3
email: [email protected] Þœªô¢ªî¦ô¢Ù 2 áì÷J 2020 One Mark Question 1. What is Reproduction? A: The production of new organisms from the existing organism of the same species is known as Reproduction. 2. What is the difference between Sexual and Asexual Reproduction? A: Only one parent is needed in Asexual reproduction whereas two parents are needed in Sexual reproduction. 3. What is Budding? A: A small part of the body of the parent organ- ism grows out as a bud; which then detach- es and then become a new organism. 4. What is Binary fission? A: In unicellular organism like euglena asexual reproduction takes place by a method bina- ry fission in which single cell divides into two daughter cell identical to the parent cell. 5. What are Epiphyllous bud? A: In Bryophyllum buds are present in the depression of leaf margin. They are called epiphyllous buds. When they are placed in soil they develop into young plants. 6. What is Grafting? A: Grafting is a technique of inserting a part of one plant into another plant in such a way that the two will unite and continue their growth. 1. What is Progeny? A: Off springs (or) next generation of existing species 2. What is scion? A: The upper part of the union in grafting is called scion. 3. What is root stock? A: The lower part of the union in grafting is called root stock. 4. What are layers? A: Stem (or) Branches that form roots while still attached to the parental plants are called layers. 5. What is foetus? A: Embryo from third onwards is called foetus 6. What is ovulation? A: The discharge of ovum from the ovarian follicle is called ovulation. 1. Why do fish and frog produce a huge number of eggs each year? A: 1) Fish and frogs are oviparous animals 2) They lay eggs in water which results in external fertilisation. 3) There is high risk in external fertilisation and minimises the chances of fertilisation due to external factors. 4) If they lay eggs in little quantities there will be no chance of fertilisation because some of them may be washed away (or) become prey to predators. Hence, fish and frog lay eggs in huge number to improve the chances of fertilisation. 2. Give examples and explain what is meant by external fertilization? A: 1) If the fusion of sperm and ova occurs out side the body of the animal is called external fertilisation. 2) It occurs mostly in aquatic animals like fish and frogs. 3. What is job of Amniotic Sac? A: 1) The Amnion grows around the embryo. 2) The cavity within the amnion become filled with a fluid called Amniotic fluid. 3) The embryo develops in the amniotic cavity which keeps the embryo moist and protects it from minor mechanical injury. 4. When the foetus is growing inside the uterus it need nutrients. What provide nutrients? A: 1) Nutrients need for growth and develop- ment 2) Placenta is a tissue formed by the cells from embryo 3) Placenta is formed around 12 weeks of preg- nancy and provides nourishment to embryo 4) The blood system of mother and foetus are separated by a thin membrane made of cells that allows exchange mainly by diffusion. 5) So, the nutrients diffuses from the blood system of mother into blood system of the foetus in placenta. 5. What would be the consequences if there is no meiosis in organisms that reproduce sexually. A: 1) If meiosis not occurs the chromosome number will be doubled in the formed zygote. 2) The characters of the off spring are unusual and it may leads to the death of individual and eventually extinction of that species takes place. Mounika S Kumari Subject Expert Writer Target-2020 Tenth Biology 100 100 Reproduction The Generating system 1 2 Mark Questions A: Grafting 1) In grafting a branch of a desired variety is grafted onto another plant. 2) It is commonly used for the prop- agation of trees; shrubs grown commercially. 3) It is a method of asexual plant propagation wide- ly used in agricul- ture and horticul- ture. 4) This technique is used in plant to get desirable characters e.g.: Apple, Rose etc Layering 1) In layering first the roots are formed on a stem of another plant and after that the stem is cut off and is planted as a new plant. 2) Plant grown from layering will fruit early than the one grown from the seeds. 