Physics-
General
Easy
Question
In Young's double slit experiment, 12 fringes are obtained to be formed in a certain segment of the screen when light of wavelength 600 nm is used. If wavelength of light is changed to 400 nm, number of fringes observed in the same segment of the screen is given by
- 18
- 24
- 30
- 36
The correct answer is: 18
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physics-
Intensity of central bright fringe due to interference of two identical coherent monochromatic sources is I. If one of the source is switched off, then intensity of central bright fringe becomes
Intensity of central bright fringe due to interference of two identical coherent monochromatic sources is I. If one of the source is switched off, then intensity of central bright fringe becomes
physics-General
maths-
If P (a cos
, bsin
) is a point on an ellipse
, then '
' is –
If P (a cos
, bsin
) is a point on an ellipse
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' is –
maths-General
Maths-
If the normal at the point P(
) to the ellipse
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If the normal at the point P(
) to the ellipse
intersects it again at the point Q(2
) then cos
=
Maths-General
maths-
If a tangent to ellipse
+
= 1 makes an angle
with x- axis, then square of length of intercept of tangent cut between axes is-
Let tangent is
+
= 1
Slope is tan
= –
S… (1)
square of length of intercept is
=
Length is
… (2)
Now use value of tan from (1)
Slope is tan
=
Now use value of tan from (1)
If a tangent to ellipse
+
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with x- axis, then square of length of intercept of tangent cut between axes is-
maths-General
Let tangent is
+
= 1
Slope is tan
= –
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square of length of intercept is
=
Length is
… (2)
Now use value of tan from (1)
Slope is tan
=
Now use value of tan from (1)
physics-
Vibrating tuning fork of frequency
is placed near the open end of a long cylindrical tube. The tube has a side opening and is fitted with a movable reflecting piston. As the piston is moved through
the intensity of sound changes from a maximum to minimum. If the speed of sound is
then
is

When the piston is moved through a distance of
the path difference produced is 
This must be equal to
for maximum to change to minimum.

So,
This must be equal to
So,
Vibrating tuning fork of frequency
is placed near the open end of a long cylindrical tube. The tube has a side opening and is fitted with a movable reflecting piston. As the piston is moved through
the intensity of sound changes from a maximum to minimum. If the speed of sound is
then
is

physics-General
When the piston is moved through a distance of
the path difference produced is 
This must be equal to
for maximum to change to minimum.

So,
This must be equal to
So,
maths-
PQ and QR are two focal chords of an ellipse and the eccentric angles of P,Q,R and
,
respectively then tan
tan
is equal to -
P (a cos 2
R (a cos 2
chord's PQ equation
PQ passes through the focus (ae, 0)
e =
PR passes through the focus (– ae, 0) the
– e =
Apply componendo and dividendo, we get
tan
PQ and QR are two focal chords of an ellipse and the eccentric angles of P,Q,R and
,
respectively then tan
tan
is equal to -
maths-General
P (a cos 2
R (a cos 2
chord's PQ equation
PQ passes through the focus (ae, 0)
e =
PR passes through the focus (– ae, 0) the
– e =
Apply componendo and dividendo, we get
tan
maths-
The radius of the circle passing through the points of intersection of ellipse
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Two curves are symmetrical about both axes and intersect in four points, so, the circle through their points of intersection will have centre at origin.
Solving
= 0 and
= 1, we get
= 
Therefore radius of circle
=
= 
Solving
Therefore radius of circle
=
The radius of the circle passing through the points of intersection of ellipse
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maths-General
Two curves are symmetrical about both axes and intersect in four points, so, the circle through their points of intersection will have centre at origin.
Solving
= 0 and
= 1, we get
= 
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=
= 
Solving
Therefore radius of circle
=
maths-
If
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If
are the eccentric angles of the extremities of a focal chord of an ellipse, then the eccentricity of the ellipse is -
maths-General
maths-
If
is the angle between the diameter through any point on a standard ellipse and the normal at the point, then the greatest value of tan
is–
Any point P on ellipse is (a cos
, b sin
)
Equation of the diameter CP is y =
x
The normal to ellipse at P is
ax sec
– by cosec
= a2e2
Slopes of the lines CP and the normal GP are
tan
and
tan 

