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A firm is in equilibrium when it produces that amount of output at which the difference between total revenue(TR) and total cost (TC), i.e., total profits, is maximum.

It is the total income of a company and is calculated by multiplying the quantity of goods sold by the price of the goods.

(b) Earning maximum profit

Normal price is fixed in the Long period.

Correct answer is (a) Zero

Slope of supply curve is Positive.

Traders enjoy Normal profit at equilibrium price. 

The difference between total revenue and total variable cost is called gross profit. It is calculated like this : Gross Profit = TR – TVC

Secular price is fixed in the Very long Period.

(c) Demand and supply are equal

Following are the two conditions for equilibrium of a firm by MC = MR method:

1. The first and foremost condition of a firm’s equilibrium is that its MC should be equal to MR.
2. MC Curve should intersect MR Curve from below, i.e., MC should be rising at the point of equilibrium.

To maximize his profit, a producer will produce upto that quantity at which the following two conditions are fulfilled:

1. Marginal Revenue (MR) = Marginal Cost (MC)
2. MC should be rising after that point of production.

(a) Increase

• Total Revenue – The amount of money received by the sale of an item by a firm is called total revenue. In the form of formula, Total Revenue = Quantity Sold × price (per unit).
• Total Cost – Total cost is the total expenditure on the production of certain quantity of a commodity.
  In the form of formula, Total Cost = Total Fixed Cost + Total Variable Cost.

Correct answer is (a) MR = MC

Demand plays a dominant role in determining market price .

The maximum benefit to a firm is at the production level where the difference between total revenue and the total cost is highest. It is the also the state of equilibrium of the firm. At this stage, the total cost is the lowest in comparison to total revenue and production level.

Demand and supply play a dominant role in determining equilibrium price in the long period.

The concept of equilibrium price is Theoretical.

(a) Remain constant

Demand plays a dominant role in determining equilibrium price in the short period.

An industry is in equilibrium at a price and output at which its market demand equals its market supply.

(a) MR = MC and MC cuts MR from below

Profit will be highest at that level of output where marginal cost coincides with the marginal reveue, i.e., MC = MR.

Marginal revenue means the addition made to the total revenue by selling an additional emit of the commodity.

The main difference between the equilibrium of a firm and an industry is the following:

1. Industry is a group of firms which are producing a homogeneous product.
2. An industry is in equilibrium when all the firms are operating and no new firm enters the market or no existing firm leaves the industry.
3. Industry equilibrium is determined by conditions of demand and supply. The industry will be in the condition of equilibrium when all firms are in equilibrium, no new firms enter and no old firms leave the industry.
4. Industry will be in the position of equilibrium in the long run because all the possible adjustments can be made. Long run equilibrium of an industry is more stable.

Break Even Point. At this point, the firm neither earns profit nor suffers loss.

Following are the drawbacks –
(i) It is difficult to determine the maximum distance between total revenue and total cost.
(ii) It is not possible to determine the per unit cost on basis of diagram.

According to marginal revenue and marginal cost approach, a producer will be in equilibrium when two conditions are fulfilled i.e., (i) MC=MR and (ii) MC must cut MR from below. This is a better method to analyse the equilibrium point of a firm, since both optimum production and total profit can be easily determined by it.

(a) Abnormal Profit

Break-even for a firm occurs when it is able to cover all its costs of production. Under this situation, the firm earns only normal profit, i.e. neither super normal profits nor super normal losses. This situation prevails at the point where Total Cost is equal to Total Revenue, i.e. TR = TC or AR = AC.

Equilibirum price and production implies that quantity at which the firm earns highest profit. Above and below this point, the production and price both are not optimum to maximise the firm’s profit.

False. 

Height of the cone = r cm. 

Diameter of the base = r cm. 

Therefore, volume of the cone = 1/3 π(r/2)².r

= 1/12 πr³

According to the question,

Edge of cube, l = 2r

Then, diameter of the cone = 2r

⇒ radius of the cone = 2r/2

= r

Height of the cone, h = height of the cube

= 2r

Volume of the cone is given by,

Volume of cone = 1/3 πr²h

= 1/3 πr²(2r)

= 2/3 πr³

= Volume of hemisphere of radius r

Hence, the given statement “the volume of the largest right circular cone that can be fitted in a cube whose edge is 2r equals to the volume of a hemisphere of radius r” is true.

Given,

The side of the cube = 9 cm

The largest cone that can be cut from cube will have the base diameter = side of the cube

2r = 9

r = 9/2 cm = 4.5 cm

And,

Height of cone = side of cube

So, height of cone (h) = 9 cm

Thus,

Volume of the largest cone to fit in = 1/3 π × r² × h

= 1/3 π × 4.5² × 9

= 190.93 cm³

Therefore, the volume of the largest cone to fit in the cube has a volume of 190.93 cm^3.

