V - Learn Digital Classes | 2nd PU Online Class - 02 Continued....(CMB)

Added: 2026-05-12

[00:02:14]Okay.

[00:02:17]Good afternoon students.

[00:02:24]Put attendance.

[00:02:28]So due to some technical issue. So we have started with Okay.

[00:03:16]So cold base reaction complete.

[00:03:22]So reaction reaction reaction complete reaction. Okay. So that is one of the important name reaction preparation of salicylic acid from phenol and phoxideion. Okay. Okay. Okay.

[00:04:02]The next one important reaction. Next one important named reaction. So second one important named reaction. So remer time reaction.

[00:04:14]Remrman reaction. Okay. Remrmon reaction. This is another one important name reaction for the preparation of for the preparation of salicyella deihide from phen. Okay. So either coal based reactions or remot reaction is very important for board exams. Okay. So similar type of reaction which type of reaction undergo based reaction means sodium.

[00:04:58]So it under go caroxilation reaction and it also under go electrofilic substitution reaction. So statement so what is the purpose we are adding carbon dioxide right why we are using sodium phenoxide instead of phenol so electrofile is a weak sorry say carbon dioxide is a weak electrofile and sodium phoxide is a sodium phoxide is a highest reactive species okay for that reason We are using sodium phenoxide instead of phenol in coalbased reaction.

[00:05:40]Okay. What is the possible product of coldbased reaction? Formation of salicylic acid. Right. The second one is remeral reaction. Okay. Remran reaction.

[00:05:52]So remor time and reaction when phenol when phenol is react with is react with chloroform chloroform plus aquous na aquous na right phenol is treated with chloroform in presence of aquous koh what is aquous koh na which is dissolved in water.

[00:06:23]Right? What is the addition product? We are obtained.

[00:06:28]So we are obtained this addition product. Okay? Again CH Cl2. This is the addition product. We are obtained. Again this addition product is react with NaOH. Sodium hydroxide react. What we are getting?

[00:06:49]We are getting O Na+ and C HO. Then this will undergo acidification, right? Acidification.

[00:07:00]What will we get? We get O C HO, right?

[00:07:09]What is the product?

[00:07:17]What is the name of this compound?

[00:07:21]Put into your chart.

[00:07:25]Right?

[00:07:29]Sali deihide.

[00:07:33]What is the name of the product?

[00:07:35]Salicyal deihide. Okay. So, one one re one important name of reaction is coalbase reaction. Cold based reaction means preparation of salicylic acid from sodium phenoxide. Then preparation of salicylic salicylic alihide from phenol is an reimon reaction. Okay, there are the two important reaction question.

[00:08:03]What is the reaction intermediate is obtained during the reaction between chloroform and NaOH? Right. Question reaction intermediate right intermediate.

[00:08:20]Right.

[00:08:22]It is a reaction intermediate is obtained.

[00:08:27]Reaction intermediate.

[00:08:30]Obtained in this reaction is carbine.

[00:08:36]Carbine. Carbine is a reaction intermediate. Carbon having a carbon having a sex state of electron having a lone pair of electron.

[00:08:46]Right. Question. What is the reaction intermediate is obtained during obtained during remral and reaction questions. Carbine is obtained during the remot reaction during salicyard deihide preparation. Right. So okay. So this is one of the important reaction addition product then this one is main product. Okay.

[00:09:15]Then next.

[00:09:22]Okay.

[00:09:27]Next reaction. So next reaction.

[00:09:32]Okay.

[00:09:34]Put a thumb in chat. So we will go to next topic.

[00:09:51]Okay.

[00:09:54]The next reaction. Okay. The third reaction.

[00:10:00]Third reaction. Reduction of phenol.

[00:10:06]Reduction of phenol with with zinc dust.

[00:10:16]Zinc dust. Okay. This is another one important reaction. Right. Phenol zinc dust reaction. What is the possible reaction taking place? Reduction reaction taking place. Right? What is reduction in terms of oxygen and hydrogen? In terms of oxygen and hydrogen addition of hydrogen or removal of oxygen is nothing but a reduction right in the preparation benzin preparation so we are reacting with zinc dust right okay it's a possible reaction when phenol when phenol is react with is react with zinc dust. So this mean what is the meaning of that one? We are heating zinc dust.

