Maths-
General
Easy

Question

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.

  1. If both Statement-1 and Statement-2 are true and the Statement-2 is correct explanation of the Statement-1.    
  2. If both Statement-1 and Statement-2 are true but Statement-2 is not correct explanation of the Statement-1.    
  3. If Statement-1 is true but the Statement-2 is false.    
  4. If Statement-1 is false but Statement-2 is true    

The correct answer is: If both Statement-1 and Statement-2 are true but Statement-2 is not correct explanation of the Statement-1.

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Related Questions to study

General
physics-

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

According 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

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
According 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
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
physics-

Radius of a conductor increases uniformly from left end to right end as shown in fig  Material of the conductor is isotropic and its curved surface is thermally insulated from surrounding. Its ends are maintained at temperatures T subscript 1 end subscript and T subscript 2 end subscript left parenthesis T subscript 1 end subscript greater than T subscript 2 end subscript right parenthesis: If, in steady state, heat flow rate is equal to H, then which of the following graphs is correct

Since the curved surface of the conductor is thermally insulated, therefore, in steady state, the rate of flow of heat at every section will be the same. Hence the curve between H and x will be straight line parallel to x-axis

Radius of a conductor increases uniformly from left end to right end as shown in fig  Material of the conductor is isotropic and its curved surface is thermally insulated from surrounding. Its ends are maintained at temperatures T subscript 1 end subscript and T subscript 2 end subscript left parenthesis T subscript 1 end subscript greater than T subscript 2 end subscript right parenthesis: If, in steady state, heat flow rate is equal to H, then which of the following graphs is correct

physics-General
Since the curved surface of the conductor is thermally insulated, therefore, in steady state, the rate of flow of heat at every section will be the same. Hence the curve between H and x will be straight line parallel to x-axis
General
physics-

Water and turpentine oil (specific heat less than that of water) are both heated to same temperature. Equal amounts of these placed in identical calorimeters are then left in air

As we know, Rate of cooling proportional to fraction numerator 1 over denominator s p e c i f i c blank h e a t left square bracket c right square bracket end fraction
because c subscript o i l end subscript less than c subscript W a t e r end subscript
rightwards double arrow open parentheses R a t e blank o f blank c o o l i n g close parentheses subscript o i l end subscript greater than open parentheses R a t e blank o f blank c o o l i n g close parentheses subscript W a t e r end subscript

It is clear that, at a particular time after start cooling, temperature of oil will be less than that of water
So graph B represents the cooling curve of oil and A represents the cooling curve of water

Water and turpentine oil (specific heat less than that of water) are both heated to same temperature. Equal amounts of these placed in identical calorimeters are then left in air

physics-General
As we know, Rate of cooling proportional to fraction numerator 1 over denominator s p e c i f i c blank h e a t left square bracket c right square bracket end fraction
because c subscript o i l end subscript less than c subscript W a t e r end subscript
rightwards double arrow open parentheses R a t e blank o f blank c o o l i n g close parentheses subscript o i l end subscript greater than open parentheses R a t e blank o f blank c o o l i n g close parentheses subscript W a t e r end subscript

It is clear that, at a particular time after start cooling, temperature of oil will be less than that of water
So graph B represents the cooling curve of oil and A represents the cooling curve of water
General
physics-

Variation of radiant energy emitted by sun, filament of tungsten lamp and welding are as a function of its wavelength is shown in figure. Which of the following option is the correct match?

lambda subscript m end subscript T equals c o n s t a n t
From the graph T subscript 3 end subscript greater than T subscript 2 end subscript greater than T subscript 1 end subscript
Temperature of sun will be maximum

Variation of radiant energy emitted by sun, filament of tungsten lamp and welding are as a function of its wavelength is shown in figure. Which of the following option is the correct match?

physics-General
lambda subscript m end subscript T equals c o n s t a n t
From the graph T subscript 3 end subscript greater than T subscript 2 end subscript greater than T subscript 1 end subscript
Temperature of sun will be maximum
General
physics-

Six identical metallic rods are joined together in a pattern as shown in the figure. Points A and D are maintained at temperature 60 ℃ and 240 ℃. The temperature of the junction B will be

R equals fraction numerator l over denominator K A end fraction
fraction numerator T subscript A end subscript minus T subscript B end subscript over denominator R end fraction equals fraction numerator T subscript B end subscript minus T subscript C end subscript over denominator R end fraction equals fraction numerator T subscript C end subscript minus T subscript D end subscript over denominator R end fraction
60 minus T subscript B end subscript equals T subscript B end subscript minus T subscript C end subscript(i)

60 minus T subscript B end subscript equals T subscript C end subscript minus 240(ii)
Solving (i) and (ii)
T subscript B end subscript equals 120 ℃

Six identical metallic rods are joined together in a pattern as shown in the figure. Points A and D are maintained at temperature 60 ℃ and 240 ℃. The temperature of the junction B will be

physics-General
R equals fraction numerator l over denominator K A end fraction
fraction numerator T subscript A end subscript minus T subscript B end subscript over denominator R end fraction equals fraction numerator T subscript B end subscript minus T subscript C end subscript over denominator R end fraction equals fraction numerator T subscript C end subscript minus T subscript D end subscript over denominator R end fraction
60 minus T subscript B end subscript equals T subscript B end subscript minus T subscript C end subscript(i)

60 minus T subscript B end subscript equals T subscript C end subscript minus 240(ii)
Solving (i) and (ii)
T subscript B end subscript equals 120 ℃
General
physics-

Which curve shows the rise of temperature with the amount of heat supplied, for a piece of ice?

