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CBSE mathematics

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CBSEENMA12035689
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If A is a square matrix such that straight A squared equals straight A comma then write the value of 7 straight A minus left parenthesis straight I plus straight A right parenthesis cubed comma where I is an identity matrix.

Solution

Given that straight A squared equals straight A
We need to find the value of 7 straight A minus left parenthesis straight I plus straight A right parenthesis cubed comma Where I is the identity matrix.
Thus, 
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CBSEENMA12035690
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If space open square brackets table row cell straight x minus straight y end cell cell space straight z end cell row cell 2 straight x minus straight y end cell cell space straight w end cell end table close square brackets space equals space open square brackets table row cell negative 1 end cell cell space 4 end cell row 0 cell space 5 end cell end table close square brackets comma space find space the space value space of space straight x plus straight y.

Solution

Given space that space open square brackets table row cell straight x minus straight y end cell straight z row cell 2 straight x minus straight y end cell straight w end table close square brackets space equals space open square brackets table row cell negative 1 end cell cell space 4 end cell row cell space space 0 end cell cell space 5 end cell end table close square brackets
We need to find the value of x+y.
open square brackets table row cell straight x minus straight y end cell straight z row cell 2 straight x minus straight y end cell straight w end table close square brackets space equals space open square brackets table row cell negative 1 end cell cell space 4 end cell row cell space space 0 end cell 5 end table close square brackets


Two matrices A and B are equal to each other, if they have the same dimensions and the same elements
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CBSEENMA12035691
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If space tan to the power of negative 1 end exponent straight x plus tan to the power of negative 1 end exponent straight y space equals space straight pi over 4 comma space xy less than 1 comma space then space write space the space value space of space straight x plus straight y plus xy.

Solution

Given that tan to the power of negative 1 end exponent straight x plus tan to the power of negative 1 end exponent straight y space equals straight pi over 4 space and space xy less than 1.
We need to find the value of x+y+xy.
tan to the power of negative 1 end exponent straight x plus tan to the power of negative 1 end exponent straight y space equals space straight pi over 4
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CBSEENMA12035692
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If open vertical bar table row cell 3 straight x end cell cell space 7 end cell row cell negative 2 end cell cell space 4 end cell end table close vertical bar space equals open vertical bar table row 8 cell space 7 end cell row 6 cell space 4 end cell end table close vertical bar comma find the value of x.

Solution

Given that open vertical bar table row cell 3 straight x end cell cell space space 7 end cell row cell negative 2 end cell cell space 4 end cell end table close vertical bar space equals space open vertical bar table row 8 cell space space space 7 end cell row 6 cell space space space 4 end cell end table close vertical bar
We need to find the value of x
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CBSEENMA12035695
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If straight R equals open curly brackets open parentheses straight x comma space straight y close parentheses colon straight x plus 2 straight y space equals space 8 close curly brackets is a relation on N, write the range of R.

Solution

The set of natural numbers, N, = {1, 2, 3, 4, 5, 6.....}
The relation is given as
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