[00:11:14]What is the possible product we are obtained? We are obtained benzene along with zinc oxide right zinc oxide formation. So this is the process to removal of oxygen in the phenol. So the process called it reduction reduction taking place right this is the important reaction for the preparation of benzene also in your first year hydrocarbon chapter that is aromatic hydrocarbon sub chapter. So one of the important reaction for the preparation of benzene is nothing but an reduction of phenol with zinc dust right phenol zinc dust react. So what are the product we are obtaining? We are obtained a we are obtained benzene. Benzene is the product. Okay.

[00:12:15]This is another one important special reactions of phenol. Okay. One is preparation of salicyolihide and preparation of salicylic acid. The another one is oxid reduction of phenol with the zinc dust. Okay. Next fourth one reaction reduction. So oxidation reaction.

[00:12:43]The next reaction is oxidation of oxidation of phenol. Right? Oxidation of phenol. How phenol undergo oxidation taking place? Okay. See I'm taking phenol. What is oxidation reaction taking place?

[00:13:04]So addition of oxygen and removal of hydrogen. But reduction means reduction means addition of hydrogen and removal of oxygen. So previous reaction we have studied the reduction. For in this reaction we have studied the oxidation oxidation of phenol. When phenol is react with the oxidizing agent, oxidizing agent, what is a possible oxidizing agent? So, Na2 CR27.

[00:13:33]This is oxidizing agent. Sodium dromate.

[00:13:37]What is the reagent? Oxidizing agent we are used sodium dromate. And in presence of acid H2SO4, what is the possible product? We are obtained. The possible product we are obtaining is benzoquen.

[00:13:56]What is a possible product?

[00:13:59]Benzoquinon.

[00:14:02]Benzquinon we are obtained. Okay.

[00:14:05]Conjugated dine. What is another name?

[00:14:09]Conjugated dine. We are optional. Okay. Conjugated dine. Right. These are the four important reaction of four important reaction of phenol special reaction. One is preparation of salicylic acid from sodium phoxide that is nothing but an coal base reaction. The next is preparation of salicylic deihide from phenol. It is reertimon reaction. The another one reaction is reduction of phenol using zinc dust. So preparation of benzene from phenol phen sorry benzin phenol reduction benzene.

[00:14:50]What is the reagent? We are used zinc dust. The fourth important reaction is oxidation of phenol. So we are oxidized the phenol using a using a oxidizing agent sodium dromate and in presence of H2SO4 what we are getting conjugated or benzoquenone benzoquenone right. So next reaction of reaction special reaction and types of reaction is over. Okay.

[00:15:33]We are going to next topic. Okay. Next topic.

[00:15:42]Hope you understand.

[00:15:52]reactions.

[00:15:56]Okay.

[00:15:59]Okay. Okay.

[00:16:06]Okay. Okay. Okay.

[00:16:10]So the my next topic in alcohol, phenols and ether chapter is some commercially important some commercially important alcohol.

[00:16:28]Some commercially important alcohol. Right? Some commercially important alcohol. Okay. So along with that name reaction this part is also important for board exam. Okay.

[00:16:47]The first one is the first one is methanol. Okay. What is the formula for methanol? Methanol is also known as wood desperate. The another name of methanol is wood desperate. Yeah.

[00:17:10]In earlier days that methanol is obtained by right that methanol is obtained by destructive distillation of destructive distillation of wood.

[00:17:29]So that's why the name spirit destructive distillation of the earlier days preparation. Okay. But nowadays right commercially how methanol is obtained? Commercialally preparation. Okay. Okay. C H3 or methanol. So prep earlier.

[00:17:57]So is prepared in earlier days by destructive distillation of wood. So that's why the another name of methanol is wood spirit. Methanol the formula is C H3.

[00:18:12]Methanol is also known as wood spirit.

[00:18:15]Wood spirit. Okay. How methanol is prepar prepared? Okay. Methanol commercially prepared.

[00:18:25]So how methanol is how methanol is prepared commercially?

[00:18:37]Okay.

[00:18:41]How methanol is prepared commercially?

[00:18:44]Okay.

[00:18:46]Commercially methanol is obtained by catalytic hydrogenation of catalytic hydrogenation of carbon monoxide. Right?

[00:18:56]Catalytic hydrogenation of carbon monoxide plus 2 H2. This is catalytic hydrogenation in in presence of high temperature and high pressure. High temperature and high pressure along with along with the catalyst along with the catalyst. Catalyst now zinc oxide and chromium triioxide. What are all the catalyst? We are used for the preparation of methanol.

