2016-10-22

CBSE Previous Year Question Papers Class 10 Science SA2 Outside Delhi 2016

Time allowed: 3 hours                                                                                        Maximum marks: 90
General Instructions:

The Question Paper comprises two Sections, A and B. You are to attempt both the Sections.

All questions are compulsory.

There is no choice in any of the questions.

All questions of Section-A and all questions of Section B are to be attempted separately.

Question numbers 1 to 3 in Section A are one mark questions. These are to be answered in one word or in one sentence.

Question numbers 4 to 6 in Section A are two marks questions. These are to be answered in about 30 words each.

Question numbers 7 to 18 in Section A are three marks questions. These are to be answered in about 56 words each.

Question numbers 19 to 24 in Section A are five marks questions, these are to be answered in about 70 words each.

Question numbers 25 to 33 in Section B are multiple choice questions based on practical skills. Each question is a one mark question. You are to select one most appropriate response out of the four provided to you.

Question numbers 34 to 36 in Section B are two marks questions based on practical skills. These are to be answered in brief.

SET I

SECTION A
Question.1. Write the name and structure of an alcohol with three carbon atoms in its molecule.
Answer. Name of an alcohol: Propanol


Question.2. What happens when a mature spirogyra filament attains considerable length?
Answer. When a mature spirogyra filament attains considerable length, it breaks up into smaller fragments or pieces, and each fragment grows into a new filament or individual.

Question.3. The depletion of ozone layer is a cause of concern. Why?
Answer. The depletion of ozone layer is a cause of concern because ozone shields the surface of the earth from harmful ultraviolet radiations coming from the Sun. These radiations are very harmful and can cause skin cancer and other health problems in human beings. Moreover ozone protects the ecosystem from damage.

Question.4. Name the type of mirrors used in the design of solar furnaces. Explain how high temperature is achieved by this device.
Answer. Concave mirrors are used in the design of solar furnaces.

When a solar furnace is placed at the focus of a large concave mirror (called reflector), it focuses a parallel beam of light on the furnace, as a result a temperature is achieved after some time.

Question.5. “What was Chipko Andolan”? How did this Andolan ultimately benefit the local people and the environment?
Answer. Chipko Movement. Chipko Movement is an example of contribution of common people towards the conservation of forests. The Chipko Movement also called ‘Hug the tree’ movement originated from an incident in a remote village called ‘Reni’ in Garhwal (Himalayas), where the people of this village clasped the tree trunks with their arms to protect them from being cut down by a contractor’s workers. The people acted this way because they knew that this mass deforestation would spoil their healthy environment. The forest trees were thus saved.

The Chipko Movement quickly spread across all the communities and helped in the conservation of forests and thus helped in safeguarding the environment.

Question.6. “Burning of fossil fuels results in global warming”. Give reasons to justify this statement.
Answer. When fossil fuels (coal and petroleum based fuels like petrol, diesel etc.) are burnt, they produce C02, CO, water vapours, S02, oxides of nitrogen.

Though C02 is not a poisonous gas but it is a green house gas which traps sun’s heat energy falling on the earth. The burning of more and more of fossil fuels is increasing the amount of carbon dioxide in the atmosphere causing increased greenhouse effect leading to global warming.

Question.7. Write chemical equation of the reaction of ethanoic acid with the following:
(a) Sodium; (b) Sodium hydroxide; (c) Ethanol
Write the name of one main product of each reaction.
Answer.


Question.8. An aldehyde as well as a ketone can be represented by the same molecular formula, say C3H6O. Write their; language of science.
Answer.


They are called isomers because both have same molecular formula but different structural formula (having different functional groups).

Question.9. An element ‘X’ belongs to 3rd period and group 16 of the Modern Periodic Table.
(a) Determine the number of valence electrons and the valency of ‘X’.
(b) Molecular formula of the compound when ‘X’ reacts with hydrogen and write its electron dot structure.
(c) Name the element ‘X’ and state whether it is metallic or non-metallic.
Answer.

