Maths-
General
Easy

Question

Statement - I : Let f(x) be a function such that f left parenthesis x minus 1 right parenthesis plus f left parenthesis x plus 1 right parenthesis equals square root of 2 f left parenthesis x right parenthesis for all x element of R then f is periodic
Statement - II : There exists a function with period 8

  1. Statement - 1 is true, Statement - 2 is True; Statement - 2 is a correct explanation for Statement - 1    
  2. Statement - 1 is true, Statement - 2 is True; Statement - 2 is NOT a correct explanation for Statement - 1    
  3. Statement - 1 is True, Statement - 2 is False    
  4. Statement - 1 is False, Statement - 2 is True    

The correct answer is: Statement - 1 is true, Statement - 2 is True; Statement - 2 is NOT a correct explanation for Statement - 1


    table row cell text end text text R end text text e end text text p end text text l end text text a end text text c end text text i end text text n end text text g end text text end text x minus 1 text end text text b end text text y end text text end text x comma text end text text w end text text e end text text end text text g end text text e end text text t end text text end text f left parenthesis x right parenthesis plus f left parenthesis x plus 2 right parenthesis equals square root of 2 f left parenthesis x plus 1 right parenthesis horizontal ellipsis horizontal ellipsis left parenthesis 1 right parenthesis end cell row cell text end text text A end text text g end text text a end text text i end text text n end text text end text text r end text text e end text text p end text text l end text text a end text text c end text text i end text text n end text text g end text text end text x text end text text b end text text y end text text end text x plus 2 f left parenthesis x plus 2 right parenthesis plus left parenthesis x plus 4 right parenthesis equals square root of 2 f left parenthesis x plus 3 right parenthesis horizontal ellipsis horizontal ellipsis left parenthesis 2 right parenthesis end cell row cell text end text text A end text text d end text text d end text text i end text text n end text text g end text text end text text ( end text text 1 end text text ) end text text end text text a end text text n end text text d end text text end text text ( end text text 2 end text text ) end text text , end text text end text text w end text text e end text text end text text g end text text e end text text t end text text end text end cell end table
    table row cell table row cell f open parentheses x close parentheses plus 2 f open parentheses x plus 2 close parentheses plus f open parentheses x plus 4 close parentheses end cell cell equals square root of 2 open curly brackets f open parentheses x plus 1 close parentheses plus f open parentheses x plus 3 close parentheses close curly brackets end cell row blank cell equals square root of 2 square root of 2 f open parentheses x plus 2 close parentheses end cell row blank cell equals 2 f open parentheses x plus 2 close parentheses end cell end table end cell row cell rightwards double arrow f open parentheses x close parentheses plus f open parentheses x plus 4 close parentheses equals 0 minus horizontal ellipsis open parentheses 3 close parentheses end cell row cell rightwards double arrow f open parentheses x plus 4 close parentheses plus f open parentheses x plus 8 close parentheses equals 0 horizontal ellipsis horizontal ellipsis.. open parentheses 4 close parentheses end cell end table
    Subtracting (4) and (3)
    we obtain f(x) = f(x + 8)
    Thus f is periodic
    We know that the period of the function kx – [kx] is 1/k.
    text A function with period  end text 8 text  is  end text fraction numerator 1 over denominator 8 end fraction x minus open square brackets fraction numerator 1 over denominator 8 end fraction x close square brackets

    Related Questions to study

    General
    maths-

    An ellipse has foci at (9, 20) and (49, 55) in the xy-plane and is tangent to the x axis. The length of its major axis is :

    An ellipse has foci at (9, 20) and (49, 55) in the xy-plane and is tangent to the x axis. The length of its major axis is :

    maths-General
    General
    maths-

    If the ellipse fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent minus 3 end fraction minus fraction numerator y to the power of 2 end exponent over denominator a plus 4 end fraction equals 1 is inscribed in square of side length a square root of 2 comma then a is

    If the ellipse fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent minus 3 end fraction minus fraction numerator y to the power of 2 end exponent over denominator a plus 4 end fraction equals 1 is inscribed in square of side length a square root of 2 comma then a is

    maths-General
    General
    maths-

    The area of the quadrilateral formed by the tangents at the ends of latus-rectum of 5 x to the power of 2 end exponent plus 9 y to the power of 2 end exponent equals 45 is

    The area of the quadrilateral formed by the tangents at the ends of latus-rectum of 5 x to the power of 2 end exponent plus 9 y to the power of 2 end exponent equals 45 is

    maths-General
    parallel
    General
    maths-

    In the standard ellipse, the lines joining the ends of the minor axis to one focus are at right angles. The distance between the focus and the nearer vertex is square root of 10 minus square root of 5 The equation of the ellipse

