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If f colon R not stretchy rightwards arrow left parenthesis 0 comma 1 right square bracket defined by f left parenthesis x right parenthesis equals fraction numerator 1 over denominator x squared plus 1 end fraction comma text  then  end text f text  is  end text

Maths-General

  1. not one-one
  2. not onto
  3. not one-one but onto
  4. one-one but not onto

    Answer:The correct answer is: not one-one but onto

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    The number of ways one can arrange words with the letters of the word ’ so that ↑MADHURI↑ always vowels occupy the beginning, middle and end places is

    3 vowels, 3 places equals 3! remaining i n 4!
    Total equals 3! 4!

    The number of ways one can arrange words with the letters of the word ’ so that ↑MADHURI↑ always vowels occupy the beginning, middle and end places is

    maths-General
    3 vowels, 3 places equals 3! remaining i n 4!
    Total equals 3! 4!
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    An ant goes from P to Q on a circular path in 20 second Radius OP=10 m . What is the average speed and average velocity of it ?

    An ant goes from P to Q on a circular path in 20 second Radius OP=10 m . What is the average speed and average velocity of it ?

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    Which of the following functions is not injective?

    Which of the following functions is not injective?

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    General
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    The number of one one onto functions that can be defined from A={a,b,c,d} into B={1,2,3,4} is

    n factorial

    The number of one one onto functions that can be defined from A={a,b,c,d} into B={1,2,3,4} is

    maths-General
    n factorial
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    The variation of intensity of magnetization left parenthesis I right parenthesis with respect to the magnetizing field (H) in a diamagnetic substance is described by the graph in figure.

    For a dia-magnetic substance, I is negative and negative I proportional to H. Therefore, the variation is represented by O C o r O D. As magnetisation is small, O C is better choice.

    The variation of intensity of magnetization left parenthesis I right parenthesis with respect to the magnetizing field (H) in a diamagnetic substance is described by the graph in figure.

    physics-General
    For a dia-magnetic substance, I is negative and negative I proportional to H. Therefore, the variation is represented by O C o r O D. As magnetisation is small, O C is better choice.
    General
    physics-

    A wire of length Land radius a rigidly fixed at one end. On stretching the other end of the wire with a force F, the increase in its length is l. If another wire of same material but of length 2L and radius 2 a is stretched with a force 2F, the increase in its length will be

    Young’s modulus Y equals fraction numerator F L over denominator A l end fraction
    equals fraction numerator F L over denominator pi a to the power of 2 end exponent l end fraction
    Since for same material Young’s modulus is same, i e comma
    Y subscript 1 end subscript equals Y subscript 2 end subscript
    orfraction numerator F L over denominator pi a to the power of 2 end exponent l end fraction equals fraction numerator open parentheses 2 F close parentheses left parenthesis 2 L right parenthesis over denominator pi open parentheses 2 a close parentheses to the power of 2 end exponent l ʹ end fraction
    orl to the power of ´ end exponent equals l

    A wire of length Land radius a rigidly fixed at one end. On stretching the other end of the wire with a force F, the increase in its length is l. If another wire of same material but of length 2L and radius 2 a is stretched with a force 2F, the increase in its length will be

    physics-General
    Young’s modulus Y equals fraction numerator F L over denominator A l end fraction
    equals fraction numerator F L over denominator pi a to the power of 2 end exponent l end fraction
    Since for same material Young’s modulus is same, i e comma
    Y subscript 1 end subscript equals Y subscript 2 end subscript
    orfraction numerator F L over denominator pi a to the power of 2 end exponent l end fraction equals fraction numerator open parentheses 2 F close parentheses left parenthesis 2 L right parenthesis over denominator pi open parentheses 2 a close parentheses to the power of 2 end exponent l ʹ end fraction
    orl to the power of ´ end exponent equals l
    General
    physics-

    The diagram shows a force-extension graph for a rubber band. Consider the following statements
    I. It will be easier to compress this rubber than expand it
    II. Rubber does not return to its original length after it is stretched
    III. The rubber band will get heated if it is stretched and released
    Which of these can be deduced from the graph

