General
Easy
Maths-

Domain of definition of the functionf left parenthesis x right parenthesis equals fraction numerator 3 over denominator 4 minus x to the power of 2 end exponent end fraction plus l o g subscript 10 end subscript invisible function application open parentheses x to the power of 3 end exponent minus x close parentheses, is

Maths-General

  1. left parenthesis 1 , 2 right parenthesis    
  2. left parenthesis 1 , 2 right parenthesis union left parenthesis 2 comma infinity right parenthesis    
  3. left parenthesis negative 1 , 0 right parenthesis union left parenthesis 1 , 2 right parenthesis    
  4. left parenthesis negative 1 , 0 right parenthesis union left parenthesis 1 , 2 right parenthesis union left parenthesis 2 comma infinity right parenthesis    

    Answer:The correct answer is: left parenthesis negative 1 , 0 right parenthesis union left parenthesis 1 , 2 right parenthesis union left parenthesis 2 comma infinity right parenthesis

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    Related Questions to study

    General
    physics-

    Velocity-time graph of a particle of mass 2 kg moving in a straight line is as shown in figure. Work done by all forces on the particle is

    Initial velocity of particle, v subscript i end subscript equals 20 blank m s to the power of negative 1 end exponent
    Final velocity of the particle, v subscript f end subscript equals 0
    According to work-energy theorem,
    W subscript n e t end subscript equals increment K E equals K subscript f end subscript minus K subscript i end subscript
    equals fraction numerator 1 over denominator 2 end fraction m left parenthesis v subscript f end subscript superscript 2 end superscript minus v subscript i end subscript superscript 2 end superscript right parenthesis
    equals fraction numerator 1 over denominator 2 end fraction cross times 2 left parenthesis 0 to the power of 2 end exponent minus 20 to the power of 2 end exponent right parenthesis
    equals negative 400 blank J

    Velocity-time graph of a particle of mass 2 kg moving in a straight line is as shown in figure. Work done by all forces on the particle is

    physics-General
    Initial velocity of particle, v subscript i end subscript equals 20 blank m s to the power of negative 1 end exponent
    Final velocity of the particle, v subscript f end subscript equals 0
    According to work-energy theorem,
    W subscript n e t end subscript equals increment K E equals K subscript f end subscript minus K subscript i end subscript
    equals fraction numerator 1 over denominator 2 end fraction m left parenthesis v subscript f end subscript superscript 2 end superscript minus v subscript i end subscript superscript 2 end superscript right parenthesis
    equals fraction numerator 1 over denominator 2 end fraction cross times 2 left parenthesis 0 to the power of 2 end exponent minus 20 to the power of 2 end exponent right parenthesis
    equals negative 400 blank J
    General
    physics-

    A frictionless track A B C D E ends in a circular loop of radius R. A body slides down the track from point A which is it a height h equals 5 blank c m. Maximum value of R for the body to successfully complete the loop is

    Condition for vertical looping
    h equals fraction numerator 5 over denominator 2 end fraction r equals 5 c m blank therefore r equals 2 blank c m

    A frictionless track A B C D E ends in a circular loop of radius R. A body slides down the track from point A which is it a height h equals 5 blank c m. Maximum value of R for the body to successfully complete the loop is

    physics-General
    Condition for vertical looping
    h equals fraction numerator 5 over denominator 2 end fraction r equals 5 c m blank therefore r equals 2 blank c m
    General
    physics-

    The force acting on a body moving along x-axis varies with the position of the particle as shown in the fig

    The body is in stable equilibrium at

    When particle moves away from the origin then at position x equals x subscript 1 end subscript force is zero and at x greater than x subscript 1 end subscript, force is positive (repulsive in nature) so particle moves further and does not return back to original position i. e. the equilibrium is not stable Similarly at position x equals x subscript 2 end subscript force is zero and at x greater than x subscript 2 end subscript, force is negative (attractive in nature) So particle return back to original position i. e. the equilibrium is stable

    The force acting on a body moving along x-axis varies with the position of the particle as shown in the fig

    The body is in stable equilibrium at

    physics-General
    When particle moves away from the origin then at position x equals x subscript 1 end subscript force is zero and at x greater than x subscript 1 end subscript, force is positive (repulsive in nature) so particle moves further and does not return back to original position i. e. the equilibrium is not stable Similarly at position x equals x subscript 2 end subscript force is zero and at x greater than x subscript 2 end subscript, force is negative (attractive in nature) So particle return back to original position i. e. the equilibrium is stable
    General
    physics-

    The pointer reading v divided by s load graph for a spring balance is as given in the figure. The spring constant is

    Spring constant k equals fraction numerator F over denominator x end fraction equals Slope of curve
    therefore k equals fraction numerator 4 minus 1 over denominator 30 end fraction equals fraction numerator 3 over denominator 30 end fraction equals 0.1 blank k g divided by c m

