Maths-
General
Easy
Question
If
then ![D equals](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB4AAAANCAYAAAC+ct6XAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAALFJREFUeNpjYMAEP4D4PxL+AsSrgFiegYZABYgvIPGZgFgSiHOA+CEQB9HK4gAgXopDLhSIP0EdQ3VQD8QleORBwW5KC4tBcemHR34vELtgEf9PBMYLbkHjFBe4D8Si1PYtEzQocQEuIH5Ji2A2hwYlLhAPxLNxyFEU1JFAPBeP/CUg1qOFjycBcSIOuQlQTBOwDog9kPhsQOwGxNuAeBotS613SPHxB5qQQIWJJcNwAgBkUjKmYxGLegAAAFN0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+RDwvbWk+PG1vPj08L21vPjwvbWF0aD44VIUcAAAAAElFTkSuQmCC)
- none
The correct answer is: ![1 plus a to the power of 2 end exponent plus b to the power of 2 end exponent plus c to the power of 2 end exponent](data:image/png;base64,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)
In the question we were asked find the determinant of a given matrix
![open vertical bar table row cell a squared plus 1 end cell cell a b end cell cell a c end cell row cell b a end cell cell b squared plus 1 end cell cell b c end cell row cell c a end cell cell c b end cell cell c squared plus 1 end cell end table close vertical bar](data:image/png;base64,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)
Let us solve the matrix
Given matrix can be written as
![a squared plus 1 left parenthesis left parenthesis b squared plus 1 right parenthesis left parenthesis c squared plus 1 right parenthesis minus left parenthesis b c right parenthesis left parenthesis c b right parenthesis right parenthesis minus a b left parenthesis b a left parenthesis c squared plus 1 right parenthesis minus b c left parenthesis c a right parenthesis right parenthesis plus a c left parenthesis b a left parenthesis c squared plus 1 right parenthesis minus b c left parenthesis c a right parenthesis right parenthesis](data:image/png;base64,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)
After solving the expression we get ![1 plus a to the power of 2 end exponent plus b to the power of 2 end exponent plus c to the power of 2 end exponent](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHMAAAARCAYAAADuf5O3AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAetJREFUeNrtmEFEBGEUx8fK6rCiQ4eVRJJ0TZIOXTqtpGvHFR06JdFhrSSRDh26dUqSSPaUbslK16xOiY4ra29JkmV6j3+Mz0ffzOw3b2aaP392Pjvm570373vfOE4mU7nwN/mBPPrPOVIBnSOvkR8zjvRAf2Uc6YCeI9fjzjFGrpIbMUuk7eB9ogOYqIi2PyIckz85zsir2KviItvB4734yfC/XOzXYJKUL44gyXSloQOyLJEvDIvqhtwnHBvfHLaTyS1th9zCtMptfVgoeNvkCnjesDffaQqIWcZDTOZ+VCAfkJuIT43cH5TDdjL5bTsCICf2Em+IRPD42a/kLQ/PoeZtdTW2wVPA5L6HQs6TN8kLQTlsJnMZAfTqlFwSCt4LeUJZ4yC+d/nMbKp9FHqkD3cNrBO3sBllra5ps0E+MPhlyWGSVdUbMplheNqelhp5Jfm9Rz0G8O8PC1+PTDSN4lLFxXYrwDNFvneEghHknrZyPWvh646fln+iWd/AeTtqnhKGncQks4k29isO2pUQP+9NZWUtj3NnUYBnkvycpGTuko/RXnmfPMfkKsFfwwA0j+tBrJUF49nAJNuDQWwd3asrG7cNVTDRVvGWtjRHkyjEz11EQjsIpASHV0MYCDvoECtOwjTgZAqtH1ePsy1qcN9EAAAAynRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtbj4xPC9tbj48bW8+KzwvbW8+PG1zdXA+PG1pPmE8L21pPjxtbj4yPC9tbj48L21zdXA+PG1vPis8L21vPjxtc3VwPjxtaT5iPC9taT48bW4+MjwvbW4+PC9tc3VwPjxtbz4rPC9tbz48bXN1cD48bWk+YzwvbWk+PG1uPjI8L21uPjwvbXN1cD48L21hdGg+jyLDBAAAAABJRU5ErkJggg==)
Hence option A is the correct option
Related Questions to study
maths-
Let
such that
, then maximum value of
is
Let
such that
, then maximum value of
is
maths-General
Maths-
Statement‐I : The inverse of the matrix
where
is ![B equals left square bracket a subscript i j to the power of negative 1 end exponent end subscript right square bracket subscript n cross times n end subscript](data:image/png;base64,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)
Statement‐II : The inverse of singular matrix does not exist.
