Maths-
General
Easy
Question
Polar of origin (0, 0) w.r.t. the circle
touches the circle
, if
Hint:
In this question, we have to find the correct option if Polar of origin (0, 0) w. r. t. the circle
touches the circle
. As we know that the polar of equation is 0. So, using this and putting P (0,0), we can find a equation for perpendicular distance of a point P
and center (0,0) we can find the value of r and solving that we will get the correct option.
The correct answer is: 
Related Questions to study
physics-
Electrons ejected from the surface of a metal, when light of certain frequency is incident on it, are stopped fully by a retarding potential of 3 volts Photo electric effect in this metallic surface begins at a frequency 6 x 1014s -1 The frequency of the incident light in s-1 is [h=6 x 10-34J-sec;charge on the electron=1.6x10-19C]
Electrons ejected from the surface of a metal, when light of certain frequency is incident on it, are stopped fully by a retarding potential of 3 volts Photo electric effect in this metallic surface begins at a frequency 6 x 1014s -1 The frequency of the incident light in s-1 is [h=6 x 10-34J-sec;charge on the electron=1.6x10-19C]
physics-General
physics-
Trajectories of two projectiles are shown in figure. Let
and
be the time periods and
and
their speeds of projection. Then

Maximum height and time of flight depend on the vertical component of initial velocity

Here
Range


Here
Range
Trajectories of two projectiles are shown in figure. Let
and
be the time periods and
and
their speeds of projection. Then

physics-General
Maximum height and time of flight depend on the vertical component of initial velocity

Here
Range


Here
Range
physics-
A body is projected up a smooth inclined plane with a velocity
from the point
as shown in figure. The angle of inclination is
and top
of the plane is connected to a well of diameter 40 m. If the body just manages to cross the well, what is the value of
? Length of the inclined plane is
, and 

Let
be the velocity acquired by the body at
which will be moving making an angle
with the horizontal direction. As the body just crosses the well so 
or
or
Taking motion of the body from
to
along the inclined plane we have


As

or
or 
or
or
Taking motion of the body from
As
or
A body is projected up a smooth inclined plane with a velocity
from the point
as shown in figure. The angle of inclination is
and top
of the plane is connected to a well of diameter 40 m. If the body just manages to cross the well, what is the value of
? Length of the inclined plane is
, and 

physics-General
Let
be the velocity acquired by the body at
which will be moving making an angle
with the horizontal direction. As the body just crosses the well so 
or
or
Taking motion of the body from
to
along the inclined plane we have


As

or
or 
or
or
Taking motion of the body from
As
or
Maths-
The equation of the circumcircle of the triangle formed by the lines
and y=0 is
The equation of the circumcircle of the triangle formed by the lines
and y=0 is
Maths-General
physics-
Which of the substance
or
has the highest specific heat? The temperature
time graph is shown

Substances having more specific heat take longer time to get heated to a higher temperature and longer time to get cooled.

If we draw a line parallel to the time axis then it cuts the given graphs at three different points. Corresponding points on the times axis shows that


If we draw a line parallel to the time axis then it cuts the given graphs at three different points. Corresponding points on the times axis shows that
Which of the substance
or
has the highest specific heat? The temperature
time graph is shown

physics-General
Substances having more specific heat take longer time to get heated to a higher temperature and longer time to get cooled.

If we draw a line parallel to the time axis then it cuts the given graphs at three different points. Corresponding points on the times axis shows that


If we draw a line parallel to the time axis then it cuts the given graphs at three different points. Corresponding points on the times axis shows that
physics-
The figure shows a system of two concentric spheres of radii
and
and kept at temperatures
and
respectively. The radial rate of flow of heat in a substance between the two concentric spheres, is proportional to

To measure the radial rate of heat flow, we have to go for integration technique as here the area of the surface through which heat will flow is not constant.

Let us consider an element (spherical shell) of thickness d
and radius
as shown in figure. Let us first find the equivalent thermal resistance between inner and outer sphere.
Resistance of shell=


=
Rate of heat flow = H
=
=


Let us consider an element (spherical shell) of thickness d
Resistance of shell=
=
Rate of heat flow = H
=
=
The figure shows a system of two concentric spheres of radii
and
and kept at temperatures
and
respectively. The radial rate of flow of heat in a substance between the two concentric spheres, is proportional to

physics-General
To measure the radial rate of heat flow, we have to go for integration technique as here the area of the surface through which heat will flow is not constant.