    The pointer reading v divided by s load graph for a spring balance is as given in the figure. The spring constant is

    physics-General
    Spring constant k equals fraction numerator F over denominator x end fraction equals Slope of curve
    therefore k equals fraction numerator 4 minus 1 over denominator 30 end fraction equals fraction numerator 3 over denominator 30 end fraction equals 0.1 blank k g divided by c m
    General
    physics-

    The force F acting on a particle moving in a straight line is shown in figure. What is the work done by the force on the particle in the 1st meter of the trajectory

    Work done open parentheses W close parentheses equals Area under curve of F-x graph
    = Area of triangle O A B equals fraction numerator 1 over denominator 2 end fraction cross times 5 cross times 1 equals 2.5 blank J

    The force F acting on a particle moving in a straight line is shown in figure. What is the work done by the force on the particle in the 1st meter of the trajectory

    physics-General
    Work done open parentheses W close parentheses equals Area under curve of F-x graph
    = Area of triangle O A B equals fraction numerator 1 over denominator 2 end fraction cross times 5 cross times 1 equals 2.5 blank J
    General
    physics-

    If w subscript 1 end subscript comma w subscript 2 blank a n d blank W subscript 3 end subscript end subscript represent the work done in moving a particle from A to B along three different paths 1, 2 and 3 respectively(as shown)in the gravitational field of a point mass m. Find the correct relation between w subscript 1 end subscript comma w subscript 2 end subscript a n d blank w subscript 3 end subscript

    Gravitational field is a conservative force field. In a conservative force field work done is path independent.
    therefore blank W subscript 1 end subscript equals W subscript 2 end subscript equals W subscript 3 end subscript

    If w subscript 1 end subscript comma w subscript 2 blank a n d blank W subscript 3 end subscript end subscript represent the work done in moving a particle from A to B along three different paths 1, 2 and 3 respectively(as shown)in the gravitational field of a point mass m. Find the correct relation between w subscript 1 end subscript comma w subscript 2 end subscript a n d blank w subscript 3 end subscript

    physics-General
    Gravitational field is a conservative force field. In a conservative force field work done is path independent.
    therefore blank W subscript 1 end subscript equals W subscript 2 end subscript equals W subscript 3 end subscript
    General
    physics-

    Given below is a graph between a variable force left parenthesis F right parenthesis (along y-axis) and the displacement left parenthesis X right parenthesis (along x-axis) of a particle in one dimension. The work done by the force in the displacement interval between 0 blank m and 30 blank m is

    Given below is a graph between a variable force left parenthesis F right parenthesis (along y-axis) and the displacement left parenthesis X right parenthesis (along x-axis) of a particle in one dimension. The work done by the force in the displacement interval between 0 blank m and 30 blank m is

    physics-General
    General
    physics-

    A particle of mass m moving with a velocity u makes an elastic one dimensional collision with a stationary particle of mass m establishing a contact with it for extremely small time T. Their force of contact increases from zero to F subscript 0 end subscript linearly in time T divided by 4, remains constant for a further time T divided by 2 and decreases linearly from F subscript 0 end subscript to zero in further time T divided by 4 as shown. The magnitude possessed by F subscript 0 end subscript is

    Change in momentum = Impulse
    = Area under force-time graph
    therefore m v equals Area of trapezium
    rightwards double arrow m v equals fraction numerator 1 over denominator 2 end fraction open parentheses T plus fraction numerator T over denominator 2 end fraction close parentheses F subscript 0 end subscript rightwards double arrow m v equals fraction numerator 3 T over denominator 4 end fraction F subscript 0 end subscript rightwards double arrow F subscript 0 end subscript equals fraction numerator 4 m u over denominator 3 T end fraction

    A particle of mass m moving with a velocity u makes an elastic one dimensional collision with a stationary particle of mass m establishing a contact with it for extremely small time T. Their force of contact increases from zero to F subscript 0 end subscript linearly in time T divided by 4, remains constant for a further time T divided by 2 and decreases linearly from F subscript 0 end subscript to zero in further time T divided by 4 as shown. The magnitude possessed by F subscript 0 end subscript is

    physics-General
    Change in momentum = Impulse
    = Area under force-time graph
    therefore m v equals Area of trapezium
    rightwards double arrow m v equals fraction numerator 1 over denominator 2 end fraction open parentheses T plus fraction numerator T over denominator 2 end fraction close parentheses F subscript 0 end subscript rightwards double arrow m v equals fraction numerator 3 T over denominator 4 end fraction F subscript 0 end subscript rightwards double arrow F subscript 0 end subscript equals fraction numerator 4 m u over denominator 3 T end fraction
    General
    physics-

    If reaction is R and coefficient of friction isblank mu, what is work done against friction in moving a body by distance d?


