General
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If the system of equations x plus y plus z equals 6 comma x plus 2 y plus lambda z equals 0 comma x plus 2 y plus 3 z equals 10 has no solution, then lambda equals

Maths-General

  1. 4    
  2. 3    
  3. 5    
  4. 2    

    Answer:The correct answer is: 3

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    General
    maths-

    Consider the system of linear equations: x subscript 1 end subscript plus 2 x subscript 2 end subscript plus x subscript 3 end subscript equals 3 semicolon 2 x subscript 1 end subscript plus 3 x subscript 2 end subscript plus x subscript 3 end subscript equals 3x subscript 1 end subscript plus 5 x subscript 2 end subscript plus 2 x subscript 3 end subscript equals 1 The system has

    Consider the system of linear equations: x subscript 1 end subscript plus 2 x subscript 2 end subscript plus x subscript 3 end subscript equals 3 semicolon 2 x subscript 1 end subscript plus 3 x subscript 2 end subscript plus x subscript 3 end subscript equals 3x subscript 1 end subscript plus 5 x subscript 2 end subscript plus 2 x subscript 3 end subscript equals 1 The system has

    maths-General
    General
    physics-

    Two bars of thermal conductivities K and 3 K and lengths 1 c m and 2 c m respectively have equal cross-sectional area, they are joined lengths wise as shown in the figure. If the temperature at the ends of this composite bar is 0 ℃ and 100 ℃ respectively (see figure), then the temperature ϕ of the interface is

    Temperature of interface
    theta equals fraction numerator K subscript 1 end subscript theta subscript 1 end subscript l subscript 2 end subscript plus K subscript 2 end subscript theta subscript 2 end subscript l subscript 1 end subscript over denominator K subscript 1 end subscript l subscript 2 end subscript plus K subscript 2 end subscript l subscript 1 end subscript end fraction equals fraction numerator K cross times 0 cross times 2 plus 3 K cross times 100 cross times 1 over denominator K cross times 2 plus 3 K cross times 1 end fraction
    equals fraction numerator 300 K over denominator 5 K end fraction equals 60 ℃

    Two bars of thermal conductivities K and 3 K and lengths 1 c m and 2 c m respectively have equal cross-sectional area, they are joined lengths wise as shown in the figure. If the temperature at the ends of this composite bar is 0 ℃ and 100 ℃ respectively (see figure), then the temperature ϕ of the interface is

    physics-General
    Temperature of interface
    theta equals fraction numerator K subscript 1 end subscript theta subscript 1 end subscript l subscript 2 end subscript plus K subscript 2 end subscript theta subscript 2 end subscript l subscript 1 end subscript over denominator K subscript 1 end subscript l subscript 2 end subscript plus K subscript 2 end subscript l subscript 1 end subscript end fraction equals fraction numerator K cross times 0 cross times 2 plus 3 K cross times 100 cross times 1 over denominator K cross times 2 plus 3 K cross times 1 end fraction
    equals fraction numerator 300 K over denominator 5 K end fraction equals 60 ℃
    General
    physics-

    The plots of intensity of radiation v e r s u s blankwavelength of three black bodies at temperatures T subscript 1 end subscript comma blank T subscript 2 end subscript a n d T subscript 3 end subscript are shown. Then,

    According to Wien’s law
    lambda subscript m end subscript proportional to fraction numerator 1 over denominator T end fraction
    And from the figure
    open parentheses lambda subscript m end subscript close parentheses subscript 1 end subscript less than open parentheses lambda subscript m end subscript close parentheses subscript 3 end subscript less than open parentheses lambda subscript m end subscript close parentheses subscript 2 end subscript
    Therefore, T subscript 1 end subscript greater than T subscript 3 end subscript greater than T subscript 2 end subscript

    The plots of intensity of radiation v e r s u s blankwavelength of three black bodies at temperatures T subscript 1 end subscript comma blank T subscript 2 end subscript a n d T subscript 3 end subscript are shown. Then,

    physics-General
    According to Wien’s law
    lambda subscript m end subscript proportional to fraction numerator 1 over denominator T end fraction
    And from the figure
    open parentheses lambda subscript m end subscript close parentheses subscript 1 end subscript less than open parentheses lambda subscript m end subscript close parentheses subscript 3 end subscript less than open parentheses lambda subscript m end subscript close parentheses subscript 2 end subscript
    Therefore, T subscript 1 end subscript greater than T subscript 3 end subscript greater than T subscript 2 end subscript
    General
    physics-