3) Layering is also utilised by horti- culture to propa- gate desirable plants. 4) This technique is used to propagate plants like jas- mine, nerium etc. H Write the difference between grafting and layering 2 Mark Questions Theory based 1. What are the different modes of sexual reproduction. Give examples. Organisms can reproduce asexually in many ways. a. Fission: Single celled organism such as paramecium, and bacteria reproduce by splitting into two (or) more offsprings. 1) This usually occurs in a symmetrical man- ner. They split into two by binary fission. When more cells are formed it is called multiple fission. 2) This often the only mode of reproduction in their organism. b. Budding: 1) A growth on the body as a bud that grow to form nearly identical copy of parent. 2) When the bud totally grow then it separates from parent and survive independently. e.g.: Yeast Hydra c. Fragmentation: 1) Some organisms can grow from a separate piece of parent organism. 2) This can be any part of parent body. 3) This happens only in the simplest organ- isms such as some flat worms, moulds, lichens, spirogyra etc. Artificial propagation: 1) Cutting - Rose 2) Grafting - Mango, Apple 3) Layering - Nerium 4) Tissue culture 2. How are sperm cells adapted for their func- tion. A: 1) Sperms are male gamates 2) Millions of sperms are produced by testes. 3) Sperm cell is adopted to carry genetic infor- mation to an egg. 4) The head of sperm cell is pointed like an arrow that allows it to piece through the egg more easily. 5) The tail allows it to swim towards the egg for fertilisation. 6) The middle piece of the sperm contains Mitochondria which provides energy for its movement towards ovum. 7) Millions of sperms compete to fertilize the ovum. 8) Semen provides nutrients for sperm to keep alive and help as a medium for the movement of sperms. 3. The menstrual cycle prepare the uterus for a fertilised egg. How long is an average menstrual cycle from start to finish. A: 1) The uterus at the time of fertilisation is beautifully adopted to receive the devel- oping embryo providing it with food and disposing of its wastes. 2) For fertilisation it is essential for production of Eggs. 3) A few days prior to this time, the uterus was normal in condition. 4) When the zygote is about to enter; the uterus enlarge and become much larger its inner wall is thick, soft and moist with fluid, its blood supply is greatly increased. 5) Menstruation cycle takes place once every 28 days from the age of puberty. Experimental based 1. Germination of seed i) Aim: Germination of seed ii) Material Required: Bengal Gramseed, Water Beaker iii) Procedure: a) Soak a few Bengal gram seeds in a water beaker over night. b) Drain the excess water and cores the seeds with wet cloth and leave them for a day. c) Keep sprinkling water at regular intervals so that they do not dry up. Observation: The germinating seed had cotyledons, plumule and radicle as its parts. 2. How do you observe the pollen grain. Aim: To observe the structure of pollen grain. Materials Required: a) Slide b) Marigold flower c) Water d) Microscope Procedure: 1) Take a slide and put a few drops of water on it. 2) Now take the flower tap it over the drop of water. 3) We can observe small dot like structures in water. Observation: Dot like structures are called pollen grain. Two nuclei are present, and has a pollen tube. Inference: Pollen tube reach the stigma and fertilise the egg to form zygote. 3. Formation of Bacterial colony in Milk. Aim: To observe the formation of Bacterial colony in milk. Requirements: Glass of milk, small quantity of curd, bowl. Procedure: 1) Take a teaspoon full of curd and mix it with around 30 teaspoons full of luke warm milk in bowl. 2) Take another spoon full of curd and mix it in 30 spoon full of cold milk in another bowl. 3) Cover both the bowl and note the time taken. Observation: Curdling occur in the bowl hav- ing luke warm milk. Inference: Curdling indicates the presence (or) increase of lacto bacillus bacteria in the luke warm milk bowl. Cold milk has not provided the medium for the rapid growth of lacto bacillus. Hence in cold milk curdling is not occurred. 4 Marks Questions seed cotyledons plumule radicle Seed germination What is Binary fission ?

