Maths-
General
Easy
Question
If A =
and (aI2 + bA)2 = A, then-
- a = b =
- a = b = 1/
- a = b =
- a = b = 1/
The correct answer is: a = b = 1/![square root of 2](data:image/png;base64,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)
In the question we were given to find the value of a and b by considering some conditions
![A squared equals open square brackets table row 0 1 row cell negative 1 end cell 0 end table close square brackets open square brackets table row 0 1 row cell negative 1 end cell 0 end table close square brackets equals open square brackets table row cell negative 1 end cell 0 row 0 cell negative 1 end cell end table close square brackets equals negative I
left parenthesis a I plus b A right parenthesis squared equals left parenthesis a I plus b A right parenthesis left parenthesis a I plus b A right parenthesis
a squared I squared plus a b I A plus b a A I plus b squared A squared
a squared I plus 2 a b A plus b squared A squared
a squared I plus 2 a b A minus b squared I
left parenthesis a squared minus b squared right parenthesis I plus 2 a b A
open square brackets table row cell a squared minus b squared end cell 0 row 0 cell a squared minus b squared end cell end table close square brackets plus 2 a b open square brackets table row 0 1 row cell negative 1 end cell 0 end table close square brackets
equals greater than open square brackets table row cell a squared minus b squared end cell cell 2 a b end cell row cell negative 2 a b end cell cell a squared minus b squared end cell end table close square brackets
B y space s o l v i n g space w e space g e t space
a equals b equals plus-or-minus fraction numerator 1 over denominator square root of 2 end 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Hence Choice 2 is correct
Related Questions to study
maths-
If A =
then (A– 2I) (A – 3I) equals-
If A =
then (A– 2I) (A – 3I) equals-
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, then A4 is equal to-
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If A =
, I is the unit matrix of the order two & a, b are arbitrary constant then
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, I is the unit matrix of the order two & a, b are arbitrary constant then
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Maths-General
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If AB = C; then A, B, C are-
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physics-
The magnitude of I in ampere is
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L2qxN+lD93bmQO8BbI5cWN3DxCxRplvKDceuWH6BOey10F9xcYbyONWx22XjwAzE8WmsF9KT93j6doF0I5arFpPgUPG8SVxbHhAvi1NiLtE5oObKho65qx16Mv2J/xIzeC7yeZY8khXyEZJJtR5H2jH20qGT/KoZnot+k14FelaZBtY0iLAbiSzfUvHv+Ut/J3TP8C2YCL1qPyUEnMW8KfRL/Fr6u/q2CGWM6twAogfKDs0Qd/5Lds9U+bQFbIHO4nUHtOAAexcXNq3MLIvMQhUjLZUFvIpYC6EJutvaXNAEElLEB2bkFuFk0LHIPy0GzfzdMP4fWeLtQIDLa7ixIyXJKIDUdQd2HxGvjhXaGdJRsNvMOoU9t6cMC783qH2W4DGdSLIiShDXeqjtYYhH8qa+GtRHoJl8/mofQTWF5afwUVdkXbfJC3A/OaoTbDD30NnWEnPEtlJbUKNyzpITUkqjtCzVff5xXw//2R9wT99ku1paz7M82Mp6RW4ZERavKNRwU/HPZumGXbN+f/rnzmRtWtFeRjtBz613QfOWUtjABn5JLH4ZHWuj2lw0YQXRZ7QRmIZcEnzIxJjgLLX7e3CdcdUh225wfP6PMyCV6f5xgSb59FbZzM3bnAmHSPDNaUfW8HUZoOBgr5MrkQ9LyY5BAMynYgcr+U1iaEsBeUDH7jPHnoq4jNIZ7TgzlnxSRHQCLTO62by7V0tGcpbEuP5Al8itCYdw3EziitTYl5Ftt2P0Yf4MwgsRQI2EAUu7UR3wtC1yjNqp4lBrbWTpg2v9MJckk67LuzZHV0KZN5euxq5vKTS5EmWorNWbXgwKerHE6h9sOoj9WesGzPEisblX/FjyCHbKU1JCN3ZN4wXZFx/JiErQ6PlKTYHjaX2yakthvt8GY4ApSNH/lSw1chI56O6A/vt9n+8CjWCJGZpovMHjPysV8x7WLZnCih4eQS9Su7Pbba0rD26NuLG/H/4K1jgg71vMGDSxHLRphZo0TFxqy+n8AzqPZhPQm1fmyzMjsKQzIUqB3Ha//GKSJTjPgQDS1fZpHgwLbtPTL4h9+cDfmVk6HD3GTl/C+cIbw1w5Auyg+5fqnjcW2bHQ6e3LjSNI3Yt9g9+yn+gh/xIVXa7YNIlwRJTXDUsiQc81NXzEZY/GpLh6giqffCCsVhhmZWfpXUFOpJDiY3+/U8lVAqVsc67Ofsitp4/ngL6XyeRdj7p6j9uOPbToHzO2rMKrnk/VRzO6ZE2LpxOKh2ZHvDQdR+GmEfAgSN7Bp3jDNgreaRtfZVLVOt/kI8+n6QOR7mHnxESHXLDsUHcIQwjMfVT4cBxbGc602DlP4Mlg+PrDUHb6D0O5oKbrcwwv6Nqo4/hXpz3t+9q314J1JAGVcaLvd8JmzyOrYTGZBaqV2rPVUlcjSk5L5ftTna8TRaq9q7nU/sBMvm3VA8iW7sC4mwT+KwlWLbW09peD9rk/stJGGZKw/OsZmHrX56AtTeGpMM8kLcvuWIcgVsrT0267APUZ+wBHYF2KI29O1HXaBoylG4TqwZkbwMC183ER8PdTbDBrDtDSUHz4oWnWeb3e1SyqWfI8eFJemQuDyigO85ncNWughw1bmx29c1ylu9i20jU0FT3lCz25CrcjvZwfYxdNgnivrGbIhJoGasL8WyXVXXFS5d5oTkPl2kj6Oft7TNHWwvOJ3DVjrbXgMH7RbLduwljqd4zYjdG11Toqr13/NB1PcrnT92wha1OUU/n6GQdBLnahIOLqUbhFJfFov9Y+DMyVgfk7imrGMAsWUxMYodxN6L2HneohQDzLFPrbVY0zq1XSyrdnBFMfHS4ka4yoqKvdCNHLeXyALWehK4kSgJ5I+dGwmeK1yJzw6IDJeJfc4I+xaNSRbLzYCPz3QjzNZo2XhqLq1mkMua307vsAsll9SN+XQ+WwZ9VhRbssaKYyGwhbLNEu1OHGHfUmx76Zn2YruqbZMYePKM3hiblHEB8wvs1HrFBT8kHJ+yUG3EHbBkkZOBR8DtATfAiIITFHmueaNTf80BN8K3aC22/WTKqcdQ1fbC2aTwJsQjXNuQNf7INeucKy4Bx7lCZ+pXGh114/wsLt3w8mROdcf3IGjjbFBIsjTJKUbpsuc32rIf9hdkjj1UG0WT2WcM09Y582TDdSlOpseGhPIsL33JV0TYN2gEuIxRlaEmuKck5e8sCfHRX+OwlcWe5F1A669yIgJ77yzKJd/Esfthr6XEJLrxEmnVHVgrFzPHw3frW8MiTzIeDDcasoascUnjI+KWzzivz1PUnmeljPK62wDhROd1ncznPJvvirBvUbXnEIbB+YiqhyVBXk9dMGJypOPpKX57zulXHA0lRgnrpMKy14e8oLrv+yLsW2Dbs3rv4KpUUecfS3VD0SQdEouO8pLXfGGEfQvD3sT1ZUe/8nP7SJzfXGeGwM2g7kDWk0Aox+OgjIl346XDIfBz80Ag8nUR9i30o1HgE2fZ1iQpaVaFQCYnK/5ypV/nK8kupbevTMMPrWHjo/feHUV+vl5rqA0R0yvYtw964i+0hcyyjgcXmHCITbDbw471pc/hzPz6od8LCyyu/OE0Nf0feSqISmWVColEvCgMF4TIESEN15Po3oNH/9ay3WFSL8DlXDFDRZIdLeGExS+wS8mwbJ7xHtjA0k9OVuVGazmwu44n7tv0Gegw+kJQxUXWS9DHAs83x8+/A9t3O1Ud7FnN2YfvLYT/IhyU0ZnwUPRmjG2G/Xagau+b2TjWSbygG4Mxn7GoJrBhGIZhGIZhGIZhGIZhGIZhGIZhGIZhGIaxX/79+x+h9RZUzdq5IAAAAABJRU5ErkJggg==)
The magnitude of I in ampere is
![](data:image/png;base64,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)
physics-General
physics-
A cord of length 64 m is used to connect a 100 kg astronaut to a space-ship whose mass is much larger than that of the astronaut. Estimate the value of the tension in the cord. Assume that the space-ship is orbiting near earth surface. Also assume that the space-ship and the astronaut fall on a straight line from the earth’s centre. The radius of the earth is 6400 km.
