ST. XAVIER’S SR. SEC. SCHOOL, CHANDIGARH€¦ · ST. XAVIER’S SR. SEC. SCHOOL, CHANDIGARH Class...

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ST. XAVIER’S SR. SEC. SCHOOL, CHANDIGARH Class 12 English Worksheet-11(Literature) TO BUILD A FIRE There's a bearded man walking through the Yukon wilderness on his way to a mining camp on Henderson Creek. Oh yeah, and there's a half-tame wolf dog following along at his heels. When the man spits into the air, he hears a snap, crackle, and pop. It tells him that it must be really cold out, because his saliva is basically exploding in mid-air. That's downright apocalyptic. The dog's instinct tells it not to travel in such cold, but the man doesn't seem all that concerned. When the man reaches Henderson Creek, he decides to follow it all the way to the camp. For some reason, walking across the ice instead of solid ground strikes him as a good idea. When he takes off his mittens, he's shocked to find his fingers go completely numb in a matter of seconds. As the man continues his journey, he thinks back to a conversation that he had with an older, more experienced man from Sulphur Creek (there seem to be a lot of creeks in the Yukon). He remembers the old-timer telling him that it's a really bad idea to travel alone in temperatures below minus fifty. But the man thinks the old- timer is a wimpy old coot and keeps walking. Ignoring the advice of an older and wiser mentor. The man lacks imagination and tends to overlook the advice. The man plunges through the ice and wets his feet. He's annoyed that he'll have to stop and build another fire. When oh when, he wonders, will he get to sit by a fire and eat bacon with the boys? He builds his second fire under a tree, but when he pulls twigs off the bottom of the tree, he causes snow to fall off the branches and put out his fire. Just his luck!Now his hands are getting really numb, and he needs to quickly build another fire to warm them. By this point, his hands are so frozen that he can only use them as stumps. He's so clumsy he ends up bungling his next fire and putting it out. Now, he realises the gravity of the situation. In desperation, he tries to kill his dog so he can cut it open and warm his hands inside its body. But without his hands, there's no way for the man to kill the dog in the first place, and his attempt to give the animal a killer bear hug fails miserably. With no options left, the man does his best to survive and starts running as hard as he can for the camp. But the place is still hours away, and he quickly runs out of energy.

Transcript of ST. XAVIER’S SR. SEC. SCHOOL, CHANDIGARH€¦ · ST. XAVIER’S SR. SEC. SCHOOL, CHANDIGARH Class...

Page 1: ST. XAVIER’S SR. SEC. SCHOOL, CHANDIGARH€¦ · ST. XAVIER’S SR. SEC. SCHOOL, CHANDIGARH Class 12 English Worksheet-11(Literature) TO BUILD A FIRE There's a bearded man walking

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

Class 12 English Worksheet-11(Literature)

TO BUILD A FIRE

There's a bearded man walking through the Yukon wilderness on his way to a

mining camp on Henderson Creek. Oh yeah, and there's a half-tame wolf dog

following along at his heels. When the man spits into the air, he hears a snap,

crackle, and pop. It tells him that it must be really cold out, because his saliva is

basically exploding in mid-air. That's downright apocalyptic. The dog's instinct tells

it not to travel in such cold, but the man doesn't seem all that concerned.

When the man reaches Henderson Creek, he decides to follow it all the way to the

camp. For some reason, walking across the ice instead of solid ground strikes him as

a good idea. When he takes off his mittens, he's shocked to find his fingers go

completely numb in a matter of seconds.

As the man continues his journey, he thinks back to a conversation that he had with

an older, more experienced man from Sulphur Creek (there seem to be a lot of

creeks in the Yukon). He remembers the old-timer telling him that it's a really bad

idea to travel alone in temperatures below minus fifty. But the man thinks the old-

timer is a wimpy old coot and keeps walking. Ignoring the advice of an older and

wiser mentor. The man lacks imagination and tends to overlook the advice.

The man plunges through the ice and wets his feet. He's annoyed that he'll have to

stop and build another fire. When oh when, he wonders, will he get to sit by a fire

and eat bacon with the boys? He builds his second fire under a tree, but when he

pulls twigs off the bottom of the tree, he causes snow to fall off the branches and put

out his fire. Just his luck!Now his hands are getting really numb, and he needs to

quickly build another fire to warm them. By this point, his hands are so frozen that

he can only use them as stumps. He's so clumsy he ends up bungling his next fire

and putting it out. Now, he realises the gravity of the situation.

