Maths-

General

Easy

Question

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 -

^{n – 2}C₃
^{n – 3}C₂
^{n – 3}C₃
None of these

The correct answer is: ^{n – 2}C₃

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 –

Maths-General

General

chemistry-

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

chemistry-General

General

Physics-

A 0.098 kg block slides down a frictionless track as shown. The vertical component of the velocity of block at $A$ is

fraction numerator 1 over denominator 2 end fraction m v to the power of 2 end exponent equals m g open parentheses 3 minus 1 close parentheses equals 2 m g

v equals square root of 4 g equals 2 square root of g

Vertical component at

A equals 2 square root of g sin invisible function application 30 degree equals square root of g

A 0.098 kg block slides down a frictionless track as shown. The vertical component of the velocity of block at $A$ is

Physics-General

fraction numerator 1 over denominator 2 end fraction m v to the power of 2 end exponent equals m g open parentheses 3 minus 1 close parentheses equals 2 m g

v equals square root of 4 g equals 2 square root of g

Vertical component at

A equals 2 square root of g sin invisible function application 30 degree equals square root of g

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 parentheses

while other particle having speed

v blank

will 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 parentheses

while other particle having speed

v blank

will 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

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 times

Area 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 times

Area 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

General

physics-

A mass $m$ slips along the wall of a semispherical surface of radius $R$ . The velocity at the bottom of the surface is

By applying law of conservation of energy

m g R equals fraction numerator 1 over denominator 2 end fraction m v to the power of 2 end exponent rightwards double arrow v equals square root of 2 R g end root

A mass $m$ slips along the wall of a semispherical surface of radius $R$ . The velocity at the bottom of the surface is

physics-General

By applying law of conservation of energy

m g R equals fraction numerator 1 over denominator 2 end fraction m v to the power of 2 end exponent rightwards double arrow v equals square root of 2 R g end root

General

physics-

Three forces of magnitudes 6N, 6N and $square root of 72$ N at a corner of a cube along three sides as shown in figure. Resultant of these forces is

The resultant of 5 N along

O C

and 5 N along

O A

R equals square root of 6 to the power of 2 end exponent plus 6 to the power of 2 end exponent end root

equals square root of 72

N along

O B

The resultant of

square root of 72

N along

O B

and

square root of 72

N along

O G

R to the power of ´ end exponent equals square root of 72 plus 72 end root equals 12

N along

O E

Three forces of magnitudes 6N, 6N and $square root of 72$ N at a corner of a cube along three sides as shown in figure. Resultant of these forces is

physics-General

The resultant of 5 N along

O C

and 5 N along

O A

R equals square root of 6 to the power of 2 end exponent plus 6 to the power of 2 end exponent end root

equals square root of 72

N along

O B

The resultant of

square root of 72

N along

O B

and

square root of 72

N along

O G

R to the power of ´ end exponent equals square root of 72 plus 72 end root equals 12

N along

O E

General

physics-

A man standing on a hill top projects a stone horizontally with speed $v subscript 0 end subscript$ as shown in figure. Taking the coordinate system as given in the figure. The coordinates of the point where the stone will hit the hill surface

Range of the projectile on an inclined plane (down the plane) is,

R equals fraction numerator u to the power of 2 end exponent over denominator g c o s to the power of 2 end exponent beta end fraction left square bracket sin invisible function application open parentheses 2 alpha plus beta close parentheses plus sin invisible function application beta right square bracket

Here,

u equals v subscript 0 end subscript comma alpha equals 0

and

beta equals theta

therefore R equals fraction numerator 2 v subscript 0 end subscript superscript 2 end superscript sin invisible function application theta over denominator g cos to the power of 2 end exponent invisible function application theta end fraction

Now

x equals R cos invisible function application theta equals fraction numerator 2 v subscript 0 end subscript superscript 2 end superscript tan invisible function application theta over denominator g end fraction

and

y equals negative R sin invisible function application theta equals blank minus fraction numerator 2 v subscript 0 end subscript superscript 2 end superscript tan to the power of 2 end exponent invisible function application theta over denominator g end fraction

A man standing on a hill top projects a stone horizontally with speed $v subscript 0 end subscript$ as shown in figure. Taking the coordinate system as given in the figure. The coordinates of the point where the stone will hit the hill surface

physics-General

Range of the projectile on an inclined plane (down the plane) is,

R equals fraction numerator u to the power of 2 end exponent over denominator g c o s to the power of 2 end exponent beta end fraction left square bracket sin invisible function application open parentheses 2 alpha plus beta close parentheses plus sin invisible function application beta right square bracket