Þœªô¢ªî¦ô¢Ù 2 áì÷J 2020 What is Binary fission?€¦ · What are Epiphyllous bud? A: In Bryophyllum buds are present in the depression of leaf margin. They are called

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Page 1: Þœªô¢ªî¦ô¢Ù 2 áì÷J 2020 What is Binary fission?€¦ · What are Epiphyllous bud? A: In Bryophyllum buds are present in the depression of leaf margin. They are called

email: [email protected]Þœªô¢ªî¦ô¢Ù 2 áì÷J 2020

One Mark Question

1. What is Reproduction?A: The production of new organisms from the

existing organism of the same species isknown as Reproduction.

2. What is the difference between Sexual andAsexual Reproduction?

A: Only one parent is needed in Asexualreproduction whereas two parents areneeded in Sexual reproduction.

3. What is Budding?A: A small part of the body of the parent organ-

ism grows out as a bud; which then detach-es and then become a new organism.

4. What is Binary fission?A: In unicellular organism like euglena asexual

reproduction takes place by a method bina-ry fission in which single cell divides into twodaughter cell identical to the parent cell.

5. What are Epiphyllous bud?A: In Bryophyllum buds are present in the

depression of leaf margin. They are calledepiphyllous buds. When they are placed insoil they develop into young plants.

6. What is Grafting?A: Grafting is a technique of inserting a part of

one plant into another plant in such a waythat the two will unite and continue theirgrowth.

1. What is Progeny?A: Off springs (or) next generation of existing

species2. What is scion?A: The upper part of the union in grafting is

called scion.3. What is root stock?A: The lower part of the union in grafting is

called root stock.4. What are layers?A: Stem (or) Branches that form roots while

still attached to the parental plants arecalled layers.

5. What is foetus?A: Embryo from third onwards is called foetus6. What is ovulation?A: The discharge of ovum from the ovarian

follicle is called ovulation.

1. Why do fish and frog produce a hugenumber of eggs each year?

A: 1) Fish and frogs are oviparous animals 2) They lay eggs in water which results in

external fertilisation.3) There is high risk in external fertilisation and

minimises the chances of fertilisation due toexternal factors.

4) If they lay eggs in little quantities there willbe no chance of fertilisation because someof them may be washed away (or) becomeprey to predators. Hence, fish and frog layeggs in huge number to improve thechances of fertilisation.

2. Give examples and explain what is meantby external fertilization?

A: 1) If the fusion of sperm and ova occurs outside the body of the animal is calledexternal fertilisation.

2) It occurs mostly in aquatic animals like fishand frogs.

3. What is job of Amniotic Sac?A: 1) The Amnion grows around the embryo.2) The cavity within the amnion become filled

with a fluid called Amniotic fluid.3) The embryo develops in the amniotic cavity

which keeps the embryo moist and protectsit from minor mechanical injury.

4. When the foetus is growing inside the uterusit need nutrients. What provide nutrients?

A: 1) Nutrients need for growth and develop-ment

2) Placenta is a tissue formed by the cells fromembryo

3) Placenta is formed around 12 weeks of preg-nancy and provides nourishment to embryo

4) The blood system of mother and foetus areseparated by a thin membrane made of cellsthat allows exchange mainly by diffusion.

5) So, the nutrients diffuses from the bloodsystem of mother into blood system of thefoetus in placenta.

5. What would be the consequences if there isno meiosis in organisms that reproducesexually.

A: 1) If meiosis not occurs the chromosomenumber will be doubled in the formedzygote.

2) The characters of the off spring are unusualand it may leads to the death of individualand eventually extinction of that speciestakes place.

Mounika S KumariSubject Expert

Writer

Target-2020

TenthBiology

100100

Reproduction The Generating system

12 Mark Questions

A: Grafting

1) In grafting abranch of adesired variety isgrafted ontoanother plant.

2) It is commonlyused for the prop-agation of trees;shrubs growncommercially.

3) It is a method ofasexual plantpropagation wide-ly used in agricul-ture and horticul-ture.

4) This technique isused in plant toget desirablecharacters

e.g.: Apple, Roseetc

Layering

1) In layering first theroots are formedon a stem ofanother plant andafter that the stemis cut off and isplanted as a newplant.

2) Plant grown fromlayering will fruitearly than the onegrown from theseeds.