tan
=
=
=
sin cos =
sin 2
The greatest value of tan
=
.1 =
.
Equation of the diameter CP is y =
The normal to ellipse at P is
ax sec
Slopes of the lines CP and the normal GP are

tan
=
The greatest value of tan
If
is the angle between the diameter through any point on a standard ellipse and the normal at the point, then the greatest value of tan
is–
maths-General
Any point P on ellipse is (a cos
, b sin
)
Equation of the diameter CP is y =
x
The normal to ellipse at P is
ax sec
– by cosec
= a2e2
Slopes of the lines CP and the normal GP are
tan
and
tan 

tan
=
=
=
sin cos =
sin 2
The greatest value of tan
=
.1 =
.
Equation of the diameter CP is y =
The normal to ellipse at P is
ax sec
Slopes of the lines CP and the normal GP are

tan
=
The greatest value of tan
physics-
A radar operates at wavelength 50.0 cm. If the beat freqency between the transmitted singal and the singal reflected from aircraft (
) is 1 kHz, then velocity of the aircraft will be
when source is fixed and observer is moving towards it

when source is moving towards observer at rest




= 900 km/hr
when source is moving towards observer at rest
= 900 km/hr
A radar operates at wavelength 50.0 cm. If the beat freqency between the transmitted singal and the singal reflected from aircraft (
) is 1 kHz, then velocity of the aircraft will be
physics-General
when source is fixed and observer is moving towards it

when source is moving towards observer at rest




= 900 km/hr
when source is moving towards observer at rest
= 900 km/hr
Maths-
The locus of P such that PA2 + PB2 = 10 where A = (2, 0) and B = (4, 0) is
The locus of P such that PA2 + PB2 = 10 where A = (2, 0) and B = (4, 0) is
Maths-General
maths-
Let L = 0 is a tangent to ellipse
+
= 1 and S,
be its foci. If length of perpendicular from S on L = 0 is 2 then length of perpendicular from
on L = 0 is
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+
= 1 and S,
be its foci. If length of perpendicular from S on L = 0 is 2 then length of perpendicular from
on L = 0 is
maths-General
maths-
The condition that the line
x + my = n may be a normal to the ellipse
+
= 1 is
The condition that the line
x + my = n may be a normal to the ellipse
+
= 1 is
maths-General
Physics-
Two blocks A and B of equal masses m kg each are connected by a light thread, which passes over a massless pulley as shown in the figure. Both the blocks lie on wedge of mass m kg. Assume friction to be absent everywhere and both the blocks to be always in contact with the wedge. The wedge lying over smooth horizontal surface is pulled towards right with constant acceleration a (
). (g is acceleration due to gravity). Normal reaction (in N) acting on block A.

Two blocks A and B of equal masses m kg each are connected by a light thread, which passes over a massless pulley as shown in the figure. Both the blocks lie on wedge of mass m kg. Assume friction to be absent everywhere and both the blocks to be always in contact with the wedge. The wedge lying over smooth horizontal surface is pulled towards right with constant acceleration a (
). (g is acceleration due to gravity). Normal reaction (in N) acting on block A.

Physics-General
physics-
Two blocks A and B of equal masses m kg each are connected by a light thread, which passes over a massless pulley as shown in the figure. Both the blocks lie on wedge of mass m kg. Assume friction to be absent everywhere and both the blocks to be always in contact with the wedge. The wedge lying over smooth horizontal surface is pulled towards right with constant acceleration a (
). (g is acceleration due to gravity) Normal reaction (in N) acting on block B is

Two blocks A and B of equal masses m kg each are connected by a light thread, which passes over a massless pulley as shown in the figure. Both the blocks lie on wedge of mass m kg. Assume friction to be absent everywhere and both the blocks to be always in contact with the wedge. The wedge lying over smooth horizontal surface is pulled towards right with constant acceleration a (
). (g is acceleration due to gravity) Normal reaction (in N) acting on block B is

physics-General