General
Easy
Maths-

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

  1. If (A) is true but (R) is false.    
  2. If both (A) and (R) are true but (R) is not the correct explanation of (A) .    
  3. If (A) is false but (R) is true.    
  4. If both (A) and (R) are true, and (R) is the correct explanation of (A) .    

    Answer:The correct answer is: If (A) is false but (R) is true.

    Book A Free Demo

    +91

    Grade*

    Related Questions to study

    General
    maths-

    Assertion: The period of f left parenthesis x right parenthesis equals s i n invisible function application 2 x c o s invisible function application left square bracket 2 x right square bracket minus c o s invisible function application 2 x s i n invisible function application left square bracket 2 x right square bracket is 1/2.
    Reason: The period of x – [x] is 1.

    Assertion: The period of f left parenthesis x right parenthesis equals s i n invisible function application 2 x c o s invisible function application left square bracket 2 x right square bracket minus c o s invisible function application 2 x s i n invisible function application left square bracket 2 x right square bracket is 1/2.
    Reason: The period of x – [x] is 1.

    maths-General
    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)
    General
    maths-

    Statement I : Graph of y = tan x is symmetrical about origin
    Statement II : Graph of y equals sec squared invisible function application x is symmetrical about y-axis

    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

    Statement I : Graph of y = tan x is symmetrical about origin
    Statement II : Graph of y equals sec squared invisible function application x is symmetrical about y-axis

    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-

    Assertion : Fundamental period of c o s invisible function application x plus c o t invisible function application x text  is  end text 2 pi.
    Reason : If the period of f(x) is T subscript 1 end subscript and the period of g(x) is T subscript 2 end subscript, then the fundamental period of f(x) + g(x) is the L.C.M. of T subscript 1 end subscript and T

    Assertion : Fundamental period of c o s invisible function application x plus c o t invisible function application x text  is  end text 2 pi.
    Reason : If the period of f(x) is T subscript 1 end subscript and the period of g(x) is T subscript 2 end subscript, then the fundamental period of f(x) + g(x) is the L.C.M. of T subscript 1 end subscript and T

    maths-General
    General
    maths-

    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.
    Statement 2 : f colon R rightwards arrow R comma space f left parenthesis x right parenthesis equals e to the power of x minus e to the power of negative x end exponentis bijective.

    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.
    Statement 2 : f colon R rightwards arrow R comma space f left parenthesis x right parenthesis equals e to the power of x minus e to the power of negative x end exponentis bijective.

    maths-General
    General
    maths-

    Assertion: The function defined by f left parenthesis x right parenthesis equals x to the power of 3 end exponent plus a x to the power of 2 end exponent plus b x plus c is invertible if and only if a to the power of 2 end exponent less or equal than 3 b.
    Reason: A function is invertible if and only if it is one-to-one and onto function.

    Assertion: The function defined by f left parenthesis x right parenthesis equals x to the power of 3 end exponent plus a x to the power of 2 end exponent plus b x plus c is invertible if and only if a to the power of 2 end exponent less or equal than 3 b.
    Reason: A function is invertible if and only if it is one-to-one and onto function.

    maths-General
    General
    maths-

    Assertion : f left parenthesis x right parenthesis equals s g n left parenthesis x minus vertical line x vertical line right parenthesiscan never become positive.
    Reason : f(x) = sgn x is always a positive function.

    Assertion : f left parenthesis x right parenthesis equals s g n left parenthesis x minus vertical line x vertical line right parenthesiscan never become positive.
    Reason : f(x) = sgn x is always a positive function.

    maths-General
    General
    maths-

    If f (x) = open curly brackets table row cell e to the power of cos invisible function application x end exponent end cell cell sin invisible function application x text for  end text vertical line x vertical line less or equal than 2 end cell row cell text 2, end text end cell cell text otherwise end text end cell end table comma text then  end text not stretchy integral subscript text -2 end text end subscript superscript 3 end superscript f ​ left parenthesis x right parenthesis d x equals close

    If f (x) = open curly brackets table row cell e to the power of cos invisible function application x end exponent end cell cell sin invisible function application x text for  end text vertical line x vertical line less or equal than 2 end cell row cell text 2, end text end cell cell text otherwise end text end cell end table comma text then  end text not stretchy integral subscript text -2 end text end subscript superscript 3 end superscript f ​ left parenthesis x right parenthesis d x equals close

    maths-General
    General
    maths-

    The value of the integral not stretchy integral subscript e to the power of negative 1 end exponent end subscript superscript e to the power of 2 end exponent end superscript open vertical bar fraction numerator log subscript e end subscript invisible function application blank x over denominator x end fraction close vertical bar dx is :