3) Layering is alsoutilised by horti-culture to propa-gate desirableplants.

4) This technique isused to propagateplants like jas-mine, nerium etc.

H Write the difference between grafting andlayering

2 Mark Questions

Theory based

1. What are the different modes of sexualreproduction. Give examples.

Organisms can reproduce asexually in manyways.a. Fission: Single celled organism such as

paramecium, and bacteria reproduce bysplitting into two (or) more offsprings.

1) This usually occurs in a symmetrical man-ner. They split into two by binary fission.When more cells are formed it is calledmultiple fission.

2) This often the only mode of reproduction intheir organism.

b. Budding:1) A growth on the body as a bud that grow to

form nearly identical copy of parent.2) When the bud totally grow then it separates

from parent and survive independently. e.g.: Yeast Hydra

c. Fragmentation:1) Some organisms can grow from a separate

piece of parent organism.2) This can be any part of parent body.3) This happens only in the simplest organ-

isms such as some flat worms, moulds,lichens, spirogyra etc.

Artificial propagation:1) Cutting - Rose 2) Grafting - Mango, Apple

3) Layering - Nerium 4) Tissue culture2. How are sperm cells adapted for their func-

tion.A: 1) Sperms are male gamates2) Millions of sperms are produced by testes.3) Sperm cell is adopted to carry genetic infor-

mation to an egg.4) The head of sperm cell is pointed like an

arrow that allows it to piece through the eggmore easily.

5) The tail allows it to swim towards the eggfor fertilisation.

6) The middle piece of the sperm containsMitochondria which provides energy for itsmovement towards ovum.

7) Millions of sperms compete to fertilize theovum.

8) Semen provides nutrients for sperm tokeep alive and help as a medium for themovement of sperms.

3. The menstrual cycle prepare the uterus fora fertilised egg. How long is an averagemenstrual cycle from start to finish.

A: 1) The uterus at the time of fertilisation isbeautifully adopted to receive the devel-oping embryo providing it with food anddisposing of its wastes.

2) For fertilisation it is essential for productionof Eggs.

3) A few days prior to this time, the uterus wasnormal in condition.

4) When the zygote is about to enter; theuterus enlarge and become much larger itsinner wall is thick, soft and moist with fluid,its blood supply is greatly increased.

5) Menstruation cycle takes place once every28 days from the age of puberty.

Experimental based

1. Germination of seedi) Aim: Germination of seedii) Material Required: Bengal Gramseed,

Water Beakeriii) Procedure:a) Soak a few Bengal

gram seeds in awater beaker overnight.

b) Drain the excesswater and coresthe seeds with wetcloth and leavethem for a day.

c) Keep sprinkling water at regular intervalsso that they do not dry up.

Observation: The germinating seed had cotyledons, plumule and radicle as its parts. 2. How do you observe the pollen grain.Aim: To observe the structure of pollen

grain.Materials Required: a) Slide b) Marigold flower c) Water d) Microscope

Procedure: 1) Take a slide and put a fewdrops of water on it.2) Now take the flower tap it over the drop of

water.3) We can observe small dot like structures in

water.Observation: Dot like structures are calledpollen grain. Two nuclei are present, and hasa pollen tube.Inference: Pollen tube reach the stigma andfertilise the egg to form zygote. 3. Formation of Bacterial colony in Milk.Aim: To observe the formation of Bacterialcolony in milk.Requirements: Glass of milk, small quantityof curd, bowl.Procedure:1) Take a teaspoon full of curd and mix it with

around 30 teaspoons full of luke warm milkin bowl.

2) Take another spoon full of curd and mix itin 30 spoon full of cold milk in another bowl.

3) Cover both the bowl and note the timetaken.

Observation: Curdling occur in the bowl hav-ing luke warm milk.Inference: Curdling indicates the presence(or) increase of lacto bacillus bacteria in theluke warm milk bowl.

Cold milk has not provided the medium forthe rapid growth of lacto bacillus. Hence incold milk curdling is not occurred.

4 Marks Questions

seed

cotyledons

plumule

radicle

Seed germination

What is Binary fission?

