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

Class 12 English Worksheet-12

B. WORDSWORTH

B Wordsworth is taken from Naipaul’s collection of short stories titled Miguel Street.

This story is narrated in first person through a boy-child’s perspective. The story

highlights the plight of a ‘poet’ whom the child encounters. The two share a very easy-

going relationship and the child seems to instinctively understand and empathize with the

‘poet’. Narrated in a humorous and fun manner, the story revolves around the themes of

solitude, alienation, admiration, love for nature and the role of the artist in the society.

This story is brought to life through the colloquial language, the rich Caribbean setting

and its exploration of the complex intricacies of human relationship and artistic

expression.

SETTING

MIGUEL STREET

CHARACTERS

NARRATOR-THE BOY

THE POET-B. WORDSWORTH

THE BOY’S MOTHER

B. Wordsworth : Analysis

Taken from a collection of short stories titled Miguel Street, V.S Naipaul’s B.

Wordsworth presents before us a complex relationship between a young boy and a

rather remarkable man which is forged with great ease and simplicity.

Revolving around the themes of identity, alienation, friendship, admiration and the

role of the artist, B Wordsworth is narrated in the first person by a little boy who

comes in contact with a man of the same name. One day, the man appears in the

narrator’s house to ‘watch the bee’s’. He’s smartly dressed, clearly unlike the beggars

who come to his house everyday. The narrator is quick to detect the coldness with

which his mother accosts the man. In contrast to her, the narrator doesn’t judge the

man and talks to him in a friendly manner. Perhaps this ease of reaching out and

communicating with the other enables the narrator-kid to know and understand the life of

an interesting, lonely man and perhaps become the only one to do so.

Wordsworth helps the narrator-kid grow and teaches him important lessons about life

and leisure. The narrator’s strict mother serves as a foil to B. Wordsworth’s

accommodating nature. He lets the boy discover things by himself and even entertains his

idea of placing the pin on water to see what happens next. He teaches the kid to delight

in everyday experiences we take for granted and presents him a fresh pair of eyes with

which to observe and soak in the wonders of the natural world.

Miguel Street, the collection from which the story is taken features many interestingly

odd characters and B. Wordsworth’s is certainly one of them. The characters in the

book often struggle with their identities and, owing to the colonial past of the region,

find themselves shaped by the colonial experience. B. Wordsworth’s story highlights the

alienation of the artist from the society he lives in and tries to come to terms with role

s/he might play in it.

One of the first things the narrator notices about the man is his English which quite unlike

that of his Trinidadian folks. Though he speaks good English, there is a hint of

artificiality about it :

His English was so good, it didn’t sound natural, and I could see my mother was worried.

Black Wordsworth calls himself the ‘greatest poet in the world ‘ and claims that William

Wordsworth was his brother. Like his Romantic counterpart who was an acclaimed

‘Nature Poet“, B. Wordsworth loves to spend time with nature But he isn’t known by

anybody as a poet. Though his marginalized status may be attributed to his color, it is

difficult to state whether he actually writes poems at all.

One cannot help but feel that he’s quite lost about his identity. Parts of his identity seem

to contradict others. He claims to be the greatest poet in the world . Yet we don’t see his

poetry. His poem remains unfinished and he seems to have fallen in an artistic paralysis

after writing the line the past is deep. He dismisses the story he tells the kid after having

narrated it with much passion. He is poet who earns his living by singing Calypso songs.

A lot in him seems to be imitation and he seems have a divided identity.

The setting and the local colour of the story gives it a very distinctive appeal. The

Caribbean setting with its palm and mango trees, the Chancellor Hill, the Race Course

and the Port of Spain, combined with the sights of Miguel Street provide a distinctive

visual appeal to the reader. On the other hand, the colloquial diction helps us ‘hear’ the

language of the people inhabiting the story. Notice this brief exchange between the

narrator’s mother and B. Wordsworth and the effect it produces:

I ran up the steps and shouted, ‘Ma, it have a man outside here. He say he want to

watch the bees. My mother came out, looked at the man and asked him in an unfriendly

way, ‘What do you want?’

The man said, ‘I want to watch your bees.

Wordsworth’s story highlights the alienation of the artist from the society he lives in

and tries to come to terms with role s/he might play in it. B.Wordsworth lives in the

margins. Nobody buys his poems and he doesn’t seem to have any agency in the public

life whatsoever. But he does have a great influence on the personal life of the boy which

results in artistic expression in the form of the boy’s narration. B. Wordsworth’s is a

poetry that is lived, not written. He lives his life like a poem.

