ST. XAVIER’S SR. SEC. SCHOOL, CHANDIGARH

Class 12 English Worksheet-13

Proposal

A Proposal, literally means a plan or a suggestion. It refers to formal or written

document, put forward for consideration by others. Based on content, a proposal

can be of different types such as:

Research Proposal

Grants Proposal

Business Proposal

Project based Proposal

In class 12th , students are required to write a proposal for implementing a project /

event and seeking its approval from the head of the institute, usually the Principal of

the school.

Requirements

The proposal requires the following headings:

Heading

Statement of objective

List of measures

Closing line

Signing off your full name

Designation

Date

SPECIMEN PAPER

English Paper 1 (Language) Specimen for Proposal Writing Question 2(b): [10] As a

member of the Student Council of your school, you have been given the responsibility of

setting up a Science Club. Write a proposal in about 150 words, stating the steps you

would take to successfully establish this particular club.

Answer:

PROPOSAL FOR SETTING UP A SCIENCE CLUB

Heading/Introduction: To foster an interest in Science outside the classroom and

introduce students to the wonders and relevance of Science in our lives, we propose to set

up a Science Club in school.

(maximum 2 sentences – 2 marks)

Objectives: A Science Club will help students overcome their phobias regarding Science.

It will be instrumental in developing the scientific curiosity of students through its

activities and programmes.

(minimum 2 points - 2 marks)

List of Measures: • The middle- school activity room will be used as the room for all

Science Club meetings and activities. • The meetings will take place once a week after

school from 2.00 pm till 3.30 pm. Any activities such as talks by scientists or

competitions will take place on Saturdays. • Membership of the Science Club will be

open to all students from Classes VI to XII. The Club President will be Mr. Sinha, our

Senior Physics Teacher. Eight other office bearers will be elected from the members of

the Club. • Club membership has been fixed at Rs. 250/- per member per year. • The Club

will have a range of activities ranging from Science Fairs, Robot making, creating

slogans and posters, documentaries and so on.

(minimum 4 points - 4 marks)

We hope that the proposal will be accepted so that the Science Club becomes a reality in

the life of the school.

XYZ (full name)

Member of student’s council (designation)

(linguistic ability - 2 marks) [Total - 10 marks]

Assignments

As the Head Boy/Head Girl of your school , you have been given the

responsibility of organising the Literary Fest in your school. Write a proposal in

about 150 words, stating the steps you would take to successfully organise this

fest.

As a member of the Arts and Crafts Society of your school, you have been

assigned the task of organising the sale of Greeting Cards and other Handicrafts

made by the students of your school. The proceeds of this sale would go to an

NGO working for helping the children of the slums. Write a proposal in about

150 words, stating the steps you would take to successfully implement this

project.

Class 12 Commerce Worksheet-9

Commercial Banks

Public Deposits

Trade Credit

Customer Advances

Factoring

Inter corporate deposits

Instalments credit

Commercial Banks: Traditionally commercial banks provide short-term finances. These

banks collect money from large number of depositors who can withdraw it at any time.

That is why commercial bank normally extend short-term financial assistance against some

security. Short-term financing facilities provided by banks are:

Bank overdraft: The companies having current accounts are allowed to withdraw

over and above the amount standing to their credit of their account. Normally a

certain maximum limit is fixed beyond which a company cannot overdraw.

Cash credit: This is the most popular form financial assistance extended by the

commercial banks to the business. In this case bank fixes a maximum limit up to

which up to which a company make borrow from it. The company is free to borrow

any amount up to the agreed limit and then repay it. It is important to note that in

this case the company shall have to pay interest on a minimum amount even if it did

not withdraw any amount.

Discounting of bills: The commercial banks also provide the facility of discounting

the bills of exchange of promissory notes before they become due for payment in

lieu of some commission.

Loan & advances: A loan is a direct advance make in lump sum which is credited

to a separate loan account in the name of the borrower. The borrower pays the

interest on the whole amount from the date of sanction. Such loans are usually

secured by pledge of specific asset.

Public Deposits: Public deposits refer to unsecured deposit invited by the non-banking

company from the public mainly to meet the short-term financial requirements.

Trade Credit: Credit extended by one firm to another during the course of business i.e.

sales or purchase of goods and services. It reflects the buyer`s power to purchase now and

pay later. The amount and terms of credit depends on the financial strength and goodwill

of the buyer.

Customer Advances: Some business houses get advances for short-term needs from their

customer and agents against their orders. Customer generally agree to make advance

payment when such goods are not easily available in the market or there is an urgent need

of goods. Nominal interest is paid on such advances to the customers.