Page 2: Þœªô¢ªî¦ô¢Ù 2 áì÷J 2020 What is Binary fission?€¦ · What are Epiphyllous bud? A: In Bryophyllum buds are present in the depression of leaf margin. They are called

1. Write about the Pyramid of numbers withexamples?

A: Pyramid of numbers shows the populationof organ-isms at eachtrophic levelin a foodchain. Forexample in aforest, theaphids arevery smalland occur inastronomical numbers, in this food chainthe ladybirds not so numerous, the insec-tivorous birds are only present in smallnumbers, and there may only be a singlepair of hawks.

2. Give reasons that why forest is animportant renewable resource?

A: Forests are rich habitat for plants and ani-mals. Forests serve as a lung for the worldand a bed of nutrients for new life to pros-per. They provide us innumerable productsto live. A forest conserves wildlife habitatsand decreases soil erosion. Sustainableforestry practices are critical for ensuringresources well into the future.

3. Natural resources are decreasing morerapidly. Guess what will be theconsequences?

A: People will struggle for lack of availability ofdifferent fuel products. Non availability offuel causes a lot of affect on transportationand industries. May be a strong necessityleads to the invention of alternativerenewable energy resources like solarequipments, wind mills, tidal power, solarcars, Hydrogen fuelled vehicles and tidalpower etc.

4. Write 4 slogans to promote awareness inpublic about the conservation ofBiodiversity?

A: Conserve nature – conserve lifeLive and – let Live Think eco friendly and – live eco friendly.Protect the environment - it protects you.

5. Draw a food web?

1 Mark Questions

1. What happens if the dissolved oxygenreduces in lake water?

A: Aquatic organisms struggle for thedissolved Oxygen and leads to death.

2. Are all the ecological pyramids alwaysupright? Explain.

A: Generally all the ecological pyramids areupright. But the pyramid of biomass isinverted.

3. Identify the dia-gram and com-ment on it?

A: These are foodchains. Foodchain shows thathow energy pass-es from oneorganism toanother.

4. Which resource in your locality is scarce?How does it affect you?

A: Fresh water is scarce in our locality. It wasabundant earlier. Polluted or contaminatedwater causes so many diseases.

5. Why do you think water became scarcemainly in Vaddicherla?

A: People were unaware of important ofrecharging of dried up wells and groundwater. They did not even think about thecultivation of alternative crops.

6. Which activity you suggest for the commu-nity based intervention?

A: I suggest community based masonry dam,percolation tanks and contour fieldbunding.

7. Write one food chains in your surround-ings?

A: Grass Goat Man

email: [email protected]Þœªô¢ªî¦ô¢Ù 2 áì÷J 2020

Pesara Prabhakar Reddy

Subject Expert

Writer

Target-2020

TenthBiology

100100

A: Names of theEcosystem and

producers

AquaticEcosystem-algae and phy-toplankton,microscopic pho-tosyntheticorganisms

Primary con-sumers/

Herbivores

Small fish,

zooplankton,

mollusks,

and the

green sea

turtle

Secondary con-sumers/ Carnivores

barracudas, Moray

eels, piranhas and

squid.

All the carnivores in

the water eat other

fish.

Tertiary consumers-Carnivores/Omnivores

Catfish, amsel fish,and parrotfish aresome of the omni-vores that live in thewater. These fish eatphytoplankton andother smaller fish likeshrimp.

6. Collect and write the information about the biotic factors of aquatic ecosystems in tabularform.

1. Write about the conceptof ecological pyramidsand explain in detailabout the energypyramid?

A: Graphic repre-sentation of thefeeding level(tropic level)of anecosystemin the shape of a pyramid is called“Ecological pyramid”. It was first intro-duced by a British ecologist Charles Eltonin 1927. In the ecological pyramid the pro-ducers (first trophic level) are representedat the base; and other successive trophiclevels (primary, secondary and tertiaryconsumers) are represented one abovethe other with top carnivores at the tip.There are three types of pyramids; pyra-mid of biomass, pyramid of number, pyra-mid of energy.Pyramid of Energy: Food is the source ofenergy for organisms. As a result of photo-synthesis, these can be made available ina suitable form of energy the food to theworld of living things, only by the greenplants the producers. From the producers,the chemical energy passes to the con-sumers from one tropic level to the nextthrough food. Organisms use most of thefood energy that they assimilate into theirbodies to fulfill their metabolic requirementsPyramid of energy is always upright.

