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In which stage of the Law of Variable Proportions does the marginal product of the variable factor become negative?

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Important Questions on Motion in a Plane

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Physics>Mechanics>Motion in a Plane>Relative Velocity in Two Dimensions

Consider a class of

5

girls and

7

boys. The number of different teams consisting of

2

girls and

3

boys that can be formed from this class, if there are two specific boys

A

and

B,

who refuse to be the members of the same team, is:

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Physics>Mechanics>Motion in a Plane>Relative Velocity in Two Dimensions

A committee of

11

member is to be formed from

8

males and

5

females. If

m

is the number of ways the committee is formed with at least

6

males and

n

is the number of ways the committee is formed with at least

3

females, then

EASY

Physics>Mechanics>Motion in a Plane>Relative Velocity in Two Dimensions

The Number of ways of choosing

10

objects out of

31

objects of which

10

are identical and the remaining

21

are distinct, is:

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Physics>Mechanics>Motion in a Plane>Relative Velocity in Two Dimensions

The value of

\sum_{r = 1}^{10} r \cdot \frac{{}^{n}C_{r}}{{}^{n}C_{r - 1}}

is equal to

EASY

Physics>Mechanics>Motion in a Plane>Relative Velocity in Two Dimensions

The stream of a river is flowing with a speed of

2 k m h^{- 1}

. A swimmer can swim at a speed of

4 km h^{- 1}

. The direction of the swimmer with respect to the flow of the river, to cross the river straight, is

HARD

Physics>Mechanics>Motion in a Plane>Relative Velocity in Two Dimensions

If in a regular polygon the number of diagonals is

54

, then the number of sides of this polygon is:

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Physics>Mechanics>Motion in a Plane>Relative Velocity in Two Dimensions

Suppose that

20

pillars of the same height have been erected along the boundary of circular stadium. If the top of each pillar has been connected by beams with the top of all its non-adjacent pillars, then the total number of beams is:

EASY

Physics>Mechanics>Motion in a Plane>Relative Velocity in Two Dimensions

Let

a_{1}, a_{2}, {\dots . . a}_{10}

be a G.P. If

\frac{a_{3}}{a_{1}} = 25,

then

\frac{a_{9}}{a_{5}}

equals:

HARD

Physics>Mechanics>Motion in a Plane>Relative Velocity in Two Dimensions

{\sum_{i = 1}^{20} (\frac{^{20} C_{i - 1}}{^{20} C_{i} +^{20} C_{i - 1}})}^{3} = \frac{k}{21},

then

k

equals

EASY

Physics>Mechanics>Motion in a Plane>Relative Velocity in Two Dimensions

There are

m

men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the men and the women by

84

, then the value of

m

is :

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Physics>Mechanics>Motion in a Plane>Relative Velocity in Two Dimensions

Let

a, b

and

c

be the

7^{t h}, 11^{t h}

and

13^{t h}

terms respectively of a non-constant A.P. If these are also the three consecutive terms of a G.P., then

\frac{a}{c}

is equal to:

EASY

Physics>Mechanics>Motion in a Plane>Relative Velocity in Two Dimensions

A force

F = 20 + 10 y

acts on a particle in

y

-direction where

F

is in Newton and

y

is in meter. Work done by this force to move the particle from

y = 0

y = 1 m

EASY

Physics>Mechanics>Motion in a Plane>Relative Velocity in Two Dimensions

A body moves from point $A$ to point $B$ under the action of a force varying in magnitude as shown in the force-displacement graph. Find the total work done by the force.

Question Image

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Physics>Mechanics>Motion in a Plane>Relative Velocity in Two Dimensions

A force

F = A y^{2} + B y + C

acts on a body in the

y

-direction. The work done by this force during a displacement from

y = - a

y = a

EASY

Physics>Mechanics>Motion in a Plane>Relative Velocity in Two Dimensions

A force

\vec{F} = (3 t \hat{i} + 5 \hat{j}) N

acts on a body due to which its position varies as

\vec{s} = (2 t^{2} \hat{i} - 5 \hat{j})

. The work done by this force in the initial

2 s

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Physics>Mechanics>Motion in a Plane>Relative Velocity in Two Dimensions

The relation between the force $F$ and position $x$ of a body is as shown in figure. The work done in displacing the body from $x = 1 m$ to $x = 5 m$ will be,

Question Image

EASY

Physics>Mechanics>Motion in a Plane>Relative Velocity in Two Dimensions

What is the work done by a man in carrying a suitcase weighing

30 kg

over his head, when he travels a distance of

10 m

in the vertical direction.

EASY

Physics>Mechanics>Motion in a Plane>Relative Velocity in Two Dimensions

If a particle is compelled to move on a given smooth plane curve under the action of given forces in the plane

\vec{F} = x \hat{i} + y \hat{j}

, then

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Physics>Mechanics>Motion in a Plane>Relative Velocity in Two Dimensions

A body of mass

3 kg

is under a force which causes a displacement given by,

S = \frac{t^{3}}{3}

(

in m

). Find the work done by the force in first

2 s

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Physics>Mechanics>Motion in a Plane>Relative Velocity in Two Dimensions

The work done by the force, $\vec{F} = A (y^{2} \hat{i} + 2 x^{2} \hat{j})$ , where $A$ is a constant and $x$ and $y$ are in meters around the path shown, is

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In which stage of the Law of Variable Proportions does the marginal product of the variable factor become negative?

Important Questions on Motion in a Plane

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