Initially on heating temperature rises from negative 73 ℃ (200K) to 0degree(273K). Then ice melts and temperature does not rise. After the whole ice has melted, temperature begins to rise until it reaches 100℃ (373K). Then it becomes constant and after that it changes to vapours.

Which curve shows the rise of temperature with the amount of heat supplied, for a piece of ice?

physics-General
Initially on heating temperature rises from negative 73 ℃ (200K) to 0degree(273K). Then ice melts and temperature does not rise. After the whole ice has melted, temperature begins to rise until it reaches 100℃ (373K). Then it becomes constant and after that it changes to vapours.
General
physics-

The graph signifies

The graph signifies

physics-General
General
physics-

The figure given below shows the cooling curve of pure wax material after heating. It cools from A to B and solidifies along B D. If L and C are respective values of latent heat and the specific heat of the liquid wax, the ratio L divided by C is

Let the quantity of heat supplied per minute be Q. Then quantity of heat supplied in 2 blank m i n equals m C left parenthesis 90 minus 80 right parenthesis
In 4 blank m i n comma blankheat supplied equals 2 m C open parentheses 90 minus 80 close parentheses
therefore 2 m blank C open parentheses 90 minus 80 close parentheses equals m L rightwards double arrow fraction numerator L over denominator C end fraction equals 20

The figure given below shows the cooling curve of pure wax material after heating. It cools from A to B and solidifies along B D. If L and C are respective values of latent heat and the specific heat of the liquid wax, the ratio L divided by C is

physics-General
Let the quantity of heat supplied per minute be Q. Then quantity of heat supplied in 2 blank m i n equals m C left parenthesis 90 minus 80 right parenthesis
In 4 blank m i n comma blankheat supplied equals 2 m C open parentheses 90 minus 80 close parentheses
therefore 2 m blank C open parentheses 90 minus 80 close parentheses equals m L rightwards double arrow fraction numerator L over denominator C end fraction equals 20
General
physics-

One end of a thermally insulated rod is kept at a temperature T subscript 1 end subscript and other at T subscript 2 end subscript. The rod is composed of two sections of lengths l subscript 1 end subscript and l subscript 2 end subscript and thermal conductivities K subscript 1 end subscript and K subscript 2 end subscript respectively. The temperature at the interface of the two sections is

Let temperature at the interface is T.
For part AB,

fraction numerator Q subscript 1 end subscript over denominator t end fraction proportional to fraction numerator open parentheses T subscript 1 end subscript minus T close parentheses K subscript 1 end subscript over denominator l subscript 1 end subscript end fraction
For part B C comma
fraction numerator Q subscript 2 end subscript over denominator t end fraction proportional to fraction numerator open parentheses T minus T subscript 2 end subscript close parentheses K subscript 2 end subscript over denominator l subscript 2 end subscript end fraction
At equilibrium, fraction numerator Q subscript 1 end subscript over denominator t end fraction equals fraction numerator Q subscript 2 end subscript over denominator t end fraction
therefore fraction numerator open parentheses T subscript 1 end subscript minus T close parentheses K subscript 1 end subscript over denominator l subscript 1 end subscript end fraction equals fraction numerator open parentheses T minus T subscript 2 end subscript close parentheses K subscript 2 end subscript over denominator l subscript 2 end subscript end fraction
rightwards double arrow T equals fraction numerator T subscript 1 end subscript K subscript 1 end subscript l subscript 2 end subscript plus T subscript 2 end subscript K 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

One end of a thermally insulated rod is kept at a temperature T subscript 1 end subscript and other at T subscript 2 end subscript. The rod is composed of two sections of lengths l subscript 1 end subscript and l subscript 2 end subscript and thermal conductivities K subscript 1 end subscript and K subscript 2 end subscript respectively. The temperature at the interface of the two sections is

physics-General
Let temperature at the interface is T.
For part AB,

fraction numerator Q subscript 1 end subscript over denominator t end fraction proportional to fraction numerator open parentheses T subscript 1 end subscript minus T close parentheses K subscript 1 end subscript over denominator l subscript 1 end subscript end fraction
For part B C comma
fraction numerator Q subscript 2 end subscript over denominator t end fraction proportional to fraction numerator open parentheses T minus T subscript 2 end subscript close parentheses K subscript 2 end subscript over denominator l subscript 2 end subscript end fraction
At equilibrium, fraction numerator Q subscript 1 end subscript over denominator t end fraction equals fraction numerator Q subscript 2 end subscript over denominator t end fraction
therefore fraction numerator open parentheses T subscript 1 end subscript minus T close parentheses K subscript 1 end subscript over denominator l subscript 1 end subscript end fraction equals fraction numerator open parentheses T minus T subscript 2 end subscript close parentheses K subscript 2 end subscript over denominator l subscript 2 end subscript end fraction
rightwards double arrow T equals fraction numerator T subscript 1 end subscript K subscript 1 end subscript l subscript 2 end subscript plus T subscript 2 end subscript K 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
General
maths-

