Maths-
General
Easy

Question

The value of integer n for which the function f left parenthesis x right parenthesis equals fraction numerator sin begin display style space end style n x over denominator sin begin display style space end style left parenthesis x divided by n right parenthesis end fraction has 4 pi as its period is

  1. 2
  2. 3
  3. 4
  4. 5

Hint:

In this question we have to find the value of n in the given function when its period is given. As by fundamental period of period T, f(x+T)=f(x) so using this we can convert f(x) into f(x+T) and later the option which satisfies the equation will be the required value of n.

The correct answer is: 2


    f left parenthesis x right parenthesis equals fraction numerator sin begin display style space end style n x over denominator sin begin display style space end style left parenthesis x divided by n right parenthesis end fraction
    Given, period =4 straight pi
    s o comma space fraction numerator sin space n straight pi over denominator sin begin display style x over n end style end fraction equals fraction numerator sin open square brackets n open parentheses x plus 4 straight pi close parentheses close square brackets over denominator sin open parentheses begin display style fraction numerator x plus 4 straight pi over denominator n end fraction end style close parentheses end fraction
rightwards double arrow fraction numerator sin space n straight pi over denominator sin begin display style x over n end style end fraction equals fraction numerator sin open parentheses n x plus 4 n straight pi close parentheses over denominator sin open parentheses begin display style x over n end style plus begin display style fraction numerator 4 straight pi over denominator n end fraction end style close parentheses end fraction
f r o m space o p t i o n s space i t space i s space o n l y space t r u e space f o r space space n equals 2

    Related Questions to study

    General
    Maths-

    cos squared space open parentheses 60 to the power of ring operator plus x close parentheses minus cos squared space open parentheses 60 to the power of ring operator minus x close parentheses element of open square brackets negative m over 2 comma m over 2 close square brackets not stretchy rightwards double arrow straight m equals

    space space space space cos squared open parentheses 60 plus x close parentheses minus cos squared open parentheses 60 minus x close parentheses
equals open square brackets cos open parentheses 60 plus x close parentheses plus cos space open parentheses 60 minus x close parentheses close square brackets open square brackets cos space open parentheses 60 plus x close parentheses minus cos open parentheses 60 minus x close parentheses close square brackets
equals open parentheses 2. cos space 60. cos space x close parentheses open parentheses negative 2. sin 60. sin space x close parentheses
equals open parentheses 2.1 half. cos space x close parentheses open parentheses negative 2. fraction numerator square root of 3 over denominator 2 end fraction. sin space x close parentheses
equals negative square root of 3. cos space x. sin space x
equals negative fraction numerator square root of 3 over denominator 2 end fraction. sin space 2 x space
F o r space m a x i m u m space v a l u e space o f space f left parenthesis x right parenthesis comma space sin space 2 x equals 1
f left parenthesis x right parenthesis equals fraction numerator negative square root of 3 over denominator 2 end fraction cross times 1 equals fraction numerator negative square root of 3 over denominator 2 end fraction
F o r space m i n i m u m space v a l u e space o f space f space left parenthesis x right parenthesis comma space sin space 2 x space equals negative 1
f left parenthesis x right parenthesis equals fraction numerator negative square root of 3 over denominator 2 end fraction cross times negative 1 equals fraction numerator square root of 3 over denominator 2 end fraction
A s space space cos squared open parentheses 60 plus x close parentheses minus cos squared open parentheses 60 minus x close parentheses element of open square brackets fraction numerator negative square root of 3 over denominator 2 end fraction comma fraction numerator square root of 3 over denominator 2 end fraction close square brackets
S o comma space m equals square root of 3

    cos squared space open parentheses 60 to the power of ring operator plus x close parentheses minus cos squared space open parentheses 60 to the power of ring operator minus x close parentheses element of open square brackets negative m over 2 comma m over 2 close square brackets not stretchy rightwards double arrow straight m equals