    A composite metal bar of uniform section is made up of length 25 blank c m of copper, 10 blank c m of nickel and 15 blank c m of aluminium. Each part being in perfect thermal contact with the adjoining part. The copper end of the composite rod is maintained at 100 ℃ and the aluminium end at 0 ℃. The whole rod is covered with belt so that no heat loss occurs at the sides. If K subscript C u end subscript equals 2 K subscript A l end subscript and K subscript A l end subscript equals 3 K subscript N i end subscript, then what will be the temperatures of C u minus N i and N i minus A l junctions respectively

    If suppose K subscript N i end subscript equals K rightwards double arrow K subscript A l end subscript equals 3 K and K subscript C u end subscript equals 6 K
    Since all metal bars are connected in series
    So open parentheses fraction numerator Q over denominator t end fraction close parentheses subscript C o m b i n a t i o n end subscript equals open parentheses fraction numerator Q over denominator t end fraction close parentheses subscript C u end subscript equals open parentheses fraction numerator Q over denominator t end fraction close parentheses subscript A l end subscript equals open parentheses fraction numerator Q over denominator t end fraction close parentheses subscript N i end subscript
    a n d blank fraction numerator 3 over denominator K subscript e q end subscript end fraction equals fraction numerator 1 over denominator K subscript C u end subscript end fraction plus fraction numerator 1 over denominator K subscript A l end subscript end fraction plus fraction numerator 1 over denominator K subscript N i end subscript end fraction equals fraction numerator 1 over denominator 6 K end fraction plus fraction numerator 1 over denominator 3 K end fraction plus fraction numerator 1 over denominator K end fraction equals fraction numerator 9 over denominator 6 K end fraction
    rightwards double arrow K subscript e q end subscript equals 2 K

    Hence, it open parentheses fraction numerator Q over denominator t end fraction close parentheses subscript C o m b i n a t i o n end subscript equals open parentheses fraction numerator Q over denominator t end fraction close parentheses subscript C u end subscript
    rightwards double arrow fraction numerator K subscript e q end subscript A left parenthesis 100 minus 0 right parenthesis over denominator l subscript C o m b i n a t i o n end subscript end fraction equals fraction numerator K subscript C u end subscript A left parenthesis 100 minus theta subscript 1 end subscript right parenthesis over denominator l subscript C u end subscript end fraction
    rightwards double arrow blank fraction numerator 2 K blank A left parenthesis 100 minus 0 right parenthesis over denominator left parenthesis 25 plus 10 plus 15 right parenthesis end fraction equals fraction numerator 6 K blank A left parenthesis 100 minus theta subscript 1 end subscript right parenthesis over denominator 25 end fraction rightwards double arrow theta subscript 1 end subscript equals 83.33 ℃
    Similar if open parentheses fraction numerator Q over denominator t end fraction close parentheses subscript C o m b i n a t i o n end subscript equals open parentheses fraction numerator Q over denominator t end fraction close parentheses subscript A l end subscript
    rightwards double arrow fraction numerator 2 K blank A left parenthesis 100 minus 0 right parenthesis over denominator 50 end fraction equals fraction numerator 3 K blank A left parenthesis theta subscript 2 end subscript minus 0 right parenthesis over denominator 15 end fraction rightwards double arrow theta subscript 2 end subscript equals 20 ℃

    A composite metal bar of uniform section is made up of length 25 blank c m of copper, 10 blank c m of nickel and 15 blank c m of aluminium. Each part being in perfect thermal contact with the adjoining part. The copper end of the composite rod is maintained at 100 ℃ and the aluminium end at 0 ℃. The whole rod is covered with belt so that no heat loss occurs at the sides. If K subscript C u end subscript equals 2 K subscript A l end subscript and K subscript A l end subscript equals 3 K subscript N i end subscript, then what will be the temperatures of C u minus N i and N i minus A l junctions respectively

    physics-General
    If suppose K subscript N i end subscript equals K rightwards double arrow K subscript A l end subscript equals 3 K and K subscript C u end subscript equals 6 K
    Since all metal bars are connected in series
    So open parentheses fraction numerator Q over denominator t end fraction close parentheses subscript C o m b i n a t i o n end subscript equals open parentheses fraction numerator Q over denominator t end fraction close parentheses subscript C u end subscript equals open parentheses fraction numerator Q over denominator t end fraction close parentheses subscript A l end subscript equals open parentheses fraction numerator Q over denominator t end fraction close parentheses subscript N i end subscript
    a n d blank fraction numerator 3 over denominator K subscript e q end subscript end fraction equals fraction numerator 1 over denominator K subscript C u end subscript end fraction plus fraction numerator 1 over denominator K subscript A l end subscript end fraction plus fraction numerator 1 over denominator K subscript N i end subscript end fraction equals fraction numerator 1 over denominator 6 K end fraction plus fraction numerator 1 over denominator 3 K end fraction plus fraction numerator 1 over denominator K end fraction equals fraction numerator 9 over denominator 6 K end fraction
    rightwards double arrow K subscript e q end subscript equals 2 K

