Maths-
General
Easy
Question
Number of values of 'p' for which the equation
possess more than two roots ,is:
- 0
- 1
- 2
- none
The correct answer is: 1
For (p2– 3p+2)x2–(p2–5p+4)x+p–p2=0tobe anidentity
p2–3p+2 =0
p = 1, 2...(i)
p2 – 5p + 4 = 0
p = 1, 4...(ii)
p – p2 = 0
p = 0, 1...(iii)
For (i), (ii) & (iii) to hold simultaneously p = 1.
Related Questions to study
maths-
Statement-1- The number
is not divisible by 11.Because
Statement-2- If p is a prime, the exponent of p in n! is
+
+
+……Where [x] denotes the greatest integer
x.
Statement-1- The number
is not divisible by 11.Because
Statement-2- If p is a prime, the exponent of p in n! is
+
+
+……Where [x] denotes the greatest integer
x.
maths-General
physics-
According to Newton’s law of cooling, the rate of cooling is proportional to
, where
is the temperature differences between the body and the surroundings and
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)
Given,
(ii)
Comparing Eqs. (i) and (ii), we get
=1
Given,
Comparing Eqs. (i) and (ii), we get
According to Newton’s law of cooling, the rate of cooling is proportional to
, where
is the temperature differences between the body and the surroundings and
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)
Given,
(ii)
Comparing Eqs. (i) and (ii), we get
=1
Given,
Comparing Eqs. (i) and (ii), we get
Maths-
satisfies the relation
then value of A and B respectively are:
satisfies the relation
then value of A and B respectively are:
Maths-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
and
: If, in steady state, heat flow rate is equal to
, 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
and
will be straight line parallel to
-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
and
: If, in steady state, heat flow rate is equal to
, 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
and
will be straight line parallel to
-axis
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 



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

It is clear that, at a particular time after start cooling, temperature of oil will be less than that of water
So graph
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 



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

It is clear that, at a particular time after start cooling, temperature of oil will be less than that of water
So graph
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?

From the graph
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
From the graph
Temperature of sun will be maximum
physics-
Six identical metallic rods are joined together in a pattern as shown in the figure. Points A and D are maintained at temperature
and
. The temperature of the junction
will be


Solving (i) and (ii)
Six identical metallic rods are joined together in a pattern as shown in the figure. Points A and D are maintained at temperature
and
. The temperature of the junction
will be

physics-General

Solving (i) and (ii)
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
(200K) to 0
(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
(200K) to 0
(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.
physics-
The graph signifies

The graph signifies

physics-General
physics-
The figure given below shows the cooling curve of pure wax material after heating. It cools from
to
and solidifies along
If
and
are respective values of latent heat and the specific heat of the liquid wax, the ratio
is

Let the quantity of heat supplied per minute be
Then quantity of heat supplied in 
In
heat supplied 

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

physics-General
Let the quantity of heat supplied per minute be
Then quantity of heat supplied in 
In
heat supplied 

In
physics-
One end of a thermally insulated rod is kept at a temperature
and other at
. The rod is composed of two sections of lengths
and
and thermal conductivities
and
respectively. The temperature at the interface of the two sections is

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


For part

At equilibrium,


For part AB,

For part
At equilibrium,
One end of a thermally insulated rod is kept at a temperature
and other at
. The rod is composed of two sections of lengths
and
and thermal conductivities
and
respectively. The temperature at the interface of the two sections is

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


For part

At equilibrium,


For part AB,

For part
At equilibrium,
maths-
If
and theperiod of
is
, then 
If
and theperiod of
is
, then 
maths-General
physics-
The adjoining diagram shows the spectral energy density distribution
of a black body at two different temperatures. If the areas under the curves are in the ratio 16 : 1, the value of temperature
is

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

physics-General
Area under
physics-
Five identical rods are joined as shown in figure. Point
and
are maintained at temperature
and
respectively. The temperature of junction
will be

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




Five identical rods are joined as shown in figure. Point
and
are maintained at temperature
and
respectively. The temperature of junction
will be

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




Maths-
If
, then
_______________
If
, then
_______________
Maths-General