Here,

u equals v subscript 0 end subscript comma alpha equals 0

and

beta equals theta

therefore R equals fraction numerator 2 v subscript 0 end subscript superscript 2 end superscript sin invisible function application theta over denominator g cos to the power of 2 end exponent invisible function application theta end fraction

Now

x equals R cos invisible function application theta equals fraction numerator 2 v subscript 0 end subscript superscript 2 end superscript tan invisible function application theta over denominator g end fraction

and

y equals negative R sin invisible function application theta equals blank minus fraction numerator 2 v subscript 0 end subscript superscript 2 end superscript tan to the power of 2 end exponent invisible function application theta over denominator g end fraction

General

physics-

A particle is acted upon by a force $F$ which varies with position $x$ as shown in the figure. If the particle at $x equals 0$ has kinetic energy of 25 J, then the kinetic energy of the particle at $x equals 16 blank m$ is

Work done

W equals

Area under

F

x

graph with proper sign

W equals

Area of triangle

A B C

+ Area of rectangle

C D E F

+ Area of rectangle

F G H I

+ Area of

I J K L

W equals open square brackets fraction numerator 1 over denominator 2 end fraction blank cross times 6 cross times 10 close square brackets plus open square brackets 4 cross times left parenthesis negative 5 right parenthesis close square brackets plus open square brackets 4 cross times 5 close square brackets plus open square brackets 2 cross times open parentheses negative 5 close parentheses close square brackets

rightwards double arrow W equals 30 minus 20 plus 20 minus 10 equals 20 blank J

….(i)
According to work energy theorem

K subscript f end subscript minus K subscript i end subscript equals W rightwards double arrow open parentheses K subscript f end subscript close parentheses subscript x equals 16 m end subscript minus open parentheses K subscript i end subscript close parentheses subscript x equals 0 m end subscript equals W

open parentheses K subscript f end subscript close parentheses subscript x equals 16 m end subscript equals open parentheses K subscript i end subscript close parentheses subscript x equals 0 m end subscript plus W

equals 25 blank J plus 20 blank J equals 45 blank J

[Using (i)]

A particle is acted upon by a force $F$ which varies with position $x$ as shown in the figure. If the particle at $x equals 0$ has kinetic energy of 25 J, then the kinetic energy of the particle at $x equals 16 blank m$ is

physics-General

Work done

W equals

Area under

F

x

graph with proper sign

W equals

Area of triangle

A B C

+ Area of rectangle

C D E F

+ Area of rectangle

F G H I

+ Area of

I J K L

W equals open square brackets fraction numerator 1 over denominator 2 end fraction blank cross times 6 cross times 10 close square brackets plus open square brackets 4 cross times left parenthesis negative 5 right parenthesis close square brackets plus open square brackets 4 cross times 5 close square brackets plus open square brackets 2 cross times open parentheses negative 5 close parentheses close square brackets

rightwards double arrow W equals 30 minus 20 plus 20 minus 10 equals 20 blank J

….(i)
According to work energy theorem

K subscript f end subscript minus K subscript i end subscript equals W rightwards double arrow open parentheses K subscript f end subscript close parentheses subscript x equals 16 m end subscript minus open parentheses K subscript i end subscript close parentheses subscript x equals 0 m end subscript equals W

open parentheses K subscript f end subscript close parentheses subscript x equals 16 m end subscript equals open parentheses K subscript i end subscript close parentheses subscript x equals 0 m end subscript plus W

equals 25 blank J plus 20 blank J equals 45 blank J

[Using (i)]

General

physics-

A bob of mass $m$ accelerates uniformly from rest to $v subscript 1 end subscript$ in time $t subscript 1 end subscript$ . As a function of $t$ , the instantaneous power delivered to the body is

From

v equals u plus a t comma v subscript 1 end subscript equals 0 plus a t subscript 1 end subscript open parentheses because a equals fraction numerator v subscript 1 end subscript over denominator t subscript 1 end subscript end fraction close parentheses

F equals m a equals m v subscript 1 end subscript divided by t subscript 1 end subscript

Velocity acquired in

t

sec

equals a t equals fraction numerator v subscript 1 end subscript over denominator t subscript 1 end subscript end fraction t