Given,

Original edge of cube = 4 cm

Original volume of cube = 4³ = 64 cm³

After cutting,

Edge of cube = 1 cm

Hence volume of new cube = 1³ = 1 cm³

Number of small cubes thus formed = \(\cfrac{64}1\) = 64

Hence , total surface area of 64 cubes = 64 × 6a² = 64 × 6 = 384 m²

Given details are,

Edge of metal cube (volume) = 12cm

Edge of smaller two cubes = 6cm, 8cm

Let edge of third cube be ‘a’ cm

So,

Volume of metal cube = sum of volume of three small cubes

12³ = 6³ + 8³ + a³

1728 = 216 + 512 + a³

a³ = 1728 – 216 – 512

= 1000

a = ³√1000

= 10cm

∴ Edge of third smaller cube is 10 cm.

Side of two equal cubes = 6 cm

When we join, two cubes face to face formed a cuboid.

Dimensions of a cuboid are: 

Length = 6 cm + 6 cm = 12 cm 

Breadth = 6 cm 

Height = 6 cm 

Therefore, volume of cuboid = lbh 

= 12 x 6 x 6 

= 432 cm³

Correct option is (B) \(10a^2\)

Two cubes of each edge a is joined end to end then the length of formed cuboid = 2a,

breadth of formed cuboid = a and

height of formed cuboid = a.

\(\therefore\) Surface area of resultant cuboid \(=2\,(2a\times a+a\times a+a\times 2a)\)

\(=2\,(2a^2+a^2+2a^2)\)

\(=2\times5a^2=10a^2\)

Correct option is  B) 10a²

Correct option is D. 20

Given,

Side of cube = 3 cm

Dimension of cuboid = 10 cm × 9cm × 6 cm

Volume of cuboid = 10 × 9 × 6 = 540 cm³

Volume of cube = a³ = 3³ = 27 cm³

Number of cubes can be formed = \(\cfrac{volume\,of\,cuboid}{vlume\,of\,cube}\)

= \(\cfrac{540}{27}\) = 20

Correct option is  B) 512 cm³ 

Remove small word from question volume of cube whose edge length is 4 cm is v = a³ = 4³ = 64 cm³.

∴ volume of 8 equal cubes whose edge length are 4 cm = 8 v = 8 × 64 = 512 cm³.

Since, given cube is cut in 8 equal cubes of each edge is 4 cm.

Therefore, volume of given cube = 8 × volume of one cube whose edge length is 4 cm.

= 8 × 4³ = 8 × 64 = 512 cm³.

Correct option is (A) 432

Length of resultant cuboid = 6+6 = 12 cm,

breadth of resultant cuboid = 6 cm and

height of resultant cuboid = 6 cm.

\(\therefore\) Volume of resultant cuboid \(=12\times6\times6\,cm^3\)

\(=432\,cm^3\)

Correct option is  A) 432

Answer is (C), 

since P(5) is true and P(k + 1) is true, whenever P (k) is true.

Option : (C)

The diagonals in a rhombus are perpendicular, 

So, 

∠BPC = 90° 

From triangle BPC, 

The sum of angles is 180° 

So, 

∠CBP = 180° – 40° – 90° 

= 50° 

Since, triangle ABC is isosceles 

We have, 

AB = BC 

So, 

∠ACB = ∠CAB = 40° 

Again from triangle APB, 

∠PBA = 180° – 40° – 90° = 50°

Again, triangle ADB is isosceles, 

So, 

∠ADB = ∠DBA = 50°

∠ADB = 50°

Option : (B)

Given : 

ABCD is a parallelogram 

AC is a bisector of angle BAD 

∠BAC = 35° 

∠A = 2∠BAC 

∠A = 2(35°) 

∠A = 70° 

∠A + ∠B = 180° 

(Adjacent angles of parallelogram are supplementary) 

70 + ∠B = 180° 

∠B = 110°

Correct option is D) bh

PQRS is a rectangle with PS = 5 cm and PR = 13 cm (Given) 

In △PSR: 

Using Pythagoras theorem, 

SR² = PR² – PS² 

= (13)² – (5)² 

= 169 – 25 

= 114 

or SR = 12 

Now, Area of △RAS = 1/2 x SR x PS 

= 1/2 x 12 x 5 

= 30 

Therefore, Area of △RAS is 30 cm².

Correct option is C) \(\frac{1}{2}\) bh

Option : (C)

Given that, 

∠ABD = ∠ABP = 50° 

∠PBC +∠ABP = 90° 

(Each angle of a rectangle is a right angle) 

∠PBC = 40° 

Now, 

PB = PC 

(Diagonals of a rectangle are equal and bisect each other) 

Therefore, 

∠BCP = 40° (Equal sides has equal angle) 

In triangle BPC, 

∠BPC + ∠PBC + ∠BCP = 180° 

(Angle sum property of a triangle) 

∠BPC = 100° 

∠BPC + ∠DPC = 180° (Angles in a straight line) 

∠DPC = 180° – 100° 

= 80°

Given that, 

PQRS is a rectangle 

PS = 5 cm 

PR = 13 cm 

In triangle PSR, 

by using Pythagoras theorem

SR² = PR² – PS² 

SR² = (13)² – (5)² 

SR² = 169 – 25 

SR² = 114 

SR = 12 cm 

We have to find the area ΔRAS,

Area (ΔRAS) = \(\frac{1}{2}\) x Base x Height

= \(\frac{1}{2}\) x SR x PS

= \(\frac{1}{2}\) x 12 x 5

= 30 cm²

Hence, 

Area (ΔRAS) is 30 cm²