The theme of the relationship between art and material wealth is found in the

utterances of B. Wordsworth and the hardships he has to face to eke out a living by

selling his poems for twenty cents and signing Calypso songs. When the narrator’s

mother refuses to buy his poem, his response, though a funny one, has some truth in it :

My mother say she ain’t have four cents.’

Wordsworth said, ‘It is the poet’s tragedy.’

Again, later in the story, we find him unable to be able to believe that material well-being

would be his share even if he wrote the greatest poem in the world :

But you will be the richest man in the world when you write the greatest poem ?’

He didn’t reply.

This silence on his part speaks volumes about the chasm that exists between poetry and

material prosperity.

Whether B. Wordsworth actually writes good poems or whether he is a delusional person

fancying himself a poet is an unimportant question. Such assessment makes the very

mistake which the narrator avoids – of placing a value judgment on B. Wordsworth’s

worth. What is more important is his personal life, the past he’s been through and the

relationship he develops with the boy. When his story about the girl and the child is

taken into account, the line “The past is deep” which he takes a full month to write bears

a completely different meaning rather than when viewed as a disjointed utterance of a

madman.

It is true that B.Wordsworth comes across as a strange person but it is this very

‘strangeness’ which endears him .He cares about the ‘lesser things’ in life and can see

himself as a part of the universe. His lazy loiterings may appear as escapism but if at all,

it is an escape to discovery. This is perhaps what the narrator feels when he lies on the

grass with B.Wordsworth after getting thrashed by his mom, watching the night sky :

I felt like nothing, and at the same time I had never felt so big and great in all my life. I

forgot all my anger and all my tears and all my blows.

Furthermore, he also comes across as a kind person with a great degree of emotional

intelligence. Before his death, he makes the narrator promise to never return after he’s

told him a funny story: of how all he’d said about the poet’s wife was a lie. His voice

breaks in the process. It might be a lie, it might not. What seems to be the case though is

that it was a true story and that he’s lying now. If so, it is actually a profound gesture

he’s making here. B. Wordsworth is undoubtedly a lonely man. He finds a friend in the

young narrator with whom he can share his loneliness and transforms the boy’s outlook

towards life. However, when he knows his end is near, he attempts to erase his

existence from the mind of the young boy by saying that everything he’s ever said is a

lie. After having expressed his credo to perhaps the only person through his story, he tries

to erase his memory from the very person’s mind so as to relieve him from the burden of

missing someone and allow him to explore life in his own terms. In short, he tries to

negate himself for the sake of the other which is perhaps the most profound gesture a

human being can make. This noble gesture of self-effacement carries a note of

sacrifice with it.

The final paragraphs portray a poignant picture of B. Wordsworth’s fate. A year after his

last visit the narrator walks along Alberto Street only to find B. Wordsworth’s hut

replaced by a two-storied building. The mango, the plum and the coconut trees have all

been cut down. The hard, man-made material replaces the living signs of nature and the

last line is an awfully sad one which sums up the life of B Wordsworth:

It was just as though B. Wordsworth had never existed.

This strange story about a ‘strange’ person may appear humorous at first sight but at its

core lies a tragedy of tremendous magnitude: one with a profound lesson that can

radically change one’s outlook towards people, places and the very nature of human

existence.

CHARACTER ANALYSIS

In this B. Wordsworth character analysis, we will analyse the characters of B.

Wordsworth and the young boy.

In B. Wordsworth, we are presented with the most peculiar character – a poet who is

conflicted about his identity. He uses a young boy as a medium to make true whatever he

wished was true about his life, in the time that he spent with the young narrator. Through

his conversations with the boy, we come to know that B. Wordsworth believed himself to

be a great poet working on one of the greatest poems of all times. At the end of the story,

when the poet finally confesses to the young boy that everything he had said about

himself was made up, then our suspicions that the poet was suffering from a deep identity

crisis get confirmed. Perhaps the poet was unhappy with the life he led and harboured in

his heart the deep desire to become the greatest poet of all time. This is why when he

found trusting audience with the young boy, he started speaking about his desires as if

they were a reality. This dissatisfaction that the poet had with his life makes us question

the life of poets in general. B. Wordsworth mentioned that it was the “poet’s tragedy” to

not have his work sold and be given the recognition they deserved. Perhaps this lack of

recognition plagued the poet. Additionally, we also get to discover the artistic paralysis

that B. Wordsworth underwent, unable to produce poetry. This gives us insights into the

creative struggle the process of artistic creation can be.