In desperation, he tries to kill his dog so he can cut it open and warm his hands

inside its body. But without his hands, there's no way for the man to kill the dog in

the first place, and his attempt to give the animal a killer bear hug fails miserably.

With no options left, the man does his best to survive and starts running as hard as

he can for the camp. But the place is still hours away, and he quickly runs out of

energy.

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He scolds himself for acting so shamefully and decides to meet death with dignity.

With his last spark of brain activity, he imagines himself alongside his camp friends,

discovering his own body the next day. Then he's transported into a warm room

with the old man from Sulphur Creek. He admits to the old-timer that he was wrong

about traveling alone, and then finally croaks.

The dog waits for him to get up out of the snow; but after it smells death on him, the

animal howls into the night sky. When it's finished howling, it forgets about the man

and continues along the creek toward the camp, where it knows there will be a

warm fire and some tasty grub. Man's best friend indeed.

IMPORTANT POINTS TO REFLECT ON

An unnamed man is making his way through the white snow of Alaska. And it's

really, really cold out.

He's not concerned about the cold or the lack of sunlight, but not because he's used

to it. He's actually a chechaquo, or "newcomer" to the Yukon.

The narrator then tells us that the man's "trouble" is that "he is without

imagination" (3).

See, the guy knows the day is cold, but doesn't really spend any time wondering

about how his frail human body will stand up to it. He doesn't seem to grasp how

tiny and ant-like he is in this giant abyss of arctic snow.

Spitting into the air, the man hears a sharp crackle and realizes that his saliva has

frozen before hitting the snow. This means that it must be colder than fifty degrees

below zero.

The narrator tells us that the man is heading for a mining camp on Henderson

Creek, where a bunch of his buddies are waiting for him with a nice fire and some

tasty bacon.

Traveling alongside the man is a native husky, which is closer to a wolf than your

average dog. The husky isn't all that happy about traveling in such chilly weather,

but it stays on the man's heels, hoping that the man will soon stop to make a nice

cozy fire.

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There are nine hours of hiking ahead of the man, so we readers get the sense that

he's a pretty tough dude, even if he doesn't know all that much about the Klondike.

When he finally reaches Henderson Creek, the man starts walking along the ice.

The creek is frozen to the bottom, but there are some underground hot springs that

make little pockets of water in the ice, and it's very dangerous to get your feet wet

when it's so cold out. Did we mention that it's really, really cold?

Always the gentleman, the man decides to send the dog ahead of him.

As expected, the dog breaks through the ice and gets it legs wet. The man helps

get the ice off the animal's feet, and is surprised by how quickly his fingers go

numb when he takes them out of his mittens.

After he stops to build a fire (Title!), the man whips out his half-frozen biscuits

and chows down.

When he gets up, the dog is reluctant to leave the fire, for obvious reasons.

After walking for a while longer, the man breaks through the ice himself and has

to stop and build a fire all over again to dry his boots and warm his feet.

As he builds a new fire, he thinks about an old man from Sulphur Creek who told

him that folks should never travel alone in the Yukon when it's colder than fifty

degrees below zero.

But he thinks the old-timer is a little too "womanish" and gives himself a big pat

on the back for being a "real" man. Of course when he tries to build his next fire,

he can barely grip a twig with his fingers. Yeah, super manly.

The man gets another fire going; but he's made a mistake by building it under a

spruce tree.

When he keeps pulling twigs off the tree, he shakes the thing so that a bunch of

snow falls off its branches and buries his fire. He almost freaks out at his bad luck,

but stays calm and starts to build another fire.

The man has more trouble this time around because his fingers are so numb he

can't pull a single match away from his pack of seventy. He tears one out with his

teeth, but when he tries to hold the lit match to a piece of birch bark, the smoke

goes up his nose and almost makes him cough up a lung.

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For his next attempt, he lights all of his matches at once and just holds them to the

kindling by using his hands as stumps.

