Maths-
General
Easy

Question

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

  1. n + 1Cr +1    
  2. n+2Cr    
  3. n+2Cr+1    
  4. n+1Cr    

The correct answer is: n+2Cr+1

Book A Free Demo

+91

Grade*

Related Questions to study

General
maths-

The number of ways is which an examiner can assign 30 marks to 8 questions, giving not less than 2 marks to any question is -

The number of ways is which an examiner can assign 30 marks to 8 questions, giving not less than 2 marks to any question is -

maths-General
General
physics-

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, similarly linear momentum of reflected water per second 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

physics-General
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, similarly linear momentum of reflected water per second 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
General
physics-

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

physics-General
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
General
physics-

Two small particles of equal masses start moving in opposite directions from a point A in a horizontal circular orbit. Their tangential velocities are vand 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 xand 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
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 vand 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 xand 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
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
General
maths-

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

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

maths-General
General
maths-

The number of non-negative integral solutions of x + y + z  n, where n  N is -

The number of non-negative integral solutions of x + y + z  n, where n  N is -

maths-General
General
maths-

Between two junction stations A and B there are 12 intermediate stations. The number of ways in which a train can be made to stop at 4 of these stations so that no two of these halting stations are consecutive is -

Between two junction stations A and B there are 12 intermediate stations. The number of ways in which a train can be made to stop at 4 of these stations so that no two of these halting stations are consecutive is -

maths-General
General
maths-

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 -

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 -

maths-General
General
maths-

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 -

maths-General
General
maths-

The number of rectangles in the adjoining figure is –

The number of rectangles in the adjoining figure is –

maths-General
General
chemistry-

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

chemistry-General
General
physics-

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 blank a n d blank 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 blank,these two particles will again reach The point A ?

A s first collision one particle having speed 2v will rotate
240 degree open parentheses o r fraction numerator 4 pi over denominator 3 end fraction close parentheseswhile other particle having speed v blankwill rotate
120 degree open parentheses o r fraction numerator 2 pi over denominator 3 end fraction close parentheses. At first collision they will exchange their velocities. Now as shown in figure, after two collisions they will again reach at 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 blank a n d blank 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 blank,these two particles will again reach The point A ?

physics-General
A s first collision one particle having speed 2v will rotate
240 degree open parentheses o r fraction numerator 4 pi over denominator 3 end fraction close parentheseswhile other particle having speed v blankwill rotate
120 degree open parentheses o r fraction numerator 2 pi over denominator 3 end fraction close parentheses. At first collision they will exchange their velocities. Now as shown in figure, after two collisions they will again reach at point A.
General
physics-

The trajectory of a particle moving in vast maidan is as shown in the figure. The coordinates of a position A are open parentheses 0 , 2 close parentheses. The coordinates of another point at which the instantaneous velocity is same as the average velocity between the points are

The trajectory of a particle moving in vast maidan is as shown in the figure. The coordinates of a position A are open parentheses 0 , 2 close parentheses. The coordinates of another point at which the instantaneous velocity is same as the average velocity between the points are

physics-General
General
physics-

The potential energy of a particle varies with distance x as shown in the graph.
The force acting on the particle is zero at

F equals fraction numerator negative d U over denominator d x end fraction it is clear that slope of U minus x curve is zero at point B and C
therefore F equals 0 for point B and C

The potential energy of a particle varies with distance x as shown in the graph.
The force acting on the particle is zero at

physics-General
F equals fraction numerator negative d U over denominator d x end fraction it is clear that slope of U minus x curve is zero at point B and C
therefore F equals 0 for point B and C
General
physics-

A 10 k g mass moves along x-axis. Its acceleration as a function of its position is shown in the figure. What is the total work done on the mass by the force as the mass moves from x equals 0 to x equals 8 blank c m

Work done = Area covered in between force displacement curve and displacement axis
= Mass cross timesArea covered in between acceleration-displacement curve and displacement axis
equals 10 cross times fraction numerator 1 over denominator 2 end fraction open parentheses 8 cross times 10 to the power of negative 2 end exponent cross times 20 cross times 10 to the power of negative 2 end exponent close parentheses equals 8 cross times 10 to the power of negative 2 end exponent J

A 10 k g mass moves along x-axis. Its acceleration as a function of its position is shown in the figure. What is the total work done on the mass by the force as the mass moves from x equals 0 to x equals 8 blank c m

physics-General
Work done = Area covered in between force displacement curve and displacement axis
= Mass cross timesArea covered in between acceleration-displacement curve and displacement axis
equals 10 cross times fraction numerator 1 over denominator 2 end fraction open parentheses 8 cross times 10 to the power of negative 2 end exponent cross times 20 cross times 10 to the power of negative 2 end exponent close parentheses equals 8 cross times 10 to the power of negative 2 end exponent J