    Hence, it open parentheses fraction numerator Q over denominator t end fraction close parentheses subscript C o m b i n a t i o n end subscript equals open parentheses fraction numerator Q over denominator t end fraction close parentheses subscript C u end subscript
    rightwards double arrow fraction numerator K subscript e q end subscript A left parenthesis 100 minus 0 right parenthesis over denominator l subscript C o m b i n a t i o n end subscript end fraction equals fraction numerator K subscript C u end subscript A left parenthesis 100 minus theta subscript 1 end subscript right parenthesis over denominator l subscript C u end subscript end fraction
    rightwards double arrow blank fraction numerator 2 K blank A left parenthesis 100 minus 0 right parenthesis over denominator left parenthesis 25 plus 10 plus 15 right parenthesis end fraction equals fraction numerator 6 K blank A left parenthesis 100 minus theta subscript 1 end subscript right parenthesis over denominator 25 end fraction rightwards double arrow theta subscript 1 end subscript equals 83.33 ℃
    Similar if open parentheses fraction numerator Q over denominator t end fraction close parentheses subscript C o m b i n a t i o n end subscript equals open parentheses fraction numerator Q over denominator t end fraction close parentheses subscript A l end subscript
    rightwards double arrow fraction numerator 2 K blank A left parenthesis 100 minus 0 right parenthesis over denominator 50 end fraction equals fraction numerator 3 K blank A left parenthesis theta subscript 2 end subscript minus 0 right parenthesis over denominator 15 end fraction rightwards double arrow theta subscript 2 end subscript equals 20 ℃
    General
    physics-

    A student takes 50 g m wax (specific heat equals 0.6 blank k c a l divided by k g ℃) and heats it till it boils. The graph between temperature and time is as follows. Heat supplied to the wax per minute and boiling point are respectively

    Since specific heat equals 0.6 k c a l divided by g cross times ℃ equals 0.6 blank c a l divided by g cross times ℃
    From graph it is clear that in a minute, the temperature is raised from 0 ℃ to 50 ℃.
    rightwards double arrow Heat required for a minute equals 50 cross times 0.6 cross times 50 equals 1500 blank c a l
    Also from graph, Boiling point of wax is 200 ℃

    A student takes 50 g m wax (specific heat equals 0.6 blank k c a l divided by k g ℃) and heats it till it boils. The graph between temperature and time is as follows. Heat supplied to the wax per minute and boiling point are respectively

    physics-General
    Since specific heat equals 0.6 k c a l divided by g cross times ℃ equals 0.6 blank c a l divided by g cross times ℃
    From graph it is clear that in a minute, the temperature is raised from 0 ℃ to 50 ℃.
    rightwards double arrow Heat required for a minute equals 50 cross times 0.6 cross times 50 equals 1500 blank c a l
    Also from graph, Boiling point of wax is 200 ℃
    General
    maths-

    If A equals open curly brackets table attributes columnalign left end attributes row i 0 row 0 cell negative i end cell end table close curly brackets then A2 equals

    If A equals open curly brackets table attributes columnalign left end attributes row i 0 row 0 cell negative i end cell end table close curly brackets then A2 equals

    maths-General
    General
    physics-

    The coefficient of thermal conductivity of copper is 9 times that of steel. In the composite cylindrical bar shown in the figure, what will be the temperature at the junction of copper and steel?

    Temperature of interface
    theta equals fraction numerator K subscript 1 end subscript theta subscript 1 end subscript l subscript 2 end subscript plus K subscript 2 end subscript theta subscript 2 end subscript l subscript 1 end subscript over denominator K subscript 1 end subscript l subscript 2 end subscript plus K subscript 2 end subscript l subscript 1 end subscript end fraction
    It is given that K subscript C u end subscript equals 9 K subscript s end subscript. So, if K subscript s end subscript equals K subscript 1 end subscript equals K, then
    K subscript C u end subscript equals K subscript 2 end subscript equals 9 K
    rightwards double arrow theta equals fraction numerator 9 K cross times 100 cross times 6 plus K cross times 0 cross times 18 over denominator 9 K cross times 6 plus K cross times 18 end fraction
    equals fraction numerator 5400 K over denominator 72 K end fraction equals 75 ℃

    The coefficient of thermal conductivity of copper is 9 times that of steel. In the composite cylindrical bar shown in the figure, what will be the temperature at the junction of copper and steel?

