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
(i)Given,
(ii)Comparing Eqs. (i) and (ii), we get
=1According 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
(i)Given,
(ii)Comparing Eqs. (i) and (ii), we get
=1Maths-
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
and will be straight line parallel to -axisRadius 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
and will be straight line parallel to -axisphysics-
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
represents the cooling curve of oil and represents the cooling curve of waterWater 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
represents the cooling curve of oil and represents the cooling curve of waterphysics-
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
(i)
(ii)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
(i)(ii)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.
(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.
(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 
Then quantity of heat supplied in In
heat supplied 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
Inheat supplied
Then quantity of heat supplied in In
heat supplied 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
[Given]Area under
curve represents the emissive power of body and emissive power 
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
[Given]Area under
curve represents the emissive power of body and emissive power 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
then, the given combination can be redrawn as followsFive 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
then, the given combination can be redrawn as followsMaths-
If 
, then 
_______________
If , then _______________
Maths-General