[00:19:26]Right? What is the possible reaction?

[00:19:29]Catalytic hydrogenation of catalytic hydrogenation of carbon monoxide. Carbon monoxide hydrogen addition in presence of catalyst. So that's why the name catalytic hydrogenation of carbon monoxide. What is the catalyst name?

[00:19:46]Zinc oxide and chromium triioxide. This is the catalyst. What is the possible reaction condition? The possible reaction condition is 200 to 300 atmospheric pressure and 573 to 673 Kelvin temperature.

[00:20:08]673 Kelvin temperature. What is the product we are obtaining? We are obtaining the product methanol. We are obtained the product methanol. Okay. So combination we call it as water gas water gas. Okay. This is the one of the method which method commercial method for the preparation of methanol. Right.

[00:20:34]What is the common name of methanol? So it is known as wood spirit. Wood spirit.

[00:20:43]Right.

[00:20:47]Right. When water gas, what is the water gas? It is a combination of carbon monoxide and hydrogen. Water gas. The mixture of carbon monoxide and water is known as water gas. That carbon monoxide undergo catalytic hydrogenation.

[00:21:08]Catalytic hydrogenation in presence of zinc oxide and chromium triioxide at 200 to 300 atmospheric pressure and 573 to 673 Kelvin temperature we are getting the methanol right this is commercially commercially prepared methanol right next so the advantage disadvantage right what's the advantages of methanol and what is Disadvantages of methanol.

[00:21:41]Advantages.

[00:21:42]Disadvantages.

[00:21:44]Advantages of Advantages of methanol.

[00:21:50]Right. Advantages of methanol. Methanol is used as solvents in paints. Right?

[00:21:58]Solvents in paints.

[00:22:00]Solvents.

[00:22:02]The next it is also used for the manufacturers of formal deihide right important organic compound formalihide manufactur.

[00:22:13]Then next we are used paints.

[00:22:19]Okay then next what is the disadvantages?

[00:22:26]What is the disadvantages of methanol?

[00:22:30]Even small amount of methanol is intake to human body it cause blindness.

[00:22:36]It cause blindness and blindness and so overtaking of methanol cause death right human body inject so it causes blindness. So later on the more methanol is intake to the human body it may cause death also. Okay. The next so methanol undergo oxidation. Why blindness and it causes death? Right?

[00:23:08]What is the reason?

[00:23:11]Methanol that methanol undergo oxidation with air with air it form alihide.

[00:23:22]It form alihide and it will undergo oxidation. It will form formic acid. It will form formic acid. Formalihide formation again formalihide. It form formalihide and later it form formic acid. This is the reason why methanol is more poisonous to the human body. Right?

[00:23:44]I hope you understand what is the disadvantages of methanol.

[00:23:49]Right? It causes blindness even small intake of methanol to the human body. So large intake it causes death because it forms further oxidizes it form formalihide. Formal deihide further oxidizes formic acid right.

[00:24:07]Corrosiveness corrosiveness human sensitive.

[00:24:19]Okay.

[00:24:22]Methanol complete. Last topic preparation of ethanol by commercial method.

[00:24:35]Next topic.

[00:24:39]Okay. Put a thumb.

[00:24:51]Okay.

[00:25:02]So we will go to next topic.

[00:25:16]The second one is ethanol. Okay. C2 H5O, right? How ethanol is manufactured commercially? Okay.

[00:25:37]So commercially ethanol is produced by anorobic fermentation.

[00:25:44]Right? Commercially ethanol is manufactured by anorobic anorobic fermentation.

[00:25:54]Fermentation anorobic fermentation of sugar. Okay.

[00:26:00]So sugar Right.

[00:26:12]So that we call it as molasses.

[00:26:14]Right. That molasses containing sugar content. Right? That molasses containing sugar content. Sugar came in the last part in after removing the juice. Sugar juice that we call it as molasses.

[00:26:29]Right? That molass is containing small amount of sugar. That sugar is responsible for the preparation of ethanol. Right?

[00:26:38]Understand? What is molasses?

[00:26:41]This is the final part of sugar cane.

[00:26:44]Sugar cane juice. Okay.

[00:26:49]Next.

[00:27:01]Okay. Ethanol.

[00:27:03]So how ethanol is prepared commercially?