Factoring: A factor is a financial institution which offers services relating to management

and financing of debt arising out of credit sale. Factoring. Finance company or factor

provide finance to business concern through outright purchase of accounts receivables or

against the security of accounts receivable.

Inter-corporate Deposits: When a company borrows funds for a short period from another

company, it is known as inter-corporate deposits. Rate of interest payable on inter-

corporate deposits funds is lower than bank loans. These deposits are very convenient and

popular as no legal formalities are involved.

Instalment Credit: In this mode of finance, assets are purchased and possession of the

goods is taken immediately but the payment is made in instalment over a pre-determined

period of time. Interest is paid on the unpaid price. Under this arrangement the ownership

of the asset remains with the supplier until all instalments are paid by the buyer. Rate of

interest is normally high.

Assignment:

Question 1 (Short Answer)

Define briefly the following with reference to source of short-term finance for a Joint Stock

Company.

Public Deposits

Trade Credit

Customer Advances

Factoring

Inter corporate deposits

Instalments credit

Question 2 (Long answer)

Briefly explain the various types of short-term financing facilities provided by commercial

bank to a Joint Stock Company.

Class 12 Economics Worksheet-13

TOPIC-DEMAND AND LAW OF DEMAND

Read the text given below and answer the following questions

What do you mean by demand ?

What are the features of demand definition? . Read the chapter thoroughly for better understanding .

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Class 12 Maths Worksheet-13

INVERSE TRIGNOMETRIC FUNCTIONS:

Consider the sine function f(x) = y= sin x, Df = R and Rf = [-1,1]

Therefore y = sin-1x called inverse sine function or arc sine function has Domain [-1,1] and

Range [ −𝜋

2 ,

𝜋

2 ] . The angles lying in [ −

𝜋

2 ,

𝜋

2 ] is called its Principal Value Branch.

Lets learn all the Principal Values

Inverse Function Principal Value Branch

or Principal Values

Remarks ( Just for understanding)

sin−1 𝑥 [−𝜋

2 ,

𝜋

2 ] Because sin

𝜋

2 =1 and sin (-

𝜋

2 ) = -1

cos−1 𝑥 [ 0, 𝜋 ] Because cos 0 = 1 and cos 𝜋 = -1

tan−1 𝑥 (−𝜋

2 ,

𝜋

2 ) Because tan x is not defined at −

𝜋

2 and

𝜋

2

cosec−1 𝑥 [−𝜋

2 , 0 ) ∪ ( 0,

𝜋

2 ] Because cosec x is not defined at 0

sec−1 𝑥 [ 0, 𝜋

2 ) ∪ (

𝜋

2 , 𝜋 ] Because sec x is not defined at

𝜋

2

cot−1 𝑥 (0, 𝜋 ) Because cot x is not defined at 0 and 𝜋 both

Finding the Principal Values

The following simple steps should be followed in order to find the Principal value of a given

inverse function.

STEP 1: Find out the quadrants in which Principal value lies.

STEP 2: Find out the quadrant according to sign convention of II I

Trigonometric function.

STEP 3: Principal value will lie in the common quadrant from

STEP 1 and STEP 2

STEP 4: The quadrants can be accessed with this rule III IV

shown in the image.

If f is a real function f defined by y = f(x) is invertible ( one –one and onto) then f-1 is given

by x = f -1 (y) for all x ∈ Df and y ∈Rf

In other words, Domain of f becomes Range of f -1 and vice versa.

0 + 𝝅 -

−𝝅 + 0 -

Illustration 1: Find the principal value of sin−1 (−√3

2 )

Solution: As we can see that Principal Value of The negative sign of sin function

sin-1x ∈ [−𝜋

2 ,

𝜋

2 ] I, IV Quadrants III, IV Quadrants

Therefore required Principal value will lie in common quadrant IV which can be accessed by

x = 0- 𝜋

3 , therefore the principal value of sin−1 (

−√3

2 ) is -

𝜋

3

Illustration 2: Find the principal value of sec−1 ( −2 )

Solution: As we can see that Principal Value of The negative sign of sin function

sec-1x ∈ [ 0, 𝜋

2 ) ∪ (

𝜋

2 , 𝜋 ] I, II Quadrants II, III Quadrants

Therefore required Principal value will lie in common quadrant II which can be accessed by

x = 𝜋 - 𝜋

3 =

2𝜋

3 , therefore the principal value of sec−1 ( −2 ) is

2𝜋

3

Illustration 3:Find the Principal value of sin−1(sin3𝜋

5 )