Hence option D is the suitable option
Statement‐I : The inverse of the matrix
where
is ![B equals left square bracket a subscript i j to the power of negative 1 end exponent end subscript right square bracket subscript n cross times n end subscript](data:image/png;base64,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)
Statement‐II : The inverse of singular matrix does not exist.
Maths-General
Hence option D is the suitable option
maths-
Let
be a
matrix and let
, where
for
If the determinant of
is 2, then the determinant of the matrix
is ‐
Let
be a
matrix and let
, where
for
If the determinant of
is 2, then the determinant of the matrix
is ‐
maths-General
physics-
The power factor of the circuit is
The capacitance of the circuit is equal to
![](data:image/png;base64,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)
The power factor of the circuit is
The capacitance of the circuit is equal to
![](data:image/png;base64,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)
physics-General
physics-
In a L–R decay circuit, the initial current at t = 0 is I. The total charge that has flown through the resistor till the energy in the inductor has reduced to one–fourth its initial value, is
In a L–R decay circuit, the initial current at t = 0 is I. The total charge that has flown through the resistor till the energy in the inductor has reduced to one–fourth its initial value, is
physics-General
physics-
The current in the given circuit is increasing with a rate a = 4 amp/s. The charge on the capacitor at an instant when the current in the circuit is 2 amp will be :
<img src="https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/610610/1/1102617/Picture43.png" alt=""
The current in the given circuit is increasing with a rate a = 4 amp/s. The charge on the capacitor at an instant when the current in the circuit is 2 amp will be :
<img src="https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/610610/1/1102617/Picture43.png" alt=""
physics-General
physics-
The radius of curvature of the left and right surface of the concave lens are 10cm and 15cm respectively. The radius of curvature of the mirror is 15cm
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)
The radius of curvature of the left and right surface of the concave lens are 10cm and 15cm respectively. The radius of curvature of the mirror is 15cm
![](data:image/png;base64,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)
physics-General
physics-
An object O is kept infront of a converging lens of focal length 30cm behind which there is a plane mirror at 15cm from the lens
![](data:image/png;base64,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)
