General
Easy
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

Maths-General

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

    Answer:The correct answer is: If both (A) and (R) are true, and (R) is the correct explanation of (A) .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

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    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
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    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-

    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
    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
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    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-

    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-

    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
    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
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    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
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    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-

    Let x to the power of 2 end exponent not equal to n pi minus 1 comma n element of N, then integral x square root of fraction numerator 2 s i n invisible function application open parentheses x to the power of 2 end exponent plus 1 close parentheses minus s i n invisible function application 2 open parentheses x to the power of 2 end exponent plus 1 close parentheses over denominator 2 s i n invisible function application open parentheses x to the power of 2 end exponent plus 1 close parentheses plus s i n invisible function application 2 open parentheses x to the power of 2 end exponent plus 1 close parentheses end fraction end root d x is equal to:

    Let x to the power of 2 end exponent not equal to n pi minus 1 comma n element of N, then integral x square root of fraction numerator 2 s i n invisible function application open parentheses x to the power of 2 end exponent plus 1 close parentheses minus s i n invisible function application 2 open parentheses x to the power of 2 end exponent plus 1 close parentheses over denominator 2 s i n invisible function application open parentheses x to the power of 2 end exponent plus 1 close parentheses plus s i n invisible function application 2 open parentheses x to the power of 2 end exponent plus 1 close parentheses end fraction end root d x is equal to:

    maths-General
    General
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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

    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

    maths-General