The other prominent character in the story is the young boy. The boy is a sensitive

individual who lends a patient, compassionate ear to B. Wordsworth. Perhaps it was

because of the young boy’s willingness to listen without judgement that B. Wordsworth

could open up about his deepest desires regarding the kind of person he wanted to be.

However, the young boy believed everything the poet said to him, without adding a pinch

of salt. This makes us understand that the boy was naive and perhaps too trusting for his

own good.

ASSIGNMENTS TO DO

“B. Wordsworth” is a “coming-of-age” story of a little boy. Discuss.

Discuss the themes depicted in the story.

In ‘’B. Wordsworth” Naipaul contrasts two modes of life. Discuss.

B. Wordsworth is a short story explains the unusual relationship between old man

and boy. Discuss.

Was B. Wordsworth an escapist? Discuss

How is the issue of identity reflected in the story?

What does the boy learn from B. Wordsworth?

Discuss the dark humour and symbolism by B. Wordsworth.

What incidents can you cite to prove that the boy liked to be with this poet?

Or

Describe some of the occasions when the two are together as friends.

What are somethings that narrator and B. Wordsworth do together? How does the

world change for the narrator?

What does B. Wordsworth tell the narrator on his deathbed? How does the

narrator respond to B. Wordsworth’s revelation?

Class 12 Physics Worksheet-12

Class 12 CHEMISTRY WORKSHEET-12

SURFACE CHEMISTRY CONTINUED

COLLOIDS

Colloid is a state of matter. Any substance can be brought into the colloidal state by

suitable means. It’s an intermediate state between true solutions and suspension. This

state actually depends upon the particle size. Colloids have a particle size of 1nm to

1000nm.Depending upon the size of the solute particles the solutions can be categorised

as true solution, suspension and colloids.

True solution:

(i) It is homogeneous.

(ii) The diameter of the particles is less than 1 nm.

(iii) It passes through filter paper.

(iv) Its particles cannot be seen under a microscope.

Colloids:

(i) It appears to be homogeneous but is actually heterogeneous.

(ii) The diameter of the particles is 1 nm to 1000 nm.

(iii) It passes through ordinary filter paper but not through ultra-filters.

(iv) Its particles can be seen by a powerful microscope due to scattering of light.

Suspension:

(i) It is heterogeneous.

(ii) The diameter of the particles are larger than 1000 nm.

(iii) It does not pass through filter paper.

(iv) Its particles can be seen even with naked eye.

A colloid is a heterogeneous system in which one substance called dispersed phase is

dispersed in another substance which is called dispersion medium. Colloids may be

combination of different physical states of the dispersed phase and the dispersion medium

(gas in liquid, liquid in solid, solid in gas etc.)

COLLOIDS CAN BE CLASSIFIED IN THREE DIFFERENT WAYS

• ON THE BASIS OF PHYSICAL STATE OF DISPERSED PHASE AND

DISPERSION MEDIUM

• ON THE BASIS OF NATURE OF INTERACTION BETWEEN

DISPERSED PHASE AND DISPERSION MEDIUM

i)Lyophobic sols ii) Lyophilic sols

LYOPHOBIC SOLS:

(i) These colloids are liquid hating.

(ii) In these colloids the particles of dispersed phase have no affinity for the dispersion

medium.

(iii) They are not stable.

(iv) They can be prepared by mixing substances directly.

(v) They need stabilizing agents for their preservation.

(vi) They are irreversible sols.

LYOPHILIC SOLS:

(i) These colloids are liquid loving.

(ii) In these colloids, the particles of dispersed phase have great affinity for the dispersion

medium.

(iii) They are stable.

(iv) They cannot be prepared by mixing substances directly. They are prepared only by

special methods.

(v) They do not need stabilizing agents for their preservation.

(vi) They are reversible sols.

• ON THE BASIS OF TYPES OF PARTICLES OF THE DISPERSED PHASE

i)Multimolecular ii) Macromolecular iii) Associated colloids

1. Multimolecular colloids: The colloids in which the colloidal particles consist of

aggregates of atoms or small molecules. The diameter of the colloidal particle

formed is less than 1 nm.

2. Macromolecular colloids: These are the colloids in which the dispersed particles

are themselves large molecules (usually polymers). Since these molecules have

dimensions comparable to those of colloids particles, their dispersions are called

macromolecular colloids, e.g., proteins, starch and cellulose form macromolecular

colloids.

3. Associated colloids (Micelles): Those colloids which behave as normal, strong

electrolytes at low concentrations, but show colloidal properties at higher

concentrations due to the formation of aggregated particles of colloidal

dimensions. Such substances are also referred to as associated colloids. These

aggregates of soaps or detergents are called micelles.

