Find the middle term in the expansion of

b) Find the middle term in the expansion of

Solution

We have n = 9 which is odd. Hence there must be 9 + 1 = 10 terms,

which is even. This implies that there are two middle terms. They are

Now,

Again,

Grade XII Mathmatics Importaint Queston with Solution.

a) In an examination paper containing 10 questions, a candidate has to answer 7 questions. If two questions are made compulsory, in how many ways can he choose 7 questions in all? [2]

Solution

If two questions are compulsory, then the candidate has to select 5 questions from the remaining 8 questions. Therefore, he can choose 5 questions from 8 questions in

The Lost Doll

The Lost Doll

              Maria Del Carmen is the only child of Roberto and Rosa Soto. She is beautiful, right, kind and loving child. However, she is sick from the day of her birth. As time passes, she becomes more and more weak and finally she dies when she turns four. Since everyone in the village loves the child, all of them attend her funeral. They bury the child in the cemetery outside the village.

              After some days, Rosa gives Carmen’s clothes and playthings to the priest from another village. She gives them so that she will be able to forget Carmen easily. Moreover, the doctor says that she won’t be able to give birth to another baby after Carmen. But Roberto doesn’t become happy to hear this. He wants to save the things because he still hopes that Rosa will give birth to another child. He consoles her that because Rosa was busy in taking care of Carmen, god didn’t send her another child. Roberto then remembers the doll with which Carmen often used to play and asks Rosa whether she has given that doll too. But Rosa says the doll was not with other things. They search for the doll everywhere but they can’t find it.

              Rosa becomes pregnant and on the first anniversary of the death of Carmen she gives birth to another baby. It was good news for them so the priest also gives the name ‘Evangelina’ to the child which means good news. As Evangelina grows up she looks more and more like Carmen. Her actions and characters are also similar to her sister. The only difference is that Evangelina is healthy. One day, when Evangelina turns four, she asks her mother whether she was sick for a long time back. But the mother says it was not she but her sister was sick. Evangelina insists that she remembers it very well and also asks her auntie about it. She also adds that she had a doll with blue eyes and red dress and she had put it under a big tree in the yard. She then takes them to that place and asks to dig there. When they dig the ground they find the doll there. Rosa can’t believe her eyes and becomes speechless. But when Rosa’s sister asks Evangelina to tell everything about what she remembers, she says that when she was sick the priest prayed with his hand on her head. Then she went to sleep. A real nice man woke her up and took her. But he didn’t allow her to take the doll with her. So, she put the doll under the tree. Rosa becomes shocked when she hears the whole story.

              This is the story of reincarnation or rebirth in which Carmen is reborn as Evangelina. She is not only reborn but remembers everything that happened to her in her previous life.

The House Call

The House Call

It is a day after Christmas, 1903, 9:30 in the evening. A famous German Surgeon, Dr. Emil Braun is sitting in the dining room of his apartment in Berlin. He had performed and supervised difficult surgical operations that day for more than eight hours. So, he is trying to write notes and have dinner also. But he is too tired so he becomes asleep on the table. He wakes up when he hears a doorbell and also hears a girl saying to his wife that her mother is very sick. The doctor then goes to the door and there he sees a thin little girl wearing cotton dress, old shoes and shawl. The girl wants to take the doctor because her mother was dying. Though the doctor was very tired, he becomes ready to make a house call because he is very dutiful.

              The doctor picks up his black bag and goes out in the night. In the light rain he follows the girl but the girl walks very fast in the street. She stops only at each corner for a moment to see if the doctor is coming. The doctor tries to catch up with her to ask few questions but he can’t meet her. The girl takes him through the poorest part of Berlin to an old tenement house. Then she starts to climb the stairs of the house. There also the doctor follows her but could not catch up. Finally they reach the fifth floor. Standing in front of a doorway she says that her mother is in the room. She thanks the doctor and the doctor also thanks her for being obedient daughter and enters the room.

              In the dim light, he sees a woman lying in a bed. He recognizes the woman as Elda who once worked as maintenance staff at the hospital. He also finds she was suffering from pneumonia and gives some medicine. Elda had gone to the country to live with her brother and the doctor didn’t know that she is back. He starts talking to Elda and tells her that her daughter is much bigger whom she had sent the night to call him. But Elda says that she came to the city after her daughter died of flu in September before three months. She also shows the shawl and shoed of the little girl which she has kept to remember her daughter. The doctor becomes very surprised and looks around the room. But he can’t find the girl. When he closely looks at the shoe and shawl he finds them wet too. Elda says that the doctor is mistaken about her daughter. The doctor agrees and doesn’t say anything to Elda about what happened that night and when Elda becomes asleep he comes out of the room.

