The value of 50c4 + sum_(r=1)^(6)56-rt_(3) is

Maths-

General

Easy

Question

The value of ⁵⁰C₄ + $not stretchy sum subscript r equals 1 end subscript superscript 6 end superscript 56 minus r C subscript 3 end subscript$ is -

⁵⁵C₄
⁵⁵C₃
⁵⁶C₃
⁵⁶C₄

The correct answer is: ⁵⁶C₄

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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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A mass of $100 blank g$ strikes the wall with speed $5 blank m divided by s$ at an angle as shown in figure and it rebounds with the same speed. If the contact time is $2 cross times 10 to the power of negative 3 end exponent s e c$ , what is the force applied on the mass by the wall

Force = Rate of change of momentum
Initial momentum

stack P with rightwards arrow on top subscript 1 end subscript equals m v sin invisible function application theta stack i with hat on top plus m v cos invisible function application theta blank stack j with hat on top

Final momentum

stack P with rightwards arrow on top subscript 2 end subscript equals negative m v sin invisible function application theta stack i with hat on top plus m v cos invisible function application theta blank stack j with hat on top

therefore stack F with rightwards arrow on top equals fraction numerator increment stack P with rightwards arrow on top over denominator increment t end fraction equals fraction numerator negative 2 m v sin invisible function application theta over denominator 2 cross times 10 to the power of negative 3 end exponent end fraction

Substituting

m equals 0.1 blank k g comma blank v equals 5 blank m divided by s comma blank theta equals 60 degree

Force on the ball

stack F with rightwards arrow on top equals negative 250 square root of 3 N

Negative sign indicates direction of the force

A mass of $100 blank g$ strikes the wall with speed $5 blank m divided by s$ at an angle as shown in figure and it rebounds with the same speed. If the contact time is $2 cross times 10 to the power of negative 3 end exponent s e c$ , what is the force applied on the mass by the wall

physics-General

Force = Rate of change of momentum
Initial momentum

stack P with rightwards arrow on top subscript 1 end subscript equals m v sin invisible function application theta stack i with hat on top plus m v cos invisible function application theta blank stack j with hat on top

Final momentum

stack P with rightwards arrow on top subscript 2 end subscript equals negative m v sin invisible function application theta stack i with hat on top plus m v cos invisible function application theta blank stack j with hat on top

therefore stack F with rightwards arrow on top equals fraction numerator increment stack P with rightwards arrow on top over denominator increment t end fraction equals fraction numerator negative 2 m v sin invisible function application theta over denominator 2 cross times 10 to the power of negative 3 end exponent end fraction

Substituting

m equals 0.1 blank k g comma blank v equals 5 blank m divided by s comma blank theta equals 60 degree

Force on the ball

stack F with rightwards arrow on top equals negative 250 square root of 3 N

Negative sign indicates direction of the force

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If the locus of the mid points of the chords of the ellipse $fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction plus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction equals 1$ , drawn parallel to $y equals m subscript 1 end subscript x$ is $y equals m subscript 2 end subscript x$ then $m subscript 1 end subscript m subscript 2 end subscript equals$

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

Linear momentum of water striking per second to the wall

P subscript 1 end subscript equals m v equals A v rho blank v equals A v to the power of 2 end exponent blank rho

P subscript r end subscript equals A v to the power of 2 end exponent rho

Now making components of momentum along

x

- axes and

y

-axes. Change in momentum of water per second

equals P subscript i end subscript cos invisible function application theta plus P subscript r end subscript cos invisible function application theta

equals 2 A v to the power of 2 end exponent blank rho cos invisible function application theta

By definition of force, force exerted on the Wall

equals 2 A v to the power of 2 end exponent blank rho cos invisible function application theta

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

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Linear momentum of water striking per second to the wall

P subscript 1 end subscript equals m v equals A v rho blank v equals A v to the power of 2 end exponent blank rho