Power

equals F cross times v equals fraction numerator m v subscript 1 end subscript over denominator t subscript 1 end subscript end fraction cross times fraction numerator v subscript 1 end subscript t over denominator t subscript 1 end subscript end fraction equals fraction numerator m v subscript 1 end subscript superscript 2 end superscript t over denominator t subscript 1 end subscript superscript 2 end superscript end fraction

A bob of mass $m$ accelerates uniformly from rest to $v subscript 1 end subscript$ in time $t subscript 1 end subscript$ . As a function of $t$ , the instantaneous power delivered to the body is

physics-General

From

v equals u plus a t comma v subscript 1 end subscript equals 0 plus a t subscript 1 end subscript open parentheses because a equals fraction numerator v subscript 1 end subscript over denominator t subscript 1 end subscript end fraction close parentheses

F equals m a equals m v subscript 1 end subscript divided by t subscript 1 end subscript

Velocity acquired in

t

sec

equals a t equals fraction numerator v subscript 1 end subscript over denominator t subscript 1 end subscript end fraction t

Power

equals F cross times v equals fraction numerator m v subscript 1 end subscript over denominator t subscript 1 end subscript end fraction cross times fraction numerator v subscript 1 end subscript t over denominator t subscript 1 end subscript end fraction equals fraction numerator m v subscript 1 end subscript superscript 2 end superscript t over denominator t subscript 1 end subscript superscript 2 end superscript end fraction

General

physics-

An aeroplane is flying in a horizontal direction with a velocity $600 k m h to the power of negative 1 end exponent$ at a height of 1960 m. when it is vertically above the point $A$ on the ground, a body is dropped from it. The body strikes the ground at point $B$ . Calculate the distance $A B$

From

h equals fraction numerator 1 over denominator 2 end fraction g t to the power of 2 end exponent

We have

t subscript O B end subscript equals square root of fraction numerator 2 h subscript O A end subscript over denominator g end fraction end root

equals square root of fraction numerator 2 cross times 1960 over denominator 9.8 end fraction end root equals 20 s

Horizontal distance

A B equals v t subscript O B end subscript

equals open parentheses 600 cross times fraction numerator 5 over denominator 18 end fraction close parentheses left parenthesis 20 right parenthesis

equals 3333.33 blank m equals 3.33 blank k m

An aeroplane is flying in a horizontal direction with a velocity $600 k m h to the power of negative 1 end exponent$ at a height of 1960 m. when it is vertically above the point $A$ on the ground, a body is dropped from it. The body strikes the ground at point $B$ . Calculate the distance $A B$

physics-General

From

h equals fraction numerator 1 over denominator 2 end fraction g t to the power of 2 end exponent

We have

t subscript O B end subscript equals square root of fraction numerator 2 h subscript O A end subscript over denominator g end fraction end root

equals square root of fraction numerator 2 cross times 1960 over denominator 9.8 end fraction end root equals 20 s

Horizontal distance

A B equals v t subscript O B end subscript

equals open parentheses 600 cross times fraction numerator 5 over denominator 18 end fraction close parentheses left parenthesis 20 right parenthesis

equals 3333.33 blank m equals 3.33 blank k m

General

Maths-

If the equation $fraction numerator x to the power of 2 end exponent over denominator 9 minus k end fraction plus fraction numerator y to the power of 2 end exponent over denominator 5 minus k end fraction equals 1$ represents an ellipse then

Maths-General

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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 -

n – 2C3 n – 3C2 n – 3C3 None of these

The correct answer is: n – 2C3

Related Questions to study

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 -

The number of rectangles in the adjoining figure is –

The number of rectangles in the adjoining figure is –

Assertion :this equilibrium favours backward direction.Reason :is stronger base than

Assertion :this equilibrium favours backward direction.Reason :is stronger base than

A 0.098 kg block slides down a frictionless track as shown. The vertical component of the velocity of block at is

A 0.098 kg block slides down a frictionless track as shown. The vertical component of the velocity of block at is

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

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

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

A mass moves along -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 to

A mass moves along -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 to

A mass slips along the wall of a semispherical surface of radius . The velocity at the bottom of the surface is

A mass slips along the wall of a semispherical surface of radius . The velocity at the bottom of the surface is

Three forces of magnitudes 6N, 6N and N at a corner of a cube along three sides as shown in figure. Resultant of these forces is

Three forces of magnitudes 6N, 6N and N at a corner of a cube along three sides as shown in figure. Resultant of these forces is

