General
Easy
Maths-

Period of sin space x sin space open parentheses 120 to the power of ring operator minus x close parentheses sin space open parentheses 120 to the power of ring operator plus x close parentheses is

Maths-General

  1. pi
  2. fraction numerator 2 pi over denominator 3 end fraction
  3. pi over 3
  4. pi over 2

    Answer:The correct answer is: fraction numerator 2 pi over denominator 3 end fraction

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    Related Questions to study

    General
    physics-

    A particle starts from rest at t equals 0 and undergoes an acceleration a in m s to the power of negative 2 end exponent with time t in seconds which is as shown

    Which one of the following plot represents velocity V in m s to the power of negative 1 end exponent versus time t in seconds


    Takingthe motion from 0 to 2 blank s
    u equals 0 comma blank a equals 3 m s to the power of negative 2 end exponent comma blank t equals 2 s comma blank v equals ?
    v equals u plus a t equals 0 plus 3 cross times 2 equals 6 m s to the power of negative 1 end exponent
    Taking the motion from 2 blank s to 4 blank s
    v equals 6 plus open parentheses negative 3 close parentheses open parentheses 2 close parentheses equals 0 m s to the power of negative 1 end exponent

    A particle starts from rest at t equals 0 and undergoes an acceleration a in m s to the power of negative 2 end exponent with time t in seconds which is as shown

    Which one of the following plot represents velocity V in m s to the power of negative 1 end exponent versus time t in seconds

    physics-General

    Takingthe motion from 0 to 2 blank s
    u equals 0 comma blank a equals 3 m s to the power of negative 2 end exponent comma blank t equals 2 s comma blank v equals ?
    v equals u plus a t equals 0 plus 3 cross times 2 equals 6 m s to the power of negative 1 end exponent
    Taking the motion from 2 blank s to 4 blank s
    v equals 6 plus open parentheses negative 3 close parentheses open parentheses 2 close parentheses equals 0 m s to the power of negative 1 end exponent
    General
    maths-

    Period of cos to the power of 6 space x plus sin to the power of 6 space x is

    Period of cos to the power of 6 space x plus sin to the power of 6 space x is

    maths-General
    General
    physics-

    Two inclined planes are located as shown in figure. A particle is projected from the foot of one frictionless plane along its line with a velocity just sufficient to carry it to top after which the particle slides down the other frictionless inclined plane. The total time it will take to reach the point C is

    The time of ascent = time of descent equals t subscript 0 end subscript
    T equals total time of flight equals 2 t subscript 0 end subscript

    sin invisible function application 45 degree equals fraction numerator 9.8 over denominator B C end fraction equals fraction numerator 9.8 over denominator s end fraction
    therefore blank s equals 9.8 square root of 2
    therefore blank s equals u t plus fraction numerator 1 over denominator 2 end fraction a t to the power of 2 end exponent
    s equals 0 cross times t plus fraction numerator 1 over denominator 2 end fraction left parenthesis g sin invisible function application 45 degree right parenthesis t subscript 0 end subscript superscript 2 end superscript
    or 9.8 square root of 2 equals fraction numerator 9.8 over denominator 2 square root of 2 end fraction t subscript 0 end subscript superscript 2 end superscript
    therefore blank t subscript 0 end subscript superscript 2 end superscript equals 4
    therefore blank t subscript 0 end subscript equals 2 s
    therefore blank T equals 2 t subscript 0 end subscript minus 4 s

    Two inclined planes are located as shown in figure. A particle is projected from the foot of one frictionless plane along its line with a velocity just sufficient to carry it to top after which the particle slides down the other frictionless inclined plane. The total time it will take to reach the point C is

    physics-General
    The time of ascent = time of descent equals t subscript 0 end subscript
    T equals total time of flight equals 2 t subscript 0 end subscript

    sin invisible function application 45 degree equals fraction numerator 9.8 over denominator B C end fraction equals fraction numerator 9.8 over denominator s end fraction
    therefore blank s equals 9.8 square root of 2
    therefore blank s equals u t plus fraction numerator 1 over denominator 2 end fraction a t to the power of 2 end exponent
    s equals 0 cross times t plus fraction numerator 1 over denominator 2 end fraction left parenthesis g sin invisible function application 45 degree right parenthesis t subscript 0 end subscript superscript 2 end superscript
    or 9.8 square root of 2 equals fraction numerator 9.8 over denominator 2 square root of 2 end fraction t subscript 0 end subscript superscript 2 end superscript
    therefore blank t subscript 0 end subscript superscript 2 end superscript equals 4
    therefore blank t subscript 0 end subscript equals 2 s
    therefore blank T equals 2 t subscript 0 end subscript minus 4 s
    General
    physics-