    Maths-General
    space space space space cos squared open parentheses 60 plus x close parentheses minus cos squared open parentheses 60 minus x close parentheses
equals open square brackets cos open parentheses 60 plus x close parentheses plus cos space open parentheses 60 minus x close parentheses close square brackets open square brackets cos space open parentheses 60 plus x close parentheses minus cos open parentheses 60 minus x close parentheses close square brackets
equals open parentheses 2. cos space 60. cos space x close parentheses open parentheses negative 2. sin 60. sin space x close parentheses
equals open parentheses 2.1 half. cos space x close parentheses open parentheses negative 2. fraction numerator square root of 3 over denominator 2 end fraction. sin space x close parentheses
equals negative square root of 3. cos space x. sin space x
equals negative fraction numerator square root of 3 over denominator 2 end fraction. sin space 2 x space
F o r space m a x i m u m space v a l u e space o f space f left parenthesis x right parenthesis comma space sin space 2 x equals 1
f left parenthesis x right parenthesis equals fraction numerator negative square root of 3 over denominator 2 end fraction cross times 1 equals fraction numerator negative square root of 3 over denominator 2 end fraction
F o r space m i n i m u m space v a l u e space o f space f space left parenthesis x right parenthesis comma space sin space 2 x space equals negative 1
f left parenthesis x right parenthesis equals fraction numerator negative square root of 3 over denominator 2 end fraction cross times negative 1 equals fraction numerator square root of 3 over denominator 2 end fraction
A s space space cos squared open parentheses 60 plus x close parentheses minus cos squared open parentheses 60 minus x close parentheses element of open square brackets fraction numerator negative square root of 3 over denominator 2 end fraction comma fraction numerator square root of 3 over denominator 2 end fraction close square brackets
S o comma space m equals square root of 3
    General
    Maths-

    cos squared space open parentheses 60 to the power of ring operator minus x close parentheses plus cos squared space open parentheses 60 to the power of ring operator plus x close parentheses element of

    space space space space cos squared space open parentheses 60 to the power of ring operator minus x close parentheses plus cos squared space open parentheses 60 to the power of ring operator plus x close parentheses
equals open parentheses cos space open parentheses 60 plus x close parentheses plus cos open parentheses 60 minus x close parentheses close parentheses squared minus 2 cos space open parentheses 60 minus x close parentheses. cos space open parentheses 60 plus x close parentheses
equals open parentheses 2. cos space 60. cos space x close parentheses squared minus open parentheses cos space 2 x space plus cos space 120 space close parentheses
equals 4 cross times 1 fourth cross times cos squared x minus cos space 2 x space minus open parentheses fraction numerator negative 1 over denominator 2 end fraction close parentheses
equals cos squared x minus cos space 2 x plus 1 half
equals cos squared x minus 2 cos squared x plus 1 plus 1 half
equals 3 over 2 minus cos squared x
    For maximum value of f (x), cos squared x equals 0
    f (x)=3 over 2 minus 0 equals 3 over 2
    For minimum value of f (x), cos squared x equals 1
    f (x)=3 over 2 minus 1 equals 1 half
    So, cos squared space open parentheses 60 to the power of ring operator minus x close parentheses plus cos squared space open parentheses 60 to the power of ring operator plus x close parentheses element of open square brackets 1 half comma 3 over 2 close square brackets.

    cos squared space open parentheses 60 to the power of ring operator minus x close parentheses plus cos squared space open parentheses 60 to the power of ring operator plus x close parentheses element of

    Maths-General
    space space space space cos squared space open parentheses 60 to the power of ring operator minus x close parentheses plus cos squared space open parentheses 60 to the power of ring operator plus x close parentheses
equals open parentheses cos space open parentheses 60 plus x close parentheses plus cos open parentheses 60 minus x close parentheses close parentheses squared minus 2 cos space open parentheses 60 minus x close parentheses. cos space open parentheses 60 plus x close parentheses
equals open parentheses 2. cos space 60. cos space x close parentheses squared minus open parentheses cos space 2 x space plus cos space 120 space close parentheses
equals 4 cross times 1 fourth cross times cos squared x minus cos space 2 x space minus open parentheses fraction numerator negative 1 over denominator 2 end fraction close parentheses
equals cos squared x minus cos space 2 x plus 1 half
equals cos squared x minus 2 cos squared x plus 1 plus 1 half
equals 3 over 2 minus cos squared x
    For maximum value of f (x), cos squared x equals 0
    f (x)=3 over 2 minus 0 equals 3 over 2
    For minimum value of f (x), cos squared x equals 1
    f (x)=3 over 2 minus 1 equals 1 half
    So, cos squared space open parentheses 60 to the power of ring operator minus x close parentheses plus cos squared space open parentheses 60 to the power of ring operator plus x close parentheses element of open square brackets 1 half comma 3 over 2 close square brackets.
    General
    physics-

    The effective capacitance between points X and Y shown in figure. Assuming C subscript 2 end subscript equals 10 blank muF and that outer capacitors are all 4 blank muF is

    The arrangement shows a Wheatstone bridge.
    As fraction numerator C subscript 1 end subscript over denominator C subscript 3 end subscript end fraction equals fraction numerator C subscript 4 end subscript over denominator C subscript 5 end subscript end fraction equals 1 comma blanktherefore the bridge is balanced.
    fraction numerator 1 over denominator C subscript s subscript 1 end subscript end subscript end fraction equals fraction numerator 1 over denominator 4 end fraction plus fraction numerator 1 over denominator 4 end fraction equals fraction numerator 2 over denominator 4 end fraction equals fraction numerator 1 over denominator 2 end fraction comma C subscript s subscript 1 end subscript end subscript equals 2 mu blank F
    Similarly, C subscript s end subscript subscript 2 end subscript equals 2 mu blank F
    therefore effective capacitance
    equals C subscript p end subscript equals C subscript s end subscript subscript 1 end subscript plus C subscript s end subscript subscript 2 end subscript equals 2 plus 2 plus equals 4 mu blank F