If n element of N comma and theperiod of fraction numerator c o s invisible function application n x over denominator s i n invisible function application open parentheses fraction numerator x over denominator n end fraction close parentheses end fraction is 4 pi, then n equals

text L.C.M. of  end text open parentheses fraction numerator 2 pi over denominator n end fraction comma 2 pi n close parentheses equals 4 pi

If n element of N comma and theperiod of fraction numerator c o s invisible function application n x over denominator s i n invisible function application open parentheses fraction numerator x over denominator n end fraction close parentheses end fraction is 4 pi, then n equals

maths-General
text L.C.M. of  end text open parentheses fraction numerator 2 pi over denominator n end fraction comma 2 pi n close parentheses equals 4 pi
General
physics-

The adjoining diagram shows the spectral energy density distribution E subscript lambda end subscript of a black body at two different temperatures. If the areas under the curves are in the ratio 16 : 1, the value of temperature T is

fraction numerator A subscript T end subscript over denominator A subscript 2000 end subscript end fraction equals fraction numerator 16 over denominator 1 end fraction [Given]
Area under e subscript lambda end subscript minus lambda curve represents the emissive power of body and emissive power proportional to T to the power of 4 end exponent
rightwards double arrow fraction numerator A subscript T end subscript over denominator A subscript 2000 end subscript end fraction equals open parentheses fraction numerator T over denominator 2000 end fraction close parentheses to the power of 4 end exponent rightwards double arrow fraction numerator 16 over denominator 1 end fraction equals open parentheses fraction numerator T over denominator 2000 end fraction close parentheses to the power of 4 end exponent rightwards double arrow T equals 4000 K

The adjoining diagram shows the spectral energy density distribution E subscript lambda end subscript of a black body at two different temperatures. If the areas under the curves are in the ratio 16 : 1, the value of temperature T is

physics-General
fraction numerator A subscript T end subscript over denominator A subscript 2000 end subscript end fraction equals fraction numerator 16 over denominator 1 end fraction [Given]
Area under e subscript lambda end subscript minus lambda curve represents the emissive power of body and emissive power proportional to T to the power of 4 end exponent
rightwards double arrow fraction numerator A subscript T end subscript over denominator A subscript 2000 end subscript end fraction equals open parentheses fraction numerator T over denominator 2000 end fraction close parentheses to the power of 4 end exponent rightwards double arrow fraction numerator 16 over denominator 1 end fraction equals open parentheses fraction numerator T over denominator 2000 end fraction close parentheses to the power of 4 end exponent rightwards double arrow T equals 4000 K
General
physics-

Five identical rods are joined as shown in figure. Point A and C are maintained at temperature 120 ℃ and 20 ℃ respectively. The temperature of junction B will be

If thermal resistance of each rod is considered R then, the given combination can be redrawn as follows

open parentheses H e a t blank c u r r e n t close parentheses subscript A C end subscript equals open parentheses H e a t blank c u r r e n t close parentheses subscript A B end subscript
fraction numerator left parenthesis 120 minus 20 right parenthesis over denominator 2 R end fraction equals fraction numerator left parenthesis 120 minus theta right parenthesis over denominator R end fraction rightwards double arrow theta equals 70 ℃

Five identical rods are joined as shown in figure. Point A and C are maintained at temperature 120 ℃ and 20 ℃ respectively. The temperature of junction B will be

physics-General
If thermal resistance of each rod is considered R then, the given combination can be redrawn as follows

open parentheses H e a t blank c u r r e n t close parentheses subscript A C end subscript equals open parentheses H e a t blank c u r r e n t close parentheses subscript A B end subscript
fraction numerator left parenthesis 120 minus 20 right parenthesis over denominator 2 R end fraction equals fraction numerator left parenthesis 120 minus theta right parenthesis over denominator R end fraction rightwards double arrow theta equals 70 ℃
General
maths-

If s i n invisible function application x equals 1 divided by 2, then s i n invisible function application 3 x equals_______________

If s i n invisible function application x equals 1 divided by 2, then s i n invisible function application 3 x equals_______________

maths-General
General
physics-

Which one of the following is v subscript m end subscript minus T graph for perfectly black body? v subscript m end subscriptis the frequency of radiation with maximum intensity, T is the absolute temperature.

Intensity is directly proportional to energy.

Which one of the following is v subscript m end subscript minus T graph for perfectly black body? v subscript m end subscriptis the frequency of radiation with maximum intensity, T is the absolute temperature.

physics-General
Intensity is directly proportional to energy.