The fire kindles, but when the man tries to load some more fuel onto it, he breaks

up the fire with his clumsy hands and scatters the pieces in all directions. They all

go up in smoke, and now the man knows he's in really big trouble.

He starts to wonder if the old-timer from Sulphur Creek might have been right

about this never-travel-alone business.

When it seems like he's out of options, the man gets a crazy idea and starts to look

at his dog as if it were a giant mitten. He thinks that if he can kill the dog, he can

plunge his hands into its body and warm them until the feeling comes back.

Next thing you know, he tackles the dog, only to realize that there's no way he can

kill the animal. He can't use his hands to grab a knife or strangle the thing, so he

gives up and the insulted dog runs forty feet away and stops there to watch the

man.

The man realizes that there's a pretty good chance he's going to die, so he starts

running as fast as he can in the direction of the mining camp.

He feels his body heat up at first and grows optimistic. But then he runs out of gas

and realizes that he'll never make it. He feels ashamed for running around like

some shmuck, so he decides to meet death with dignity.

Lying down in the snow, the man drifts off into sleep.

As he dies, he has a vision of himself with his crowd of buddies discovering his

own body the next day. Then he thinks of the old timer who warned him against

traveling alone, and admits that he was world-class idiot to do so.

The man dies.

The dog doesn't know what's going on at first, but after it catches the smell of

death, it howls for a while and then trots off toward the camp, where it knows it

can get food and have a nice fire. And bacon.

QUESTIONS TO ANSWER

1. How does "To Build a Fire" reflect the philosophy of Naturalism?

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2. In "To Build a Fire," how does the dog’s point of view about the setting differ

from the man’s? Why? Support your conclusions with textual evidence.

3. Why do you suppose the author begins and ends this paragraph with the words "he

was safe" in "To Build a Fire"?

4. Why does the main character not succeed in "To Build a Fire"?

5. How does the conclusion of the story contribute to its overall meaning? Consider

the fates of both the man and the dog in your answer.

6. After the protagonist of "To Build A Fire" drops the matches in the snow, describe

how he finally picks them up and lights them.

7. What is the weather like at day break when the story "To Build a Fire" begins?

What do you think this foreshadows for the rest of the story?

8. Why do you think the protagonist of "To Build A Fire" is referred to as "the man"

as opposed to being given a name?

9. What are the man's character traits in Jack London's "To Build a Fire"?

10. How does "To Build a Fire" by Jack London reflect the philosophy of

Transcendentalism?

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Class 12 Accounts Worksheet-11

REVALUATION OF ASSETS AND REASSESSMENT OF LIABILITIES

At the admission of a partner, assets of the firm are revalued, and liabilities reassessed

because the incoming partner should neither benefit nor suffer because of change in the

value of assets or amount of liabilities on the date of admission.

Revaluation of assets and reassessment of liabilities is done with the help of a new

account called ‘Revaluation Account.’ Sometimes this account is also called as ‘Profit

& Loss Adjustment A/c’. It is a Nominal Account.

Following journal entries are passed for the purpose of revaluation:

i. For Decrease in the value of Assets:

Revaluation A/c …Dr.

To Assets A/c

(Decrease in the value of Assets)

ii. For Increase in the value of Assets:

Assets A/c …Dr.

To Revaluation A/c

(For increase in the value of assets)

iii. For Increase in the value of liabilities:

Revaluation A/c …Dr.

To Liabilities A/c

(For increase in the value of liabilities)

iv. For Decrease in the value of Liabilities:

Liabilities A/c …Dr.

To Revaluation A/c

(For decrease in value of liabilities) [email protected]

Based on above entries, a Revaluation A/c or Profit and Loss Adjustment A/c is

prepared. If the credit side of this account is in excess (credit balance), it reveals

a profit and if the debit side is in excess (debit balance), it will reveal a loss.

Such profit or loss will be divided between the old partners in their old profit-

sharing ratio.

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Following entries are passed for this purpose:

a) When revaluation account shows profit:

Revaluation A/c …Dr.

To A’s Capital A/c

To B’s Capital A/c …Dr.