    I minus Vcharacteristic of a copper wire of length L and area of cross-section A is shown in figure. The slope of the curve becomes

    Slope of graph
    equals fraction numerator I over denominator V end fraction equals fraction numerator 1 over denominator R end fraction
    If experiment is performed at higher temperature then resistance increase and hence slope decrease, choice (a) is wrong.
    Similarly in choice (b) and (c) resistance increase.
    But for choice (d) resistance R increases, so slope decreases

    I minus Vcharacteristic of a copper wire of length L and area of cross-section A is shown in figure. The slope of the curve becomes

    physics-General
    Slope of graph
    equals fraction numerator I over denominator V end fraction equals fraction numerator 1 over denominator R end fraction
    If experiment is performed at higher temperature then resistance increase and hence slope decrease, choice (a) is wrong.
    Similarly in choice (b) and (c) resistance increase.
    But for choice (d) resistance R increases, so slope decreases
    General
    physics-

    v minus t graph for a particle is as shown. The distance travelled in the first 4 blank s is

    Distance covered equalsArea enclosed by v minus t graph
    equals Area of triangle equals fraction numerator 1 over denominator 2 end fraction cross times 4 cross times 8 equals 16 blank m

    v minus t graph for a particle is as shown. The distance travelled in the first 4 blank s is

    physics-General
    Distance covered equalsArea enclosed by v minus t graph
    equals Area of triangle equals fraction numerator 1 over denominator 2 end fraction cross times 4 cross times 8 equals 16 blank m
    General
    physics-

    A particle starts from rest. Its acceleration left parenthesis a right parenthesis versus time left parenthesis t right parenthesis is as shown in the figure. The maximum speed of the particle will be

    The area under acceleration time graph gives change in velocity. As acceleration is zero at the end of 11 blank s e c

    i.e. v subscript m a x end subscript equalsArea ofblank increment O A B
    equals fraction numerator 1 over denominator 2 end fraction cross times 11 cross times 10 equals 55 blank m divided by s

    A particle starts from rest. Its acceleration left parenthesis a right parenthesis versus time left parenthesis t right parenthesis is as shown in the figure. The maximum speed of the particle will be

    physics-General
    The area under acceleration time graph gives change in velocity. As acceleration is zero at the end of 11 blank s e c

    i.e. v subscript m a x end subscript equalsArea ofblank increment O A B
    equals fraction numerator 1 over denominator 2 end fraction cross times 11 cross times 10 equals 55 blank m divided by s
    General
    physics-

    The time taken by a block of wood (initially at rest)to slide down a smooth inclined plane 9.8 blank mlong (angle of inclination is 30 degree) is

    For one dimensional motion along a plane
    S equals u t plus fraction numerator 1 over denominator 2 end fraction a t to the power of 2 end exponent rightwards double arrow 9.8 equals 0 plus fraction numerator 1 over denominator 2 end fraction g sin invisible function application blank 30 degree t to the power of 2 end exponent rightwards double arrow t equals 2 s e c

    The time taken by a block of wood (initially at rest)to slide down a smooth inclined plane 9.8 blank mlong (angle of inclination is 30 degree) is

    physics-General
    For one dimensional motion along a plane
    S equals u t plus fraction numerator 1 over denominator 2 end fraction a t to the power of 2 end exponent rightwards double arrow 9.8 equals 0 plus fraction numerator 1 over denominator 2 end fraction g sin invisible function application blank 30 degree t to the power of 2 end exponent rightwards double arrow t equals 2 s e c
    General
    physics-

    Consider a thin square sheet of side L and thickness t comma made of a material of resistivity rho. The resistance between two opposite faces, shown by the shaded areas in the figure is

    R equals fraction numerator rho open parentheses L close parentheses over denominator A end fraction equals fraction numerator rho L over denominator t L end fraction equals fraction numerator rho over denominator t end fraction
    i e comma blank R is independent of L.
    Hence the correct option is (c).