Question.10. An element ‘X! has mass number 35 and number of neutrons 18. Write atomic number and electronic configuration of ‘X’. Also write group number, period number and valency of ‘X’.
Answer. ‘X’

Mass number 5= 35 No. of neutrons = 18

Atomic number of X = Mass number – Number of neutrons = 35 – 18 = 17

K L M

Thus, electronic configuration of X = 2, 8, 7

Group number = 17th    Period number = 3rd

Valency = 8-7 = 1

Question.11. Define reproduction. How does it help in providing stability to the population of species?
Answer. The production of new organisms from the existing organisms of the same species is known as reproduction. It is essential for the survival of a species on earth. It helps in replacing the lost section of the population due to death and various other causes.

Populations of organisms live in well defined places called niches in the ecosystem using their ability to reproduce.

Reproduction involves DNA copying which is the source of information for making proteins thereby controlling body design.

These body designs allow the organism to use a particular niche for the stability of the population of a species.

Minor variations may also lead to the stability of the species.

Question.12. Explain the term “Regeneration” as used in relation to reproduction of organisms. Describe briefly how regeneration is carried out in multicellular organisms like Hydra.
Answer. Regeneration is a mode of asexual reproduction in some organisms. The process of getting back a full organism from its body parts is called regeneration. The simple multicellular animals like hydra and planaria show regeneration.
Regeneration in hydra:

If the body of hydra gets cut into a number of pieces, then each body piece can regenerate into a complete hydra by growing all the missing parts.

The regeneration of an organism from its cut body part occurs by the process of growth and development.

The cells of cut body parts divide rapidly to make a ball of cells.

The cells then become specialised to form different types of tissues which again form various organs and body parts.

Question.13. (a) List two reasons for the appearance of variations among the progeny formed by sexual reproduction.
(b)

(i) Name the part marked ‘A’ in the diagram.
(ii) How does ‘A’ reach part ‘B’?
(iii) State the importance of part ‘C.
(iv) What happens to the part marked ‘D’ after fertilisation is over?
Answer. (a) The appearance of variations among the progeny formed by sexual reproduction is due to the following reasons:

(i) Sexual reproduction takes place by the combination of two germ cells produced by two different individuals. Fusion of the male and female gametes.

(ii) Each time zygote is formed by the new combination of variants.

(b) (i) A => Pollen grains .

(ii) Pollen grains, i.e., ‘A’ reach part ‘B’, i.e., stigma of the carpel by the process of pollination.

Pollination is carried out by insects (like bees, butterfuly, etc.), birds, wind, water, etc.

(in) ‘C’ => Pollen tube Pollen tube grows downward through the style towards the female gamete in the ovary. Pollen tube helps the male gamete reach the egg or ovule (female gamete).

(iv) ‘D’ => Fertilised egg or Zygote . The fertilized egg (or zygote) divides several times to form an embryo within the ovule.

Question.14. How does Mendel’s experiment show that traits are inherited independently?
Answer. See Q. 21(F), 2015 (I Outside Delhi).

Question.15. “Two areas of study namely ‘evolution’ and ‘classification’ are interlinked”. Justify this statement.
Answer. Classification of organisms is based on relative similarities and differences in their internal and external structures. Similarities among organisms will allow us to group them and study the groups and classify them. Some basic characteristics will be shared by most organisms. The more characteristics the two species will have in common, the more closely they are related. The more closely they are related, the more recently they have had a common ancestor. So we can say that classification of a species is in fact a reflection of their evolutionary relationship.

Question.16. The image of an object formed by a mirror is real, inverted and is of magnification -1. If the image is at a distance of 40 cm from the mirror, where is the object placed? Where would the image be if the object is moved 20 cm towards the mirror? State reason and also draw ray diagram for the new position of the object to justify your answer.
Answer.

Question.17. Describe an activity to show that the colours of white light splitted by a glass pr ism can be recombined to get white light by another identical glass prism. Also draw ray- diagram to show the recombination of the spectrum of white light.
Answer. See Q. 17, 2016 (III Delhi).

Question.18. The activities of man had adverse effects on ail forms of living organisms in the biosphere. Unlimited exploitation of nature by man disturbed the delicate ecological balance between the living and non-living components of the biosphere. The unfavourable conditions created by man himself threatened the survival not only of himself but also the entire living organisms on the mother earth. One of your classmates is an active member of ‘Eco-club’ of your school which is creating environmental awareness amongst the school students, spreading the same in the society and also working hard for preventing environmental degradation cf the surroundings.
(a) Why is it necessary to conserve our environment?
(b) State the importance of green and blue dust-bins in the safe disposal of the household waste.
(c) List two values exhibited by your classmate who is an active member of Eco-club
of your school.
Answer. (a) It is necessary to conserve our environment because of the following reasons:

(i) To save natural resources like air, water and soil from pollution which are essential for our survival.