(Being profit on revaluation credited to

Old Partners’ Capital A/cs in old ratio)

b) When revaluation account shows loss:

A’s Capital A/c …Dr

B’s Capital A/c …Dr

To Revaluation A/c

(Being loss on revaluation debited to

Old Partners’ Capital A/cs in old ratio)

Proforma of Revaluation Account given below:

Dr REVALUATION ACCOUNT Cr

Particulars

To Decrease in the value of assets

To Increase in the value of liabilities

To Unrecorded liabilities

To Profit on Revaluation

(Balancing figure)

transferred to old partners’

capital accounts in old ratio.

Rs. Particulars

By Increase in value of assets

By Decrease in value of liabilities

By Unrecorded assets

By Loss on Revaluation

(Balancing figure)

transferred to old partners’

capital accounts in old ratio.

Rs

.

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ACCOUNTING TREATMENT OF RESERVES AND ACCUMULATED

PROFITS OR LOSSES

At the time of admission, if there is any General Reserve, Reserve Fund or the balance of

Profit & Loss Account appearing in the balance sheet, it must be transferred to Old

Partners’ Capital A/c in their Old Ratio even if the question is silent about this. The

new partner is not entitled to any share of such reserves or profits.

Following journal entries are recorded for this purpose:

a. For distributing Reserves and Accumulated Profits:

General Reserve A/c …Dr.

Reserve Fund A/c …Dr.

Profit & Loss A/c (Credit balance) …Dr.

To A’s Capital A/c

To B’s Capital A/c

(Being accumulated profits transferred to

old partners’ capital A/cs in old ratio.)

b. For distributing accumulated losses:

A’s Capital A/c …Dr.

B’s Capital A/c …Dr.

To Profit & Loss A/c (Debit balance)

To Deferred Revenue Expenditure A/c

To Advertisement Suspense A/c

(Being accumulated losses transferred to

Old partners’ capital A/c in old ratio.) [email protected]

For distributing surplus of Specific Reserves:

The firm may have created some specific reserves like ‘Workmen’s Compensation

Reserve’ or ‘Investment Fluctuation Reserve’ to meet certain future obligations. If

such reserves are more than actual claims that excess balance will be transferred to

capital accounts of old partners in old ratio.

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Following journal entry will be passed for this purpose:

[email protected]

Workmen’s Compensation Reserve A/c …Dr

Investment Fluctuation Reserve A/c …Dr

To A’s Capital A/c

To B’s Capital A/c

(Being surplus in specific reserves transferred to old

Partners’ capital A/c in old ratio.)

Note: Employee’s Provident Fund or Employee’s Saving Account appearing on the

Liabilities side of the Balance Sheet are not distributed among old partners as they

are not reserves but are the outside liabilities payable by the firm.

ACCOUNTING TREATMENT OF INVESTMENT FLUCTUATION RESERVE:

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ACCOUNTING TREATMENT OF WORKMEN COMPENSATION RESERVE:

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JOURNAL ENTRIES FOR REVALUATION OF ASSETS AND LIABILITIES:

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ASSIGNMENT: SOLVE THE FOLLOWING QUESTIONS AFTER GOING

THROUGH THE ABOVE WORKSHEET.

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Page 19: ST. XAVIER’S SR. SEC. SCHOOL, CHANDIGARH€¦ · ST. XAVIER’S SR. SEC. SCHOOL, CHANDIGARH Class 12 English Worksheet-11(Literature) TO BUILD A FIRE There's a bearded man walking

************************************************************

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Class 12 Economics Worksheet-11

TOPIC- BALANCE OF PAYMENTS AND EXCHANGE RATE

Read the text given below and answer the following questions

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P.S- DO ANY FOUR CAUSES AND METHODS TO CORRECT DISEQILLIBRIUM IN THE BALANCE OF PAYMENTS

Very Short Answer Questions (2 marks)

Question 1. Distinguish between autonomous and accommodating capital flows

in the balance of payments .

Question 2. Define balance of trade..

Short Answer Questions (3 marks)

Question 1.Distinguish between balance of current account and balance of

capital account .

Long Answer Questions (6 marks)

Question1- What do you mean by deficit in the balance of payments ?Explain the

factors which give rise to deficit in the balance of payments.

Question 2-Explain any four methods of correcting disequilibrium in the balance of payments of a country..