An object O is kept infront of a converging lens of focal length 30cm behind which there is a plane mirror at 15cm from the lens
![](data:image/png;base64,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)
physics-General
physics-
A diminished image of an object is to be obtained on a large screen 1 m from it. This can be achieved by
A diminished image of an object is to be obtained on a large screen 1 m from it. This can be achieved by
physics-General
physics-
A curved surface of radius R separates two medium of refractive indices
and
2 as shown in figures A and B Identify the correct statement(s) related to the formation of images of a real object O placed at x from the pole of the concave surface, as shown in figure B
![](data:image/png;base64,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)
A curved surface of radius R separates two medium of refractive indices
and
2 as shown in figures A and B Identify the correct statement(s) related to the formation of images of a real object O placed at x from the pole of the concave surface, as shown in figure B
![](data:image/png;base64,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)
physics-General
physics-
A curved surface of radius R separates two medium of refractive indices
and
as shown in figures A and B Choose the correct statement(s) related to the virtual image formed by object O placed at a distance x, as shown in figure A
![](data:image/png;base64,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)
A curved surface of radius R separates two medium of refractive indices
and
as shown in figures A and B Choose the correct statement(s) related to the virtual image formed by object O placed at a distance x, as shown in figure A
![](data:image/png;base64,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)
physics-General
physics-
A curved surface of radius R separates two medium of refractive indices
and
as shown in figures A and B Choose the correct statement(s) related to the real image formed by the object O placed at a distance x, as shown in figure A
![](data:image/png;base64,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)
A curved surface of radius R separates two medium of refractive indices
and
as shown in figures A and B Choose the correct statement(s) related to the real image formed by the object O placed at a distance x, as shown in figure A
![](data:image/png;base64,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)
physics-General
physics-
Two refracting media are separated by a spherical interface as shown in the figure. PP’ is the principal axis, m1 and m2 are the refractive indices of medium of incidence and medium of refraction respectively. Then :