(ii) To maintain ecological balance in nature.

(iii) The environment provides us fresh air to breathe, a number of useful products such as wood, paper, medicines, etc. The ozone layer of the environment also protects us from harmful ultraviolet radiations from the sun.

(b) Green dustbins are used for biodegradable wastes, and Blue dustbins are used for non-biodegradable wastes.
Importance of two types of dustbins:

(i) Disposal of wastes after separating them into biodegradable and non- biodegradable wastes in separate dustbins and treating wastes properly before dumping in landfills.

(ii) Segregation of biodegradable and non-biodegradable wastes occur without wasting time and energy.

(c) Values: Cooperative spirit, concern about environment, civic sense, sensitive human being.

Question.19. A carbon compound ‘P’ on heating with excess cone. H2S04 forms another carbon compound ‘Q’ which on addition of hydrogen in the presence of nickel catalyst forms a saturated carbon compound ‘R’. One molecule of ‘R’ on combustion, forms two molecules of carbon dioxide and three molecules of water. Identify P, Q and R and write chemical equations for the reactions involved.
Answer.

Question.20. What is placenta? Describe its structure. State its functions in case of a pregnant human female.
Answer. Placenta. It is a special tissue that helps human embryo in obtaining nutrition from mother’s blood. It serves as a link between the mother’s body and the baby.

Structure and function. After fertilisation, zygote is formed which develops into an embryo. The embryo gets nutrition from the mother’s blood with the help of a special tissue called placenta. This is a disc which is embedded in the uterine wall. It contains thousands of villi on the embryo’s side of the tissue, on the mother’s side are blood spaces, which surround the villi. This provides a large surface area for glucose, nutrients and oxygen to pass from the mother to the embryo. In this way, embryo gets its nutrition. The wastes produced by the foetus are also removed through the placenta. It also functions as an endocrine gland and secretes hormones necessary for maintaining pregnancy.

Question.21. Define evolution. How does it occur? Describe how fossils provide us evidences in support of evolution.
Answer. Evolution. Evolution is the sequence of gradual changes which take place in the primitive organisms over millions of years in which new species are produced.
How it occurs?

It is through the constant process of evolution taking place in the organisms since the origin of life that such an enormous variety of plants and animals have come to exist on this earth at present.

There is an inbuilt tendency to variation during reproduction due to errors in DNA copying and as a result of sexual reproduction.

Relationship between fossils and evolution:

Fossils are the remains of impressions of dead plants or animals which died millions of years ago. The study of fossils helps us to know about the evolution of species. Fossils tell us how new species are developed from the old. Fossils provide evidence of evolution by revealing characteristics of past organisms and the changes that have occurred m these organisms to give rise to present organisms Therefore, fossils have an importance in deciding evolutionary relationship.

For example, a fossil called Archaeopteryx has feathered wings like birds but teeth and tail like reptiles hence suggesting that birds and reptiles had a common ancestor.

Question.22. It is desired to obtain an erect image of an object, using concave mirror of focal length of 12 cm.
(i) What should be the range of distance of an object placed in front of the mirror?
(ii) Will the image be smaller or larger than the object? Draw a ray diagram to show the formation of image in this case.
(iii) Where will the image of this object be, if it is placed 24 cm in front of the mirror?
Draw a ray diagram for this situation also to justify your answer.
Show the positions of the pole, the principal focus and the centre of curvature in the above ray diagrams.
Answer. In a concave mirror an erect image w ill be obtained when the object is placed between pole and focus ; of the mirror.

Focal length, f = 12 cm

(i) Therefore, the range of object distance is between 0 cm to <12 cm (from zero to less than 12 cm).

(ii) Image formed wall be magnified, i.e., larger than the object.

(iii) If the object is placed at 24 cm in from of the mirror, it means that object is placed at 2f, i.e., at the centre of curvature (at C) of the mirror.

The real, inverted and same size (of the object) image will also be formed at 24 cm.