              The little girl of the story can be taken as the spirit of Elda’s daughter who perhaps hears the praying of her sick mother and comes out of the grave. She takes Dr. Braun to her mother and returns back to the grave.

Fear

Fear

              Fear is a psychological story from Mexico with Armando Gonzalez as its main character. The story examines how baseless fear results in nervousness and how things get worse when people become unnecessarily nervous.

              Armando goes to a bank in Mexico to withdraw 50000 pesos. He has a dream to buy a house with this money. The bank teller asks unnecessary questions and counts the money loudly which helps to increase Armando’s fear. As he leaves the bank he puts his hat on backwards due to nervousness. A number of people look at him and a heavy man looks at Armando twice in the bank.

              Armando starts sweating with fear because he thinks that somebody is going to rob him. His mouth becomes dry and his heart starts beating faster. He holds the wad of money tightly because the amount he had was the whole world to him and his family. As they had many people to feed, the couple has earned the money with great difficulty. Their dream is to buy a house to live which will be a house that they could call their own. It will be the happiest day of their life. But the dream is in danger now because Armando thinks that he could be robbed at any moment and the dream would be stolen from him. He regrets having not taken the cheque.

              As Armando waits for the right bus, his fear increases more when he sees the same heavy man standing next to him. After getting on the bus he finds the heavy man there too, it greatly adds to his fear and horror. He thinks the heavy man and the other three boys talking to him are the members of a street gang and are going to rob him. He has the same feeling when other people in the bus look at him. He thinks that they are looking at him because they know he has money in his pocket. Actually people are looking at him because he has still his hat on backwards. He becomes very nervous and can’t think straight. With this in mind Armando decides to change the bus so that he will be safe from potential robbers.

              To his great surprise, the three boys get off the bus at the same station as Gonzalez. At this, feelings of hot and cold run through his body. He finds himself in an area without buildings nearby. The boys walk in the direction of Armando. He thinks they are after him and cries frantically for help. He goes to an area full of rubbish and junk and stumbles over something. Though he asks the scavengers for help they can’t hear him. The three boys come near him and he weeps like a baby. He asks them to leave a poor and honest man alone. The boys ask him if they can help him, Armando can’t believe his ears because he had thought that they are there to rob him. The boys introduce themselves as students who had come to the city for a football tournament. The boys also explain that they had taken the wrong bus and had to get off.

              After asking the boys many questions, Armando confirms that he is safe. He stops sweating and puts his hat straight. His dream of buying and living in his own house is not harmed.

The Loving Mother

The Loving Mother

              The story The Loving Mother is about a mother’s love for her child. It talks about how a mother’s spirit is not in peace after leaving behind a small child. Even after the death the mother comes back to the child in order to look after her. Since it talks about spirit and ghost it is a supernatural story.

              Shoji Sakota is a pharmacist in Sapporo, a city in northern part of Japan. He lives alone in an apartment behind the drugstore. His wife has died earlier. The building being the same he sometimes works till late. One stormy night Shoji Sakota is busy preparing his annual business report. At about midnight there is a knock at the door. He ignores the knock and goes back to his work. When there is s knock for second time he thinks it could be the wind. The knock is louder next time and he goes towards the door thinking that it could be an emergency. He turns on the light and is surprised to see a young woman standing there. Thinking that it might be a trick to rob him he doesn’t open the door. Rather, he says that the pharmacy will be opened at 8 o’clock next morning.

              But the woman pleads that her daughter needs something immediately. Thinking it to be an emergency he lets her in. A thin, young woman stands in front of Mr. Sakota bending her head. Her dress is worn out and her hair is uncombed. But as she raises her head and looks at Mr. Sakota, it seemed that her eyes are looking through him and not at him. She says that she needs ame for her baby. The doctor gives her ame and she goes her way. For him it was a strange request in the night. Not long after he is back at the desk, he decides to stop working for the night because he can’t remove the image of the strange visitor out of his mind.

              The next two nights the same thing happens. It is strange why she comes at night and not during the day when the shop is open. When she comes for the fourth night the pharmacist’s photographer friend takes some photographs of the woman from a hiding place. When the film is developed, the things of the store are there but not the picture of that woman. When she comes the fifth night they decide to follow her so that they could find out who she was and what she was doing. The woman finds that she is being followed but it doesn’t matter to her. She acts as though she wants them to see where she is going.