[00:27:06]Okay. Ethanol is prepared by commercially by right using molasses right. The molasses containing sugar right because grapes containing sugar content right along with the most important yeast along with the sugar. Sugar plus ye east under go anorobic fermentation we are getting ethanol. Right? Sugar plus yeast anorobic fermentation we are getting ethanol. Okay. Preparation that molasses containing sugar content sugar juice extract.

[00:27:52]The next that juice containing sugar C12 H22021.

[00:28:00]This is the chemical formula of sucrose.

[00:28:03]Right? Sucrossse. Sucrose is treated with water in presence of In presence of enzyme invertise.

[00:28:15]In presence of enzyme invertise, it form it form C6 H126 plus C6 H1206. Then these two compounds are isomer.

[00:28:32]compound glucose plus fructose. glucose plus fructose right that sucrose is extracted with water and treated with a important enzyme invertise that invertise enzyme fermented the sucrose into glucose and the fructose convert right again that glucose and fructose again treated with again treated with another enzyme another enzyme zy Zymase what it produce? What it produce?

[00:29:11]C2 H5O H plus 2 CO2 2 CO2. So this is how ethanol is manufactured commercially by fermentation of sugar that is molasses.

[00:29:26]Okay.

[00:29:27]The next ethanol. What is the first step for the preparation of ethanol? By fermentation of sugar C12 H21.

[00:29:44]So it is extracted with water in presence of enzyme. In presence of enzyme invertise invertise what it form?

[00:29:54]There are two compounds C6 H1206 plus C6 H1206.

[00:30:01]So that is glucose glucose and fructose. Right? What is the second reaction? That second reaction is again that glucose and fructose is treated with another enzyme zyase. Zyase what it produce?

[00:30:20]two moles of ethanol along with the two moles of carbon dioxide. Two moles of carbon dioxide.

[00:30:29]Okay.

[00:30:31]So this one is ethanol along with carbon dioxide. So this is the two important reaction. Okay. So the continue part.

[00:30:49]Okay. So next session say 10% alcohol 9% alcohol next 100% alcohol next 20% ethanol plus 80% so important named reaction along with reduction and oxidation of phenol then commercial preparation of methanol and ethanol. Okay.

[00:31:26]So I am ending the session.

[00:31:29]Okay.

[00:31:31]Session start.

[00:31:46]So exact mathematics start session.

[00:43:24]Good afternoon friends.

[00:43:28]Audible.

[00:43:36]Okay. First name mention name section.

[00:43:52]So yesterday we discussed the concept that is a derivative derivative on inverse trigonometric functions.

[00:44:13]So previous class inverse functions.

[00:44:21]So there is some properties.

[00:44:45]This is Arab long.

[00:45:04]Okay, everyone joined.

[00:45:09]Shall I start?

[00:45:36]Good afternoon.

[00:45:57]Send this time.

[00:46:12]Okay. So listen on inverse trigonometric functions. So already function next year. So yesterday so there is a property yesterday we discussed that is sin inverse of sin x sin inverse of sin x which is equal to x and sin of sin inverse x which is equal to x.

[00:46:44]So sin inverse of sin x= x and sin of sin inverse x which is equal to x.

[00:46:50]There's a one condition that is sin inverse that x belongs to for all x belongs to closer interval minus<unk> by2 to<unk> by 2 sin inverse of sin x which is equal to x that is for all x belongs to closer interval minus<unk> by 2 to<unk> by 2 in this case sin of sin inverse x which is equal to x that is for all x comes from that is closer interval -1 to 1 so conditions important So inverse x belongs to option option.

[00:47:28]So next inverse trigonometric functions just difference sin inverse of sin x is also x sin of sin inverse x is also x that is x belongs to closer interval -2 to<unk> by 2. Here x belongs to closer interval minus1 to 1.

[00:47:51]So yesterday last question. Okay. First concept.

[00:47:56]So next question.

[00:48:00]So again we know that the formulas sin 2x sin 2x is equal to sin 2x = 2 sin x into cos x. Again there is one more formula sin 2x sin 2x = 2 tan x / 1 + tan² x formulas for sin 2x raise your hand so that right so again cos 2x X formula that is cos 2x which is equal to what is that cos 2x = yes yes cos 2x is equal to cos² x - sin² x another formula in terms of sin cos 2x which is equal to 1 - 2 sin² x again in terms of cos cos 2x is equal to 2 cos² x -1 1 again cos 2x = 1 - tan^ x / 1 + tan² x. So for solan 2x tan 2x= 2 tan x / 1 - tan² x tan 2x = 2 tan x 1 - tan² x.

