/PFF19QpUoVfvvtN0qUKMGzZ89o0qQJ8fHxqFQq2rdvT3h4uMFNd2u2eAzFy2QylEolhw4dIiIiAoVCwfjx46lduzZpaWk5WlAyFJ85XKBAAVauXMmCBQvo27cvfn5+WdrN7YUlU2Fr92nh9e/24cOHLFu2jJiYGBYvXkyzZs2y9PVNwClHVolEglKp5MCBAyQkJPD5558D/3dV6IcffohEItGv6B47doxbt27xxRdfUKpUKbRaLRqNhmrVqlGrVi327dtHYmIiAEWLFmX37t3s27ePQ4cOMXHiRDw9PY32w1QfzY3XaDS4urrSrFkz1q5dS82aNWnXrh0LFiwAsGgea65ZrMPd3Z2jR4+yYsUKfH19ja585/bCkrE6s2sru35oNBqKFy9Or1696NevHwMGDGD27NlZnu9NwLxhzkaY+vJnRqPRkJycjFwuz7JE7+3tTcmSJYmLiwPg/v37ABQpUiRLWxUqVADgzp07VKpUCYCyZcvq82m1WpMLFBKJxOiIZizNULxWq0UikVC0aFHCwsJ47733GDVqlP7KTnd39yzbO5bUn34hRheWy+Xcv3+fSZMm4eHhwffff5+hrKEy6cOG2rImbKpOY58tSdM5ebRp04aaNWsyZcoUzp07x4wZM96o7R27j6zmCFYQBPLly0ft2rVJTEzk33//zVDWxcUFV1dXXrx4wa1bt3jx4oXRunVm9/379/VzNI1Go/8RBCHbPtlqhBUEAY1Gg0KhoGPHjmzbto1Hjx7RokULjh49anSENWc0zRyv+zIvW7aMp0+fMnDgQIoVK2azeaqpPlo6Cps7V82uThcXF959910iIiJIS0ujYcOGnD17ljcFh5jBuv9MUz8AtWrV4ssvv2TFihVs3boViUTCgwcPmD9/Pjdu3KBIkSKUKVOGypUrA+hN3fTcvXsXgDp16qBQKEyOkub02ZI0Y/GC8Pqwd82aNVm7di2ff/45LVu2ZNasWUb7YqlZ7O7uzu+//86+ffsIDAykQYMGGe6QsrVAranDWH2m2squH4Ig4O3tzfDhw2nbti1t2rRhzZo1RtvNS9hNrBKJhAIFCuDu7m7Wj0QiITQ0lJUrV/Lhhx/qtxq++eYb8uXLh6enJxUqVEAul1O9enU8PT05d+4cSUlJ+hXipKQkLly4QNWqVSlcuLBZfbTnKAvo3wiwYsUK5syZQ2BgIImJiTm6aNzV1ZWzZ8+yYMEC6tevT6dOnQx6UOX2iJldnabqy0kavN5T7tKlC1OmTGH27NmMHj2avI7dxCoIAk+fPuXFixdZfuLj4zP8pKSkEB0dzd27d/Hy8mLz5s2kpKSQnJzMX3/9hbu7OwULFqRx48YAfPvtt/j5+TFp0iT++OMPfZs9e/bk8uXLREREULJkSbP34nIiWEvL6Mzwr776iv3796NSqWjWrBl79+61eDSF16ujT58+ZdasWbx69YqgoCC9D645I7atBGlJnbmVJpfLadCgAbNmzeLixYu0bNmSGzdukFexqxmsUCgM/ri5ueHm5qYPAxkcteVyOW5ubri6uvLPP/+wY8cOWrZsSZMmTYDXX/jly5czZcoUAgMD9XPa3bt3c+7cOfz8/PRzOHOFZq1ZbI25rEsrWbIkK1asoGvXrrRr147JkydbZLZLJK/3VHfu3MmFCxcYPXo05cuXz3CQ3Nw+O3Lemrl8TtK0Wi0lSpRgwoQJVKxYkaZNm2b4g56XsOs+66tXr7LdZ9UJaufOnYwdO5bjx4/r006dOkX//v3x8PBg4cKFlC9fPsOKoClz01hb5mDtCZ+ctH3o0CEGDx5MhQoVmDx5MmXLltX/wTFWj6urK4cOHeKXX36hTZs29O/fn6SkJIPtWbtna+v9Vkvry8merEqlYs+ePSxatIhu3brRt2/fLG07M063z2pIcBqNhvnz5/Phhx9SsWJF1q9fn0GounI6cy/9j6VtWZPPkrmquXU2btyYgwcPUrhwYZo3b87mzZtNvhRKLpdz9epVZs+eTenSpQkMDCQ5OTlDvuxGPkP9cuS81VDY2jR4vVrcpk0bpk2bxtatWwkICODBgwfkFZxOrOnR+bNWq1aN9evXc+3aNVauXEmhQoXMdkDPDmc1i+G1Q8P8+fMJDQ0lODiYcePG6Q+0py8nk8l49eoVy5Yt4+rVq4wePdrovUXZfaGN9Ss35q3W1peTtLS0NKpUqcLUqVN5+fIl33zzDceOHTPaL2fCqcWqVCqpWLEiV69eZd++fVSqVMmmI2b6/OaUsWZhyZyy2dUbHBzMn3/+ybFjx/j22285c+YMarVaf/pIKpVy5MgR9u3bx7hx46hWrVqGN5NbKixz8+V0FM5JfTlJ02g0eHt7Ex4eTsuWLRkwYABr1qxx+sMATi1WHeaatemxRljmCtZa4VmbptVqqVu3Lrt27aJKlSq0adOGlStXkpKSgqurq94Lys/PDz8/P/08NbvnyBw21yzOrpytFpasLW9OmlarRaFQ0KdPH4YOHcrChQsJCwvTe8U5I3lCrNaOaI4yi3MjTaPRIJPJiIqKIjw8nClTpjBmzBjOnTvHrFmzkEqlDBgwAKVSqR9xs6vbHGEYyufoeWvmcE5Gb91W2cSJEzl9+jSBgYGcPHnSKc/I5gmxgnXCS182N9rKTnjWzFXNGbn9/f3ZunUrN27c4NNPP+XKlStMnTqVfPnyZfiS2crcNTefPeetmevLSVpKSgqVKlUiKioKLy8vQkJC2L59u9G3BjoKuzry2wJ7CdbZqVmzJnPmzGHcuHE0b96c999/H0EQDJ6TteWdTobicuteptyoz9QxPW9vbyZPnszmzZuZP38+Dx48oGPHjhQqVChLfxyBXfdZt27datY1kq6urhw+fJiVK1eybNkyXr58mSVPTrqdW49s7b6qtf2RSCR4eHigUqkyvCTLWtEZK5/T87bG0rPbb7WkvKn6JBLjb8JLH9bt1RcsWJCjR4+ycOFCmjRpwvDhw/nggw8c/mYAu4m1VatWZp/kFwQBV1dX/ftx3rRR0RG87b9DS55f9/1TKBQkJCTQunVr+vfvj5eXVy72MHvsJlYREZGckWcWmERE3nZEsYqI5BHsshr86NEj1q9frz9TqZvEFy5cmFKlStGgQQN7dENEJFvi4uLYu3cvT548wd3dnZSUFFQqFRLJ6yN3LVu2xMfHxyF9y3WxLliwgB07dqDVavUHwNVqNWvXrqVgwYJMmDBBFKuI05CSkkJsbCyLFy/mzp071K9fn+rVq/Pq1Sv27NnDtm3bmDRpkv7SPrsi5CLjx48X5HK50KNHDyE1NVUfr1QqBT8/P8HT01NISEjIzS6IiFhFjx49BA8PD2HXrl36uODgYAEQwsLChJcvX9q9T7k2Z509ezZjx45lwIABzJs3L8NmvYuLC2FhYXh5eVGwYMHc6oKIiFXcunWLa9euUadOHf3tmIB+68ZRroi5ItZHjx4xceJEKlasyKhRo7JsJkskEsqVK0dUVFRuNC8ikiOuXLlCbGws5cuXz7C3evHiRQDq1atH/vz57d6vXBHr8uXLiYuL47vvvsPDw8NgnqJFi+Lr65sbzYuI5Ig7d+7w8OFDatasSdGiRQGIioriyJEjjB071mE3/ufKAlN0dDRqtZr69eub/boMERFn4fbt2wCsWbOGs2fPEhcXR8mSJVm4cCH/+9//jA5AuY3NlaRSqXj48CEA1atXN3ilpoiIs/Ls2TMuX75M2bJl+frrryldujRSqZRDhw6xdOlS/a2a5vi42xqbizUxMVE/AX+TXl0g8nZw8+ZNLl++zEcffUTv3r0pXrw48PqKoQEDBvDy5UsWLVpE+fLl7d43mw97Xl5eetP3xo0bBk9TKJVKunfvztOnT23dvIhIjrhy5QoXLlzg3Xff1QsV4N1336VkyZLs37+fJ0+eOKRvuWKj6u7zjY6OznKAV6vVsmnTJkqVKmX07W0iIo7i0qVLSKVSqlWrliH+999/JzY2lgYNGugXnexNroh1+vTpVKxYkZkzZzJjxgz9Kwa1Wi1+fn5cv36dYcOGOfx8oIhIeu7cucPZs2fx9PTMsP+/ZMkSoqKicHNzY9iwYfq3Edqd3PK2uH79utChQwdBLpcLlSpVEqpUqSL4+PgI0dHRwqNHj3KrWRERi3n16pUwYcIEoWDBgoJMJhMAwcvLS6hatapQrVo1QSaTCV26dBH++eefDJ549iZXz7PGxcXx4MGDDA78derUeesPQos4F1qtlnv37vHo0SO9p51Go8ngqZTZQcIRiIfPRUTyCOImqIhIHkEUq4hIHkEUq4hIHkEUq4hIHkEUq4hIHkEUq4hIHkEUq4hIHkEUq4hIHkEUq4hIHkEUq4hIHkEUq4hIHkEUq4hIHkEUq4hIHkEUq4hIHkEUq4hIHkEUq4hIHkEUq4hIHkEUq4hIHkEUq4hIHkEUq4hIHkEUq4hIHkEUq4hIHkEUq4hIHkEUq4hIHuH/ATHaVqGuLK7PAAAAAElFTkSuQmCC)
A ray of light incident normally on an isosceles right angled prism travels as shown in the figure. The least value of the refractive index of the prism must be
![](data:image/png;base64,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)
physics-General