    Area of hysterisis loop gives the energy loss in the process of stretching and unstretching of rubber band and this loss will appear in the form of heating

    The diagram shows a force-extension graph for a rubber band. Consider the following statements
    I. It will be easier to compress this rubber than expand it
    II. Rubber does not return to its original length after it is stretched
    III. The rubber band will get heated if it is stretched and released
    Which of these can be deduced from the graph

    physics-General
    Area of hysterisis loop gives the energy loss in the process of stretching and unstretching of rubber band and this loss will appear in the form of heating
    General
    physics-

    A wire left parenthesis Y equals 2 cross times 10 to the power of 11 end exponent N m to the power of negative 2 end exponent right parenthesis has length 1 m and cross-sectional area 1 m m to the power of negative 2 end exponent. The work required to increase the length by 2 mm is

    Work done = fraction numerator 1 over denominator 2 end fraction blank F increment l
    fraction numerator equals blank fraction numerator 1 over denominator 2 end fraction fraction numerator Y A increment l to the power of 2 end exponent over denominator l end fraction over denominator fraction numerator 2 cross times 10 to the power of 11 end exponent cross times 10 to the power of negative 6 end exponent open parentheses 2 cross times 10 to the power of negative 3 end exponent close parentheses to the power of 2 end exponent over denominator 2 cross times 1 end fraction end fraction open vertical bar table row cell Y equals fraction numerator F l over denominator A increment l end fraction end cell row cell o r blank F equals fraction numerator Y A increment l over denominator l end fraction end cell end table close
    = 4cross times 10 to the power of negative 1 end exponent blank J equals 0.4 blank J

    A wire left parenthesis Y equals 2 cross times 10 to the power of 11 end exponent N m to the power of negative 2 end exponent right parenthesis has length 1 m and cross-sectional area 1 m m to the power of negative 2 end exponent. The work required to increase the length by 2 mm is

    physics-General
    Work done = fraction numerator 1 over denominator 2 end fraction blank F increment l
    fraction numerator equals blank fraction numerator 1 over denominator 2 end fraction fraction numerator Y A increment l to the power of 2 end exponent over denominator l end fraction over denominator fraction numerator 2 cross times 10 to the power of 11 end exponent cross times 10 to the power of negative 6 end exponent open parentheses 2 cross times 10 to the power of negative 3 end exponent close parentheses to the power of 2 end exponent over denominator 2 cross times 1 end fraction end fraction open vertical bar table row cell Y equals fraction numerator F l over denominator A increment l end fraction end cell row cell o r blank F equals fraction numerator Y A increment l over denominator l end fraction end cell end table close
    = 4cross times 10 to the power of negative 1 end exponent blank J equals 0.4 blank J
    General
    physics

    The graph of position not stretchy rightwards arrow time shown in the figure for a particle is not possible because ....

    The graph of position not stretchy rightwards arrow time shown in the figure for a particle is not possible because ....

    physicsGeneral
    General
    physics-

    The pressure applied from all directions on a cube is P. How much its temperature should be raised to maintain the original volume? The volume elasticity of the cube is beta and the coefficient of volume expansion is alpha

    If coefficient of volume expansion is alpha and rise in temperature is increment theta then increment V equals V alpha increment theta rightwards double arrow fraction numerator increment V over denominator V end fraction equals alpha increment theta
    Volume elasticity beta equals fraction numerator P over denominator increment V divided by V end fraction equals fraction numerator P over denominator alpha increment theta end fraction rightwards double arrow increment theta equals fraction numerator P over denominator alpha beta end fraction

    The pressure applied from all directions on a cube is P. How much its temperature should be raised to maintain the original volume? The volume elasticity of the cube is beta and the coefficient of volume expansion is alpha

    physics-General
    If coefficient of volume expansion is alpha and rise in temperature is increment theta then increment V equals V alpha increment theta rightwards double arrow fraction numerator increment V over denominator V end fraction equals alpha increment theta
    Volume elasticity beta equals fraction numerator P over denominator increment V divided by V end fraction equals fraction numerator P over denominator alpha increment theta end fraction rightwards double arrow increment theta equals fraction numerator P over denominator alpha beta end fraction
    General
    physics-

    Curie-Weiss law is obeyed by iron

    Iron is a ferromagnetic substance and ferromagnetic substance obeys Curie-Weiss law above its Curie temperature.