[00:49:43]So shall we move further formulas that is sin 3x sin 3x for sin 3x 3 sin x - 4 sinq x sin 3x that is 3 sin x - 4 sin cube x cos 3x is equal to 4 cos x - 3 cos x 4 cos 2x - 3 cos x correct foretting.

[00:50:34]Okay. So again tan 3x 3 tan x - tan x / 1 - 3 tan² xometry.

[00:50:56]Okay.

[00:51:01]So previous class that is y = sin inverse 2x / 1 + x² Right.

[00:51:30]Okay. So, here is the question. y = sin inverse 2x 1 + x². So inverse function.

[00:51:46]So if in case put x= tan tan theta x so put x= tan theta.

[00:52:01]So for sin inverse of 2 into tan theta / 1 + tan²a is it right? So here we know that the formula sin 2 theta that is sin 2x which is equal to 2 tan x 1 + tan square x formula we use sin inverse of 2 tan 1 + tan square what we can write it as so we can write it as sin 2 theta so sin inverse of sin 2 theta is 2 theta here x= tan theta then that implies theta is equal to tan inverse x. So that's why 2 into tan inverse x. This method we have to follow here.

[00:52:55]So problem solution.

[00:53:00]So first given function given y = sin inverse of 2x / 1 + x². So put x= x = tan that implies theta = tan inverse x.

[00:53:21]So that implies y = sin inverse of 2 into x + tan 2 tan theta / 1 + tan² theta.

[00:53:37]Is that right? All of you getting so y= sin inverse of so 2 tan theta 1 + tan square sin 2 theta we can write it as sin 2 theta because sin 2 theta we know that sin 2 theta is equal to 2 tan theta / 1 + tan² theta.

[00:54:01]So can we write it as sin y = 2x 1 + x² and then sin y.

[00:54:14]So it's a lengy procedure. So inverse sin y= 2x 1 + xen okay y= 2x + so that's why we are using the properties So we can guess it. So for any question what is that tan x we can starting just observe the question which we have to subute.

[00:55:08]So just tan x this function will become so tan xan can sin 2 theta. So that's why y= sin inverse of sin we know that the property sin inverse of sin theta we can write it as theta sin inverse of sin theta we can write it as theta that's why y = sin inverse of sin 2 theta which is equal to 2 theta is it clear so y= here 2 theta is there that's why sin inverse of sin 2 theta can be written as 2 theta. So yourta is nothing but theta is nothing but tan inverse x because we substute here x= tan theta that implies theta is equal to tan inverse x. Now differentiate just simplification. Now we are differentiate with respect to x on both side. differentiate with respect to x on both side because here doing that is derivative in the inverse trigonometric functions derivative on inverse trigonometric functions. So just simplification. Now we are differentiating with respect to x on both sides that is differentation of y is nothing but dy by dx. Differentiation of y is nothing but dy by dx 2 as it is it is a constant term. Differentiation of tan inverse x is d by dx of tan inverse x which is equal to 1 by 1 + x².

[00:57:10]Here is the formula. So differentiation of tan inverse x is 1x 1 + x².

[00:57:17]Therefore, dy by dx which is equal to 2 / 1 + tan².

[00:57:34]Is there any doubt?

[00:57:40]Okay.

[00:57:41]is right answer please help me repeat. Okay. So here is the question y = sin inverse 2x / 1 + x². So here substituting that is x is put x= tan theta. So that theta implies tan inverse x because we know that the formula sin 2 theta is nothing but 2 tan theta / 1 + tan square theta. That's why we are substituting here tan theta. So y is equal to sin inverse of 2 tan theta 1 + tan square theta can be written as sin 2 theta. So we know that the property that is sin inverse of sin theta which is equal to theta where theta belongs to closed interval minus<unk> by 2 to import conditions important again. So here sin inverse of sin 2 theta can be written as 2 theta theta is nothing but tan inverse x. So simplification next we are doing differentiation that is differentiate with respect to x on both side. So differentation of y is nothing but dy by dx which is equal to 2 tan inverse x.

[00:59:10]Differentiation of 2 tan inverse x 2 is a constant term differentiation of tan inverse x is 1 by 1 + x². That's why dy by dx which is equal to 2 / 1 + xy.