              A few blocks away, she enters an old apartment building and disappears through a door at the end of a dark narrow hallway. They go inside and find the switch despite darkness. They see a baby, perhaps eight or nine months old, licking ame on a stick. The child looks happy and satisfied. Beside her a woman lies, appearing to be asleep. They think that it is the same woman and couldn’t be asleep so fast. They think she is perhaps acting. Mr. Sakota goes near her and touches the shoulder. Finding her body cold and lifeless he says she is dead. He looks more closely and finds that she has been dead for a number of days.

“MY HEART LEAPS UP WHEN I BEHOLD”

“MY HEART LEAPS UP WHEN I BEHOLD”

              The poem “My Heart Leaps Up When I Behold” is written by William Wordsworth an English poet and worshiper of nature and simplicity. The poem is based on the recollection of poet’s childhood experience and feelings that bear the stamp of continuity.

              The poem deals with the spontaneous overflow of those powerful feelings and joys as felt by the heart of the poet in his childhood and manhood at the sight of rainbow in the sky and the poet hopes to feel the same in the old age.

              The poet describes the influence of a rainbow upon his heart. According to his words, he feels overjoyed to see it in the sky and his heart leaps up every time he notices a rainbow. He further points out that he used to feel the same joy and happiness when he was a child and he does feel the same experience in his old age. In the absence of such feelings, the poet admits he will prefer death as an alternative. The poem ends with the wish of the poet for his days to be bound with each other by natural piety.

              The poem consists of a well-known paradox “The child is a father of the Man”. It implies that as a child for the first time he felt the joy while looking at the nature in the form of a rainbow and every child does have some kind of experience before he attains manhood. In this regard he is senior to man and therefore the father of the man.

“SPEAKING OF CHILDREN”

“SPEAKING OF CHILDREN”

- By Barbara Holland

Q. Does this essay speak in favour or against having many children? Give reasons.

The essay “Speaking of Children” is written by an American Writer, Barbara Holland. It is an informal piece of writing made lively and effective through the device of conversation. It examines the negative aspects of having more than one child. Hence it speaks against having many children.

              The advantages of parents for having one child are quite obvious. One child is an appendage and it can be outnumbered by parents. It can be carried along on pleasure trips. The most important of all is the privacy, which remains intact. On the contrary, plural children will be the end of advantages and the beginning of disadvantages. They will be counter-culture in the house and the parents will be outnumbered. There will be no place left in the living room because of the toys all over. Long pleasure trips will be shortened. The parents will be obliged to adjust themselves according to new situation. First priority will have to be given to the children and their matters. The house will be at sixes and sevens. Above all, there will be no privacy for the wife and the husband. They will be interfered and interrupted by the children at every possible moment. Surprisingly enough, due to lack of proximity, the husband and wife will be reduced to the state of strangers unless some solution is found out to end the new problem.

              Since the writer has focused on the enlargement of the disadvantages for having plural children. It is clear that she against having plural children.

              Question: Summarize the main idea of this essay in one paragraph.

Write down the second paragraph of the above answer.

“LOOK AT TEACUP”

“LOOK AT TEACUP”

              “Look at Teacup” is a complicated essay with a great deals of hidden meaning to be read in between the lines. The essay abounds with rich as well as vivid description of China dishes especially tea cups and scattered information about the writer’s parents, her relation with mother and her views.

              As for the tea cups, they were made in Czechoslovakia and bought in 1939 by her mother. These cups which have been given to the author have a tiny “Czechoslovakia” stamped on the bottom. Each piece is thin and transparent having the palest water-green shade. One can see thin bands of gold around the edges of the saucer and cup. There is also a band of gold on the inner circle of the saucer. Inside the cup, flowers are depicted in different falling attitudes. It seems that as if someone had scattered a bouquet and the flowers appear to be caught in falling motion. One tends to notice a special significance attached to the cups because frequent references are made throughout the essay. In one place, the writer admits that there is a slur of recollection about the flowers, something imprecise, seductive and foggy, but held together with a bright bolt of accuracy-perhaps a piercing glance from a long dead uncle, whose face, all the features has otherwise faded. In another occasion, she wonders if someone with an important black umbrella had considered the future of teacups. A Prior to that she refers to an English politician his shaking a nation away while furling his black umbrella. Further she alludes to the falling of bodies, bombs and countries. Once can see a thread of associations. They indicate the degeneration that took place in Europe in general and disintegration in Czechoslovakia in particular during the Second World War. The teacups with the painting of falling flowers are relies of the disintegration process that began in Czechoslovakia with Munich Agreement signed on 29 September 1938 by the leaders of UK, France, Germany and Italy. Under this pact, the country was compelled to surrender its Sudetenland to Germany, Neville Chamberlain, the Prime Minister of Britain and his policy of appeasement failed to prevent the war. The umbrella he carried to Munich with him was called as the taint of Munich. The writer seems to suggest that the English politician with an important black umbrella also played a role in the disintegration of Czechoslovakia that is in the fall of Flowers from bouquet.

