Maths-
General
Easy

Question

lf f left parenthesis theta right parenthesis equals open vertical bar table row 1 cell c o s theta end cell 1 row cell negative s i n theta end cell 1 cell negative c o s theta end cell row cell negative 1 end cell cell s i n theta end cell 1 end table close vertical bar negative 12 x2 and A and 8 are respecively the maximum and the minimum values of left parenthesis theta right parenthesis , then (A, B) is equal to

  1. left parenthesis 3 comma blank minus 1 right parenthesis    
  2. left parenthesis 42 minus square root of 2 right parenthesis    
  3. left parenthesis 2 plus square root of 2 comma 2 minus square root of 2 right parenthesis    
  4. left parenthesis 2 plus square root of 2 comma blank minus 1 right parenthesis    

The correct answer is: left parenthesis 2 plus square root of 2 comma 2 minus square root of 2 right parenthesis


    1 blank c o s blank theta blank 1
    f left parenthesis theta right parenthesis equals negative blank s i n blank theta blank 1 blank minus blank c o s blank theta
    negative 1 blank s i n blank theta blank 1
    Therefore,
    f left parenthesis theta right parenthesis equals 1 left parenthesis 1 plus blank s i n blank theta blank c o s blank theta right parenthesis minus blank c o s blank theta left parenthesis negative blank s i n blank theta minus blank c o s blank theta right parenthesis plus 1 left parenthesis negative s i n to the power of 2 end exponent theta plus 1 right parenthesis
    equals 1 plus blank s i n blank 2 theta plus 2 c o s to the power of 2 end exponent theta equals 1 plus blank s i n blank 2 theta plus 1 plus blank c o s blank 2 theta
    equals 2 plus square root of 2 left curly bracket blank s i n blank left parenthesis 2 theta plus fraction numerator p over denominator 4 end fraction right parenthesis right curly bracket
    Therefore, m a x blank. f left parenthesis theta right parenthesis equals 2 plus square root of 2 and m i n blank. f left parenthesis theta right parenthesis equals 2 minus square root of 2 since,
    negative 1 less or equal than blank s i n blank left parenthesis 2 theta plus fraction numerator p over denominator 4 end fraction right parenthesis less or equal than 1
    Hence, the correct answer is option (c).

    Related Questions to study

    General
    Physics-

    Binding energy pernucleonversus mass number curve for nuclei is shown in the figure. W,X,Y and Z are fournuclei indicate don the curve.Theprocessthatwouldrelease

    Binding energy pernucleonversus mass number curve for nuclei is shown in the figure. W,X,Y and Z are fournuclei indicate don the curve.Theprocessthatwouldrelease

    Physics-General
    General
    Physics-

    Which of the plots shown in the figure represents speed(vn) of the electron in a hydrogen atom as a function of theprincipalquantumnumber(n)?

    Which of the plots shown in the figure represents speed(vn) of the electron in a hydrogen atom as a function of theprincipalquantumnumber(n)?

    Physics-General
    General
    Maths-

    lf the Rolle’s theorem holds for the function f left parenthesis x right parenthesis equals 2 x cubed plus a x squared plus b x in the interval [−1, 1] for the point c equals fraction numerator 1 over denominator 2 end fraction , then the value of 2a+b is

    lf the Rolle’s theorem holds for the function f left parenthesis x right parenthesis equals 2 x cubed plus a x squared plus b x in the interval [−1, 1] for the point c equals fraction numerator 1 over denominator 2 end fraction , then the value of 2a+b is

    Maths-General
    parallel
    General
    Physics-

    Ifu subscript 1 end subscriptis the frequency of the series limit of Lymanseries, u subscript 2 end subscriptis the frequency of the firstline of Lymanseries and
    u3 is the frequency of the series limit of the Balmer seriesthen

    Ifu subscript 1 end subscriptis the frequency of the series limit of Lymanseries, u subscript 2 end subscriptis the frequency of the firstline of Lymanseries and
    u3 is the frequency of the series limit of the Balmer seriesthen

    Physics-General
    General
    Physics-

    The diagram shows the energy levels for an electron in acertainatom. Which transitionshown represents theemissionofaphotonwiththemostenergy?

    The diagram shows the energy levels for an electron in acertainatom. Which transitionshown represents theemissionofaphotonwiththemostenergy?

    Physics-General
    General
    Physics-

    Thestopping potentialopen parentheses V subscript 0 end subscript close parentheses, versus frequency(v) plotofasubstance is
    shown in figure, the threshold wavelengthis

    Thestopping potentialopen parentheses V subscript 0 end subscript close parentheses, versus frequency(v) plotofasubstance is
    shown in figure, the threshold wavelengthis

    Physics-General
    parallel
    General
    Physics-

    Thefigureshowsaplotofphotocurrentversusanodepotentialforaphotosensitivesurfaceforthreedifferent radiations.Whichoneofthefollowingisacorrectstatement?

    Thefigureshowsaplotofphotocurrentversusanodepotentialforaphotosensitivesurfaceforthreedifferent radiations.Whichoneofthefollowingisacorrectstatement?