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Class 12 Maths Worksheet-11

Functions: A given relation becomes a function from X→ Y iff each element of set X has a unique image

in set Y. In other words, there are two characteristics to be seen in a function;

1) Each element of set X has a image in Y

2) No element of set X can have more than one image but two or more elements of X can have the

same image.

Based on these two characteristics, Functions can be categorized into :

One One Function ( Injective Function) Many One Function

If for each element x∈X, there is a single image y∈Y If for more than one elements x1, x2,… ∈ X ,

i.e. for x1 ≠x2 , f(x1)≠ f(x2) There is a single image y∈ Y

i.e. . for x1 ≠x2 , f(x1)= f(x2

Onto Function ( Surjective Function) Into Function

If each element of y ∈Y is the image of at least If there exists at least one element y∈Y which

one element x∈ X i.e. no element is left in set Y is not the image of x∈X i.e. there are one or

more elements left in set Y which are not the

image of any element of X

A function which is one one as well as onto is called Bijective Function.

REMARKS:

If A and B are two non empty finite sets with m and n elements respectively, then

(i) The number of functions from A to B = nm

(ii) The number of one-one functions from A to B = nPm if m≤ n

0 if m >n

(iii) The number of onto functions from A to B = σ (−1)𝑛−𝑟𝑛𝑟=1 nCr rm if n≤m

0 if n>m

(iv) The number of one one onto functions from A to B = m! if m =n

0 if m ≠n

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Illustration 8: Show that f: N→N , defined by f(x)= 2x is one-one but not onto. But f: R→R defined by

f(x)=2x is one-one and onto.

Solution: As we can see, f(1) =2, f(2) = 4, f(3) =6 and so on. That means for x1, x2 ∈ N if x1 ≠ x2 then

f(x1 ) ≠ f(x2) therefore f is one-one function.

Also since there are many elements left in second set which are not the images of any element in first set.

for 1, 3, 5…………. ∈ second set N , there is no pre Image in the first set N , therefore f is not Onto.

N N R R

But in another case if f :R→R then there exists f(x) = 2x or y = 2x or x = 𝑦

2 ∈ domain of f. Hence f is

Onto.

Illustration 9: Show that the greatest integer function (Gint Function) defined on R→ R is neither one-

one nor onto.

Solution: f(x)= [x]

Since f ( 1≤ x <2) = 1 that means all the elements between 1 & 2 have their Gint as 1, therefore f is not

one-one.

Similarly Gint function f(x) = [x] only gives integer as answer therefore all non integers in the second set

will be left unmapped. So f(x) is not Onto also.

1

2

3

4

5

6

1

2

3

4

5

6

1/2

1

3/2

2

5/2

3

1

2

3

4

5

6

Important Recall

The elements of first set i.e. {1,2,3,4,5,6…..}are Domain of f or Df

The elements of second set i.e. {1,2,3,4,5,6….} are Co-Domain of f

The elements of second set that are mapped i.e. {2,4,6,…} are Range of f or Rf

So it is very clear that a given function will be Onto only if Co-Domain =Range

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Illustration 10: Show that the function f: R→ R defined by f(x) = 2x3 -7 is bijective.

Solution:

To Prove one-one: Let a,b ∈ R ( first set) such that f(a) = f(b)

⇒ 2a3 – 7 = 2b3 – 7 or 2a3 = 2b3 or 2(a3 –b3) = 0

⇒ 2 (a-b) (a2 + ab+ b2) = 0 which gives a-b= 0 or a= b

Thus , if f(a) = f(b) gives a=b , it proves that each element has a different image. i.e. f is one-one.

To Prove Onto: Consider any y∈R (co –domain of f )

Then f(x) = y ⇒ 2x3 -7 = y or x3 = 𝑦+7

2 or x = (

𝑦+7

2 )

1

3 ∈ R

Thus for all y∈R (co –domain of f ) , there exists x = (𝑦+7

2 )

1

3 ∈ R (domain of f) such that

f(x) = f ( (𝑦+7

2 )

1

3 ) = 2 { (𝑦+7

2 )

1

3 }3 – 7 = 2 ( 𝑦+7

2 ) – 7 = y

⇒ every element in co domain of f has its pre image in the domain of f.

Therefore f is Onto . Hence f is bijective.