              The close association between the cups and a country is obvious in many expressions. One can notice it in the following expressions that “the cps was discontinued because a country was discontinued” and a country” lost its pure science of flinging glowers into the sides of teacups. Hence “the cup” stands for the relic and the evidence of the mid-century bonfire that is Second World War.

              The second aspect of the story is concerned with the unusual treatment of marriage, family and mother – daughter relationship. The writer is said to have been married in 1939 at the offing of the Second World War. This helped her escape the magnitude of history by retreating into pragmatism. Hence the writer associates the marriage with the fall of the flowers.

              At one place in the essay, she mentions that her mother’s cello voice was drowned somewhere in the sound of falling flowers, in marriage, in the thought of bombs falling on women with flowers, with teacups. Her marriage was the old bow pulled across the cello followed by the long low moan of another generation. On account of such association, the writer uses the word “fall” as the synonym of marriage and refuses to marry at all. Her announcement “We don’t get married anymore” indicates that she is not alone in having such interpretation. Likewise, one can see the similar treatment given to the concept of family and mother-daughter relationship. For the mother, family is the most important thing in the world where as for the daughter, the writer; the work is the most important thing. In spite of such an opinion, mother’s voice sounded a farewell, the first of all those good-byes mothers say to their daughters. She seemed to know that family and separation would always go together. Mothers and daughters are bound to say good-bye to one another. Their relationship ends with parting. The writer’s mother illustrates the same point by saying that they did not have any emotional relationships with their mothers.

“A WORN PATH”

“A WORN PATH”

              “A Worn Path” is the story about an old Negro woman, Phoenix Jackson who undertakes a long hazardous journey from her country area up to city. She does it to fetch medicine for her grandson suffering from chronic throat trouble. It is written by An American novelist, Eudora Welty. She takes the readers into old phoenix’s mind with great delicacy and discloses her firm dignity. The story is filled with such minute details about various obstacles overcome by Jackson that it gives the impression of a story of heroism. During a Christmas time Phoenix Jackson leaves the country for the city with dreadful cold around. Being rather old and small, she walks along a path slowly through the pinewoods. She comes across various obstacles till she reaches the hospital for medicine. The first obstacle that old woman of about hundred years old encounters is the frozen earth in front of her. While tapping it with a thin small care, she moves ahead. Because of her shoe-laces trailing along from her unlaced shoes. She is about the stumble down at one place.

              Since, it is a journey through pinewood. She should be quite careful so as the avoid snakes and wild animals on the path. So switching at the brush with her cane, she manages to keep out of the obstacles one after another. The path leads her up hill. No sooner does she pass this obstacle, she is caught by a thorny bush. Once she stands free of it, she finds another one ahead of her. This time it is log across the creek and she has to walk on it with balanced steps. At this juncture she speaks to herself that she is not as old as she thinks. This reminds the readers of an Egyptian myth of bird phoenix that consumers itself by fire after every five hundred years and rises renewed from its own ashes. Likewise phoenix Jackson by undertaking the painful and hazardous journey rejuvenates herself every now and then.

Thus obstacles continue to appear all along her path. At one place, she has to move through a barbed wire fence. Then she passes through a failed of dead corn, a maze. In one place, she mistakes a scarecrow for a ghost. A dog also knocks her down. On the way she meets a white man and diverts his attention to a dog so that she can pick up a nickel that has fallen off his pocket. Finally she reaches the hospital, takes medicine for the grandson and comes out with a nickel given by an attendant. She decides to buy a windmill for the grandson. Now her steps begin on the stairs, going down. The story may have allegorical and symbolical reference for the movement of the black against the violation of their rights.

THE THREE DAY BLOW

THE THREE DAY BLOW

              “The Three Day Blow” is a story with an analogy between the three day blow and the mental ordeal of the protagonist Nick. The story, which is written by an American writer Ernest Hemingway, traces a movement from conflict, through separation and suffering to reconciliation. It conveys the fullness of a formal ritual.