Question.23.(a) Define optical centre of a spherical lens.
(b) A divergent lens has a focal length of 20 cm. At what distance should an object of height 4 cm from the optical centre of the lens be placed so that its image is formed 10 cm away from the lens. Find the size of the image also.
(c) Draw a ray diagram to show the formation of image in above situation.
Answer. (a) Optical centre of the lens. It is a point within the lens that lies on the principal axis through which avay of light passes undeflected.

Question.24. What is atmospheric refraction? Use this phenomenon to explain the following natural events.
(a) Twinkling of stars (b) Advanced sun-rise and delayed sun-set
Draw diagrams to illustrate your answers.
Answer. Atmospheric refraction. The refraction of light caused by the earth’s atmosphere having air layers of varying optical densities is called atmospheric refraction.

(a) Twinkling of stars. See Q. 7, 2014 (III Delhi).

(b) Advanced sun-rise and delayed sun-set. See Q. 4, 2011 (I Outside Delhi).

It is also due to atmospheric refraction that we can still see the sun for about 2 minutes even after the sun has set below the horizon. At sunset, the apparent position of the sun is visible to us and not the actual position because of the bending of light rays effect.

So, the time from sunrise to sunset is lengthened by about 2 + 2 = 4 minutes because of atmospheric refraction.

SECTION B
Question.25. A student puts a drop of reaction mixture of a saponification reaction first on a blue litmus paper and then on a red litmus paper. He may observe that:
(a) There is no change in the blue litmus paper and the red litmus paper turns white.
(b) There is no change in the red litmus paper and the blue litmus paper turns red.
(c) There is no change in the blue litmus paper and the red litmus paper turns blue.
(d) No change in colour is observed in both the litmus papers.
Answer. (c)

Question.26. For preparing soap in the laboratory we require an oil and a base. Which of the following combination of an oil and a base would be best suited for the preparation of soap?
(a) Castor oil and calcium hydroxide (b) Turpentine oil and sodium hydroxide
(c) Castor oil and sodium hydroxide (d) Mustard oil and calcium hydroxide
Answer. (c)

Question.27. In the neighbourhood of your school, hard water required for an experiment is not available. Select from the following groups of salts available in your school, a group each member of which, if dissolved in distilled water, will make it hard:
(a) Sodium chloride, calcium chloride (b) Potassium chloride, sodium chloride
(c) Sodium chloride, magnesium chloride (d) Calcium chloride, magnesium chloride
Answer. (d)

Question.28. A student while observing an embryo of a pea seed in the laboratory listed various parts of the embryo as given below:
On examining the list the teacher remarked that only three parts are correct.
Select three correct parts from the following list: 1
(a) Testa, Radicle, Cotyledon (b) Tegmen, Radicle, Micropyle
(c) Cotyledon, Plumule, Testa (d) Radicle, Cotyledon, Plumule
Answer. (d)

Q.29. If you are asked to select a group of two vegetables, out of the following, having homologous structures which one would you select?
(a) Carrot and radish (b) Potato and sweet potato
(c) Potato and tomato (d) Lady finger and potato
Answer. (a)

Question.30. To determine the approximate value of the focal length of a given concave mirror, you focus the image of a distant object formed by the mirror on a screen. The image obtained on the screen, as compared to the object is always:
(a) Laterally inverted and diminished (b) Inverted and diminished
(c) Erect and diminished (d) Erect and highly diminished
Answer. (b)

Question.31. Suppose you have focused on a screen the image of candle flame placed at the farthest end of the laboratory table using a convex lens. If your teacher suggests you to focus the parallel rays of the Sun, reaching your laboratory table, on the same screen, what you are expected to do is to move the:
(a) lens slightly towards the screen (b) lens slightly away from the screen
(c) lens slightly towards the Sun (d) lens and screen both towards the Sun
Answer. (a)

Question.32. In your laboratory you trace the path of light rays through a glass slab for different values of angle of incidence (∠i) and in each case measure the values of the corresponding angle of refraction (∠r) and angle of emergence (∠e). On the basis of your observations your correct conclusion is:
(a) ∠i is more than ∠r, but nearly equal to Ze
(b) ∠i is less than ∠r, but nearly equal to ∠e
(c) ∠i is more than ∠e, but nearly equal to ∠r
(d) ∠i is less than ∠e, but nearly equal to ∠r
Answer. (a)

Question.33. In the following ray diagram the correctly marked angles are:

(a) ∠i and ∠e (b) ∠A and ∠D
(c) ∠i, ∠e and ∠D (d) ∠r, ∠A and ∠D
Answer. (d)

Question.34. A student adds a spoon full of powdered sodium hydrogen carbonate to a flask containing ethanoic acid. List two main observations, he must note in his note book, about the reaction that takes place. Also write chemical equation for the reaction.
Answer. When sodium hydrogen carbonate is added to a flask containing ethanoic acid, then

brisk effervescence will be formed because of CO2 gas escaping from the reaction mixture.

evolution of colourless and odourless gas. Some amount of heat is evolved during the reaction.

