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According to Newton’s law of cooling, the rate of cooling is proportional to open parentheses increment theta close parentheses to the power of n end exponent, where increment theta is the temperature differences between the body and the surroundings andn is equal to

Physics-General

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    Answer:The correct answer is: 1According to Newton’s law of cooling the rate of loss of heat of a body is directly proportional to the difference in temperature of the body, i e comma
    negative fraction numerator d Q over denominator d t end fraction proportional to left parenthesis increment theta right parenthesis (i)
    Given, negative fraction numerator d Q over denominator d t end fraction proportional to open parentheses increment theta close parentheses to the power of n end exponent (ii)
    Comparing Eqs. (i) and (ii), we get
    n=1

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    Statement-1- The number blank to the power of 1000 end exponent C subscript 500 end subscript is not divisible by 11.Because
    Statement-2- If p is a prime, the exponent of p in n! is open square brackets fraction numerator n over denominator p end fraction close square brackets+ open square brackets fraction numerator n over denominator p to the power of 2 end exponent end fraction close square brackets+ open square brackets fraction numerator n over denominator p to the power of 3 end exponent end fraction close square brackets+……Where [x] denotes the greatest integer less or equal than x.

    Statement-1- The number blank to the power of 1000 end exponent C subscript 500 end subscript is not divisible by 11.Because
    Statement-2- If p is a prime, the exponent of p in n! is open square brackets fraction numerator n over denominator p end fraction close square brackets+ open square brackets fraction numerator n over denominator p to the power of 2 end exponent end fraction close square brackets+ open square brackets fraction numerator n over denominator p to the power of 3 end exponent end fraction close square brackets+……Where [x] denotes the greatest integer less or equal than x.

    maths-General
    General
    maths-

    text  If  end text y equals e to the power of 4 x end exponent plus 2 e to the power of negative x end exponent satisfies the relation fraction numerator d cubed y over denominator d x cubed end fraction plus A fraction numerator d y over denominator d x end fraction plus B y equals 0 then value of A and B respectively are:

    text  If  end text y equals e to the power of 4 x end exponent plus 2 e to the power of negative x end exponent satisfies the relation fraction numerator d cubed y over denominator d x cubed end fraction plus A fraction numerator d y over denominator d x end fraction plus B y equals 0 then value of A and B respectively are:

    maths-General
    General
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    Number of values of 'p' for which the equationopen parentheses p squared minus 3 p plus 2 close parentheses x squared minus open parentheses p squared minus 5 p plus 4 close parentheses x plus p minus p squared equals 0 possess more  than two roots ,is:

    For (p2– 3p+2)x2–(p2–5p+4)x+p–p2=0tobe anidentity
    p2–3p+2 =0 rightwards double arrow p = 1, 2...(i)
    p2 – 5p + 4 = 0 rightwards double arrow p = 1, 4...(ii)
    p – p2 = 0 rightwards double arrow p = 0, 1...(iii)
    For (i), (ii) & (iii) to hold simultaneously p = 1.

    Number of values of 'p' for which the equationopen parentheses p squared minus 3 p plus 2 close parentheses x squared minus open parentheses p squared minus 5 p plus 4 close parentheses x plus p minus p squared equals 0 possess more  than two roots ,is:

    maths-General
    For (p2– 3p+2)x2–(p2–5p+4)x+p–p2=0tobe anidentity
    p2–3p+2 =0 rightwards double arrow p = 1, 2...(i)
    p2 – 5p + 4 = 0 rightwards double arrow p = 1, 4...(ii)
    p – p2 = 0 rightwards double arrow p = 0, 1...(iii)
    For (i), (ii) & (iii) to hold simultaneously p = 1.
    General
    maths-

    Let p, qelement of{1,2,3,4}.Then number of equation of the form px2+qx+1=0,having real roots ,is

    q2–4pgreater or equal than0
    q=2 rightwards double arrow p=1
    q=3rightwards double arrow p=1,2
    q=4rightwards double arrow p=1,2,3,4
    Hence 7 values of (p, q)7equationsarepossible.

    Let p, qelement of{1,2,3,4}.Then number of equation of the form px2+qx+1=0,having real roots ,is

    maths-General
    q2–4pgreater or equal than0
    q=2 rightwards double arrow p=1
    q=3rightwards double arrow p=1,2
    q=4rightwards double arrow p=1,2,3,4
    Hence 7 values of (p, q)7equationsarepossible.
    General
    maths-

    The differential equation of all circles which pass through the origin and whose centres lie on y-axis is

    The differential equation of all circles which pass through the origin and whose centres lie on y-axis is

    maths-General
    General
    physics-

    A simple magnifying lens is used in such a way that an image is formed at 25 cm away from the eye. In order to have 10 times magnification, the focal length of the lens should be

    fraction numerator D over denominator F end fraction or fraction numerator 25 over denominator F end fraction

    A simple magnifying lens is used in such a way that an image is formed at 25 cm away from the eye. In order to have 10 times magnification, the focal length of the lens should be

    physics-General
    fraction numerator D over denominator F end fraction or fraction numerator 25 over denominator F end fraction
    General
    maths-

    If x fraction numerator d y over denominator d x end fraction equals y left parenthesis log space y minus log space x plus 1 right parenthesis then the solution of the equation is :

    If x fraction numerator d y over denominator d x end fraction equals y left parenthesis log space y minus log space x plus 1 right parenthesis then the solution of the equation is :

    maths-General
    General
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    The degree of the differential equation satisfying square root of 1 plus x squared end root plus square root of 1 plus y squared end root equals A open parentheses x square root of 1 plus y squared end root minus y square root of 1 plus x squared end root close parentheses is

