Maths-
The cartesian equation of
is
Maths-General
Answer:The correct answer is: 
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maths-
The polar equation of
is
The polar equation of
is
maths-General
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The equation of the line passing through pole and
is
The equation of the line passing through pole and
is
maths-General
maths-
The polar equation of the straight line passing through
and parallel to the initial line is
The polar equation of the straight line passing through
and parallel to the initial line is
maths-General
maths-
The polar equation of the straight line passing through
and perpendicular to the initial line is
The polar equation of the straight line passing through
and perpendicular to the initial line is
maths-General
maths-
The angle between the lines
and
is
The angle between the lines
and
is
maths-General
maths-
The number of points in the Cartesian plane with integral co-ordinates satisfying the inequalities |x|
k, |y|
k, |x – y|
k ; is-
|x|
k
–k
x
k ….(1)
& |y|
k
–k
y
k ….(2)

& |x – y|
k
|y – x|
k
–k
y – x
k
x – k
y
x + k ….(3)
Number of points having integral coordinates
= (2k + 1)2 – 2
= (3k2 + 3k + 1).
& |y|

& |x – y|
= (2k + 1)2 – 2
= (3k2 + 3k + 1).
The number of points in the Cartesian plane with integral co-ordinates satisfying the inequalities |x|
k, |y|
k, |x – y|
k ; is-
maths-General
|x|
k
–k
x
k ….(1)
& |y|
k
–k
y
k ….(2)

& |x – y|
k
|y – x|
k
–k
y – x
k
x – k
y
x + k ….(3)
Number of points having integral coordinates
= (2k + 1)2 – 2
= (3k2 + 3k + 1).
& |y|

& |x – y|
= (2k + 1)2 – 2
= (3k2 + 3k + 1).
physics-
Two tuning forks
and
are vibrated together. The number of beats produced are represented by the straight line
in the following graph. After loading
with wax again these are vibrated together and the beats produced are represented by the line
If the frequency of
is
the frequency of
will be

On waxing
Two tuning forks
and
are vibrated together. The number of beats produced are represented by the straight line
in the following graph. After loading
with wax again these are vibrated together and the beats produced are represented by the line
If the frequency of
is
the frequency of
will be

physics-General
On waxing
maths-
A is a set containing n elements. A subset P1 is chosen, and A is reconstructed by replacing the elements of P1. The same process is repeated for subsets P1, P2, … , Pm, with m > 1. The Number of ways of choosing P1, P2, …, Pm so that P1
P2
…
Pm= A is -
Let A = {a1, a2,…..an}.
For each ai (1
i
n), either ai
Pj or ai
Pj (1
j
m) . Thus, there are 2m choices in which ai (1
j
n) may belong to the Pj
s.
Also there is exactly one choice, viz., ai
Pj for j = 1, 2, …, m, for which ai
P1
P2
...
Pm.
Therefore, ai
P1
P2
….
Pm in (2m – 1) ways . Since there are n elements in the set A, the number of ways of constructing subsets
P1, P2, ….. , Pm is (2m – 1)n
For each ai (1
Also there is exactly one choice, viz., ai
Therefore, ai
P1, P2, ….. , Pm is (2m – 1)n
A is a set containing n elements. A subset P1 is chosen, and A is reconstructed by replacing the elements of P1. The same process is repeated for subsets P1, P2, … , Pm, with m > 1. The Number of ways of choosing P1, P2, …, Pm so that P1
P2
…
Pm= A is -
maths-General
Let A = {a1, a2,…..an}.
For each ai (1
i
n), either ai
Pj or ai
Pj (1
j
m) . Thus, there are 2m choices in which ai (1
j
n) may belong to the Pj
s.
Also there is exactly one choice, viz., ai
Pj for j = 1, 2, …, m, for which ai
P1
P2
...
Pm.
Therefore, ai
P1
P2
….
Pm in (2m – 1) ways . Since there are n elements in the set A, the number of ways of constructing subsets
P1, P2, ….. , Pm is (2m – 1)n
For each ai (1
Also there is exactly one choice, viz., ai
Therefore, ai
P1, P2, ….. , Pm is (2m – 1)n
maths-
If a hyperbola passing through the origin has
and
as its asymptotes, then the equation of its tranvsverse and conjugate axes are
If a hyperbola passing through the origin has
and
as its asymptotes, then the equation of its tranvsverse and conjugate axes are
maths-General
physics-
Which of the following curves represents correctly the oscillation given by 

Given equation 
At
This is case with curve marked
At
This is case with curve marked
Which of the following curves represents correctly the oscillation given by 

physics-General
Given equation 
At
This is case with curve marked
At
This is case with curve marked
maths-
In a triangle ABC, if a : b : c = 7 : 8 : 9, then cos A : cos B equals to
In a triangle ABC, if a : b : c = 7 : 8 : 9, then cos A : cos B equals to
maths-General
physics-
A small source of sound moves on a circle as shown in the figure and an observer is standing on
Let
and
be the frequencies heard when the source is at
and
respectively. Then

At point
source is moving away from observer so apparent frequency
(actual frequency) At point
source is coming towards observer so apparent frequency
and point
source is moving perpendicular to observer so 
Hence
Hence
A small source of sound moves on a circle as shown in the figure and an observer is standing on
Let
and
be the frequencies heard when the source is at
and
respectively. Then

physics-General
At point
source is moving away from observer so apparent frequency
(actual frequency) At point
source is coming towards observer so apparent frequency
and point
source is moving perpendicular to observer so 
Hence
Hence
maths-
(Area of
GPL) to (Area of
ALD) is equal to
(Area of
GPL) to (Area of
ALD) is equal to
maths-General
maths-
The polar equation of the circle with pole as centre and radius 3 is
The polar equation of the circle with pole as centre and radius 3 is
maths-General
maths-
The equation of the circle passing through pole and centre at (4,0) is
The equation of the circle passing through pole and centre at (4,0) is
maths-General