Maths-
General
Easy
Question
The sum of all integers between 50 and 500 which are divisible by 7 is
- 18696
- 15696
- 17696
- 14696
Hint:
Find the number of terms in the series. Then find sum to n terms by the formula.
The correct answer is: 17696
Detailed Solution
The series of integers divisible by 7 between 50 and 500 are 56, 63, 70, …, 497
Let the number of terms be ‘n’
So, a = 56, d = 63-56 = 7,
= 497
To find number of terms, use formula
![a subscript n space equals space a plus left parenthesis n minus 1 right parenthesis d](data:image/png;base64,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)
Substituting the known values in above
![rightwards double arrow 497 space equals space 56 plus left parenthesis n minus 1 right parenthesis 7
rightwards double arrow 497 space equals space 56 plus 7 n minus 7
rightwards double arrow 497 space equals space 49 plus 7 n
rightwards double arrow n space equals space 448 over 7 space equals space 64](data:image/png;base64,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)
Now by using the formula
![S subscript n space equals space n over 2 open square brackets a space plus space l close square brackets space comma space w h e r e
S subscript n space equals space S u m space o f space n space t e r m s
n space equals space n u m b e r space o f space t e r m s space equals space 64
a space equals space f i r s t space t e r m space equals space 56
l space equals space l a s t space t e r m space equals space 497
S u b s t i t u t i n g space t h e s e space v a l u e s
space
rightwards double arrow S subscript n space equals space 64 over 2 open square brackets 56 space plus space 497 close square brackets
rightwards double arrow S subscript n space equals space 32 open square brackets 56 space plus space 497 close square brackets
rightwards double arrow S subscript n space equals space 17696](data:image/png;base64,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)
Thus, the sum of all integers between 50 and 500 which are divisible by 7 is 17696.
Related Questions to study
Maths-
digits )=
digits )=
Maths-General
maths-
In a
as shown in figure given that
, then the value of
is
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486056/1/912662/Picture2.png)
In a
as shown in figure given that
, then the value of
is
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486056/1/912662/Picture2.png)
maths-General
physics-
A bob of mass M is suspended by a massless string of length L. The horizontal velocity
at position A is just sufficient to make it reach the point B. The angle
at which the speed of the bob is half of that at A, satisfies
![](data:image/png;base64,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)
A bob of mass M is suspended by a massless string of length L. The horizontal velocity
at position A is just sufficient to make it reach the point B. The angle
at which the speed of the bob is half of that at A, satisfies
![](data:image/png;base64,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)
physics-General
physics-
A particle of mass
attracted with a string of length
is just revolving on the vertical circle without slacking of the string. If
and
are speed at position
and
then
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486040/1/912428/Picture514.png)
A particle of mass
attracted with a string of length
is just revolving on the vertical circle without slacking of the string. If
and
are speed at position
and
then
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486040/1/912428/Picture514.png)
physics-General
physics-
A bob of mass
is suspended by a massless string of length
. The horizontal velocity
at position
is just sufficient to make it reach the point
. The angle
at which the speed of the bob is half of that at
, satisfies
![](data:image/png;base64,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)
A bob of mass
is suspended by a massless string of length
. The horizontal velocity
at position
is just sufficient to make it reach the point
. The angle
at which the speed of the bob is half of that at
, satisfies
![](data:image/png;base64,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)
physics-General
physics-
A body of mass
is moving with a uniform speed
along a circle of radius
, what is the average acceleration in going from
to
?
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486038/1/912395/Picture512.png)
A body of mass
is moving with a uniform speed
along a circle of radius
, what is the average acceleration in going from
to
?
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486038/1/912395/Picture512.png)
physics-General
Physics-
Figure shows four paths for a kicked football. Ignoring the effects of air on the flight, rank the paths according to initial horizontal velocity component, highest first
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/905880/1/912384/Picture507.png)
Figure shows four paths for a kicked football. Ignoring the effects of air on the flight, rank the paths according to initial horizontal velocity component, highest first
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/905880/1/912384/Picture507.png)
Physics-General
physics-
A boy throws a cricket ball from the boundary to the wicket-keeper. If the frictional force due to air cannot be ignored, the forces acting on the ball at the position X are respected by
![](data:image/png;base64,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)
A boy throws a cricket ball from the boundary to the wicket-keeper. If the frictional force due to air cannot be ignored, the forces acting on the ball at the position X are respected by
![](data:image/png;base64,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)
physics-General
physics-
In a two dimensional motion of a particle, the particle moves from point
, position vector
. If the magnitudes of these vectors are respectively,
=3 and
and the angles they make with the
-axis are
and 15
, respectively, then find the magnitude of the displacement vector
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486034/1/912281/Picture490.png)
In a two dimensional motion of a particle, the particle moves from point
, position vector
. If the magnitudes of these vectors are respectively,
=3 and
and the angles they make with the
-axis are
and 15
, respectively, then find the magnitude of the displacement vector
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486034/1/912281/Picture490.png)
physics-General
Physics-
A particle is moving on a circular path of radius
with uniform velocity
. The change in velocity when the particle moves from
to
is![blank left parenthesis angle P O Q equals 40 degree right parenthesis](data:image/png;base64,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)
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/905851/1/912216/Picture489.png)
A particle is moving on a circular path of radius
with uniform velocity
. The change in velocity when the particle moves from
to
is![blank left parenthesis angle P O Q equals 40 degree right parenthesis](data:image/png;base64,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)
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/905851/1/912216/Picture489.png)
Physics-General
Physics-
From an inclined plane two particles are projected with same speed at same angle
, one up and other down the plane as shown in figure, which of the following statements is/are correct?
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/905855/1/912209/Picture487.png)
From an inclined plane two particles are projected with same speed at same angle
, one up and other down the plane as shown in figure, which of the following statements is/are correct?
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/905855/1/912209/Picture487.png)
Physics-General
physics-
A string of length
is fixed at one end and carries a mass
at the other end. The string makes
revolutions per
around the vertical axis through the fixed end as shown in figure , then tension in the string is![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486030/1/912200/Picture486.png)
A string of length
is fixed at one end and carries a mass
at the other end. The string makes
revolutions per
around the vertical axis through the fixed end as shown in figure , then tension in the string is![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486030/1/912200/Picture486.png)
physics-General
physics-
A piece of wire is bent in the shape of a parabola
-axis vertical) with a bead of mass
on it. The bead can side on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the
-axis with a constant acceleration
. The distance of the new equilibrium position of the bead, where the bead can stay at rest with respect to the wire, from the
-axis is
![](data:image/png;base64,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)
A piece of wire is bent in the shape of a parabola
-axis vertical) with a bead of mass
on it. The bead can side on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the
-axis with a constant acceleration
. The distance of the new equilibrium position of the bead, where the bead can stay at rest with respect to the wire, from the
-axis is
![](data:image/png;base64,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)
physics-General
physics-
A frictionless track
ends in a circular loop of radius
figure. A body slides down the track from point
which is at a height
cm. Maximum value of
for the body to successfully complete the loop is
![](data:image/png;base64,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)
A frictionless track
ends in a circular loop of radius
figure. A body slides down the track from point
which is at a height
cm. Maximum value of
for the body to successfully complete the loop is
![](data:image/png;base64,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)
physics-General
Physics-
The resultant of a system of forces shown in figure is a force of 10 N parallel to given forces through
, where
equals
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/905679/1/912154/Picture483.png)
The resultant of a system of forces shown in figure is a force of 10 N parallel to given forces through
, where
equals
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/905679/1/912154/Picture483.png)
Physics-General