    The degree of the differential equation satisfying square root of 1 plus x squared end root plus square root of 1 plus y squared end root equals A open parentheses x square root of 1 plus y squared end root minus y square root of 1 plus x squared end root close parentheses is

    maths-General
    General
    physics-

    Maximum kinetic energy (Ek ) of a photoelectron varies with the frequency ( v ) of the incident radiation as

    Maximum kinetic energy (Ek ) of a photoelectron varies with the frequency ( v ) of the incident radiation as

    physics-General
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    If f(x) is a differentiable function satisfying f(x+ y)= f(x)f(y) straight for all x, y element of R and f'(0)=2 then f(x)=

    table row cell f left parenthesis x plus y right parenthesis equals f left parenthesis x right parenthesis f left parenthesis y right parenthesis         rightwards double arrow         f left parenthesis x right parenthesis equals k e to the power of x f left parenthesis 0 right parenthesis end exponent text end text text w end text text h end text text e end text text r end text text e end text text end text k text end text text i end text text s end text text end text text a end text text end text text c end text text o end text text n end text text s end text text t end text text a end text text n end text text t end text text end text end cell row cell text end text text A end text text s end text text end text f to the power of ´ end exponent left parenthesis 0 right parenthesis equals 2         rightwards double arrow         k equals 1 rightwards double arrow f left parenthesis x right parenthesis equals e to the power of 2 x end exponent end cell end table rightwards double arrow f left parenthesis x right parenthesis equals k e to the power of 2 x end exponent

    If f(x) is a differentiable function satisfying f(x+ y)= f(x)f(y) straight for all x, y element of R and f'(0)=2 then f(x)=

    maths-General
    table row cell f left parenthesis x plus y right parenthesis equals f left parenthesis x right parenthesis f left parenthesis y right parenthesis         rightwards double arrow         f left parenthesis x right parenthesis equals k e to the power of x f left parenthesis 0 right parenthesis end exponent text end text text w end text text h end text text e end text text r end text text e end text text end text k text end text text i end text text s end text text end text text a end text text end text text c end text text o end text text n end text text s end text text t end text text a end text text n end text text t end text text end text end cell row cell text end text text A end text text s end text text end text f to the power of ´ end exponent left parenthesis 0 right parenthesis equals 2         rightwards double arrow         k equals 1 rightwards double arrow f left parenthesis x right parenthesis equals e to the power of 2 x end exponent end cell end table rightwards double arrow f left parenthesis x right parenthesis equals k e to the power of 2 x end exponent
    General
    maths-

    If f(x) = ax2+ bx + c such that f(p) + f(q) = 0 where anot equal to0 ; p , qelement ofR then number of real roots of equation f(x) = 0in interval [p, q] is

    f(p)=–f(q) rightwards double arrow eitherf(p)f(q)<0 or f(p) =0=f(q)
    rightwards double arrow exactlyonerootin(p,q) orrootsarepandq

    If f(x) = ax2+ bx + c such that f(p) + f(q) = 0 where anot equal to0 ; p , qelement ofR then number of real roots of equation f(x) = 0in interval [p, q] is

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    If f(x) is a polynomial of degree five with leading coefficient one such that  f(1)=12,f(2)=22,f(3)=32,f(4)=42,f(5)=52 then

    f left parenthesis x right parenthesis minus x to the power of 2 end exponent equals left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis left parenthesis x minus 3 right parenthesis left parenthesis x minus 4 right parenthesis left parenthesis x minus 5

    If f(x) is a polynomial of degree five with leading coefficient one such that  f(1)=12,f(2)=22,f(3)=32,f(4)=42,f(5)=52 then

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    physics-

    A 60 watt bulb is hung over the center of a table 4 m cross times 4 m at a height of 3 m. The ratio of the intensities of illumination at a point on the centre of the edge and on the corner of the table is

    A 60 watt bulb is hung over the center of a table 4 m cross times 4 m at a height of 3 m. The ratio of the intensities of illumination at a point on the centre of the edge and on the corner of the table is

    physics-General
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    physics-

    Lux is equal to

    I equals fraction numerator L over denominator r to the power of 2 end exponent end fraction

    Lux is equal to

    physics-General
    I equals fraction numerator L over denominator r to the power of 2 end exponent end fraction
    General
    physics-

    Five lumen/watt is the luminous efficiency of a lamp and its luminous intensity is 35 candela. The power of the lamp is

    Efficiency of light source
    eta equals fraction numerator phi over denominator p end fraction..... (i)
    and L equals fraction numerator phi over denominator 4 pi end fraction..... (ii)
    From equation (i) and (ii)
    rightwards double arrow p equals fraction numerator 4 pi L over denominator eta end fraction equals fraction numerator 4 pi cross times 35 over denominator 5 end fraction almost equal to 88 W.

    Five lumen/watt is the luminous efficiency of a lamp and its luminous intensity is 35 candela. The power of the lamp is

    physics-General
    Efficiency of light source
    eta equals fraction numerator phi over denominator p end fraction..... (i)
    and L equals fraction numerator phi over denominator 4 pi end fraction..... (ii)
    From equation (i) and (ii)
    rightwards double arrow p equals fraction numerator 4 pi L over denominator eta end fraction equals fraction numerator 4 pi cross times 35 over denominator 5 end fraction almost equal to 88 W.