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If f colon left square bracket 0 comma 1 right square bracket not stretchy rightwards arrow left square bracket negative 1 comma 3 right square bracket defined by f left parenthesis x right parenthesis equals x squared plus x plus 1 text , then  end text f text  is  end text

Maths-General

  1. onto
  2. one one
  3. a function
  4. one one onto

    Answer:The correct answer is: one one

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    Two thin metallic strips, carrying current in the direction shown, cross each other perpendicularly without touching but being close to each other, as shown in the figure. The regions which contain some points of zero magnetic induction are

    ) II and IV

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    Two thin metallic strips, carrying current in the direction shown, cross each other perpendicularly without touching but being close to each other, as shown in the figure. The regions which contain some points of zero magnetic induction are

    physics-General
    ) II and IV

    Hence, magnetic induction in region I and IV will be zero.
    General
    maths-

    A equals left curly bracket x colon negative 1 less or equal than x less or equal than 1 right curly bracket. f colon A not stretchy rightwards arrow A defined by f left parenthesis x right parenthesis equals x vertical line x vertical linetext  Then  end text f text  is  end text

    A equals left curly bracket x colon negative 1 less or equal than x less or equal than 1 right curly bracket. f colon A not stretchy rightwards arrow A defined by f left parenthesis x right parenthesis equals x vertical line x vertical linetext  Then  end text f text  is  end text

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    maths-General
    General
    physics

    The distance travelled by a particle is given by S=3+2t +5t2The initial velocity of the particle is…..

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    physicsGeneral
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    physicsGeneral
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    A cell is connected between the points A and C of a circular conductor ABCD with O as centre and angle A O C equals 60 degree. If B subscript 1 and B subscript 2 are the magnitudes of the magnetic fields at O due to the currents in  ABC and ADC respectively, then ratio fraction numerator B subscript 1 end subscript over denominator B subscript 2 end subscript end fraction is

    From Biot-Savart law the magnetic field at the centre is directly proportional to the length of current carrying segment.
    therefore fraction numerator B subscript 1 end subscript over denominator B subscript 2 end subscript end fraction equals fraction numerator l e n g t h blank o f blank A B C over denominator l e n g t h blank o f blank A D C end fraction
    equals fraction numerator a n g l e blank s u b t e n d e d blank b y blank A B C over denominator a n g l e blank s u b t e n d e d blank b y blank A D C end fraction
    equals fraction numerator left parenthesis 360 degree minus 60 degree right parenthesis over denominator 60 degree end fraction equals fraction numerator 300 over denominator 60 end fraction equals fraction numerator 5 over denominator 1 end fraction

    A cell is connected between the points A and C of a circular conductor ABCD with O as centre and angle A O C equals 60 degree. If B subscript 1 and B subscript 2 are the magnitudes of the magnetic fields at O due to the currents in  ABC and ADC respectively, then ratio fraction numerator B subscript 1 end subscript over denominator B subscript 2 end subscript end fraction is

    physics-General
    From Biot-Savart law the magnetic field at the centre is directly proportional to the length of current carrying segment.
    therefore fraction numerator B subscript 1 end subscript over denominator B subscript 2 end subscript end fraction equals fraction numerator l e n g t h blank o f blank A B C over denominator l e n g t h blank o f blank A D C end fraction
    equals fraction numerator a n g l e blank s u b t e n d e d blank b y blank A B C over denominator a n g l e blank s u b t e n d e d blank b y blank A D C end fraction
    equals fraction numerator left parenthesis 360 degree minus 60 degree right parenthesis over denominator 60 degree end fraction equals fraction numerator 300 over denominator 60 end fraction equals fraction numerator 5 over denominator 1 end fraction
    General
    physics-

    Current I is flowing in conductor shaped as shown in the figure. The radius of the curved part is r and the length of straight portion is very large. The value of the magnetic field at the centre O will be