A man standing on a hill top projects a stone horizontally with speed as shown in figure. Taking the coordinate system as given in the figure. The coordinates of the point where the stone will hit the hill surface

A man standing on a hill top projects a stone horizontally with speed as shown in figure. Taking the coordinate system as given in the figure. The coordinates of the point where the stone will hit the hill surface

A particle is acted upon by a force which varies with position as shown in the figure. If the particle at has kinetic energy of 25 J, then the kinetic energy of the particle at is

A particle is acted upon by a force which varies with position as shown in the figure. If the particle at has kinetic energy of 25 J, then the kinetic energy of the particle at is

A bob of mass accelerates uniformly from rest to in time . As a function of , the instantaneous power delivered to the body is

A bob of mass accelerates uniformly from rest to in time . As a function of , the instantaneous power delivered to the body is

An aeroplane is flying in a horizontal direction with a velocity at a height of 1960 m. when it is vertically above the point on the ground, a body is dropped from it. The body strikes the ground at point . Calculate the distance

An aeroplane is flying in a horizontal direction with a velocity at a height of 1960 m. when it is vertically above the point on the ground, a body is dropped from it. The body strikes the ground at point . Calculate the distance

If the equation represents an ellipse then

If the equation represents an ellipse then

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^{n – 2}C₃
^{n – 3}C₂
^{n – 3}C₃
None of these

The correct answer is: ^{n – 2}C₃

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 $C H subscript 2 end subscript C O O to the power of minus end exponent$

A 0.098 kg block slides down a frictionless track as shown. The vertical component of the velocity of block at $A$ is

A 0.098 kg block slides down a frictionless track as shown. The vertical component of the velocity of block at $A$ is

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

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

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

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 $x equals 8 blank c m$

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 $x equals 8 blank c m$

A mass $m$ slips along the wall of a semispherical surface of radius $R$ . The velocity at the bottom of the surface is

A mass $m$ slips along the wall of a semispherical surface of radius $R$ . The velocity at the bottom of the surface is

Three forces of magnitudes 6N, 6N and $square root of 72$ N at a corner of a cube along three sides as shown in figure. Resultant of these forces is

Three forces of magnitudes 6N, 6N and $square root of 72$ N at a corner of a cube along three sides as shown in figure. Resultant of these forces is

A man standing on a hill top projects a stone horizontally with speed $v subscript 0 end subscript$ as shown in figure. Taking the coordinate system as given in the figure. The coordinates of the point where the stone will hit the hill surface

A man standing on a hill top projects a stone horizontally with speed $v subscript 0 end subscript$ as shown in figure. Taking the coordinate system as given in the figure. The coordinates of the point where the stone will hit the hill surface

A particle is acted upon by a force $F$ which varies with position $x$ as shown in the figure. If the particle at $x equals 0$ has kinetic energy of 25 J, then the kinetic energy of the particle at $x equals 16 blank m$ is

A particle is acted upon by a force $F$ which varies with position $x$ as shown in the figure. If the particle at $x equals 0$ has kinetic energy of 25 J, then the kinetic energy of the particle at $x equals 16 blank m$ is

A bob of mass $m$ accelerates uniformly from rest to $v subscript 1 end subscript$ in time $t subscript 1 end subscript$ . As a function of $t$ , the instantaneous power delivered to the body is

A bob of mass $m$ accelerates uniformly from rest to $v subscript 1 end subscript$ in time $t subscript 1 end subscript$ . As a function of $t$ , the instantaneous power delivered to the body is

An aeroplane is flying in a horizontal direction with a velocity $600 k m h to the power of negative 1 end exponent$ at a height of 1960 m. when it is vertically above the point $A$ on the ground, a body is dropped from it. The body strikes the ground at point $B$ . Calculate the distance $A B$

An aeroplane is flying in a horizontal direction with a velocity $600 k m h to the power of negative 1 end exponent$ at a height of 1960 m. when it is vertically above the point $A$ on the ground, a body is dropped from it. The body strikes the ground at point $B$ . Calculate the distance $A B$

If the equation $fraction numerator x to the power of 2 end exponent over denominator 9 minus k end fraction plus fraction numerator y to the power of 2 end exponent over denominator 5 minus k end fraction equals 1$ represents an ellipse then

If the equation $fraction numerator x to the power of 2 end exponent over denominator 9 minus k end fraction plus fraction numerator y to the power of 2 end exponent over denominator 5 minus k end fraction equals 1$ represents an ellipse then