    Consider a thin square sheet of side L and thickness t comma made of a material of resistivity rho. The resistance between two opposite faces, shown by the shaded areas in the figure is

    physics-General
    R equals fraction numerator rho open parentheses L close parentheses over denominator A end fraction equals fraction numerator rho L over denominator t L end fraction equals fraction numerator rho over denominator t end fraction
    i e comma blank R is independent of L.
    Hence the correct option is (c).
    General
    physics-

    The plot represents the flow of current through a wire at three different times.

    The ratio of charges flowing through the wire at different times is

    ) 2 : 3 : 3
    Therefore, charge is equal to area under the curve.
    ∴ Ist rectangle =q=lb=2
    IInd rectangle =q=lb=2
    I I I r d blank t r i a n g l e equals q equals fraction numerator 1 over denominator 2 end fraction l b equals 2
    Hence, ratio is 1:1:1.

    The plot represents the flow of current through a wire at three different times.

    The ratio of charges flowing through the wire at different times is

    physics-General
    ) 2 : 3 : 3
    Therefore, charge is equal to area under the curve.
    ∴ Ist rectangle =q=lb=2
    IInd rectangle =q=lb=2
    I I I r d blank t r i a n g l e equals q equals fraction numerator 1 over denominator 2 end fraction l b equals 2
    Hence, ratio is 1:1:1.
    General
    maths-

    If f left parenthesis x right parenthesis equals sin squared space open parentheses pi over 8 plus x over 2 close parentheses minus sin squared space open parentheses pi over 8 minus x over 2 close parentheses, then the period of fis

    If f left parenthesis x right parenthesis equals sin squared space open parentheses pi over 8 plus x over 2 close parentheses minus sin squared space open parentheses pi over 8 minus x over 2 close parentheses, then the period of fis

    maths-General
    General
    physics-

    Four concurrent coplanar forces in newton are acting at a point and keep it in equilibrium figure. Then values of F and theta are

    In equilibrium position along y-direction
    2 sin 60degree equals square root of 3 plus F cos invisible function application theta
    or 2 cross times fraction numerator square root of 3 over denominator 2 end fraction equals square root of 3 plus F cos invisible function application theta or F cos invisible function application theta equals 0
    As F not equal to 0
    therefore blank cos invisible function application theta equals 0 or theta equals 90 degree
    Along x-direction, F blank s i n 90 degree equals 1 plus 2 c o s 60 degree
    equals 1 plus 2 cross times fraction numerator 1 over denominator 2 end fraction
    F equals 2N

    Four concurrent coplanar forces in newton are acting at a point and keep it in equilibrium figure. Then values of F and theta are

    physics-General
    In equilibrium position along y-direction
    2 sin 60degree equals square root of 3 plus F cos invisible function application theta
    or 2 cross times fraction numerator square root of 3 over denominator 2 end fraction equals square root of 3 plus F cos invisible function application theta or F cos invisible function application theta equals 0
    As F not equal to 0
    therefore blank cos invisible function application theta equals 0 or theta equals 90 degree
    Along x-direction, F blank s i n 90 degree equals 1 plus 2 c o s 60 degree
    equals 1 plus 2 cross times fraction numerator 1 over denominator 2 end fraction
    F equals 2N
    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
    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
    physics-

    Five equal resistances, each of resistance R commaare connected as shown in figure below. A bettery of V volt is connected between A blank a n d blank B.The current flowing in F C will be

    I equals fraction numerator V over denominator R end fraction

    therefore blank C u r r e n t blank i n blank F C equals fraction numerator 1 over denominator 2 end fraction equals fraction numerator V over denominator 2 R end fraction

    Five equal resistances, each of resistance R commaare connected as shown in figure below. A bettery of V volt is connected between A blank a n d blank B.The current flowing in F C will be

    physics-General
    I equals fraction numerator V over denominator R end fraction

    therefore blank C u r r e n t blank i n blank F C equals fraction numerator 1 over denominator 2 end fraction equals fraction numerator V over denominator 2 R end fraction