    The effective capacitance between points X and Y shown in figure. Assuming C subscript 2 end subscript equals 10 blank muF and that outer capacitors are all 4 blank muF is

    physics-General
    The arrangement shows a Wheatstone bridge.
    As fraction numerator C subscript 1 end subscript over denominator C subscript 3 end subscript end fraction equals fraction numerator C subscript 4 end subscript over denominator C subscript 5 end subscript end fraction equals 1 comma blanktherefore the bridge is balanced.
    fraction numerator 1 over denominator C subscript s subscript 1 end subscript end subscript end fraction equals fraction numerator 1 over denominator 4 end fraction plus fraction numerator 1 over denominator 4 end fraction equals fraction numerator 2 over denominator 4 end fraction equals fraction numerator 1 over denominator 2 end fraction comma C subscript s subscript 1 end subscript end subscript equals 2 mu blank F
    Similarly, C subscript s end subscript subscript 2 end subscript equals 2 mu blank F
    therefore effective capacitance
    equals C subscript p end subscript equals C subscript s end subscript subscript 1 end subscript plus C subscript s end subscript subscript 2 end subscript equals 2 plus 2 plus equals 4 mu blank F
    parallel
    General
    physics-

    The four capacitors, each of 25 muF are connected as shown in figure. The DC voltmeter reads 200 V. the change on each plate of capacitor is

    Charge on each plate of each capacitor
    Q equals plus-or-minus C V equals plus-or-minus 25 cross times 10 to the power of negative 6 end exponent cross times 200
    equals plus-or-minus 5 cross times 10 to the power of negative 3 end exponent C

    The four capacitors, each of 25 muF are connected as shown in figure. The DC voltmeter reads 200 V. the change on each plate of capacitor is

    physics-General
    Charge on each plate of each capacitor
    Q equals plus-or-minus C V equals plus-or-minus 25 cross times 10 to the power of negative 6 end exponent cross times 200
    equals plus-or-minus 5 cross times 10 to the power of negative 3 end exponent C
    General
    physics-

    For the circuit shown in figure the charge on 4muF capacitor is

    Combined capacity of 1 blank mu F and 5 mu F blank= 1 + 5=6 blank mu F
    Now, 4 mu F blankand 6 mu F are in series.
    therefore blank fraction numerator 1 over denominator C subscript s end subscript end fraction equals fraction numerator 1 over denominator 4 end fraction plus fraction numerator 1 over denominator 6 end fraction plus fraction numerator 3 plus 2 over denominator 12 end fraction equals fraction numerator 5 over denominator 12 end fraction
    C subscript s end subscript equals fraction numerator 12 over denominator 5 end fraction mu F
    Charge in the arm containing 4 mu F blankcapacitor is
    q equals C subscript s end subscript cross times V equals fraction numerator 12 over denominator 5 end fraction cross times 10 equals 24 blank mu C

    For the circuit shown in figure the charge on 4muF capacitor is

    physics-General
    Combined capacity of 1 blank mu F and 5 mu F blank= 1 + 5=6 blank mu F
    Now, 4 mu F blankand 6 mu F are in series.
    therefore blank fraction numerator 1 over denominator C subscript s end subscript end fraction equals fraction numerator 1 over denominator 4 end fraction plus fraction numerator 1 over denominator 6 end fraction plus fraction numerator 3 plus 2 over denominator 12 end fraction equals fraction numerator 5 over denominator 12 end fraction
    C subscript s end subscript equals fraction numerator 12 over denominator 5 end fraction mu F
    Charge in the arm containing 4 mu F blankcapacitor is
    q equals C subscript s end subscript cross times V equals fraction numerator 12 over denominator 5 end fraction cross times 10 equals 24 blank mu C
    General
    Maths-

    The minimum and maximum values of sin to the power of 4 x plus cos to the power of 4 space x are

    space space space space space sin to the power of 4 x plus cos to the power of 4 space x
equals open parentheses sin squared x close parentheses squared plus open parentheses cos squared x close parentheses squared
equals open parentheses sin squared x plus cos squared x close parentheses squared minus 2 sin squared x. cos squared x
equals 1 minus fraction numerator sin squared space 2 x over denominator 2 end fraction
F o r space m a x i m u m space v a l u e space o f space f left parenthesis x right parenthesis comma sin space 2 x equals 0
S o comma space f left parenthesis x right parenthesis equals 1 minus 0 over 2 equals 1
F o e space m i n i m u m space v a l u e space o f space f left parenthesis x right parenthesis comma space sin space 2 x space equals 1
S o comma space f left parenthesis x right parenthesis equals 1 minus 1 squared over 2 equals 1 half

