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

Download the PDF Sample Papers Free for off line practice and view the Solutions online.

CBSE Class 12 Mathematics Solved Question Paper 2014

Short Answer Type

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.

783 Views

2. $If space open square brackets table row cell straight x minus straight y end cell cell space straight z end cell row cell 2 straight x minus straight y end cell cell space straight w end cell end table close square brackets space equals space open square brackets table row cell negative 1 end cell cell space 4 end cell row 0 cell space 5 end cell end table close square brackets comma space find space the space value space of space straight x plus straight y.$

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

straight a subscript ij space equals space straight b subscript ij comma space space space for space straight i space equals space 1 comma 2 comma.... comma straight n and space straight j space equals space 1 comma space 2.... comma space straight m. rightwards double arrow space space space straight x minus straight y space equals negative 1 space.... left parenthesis 1 right parenthesis 2 straight x minus straight y equals 0..... left parenthesis 2 right parenthesis Equation space left parenthesis 2 right parenthesis minus left parenthesis 1 right parenthesis space is space straight x space equals space 1 Substituting space the space value space of space straight x space equals space 1 space in space equation space left parenthesis 1 right parenthesis comma space we space have 1 minus straight y space equals space minus 1 rightwards double arrow straight y space equals space 2 Therefore comma space straight x plus straight y space equals space 1 plus 2 space equals space 3

168 Views

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.

226 Views

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.

196 Views

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.

271 Views

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.

237 Views

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

162 Views

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).

247 Views

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

154 Views

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.