Subject

Mathematics

Class

CBSE Class 12

Pre Boards

Practice to excel and get familiar with the paper pattern and the type of questions. Check you answers with answer keys provided.

Sample Papers

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 Multiple Choice QuestionsShort Answer Type

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1.

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.


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, 

7 straight A minus left parenthesis straight I plus straight A right parenthesis cubed space equals space 7 straight A minus open parentheses straight I cubed plus 3 straight I squared straight A plus 3 IA squared plus straight A cubed close parentheses
space space rightwards double arrow space 7 straight A minus left parenthesis straight I plus straight A right parenthesis cubed space equals space 7 straight A minus open parentheses straight I cubed plus 3 straight A plus 3 straight A squared plus straight A squared cross times straight A close parentheses space space open square brackets straight I cubed space equals space straight I comma space straight I squared straight A equals straight A comma space IA squared equals straight A squared close square brackets
space space rightwards double arrow space 7 straight A minus left parenthesis straight I plus straight A right parenthesis cubed equals 7 straight A minus open parentheses straight I plus 3 straight A plus 3 straight A plus straight A close parentheses space space space open square brackets because straight A squared equals straight A close square brackets
space space rightwards double arrow 7 straight A minus left parenthesis straight I plus straight A right parenthesis cubed equals 7 straight A minus straight I minus 3 straight A minus 3 straight A minus straight A
space space space rightwards double arrow 7 straight A minus left parenthesis straight I plus straight A right parenthesis cubed equals 7 straight A minus straight I minus 7 straight A
space space space space rightwards double arrow 7 straight A minus left parenthesis straight I plus straight A right parenthesis cubed equals negative straight I

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2. 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.
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3. 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.
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4.

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.

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5.

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.

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6.

Find the value(s) of x for which y = open square brackets straight x left parenthesis straight x minus 2 right parenthesis close square brackets squared is an increasing function.

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7.

Find the equations of the tangent and normal to the curve straight x squared over straight a squared minus straight y squared over straight b squared equals 1 space at space the space point space open parentheses square root of 2 straight a comma space straight b close parentheses.

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8.

If the function f: R rightwards arrow R  be given by straight f left parenthesis straight x right parenthesis space equals space straight x squared plus 2 space space and space straight g space colon thin space straight R rightwards arrow space straight R be given by straight g left parenthesis straight x right parenthesis space equals fraction numerator straight x over denominator straight x minus 1 end fraction comma space straight x not equal to 1 comma find fog and gof and hence find fog (2) and gof ( −3).

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9.

Prove that
tan to the power of negative 1 end exponent open square brackets fraction numerator square root of 1 plus straight x end root minus square root of 1 minus straight x end root over denominator square root of 1 plus straight x end root plus square root of 1 minus straight x end root end fraction close square brackets space equals space straight pi over 4 minus 1 half cos to the power of negative 1 end exponent straight x comma space space fraction numerator negative 1 over denominator square root of 2 end fraction less or equal than straight x less or equal than 1

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10.

Prove that
If tan to the power of negative 1 end exponent open parentheses fraction numerator straight x minus 2 over denominator straight x minus 4 end fraction close parentheses plus tan to the power of negative 1 end exponent open parentheses fraction numerator straight x plus 2 over denominator straight x plus 4 end fraction close parentheses equals straight pi over 4 comma find the value of x.

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