[00:59:28]Is it clear?

[00:59:32]So next problem.

[00:59:36]So that is sin 2x. Already you know that sin 2x = 2 sin x into cos x sin 2x which is equal to 2 tan x / 1 + tan² x.

[00:59:55]So cos 2x which is equal to cos² x - sin² x cos 2x = 1 - 2 sin² x again cos 2x = 2 cos² x - 1 cos 2x = 1 - tan² x / 1 + tan² Please note down the formulas.

[01:00:32]So again some inverse trigonometric properties.

[01:00:36]Sin inverse of sin x which is equal to x. Again sin of sin inverse x which is equal to x. Here for all x belongs to clos interval minus<unk> by2 to<unk> by2. Here for all x belongs to closer interval -1 cos inverse of cos x which is equal to x x in place of x they given theta then sin inverse of sin theta which is also given by theta of getting please note on formulas.

[01:01:27]So tan 3 theta also sin 3 tan 3 theta. So tan 3x 3 tan x - tanq x / 1 - 3 tan² x Hello foretting.

[01:02:07]Is it over?

[01:02:15]Shall we move to next question?

[01:02:24]Okay.

[01:02:28]Now, next question that is y = y = tan inverse of next question. Y = tan inverse of 3x - xq / 1 - 3x² where x is greater than - 1x <unk>3 less than 1x<unk>3.

[01:03:05]Here is the question. y = tan inverse of 3x - x / 1 - 3x².

[01:03:15]So express is replaced by tan 3x tan 3x tan tan x So again, no problem.

[01:03:59]Okay.

[01:04:01]3x.

[01:04:07]Okay. Because we know that the formula tan 3x = 3 tan x - tan x / 1 - 3 tan x formula.

[01:04:22]So put x = tan put x= tan theta tan xus.

[01:04:34]So put x= tan theta. So that implies theta is equal to tan inverse x.

[01:04:44]So solution.

[01:04:50]Yes. Put x= tan x tan.

[01:05:03]Okay. 3D 1 + x² right answer.

[01:05:17]So put x= tan theta which is equal to that implies theta is equal to tan inverse x. So the plus x + y = tan inverse of 3 tan theta minus tanq theta / 1 - 3 tan² theta.

[01:05:44]So we know that the formula it can be written as y = tan inverse of tan 3 theta.

[01:05:52]y = tan inverse of tan 3 theta. So that implies y = tan inverse of tan theta can be written as. So already property tan inverse of tan theta can be written as theta. tan inverse of tan theta can be written as theta.

[01:06:15]So that is 2 uh 3 theta sorry tan inverse of tan 3 theta is 3 theta. So here theta is nothing but tan inverse x that's why y = 3 in place of theta we are writing tan inverse x y = 3 tan inverse x differentiate with respect to x on both side differentiate with respect to x on both side.

[01:06:48]So differentiation of y is nothing but dy by dx which is equal to 3 into dy dx of tan inverse x that is 3 into 1 by 1 + x². So 3 into 1 is 3 3 by 1 + x² it is the solution.

[01:07:18]All of you getting right?

[01:07:21]Is there any doubt?

[01:07:28]Is there any doubt formulas already discuss? So inverse formulas it is a derivative of differentiation of sin x which is equal to 1x roo<unk> of 1 - x² differentiation of cos inverse x is - 1x roo<unk> of 1 - x² again differentiation of tan inverse x is 1 by 1 + x² formulas so inverse inverse function formulas Okay, take on the next question.

[01:08:14]Y = Take on the next question. Y = cos inverse of 1 - x² / 1 + x² where x is greater than 0 less than 1.

[01:08:34]So x= body support.

[01:09:15]Why you subuting the tan x?

[01:09:19]Yes, it is a formula because cos 2x formula we know that cos 2x= cos 2x which is equal to 1 - tan² x / 1 + tan x we know that so that's why we are substituting put x = tan theta put x = tan theta that implies theta is equal to tan inverse x.

[01:09:52]So put x= tan theta that implies theta is equal to tan inverse x.

[01:10:01]Yes, right.

[01:10:11]So 2 by 1 + x².

[01:10:27]So here that implies y = cos inverse of 1 - tan square theta / 1 + tan² theta.

[01:10:40]So that implies y = cos inverse of 1 - tan square theta 1 + tan square theta can be written as cos 2 theta.