![](data:image/png;base64,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)
Two refracting media are separated by a spherical interface as shown in the figure. PP’ is the principal axis, m1 and m2 are the refractive indices of medium of incidence and medium of refraction respectively. Then :
![](data:image/png;base64,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)
physics-General
physics-
In the figure shown a point object O is placed in air on the principal axis. The radius of curvature of the spherical surface is 60 cm. If is the final image formed after all the refractions and reflections
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIsAAACNCAYAAACHQIniAAARtElEQVR4nO2de1CU1RvHv8ByR1RIEFnACxCgIIGgyEVWDUUwcNQg73gJJ5nxMkxmpmM2w88kG2sq03SwAhU1AUnRzHaRuGwpXpCbXNS4GCoJC8u6C+z5/eG0o0Hxgu+7FzifGf7Y3XOe51n4ct5zfY4eIYSAQmGAvqYDoOgOVCwUxlCxUBhDxUJhDBULhTFULBTGULFQGEPFQmEMFQuFMVQsFMZQsVAYQ8VCYQwVC4UxVCwUxlCxUBhDxUJhDBULhTFULBTGULFQGEPFQmEMFQuFMVQsFMZQsVAYQ8VCYQxP0wFwQWpqKsrLy+Hq6qrpUDinubkZa9euhaWlJee+BpVYCCHYt28f9u3bh5CQEHR0dGg6JM45f/48goOD4eXlhcLCQrS1tcHIyAgeHh5wcHBg1degEYtUKsWqVasgl8tRWloKKysrTYekFioqKiAUCtHQ0IDg4GBYW1tz5mtQ9FkaGhoQFBQEFxcXZGVlDRmh/I1AIEB0dDSnQgEGgVgqKysRHByMhIQEJCUlQU9PT9MhaZT29nZcvnwZtbW1rNvW6cdQRUUFQkND8b///Q9xcXGaDkdj3LlzB1VVVTA0NMTIkSMRFBQEExMT1v3orFjq6+sRHh4+5IUCAObm5oiOjubcj04+hiQSCSIiIrBz506NCqWpqUljvp/H3t6+x3tcpN3RObF0d3cjJiYGixcv5lwo3d3duHTpElasWIGpU6fi8ePHqs/u37+PsrIyHDhwADNnzoS7uzuKi4s5jaevWAsLC5GZmYkff/wR9+7dY98J0TG2bNlCli9frhZf3d3d5Pbt24QQQvbv30+OHDmi+uy7774jHR0dJDMzkxBCSEFBAQkMDFRLXM8zd+5c8vHHH5P09HRSV1fHqS+d6rP88MMPEAqFKCgoYFwnNzcXqamp8PT0RE5ODpKTkzFp0qQXykgkEmRlZfWoKxAIMHHiRBBCYGVlhaioKNVnSqUSpqamqve8vb1hY2MzwG/2cggEAvj5+XHviFMpskhdXR1xdHQk1dXV/aonk8mIk5MTefLkCUlNTSXvvfdejzJPnz4lt27d6vHT2tpKurq6yOHDh8no0aOJWCwmhBBSWVlJCgoKXrBx4sQJkpeXN/AvOEDmzp1LfvvtN9VrmUxGcnNz+/17YoLOtCzr16/Hjh07MGHChH7V4/F4sLS0xIgRI2Bvb99rq0QIgUKh6PG+UqmEgYEB1qxZA3t7e+zduxenT5+GWCzGsmXLVOVKS0thbm6OoKCg/n8xFrh//z5qa2thYGAAc3NzTJ8+HcOHD2fdj06I5eTJk5DJZFi7di1rNqVSKSorK+Hl5QUTExP4+vr+Z3kfHx94enqCEAJCiGryr7GxERKJBJGRkZDJZOju7oaFhQVrcTKhq6sLb775JvT1uR2vaL1Y5HI5du7ciezs7AHVv3HjBkxMTFBfX4+SkhK0tLRAIpFgx44dePfdd+Hj44NTp07h1Vdf7VG3vb0dcXFxmD17NuRyORITE3H79m14enoCAP766y+sWrUKXV1dAAALC4te+z5cM2HCBM6FAkD7+yyffPIJ2b59O6s2m5qaSFRUFOns7CSRkZFEoVCwal+d/N1nUSqV5Pr16+TMmTMkOzub1NTUsO5Lq1uWtrY2pKSkQCwWs2rXxsYGzs7OKCwsxAcffABDQ0NW7asboVCImpoa+Pr6YsGCBZz50Wqx7N+/H2+//TbMzc1ZtSuTySAUCtHW1gYejwd7e3vw+XxWfagTdQ2dtVYsEokEx44dw82bN1m3fefOHXz66acICAhAY2MjcnNzsXTpUtb9aAKlUoni4mJYW1tj3LhxrNrWWrF89dVXiIqKgpGREeu2DQwMkJaWhrNnz2L8+PFYsmQJ6z7USVNTE06fPg0AMDExwbRp0/DKK6+w7kePEO276EGpVMLBwQFXrlzp