1. Check whether the function f: Z →Z defined by f(x)= x2 is injective or surjective?

Ans: neither injective nor surjective

2. Let I be the set of integers , show that the function f: I→ I defined by f(x) = |x| is neither one-

one nor onto.

3. Let A = {1,2,3}, B= {4,5,6,7} and f: {(1,4), (2,5), (3,6)} be a function from A to B. Show

that f is one-one but not onto.

4. Let f: R→R be defined by f(x) = 1 + x2, check the nature of function. Ans: Many one, Into

5. Let A = R-{2} and B = R-{2}. Show that the function f: A→B defined by

f(x) = 𝑥−1

𝑥−2 is bijective.

6. If the function f: I→ I is defined by f(x) = 2𝑥 + 1, 𝑖𝑓 𝑥 𝑖𝑠 𝑜𝑑𝑑 2𝑥 − 1, 𝑖𝑓 𝑥 𝑖𝑠 𝑒𝑣𝑒𝑛

Find (i) f(3) (ii) f(4) (iii) x if f(x) = -9 (iv) Is this function one-one ?

Ans: (i) 7 (ii) 7 (iii) -4, -5 (iv) No

7. Is the function f: N→N defined by f(m) = m2 + m+2 one-one? Justify your answer. Ans: Yes

8. A function f: R→R is defined by f(x) = | 2x-3 | , Is f one-one ? Is f onto? Ans: No, No

Remember in such a case where

picking up elements is not easy

(because of real number system), The

following method is followed

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Illustration 11: Let f = {(0,4), (2,5), (3,7)}, g = { (4,2), (5,0), (7,2)}

Find (i) domain of f and g (ii) range of f and g (iii) fog (iv) gof

Solution: (i) Domain of f or Df = { 0,2,3}, Domain of g or Dg = {4,5,7}

(ii) Range of f or Rf = {4,5,7}, Range of g or Rg = {2,0}

(iii) fog = f {g(x)} means x values are to be taken from g and their corresponding elements will be

taken from f

Therefore (fog) (4) = f {g(4)} = f(2) = 5

Similarly (fog)(5) = f{g(5)} = f(0) = 4

Also (fog)(7) = f{g(7)} = f(2) = 5

Thus fog = { (4,5), (5,4), (7,5) }

(iv) Similarly gof = {(0,2), (2,0), (3,2)}

Illustration 12: Find gof and fog when f: R→R , g : R→R are defined by f(x) = 8x3 , g(x)= x1/3

Solution: (gof)(x)= g{ f(x)}= g {8x3} = ( 8x3)1/3 = [ (2x)3]1/3 = 2x

(fog)(x)= f{g(x)}= f{x1/3} = 8( x1/3 )3 = 8x

Which also proves that fog ≠ gof

Illustration 13: Let A = R –{7

5 } , B = R – {

3

5 }, functions f: A→B and g: B→A be defined by f(x)=

3𝑥+4

5𝑥−7

.g(x)= 7𝑥+4

5𝑥−3 , Show that fog = IB,gof = IA where IA and IB are identity functions on A and B respectively.

Solution: (fog)(x) = f { g(x)}= f { 7𝑥+4

5𝑥−3 } =

3 ( 7𝑥+4

5𝑥−3 )+4

5 (7𝑥+4

5𝑥−3 )−7

= 21𝑥+12+20𝑥−12

35𝑥+20−35𝑥+21 =

41 𝑥

41 = x , Therefore fog is identity function.

Now (gof)(x) = g { f(x)} = g { 3𝑥+4

5𝑥−7 } =

7 (3𝑥+4

5𝑥−7 )+4

5 (3𝑥+4

5𝑥−7 )−3

= 21𝑥+28+20𝑥−28

15𝑥+20−15𝑥+21 =

41𝑥

41 = x , Therefore gof is also an identity function.