PREPARATION OF LYOPHILIC AND LYOPHOBIC SOLS

Lyophilic sols are prepared simply by the stirring dispersed phase with dispersion

medium. Examples include sol of starch, gelatin, egg albumin.

Lyophobic sols can be prepared by two types of methods:

DISPERSION CONDENSATION

Mechanical Dispersion Change of Physical state

Bredig’s arc method Chemical method

Peptisation Exchange of solvent

DISPERSION METHOD: Large particles of substances are broken, into smaller

particles in the presence of dispersion medium. They are stabilized by adding some

suitable stabilizer.

1. Mechanical Dispersion: In this method making a colloid by milling a given solid and

the powder produced is dispersed into a given dispersing medium. The colloidal mill

consists of two steel plates nearly touching to each other and rotating in opposite

directions with high speed. The solid particles are turn off to colloidal size and dispersed

in liquid to give colloidal sol.The colloidal graphite printing inks are made by this

method.

2. Electro-dispersion Method: ( Bredig's arc method ): This method is suitable for the

preparation of colloidal solution of metals like gold, silver, platinum etc.

An electric arc is struck between the electrodes of metal immersed in the dispersion

medium [ such as water and alkali].The intense heat of the arc vaporizes some of the

metal, which then condenses to form particles of colloidal size. The water is cooled by

immersing the container in a cold bath.

3.Peptisation: In this method converting a precipitate into a colloidal sol by shaking it

with the dispersion medium, in the presence of small amount of electrolyte. The

electrolyte used is called as peptizing agent.

Example:

(i) Ferric hydroxide yields a sol by adding ferric chloride.

Freshly prepared Fe(OH)3 is shaken with aqueous solution of FeCl3 ( peptising agent) it

adsorbs Fe3+ ions and breaks up into small sized particles of type Fe(OH)3 / Fe3+ .

( i ) Silver chloride can be converted into a sol by adding hydrochloric acid.

CONDENSATION METHOD: In this method in which molecules of the dispersed

phase aggregate(come together) to form colloidal particles.

1. Change Of Physical State: Colloidal solution of certain elements such as mercury and

sulphur are obtained by passing their vapour through cold water containing a suitable

stabilizer such as ammonium salt or citrate.

2. Chemical Methods: It involves chemical reactions in a medium in which the dispersed

phase is sparingly soluble.

( i ) Double Decomposition: A sloe steam of hydrogen sulphide gas is passing through

cold solution of arsenious oxide to form an arsenic sulphide sol. This is continued till the

yellow colour of the sol attains maximum intensity.

As2O3 + 3H2S → As2S3 + 3H2O

(Yellow sol)

(Arsenic sulphide)

( iii ) Oxidation: Passing hydrogen sulphide into a solution of sulphur dioxide to form a

colloidal solution of sulphur

2H2S + SO2 → 2H2O + 3S

( iv ) Reduction: silver/gold/ sol can be obtained by treating dilute solution of silver

nitrate with organic reducing agents like tannic acid.

AgNO3 + Tannic acid → Ag sol.

AuCl3 + Tannic acid → Au sol.

4. Exchange Of solvent: A solution of sulphur/phosphorus in alcohol is poured into

water, a colloidal solution of sulphur/phosphorus is obtained due to low solubility

in water. Sulphur and phosphorus are soluble in alcohol but insoluble in water. So,

an alcoholic solution of sulphur/phosphorus is poured in excess of water in which

it is relatively less soluble.

Class 12 Biology Worksheet-12

CHAPTER-Sexual Reproduction in Flowering Plants

(CONTINUED)

FERTILIZATION- Fertilization in angiosperms is unique. It is called double

fertilization. This is because there are two male gametes (sperms) per pollen tube. One of

the sperm fertilizes the egg cell to form zygote while remaining sperm fuses with two

polar nuclei to form a triploid endosperm nucleus.

IMPORTANT EVENTS IN FERTILIZATION ARE FOLLOWING:

EMBRYO

Embryo develops from the zygote so it is diploid in nature. It is developed at the

micropylar end, where the zygote is situated.

The development of the zygote into an embryo takes place only after certain amount of

endosperm is formed. This is an adaptation to provide assured nutrition to the developing

embryo. The zygote gives rise to the proembryo and subsequently to the globular heart

shaped and mature embryo.

NOTE: Draw well labeled diagram of

a) Various stages of the development of embryo.

b) Dicot embryo and Monocot embryo.