    B subscript A end subscript equals 0

    B subscript B end subscript equals blank fraction numerator mu subscript 0 end subscript over denominator 4 pi end fraction fraction numerator left parenthesis 2 pi minus pi divided by 2 right parenthesis I over denominator r end fraction blank circled times equals fraction numerator mu subscript 0 end subscript over denominator 4 pi end fraction fraction numerator 3 pi I over denominator 2 r end fraction
    B subscript C end subscript equals fraction numerator mu subscript 0 end subscript I over denominator 4 pi r end fraction circled times
    So, net magnetic field at the centre
    equals B subscript A end subscript plus B subscript B end subscript plus blank B subscript C end subscript
    equals 0 plus fraction numerator mu subscript 0 end subscript over denominator 4 pi end fraction fraction numerator 3 pi I over denominator 2 r end fraction plus fraction numerator mu subscript 0 end subscript I over denominator 4 pi r end fraction equals fraction numerator mu subscript 0 end subscript over denominator 4 pi end fraction fraction numerator I over denominator r end fraction open parentheses fraction numerator 3 pi over denominator 2 end fraction plus 1 close parentheses

    Current I is flowing in conductor shaped as shown in the figure. The radius of the curved part is r and the length of straight portion is very large. The value of the magnetic field at the centre O will be

    physics-General
    B subscript A end subscript equals 0

    B subscript B end subscript equals blank fraction numerator mu subscript 0 end subscript over denominator 4 pi end fraction fraction numerator left parenthesis 2 pi minus pi divided by 2 right parenthesis I over denominator r end fraction blank circled times equals fraction numerator mu subscript 0 end subscript over denominator 4 pi end fraction fraction numerator 3 pi I over denominator 2 r end fraction
    B subscript C end subscript equals fraction numerator mu subscript 0 end subscript I over denominator 4 pi r end fraction circled times
    So, net magnetic field at the centre
    equals B subscript A end subscript plus B subscript B end subscript plus blank B subscript C end subscript
    equals 0 plus fraction numerator mu subscript 0 end subscript over denominator 4 pi end fraction fraction numerator 3 pi I over denominator 2 r end fraction plus fraction numerator mu subscript 0 end subscript I over denominator 4 pi r end fraction equals fraction numerator mu subscript 0 end subscript over denominator 4 pi end fraction fraction numerator I over denominator r end fraction open parentheses fraction numerator 3 pi over denominator 2 end fraction plus 1 close parentheses
    General
    physics-

    For the arrangement shown in figure the time interval after which the water jet ceases to cross the wall (area of cross section of tank is A and orifice is ‘a’)

    Velocity of efflux = square root of 2 g h end root
    Find ‘h’ to have range of ejected water greater or equal than x
    rightwards double arrow x equals square root of 2 g h end root. square root of fraction numerator 2 y over denominator g end fraction end root rightwards double arrow h equals fraction numerator x to the power of 2 end exponent over denominator 4 y to the power of 2 end exponent end fraction
    time taken by liquid to drain out from H to h is equals fraction numerator A over denominator a end fraction square root of fraction numerator 2 over denominator g end fraction end root open square brackets square root of H minus square root of h close square brackets

    For the arrangement shown in figure the time interval after which the water jet ceases to cross the wall (area of cross section of tank is A and orifice is ‘a’)

    physics-General
    Velocity of efflux = square root of 2 g h end root
    Find ‘h’ to have range of ejected water greater or equal than x
    rightwards double arrow x equals square root of 2 g h end root. square root of fraction numerator 2 y over denominator g end fraction end root rightwards double arrow h equals fraction numerator x to the power of 2 end exponent over denominator 4 y to the power of 2 end exponent end fraction
    time taken by liquid to drain out from H to h is equals fraction numerator A over denominator a end fraction square root of fraction numerator 2 over denominator g end fraction end root open square brackets square root of H minus square root of h close square brackets
    General
    physics-

    Figure shows a stream of fluid emerging from a tube in the base of an open fixed tank. The expression of ‘y’ (Maximum height traveled by jet of water) is