COMPOSITION OF FUNCTIONS

Let f: A→ B and g : B→C be two functions, then the Composite of f and g denoted by gof , is the

function f: A →C defined by (gof)(x) = g { f(x) } for all x ∈ A

Identity Function is the function

which gives same image as the pre

image. i.e. f(x)= x

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Illustration 13: If f: N→N, g: N→N and h : N→R are functions defined by f(x)= 2x, g(y)= 3y+4 and

h(z) = sinz for all x,y,z ∈ N, show that ho(gof) = (hog)of

Solution: ho(gof) and (hog)of are both functions from N to R

Foll all x ∈N , {ho(gof)}(x) = h [ g{f(x)}] = h [ g{2x}] = h [ 3(2x)+4] = h [6x+4] = sin(6x+4)

And now { (hog)of}(x) = {hog}f(x) = {hog}(2x) = h { g(2x)} = h {3(2x+4)} = h[6x+4] = sin(6x+4)

⇒ ho(gof) = (hog)of

Illustration 14: If f : R→R be the signum function defined as

f(x)=

1, 𝑥 > 0 0, 𝑥 = 0

−1, 𝑥 < 0 and g: R→R be the greatest integer function as g(x)= [x] , then determine gof

and fog coincide on (0,1]

Solution: Consider x =1

2 which ∈ (0,1]

Now (gof ) (1

2) = g { f(

1

2 ) } = g {1} = [1] = 1 [ f(x) = 1 for x=

𝟏

𝟐 which is > 0]

Now (fog)(1

2) = f{ g(

1

2 )} = f {0} = 0 [ g(

𝟏

𝟐)= g(0.5) = [0.5] = 0 ]

Therefore fog ≠ gof on (0,1]

SOLVE YOURSELVES

9. If f ={ (2,3), (3,4), (4,5), (5,5)} and g = { (3,7), (4,7), 5,11), (9,11)} , find gof.

[Hint: Same as illustration 11] Ans: { (2,7), (3,7), (4,11), (5,11)}

10. Let R be the set of real numbers , find gof and fog when f: R→R and g : R→R defined by

f(x)= x3-1, g(x) = x2 +2 Ans: (gof )(x)= x6 -2x3 +3 , (fog)(x)= x6 + 6x4+ 12x2 + 7

11. If f: R→R and g : R→R defined by f(x) = 3x2 -2, g(x)= sin 2x , find fog, gof , fof

Ans: (fog)(x) = 3 sin2 2x -2 , (gof)(x)= sin (6x2-4) , (fof)(x) = 27x4-36x2 +10

12. If f(x) = |x| and g(x) = [x] , find (fog) (−5

3 ) Ans: 2

13. If f(x) = 𝑥−1

𝑥+1 , find (fof)(x) Ans:

−1

𝑥

MORE ON FUNCTIONS IN WORKSHEET-12

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Class 12 Physical Education Worksheet-11

CHAPTER 2: TRAINING METHODS: TOPIC 2 CONTINUE

Interval training:

It is training of heart, through endurance training. If you run your heart beats at a faster

rate. “Woldemar Gerschler, a professor at the University of Freiburg in Germany and his

athletes worked closely with Dr. Hans Reindell, a physiologist, and developed interval

Training Method.

The name of the system comes from the “interval” or rest period, between the fast runs.

Gerschier and Reindell this the most important part of the workout, and they controlled it

carefully. Believing that the heart adapted and grew stronger during the interval, they

would not allow runners to being the next repeat until pulse rate had returned to 120 beats

per minute.

Interval training contains several load units of high intensity. (From sub maximal t6o0

maximal) such as short, medium and long interval methods according to the time period

of load.

Short intervals last between 45 to 60 seconds.

Medium intervals last between from 1 to 3 minutes.

Long intervals last between 3 to 5 minutes.

Warm up 400 m Recovery

period 400 m 400 m Recovery

period

Recovery

period

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Time for rest is relatively short. Resting period for short and medium interval last 60 to

90 seconds and for long interval it is approximately half of the time for which lasts one

unit, or until heart rate decreased down to 120 to 130 beats per minute. (The interval

method is not suitable for children and it can be applied to the youth training only with

great care. For an athlete of 400 m following examples can be applicable for this training.

400 m race with 80% speed.

Walking or jogging until his/her heart rate comes down to 120 to 130 per minute.

400 m race with 80% speed.

The repetitions depend upon the experience or capability of an athlete. Recovery period

and workout can be adjusted according to the level of athlete.