    The value of the integral not stretchy integral subscript e to the power of negative 1 end exponent end subscript superscript e to the power of 2 end exponent end superscript open vertical bar fraction numerator log subscript e end subscript invisible function application blank x over denominator x end fraction close vertical bar dx is :

    maths-General
    General
    maths-

    Assertion : Let f colon R minus left curly bracket 1 , 2 comma 3 right curly bracket rightwards arrow R be a function defined by f(x) = fraction numerator 1 over denominator x minus 1 end fraction plus fraction numerator 2 over denominator x minus 2 end fraction plus fraction numerator 3 over denominator x minus 3 end fraction. Then f is many-one function.
    Reason : If either f apostrophe left parenthesis x right parenthesis greater than 0 or f to the power of apostrophe left parenthesis x right parenthesis less than 0 comma for all x element ofdomain of f, then y = f(x) is one-one function.</span

    Assertion : Let f colon R minus left curly bracket 1 , 2 comma 3 right curly bracket rightwards arrow R be a function defined by f(x) = fraction numerator 1 over denominator x minus 1 end fraction plus fraction numerator 2 over denominator x minus 2 end fraction plus fraction numerator 3 over denominator x minus 3 end fraction. Then f is many-one function.
    Reason : If either f apostrophe left parenthesis x right parenthesis greater than 0 or f to the power of apostrophe left parenthesis x right parenthesis less than 0 comma for all x element ofdomain of f, then y = f(x) is one-one function.</span

    maths-General
    General
    maths-

    Assertion : Fundamental period of c o s invisible function application x plus c o t invisible function application x text  is  end text 2 pi.
    Reason : If the period of f(x) is T subscript 1 end subscript and the period of g(x) is T subscript 2 end subscript, then the fundamental period of f(x) + g(x) is the L.C.M. of T subscript 1 end subscript and T

    Assertion : Fundamental period of c o s invisible function application x plus c o t invisible function application x text  is  end text 2 pi.
    Reason : If the period of f(x) is T subscript 1 end subscript and the period of g(x) is T subscript 2 end subscript, then the fundamental period of f(x) + g(x) is the L.C.M. of T subscript 1 end subscript and T

    maths-General
    General
    maths-

    Functionf colon Z rightwards arrow Z comma f(x) = 2x + 1 is-

    Functionf colon Z rightwards arrow Z comma f(x) = 2x + 1 is-

    maths-General
    General
    maths-

    If f(x) is an even function and f to the power of apostrophe left parenthesis x right parenthesis Exist for all 'X' then f'(1)+f'(-1) is-

    that the range of x – [x] is [0 , 1) then of [x] – x is (–1 , 0]

    If f(x) is an even function and f to the power of apostrophe left parenthesis x right parenthesis Exist for all 'X' then f'(1)+f'(-1) is-

    maths-General
    that the range of x – [x] is [0 , 1) then of [x] – x is (–1 , 0]
    General
    maths-

    Statement I : Function f(x) = sinx + {x} is periodic with period 2 pi
    Statement II : sin x and {x} are both periodic with period 2 pi and 1 respectively.

    Statement I : Function f(x) = sinx + {x} is periodic with period 2 pi
    Statement II : sin x and {x} are both periodic with period 2 pi and 1 respectively.

    maths-General
    General
    maths-

    Statement I : y = f(x) =fraction numerator x to the power of 2 end exponent minus 2 x plus 4 over denominator x to the power of 2 end exponent minus 2 x plus 5 end fraction, xelement ofR Range of f(x) is [3/4, 1)
    Statement II : left parenthesis x minus 1 right parenthesis to the power of 2 end exponent equals fraction numerator 4 y minus 3 over denominator 1 minus y end fraction.

    Statement I : y = f(x) =fraction numerator x to the power of 2 end exponent minus 2 x plus 4 over denominator x to the power of 2 end exponent minus 2 x plus 5 end fraction, xelement ofR Range of f(x) is [3/4, 1)
    Statement II : left parenthesis x minus 1 right parenthesis to the power of 2 end exponent equals fraction numerator 4 y minus 3 over denominator 1 minus y end fraction.

    maths-General