Let us consider an element (spherical shell) of thickness d
and radius
as shown in figure. Let us first find the equivalent thermal resistance between inner and outer sphere.
Resistance of shell=


=
Rate of heat flow = H
=
=


Let us consider an element (spherical shell) of thickness d
Resistance of shell=
=
Rate of heat flow = H
=
=
maths-
If the line y = x + 3 meets the circle
at A and B, then equation of the circle on AB as diameter is
If the line y = x + 3 meets the circle
at A and B, then equation of the circle on AB as diameter is
maths-General
physics-
An electric lamp is fixed at the ceiling of a circular tunnel as shown is figure. What is the ratio the intensities of light at base A and a point B on the wall


An electric lamp is fixed at the ceiling of a circular tunnel as shown is figure. What is the ratio the intensities of light at base A and a point B on the wall

physics-General

physics-
The distance between a point source of light and a screen which is 60 cm is increased to 180 cm. The intensity on the screen as compared with the original intensity will be
The distance between a point source of light and a screen which is 60 cm is increased to 180 cm. The intensity on the screen as compared with the original intensity will be
physics-General
Maths-
The pole of the straight line 9x + y – 28 = 0 with respect to the circle is
Let the coordinates of the pole be (h, k).
The equation of the circle is 2x2 + 2y2 - 3x + 5y - 7 = 0.
Dividing both sides of the equation by 2,we get
x2 + y2 - 3/2 x + 5/2 y - 7/2 = 0.
The equation of polar for the point having coordinates (h, k) is
h x + k y - 3/4 (x + h) + 5/4 (y+k) - 7/2 = 0 .
Simplifying the equation, it can be written as (4h - 3)x + (4k + 5)y + (-3h + 5k - 14).
We are given that the equation of the polar is 9x + y - 28 = 0.so, the above equation and this equation represent the same line. Comparing the coefficient of the line, we get
(4h - 3) /9 = (4k + 5) /1 = (-3h + 5k - 14) /-28
Taking the first and third expression, we get
(4h - 3) /9 = (-3h + 5k - 14) /-28 .
By cross multiplication, we get
Or, -28 (4h - 3) = 9 (-3h + 5k - 14)
Or, -112h + 84 = -27h + 45k - 126
Or, -112h + 27h - 45k = -126 - 84
Or, -85h - 45k = -210
Or, -5 ( 17h + 9k ) = -210
17h + 9k = 42 . . . (1)
Taking the second and third expression, we get
(4k + 5) /1 = ( -3h + 5k - 14) /-28
By cross multiplication, we get
-28 ( 4k + 5 ) = ( -3h + 5k - 14 )
-112k - 140 = -3h + 5k - 14
3h - 112k - 5k = -14 + 140
3h - 117k = 126 . . . (2)
By solving equation (1) × 13 and equation (2) .
h = 3
By putting the value of h in equation (1) , we get
K = -1 .
Therefore, the coordinates are (3, -1) .
Hence, the correct option is (a).
The equation of the circle is 2x2 + 2y2 - 3x + 5y - 7 = 0.
Dividing both sides of the equation by 2,we get
x2 + y2 - 3/2 x + 5/2 y - 7/2 = 0.
The equation of polar for the point having coordinates (h, k) is
h x + k y - 3/4 (x + h) + 5/4 (y+k) - 7/2 = 0 .
Simplifying the equation, it can be written as (4h - 3)x + (4k + 5)y + (-3h + 5k - 14).
We are given that the equation of the polar is 9x + y - 28 = 0.so, the above equation and this equation represent the same line. Comparing the coefficient of the line, we get
(4h - 3) /9 = (4k + 5) /1 = (-3h + 5k - 14) /-28
Taking the first and third expression, we get
(4h - 3) /9 = (-3h + 5k - 14) /-28 .
By cross multiplication, we get
Or, -28 (4h - 3) = 9 (-3h + 5k - 14)
Or, -112h + 84 = -27h + 45k - 126
Or, -112h + 27h - 45k = -126 - 84
Or, -85h - 45k = -210
Or, -5 ( 17h + 9k ) = -210
17h + 9k = 42 . . . (1)
Taking the second and third expression, we get
(4k + 5) /1 = ( -3h + 5k - 14) /-28
By cross multiplication, we get
-28 ( 4k + 5 ) = ( -3h + 5k - 14 )
-112k - 140 = -3h + 5k - 14
3h - 112k - 5k = -14 + 140
3h - 117k = 126 . . . (2)
By solving equation (1) × 13 and equation (2) .
h = 3
By putting the value of h in equation (1) , we get
K = -1 .
Therefore, the coordinates are (3, -1) .
Hence, the correct option is (a).
The pole of the straight line 9x + y – 28 = 0 with respect to the circle is
Maths-General
Let the coordinates of the pole be (h, k).
The equation of the circle is 2x2 + 2y2 - 3x + 5y - 7 = 0.
Dividing both sides of the equation by 2,we get
x2 + y2 - 3/2 x + 5/2 y - 7/2 = 0.
The equation of polar for the point having coordinates (h, k) is
h x + k y - 3/4 (x + h) + 5/4 (y+k) - 7/2 = 0 .
Simplifying the equation, it can be written as (4h - 3)x + (4k + 5)y + (-3h + 5k - 14).
We are given that the equation of the polar is 9x + y - 28 = 0.so, the above equation and this equation represent the same line. Comparing the coefficient of the line, we get
(4h - 3) /9 = (4k + 5) /1 = (-3h + 5k - 14) /-28
Taking the first and third expression, we get
(4h - 3) /9 = (-3h + 5k - 14) /-28 .
By cross multiplication, we get
Or, -28 (4h - 3) = 9 (-3h + 5k - 14)
Or, -112h + 84 = -27h + 45k - 126
Or, -112h + 27h - 45k = -126 - 84
Or, -85h - 45k = -210
Or, -5 ( 17h + 9k ) = -210
17h + 9k = 42 . . . (1)
Taking the second and third expression, we get
(4k + 5) /1 = ( -3h + 5k - 14) /-28
By cross multiplication, we get
-28 ( 4k + 5 ) = ( -3h + 5k - 14 )
-112k - 140 = -3h + 5k - 14
3h - 112k - 5k = -14 + 140
3h - 117k = 126 . . . (2)
By solving equation (1) × 13 and equation (2) .
h = 3
By putting the value of h in equation (1) , we get
K = -1 .
Therefore, the coordinates are (3, -1) .
Hence, the correct option is (a).
The equation of the circle is 2x2 + 2y2 - 3x + 5y - 7 = 0.
Dividing both sides of the equation by 2,we get
x2 + y2 - 3/2 x + 5/2 y - 7/2 = 0.
The equation of polar for the point having coordinates (h, k) is
h x + k y - 3/4 (x + h) + 5/4 (y+k) - 7/2 = 0 .
Simplifying the equation, it can be written as (4h - 3)x + (4k + 5)y + (-3h + 5k - 14).
We are given that the equation of the polar is 9x + y - 28 = 0.so, the above equation and this equation represent the same line. Comparing the coefficient of the line, we get
(4h - 3) /9 = (4k + 5) /1 = (-3h + 5k - 14) /-28
Taking the first and third expression, we get
(4h - 3) /9 = (-3h + 5k - 14) /-28 .
By cross multiplication, we get
Or, -28 (4h - 3) = 9 (-3h + 5k - 14)
Or, -112h + 84 = -27h + 45k - 126
Or, -112h + 27h - 45k = -126 - 84
Or, -85h - 45k = -210
Or, -5 ( 17h + 9k ) = -210
17h + 9k = 42 . . . (1)
Taking the second and third expression, we get
(4k + 5) /1 = ( -3h + 5k - 14) /-28
By cross multiplication, we get
-28 ( 4k + 5 ) = ( -3h + 5k - 14 )
-112k - 140 = -3h + 5k - 14
3h - 112k - 5k = -14 + 140
3h - 117k = 126 . . . (2)
By solving equation (1) × 13 and equation (2) .
h = 3
By putting the value of h in equation (1) , we get
K = -1 .
Therefore, the coordinates are (3, -1) .
Hence, the correct option is (a).
physics-
Three rods of equal length
are joined to form an equilateral triangle
O is the mid point of
Distance
remains same for small change in temperature. Coefficient of linear expansion for
and
is same,
but that for
is
Then

