Maths-

#### If ^{n}C_{r} denotes the number of combinations of n things taken r at a time, then the expression ^{n}C_{r+1} + ^{n}C_{r –1} + 2 × ^{n}C_{r} equals-

Maths-General

^{n+1}C_{r}
^{n + 1}C_{r +1}
^{n+2}C_{r}
^{n+2}C_{r+1}

^{n+1}C_{r}^{n + 1}C_{r +1}^{n+2}C_{r}^{n+2}C_{r+1}#### Answer:The correct answer is: ^{n+2}C_{r+1}

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### Related Questions to study

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#### If the locus of the mid points of the chords of the ellipse , drawn parallel to is then

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#### An intense stream of water of cross-sectional area strikes a wall at an angle with the normal to the wall and returns back elastically. If the density of water is and its velocity is ,then the force exerted in the wall will be

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Now making components of momentum along - axes and -axes. Change in momentum of water per second

By definition of force, force exerted on the Wall

Now making components of momentum along - axes and -axes. Change in momentum of water per second

By definition of force, force exerted on the Wall

#### An intense stream of water of cross-sectional area strikes a wall at an angle with the normal to the wall and returns back elastically. If the density of water is and its velocity is ,then the force exerted in the wall will be

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Linear momentum of water striking per second to the wall , similarly linear momentum of reflected water per second

Now making components of momentum along - axes and -axes. Change in momentum of water per second

By definition of force, force exerted on the Wall

Now making components of momentum along - axes and -axes. Change in momentum of water per second

By definition of force, force exerted on the Wall

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#### The force required to stretch a spring varies with the distance as shown in the figure. If the experiment is performed with above spring of half length, the line will

When the length of spring is halved, its spring constant will becomes double

Slope of force displacement graph gives the spring constant of spring

If becomes double then slope of the graph increases graph shifts towards force- axis

Slope of force displacement graph gives the spring constant of spring

If becomes double then slope of the graph increases graph shifts towards force- axis

#### The force required to stretch a spring varies with the distance as shown in the figure. If the experiment is performed with above spring of half length, the line will

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When the length of spring is halved, its spring constant will becomes double

Slope of force displacement graph gives the spring constant of spring

If becomes double then slope of the graph increases graph shifts towards force- axis

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If becomes double then slope of the graph increases graph shifts towards force- axis

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#### A mass of strikes the wall with speed at an angle as shown in figure and it rebounds with the same speed. If the contact time is , what is the force applied on the mass by the wall

Force = Rate of change of momentum

Initial momentum

Final momentum

Substituting

Force on the ball

Negative sign indicates direction of the force

Initial momentum

Final momentum

Substituting

Force on the ball

Negative sign indicates direction of the force

#### A mass of strikes the wall with speed at an angle as shown in figure and it rebounds with the same speed. If the contact time is , what is the force applied on the mass by the wall

physics-General

Force = Rate of change of momentum

Initial momentum

Final momentum

Substituting

Force on the ball

Negative sign indicates direction of the force

Initial momentum

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Substituting

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Negative sign indicates direction of the force

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#### The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is-

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#### Two small particles of equal masses start moving in opposite directions from a point in a horizontal circular orbit. Their tangential velocities are and , respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other than that at , these two particles will again reach the point

Let initially particle is moving in anticlockwise direction and in clockwise direction

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After first collision at B, velocities of particles get interchanged, ., will move with and particle with

Second collision will take place at point C. Again at this point velocities get interchanged and third collision take place at point A

So, after two collision these two particles will again reach the point A

As the ratio of velocities of and particles are , therefore ratio of their distance covered will be in the ratio of . It means they collide at point B

After first collision at B, velocities of particles get interchanged, ., will move with and particle with

Second collision will take place at point C. Again at this point velocities get interchanged and third collision take place at point A

So, after two collision these two particles will again reach the point A

#### Two small particles of equal masses start moving in opposite directions from a point in a horizontal circular orbit. Their tangential velocities are and , respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other than that at , these two particles will again reach the point

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Let initially particle is moving in anticlockwise direction and in clockwise direction

As the ratio of velocities of and particles are , therefore ratio of their distance covered will be in the ratio of . It means they collide at point B

After first collision at B, velocities of particles get interchanged, ., will move with and particle with

Second collision will take place at point C. Again at this point velocities get interchanged and third collision take place at point A

So, after two collision these two particles will again reach the point A

As the ratio of velocities of and particles are , therefore ratio of their distance covered will be in the ratio of . It means they collide at point B

After first collision at B, velocities of particles get interchanged, ., will move with and particle with

Second collision will take place at point C. Again at this point velocities get interchanged and third collision take place at point A

So, after two collision these two particles will again reach the point A

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#### In a model, it is shown that an arch of abridge is semi-elliptical with major axis horizontal. If the length of the base is 9 m and the highest part of the bridge is 3 m from the horizontal, the best approximation of the height of the arch, 2 m from the centre of the base is

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#### If n objects are arranged in a row, then the number of ways of selecting three of these objects so that no two of them are next to each other is -

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