    Curie-Weiss law is obeyed by iron

    physics-General
    Iron is a ferromagnetic substance and ferromagnetic substance obeys Curie-Weiss law above its Curie temperature.
    General
    physics-

    If the B minus H curves of two samples of P and Q of iron are as shown below, then which one of the following statements is correct?

    For permanent magnet we prefer a material with high retentivity (so as to make a stronger magnet) and high coercivity (so that magnetization may not be wiped out easily). For electromagnet we prefer high saturated magnetism, low coercivity and least possible area of hysteresis loop so that electromagnet develops high magnetization, is easily demagnetized and energy loss in a magnetization cycle is least. Therefore, Pis suitable for making permanent magnet and Q for making electromagnet.

    If the B minus H curves of two samples of P and Q of iron are as shown below, then which one of the following statements is correct?

    physics-General
    For permanent magnet we prefer a material with high retentivity (so as to make a stronger magnet) and high coercivity (so that magnetization may not be wiped out easily). For electromagnet we prefer high saturated magnetism, low coercivity and least possible area of hysteresis loop so that electromagnet develops high magnetization, is easily demagnetized and energy loss in a magnetization cycle is least. Therefore, Pis suitable for making permanent magnet and Q for making electromagnet.
    General
    physics-

    Among the following properties describing diamagnetism identify the property that is wrongly stated

    Diamagnetic materials have negative susceptibility. Thus, (c) is wrongly stated.

    Among the following properties describing diamagnetism identify the property that is wrongly stated

    physics-General
    Diamagnetic materials have negative susceptibility. Thus, (c) is wrongly stated.
    General
    physics-

    Permanent magnet has properties retentivity and coercivity respectively

    The materials for a permanent magnet should have high retentivity (so that the magnet is strong) and high coercivity (so that the magnetism is not wiped out by stray magnetic fields). As the material in this case is never put to cyclic changes of magnetization, hence hysteresis is immaterial.

    Permanent magnet has properties retentivity and coercivity respectively

    physics-General
    The materials for a permanent magnet should have high retentivity (so that the magnet is strong) and high coercivity (so that the magnetism is not wiped out by stray magnetic fields). As the material in this case is never put to cyclic changes of magnetization, hence hysteresis is immaterial.
    General
    physics-

    The magnetic susceptibility of a paramagnetic substance at negative 73 degree C is 0.0060, then its value atnegative 173 degreeC will be

    X subscript m end subscript proportional to fraction numerator 1 over denominator T end fraction comma Therefore,
    fraction numerator X subscript 2 end subscript over denominator X subscript 1 end subscript end fraction equals fraction numerator T subscript 1 end subscript over denominator T subscript 2 end subscript end fraction
    fraction numerator X subscript 2 end subscript over denominator 0.0060 end fraction equals fraction numerator 273 minus 73 over denominator 273 minus 173 end fraction equals fraction numerator 200 over denominator 100 end fraction equals 2
    Or X subscript 2 end subscript equals 2 cross times 0.0060 equals 0.0120

    The magnetic susceptibility of a paramagnetic substance at negative 73 degree C is 0.0060, then its value atnegative 173 degreeC will be

    physics-General
    X subscript m end subscript proportional to fraction numerator 1 over denominator T end fraction comma Therefore,
    fraction numerator X subscript 2 end subscript over denominator X subscript 1 end subscript end fraction equals fraction numerator T subscript 1 end subscript over denominator T subscript 2 end subscript end fraction
    fraction numerator X subscript 2 end subscript over denominator 0.0060 end fraction equals fraction numerator 273 minus 73 over denominator 273 minus 173 end fraction equals fraction numerator 200 over denominator 100 end fraction equals 2
    Or X subscript 2 end subscript equals 2 cross times 0.0060 equals 0.0120