2. How can we prevent ourselves and otherliving beings from the harmful effects of theuse of toxic material as pesticides?

A: Rotation of crops: Growing differentcrops on a particular piece of land in suc-cessive years reduces the occurrence ofpests and damage to the crops from yearto year in that area.Studying the life histories of the pests:By understanding how the pests spreadand its stages in life history, the seeds canbe sown at that time to reduce the damageto the crop.Biological control: Introducing naturalpredators or parasites of the pests.Sterility: Rendering the males of a pestspecies sterileGenetic strains: The development ofgenetic strains (genetically modifiedplants) which are resistant to certain pest.Environmental ethics: This is concernedwith morality of human activities as theyaffect the environment. People need toknow besides laws regarding environmentthere are some basic ethics what is rightand what is wrong in view of environmentare some of the methods to be used.

3. Write about the Community based inter-ventions and farmer based interventionswith examples?

A: Community-based interventions refer tomulti component interventions that gen-erally combine individual and environmen-tal change strategies across multiple set-tings aiming to promote well-being amongpopulation groups in a defined local com-munity. e.g.: water storage structures

(earthen and mason-ry dams), mini perco-lation pits and fieldbunding, waterrecharge systems bybuilding dykes or bar-riers to retain therunoff rain water, for-mation of users groupfor each water storage structure are somecommunity based interventions. The agricultural interventions aim toimprove the status of farmers by Soil andwater conservation measures implement-ed in individual fields are called Farmer-based interventions. e.g.: broad bed fur-

row (BBF) landformand contour planting,field bunding aroundboundaries in rectan-gular or in contours toconserve rain water.Planting Gliricidia onfield bunds to strength-en them and make thesoil nitrogen-rich.

Encourage farmers to use water resourcejointly and irrigate land using micro irriga-tion techniques are some farmer basedinterventions.

4. What is sustainable development? How isit useful us?

A: Development and conservation can coexistin harmony. When we use the environmentin ways that ensure we have resources forthe future, it is called sustainable develop-ment. In other terms when we use the envi-ronment in ways that ensure we have

resources for the future, it is called sustain-able development. There are many differentresources we need to manage and con-serve to live sustainable. The earth’s natur-al resources include air, water, soil, miner-als, fuels, plants and animals i.e. all thethings we need to survive such as food,water, air and shelter. Conservation is thepractice of caring for these naturalresources, so all living things can be bene-fited from them now and in the future.

5. Write about the 4 R’s needed for the pro-tection and conservation of environment?

A: We have to follow the 4 R’s needed for theprotection and conservation of environ-ment. They are Reduce, Reuse, Recycleand Recover.

Reduce: We can save water by repairingleaky taps and avoiding a shower or switchingoff unnecessary lights and fans.Reuse: things that you often tend to throwaway, like paper and wrapping papers. Thiswould save plants and minimize pollution.Recycle: It is the process of converting wastematerials into new materials and objects(e.g.:) some metals, glass, paper etc.Recycling may not always be a very goodoption as recycling plastic is a tricky processand can cause havoc. The chief problem liesin plastics’ complexity. Recover: When we cut trees to constructindustries or roads for transportation, it isimportant to grow trees in other areas.Extra: Recently one more R is added to 4R’s. That is Refuse. Refuse any plastic or nonbiodegradable item to conserve nature is themain aim.

4 Marks Questions

2 Marks Questions A:

Forests are bed of nutrients!