P subscript r end subscript equals A v to the power of 2 end exponent rho

Now making components of momentum along

x

- axes and

y

-axes. Change in momentum of water per second

equals P subscript i end subscript cos invisible function application theta plus P subscript r end subscript cos invisible function application theta

equals 2 A v to the power of 2 end exponent blank rho cos invisible function application theta

By definition of force, force exerted on the Wall

equals 2 A v to the power of 2 end exponent blank rho cos invisible function application theta

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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 $O A$ will

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

open square brackets B e c a u s e blank k proportional to fraction numerator 1 over denominator x end fraction proportional to fraction numerator 1 over denominator L end fraction therefore k proportional to fraction numerator 1 over denominator L end fraction close square brackets

Slope of force displacement graph gives the spring constant

left parenthesis k right parenthesis

of spring
If

k

becomes double then slope of the graph increases

i. e.

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 $O A$ will

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

open square brackets B e c a u s e blank k proportional to fraction numerator 1 over denominator x end fraction proportional to fraction numerator 1 over denominator L end fraction therefore k proportional to fraction numerator 1 over denominator L end fraction close square brackets

Slope of force displacement graph gives the spring constant

left parenthesis k right parenthesis

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Two small particles of equal masses start moving in opposite directions from a point $A$ in a horizontal circular orbit. Their tangential velocities are $v$ and $2 v$ , respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other than that at $A$ , these two particles will again reach the point $A$

Let initially particle

x

is moving in anticlockwise direction and

y

in clockwise direction
As the ratio of velocities of

x

and

y

particles are

fraction numerator v subscript x end subscript over denominator v subscript y end subscript end fraction equals fraction numerator 1 over denominator 2 end fraction

, therefore ratio of their distance covered will be in the ratio of

2 blank colon 1

. It means they collide at point B

After first collision at B, velocities of particles get interchanged,

i. e

x

will move with

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and particle

y

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v

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 $A$ in a horizontal circular orbit. Their tangential velocities are $v$ and $2 v$ , respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other than that at $A$ , these two particles will again reach the point $A$

physics-General

Let initially particle

x

is moving in anticlockwise direction and

y

in clockwise direction
As the ratio of velocities of

x

and

y

particles are

fraction numerator v subscript x end subscript over denominator v subscript y end subscript end fraction equals fraction numerator 1 over denominator 2 end fraction

, therefore ratio of their distance covered will be in the ratio of

2 blank colon 1

. It means they collide at point B

After first collision at B, velocities of particles get interchanged,

i. e

x

will move with

2 v

and particle

y

with

v

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Question

The value of 50C4 + is -

55C4 55C3 56C3 56C4

Answer

The correct answer is: 56C4

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The value of ⁵⁰C₄ + $not stretchy sum subscript r equals 1 end subscript superscript 6 end superscript 56 minus r C subscript 3 end subscript$ is -

⁵⁵C₄
⁵⁵C₃
⁵⁶C₃
⁵⁶C₄

The correct answer is: ⁵⁶C₄

A mass of $100 blank g$ strikes the wall with speed $5 blank m divided by s$ at an angle as shown in figure and it rebounds with the same speed. If the contact time is $2 cross times 10 to the power of negative 3 end exponent s e c$ , what is the force applied on the mass by the wall

A mass of $100 blank g$ strikes the wall with speed $5 blank m divided by s$ at an angle as shown in figure and it rebounds with the same speed. If the contact time is $2 cross times 10 to the power of negative 3 end exponent s e c$ , what is the force applied on the mass by the wall

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

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

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

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

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 $O A$ will

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 $O A$ will

The number of numbers between 1 and 10¹⁰ which contain the digit 1 is -

The number of numbers between 1 and 10¹⁰ which contain the digit 1 is -

Assertion :this equilibrium favours backward direction.
Reason :is stronger base than $C H subscript 2 end subscript C O O to the power of minus end exponent$

Assertion :this equilibrium favours backward direction.
Reason :is stronger base than $C H subscript 2 end subscript C O O to the power of minus end exponent$