    The minimum and maximum values of sin to the power of 4 x plus cos to the power of 4 space x are

    Maths-General
    space space space space space sin to the power of 4 x plus cos to the power of 4 space x
equals open parentheses sin squared x close parentheses squared plus open parentheses cos squared x close parentheses squared
equals open parentheses sin squared x plus cos squared x close parentheses squared minus 2 sin squared x. cos squared x
equals 1 minus fraction numerator sin squared space 2 x over denominator 2 end fraction
F o r space m a x i m u m space v a l u e space o f space f left parenthesis x right parenthesis comma sin space 2 x equals 0
S o comma space f left parenthesis x right parenthesis equals 1 minus 0 over 2 equals 1
F o e space m i n i m u m space v a l u e space o f space f left parenthesis x right parenthesis comma space sin space 2 x space equals 1
S o comma space f left parenthesis x right parenthesis equals 1 minus 1 squared over 2 equals 1 half
    parallel
    General
    physics-

    Figure shows a network of eight resistors, each equal to 2blank capital omega, connected to a 3V battery of negligible internal resistance. The current I in the circuit is

    Figure shows a network of eight resistors, each equal to 2blank capital omega, connected to a 3V battery of negligible internal resistance. The current I in the circuit is

    physics-General
    General
    physics-

    The equivalent resistance between A blank a n d blank B in the given circuit is

    The equivalent resistance between A blank a n d blank B in the given circuit is

    physics-General
    General
    chemistry-

    Which of the following is/are the rate determining step(s) of the given reaction?

    Which of the following is/are the rate determining step(s) of the given reaction?

    chemistry-General
    parallel
    General
    Maths-

    Maximum value of  fraction numerator 1 over denominator square root of 7 sin space x plus square root of 29 cos space x plus 7 end fraction

    Maximum value of  fraction numerator 1 over denominator square root of 7 sin space x plus square root of 29 cos space x plus 7 end fraction

    Maths-General
    General
    Maths-

    The minimum and maximum values of 2 square root of 2 cos space x plus sin space x are

    f(x) = 2 square root of 2 cos space x plus sin space x
    As minimum and maximum value of a sin x + b cos x is negative square root of a squared plus b squared end root a n d space space square root of a squared plus b squared end root
    So, minimum value equals negative square root of 1 squared plus open parentheses 2 square root of 2 close parentheses squared end root equals negative square root of 9 equals negative 3
    Maximum value =equals square root of 1 squared plus open parentheses 2 square root of 2 close parentheses squared end root equals square root of 9 equals 3

    The minimum and maximum values of 2 square root of 2 cos space x plus sin space x are

    Maths-General
    f(x) = 2 square root of 2 cos space x plus sin space x
    As minimum and maximum value of a sin x + b cos x is negative square root of a squared plus b squared end root a n d space space square root of a squared plus b squared end root
    So, minimum value equals negative square root of 1 squared plus open parentheses 2 square root of 2 close parentheses squared end root equals negative square root of 9 equals negative 3
    Maximum value =equals square root of 1 squared plus open parentheses 2 square root of 2 close parentheses squared end root equals square root of 9 equals 3
    General
    chemistry-


    (A) and(C) are different compound s and rotate the plane-polarised light in the same direction, andboth are dextrorotatory. Both (A) and(C) do not show diastereomers, whichof the following statements are correct?


    (A) and(C) are different compound s and rotate the plane-polarised light in the same direction, andboth are dextrorotatory. Both (A) and(C) do not show diastereomers, whichof the following statements are correct?

    chemistry-General
    parallel
    General
    chemistry-

    Which of the following dienes and dienophiles could be used to synthesise the following compound (A) ?

    Which of the following dienes and dienophiles could be used to synthesise the following compound (A) ?

    chemistry-General
    General
    Maths-

    16 sin x cos space x cos space 2 x cos space 4 x cos space 8 x element of

    16 sin x cos space x cos space 2 x cos space 4 x cos space 8 x element of

    Maths-General
    General
    physics-

    Five conductors are meeting at a point x as shown in the figure. What is the value of current in fifth conductor?

    According to Kirchhoff’s first law
    (5A)+(4A)+(-3A)+(-5A)+I=0
    Or I=-1A

    Five conductors are meeting at a point x as shown in the figure. What is the value of current in fifth conductor?

    physics-General
    According to Kirchhoff’s first law
    (5A)+(4A)+(-3A)+(-5A)+I=0
    Or I=-1A
    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.