------------------------------------------------------------------------------------------------

Class 12 Maths Worksheet-12

Illustration 15: If f: {5,6,7} → {1,2,3,4} defined by f= {(5,4), (6,3), (7,2)} then find f-1

Solution: We see that range of f is {4,3,2} which is not equal to co-domain{1,2,3,4}

In other words ‘1’ is left unmapped. Therefore f is not onto. Hence f is not invertible.

Illustration 16: Let S= {1,2,3} . Determine whether f: S→S has inverse , if f is defined by f =

{(1,3), (3,2), (2,1)}

Solution: f is invertible because it is one-one as well as onto.

As is clear from the arrow diagram.

Therefore f -1 = { (3,1), (2,3), (1,2) }

Illustration 17: f : X →Y defined on X ={ -1, 0, 1, 2} and Y = { 2,3}

And f(x) =2 for x = -1, 0, 1 and f(2) =3 , Is f invertible?

Solution: Since f(-1) = 2, f(0)= 2, f(1)= 2 and f(2) =3

Each element of x ∈X has a unique image in Y but -1, 0, 1 have the same image.

Therefore f is not one-one. Hence f is not invertible.

INVERTIBLE FUNCTIONS

Let a function f: X→ Y be one-one and onto , It means for every y∈Y there exists at least

one element x∈X such that f(x)=y. Also this element of x is unique because f is one-one.

Then see from the other way round, Every element x∈X has a pre image in Y also.

Therefore we can defined a function , say g, from Y to X such that g(y) = x for all y∈Y

To conclude : if f is one-one and onto function, it is invertible function, and f: X→ Y

Then f-1: Y→ X is called Inverse function of f. So it clear that

(i) Domain of f-1 = range of f

(ii) Range of f-1 = domain of f

1

2

3

1

2

3

Illustration 18: Let f : N → Y be a function defined as f(x) = 4x +3 , where Y = { y: y = 4x+3,

x∈N}. Show that f is invertible. Also find the inverse function.

Solution: To check whether f is one –one or not:

Consider any x1, x2 ∈N such that f(x1) = f(x2 )

⇒ 4x1 + 3 = 4x2 + 3 or x1 = x2 , therefore f is one-one.

To check whether f is onto or not:

f(1)= 4(1)+3 =7 , f(2) = 4(2) + 3 =11, f(3) = 4(3) + 3 = 15 …………………….

Which shows that range of f = Y = co-domain of f . Therefore f is onto. Hence f is invertible.

To find f -1

Let f(x) = y or 4x + 3 = y or x = 𝑦−3

4

Since f is invertible , f -1(y) = x = 𝑦−3

4

Thus the inverse of f is given by f -1(y) = 𝑦−3

4

Illustration 19: Let A = R-{3}, B = R-{1}. Consider the function f: A→B defined by f(x) = 𝑥−2

𝑥−3.

Show that f is invertible and hence find f -1

Solution: To check whether f is one-one or not:

Let x1, x2 ∈ A such that f(x1) = f(x2 )

⇒ 𝑥1−2

𝑥1−3 =

𝑥2−2

𝑥2−3 ⇒ x1 x2 -3x1-2x2 + 6 = x1x2 -2x1 -3x2 + 6

⇒ -3x1 + 2x1 = - 3x2 + 2x2 ⇒ x1 = x2 ⇒ f is one-one.

To check whether f is onto or not:

Let f(x)= y ⇒ 𝑥−2

𝑥−3. = y

⇒ x-2 = xy -3y ⇒ x (1-y) = -3y +2 ⇒ x = −3𝑦+2

1−𝑦

As y ∈R and y ≠ 1, −3𝑦+2

1−𝑦 ∈ R

Also −3𝑦+2

1−𝑦 ≠ 3 because if

−3𝑦+2

1−𝑦 = 3 ⇒ -3y + 2= 3-3y ⇒ 2 = 3, which is impossible.

Thus x = −3𝑦+2

1−𝑦 ∈ A (domain of f) such that

f(x)= f( −3𝑦+2

1−𝑦 ) =

−3𝑦+2

1−𝑦 −2

−3𝑦+2

1−𝑦 −3

= −3𝑦+2−2+2𝑦

−3𝑦+2−3+3𝑦 = y

⇒ every element in B has pre image in A ⇒ f is onto.

Hence f is one-one as well as onto. Therefore, f is invertible.

Now if f(x) = y then x = f -1 (y)

Therefore f -1 (y) = −3𝑦+2

1−𝑦

Illustration 20: Consider the function f: R+ → [-5, ∞) defined by f(x) = 9x2 + 6x-5 , where R+ is

the set of all positive real numbers. Show that f is invertible and find its inverse. Find -1 (43) also.