Grass (10,000 kcal)

Frog (100 kcal)

Snake (10 kcal)

Hawk (1 kcal)

Grasshopper (1000 kcal)

Page 3: Þœªô¢ªî¦ô¢Ù 2 áì÷J 2020 What is Binary fission?€¦ · What are Epiphyllous bud? A: In Bryophyllum buds are present in the depression of leaf margin. They are called

2 Marks Questions

x 21. Show that Lt = 1.

x2 x 2A: As x 2 we have x 2 then x 2 =

(x 2) x 2(x 2)

Lt = Lt = 1x2 x 2 x2 (x 2)

x2 + 3x + 22. Compute Lt

x3 x2 6x + 9x2 + 3x + 2 32 + 3(3) + 2

A: Lt = x3 x2 6x + 9 32 6(3) + 9

9 + 9 + 2 20= = =

9 18 + 9 011x3 3x + 4

3. Compute Lt x 13x3 5x2 + 7

1A: As x then 0

x 11x3 3x + 4

Lt x 13x3 5x2 + 7

3 4x3 (11 + )x2 x3

= Lt 1 5 7 0 x3(13 + )x

x x3

11 0 + 0 11= =

13 0 + 0 13

4 Marks Questions

1. If f is a function given by K2x K if x 1

f(x) = { 2 if x 1 is continuous function on R, then find thevalue of K?

A: Since f is continuous on R, so it is continu-ous at x = 1.Lt f(x) = Lt f(x) = f(1)

x1+ x1

K2 K = 2 = K2 K K2 K 2 = 0(K + 1) (K 2) = 0 K = 1 or K = 2

2. Check the continuity of the following function at 2.

x2 4 if 0 x 2

f(x) = 2 { 0 if x = 22 8x3 if x 2

x2 4 4 4A: Lt f(x) = Lt = = 0x2 x2 2 2

8 8Lt f(x) = Lt (2 ) = (2 )

x2+ x2+ x3 8= 2 1 = 1

Lt f(x) Lt f(x)x2 x2+

Lt f(x) does not existsx2

At x = 2, f(x) is discontinuous.

email: [email protected]Þœªô¢ªî¦ô¢Ù 2 á÷ìJ 2020

Target-2020Junior Inter

Mathematics -1B100100

B. Eswara RaoSubject Expert

Writer

7 Marks Questions

1. If y = xa2 + x2 + a2log (x +

a2 + x2) Then

dyprove that = 2

a2 + x2

dx

A: if y = xa2 + x2 + a2log (x +

a2 + x2)

dyL.H.S =

dx 2x

= x. + a2 + x2 (1)

2a2 + x2

1 2x+ a2 [1 + ](x +

a2 + x2) 2

a2 + x2

x2 a2

= + a2 + x2 +

a2 + x2 (x +

a2 + x2)

x2 + a2 + x[ ]x2 + a2

x2 + a2

= + a2 + x2 = 2

a2 + x2 = R.H.S

a2 + x2

dy2. If y = xtanx + sinxcosx then find

dx

A: y = u + v where u = xtanx and v = sinxcosx

dy du dv = + .............(1)dx dx dx

Now u = xtanx

take log on both sides

log u = tanx.log x

1 dy 1. = tanx. + sec2x.logxu dx xdu tanx = xtanx ( + sec2 x.logx)dx x

v = sinxcosx

take log on both sides

log v = cosx. log sin x

1 du cos x . = cos x. + log sin x (sin x)v dx sin x

dv cos2 x = sin xcos x ( sin x. log sin x)dx sin x

du dvsubstitute , functions in (1), we get

dx dx

dy tan x = xtanx [ + sec2 x. logx]dx x

cos2+ sinxcos x [ sinx. log sinx]sinx

3. If 1 x2 +

1 y2 = a(x y) then show that

dy 1 y2

= .dx 1 x2

A: Given that 1 x2 +

1 y2 = a(x y)

put x = sin A A = sin1x also

1 x2 =

1 sin2 A = cos A

y = sin B B = sin1 y also

1 y2 =

1 sin2 B = cos B

1 sin2 A +

1 sin2 B = a(sin A sin B)