    physics-General
    Temperature of interface
    theta equals fraction numerator K subscript 1 end subscript theta subscript 1 end subscript l subscript 2 end subscript plus K subscript 2 end subscript theta subscript 2 end subscript l subscript 1 end subscript over denominator K subscript 1 end subscript l subscript 2 end subscript plus K subscript 2 end subscript l subscript 1 end subscript end fraction
    It is given that K subscript C u end subscript equals 9 K subscript s end subscript. So, if K subscript s end subscript equals K subscript 1 end subscript equals K, then
    K subscript C u end subscript equals K subscript 2 end subscript equals 9 K
    rightwards double arrow theta equals fraction numerator 9 K cross times 100 cross times 6 plus K cross times 0 cross times 18 over denominator 9 K cross times 6 plus K cross times 18 end fraction
    equals fraction numerator 5400 K over denominator 72 K end fraction equals 75 ℃
    General
    physics-

    Two metal cubes A and B of same size are arranged as shown in the figure. The extreme ends of the combination are maintained at the indicated temperatures. The arrangement is thermally insulated. The coefficients of thermal conductivity of A and B are 300 W divided by m ℃ and 200 W divided by m ℃, respectively. After steady state is reached, the temperature of the interface will be

    Temperature of interface T equals fraction numerator K subscript 1 end subscript theta subscript 1 end subscript plus K subscript 2 end subscript theta subscript 2 end subscript over denominator K subscript 1 end subscript plus K subscript 2 end subscript end fraction
    equals fraction numerator 300 cross times 100 plus 200 cross times 0 over denominator 300 plus 200 end fraction equals 60 ℃

    Two metal cubes A and B of same size are arranged as shown in the figure. The extreme ends of the combination are maintained at the indicated temperatures. The arrangement is thermally insulated. The coefficients of thermal conductivity of A and B are 300 W divided by m ℃ and 200 W divided by m ℃, respectively. After steady state is reached, the temperature of the interface will be

    physics-General
    Temperature of interface T equals fraction numerator K subscript 1 end subscript theta subscript 1 end subscript plus K subscript 2 end subscript theta subscript 2 end subscript over denominator K subscript 1 end subscript plus K subscript 2 end subscript end fraction
    equals fraction numerator 300 cross times 100 plus 200 cross times 0 over denominator 300 plus 200 end fraction equals 60 ℃
    General
    maths-

    The perimeter of a straight triangleis 6 times the A.M of the sines of its angles if the side text  'a'  end textis , then the angle A is

    The perimeter of a straight triangleis 6 times the A.M of the sines of its angles if the side text  'a'  end textis , then the angle A is

    maths-General
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    maths-

    If the angles of triangle are in the ratio 1:1:4 then ratio of the perimeter of triangle to its largest side

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    maths-General
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    How to define Wavy Curve Method f(x)?

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    maths-General
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    maths-

    The angles of a triangle are in the ratio 3:5:10.Then ratio of smallest to greatest side is

    The angles of a triangle are in the ratio 3:5:10.Then ratio of smallest to greatest side is

    maths-General
    General
    maths-

    text  If  end text f left parenthesis 9 right parenthesis equals 9 comma f to the power of 1 left parenthesis 9 right parenthesis minus 4 comma text  then  end text fraction numerator L t over denominator x not stretchy rightwards arrow t end fraction fraction numerator square root of f left parenthesis x right parenthesis end root minus 3 over denominator square root of x minus 3 end fraction text  equals  end text

    text  If  end text f left parenthesis 9 right parenthesis equals 9 comma f to the power of 1 left parenthesis 9 right parenthesis minus 4 comma text  then  end text fraction numerator L t over denominator x not stretchy rightwards arrow t end fraction fraction numerator square root of f left parenthesis x right parenthesis end root minus 3 over denominator square root of x minus 3 end fraction text  equals  end text

    maths-General
    General
    maths-

    The sides of a triangle aresin invisible function application alpha comma cos invisible function application alpha text  and  end text square root of 1 plus sin invisible function application alpha cos invisible function application alpha end root text  for some  end text 0 less than alpha less than pi over 2 Then the greatest angle of the triangle is  [AIEEE 2014]

    The sides of a triangle aresin invisible function application alpha comma cos invisible function application alpha text  and  end text square root of 1 plus sin invisible function application alpha cos invisible function application alpha end root text  for some  end text 0 less than alpha less than pi over 2 Then the greatest angle of the triangle is  [AIEEE 2014]

    maths-General
    General
    maths-

    L t subscript x not stretchy rightwards arrow negative straight infinity end subscript open square brackets fraction numerator x to the power of 4 sin invisible function application open parentheses 1 over x close parentheses plus x squared over denominator open parentheses 1 plus vertical line x vertical line cubed close parentheses end fraction close square brackets equals

    L t subscript x not stretchy rightwards arrow negative straight infinity end subscript open square brackets fraction numerator x to the power of 4 sin invisible function application open parentheses 1 over x close parentheses plus x squared over denominator open parentheses 1 plus vertical line x vertical line cubed close parentheses end fraction close square brackets equals

    maths-General