st. xavier’s sr. sec. school, chandigarh · 2020-07-17 · wordsworth was his brother. like his...
TRANSCRIPT
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.