Physics-
General
Easy
Question
The sun deliverse
of electromagnetic flux to the earth's surface. The total power that is incident on a roof of dimensions 8m ,20m, will be:
- None of these
The correct answer is: ![1.6 cross times 10 to the power of 5 end exponent text end text W](data:image/png;base64,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)
Related Questions to study
maths-
If
are the eccentric angles of the extremities of a focal chord of the ellipse
, then tan ![left parenthesis alpha divided by 2 right parenthesis t a n invisible function application left parenthesis beta divided by 2 right parenthesis equals](data:image/png;base64,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)
If
are the eccentric angles of the extremities of a focal chord of the ellipse
, then tan ![left parenthesis alpha divided by 2 right parenthesis t a n invisible function application left parenthesis beta divided by 2 right parenthesis equals](data:image/png;base64,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)
maths-General
maths-
If P(
), Q
are points on ellipse and
is angle between normals at P and Q then -
If P(
), Q
are points on ellipse and
is angle between normals at P and Q then -
maths-General
physics-
The Maxwell's four equations are written as:
i) ![not stretchy contour integral stack E with rightwards arrow on top. stack d s with rightwards arrow on top equals fraction numerator q subscript 0 end subscript over denominator epsilon subscript 0 end subscript end fraction](data:image/png;base64,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)
ii) ![not stretchy contour integral stack B with rightwards arrow on top. stack d s with rightwards arrow on top equals 0](data:image/png;base64,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)
iii) ![not stretchy contour integral stack E with rightwards arrow on top. stack d l with rightwards arrow on top equals fraction numerator d over denominator d t end fraction not stretchy contour integral stack B with rightwards arrow on top. stack d s with rightwards arrow on top](data:image/png;base64,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)
iv) ![not stretchy contour integral stack B with rightwards arrow on top. stack d s with rightwards arrow on top equals mu subscript 0 end subscript epsilon subscript 0 end subscript fraction numerator d over denominator d t end fraction not stretchy contour integral stack E with rightwards arrow on top. stack d s with rightwards arrow on top](data:image/png;base64,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)
The equations which have sources of
and ![stack B with rightwards arrow on top](data:image/png;base64,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)
The Maxwell's four equations are written as:
i) ![not stretchy contour integral stack E with rightwards arrow on top. stack d s with rightwards arrow on top equals fraction numerator q subscript 0 end subscript over denominator epsilon subscript 0 end subscript end fraction](data:image/png;base64,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)
ii) ![not stretchy contour integral stack B with rightwards arrow on top. stack d s with rightwards arrow on top equals 0](data:image/png;base64,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)
iii) ![not stretchy contour integral stack E with rightwards arrow on top. stack d l with rightwards arrow on top equals fraction numerator d over denominator d t end fraction not stretchy contour integral stack B with rightwards arrow on top. stack d s with rightwards arrow on top](data:image/png;base64,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)
iv) ![not stretchy contour integral stack B with rightwards arrow on top. stack d s with rightwards arrow on top equals mu subscript 0 end subscript epsilon subscript 0 end subscript fraction numerator d over denominator d t end fraction not stretchy contour integral stack E with rightwards arrow on top. stack d s with rightwards arrow on top](data:image/png;base64,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)
The equations which have sources of
and ![stack B with rightwards arrow on top](data:image/png;base64,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)
physics-General
Maths-
The line x cos
+ y sin
= p touches the ellipse
, if :
The line x cos
+ y sin
= p touches the ellipse
, if :
Maths-General
maths-
If
and
are the eccentric angles of extremities of a focal chord of an ellipse, then the eccentricity of the ellipse is -
If
and
are the eccentric angles of extremities of a focal chord of an ellipse, then the eccentricity of the ellipse is -
maths-General
Maths-
If x cos
+ y sin
= p is a tangent to the ellipse
, then -
If x cos
+ y sin
= p is a tangent to the ellipse
, then -
Maths-General
Maths-
Equation of chord of the ellipse
joining the points P (a cos
, b sin
) and Q (a cos
, b sin
) is 7
Equation of chord of the ellipse
joining the points P (a cos
, b sin
) and Q (a cos
, b sin
) is 7
Maths-General
physics-
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
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
physics-General
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
, then '
' is –
maths-General
Maths-
If the normal at the point P(
) to the ellipse
intersects it again at the point Q(2
) then cos
=
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-
If a tangent to ellipse
+
= 1 makes an angle
with x- axis, then square of length of intercept of tangent cut between axes is-
maths-General
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
![](data:image/png;base64,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)
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
![](data:image/png;base64,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)
physics-General
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 -
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
maths-
The radius of the circle passing through the points of intersection of ellipse
= 1 and x2 – y2 = 0 is -
The radius of the circle passing through the points of intersection of ellipse
= 1 and x2 – y2 = 0 is -
maths-General