Solution: To check whether f is one-one or not:

Let x1, x2 ∈ R+ such that f ( x1) = f (x2 )

⇒ 9x12 + 6x1 – 5 = 9x2

2 + 6x2 – 5

⇒ 9 ( x12 – x2

2 ) + 6 (x1 – x2) = 0 ⇒ 9 (x1-x2)(x1+x2) + 6 (x1 – x2) = 0

⇒ 3 (x1- x2 ) {( 3x1 + 3x2) + 2} = 0 ⇒ x1 – x2 = 0 or x1 = x2 ⇒ f is one-one.

To check whether f is onto or not:

As x ∈ R+ , x ≥ 0 ⇒ 9x2 + 6x ≥ 0 ⇒ 9x2 + 6x -5 ≥ -5

⇒ Range of f = [-5, ∞) = co-domain of f .Therefore f is onto. Hence f is invertible.

To Find f -1

Let f(x) = y ⇒ 9x2 + 6x-5 = y or (3x+1)2 -6 = y

⇒ 3x+1 = √𝑦 + 6 or x = √𝑦+6 −1

3

Now f(x)= y and f is invertible, Therefore x = f -1 (y)

Thus the inverse function f -1 : [-5, ∞) →R+ is given by f -1 (y) = √𝑦+6 −1

3

f-1 (43) = √43+6 −1

3 =

7−1

3 = 2

Illustration 21:Let f:R→R be defined by f(x) = 10x +7 , find the function g:R→R such that gof =

fog = IR

Solution: Given f: R→R , f(x)= y ⇒ 10x+7 = y ⇒ x = 𝑦−7

10

consider any arbitrary element y∈R , 𝑦−7

10 ∈ R

Let us define g: R→R by g(y) = 𝑦−7

10 for all y ∈ R

Now (gof)(x) = g {f(x)} = g { 10x+7} = 10𝑥+7−7

10 = x , for all x ∈R

Simililary (fog)(y) = f {g(y)} = f{𝑦−7

10 } = 10 (

𝑦−7

10 ) + 7 = y , for all y∈R

⇒ gof = fog = IR [I is identity function i.e. f(x)=x]

SOLVE YOURSELVES:

1. Let S = {a, b, c} and T = {1, 2, 3}. Find f -1 of the following functions f from S to T ,

if it is defined by

(i) f = { (a,3), (b,2), (c,1) } Ans: Yes f-1 exists, f-1 = {(3,a), (2,b), (1,c)}

(ii) f= { (a,2), (b,1), (c,1) } Ans: No f-1 does not exist.

2. Show that the function f: R→ R defined by f(x) = 2𝑥−1

3 is one-one and onto. Also

find the inverse of the function f. Ans: f-1 (y) = 3𝑦+1

2

3. If A = R –{-3} and B = R-{2} and a function f: A→B is defined by f(x) = 2𝑥+1

𝑥+3 , then

show that the function f is one-one and onto. Hence find f -1 Ans: f-1 (y) = 1−3𝑦

𝑦−2

4. If the function f: R→ R is defined by f(x) = 5x-3 , then find the function g: R→ R such

that gof = IR = fog Ans: g(y) = 𝑦+3

5

5. If f : R→R is a function f(x) = ax –b,a,b ∈ R, a≠ 0,find f -1 Ans: f-1(y) = 𝑦+𝑏

𝑎

6. If f: R- {−3

5 } →R is a function defined by f(x)=

2𝑥

5𝑥+3 , then find f-1 Ans: f-1(y) =

3𝑦

2−5𝑦

7. If f : R+ → [-9,∞) given by f(x) = 5x2 +6x -9, where R+ is the set of all non negative

real numbers. Prove that f is invertible and hence find f-1 Ans: f-1(y) = √54+5𝑦−3

5

MORE ON FUNCTIONS CONTD. IN WORKSHEET-13………..

Class 12 Physical Education Worksheet-11

CHAPTER 2: TRAINING METHODS: TOPIC 3 WARMING UP

MEANING OF WARMING UP:

Warming up usually performed to do an activity in most refined and efficient way. It is a

short term activity and it is done prior to any competition or training. It helps the

sportsperson to prepare physically, mentally and physiologically for any type of training

or competition.

It is process in which muscles are warmed up by running, jogging, and taking some free

hand exercises prior to the training or competition. This preparation before competition

or training is called warming up: the following definitions may help to know more about

warming up.

1. “Warming up is a practice in itself”.

2. “Warming up is done to tone up the body so as to meet the ensuing activity”.

3. “Warming up consists of a series of preparatory exercises either before a training

session or competition.”