[01:10:51]So we know that the property inverse trigonometric property y= cos inverse of cos theta can be written as theta. Here in place of theta 2 theta is there that's why cos inverse of cos 2 theta can be written as 2 theta.

[01:11:09]Your data is nothing but 2 tan inverse x 2 tan inverse x. So you differentiate differentiate with respect to x on both side.

[01:11:32]Differentiate with respect to x on both side.

[01:11:37]So differentation of y is nothing but dy by dx which is equal to 2 into differentation of tan inverse x is 1 by 1 + x² that is 2 into 1 is 2 2x 1 + x² of getting right?

[01:12:05]Is there any doubt?

[01:12:29]while the next question.

[01:12:36]Okay. Okay.

[01:12:39]Note down y = next question sin inverse of 1 - x² / 1 + x² sin inverse of 1 - x² 1 + x² where x is greater than 0 less than 1 x + Same question. Inverse sin inverse.

[01:13:17]Any guess?

[01:13:23]Any guess in this format? Do you know any formula for sign in this format?

[01:13:34]Do you know any formula for sign?

[01:13:39]So again put x= dx y.

[01:13:58]So uh if in case we substitute here that x= tan theta then it will become 1 - tan square theta divid 1 + tan square theta it can be replaced by so it can return by cos 2 theta so cos 2 in terms of represent because outside here sin inverse is there so we know that the property sin inverse of sin theta that can be easily written theta cos 2 theta. Now in terms of sale format represent mara.

[01:14:55]So we know that sin of 90us theta what is that sin of 90us theta 1 - 2 sin² sin of 90us theta can be written as cos theta right so cos 2 sin of 90 - 2 1 - 2 sin square cos 2x 1 - 2 sin² x 1 - 2 sin square 1 - tan put x = tan theta that implies theta = tan inverse x y = sin inverse of 1 - tan² theta / 1 + tan² theta So here y = sin inverse of so it can as cos 2 theta. So again sin inverse of cos 2a is 2.

[01:16:37]So y is equal to sin inverse of sin of 90us sin of 90us theta is cos theta. That's why cos 2 theta can be written as replaced by sin of 90 - 2 theta. So y is equal to now it is in the form of that is a property sin inverse of sin theta.

[01:17:03]So you know the property sin inverse of sin theta is theta.

[01:17:09]Sin inverse of sin theta is theta.

[01:17:11]That's why y is equal to<unk> by 2 minus 2 theta. Here theta is replaced by 2 into tan inverse x. Now differentiate with respect to x on both side.

[01:17:37]Now differentiate with respect to x on both side.

[01:17:48]So here the differentiation of y is nothing but dy by dx which is equal to differentiation of constant that is<unk> by 2tiff differentiation of constant is zero. So again differentiation of tan inverse x is 1 by 1 + x² that's why dy by dx which is equal to -2 / 1 + x² dy by dx which is equal to -2 / 1 + x² Is there any doubt? Please raise your hand.

[01:18:53]Is it clear?

[01:19:01]Okay, that's next question.

[01:19:14]Next question.

[01:19:18]Y is equal to is it over Okay.

[01:19:53]Raise your hand.

[01:20:18]Okay. Next question.

[01:20:24]Y = cos inverse of 2x / 1 + x² where x is greater than -1 less than 1.

[01:20:38]Yes, just shown.

[01:20:42]So try express again Freom.

[01:21:38]Sure.

[01:21:49]Because we go to the top because I need Since my dear dear love your Central.

[01:22:39]This is the Okay.

[01:22:51]- 2x 1 + x² can run.

[01:23:13]Okay. So put x = tan put x= tan theta then theta implies tan inverse x.

[01:23:28]So y = cos inverse of 2 tan theta / 1 + tan² theta first is the bad boy.

[01:23:51]So y = cos inverse of 2 tan theta / 1 + tan square theta can be written as sin 2 theta.

[01:24:00]So here y = cos inverse of sin 2 theta can be written as cos of<unk> by 2 - 2 theta because we know that the property inverse geometric property cos inverse of cos theta can be written as theta.

[01:24:21]S y = cos inverse of cos theta can be written as theta that is<unk> by 2 - 2 theta.

[01:24:31]So now differentiate differentiate with respect to sorry y =<unk> by 2 - 2 into tan inverse x because that implies theta = tan inverse x. Differentiate with respect to x on both side.