    In the standard ellipse, the lines joining the ends of the minor axis to one focus are at right angles. The distance between the focus and the nearer vertex is square root of 10 minus square root of 5 The equation of the ellipse

    maths-General
    General
    chemistry-

    Three metal ions x+2, y+2, z+2 are identify in qualitative analysis. Nitrates of x+2, y+2, z+2 dissolve in three seprate test tubes and gives following observation.
    i) All solution produce carbonate precipitate with (NH4 )2CO3
    ii) Only one produce white ppt on addition of NaCl.
    iii) Out of 3 cations two produce sulphide ppt.
    iv) Sulphide of y+2 is not produce by H2S/H+ but produce when H2S is passed in basic medium.
    v) Only y+2 produce soluble sulphate
    vi) x +2 gives no ppt with dil NH4OH
    Select correct about xCO3 , y CO3 , z CO3 -

    Three metal ions x+2, y+2, z+2 are identify in qualitative analysis. Nitrates of x+2, y+2, z+2 dissolve in three seprate test tubes and gives following observation.
    i) All solution produce carbonate precipitate with (NH4 )2CO3
    ii) Only one produce white ppt on addition of NaCl.
    iii) Out of 3 cations two produce sulphide ppt.
    iv) Sulphide of y+2 is not produce by H2S/H+ but produce when H2S is passed in basic medium.
    v) Only y+2 produce soluble sulphate
    vi) x +2 gives no ppt with dil NH4OH
    Select correct about xCO3 , y CO3 , z CO3 -

    chemistry-General
    General
    chemistry-

    Read the following comprehension carefully and answer the following questions

    Read the following comprehension carefully and answer the following questions

    chemistry-General
    parallel
    General
    chemistry-

    Read the following comprehension carefully and answer the following questions

    The compound

    Read the following comprehension carefully and answer the following questions

    The compound

    chemistry-General
    General
    chemistry-

    Read the following comprehension carefully and answer the following questions

    Yellow solution (C) is an important laboratory reagent and is used in the estimation of :

    Read the following comprehension carefully and answer the following questions

    Yellow solution (C) is an important laboratory reagent and is used in the estimation of :

    chemistry-General
    General
    chemistry-

    Read the following comprehension carefully and answer the following questions

    The colour of the ppt (D) & (E) are :

    Read the following comprehension carefully and answer the following questions

    The colour of the ppt (D) & (E) are :

    chemistry-General
    parallel
    General
    chemistry-

    Moreover, the salt 'A' on heating with solid K2Cr2O7 and concentrated H2SO4 produces deep red vapours which dissolve in sodium hydroxide solution forming a yellow solution. This yellow solution gives yellow precipitate with Ba(NO3 ) 2 solution. On the basis of the aforesaid characteristic informations answer the following questions :
    Select the correct statement.

    Moreover, the salt 'A' on heating with solid K2Cr2O7 and concentrated H2SO4 produces deep red vapours which dissolve in sodium hydroxide solution forming a yellow solution. This yellow solution gives yellow precipitate with Ba(NO3 ) 2 solution. On the basis of the aforesaid characteristic informations answer the following questions :
    Select the correct statement.

    chemistry-General
    General
    chemistry-

    Statement-1 : Nessler’s reagent gives a brown precipitate with aqueous ammonia as well as with ammonium salts. Statement-2 : Aqueous ammonia gives a brown precipitate with a solution of manganese (II) chloride and hydrogen peroxide.

    Statement-1 : Nessler’s reagent gives a brown precipitate with aqueous ammonia as well as with ammonium salts. Statement-2 : Aqueous ammonia gives a brown precipitate with a solution of manganese (II) chloride and hydrogen peroxide.

    chemistry-General
    General
    chemistry-

    Statement-1 : A solution containing S2– ions gives purple / violet colour with sodium nitroprusside solution in alkaline medium.
    Statement-2 : Sodium sulphide gives black precipitate with silver nitrate solution.

    Statement-1 : A solution containing S2– ions gives purple / violet colour with sodium nitroprusside solution in alkaline medium.
    Statement-2 : Sodium sulphide gives black precipitate with silver nitrate solution.

    chemistry-General
    parallel
    General
    chemistry-

    Which of the following pairs comprises the red precipitates ?

    Which of the following pairs comprises the red precipitates ?

    chemistry-General
    General
    chemistry-

    A metal salt solution forms a yellow precipitate with potassium chromate in acetic acid, a white precipitate with dilute sulphuric acid, but gives no precipitate with sodium chloride or iodide, it is :

    A metal salt solution forms a yellow precipitate with potassium chromate in acetic acid, a white precipitate with dilute sulphuric acid, but gives no precipitate with sodium chloride or iodide, it is :

    chemistry-General
    General
    physics-

    A unit positive point charge of mass m is projected with a velocity V inside the tunnel as shown. The tunnel has been made inside a uniformly charged non conducting sphere. The minimum velocity with which the point charge should be projected such it can it reach the opposite end of the tunnel, is equal to

    A unit positive point charge of mass m is projected with a velocity V inside the tunnel as shown. The tunnel has been made inside a uniformly charged non conducting sphere. The minimum velocity with which the point charge should be projected such it can it reach the opposite end of the tunnel, is equal to

    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.