4. “Warming up is a preliminary exercise of physical and mental preparation for a

strenuous exertion.”

Types of warming up:

EXERCISES RELATED TO WARMING UP

Methods of warming up:

There are following methods of warming up which are generally used:

Method of warming consists of the following sequences and points:

Types of Warming up

1. Active warming up: in the active

warming up, a sportsman takes part in

various types of physical activities. The

temperature of the body increases up to

required level, jogging and stretching

exercises are included in such type of

warming up. There are two types of active

warming up.

2. Passive warming up: the main aim of

passive warming up is to increase to

body temperature without performing

any physical activity. In passive

warming up the body temperature is

increased usually by external means such

as by wearing heavy uniform, massage,

hot water steam, sun light and hot drinks

etc. however active warming is necessary

for getting good results along with

passive warm up.

General warming up: General warming up usually performed in all

types of activities. This type of warming up includes jogging,

running, jumping, stretching, calisthenics, striding, wind sprints and

other general exercise. It increases coordinative abilities and

flexibility of muscles and joints. It also improves muscle tone.

Specific warming up: in specific warming up, exercises are done

with implements special exercises are performed which have direct

relationship with the activity to be done. Specific types of warming

up differ from activity to activity which means game to game. For

example, a sprinter may take few starts and run for short distance

before the actual competition. A basket ball player may practice for

layup shots or free throws before the competition. This type of

warming up improves the coordinative abilities.

I. Jogging: every athlete should perform jogging or slow running for 5 to 10

minutes to increase the body temperature. For young ones it may be for 3 to

5 minutes.

II. Simple exercise: after jogging the simple exercises should be started from

relax position. it should be simple to complex.

III. Striding: it means running the distance with long strides. These strides are

long i.e. the steps should be stretched out but not too much stretched. Four

to 6 repetitions should be performed.

IV. Stretching exercises: stretching exercise one of the most critical parts of

warm up and an athlete’s performance. A stronger and healthier muscle

responds better to exercise and activities and helps in preventing athletic

injuries.

V. Wind sprints: this is the last part of warming up. It is usually done with

spikes on. In wind sprints the distance of 25 to 30 meter may be covered.

There can be 4 to 6 repetitions depending on age and experience of the

sportsperson.

VI. Warming up with warm water: Warm up with warm water is usually done

in developed countries. Taking shower is also used for getting prepared for

swimming, synchronized swimming, water polo and diving.

VII. Warm up through massage: this method is old method of warming up. It is

used in India by wrestlers to get warm up. Very rare to use now days.

VIII. By Hot drinks: some people take a cup of tea or coffee and get themselves

warmed up, but it not considered a good method. As a matter of fact, it has

been discarded on the basis of scientific experiments.

Advantages of warming up:

1. Increased muscle temperature: the temperature increases within muscles that are

used during a warm-up routine. A warmed muscle both contracts more forcefully

and relaxes more quickly.

2. Increased body temperature: this improves muscle elasticity and improves range of

motion, hence, reducing the risk of strains, muscle pulls etc.

3. Blood vessels dilate: this reduces the resistance to blood flow and lower stress on

the heart.

4. Improve efficient cooling: by activating the heat-dissipation mechanisms in the

body and efficient sweating, an athlete can cool efficiently and help prevent

overheating early in the event or race.

5. Improved range of motion: the range of motion around a joint is increased.

Increasing temperature has also been reported to decrease the stiffness of muscle

fibers during contraction.

6. Improves level of performance: after a complete warming-up, it has been observed

that it improves level of performance. All the involved muscles exert maximum

force with highest speed.

7. Increase flexibility: warming up increased flexibility but, if proper warming-up is

not done then body will be less flexible. After warming-up, we can exert the force

up to maximum reach. (distance)

8. Reduces the anxiety and tension: warm-up is very useful in reducing the anxiety

and tension of sportspersons especially at the time of competition. It is also

advantageous in helping to either reduce or increase the motivational level of

sportsperson.

9. Increase strength: there are much information’s that strength can be increased up

to some extent by proper warming-up.

10. Increases the speed of nerve impulses: warming-up increases the speed of nerve

impulses, which improves and sharpens the reaction time of sportspersons.

TOPIC 4: CONDITIONING:

Meaning of conditioning:

Warming up is a short term activity but conditioning involves a looking and

regular process. In fact, when we perform any activity, we feel fatigue in the

beginning but if we continue that activity regularly, we shall not feel fatigue. In

others words it can be concluded that our body becomes conditioned or our body

becomes modified according to that activity. It means if we do certain activities

regularly in which our various systems are involved, our systems become efficient

and conditioned.

