Physics-
General
Easy
Question
A ring consisting of two parts ADB and ACB of same conductivity k carries an amount of heat H. The ADB part is now replaced with another metal keeping the temperatures T1 and T2 constant. The heat carried increases to 2H. What should be the conductivity of the new ADB part? Given
= 3:
![](data:image/png;base64,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)
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- 2 k
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- 3 k
The correct answer is:
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Related Questions to study
physics-
Two sheets of thickness d and 2d and same area are touching each other on their face. Temperature TA , TB , TC shown are in geometric progression with common ratio r = 2. Then ratio of thermal conductivity of thinner and thicker sheet are
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)
Two sheets of thickness d and 2d and same area are touching each other on their face. Temperature TA , TB , TC shown are in geometric progression with common ratio r = 2. Then ratio of thermal conductivity of thinner and thicker sheet are
![](data:image/png;base64,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)
physics-General
physics-
Heat is conducted across a composite block of two slabs of thickness d and 2d. Their thermal conductivities are 2k and k respectively. All the heat entering the face AB leaves from the face CD. The temperature in °C of the junction EF of the two slabs is :
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)
Heat is conducted across a composite block of two slabs of thickness d and 2d. Their thermal conductivities are 2k and k respectively. All the heat entering the face AB leaves from the face CD. The temperature in °C of the junction EF of the two slabs is :
![](data:image/png;base64,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)
physics-General
physics-
One end of a 2.35m long and 2.0cm radius aluminium rod
is held at 200C. The other end of the rod is in contact with a block of ice at its melting point. The rate in
at which ice melts is [Take latent heat of fusion for ice as ![open fraction numerator 10 over denominator 3 end fraction cross times 10 to the power of 5 end exponent J times k g to the power of negative 1 end exponent close square brackets](data:image/png;base64,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)
One end of a 2.35m long and 2.0cm radius aluminium rod
is held at 200C. The other end of the rod is in contact with a block of ice at its melting point. The rate in
at which ice melts is [Take latent heat of fusion for ice as ![open fraction numerator 10 over denominator 3 end fraction cross times 10 to the power of 5 end exponent J times k g to the power of negative 1 end exponent close square brackets](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAI0AAAAqCAYAAACOR9jzAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAbSkFbcgAAA3xJREFUeNrtW1+EVFEcPsbKyhrSQ5JekvSwsiQ9JGvJylprLD3sQ5JIjyuxDys9RdLDGokkK/sQSQ/JiqyRZA09JD0kkh6SsexD1lortt+v+Q3X7Dl3zrnn3On++T4+Zs6999x7z/3m9/eOUgBgxo6GAOAsIgCAaIAMiuYY8SbxY8w+VeIDYlP4UMaAkopmiXi1x8ErxKnI90kZA0runkwHXyDWNeMLxBmsOUSjw3PiuGZ8TLYBEM0urBP3aMZ5rIU1h2h0+BNzzDbWHKJxFc0W1hyi0aFlcE+DOXRPZSmh25RRUg+Ez2vGx3MYCJel+mlTRklVNNPER5rxxRym3GUrmf830TAaxFnigLiqeeLbnC7itpjtSxBNctHY+Pl9xMcS+G6qdhthKGM+2rbVUSGeVO2K9sWY+TZlXx+EmCPuOfWKy1K3NHn30a6tjv3Ez4ZtR4mfPK85xByZd095NrdJWh3sZr8attWITz2vNcQcpRbNvNB1m0uG59LqqIq7NcU1t4hznvccnYNjwSfECc1+e4l3iWvi/vl67wc4fyEsjU4cLoKJu0HbVgcfz8XK1R6Z3zOxFD7ozDEon8c0+wxIQjEnn5nX5RprnmIJGfdkRjiugom7wdCtDnZbhzzvlecYJr4knjbsw8H9bcOxB7PiwnZSpq1w3iQQTFLRuLY6KpL1+KAzx6oIx4RfEpB3H7uRsbgnE9YmtGhCtjrYKjRitl8hfiMesJhjRmInHTjtf5fg/KUTTVruKWSrgx/0Ysz2GyLEw5Zz3CNe0+wzLaUE1/OXSjRpBsIhWx11sSY+qEtdqQO2rGe69pkypORLAc5fCNGknXIrFa7V8cKQ6bjOEU2vuaLe7Apuq2KxRuT7iFjFn8RRiCbMjfWj1VGR4NS39L8u8VQUHBCvdI2ztfkhGd4HcadrKlzroS+i4V/Ysiz6lqR+C5oIv4jgB3UnYYAeCsOq/1Vkb9E0JD6IZiJsNl8XWCzn5AfSkrpJv3BctRusHZd1ivhexnMlGhN+KyA0hiRg3hDLvtyjppMr0RwhfsEzLiyCioaLV5clrpnA2kI0LpnKLNYVorEFp7A1qS+MYm0hGteArYm1hWhcgT/FQTROOKHMr0UCEM2/Xg2/b8v9G66QcoX4uyrH3z0gmoQ4S3wl7ojJFeJJrCtEAwAQDQDRAOmLZNdrJn8B0nczkw3xpY0AAAE/dEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1mZW5jZWQgY2xvc2U9Il0iIG9wZW49IiIgc2VwYXJhdG9ycz0ifCI+PG1yb3c+PG1mcmFjPjxtbj4xMDwvbW4+PG1uPjM8L21uPjwvbWZyYWM+PG1vPiYjeEQ3OzwvbW8+PG1zdXA+PG1uPjEwPC9tbj48bW4+NTwvbW4+PC9tc3VwPjxtaT5KPC9taT48bW8+JiN4MjJDNTs8L21vPjxtc3VwPjxtcm93PjxtaT5rPC9taT48bWk+ZzwvbWk+PC9tcm93Pjxtcm93Pjxtbz4tPC9tbz48bW4+MTwvbW4+PC9tcm93PjwvbXN1cD48L21yb3c+PC9tZmVuY2VkPjwvbWF0aD6h5gEWAAAAAElFTkSuQmCC)