Solution: Let sin−1(sin3𝜋

5 ) = x , x ∈ [−

𝜋

2 ,

𝜋

2 ] and

3𝜋

5 ∈ [−

𝜋

2 ,

𝜋

2 ]

⇒ sin x = sin 3𝜋

5 = sin ( 𝜋 -

𝜋

5 ) = sin (

2𝜋

5 )

Now 2𝜋

5 ∈ [−

𝜋

2 ,

𝜋

2 ] , Therefore x =

2𝜋

5

Illustration 4: Evaluate sin ( cot−1(cot17𝜋

3 )

Solution: Let cot−1(cot17𝜋

3 ) = x , x ∈ (0, 𝜋 ) [ Principal value branch of cot-1x]

⇒ cot x = cot 17𝜋

3 = cot ( 5𝜋 +

𝜋

3 ) = cot (

2𝜋

3 )

And now 2𝜋

3 ∈ (0, 𝜋 ),

Therefore cot−1(cot17𝜋

3 ) =

2𝜋

3

So sin ( 2𝜋

3 ) = sin ( 𝜋 -

𝜋

3 ) = sin

𝜋

3 =

√3

2

Hence sin ( cot−1(cot17𝜋

3 ) =

√3

2

Illustration 5: Evaluate sin−1(sin 2)

Solution: In such cases when angles are given in radians [ 1 rad ≅ (57.27)0 ]

Therefore 2 radians ≅ (114.54) 0 and (114.54) 0 ∈ [−𝜋

2 ,

𝜋

2 ]

Therefore sin−1(sin 2) = sin−1{ 𝑠𝑖𝑛 (𝜋 -2) } = π -2 [ ∵ π -2 = 1800 – 114.540 ]

Which lies in the first quadrant or Principal value branch of sin-1 x .

Hence sin−1(sin 2) = π -2

Illustration 6: Evaluate cos { cos−1(−√3

2 ) +

𝜋

6 }

Solution: First of all we will find cos−1(−√3

2 ) by the same method done earlier.

Principal value of cos−1(𝑥) lies in Negative sign of cos comes in

I, II Quadrant II, III Quadrant

Therefore required Principal value will lie in common quadrant II

Hence cos−1(−√3

2 ) = 𝜋 -

𝜋

6 =

5𝜋

6

Therefore cos { cos−1(−√3

2 ) +

𝜋

6 } = cos {

5𝜋

6 +

𝜋

6 } = cos π = -1

SOLVE YOURSELVES:

1. Evaluate tan−1(tan 4) Ans: 4 – π

2. Find Principal value of cot−1( −1

√3 ) Ans:

2𝜋

3

3. Find Principal value of sec−1( −2

√3 ) Ans:

5𝜋

6

4. Evaluate tan−1(tan9𝜋

8 ) Ans:

𝜋

8

5. Evaluate cos−1(cos5𝜋

3 ) Ans:

𝜋

3

6. Evaluate sin { 𝜋

6 - sin−1(

−√3

2 ) } Ans: 1

7. Prove that tan−1(−1) + cos−1( −1

√2 ) =

𝜋

2

8. Using Principal values , solve cosec−1(−1) + cot−1( −1

√3 ) Ans:

𝜋

6

9. Find the value of tan−1(𝑡𝑎𝑛 5𝜋

6 ) + cos−1(𝑐𝑜𝑠

13𝜋

6 ) Ans: 0

[ Check: −𝝅

𝟔

𝝅

𝟔 ]

Illustration 7: Evaluate sin { 2 cos-1 −3

5 }

Solution: Let cos-1 −3

5 = x or cos x =

−3

5

Since we know that the Principal value of cos-1 x 𝜖 [0, 𝜋] where sin x will be positive

Now sin x = √1 − 𝑐𝑜𝑠2𝑥 = √1 − (−3

5 )2 =

4

5

sin { 2 cos-1 −3

5 }= sin 2x = 2 sin x cos x = 2 (

4

5 ) (

−3

5 ) =

−24

25

Illustration 8: Evaluate the following: tan ( 1

2 sin−1 3

5 )

Solution: Let 1

2 sin−1 3

5 = x , It means sin−1 3

5 = 2x or sin 2x =

3

5

⇒ 2 𝑡𝑎𝑛𝑥

1+ 𝑡𝑎𝑛2𝑥 =

3

5 or 3 + 3 tan2x = 10 tan x or 3 tan2x - 10 tan x + 3 = 0

( tan x -3 ) ( 3 tan x -1 ) = 0 Which gives tan x = 3 or 1

3

Now since x 𝜖 [−𝜋

4 ,

𝜋

4 ] therefore tan x 𝜖 [ -1, 1] Hence tan x =

1

3 or tan (

1

2 sin−1 3

5 ) =

1

3

SOLVE YOURSELVES:

10. Evaluate cosec { cos−1(−12

13 ) } Ans:

13

5

11. Evaluate sin { 2 cot−1( −5

12 ) } Ans:

−120

169

12. Find the value of tan−1{ 2 sin( 2 cos−1 √3

2 ) } Ans:

𝜋

3

INVERSE TRIGONOMETRIC FUNCTIONS CONTD….. IN WORKSHEET-14

REMEMBER:

𝐬𝐢𝐧−𝟏(−𝒙 ) = - 𝐬𝐢𝐧−𝟏(𝒙 )

𝐜𝐨𝐬−𝟏(−𝒙) = 𝝅 - 𝐜𝐨𝐬−𝟏 𝒙

𝐭𝐚𝐧−𝟏(−𝒙) = - 𝐭𝐚𝐧−𝟏 𝒙

𝐜𝐨𝐭−𝟏(−𝒙)= - 𝐜𝐨𝐭−𝟏 𝒙

𝐬𝐞𝐜−𝟏(−𝒙) = 𝝅- 𝐬𝐞𝐜−𝟏 𝒙

𝐜𝐨𝐬𝐞𝐜−𝟏(−𝒙)= - 𝐜𝐨𝐬𝐞𝐜−𝟏 𝒙

ALSO REMEMBER: Inverse functions can be interconverted by our

evergreen triangle method.

Supposing sin-1 3

5 = x then sin x =

3

5 3 5

4

Therefore sin-1 3

5 can be written as cos−1 4

5 or tan−1 3

4

[As it is clear from the right angled triangle]

IMPORTANT OBSERVATION: Since Principal value of inverse sine function 𝜖 [−𝜋

2 ,

𝜋

2 ]

Therefore 2x 𝜖 [−𝜋

2 ,

𝜋

2 ] or x 𝜖 [

−𝜋

4 ,

𝜋

4 ]

Class 12 Physical Education Worksheet-12

CHAPTER 2: TRAINING METHODS: TOPIC 5 COOLING DOWN

Meaning of cooling down/limbering down : The main aim of the cool down is to promote

recovery and return the body to a pre exercise, or pre work out level during a strenuous

work out your body goes through a number of stressful processes e.g. muscle fibers,

tendons and ligaments get damaged, and waste products build up within your body.

For appropriate cooling down, we should perform we should perform jogging as well as

walking for 5 to 10 minutes. This will help in decreasing the body temperature and

removing the waste products from the working muscles. After that static stretching

exercises should be performed for 5 to 10 minutes. The stretches should be held for 10 to

20 seconds. The repetition of stretch should be done at least 2 to 3 times.

Major stretching exercises of muscles for cooling down:

Quadriceps (one of the more powerful muscles of the body)

Lying on your right side

Pull left heel into left glute

Feeling the stretch in the front of the thigh.

Repeat with the right leg.

Hamstrings (group of muscles rear of the upper leg)

Lying on your back

Lift and straighten left leg directly above hips

Holding the calf or thigh

Press heel toward ceiling as you pull leg back towards chest

Repeat with the right leg

Glutes

Lying on your back

Cross right over bent left knee

Then bring left knee to chest

Holding on to back of your thigh

Gently pressing right knee wide

Repeat with right leg

Chest

Standing straight

Interlace fingers behind your back as you straighten out your arms, lift your chin

towards ceiling.

Triceps/shoulders

Take left arm overhead

Bend at elbow joint

Extend palm down centre of your back

Gently pulling elbow with opposite hand

Take same arm across the chest

Gently pulling at the elbow joint, to extend through the shoulder

Repeat with the right arm.

Core/ back

Round out your back and then invert it, making a C- shape with your spine

Repeat three times

Then sit back between your heels

Forehead on the mat

Arms extended in front of you, as you lengthen your back

Now, hit yourself on the back.

Advantages of cooling down:

There are two part5s of a cool-down. First a person does al light cardiovascular activity

such as walking to lower the heart rate, body temperature, etc. then static stretching

should be followed. Exercisers should stretch all the major muscle groups for at least 10

to 30 seconds. Some of the benefits of a cool down are listed below:

1. Normal blood circulation: during the cool-down stage, the legs help return the

blood to your heart. Muscle in the legs acts as a pump to bring blood back to the

heart. Hence, cooling down helps in bringing the blood flow in a normal mode.