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    Figure shows a stream of fluid emerging from a tube in the base of an open fixed tank. The expression of ‘y’ (Maximum height traveled by jet of water) is

    physics-General
    y equals fraction numerator u subscript y end subscript superscript 2 end superscript over denominator 2 g end fraction
    u equals square root of 2 g h end root u subscript y end subscript equals square root of 2 g h end root sin invisible function application theta rightwards double arrow y equals fraction numerator open parentheses square root of 2 g h end root sin invisible function application theta close parentheses to the power of 2 end exponent over denominator 2 g end fraction equals h sin to the power of 2 end exponent invisible function application theta
    General
    physics-

    A thin movable plate is separated from two fixed plates P subscript 1 and P subscript 2 by two highly viscous liquids of coefficients of viscosity n subscript 1 and n subscript 2 as shown, where n subscript 2 end subscript equals 9 n subscript 1 end subscript. Area of contact of movable plate with each fluid is same. If the distance between two fixed plates is ‘h’, then the distance ‘h subscript 1 end subscript’ of movable plate from upper plate such that movable plate can be moved with a finite velocity by applying the minimum possible force on movable plate is ( assume only linear velocity distribution in each liquid).

    Viscous force due to upper liquid equals n subscript 1 end subscript A open parentheses fraction numerator v minus o over denominator h subscript 1 end subscript end fraction close parentheses
    Viscous force due to lower liquid = n subscript 2 end subscript A open parentheses fraction numerator v minus o over denominator h minus h subscript 1 end subscript end fraction close parentheses
    If total force is minimum
    fraction numerator d over denominator d h subscript 1 end subscript end fraction open square brackets fraction numerator n subscript 1 end subscript over denominator h subscript 1 end subscript end fraction plus fraction numerator n subscript 2 end subscript over denominator h minus h subscript 1 end subscript end fraction close square brackets equals 0

    A thin movable plate is separated from two fixed plates P subscript 1 and P subscript 2 by two highly viscous liquids of coefficients of viscosity n subscript 1 and n subscript 2 as shown, where n subscript 2 end subscript equals 9 n subscript 1 end subscript. Area of contact of movable plate with each fluid is same. If the distance between two fixed plates is ‘h’, then the distance ‘h subscript 1 end subscript’ of movable plate from upper plate such that movable plate can be moved with a finite velocity by applying the minimum possible force on movable plate is ( assume only linear velocity distribution in each liquid).

    physics-General
    Viscous force due to upper liquid equals n subscript 1 end subscript A open parentheses fraction numerator v minus o over denominator h subscript 1 end subscript end fraction close parentheses
    Viscous force due to lower liquid = n subscript 2 end subscript A open parentheses fraction numerator v minus o over denominator h minus h subscript 1 end subscript end fraction close parentheses
    If total force is minimum
    fraction numerator d over denominator d h subscript 1 end subscript end fraction open square brackets fraction numerator n subscript 1 end subscript over denominator h subscript 1 end subscript end fraction plus fraction numerator n subscript 2 end subscript over denominator h minus h subscript 1 end subscript end fraction close square brackets equals 0
    General
    physics-

    A vertical jet of water coming out of a nozzle with velocity 20 m/s supports a plate of mass M stationary at a height h = 15m, as shown in the figure. If the rate of water flow is 1 litre per second, the mass of the plate is (Assume the collision to be inelastic).

    Force by liquid = Mg

    But and

    A vertical jet of water coming out of a nozzle with velocity 20 m/s supports a plate of mass M stationary at a height h = 15m, as shown in the figure. If the rate of water flow is 1 litre per second, the mass of the plate is (Assume the collision to be inelastic).

    physics-General
    Force by liquid = Mg

    But and

    General
    physics-

    A conical flask of mass 10 kg and base area as 103 cm2 is floating in liquid of relative density 1.2, as shown in the figure. The force that liquid exerts on curved surface of conical flask will be (Given g = 10 m/s2)


    = Buoyant force = weight
    F = 20 N in down ward direction

    A conical flask of mass 10 kg and base area as 103 cm2 is floating in liquid of relative density 1.2, as shown in the figure. The force that liquid exerts on curved surface of conical flask will be (Given g = 10 m/s2)

    physics-General

    = Buoyant force = weight
    F = 20 N in down ward direction