physics-General
physics-
The graph shown in the figure represent change in the temperature of 5 kg of a substance as it absorbs heat at a constant rate of 42 kJ min–1 The latent heat of vapourazation of the substance is :
![](data:image/png;base64,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)
The graph shown in the figure represent change in the temperature of 5 kg of a substance as it absorbs heat at a constant rate of 42 kJ min–1 The latent heat of vapourazation of the substance is :
![](data:image/png;base64,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)
physics-General
maths-
Consider the circles,
and ![S subscript 2 end subscript colon x to the power of 2 end exponent plus y to the power of 2 end exponent minus y plus 1 equals 0](data:image/png;base64,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)
Statement‐I Tangents from the point P(O, 5) on
and
are equal
Statement‐II Point P(O, 5) lies on the radical axis of the two circles.
Consider the circles,
and ![S subscript 2 end subscript colon x to the power of 2 end exponent plus y to the power of 2 end exponent minus y plus 1 equals 0](data:image/png;base64,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)
Statement‐I Tangents from the point P(O, 5) on
and
are equal
Statement‐II Point P(O, 5) lies on the radical axis of the two circles.
maths-General
maths-
Statement‐I Angle between the tangents drawn from the point P(13,6) to the circle
is 90.
Statement‐II Point
lies on the director circle of S.
Statement‐I Angle between the tangents drawn from the point P(13,6) to the circle
is 90.
Statement‐II Point
lies on the director circle of S.
maths-General
maths-
The common chord of two intersecting circles
and
can be seen from their centres at the angles of 90°& 60° respectively If the distance between their centres is equal to
then the radii of
and
are‐
The common chord of two intersecting circles
and
can be seen from their centres at the angles of 90°& 60° respectively If the distance between their centres is equal to
then the radii of
and
are‐
maths-General
maths-
If the two circles,
and
touches each other, then‐
If the two circles,
and
touches each other, then‐
maths-General
maths-
Pair of tangents are drawn from every point on the line 3x+4y=12 on the circle
Their variable chord of contact always passes through a fixed point whose co‐ordinates are ‐
Pair of tangents are drawn from every point on the line 3x+4y=12 on the circle
Their variable chord of contact always passes through a fixed point whose co‐ordinates are ‐
maths-General
maths-
The locus of the centres of the circles which cut the circles
and
orthogonally is ‐
The locus of the centres of the circles which cut the circles
and
orthogonally is ‐
maths-General
Maths-
The centre of the smallest circle touching the circles
and
is
The centre of the smallest circle touching the circles
and
is
Maths-General
Maths-
Statement -I : If – 2h = a + b, then one line of the pair of lines
bisects the angle between co-ordinate axes in positive quadrant.
Statement -II : If ax + y(2h + a) = 0 is a factor of
then b + 2h + a = 0.
Statement -I : If – 2h = a + b, then one line of the pair of lines
bisects the angle between co-ordinate axes in positive quadrant.
Statement -II : If ax + y(2h + a) = 0 is a factor of
then b + 2h + a = 0.
Maths-General
maths-
P is point on either of the two lines
at a distance of 5 units from their point of intersection. The co-ordinates of the foot of the perpendicular from P on the bisector of the angle between them are :-
P is point on either of the two lines
at a distance of 5 units from their point of intersection. The co-ordinates of the foot of the perpendicular from P on the bisector of the angle between them are :-
maths-General
Maths-
are the roots of the equation
and
are the roots of the equation
form an increasing GP, then
is equal to
are the roots of the equation
and
are the roots of the equation
form an increasing GP, then
is equal to
Maths-General
maths-
The sum of the series
is
The sum of the series
is
maths-General