97zKUCM8PBwxMTFYunQp530vrVxILCgogIODAxUKQyZOnKiWTrpWPobOnDmD2NhYTYehc1RVVaGsrAw8Hg/u7u4YP348q/a1Uixnz57F5cuXNR2GziASiVBbWws3N7cXFjvZRuvEUllZCVNTUzg5OWk6FJ0hNDRULUNnreuz5OTkICIiQtNh6DQlJSWa27BNCMH58+fR2NgIuVyOzs5OvPPOOzA2NmY9oMuXL2Pjxo2s2x3MtLS0IDMzEwqFAkZGRnjttdc4aZkZiSUpKQlmZmbYvHkzACA7OxvLly9Heno6q0cvuru7IRaLERgYyJrNoUBtbS1WrFgBU1NTbh31tXgkk8mIqakpaWlpeeF9Nzc31WYgtrhz5w7x8fFh1eZg55+bn7ikz5alpqYGhoaGPTbTODs74+rVq/D392dNuDU1NXRu5SWor69HcXExDAwM4Obmxvrvsk+xjB49Gu3t7ZDL5S/0UaRSaa9HEF6Gu3fvsj43MBT4e+js5OSEiIgIGBgYcOKnT7FYW1tjzpw5KCoqwowZMwA8W7V9/PgxwsLCWA2moaEBjo6OrNocCqhr6Myog3vkyBHs2bMH9+7dg4mJCSoqKpCZmcl6h6qxsVE9u9QHOTU1NdDT09PMDK6dnR0+++wzSKVSKJVKxMTEsBrE3zx8+BCjR4/mxPZgpqOjAxcuXIBUKlX1V9zc3Fj3068Z3KNHj6K0tBQzZszgRDAdHR0wMzNj3e5g5/bt21i2bBknO/qfp4dYvvnmG0il0h4Fr127hpMnT0KhUODw4cP49ddfWe9t19bW4sSJE3RdqB/IZDL4+/tzLhSgF7FIpVK0t7f3KPjo0SPV2RqlUonGxkbY2tqyFkhubi7a29shk8l69U/pHfLcdqTOzk4UFRWhtbUVHh4erPdZGG9+unHjBgIDA2FmZga5XI6bN2+yum3v/fffR0ZGBk6dOtXjeCnl3wkPD8esWbPA5/NhZmaGwMBAzjJAMe6zeHt7o7y8HOXl5Zg0aRLrcywbNmzA1atXh0TSQLYJCQlhdXL03+hXB9fR0ZGzeZDPP/8cUqlUa3Ke6BL/XJ/r6OhAa2sr7OzsWPWjNftZvLy8UF9fj/r6ek2HonMQQlBSUoKKigrV2e6AgADW/WiNWMaNG4fx48ejrq5O06HoHCKRCOHh4Vi0aBGnCRi1RixZWVmQy+VobGzUdCg6h0AgUJ2/5hKt2Sk3f/58zJkzB9XV1ZoORWchhODatWs4d+7c4E5t2tDQgFGjRqGurg4ymYz7jTyDiLy8PFRXV8PY2Bh+fn59pg8ZKFojluLiYri6umLq1KnIz8/H7NmzNR2SzhAQEMBJh/afaI1YEhISYGJigpaWFvzyyy9ULP2Ax3vxz9jZ2YnW1lbWj7BqjViOHz+OsWPHIiwsDEuWLEFSUpKmQ9Ip7t69i+vXr0NfXx9mZmaDe+jc3NwMa2treHp64smTJ7h79y7rWQAGKyKRCDNmzMCCBQs4HTprzWhox44dqmwGkZGRqqwAlL4JDQ2Fv78/55dcaI1YPvroIxw7dgwAEBsbi/T0dA1HpJuUlZUN/qGzk5OTKulwSEgImpqaUFlZ2WtiQMqLFBQUoLq6GoaGhvDy8uLsRKfWiEUgEKjSgenr6yMhIQEpKSnYs2ePhiPTfnx8fBAcHMy5H615DB09ehSXLl1SvV6/fj0yMzPR2dmpwah0g3/eLUQIgUQiYd2P1rQswcHBGDVqlOr18OHDERMTg4MHDyIhIUGDkekGTU1NKCoqAiEExsbGnOxv0Rqx8Hi8HoejEhMTERAQgJUrV2LYsGEaikz7EQqF8PPzw7x58zjNAKU1jyGhUNgjM+WwYcOwfv167N69W0NR6QYCgQACgWDo5JRbtmwZZs6c2eP9+Ph45OTkoKysTANR6R737t0b/EPnwsJC8Pn8HrO2hoaGSEpKQnx8PK5cuTLkb1ftjd9//x01NTXg8XhwcXHhbOisNS1LTU0NHjx40Otnb7zxBmxtbfHFF1+oOSrdwN3dHbGxsVi0aBEmT57MmR+taVm2bdvWY/X0eb788kv4+/tj9uzZcHd3V2Nk2k9vV9ZwsSdIa8SSnJwMFxcXrFq1qtfPbW1tceDAASxevBhisZj1fP66TktLCwoKCqBQKGBoaAhfX9/BKxYzM7M+c9TNmzcP+fn5iIuLYz1FmS4jFArR3NyM0NBQTs+Ka0069gcPHsDY2BhWVlb/WU6pVGLhwoVwd3ene17w7ETi7t27h1Zq0/379yMjI6PPcvr6+khLS8PPP/+Mr7/+Wg2R6RaPHj3ChQsXBvfQedKkSRgzZgyjsmZmZsjJyYFAIMCwYcMGzfUvA+XmzZuqVWd7e3u8/vrrnKQK0xqxuLi4YMSIEYzLW1tb4+LFi5g1axY6Ojqwbt06DqPTbvh8PubOncu5H615DGVkZCA/P79fdezs7CASiXDw4EHs2rWLo8i0n96yJnCxWq81LUtERARGjhzZ73o2NjYQiUSIiYlBbGwsUlJShuSZI5lMhvz8fLS3t4PH48Hb25v1q/wYtyyNjY2Ijo6GkZER7OzscP78+QE5lEqliIuLA4/Hg5WVFQ4dOgQA+PPPP/HkyZMB2bSwsEB2djbGjh2LoKAgVFVVDciOriISiXDp0iVMmTIF0dHRiIyM5