              It is the story of Nick Wemedge who intended to marry Marjorie. In order to get married with her, it was necessary for him to get back home to find a job and earn money. That was his original plan in the beginning and later he decided to stay in Charlevoix all winter so that he could be near Marge. He made a plan to go to Italy with her, visiting different places while having a lot of fun together. Unfortunately they had to break away and his plans went astray. All of a sudden, their relation came to an end. Marjorie’s mother could be responsible for it because she was regarded as being terrible. Nick was grieved to realize that he had lost her. He felt that she was gone and he had sent her away. He had no hope to see her again. The separation between Nick and Marjorie seemed to have been the outcome of conflict between Nick and Marjorie’s mother. It caused him to have a mental strain.

              In such an agony, he happened to visit the cottage of Bill when the first autumn’s storm broke out. The terrible weather condition reflected the mental agony of Nick. Being struck with grief due to the separation, he got into the cottage of Bill with a view to spend three days of his time three during the terrible wind blow. Bill was pleased to have his company. Both of them got into a long pastime activity while drinking wine and having conversation on different matters ranging over different topics such as drinks, baseball, and writing. Nick’s break up with Marjorie etc. Bill evidently looked happy for he had negative approach towards the married life. He held the view that a man is absolutely bitched and done for once he is married. He referred to Nick’s break up as a wise act. Nick was obliged to confess the matter with a tragic tone. In course of the conversation, Bill casually mentioned the possibility of Nick’s getting into it again. Nick had never thought about it. It had seemed so absolute. It made him feel better. It brought about a sudden drastic change in his way of thinking. He found himself on high spirits. He felt happy and lighter. According to the writer, nothing was finished and ever lost and also there was always a way out.

              With a new spirit, Nick suggested that they should take the guns, go down to the point and look for Bill’s father. Soon they were seen moving across the meadow towards Bill’s father. Nick was no more in a tragic mood and the wind blew everything out of his mind. This story ends with Nick being reconciled to the loss of his beloved. One can also interpret the happy ending of the story as the hint and hope of reconciliation between Nick and his beloved.

              As for the rhetorical strategy, the weather condition as described in the story presents a redaction and analogy of Nick’s suffering. The whole setting with story wind around acts as a stage with separation at one end and the reconciliation at the other's end. Being a dramatic story, it is presented in a sequence of approximately seven scenes: drinking wine, chat about baseball, discussion about literary works, habit of drinking, activities in Kitchen, view about marriage as well as Nick’s love affair with Marjorie and finally the scene of reconciliation or change of attitude.

“THE POPLAR TREE”

“THE POPLAR TREE”

- By William Cowper

“The Poplar Field” is a poem remarkable for its celebration of the rural and it is a nostalgic poem. It was written by William Cowper in a second half of the eighteenth century. The poem is based on the recollection of the poplar field in whose shade the poet passed his time listening to the melody of the blackbird. Now all the trees have been cut down. There is neither shade nor the whispering sound of the trees. The wind and the rustling song of the leaves are distant things of past. Twelve years have passed since he took a look of his favorite field. Now the trees are lying in the grass, providing seats to the people around. One can no more hear the song of the blackbird in the particular place for it has flown to another shelter. The poet is struck with grief because of it and feels that he will be dead soon before another grove will appear in the old place. The reference to his death in the near future vindicates the adverse effect of deforestation on him. Moreover it seems to suggest that it does not take as much time for deforestation as it does for reforestation. In the last stanza, he strikes the philosophical note by declaring that life is short but the pleasures of man are shorter than life. It makes the readers feel that the pleasures given by nature are unparalleled and unfortunately man himself is responsible for the destruction of these unforgettable pleasures.

              This poem can be considered as a defense of nature conservation. It shows how the conservation brings joy through the melody of birds, shade and cool wind. On the contrary, the destruction of nature deprives the man of all the pleasures for decades. There can be neither pleasant wind nor shade nor the melodious song of the birds within his reach. In the absence of nature around, the lovers of nature will be low-spirited and wish themselves dead instead of living in a polluted atmosphere. Such an atmosphere and peace will not be suitable for such living things that find peace and tranquility in the lap of nature. Moreover, the poem clearly shows the link between the deforestation and life. In other words, the destruction of nature implies the destruction of pleasures of man, ultimately leading towards the destruction of mankind.