Exercises related to conditioning:

Conditioning exercises are body movements that enhance physical fitness and

reduce the chances of sports injuries. The conditioning programmes may include

weight training, interval training, circuit training, fartlek training, aerobic

exercises, polymeric training and calisthenics exercised etc. types of conditioning

exercises may vary greatly depending of physical fitness goals. These exercises

are adaptable to any level of physical fitness i.e., from novice to experienced

sports persons.

Advantages of conditioning:

The advantages of conditioning are described below:

1. Increased blood circulation: if we perform regular exercises, our blood circulation

increases according to the requirement.

2. Stronger athletes: every sport involves the application of force. This includes just

about every skills involved nm sports such as hitting harder, throwing, blocking,

and spiking.

3. Faster athlete: making an athlete faster is a simple but complex process. Most

coache4s think that running an athlete until he or she throws up breakfast, lunch

and dinner is the best way to make an athlete faster.

4. Power full athletes: a well designed strength and conditioning program will make

an athlete more powerful by utilizing the correct exercises and implementing

polymeric the right way.

5. Confident athletes: the hard work and discipline it takes to do thing in life that you

don’t like doing or the things that are tough make you a better person and athlete.

6. Injury prevention: besides improved performance, the conditioning program is an

important step in injury prevention. Many athletes are not aware that sports

conditioning is a necessity for injury prevention. Conditioning can help develop

the strength, flexibility and agility necessary to protect joints from injury.

7. Avoids second wind: if a beginner starts to run a race, after some time, he will face

second wind because his body is not conditioned but an athlete, whose body is

well conditioned, he will not face second wind.

8. Better performance: after conditioning our all the body systems become efficient.

Various components of physical fitness are improved. So it can be concluded that

better performance can be achieved only after conditioning.

Questions regarding above topic 3 and 4 are given below:

1. What is warming up and explain the advantages of warming up?

2. Differentiate between warming up and conditioning. State any four advantages

of conditioning?

3. What do you mean by warming up discuss the types of warming up?

4. What do you mean by conditioning? Explain the advantages of conditioning in

detail.

Class 12 Computer Science Worksheet-11

Question 1

Caesar Cipher is an encryption technique which is implemented as ROT13 (‘rotate by 13

places’).

It is a simple letter substitution cipher that replaces a letter with the letter 13 places after

it in the alphabets, with the other characters remaining unchanged.

ROT13

A/a B/b C/c D/d E/e F/f G/g H/h I/i J/j K/k L/l M/m

↕ ↕ ↕ ↕ ↕ ↕ ↕ ↕ ↕ ↕ ↕ ↕ ↕

N/n O/o P/p Q/q R/r S/s T/t U/u V/v W/w X/x Y/y Z/z

Write a program to accept a plain text of length L, where L must be greater than 3 and

less than 100. Encrypt the text if valid as per the Caesar Cipher.

Test your program with the sample data and some random data:

Example 1

INPUT: Hello! How are you?

OUTPUT: The cipher text is:

Uryyb? Ubj ner lbh?

Example 2

INPUT: Encryption helps to secure data.

OUTPUT: The cipher text is:

Rapelcgvba Urycf gb frpher gngn.

Example 3

INPUT: You

OUTPUT: INVALID LENGTH

Question 2

Design a program to accept a day number (between 1 and 366), year (in 4 digits) from the

user to generate and display the corresponding date. Also, accept ‘N’ (1 <= N <= 100)

from the user to compute and display the future date corresponding to ‘N’ days after the

generated date. Display an error message if the value of the day number, year and N are

not within the limit or not according to the condition specified. Test your program with

the following data and some random data:

Example 1

INPUT:

DAY NUMBER: 255

YEAR: 2018

DATE AFTER (N DAYS): 22

OUTPUT:

DATE: 12 TH SEPTEMBER, 2018

DATE AFTER 22 DAYS: 4 TH OCTOBER, 2018

Example 2

INPUT:

DAY NUMBER: 360

YEAR: 2018

DATE AFTER (N DAYS): 45

OUTPUT:

DATE: 26 TH DECEMBER, 2018

DATE AFTER 45 DAYS: 9 TH FEBRUARY, 2019

Example 3

INPUT:

DAY NUMBER: 500

YEAR: 2018

DATE AFTER (N DAYS): 33

OUTPUT:

DAY NUMBER OUT OF RANGE.

Example 4

INPUT:

DAY NUMBER: 150

YEAR: 2018

DATE AFTER (N DAYS): 330

OUTPUT:

DATE AFTER (N DAYS) OUT OF RANGE.