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Question

If the remainders of the polynomial f(x) when divided by x minus 1 comma x minus 2 are 2,5 then the remainder of f left parenthesis x right parenthesis when divided by left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis is

  1. 0    
  2. 1-x    
  3. 2x-1    
  4. 3x-1    

The correct answer is: 3x-1

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If f open parentheses fraction numerator 3 x minus 4 over denominator 3 x plus 4 end fraction close parentheses = x + 2 then not stretchy integral f left parenthesis x right parenthesis d x is equal to

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maths-General
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Statement II : sin x and {x} are both periodic with period 2 pi and 1 respectively.

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maths-General
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Statement 1 : f : R rightwards arrow R and f left parenthesis x right parenthesis equals e to the power of x end exponent plus e to the power of negative x end exponentis bijective.
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maths-General
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Statement II : Graph of y equals sec squared invisible function application x is symmetrical about y-axis

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maths-General
y = tan x is odd function so must be symmetrical about origin & y equals s e c to the power of 2 end exponent invisible function application x is decretive of y = tan x so it must be even imply symmetrical about y-axis or vice-versa
General
maths-

Statement- 1 colon If f left parenthesis x right parenthesis equals vertical line x minus 1 vertical line plus vertical line x minus 2 vertical line plus vertical line x minus 3 vertical line Where 2 less than x less than 3 is an identity function.
Statement- 2 colon f colon A rightwards arrowR defined by f left parenthesis x right parenthesis equals x is an identity function.

(I) f left parenthesis x right parenthesis equals vertical line x minus 1 vertical line plus vertical line x minus 2 vertical line plus vertical line x minus 3 vertical line
equals 2 less than x less than 3
equals x identity function (correct)
(II) f left parenthesis x right parenthesis equals x is an identity function (correct)

Statement- 1 colon If f left parenthesis x right parenthesis equals vertical line x minus 1 vertical line plus vertical line x minus 2 vertical line plus vertical line x minus 3 vertical line Where 2 less than x less than 3 is an identity function.
Statement- 2 colon f colon A rightwards arrowR defined by f left parenthesis x right parenthesis equals x is an identity function.

maths-General
(I) f left parenthesis x right parenthesis equals vertical line x minus 1 vertical line plus vertical line x minus 2 vertical line plus vertical line x minus 3 vertical line
equals 2 less than x less than 3
equals x identity function (correct)
(II) f left parenthesis x right parenthesis equals x is an identity function (correct)
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Assertion (A) : Graph of open curly brackets left parenthesis x comma y right parenthesis divided by y equals 2 to the power of negative x end exponent text  and  end text x comma y element of R close curly brackets
Reason (R) : In the expression am/n, where a, m, n × J+, m represents the power to which a is be raised, whereas n determines the root to be taken; these two processes may be administered in either order with the same result.

Assertion (A) : Graph of open curly brackets left parenthesis x comma y right parenthesis divided by y equals 2 to the power of negative x end exponent text  and  end text x comma y element of R close curly brackets
Reason (R) : In the expression am/n, where a, m, n × J+, m represents the power to which a is be raised, whereas n determines the root to be taken; these two processes may be administered in either order with the same result.

maths-General