cos A + cos B = a(sin A sin B)A + B A B

2 cos() cos = 2 2

A + B A Ba 2 cos sin

2 2A B A Bcot = a = cot1 a

2 2A B = 2cot1 asin1 x sin1 y = 2 cot1 a

dytake

dx1 1 dy = 0

1 x2

1 y2 dx

1 1 dy = 1 x2

1 y2 dx

dy 1 y2

= .dx 1 x2

4 Marks Questions

1. Find the derivative of cotx from the firstprinciple

cosxA: Let f(x) = cotx = ; f(x + h) = cot(x + h)

sinxcos(x + h)

= sin(x + h)

f(x + h) f(x) f1(x) = Lt

h0 hcos(x + h) cosx 1

= Lt ( ) h0 sin(x + h) sinx h

cos(x + h) sinx sin(x + h)cosx = Lt

h0 h sin(x + h)sinx sinh

= Lt h0 h (sinx sin(x + h)

1= = cosec2xsin2x

2. Find the derivative of cos ax using first prin-ciple.

A: Let f(x) = cos ax, f(x + h) = cos(ax + ah)f(x + h) f(x)

f'(x) = Lt h0 h

cos(ax + ah) cos ax= Lt

h0 h

ah ah(2)sin(ax + ) sin()2 2= Lt

h0 hahsin()ah 2 = Lt sin(ax + ). . a

2 ah h0

2= sin ax . (a) = a sin ax

2 Marks Questions

1. Find the derivative of tan1(log x)A: Let y = tan1(log x)

dy 1 1 1 = =

dx 1 + (log x)2 x x[1 + (log x)2]

2. If f(x) = 2x2 + 3x 5 then prove that f' (0) +

3f'(1) = 0

A: Given that f(x) 2x2 + 3x 5

f'(x) = 4x + 3 Now f'(0) = 3

f'(1) = 4 + 3 = 1

f'(0) + 3f'(1) = 3 + 3(1) = 3 3 = 0

3. If f(x) = 1 + x + x2 + ..... + x100 then find f'(1).

A: f(x) = 1 + x + x2 + ..... + x100

2 Marks Questions

ax 11. Find Lt x0 bx 1

ex 12. Find Lt x0

1 + x 1

sinax3. Find Lt

x0 sinbx

4. Find Lt (x2 + x x)x

x2 + 5x + 25. Find Lt

x 2x2 5x + 2

3x 16. Find Lt

x0 1 + x 1

tan (x a)7. Find Lt

xa x2 a2

4 Marks Questions

cos ax cox bx{ if x 01. Show that f(x) = x2

b2 a2 if x = 0

2 is continuous at x = 0 (where a, b are real)

xsin a a sinx2. Compute Lt

xa x a

Additional Problems

Limits and Continuity

Differentiation f'(x) = 0 + 1 + 2x + .... + 100x99

100 101f'(1) = 1 + 2 + 3 + ..... + 100 = 2

= 5050dy

4. If y = log(sec x + tan x) then find .dx

A: Given that y = log (sec x + tan x)dy 1 = .(sec x tan x + sec2x)dx (sec x + tan x)

dy sec x(tan x + sec x) = = sec xdx (sec x + tan x)

dy5. If f(x) = y = x ex sinx then find (or) f'(x).

dxA: Given that f(x) = x ex sin x

f'(x) = 1.ex sin x + x ex sinx + x ex cos x= ex (sin x + x sin x + x cos x)

2 Marks Questions

dy1. If y = log (sec x + tan x) then find

dx2. If f(x) = xex sin x then find f'(x)

dy3. If y = log [sin(logx)], find

dx

4 Marks Questions

1. If y = axn+1 + bxn then prove that x2 y11 = n(n + 1)y

2. Find the derivative of following using firstprinciplei) sin2 x ii) tan2 x iii) xsin x iv) cos2 x

7 Marks Question

x x 1. If f(x) = sin1

. , g(x) = tan1

.

x

then prove that f'(x) = g'(x).

Additional Problems

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