Question.35. A student is observing a permanent slide showing sequentially the different stages of asexual reproduction taking place in yeast. Name this process and draw diagrams of what he observes in a proper sequence.
Answer. The process of reproduction in yeast is budding.

Question.36. An object of height 2.5 cm is placed at a distance of 15 cm from the optical centre ‘O’ of a convex lens of focal length 10 cm. Draw a ray diagram to find the position and size of the image formed. Mark optical centre ‘O’, principal focus F and height of the image on the diagram.
Answer.

SET II

Except for the following questions, all the remaining questions have been asked in Set-I.
SECTION A
Question.1. Write the name and structure of an alcohol with four carbon atoms in its molecule.
Answer. Name of an alcohol: Butanol

Question.2. What are those organisms called which bear both the sex organs in the same individual? Give one example of such organism.
Answer. Organisms having both the sex organs in the same individual are called Hermaphrodite. Example, Earthworm.

Question.3. Write one negative effect, on the environment, of affluent life style of few persons of a society.
Answer.

Excessive use of air conditioners which is a part of affluent lifestyle emits a lot of heat in the atmosphere.

Excessive use of packaging materials which are mostly made up of non- biodegradable material are not environment friendly.

Excessive use of petrol in vehicles also causes pollution.

Thus, affluent lifestyle results in the generation of excessive waste materials.

Question.4. “The magnification produced by a spherical mirror is -3”. List four information’s you obtain from this statement about the mirror/image.
Answer. Magnification produced by a spherical mirror, m = -3

image is 3 times magnified than the object.

image is inverted (as m has negative sign).

image is real.

nature of the mirror is concave.

Question.5. Forests are “biodiversity hot spots”. Justify this statement.
Answer. Forests are ‘biodiversity hot spots’. The measure of the biodiversity of an area is the number of species found there. Since in a forest there is a wide range of different life forms (bacteria, fungi, fern, flowering plants, nematodes, insects, birds, reptiles and so on) it can be termed a ‘biodiversity hotspot’. One of the main aims of conservation is to try and preserve the biodiversity we have inherited.

Question.6. What is water harvesting? How can this technique help in the conservation of water?
Answer. Water harvesting is a conservation technique of capturing rain water when it falls and run off and taking measures to keep the water clean.

The main purpose of water harvesting is not to hold rain water on the surface of the earth but to make rain water percolate under the ground so as to recharge ‘groundwater’. This in turn reduces dependency on rainfall for irrigation.

Question.7. On dropping a small piece of sodium in a test tube containing carbon compound ‘X’ , with molecular formula C2H6O, a brisk effervescence is observed and a gas ‘Y’ is produced. On bringing a burning splinter at the mouth of the test tube the gas evolved burns with a pop sound. Identify ‘X’ and ‘Y’. Also write the chemical equation for the reaction. Write the name and structure of the product formed, when you heat ‘X’ with excess cone, sulphuric acid.
Answer.

Question.10. Three elements ‘X’, ‘Y’ and 71 have atomic numbers 7, 8 and 9 respectively.
(a) State their positions (Group number and period number both) in the Modern Periodic Table.
(b) Arrange these elements in the decreasing order of their atomic radii.
(c) Write the formula of the compound formed when ‘X’ combines with ‘Z’.
Answer.

Question.12. In the context of reproduction of species state the main difference between fission and fragmentation. Also give one example of each.
Answer.

Question.15. With the help of an example justify the following statement:
“A trait may be inherited, but may not be expressed.”
Answer. In Mendel’s experiment with pea plants, when he cross-bed a tall pea plant with a short plea plant, he found that the first generation (F1) was of only tall plants. In the F1 progeny, no short plants were obtained. Flow ever, in the F2 generation, both tall and short plants were obtained in the ratio 3 :1 respectively. In the F2 generation, both traits — tallness and shortness were inherited where the tall character was the dominant trait and short character was the recessive trait.