    As shown a block of mass M blankis lying over rough horizontal surface. Letblank mu be the coeeficient of kinetic friction between the two surfaces in contact. The force Of friction between the block and horizontal surface is given by
    F equals mu R equals mu M g (because R equals M g right parenthesis
    To move the block without acceleration, the force (P)required will be just equal to the force of friction , ie ,
    P equals F equals mu R
    If d is the distance moved , then work done is given by
    W equals P cross times d equals mu R d

    If reaction is R and coefficient of friction isblank mu, what is work done against friction in moving a body by distance d?

    physics-General

    As shown a block of mass M blankis lying over rough horizontal surface. Letblank mu be the coeeficient of kinetic friction between the two surfaces in contact. The force Of friction between the block and horizontal surface is given by
    F equals mu R equals mu M g (because R equals M g right parenthesis
    To move the block without acceleration, the force (P)required will be just equal to the force of friction , ie ,
    P equals F equals mu R
    If d is the distance moved , then work done is given by
    W equals P cross times d equals mu R d
    General
    maths-

    A spotlight installed in the ground shines on a wall. A woman stands between the light and the wall casting a shadow on the wall. How are the rate at which she walks away from the light and rate at which her shadow grows related ?

    A spotlight installed in the ground shines on a wall. A woman stands between the light and the wall casting a shadow on the wall. How are the rate at which she walks away from the light and rate at which her shadow grows related ?

    maths-General
    General
    maths-

    Let A be a set containing 10 distinct elements, then the total number of distinct functions from A to A is-

    Let A be a set containing 10 distinct elements, then the total number of distinct functions from A to A is-

    maths-General
    General
    maths-

    The number of bijective functions from set A to itself when a contains 106 elements-

    The number of bijective functions from set A to itself when a contains 106 elements-

    maths-General
    General
    maths-

    Suppose f left parenthesis x right parenthesis equals left parenthesis x plus 1 right parenthesis squared forx greater or equal than negative 1. If g(x) is the function whose graph is the reflection of the graph of f(x) with respect to the line y = x, then g(x) equals–

    Suppose f left parenthesis x right parenthesis equals left parenthesis x plus 1 right parenthesis squared forx greater or equal than negative 1. If g(x) is the function whose graph is the reflection of the graph of f(x) with respect to the line y = x, then g(x) equals–

    maths-General
    General
    physics-

    The work done by a force acting on a body is as shown in the graph. The total work done in covering an initial distance of 20 blank m is

    Work done W equals area under F minus S graph
    = area of trapezium A B C D plus area of trapezium C E F D
    equals fraction numerator 1 over denominator 2 end fraction cross times open parentheses 10 plus 15 close parentheses cross times 10 plus fraction numerator 1 over denominator 2 end fraction cross times left parenthesis 10 plus 20 right parenthesis cross times 5
    equals 125 plus 75 equals 200 blank J

    The work done by a force acting on a body is as shown in the graph. The total work done in covering an initial distance of 20 blank m is

    physics-General
    Work done W equals area under F minus S graph
    = area of trapezium A B C D plus area of trapezium C E F D
    equals fraction numerator 1 over denominator 2 end fraction cross times open parentheses 10 plus 15 close parentheses cross times 10 plus fraction numerator 1 over denominator 2 end fraction cross times left parenthesis 10 plus 20 right parenthesis cross times 5
    equals 125 plus 75 equals 200 blank J
    General
    physics-

    A particle is acted upon by a force Fwhich varies with position xas shown in figure. If the particle at x equals 0 has kinetic energy of 25 J, then the kinetic energy of the particle at x equals 16 blank m is

    Work done=area between the graph force displacement curve and displacement
    W equals fraction numerator 1 over denominator 2 end fraction cross times 6 cross times 10 minus 5 cross times 4 plus 5 cross times 4 minus 5 cross times 2
    W equals 20 blank J
    According to work energy theorem
    increment equals K subscript E end subscript equals W
    K subscript E end subscript subscript f end subscript equals W plus increment K
    =20+25
    =45J

    A particle is acted upon by a force Fwhich varies with position xas shown in figure. If the particle at x equals 0 has kinetic energy of 25 J, then the kinetic energy of the particle at x equals 16 blank m is

    physics-General
    Work done=area between the graph force displacement curve and displacement
    W equals fraction numerator 1 over denominator 2 end fraction cross times 6 cross times 10 minus 5 cross times 4 plus 5 cross times 4 minus 5 cross times 2
    W equals 20 blank J
    According to work energy theorem
    increment equals K subscript E end subscript equals W
    K subscript E end subscript subscript f end subscript equals W plus increment K
    =20+25
    =45J