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)
A cord of length 64 m is used to connect a 100 kg astronaut to a space-ship whose mass is much larger than that of the astronaut. Estimate the value of the tension in the cord. Assume that the space-ship is orbiting near earth surface. Also assume that the space-ship and the astronaut fall on a straight line from the earth’s centre. The radius of the earth is 6400 km.
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)
physics-General
Maths-
If for a matrix A, A3 = I then A–1 equals -
If for a matrix A, A3 = I then A–1 equals -
Maths-General
physics-
The temperature of the two outer surfaces of a composite slab, consists of two materials having coefficients of thermal conductivity K and 2K and thickness x and 4x respectively
and ![text end text T subscript 1 end subscript open parentheses T subscript 2 end subscript greater than T subscript 1 end subscript close parentheses](data:image/png;base64,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)
The rate of heat transfer through slab, in a steady state is
with f equals to
![](data:image/png;base64,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)
The temperature of the two outer surfaces of a composite slab, consists of two materials having coefficients of thermal conductivity K and 2K and thickness x and 4x respectively
and ![text end text T subscript 1 end subscript open parentheses T subscript 2 end subscript greater than T subscript 1 end subscript close parentheses](data:image/png;base64,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)
The rate of heat transfer through slab, in a steady state is
with f equals to
![](data:image/png;base64,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)
physics-General
physics-
Three rods of material x and three rods of material y are connected as shown in figure all the rods are of identical length and cross section If the end A is maintained at 60
C and the junction E at 10
C, find effective Thermal Resistance Given length of each rod=l, area of cross-section=A, conductivity of x=K and conductivity of y=2K
![](data:image/png;base64,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)
Three rods of material x and three rods of material y are connected as shown in figure all the rods are of identical length and cross section If the end A is maintained at 60
C and the junction E at 10
C, find effective Thermal Resistance Given length of each rod=l, area of cross-section=A, conductivity of x=K and conductivity of y=2K
![](data:image/png;base64,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)
physics-General
physics-
One end of a copper rod of uniform cross section and of length 1.5m is kept in contact with ice and the other end with water at 100
C At what point along its length should a temperature of 200
C be maintained so that in steady sate, the mass of ice melting be equal to that of the steam produced in same interval of time? Assume that the whole system is insulated from surroundings
and ![text end text open L subscript text steam end text end subscript equals 540 c a l divided by g m close parentheses](data:image/png;base64,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)
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)
One end of a copper rod of uniform cross section and of length 1.5m is kept in contact with ice and the other end with water at 100
C At what point along its length should a temperature of 200
C be maintained so that in steady sate, the mass of ice melting be equal to that of the steam produced in same interval of time? Assume that the whole system is insulated from surroundings
and ![text end text open L subscript text steam end text end subscript equals 540 c a l divided by g m close parentheses](data:image/png;base64,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)
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)
physics-General
Maths-
If A =
, then the value of adj (adj A) is -
If A =
, then the value of adj (adj A) is -
Maths-General