Flow Chart. See Q. 14, 2013 (1 Outside Delhi).

Conclusion. Reappearance of dwarf character in F2 generation proves that the dwarf trait was inherited but not expressed in the F2 generation.

Question.16. The image of an object formed by a lens is of magnification -1. If the distance between the object and its image is 60 cm, what is the focal length of the lens? If the object is moved 20 cm towards the lens, where would the image be formed? State reason and also draw a ray diagram in support of your answer.
Answer.

Question.19. (a) Define focal length of a spherical lens.
(b) A divergent lens has a focal length of 30 cm. At what distance should an object of height 5 cm from the optical centre of the lens be placed so that its image is formed 15 cm away from the lens? Find the size of the image also.
(c) Draw a ray diagram to show the formation of image in the above situation.
Answer.

SET III

Except for the following questions, all the remaining questions have been asked in Set-I and Set-II.
SECTION A
Question.1. Write the name and structure of an aldehyde with four carbon atoms in its molecule.
Answer. Name of an aldehyde : Butanal

Question.2. List two functions of ovary of human female reproductive system.
Answer. Two functions of ovary:

To produce female gamete ovum.

To secrete female hormones estrogen and progestrone.

Question.3. In a food chain of frog, grass, insect and snake, assign trophic level of frog.
Answer. Food chain. Grass —> insect —> frog —> snake

Frog belongs to 3rd trophic level.

Question.4. The refractive indices of glass and water with respect to air are 3/2 and 4/3 respectively. If speed of light in glass is 2 x 108 m/s, find the speed of light in water.
Answer.

Question.5. List four stakeholders which may be helpful in the conservation of forests.
Answer. Four stakeholders which may be helpful in the conservation of forests:

The people who live in and around the forest and are dependent to some extent on forest products for their live hood.

The forest department of the Government which owns the forest land and controls the resources from the forest.

The industrialists who use various forest products as raw materials for their factories.

The forest and wildlife activists who want to conserve the forests and see the forests in their original condition (pristine form).

Question.6. The construction of large dams lead to social and environmental problems. List two problems of each category.
Answer. See Q. 11, 2012 (1 Outside Delhi).

Question.7. The position of eight elements in the Modern Periodic Table is given below where atomic numbers of elements are given in the parenthesis.

(i) Write the electronic configuration of Ca.
(ii) Predict the number of valence electrons in Rb.
(iii) What is the number of shells in Sr?
(iv) Predict whether K is a metal or a non-metal.
(u) Which one of these elements has the largest atom in size?
(vi) Arrange Be, Ca, Mg and Rb in the increasing order of the size of their respective atoms.
Answer.

Question.8. Write three different chemical reactions showing the conversion of ethanoic acid to sodium ethanoate. Write balanced chemical equation in each case. Write the name of the reactants and the products other than ethanoic acid and sodium ethanoate in each case.
Answer.

Question.9. An element ‘X’ belongs to 3rd period and group 13 of the Modem Periodic Table.
(a) Determine the valence electrons and the valency of ‘X’.
(b) Molecular formula of the compound formed when ‘X’ reacts with an element ‘Y’ (atomic number = 8).
(c) Write the name and formula of the compound formed when ‘X’ combines with chlorine.
Answer.

Question.17. The image formed by a spherical mirror is real, inverted and is of magnification -2. If the image is at a distance of 30 cm from the mirror, where is the object placed? Find the focal length of the mirror. List two characteristics of the image formed if the object is moved 10 cm towards the mirror.
Answer.

Question.24. (a) Define focal length of a divergent lens.
(b) A divergent lens of focal length 30 cm forms the image of an object of size 6 cm on the same side as the object at a distance of 15 cm from its optical centre. Use lens formula to determine the distance of the object from the lens and the size of the image formed.
(c) Draw a ray diagram to show the formation of image in the above situation.
Answer.

(a)

The principal focus of a diverging lens is a point on its principal axis from which light rays, originally parallel to the axis appear to diverge after passing through the diverging (concave) lens.

The distance between pole and principal focus of a diverging lens is called the focal length. In the given diagram OF is the focal length.

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