2. Helps the systems to work efficiently respiration, cardiovascular system,

circulatory system, body temperature and heart rate are gradually returned to

normal by doing cooling down which preventing an irregular beat that may be

life threatening.

3. Preventing injury: the cool down is as instrumental to the prevention of injury as

the warm up, stopping an activity without cooling down will contribute to a

buildup of toxic substances and lactic acid which will cause muscular pain and

stiffness the day after, this can restrict movement and be very painful.

4. Body temperature become normal: during high intensity, exhaustive exercises or

competition the body temperature increases more than 160 degree Fahrenheit. A

good session of cooling down helps in reducing the body temperature to normal

condition.

5. Removal of waste products: when a sports person performs training or takes part

in competition the waste products such as lactic acid, uric acid, phosphate,

sulphate chloride etc. accumulated in the body. An affecting cooling down

reduces the accumulation of such products very rapidly forms the muscle

suitably.

6. Supply of oxygen: appropriate cooling down helps in supplying the blood and

oxygen to muscles, restoring them to the position they were in before performing

training. Along this, recovery becomes fast.

7. Muscle does not remain stiff: by performing cooling down properly muscles do

not remain stiff but get relaxed speedily.

8. Reduces the chances of dizziness or fainting: the most significant function

appropriate cooling down is to reduce the chances of dizziness or fainting. When

exercises stopped spontaneously without taking time to cool down or limber

down, the heart rate slows abruptly (all of sudden) and that blood can pool (blood

to collect) in the lower body (legs and feet), causing dizziness or fainting.

Topic 6 : Isometric and isotonic exercises

Meaning and advantages of isometric exercises: isometric exercises are those exercises,

which are not visible. In fact there are no direct movements, hence they cannot be

observed. It these exercises, work are performed but it is not seen directly. In these

exercises, a group of muscles carry out tension against the other group of muscles. When

these exercises are done, muscles do not change their length. They remain fixed or

constant.

For example, if we push a concrete wall, we will be unable to move it from its place. So

we should not consider it as work. our muscles exert force, while pushing a wall, but we3

see that wor4k is not done. Because works is said to be done when the point of

application of a force moves, or we can say that ------

Work done = force x distance moved in the direction of force.

Advantages of isometric exercises:

It needs less time

It can be done any where

Every muscle can be exercised within a short period of time

It is good to maintain strength by dynamic exercises.

Increased blood flow

Decrease blood pressure

Meaning of isotonic exercises: (done against resistance) *resistance training is a form of

exercises that improves muscular strength and endurance. During a resistance training

workout, you move your limbs against resistance provided by your body weight, gravity,

bands, weighted bars or dumbbells.

The exercise in simple terms relates to muscles contractions. Any exercise in which your

muscle contracts or there is a strain or tension on the muscle is called isotonic exercises.

For example weight lifting. Ninety percent of Gym workout s is isotonic exercises. The

word isotonic is derived from the Greek words ‘iso’ which means equal and ‘tonus’

which means tone; i.e., the word isotonic implies maintaining equal muscle tone. When

you flex your biceps, it is isotonic contraction.

In isotonic exercises the weight that can be lifted 10 consecutive times but not more than

10. This is called 10 repetitions maximum (10 RM’s). The exercises are done in 3 sets of

10 repetitions each. (*RMs = repetitions maximum).

Advantages of isotonic exercise:

1. Isotonic exercise is very useful, not only in helping participants bulk up, but in

providing specific muscle responses that will be useful in a range of athletic and

recreational activities.

2. Isotonic exercise promotes the development of muscle endurance, muscle tone and

muscle strength.

3. These movements have also been shown to improve ligament and tendon strength.

4. Helps in preventing injuries.

ISOTONIC EXERCISES

5. Improve posture and develop joint stability.

6. Isotonic training helps you strengthen a muscle throughout a range of movement.

7. It is also easier to choose sports-specific exercises that mimic movements in your

sport of choice.

8. One of the main benefits of isotonic exercise is that it doesn’t require extensive

equipment. Portable items like dumb ells, kettle bells, medicine balls and other

similar tools are all ways to fit isotonic exercise into any space or environment.

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Questions regarding above topic 5 and 6 are given below:

1. What do you mean by cooling/limbering down? Enumerate the advantages of

cooling down in detail.

2. What is isometric and isotonic exercises and explain its advantages?

3. Write short notes on the following:

Isotonic exercises

Isometric exercises

Cooling down

Stretching exercises of cooling down