Neglecting
Three rods of equal length
are joined to form an equilateral triangle
O is the mid point of
Distance
remains same for small change in temperature. Coefficient of linear expansion for
and
is same,
but that for
is
Then

physics-General
Neglecting
physics-
A point source causes photoelectric effect from a small metal plate Which of the following curves may represent the saturation photocurrent as a function of the distance between the source and the metal?

A point source causes photoelectric effect from a small metal plate Which of the following curves may represent the saturation photocurrent as a function of the distance between the source and the metal?

physics-General
physics-
One of the following figures respesents the variation of particle momentum with associated de Broglie wavelength
a) 
b) 
c) 

One of the following figures respesents the variation of particle momentum with associated de Broglie wavelength
a) 
b) 
c) 

physics-General
physics-
Two circular discs A and B with equal radii are blackened. They are heated to some temperature and are cooled under identical conditions. What inference do you draw from their cooling curves?

According to Newton’s law of cooling, rate of cooling is given by

Where c is specific heat of material.
or
rate of cooling varies inversely as specific heat. From the graph, for A rate of cooling is larger. Therefore, specific heat of A is smaller.
Where c is specific heat of material.
or
Two circular discs A and B with equal radii are blackened. They are heated to some temperature and are cooled under identical conditions. What inference do you draw from their cooling curves?

physics-General
According to Newton’s law of cooling, rate of cooling is given by

Where c is specific heat of material.
or
rate of cooling varies inversely as specific heat. From the graph, for A rate of cooling is larger. Therefore, specific heat of A is smaller.
Where c is specific heat of material.
or
physics-
Which of the curves in figure represents the relation between Celsius and Fahrenheit temperatures

Which of the curves in figure represents the relation between Celsius and Fahrenheit temperatures

physics-General