    Physics-General
    General
    Physics-

    Lightofwavelength500nmisincidentonametalwithwork function2.28 eV. The de Broglie wavelengthof the emittedelectronis:

    Lightofwavelength500nmisincidentonametalwithwork function2.28 eV. The de Broglie wavelengthof the emittedelectronis:

    Physics-General
    General
    Physics-

    In an experiment on photoelectric effect, a student plotsstoppingpotentialVO against reciprocalof the wavelengthlambdaoftheincidentlightfortwodifferentmetalsAandB.Theseareshown inthefigure.

    Looking atthegraphs,youcanmostappropriatelysaythat

    In an experiment on photoelectric effect, a student plotsstoppingpotentialVO against reciprocalof the wavelengthlambdaoftheincidentlightfortwodifferentmetalsAandB.Theseareshown inthefigure.

    Looking atthegraphs,youcanmostappropriatelysaythat

    Physics-General
    parallel
    General
    Physics-

    Twoinsulatingplatesarebothuniformlychargedinsuchawaythatthepotentialdifferencebetweenthemis V subscript 2 end subscript-V subscript 1 end subscript=20V.(i.e.,plate2isatahigherpotential).The plates are separatedby d =0.1mand canbe treatedasinfinitelylarge.Anelectronisreleasedfromrestontheinner surfaceofplate1.Whatisitsspeedwhenithitsplate2?

    Twoinsulatingplatesarebothuniformlychargedinsuchawaythatthepotentialdifferencebetweenthemis V subscript 2 end subscript-V subscript 1 end subscript=20V.(i.e.,plate2isatahigherpotential).The plates are separatedby d =0.1mand canbe treatedasinfinitelylarge.Anelectronisreleasedfromrestontheinner surfaceofplate1.Whatisitsspeedwhenithitsplate2?

    Physics-General
    General
    Physics-

    Photoelectric effect experiments are performed using three different metal plates p comma q and r having work functions ϕ subscript p end subscript equals 2.0 e V comma ϕ subscript q end subscript equals 2.5 e V and ϕ subscript r end subscript equals 3.0 e V, respectively. A light beam containing wavelengths of 550 text end text n m comma 450 text end text n m and 350 text end text n m with equal intensities illuminates each of the plates. The correct I minus V graph for the experiment is:
    (Take hc equals 1240 e V n m )

    Photoelectric effect experiments are performed using three different metal plates p comma q and r having work functions ϕ subscript p end subscript equals 2.0 e V comma ϕ subscript q end subscript equals 2.5 e V and ϕ subscript r end subscript equals 3.0 e V, respectively. A light beam containing wavelengths of 550 text end text n m comma 450 text end text n m and 350 text end text n m with equal intensities illuminates each of the plates. The correct I minus V graph for the experiment is:
    (Take hc equals 1240 e V n m )

    Physics-General
    General
    Maths-

    Let f be differentiable for all x. if f(1) = -2 and f to the power of ´ end exponent open parentheses x close parentheses greater or equal than 2 for x element of [1,6], then

    Let f be differentiable for all x. if f(1) = -2 and f to the power of ´ end exponent open parentheses x close parentheses greater or equal than 2 for x element of [1,6], then

    Maths-General
    parallel
    General
    Maths-

    Given P left parenthesis x right parenthesis equals x to the power of 4 plus a x cubed plus b x squared plus alpha plus dsuch that χ=0 is the only real root of P to the power of ´ end exponent open parentheses x close parentheses equals 0.ifblank P left parenthesis negative 1 right parenthesis less than P left parenthesis 1 right parenthesis , then in the interval [−1, 1]

    Given P left parenthesis x right parenthesis equals x to the power of 4 plus a x cubed plus b x squared plus alpha plus dsuch that χ=0 is the only real root of P to the power of ´ end exponent open parentheses x close parentheses equals 0.ifblank P left parenthesis negative 1 right parenthesis less than P left parenthesis 1 right parenthesis , then in the interval [−1, 1]

    Maths-General
    General
    Physics-

    A point source is emitting light of wavelength 6000 text Å end text isplaced at a very small height h above a flat reflecting surfaceMNasshowninthefigure.

    The intensity of the reflectedlight is 36% of the incidentintensity.Interference fringes are observed on a screenplacedparalleltothereflectingsurfaceataverylargedistanceD from it. Theshapeoftheinterferencefringesonthescreenis

    A point source is emitting light of wavelength 6000 text Å end text isplaced at a very small height h above a flat reflecting surfaceMNasshowninthefigure.

    The intensity of the reflectedlight is 36% of the incidentintensity.Interference fringes are observed on a screenplacedparalleltothereflectingsurfaceataverylargedistanceD from it. Theshapeoftheinterferencefringesonthescreenis

    Physics-General
    General
    Physics-

    The figure shows the interference pattern obtained in a double-slit experiment using light of wavelength 600nm. 1,2,3,4and5aremarkedonfivefringes

    The figure shows the interference pattern obtained in a double-slit experiment using light of wavelength 600nm. 1,2,3,4and5aremarkedonfivefringes

    Physics-General
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.