OTOxz6HzoQQfPvtt9i8eTNaWlrg6OiIqKgoWFpavpTjkpIS/PTTT3j69ClmzZoFZ2dn+Pn5Yc2aNS9lNyMjAxs3bkRkZGSfw/DBwPHjx7FhwwZs2bKFc199Pob09PRgY2MDCwsLtLS0oKurC8OHD3+prJKEEJSWlqouz7a1tcW6detYSRC0YMEC+Pr6IjMzk7PkwdrEW2+9BQ8PD/U4Y5q3vbW1lcTHxxM+n09cXV3JuXPnBpT/va2tjaxevZrw+Xzi4eFBsrOzCSGEJCcnk1OnTg3IJkU9sD6DKxKJIBaLsXXr1n7V27p1K1xdXV/6MUThDtbFUl5ejk2bNuHixYv9qtfR0QEDAwMYGxsjNzcXqampAJ4doFqyZAldB8KzbRzJyclQKBRwdnZGYmIiJ1cZ/xusDZ2VSiXEYvGAEwh++OGHcHR0RGlpKQ4cOAB9fX1s3LgRfn5+nExd6ypz5szBpk2bkJKSgrS0NKSkpKgl+SDAolg2bNiA1atXo7i4eED1+Xw+xGIxvv/+ewDAyJEjkZubi7y8PLZCHDT8vde2rKwM8fHxEIlEakmazLiD+180NDSQ8PBwQgghdXV1JCwsjBDy7GKrQ4cOkYqKij5tlJeXkz/++INcuXKFODs7EwBk8uTJpKysjI0QBwVyuZxs2bKF6OnpEUNDQ7Jr1y6iUCjU5p+VlqWmpkb1+Hm+b8Hj8VBeXg53d/c+j6GmpKSoOri3bt1CUVERAEAikYAQohV9loqKCtja2g5oppkNHj58iMjISERGRsLR0VHtF3mxIhY/Pz+Ul5fj2LFj4PF4aG5uVqXQYNo8Tp8+XXXW2dTUFAKBgI3QWKO5uRmxsbE4evSoxsTC5/M5mZllCisLiSYmJsjLy8P9+/dhb2+P7du392sFGQDMzc17HMPUJqytrYd8mnjWOriurq7Ytm3bgOtrq1gkEgmSk5MxZswYXL16VdPhaBTOV52VSiWjcupIoDcQkpOTERwcjLCwsBcWT6uqqiCXy+Hi4sLJ/dbaCKf7WRQKBaZMmfKfRzy0HaFQCAcHBwBQ9b+EQiHOnDmDxMRE7N27V5PhqRVOxWJkZIT58+dj2rRpXLrhFCcnJ5w9exYA8PTpUwDP7hnYunUrMjIyIBQKNRmeWtHdf3k18dFHH2HlypWor6+HpaUlamtr4e3tDeDZUHbhwoUajlB9aM1REF2DEIL09HQsWrRIpx+z/YGKZYCcO3cOISEh0NfXh76+/pDYyknFMgDS0tKQlZUFIyMjGBgYICUlBfr6WrP3nTOoWCiMGfz/DhTWoGKhMIaKhcIYKhYKY6hYKIyhYqEwhoqFwhgqFgpjqFgojKFioTCGioXCGCoWCmOoWCiMoWKhMIaKhcIYKhYKY6hYKIyhYqEwhoqFwhgqFgpjqFgojKFioTCGioXCGCoWCmOoWCiMoWKhMOb/xj/dQjBaliwAAAAASUVORK5CYII=)
In the figure shown a point object O is placed in air on the principal axis. The radius of curvature of the spherical surface is 60 cm. If is the final image formed after all the refractions and reflections
![](data:image/png;base64,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)
physics-General
physics-
In the diagram shown, a ray of light is incident on the interface between 1 and 2 at angle slightly greater than critical angle. The light suffers total internal reflection at this interface. After that the light ray falls at the interface of 1 and 3, and again it suffers total internal reflection. Which of the following relations should hold true?
![](data:image/png;base64,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)
In the diagram shown, a ray of light is incident on the interface between 1 and 2 at angle slightly greater than critical angle. The light suffers total internal reflection at this interface. After that the light ray falls at the interface of 1 and 3, and again it suffers total internal reflection. Which of the following relations should hold true?
![](data:image/png;base64,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)
physics-General