Advantages

1. The main aim of interval training is preparation for specific competition load.

2. Interval training has a great influence on cardio-respiratory system and it is the

best way to increase the value of maximal oxygen consumption especially aerobic

performance and capacity.

3. More work out can be performed in short duration

4. The volume of training can be more when using this method.

5. The progress of an athlete can be measured easily.

6. An athlete may able to achieve his peak performance in a very shorter time

because the results of this method are instant.

7. Athletes get fair judgment easily.

Circuit Training:

Circuit training method, was developed by R.E. Morgan and G.T. Adamson in 1953 at

the University of Leeds, England. Circuit training is formal types of training in which an

athlete goes through a series of selected exercises or activates that are performed in

sequence or in a circuit. Circuits can be set up inside gymnasiums, exercise rooms, or

outside on courts and fields. There are usually six to ten stations in a circuit. The athlete

performs a specific exercise at each station and then goes to the next station. The greater

the distance between stations, the greater the degree of cardiovascular conditioning as the

individual runs from one station to the next.

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Advantages of circuit training:

It combines a number of different components of training, thus total fitness s

emphasized.

It provide interesting training environment for the athlete.

The circuit can be modifies to fit the needs of any one group or individual.

It can be adapted within the time constraints of the individual.

The trainee gains good result in a short period.

It does not require long duration to perform exercises.

A number of athletes can do circuit training according to the stations at the same

time.

All body types’ parts can be exercised.

It can be adjusted according to the age, fitness and health of the sportsperson.

In circuit training, progression in all activities is assured.

Procedure of circuit training:

Identify the possible exercise that can be performed with the available equipment.

Identify on paper 3 to 4 circuits of 6 to 10 exercise. In each circuit try to ensure that no

two consecutive exercises exercise the same muscle group e.g. do not have press ups

followed by pull ups.

Exercises as follows:

The following are some examples of circuit exercises.

Arm

Press ups, Bench dips, Pull ups.

Abdominals

Sit ups, (lower abdominal), Stomach crunch, (upper abdominal)

Lower back

Squat jumps, Compass jumps, astride jumps, Step ups.

Arms and legs

Treadmills, squat thrusts, skipping.

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Duration

30 seconds work on each exercise with a 30 seconds recovery between each

exercise.

3 sets with a 2 minute recovery between each set.

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Weight Training:

Weight training is a common type of strength training for developing the strength and

size of skeletal muscles. It uses the weight force of gravity (it the form of weighted bars,

dumbbells or weight stacks) to oppose the force generated by muscle through concentric

() or eccentric contraction.

Sports where strength training is central are bodybuilding, weightlifting, power lifting

and strongman, highland games, shot-put, discus throw, and javelin throw. Many other

sports use strength training as part of their training session e.g. track and field, basketball,

hockey baseball etc. strength training for other sports and physical activities is becoming

increasingly popular.

Generally the following exercises are included in the training schedule.

Squat, leg press, leg curl, bench press, shoulder press, lunging, crunch, leg

extension, pull down, pull up, military press, curl, calf raise, half squat, bent arm

pull over, dead lift.

The golden rule of weight training:

1. Make a proper plan to achieve the desired goals.

2. Concentrate the muscles while exercising. Focus full mental awareness on the

muscle group, which is being exercised.

3. Maintain good rhythm during exercise. Lift slowly 2 seconds for the lift (positive

stroke) and 4 seconds for getting back to start position (negative stroke).

4. Knees and elbows should be soft during most exercises, which mean that the knee

and elbow joints are never fully extended to protect them from injury.

5. Exhale during the positive stroke or exertion and inhale during negative stroke.

6. Start light and then work your way up. Always begin with smaller weights.

7. Start with larger muscles and then work the smaller ones. Bench press before

curls.

8. Rest between sets for 30 to 60 seconds and begin the new set.

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9. Rest 48 hours between workouts to help muscles recover.

10. Take professional help to chalk out your program and to teach you the correct

technique.

11. Warm up at least for 5 minutes before beginning the training session and cool

down after the session.

Question regarding above topic 2 is given below:

1. Explain the following Training methods or write a short note on the following:

Interval Training Method

Circuit Training Method

Weight Training Method.

2. Explain briefly any two methods for developing endurance?

3. Explain the procedure of conducting interval training?