[01:25:02]differential dy by dx which is equal to -2 / 1 + x² is clear foretting Okay.

[01:25:35]Okay.

[01:25:40]Okay.

[01:25:55]Okay. Next question.

[01:26:02]Y = sin inverse of 2x roo<unk> of 1 - x² where x is greater than or equal to - 1x <unk>2 less than 1x<unk>2 x is greater than equal to - 1x roo<unk>2 less than 1x roo<unk>2 Anybody mobile?

[01:27:00]Yes. Okay.

[01:27:25]This is a problem. Okay.

[01:27:48]Sinx.

[01:27:50]Yes. Sin x or cos x or sin x or cos x.

[01:28:03]Yes.

[01:28:07]That's me sin 2x= 2in x.

[01:28:18]So x + 6 sin x again roo<unk> 1 - sin square. But we know that the property identity sorry sin square x + cos² x which is = 1. So cos² x which is = 1 - sin square x cos x which is = roo<unk> 1 - sin² x. So roo<unk> of 1 - sin square sin x into cos x already. So 2 sin x into cos x.

[01:28:52]So me super next.

[01:29:05]Okay.

[01:29:14]support.

[01:29:38]Okay.

[01:29:40]Okay.

[01:29:42]So inverse that is sin inverse of 2x roo<unk> of 1 - x² which is equal to that is 2 sin inverse x 2 sin inverse x when x is greater than or = - 1x <unk>2 less than 1x roo<unk>2 is it okay? Sin inverse of 2x roo<unk> of 1 - x square which is equal to 2 sin inverse x. Same format sin inverse of 2x into roo<unk> of 1 - x² which is also called as 2 cos inverse x which is also writed as 2 cos inverse x. Here condition when x is greater than 1 by <unk>2 less than 1.

[01:30:44]Is it okay?

[01:30:54]Is it okay?

[01:30:59]X is greater than= -1<unk>2 less than 1x<unk>2 but condition greater than or equal to - 1 by<unk>2 less than 1x<unk>2 sin inverse x in case conditions so that condition will be cos x based on given condition.

[01:31:32]Is it clear?

[01:31:46]Is it clear conditions?

[01:31:51]So conditions conditions.

[01:32:16]Is it clear?

[01:32:21]Okay. Next. Is there any doubt?

[01:32:33]Is it clear?

[01:32:48]Okay.

[01:32:52]Condition.

[01:32:54]So conditions less than 1 x= sin theta in case condition put x= cos theta based on condition you decide whether sin x you're taking or cos x you have to take if they given this condition then you choose cos x otherwise you choose sin x for this condition okay inverse function.

[01:33:39]Put x= sin.

[01:33:45]Because of this condition, put x = sin theta. That implies theta is = sin inverse x. Theta = sin inverse x.

[01:34:00]So y = sin inverse of 2 into x + sin theta roo<unk> of 1 - sin² theta.

[01:34:14]So here y = sin inverse of 2 sin theta into cos theta because we know that the identity sin² theta + cos² theta which is equal to 1. That's why cos theta which is equal to roo<unk> of 1 - sin² theta.

[01:34:39]y = sin inverse of 2 sin theta into cos theta can be written as sin 2 theta. So we know that the property that is inverse trigonometric function property sin inverse of sin theta can be written as theta.

[01:34:58]Sin inverse of sin theta can be written as theta. Here 2 theta is there that's why y = 2 theta.

[01:35:06]Theta is nothing but sin inverse x.

[01:35:15]Now differentiate with respect to x on both side.

[01:35:22]Differentiate with respect to x on both sides.

[01:35:26]So we all know that differentiation of sin inverse x is differentiation of sin inverse x is yesterday we discussed this differentiation of sin inverse x is 1x roo<unk> of 1 - x² so that's why differentiation of y is nothing but dy by dx which is equal to 2 into differentiation of sin inverse x is 1 by roo<unk> 1 - x².

[01:36:06]Therefore dy by dx which is equal to 2 / roo<unk> of 1 - x².

[01:36:17]Is it clear?

[01:36:27]What are we getting?

[01:36:32]Yes s 2 roo<unk> of 1 - x² works me. Yes.

[01:36:55]So same question change y = sin inverse of 2x 1 - x² but condition x is greater than = 1x <unk>2 less than 1 x is greater than or equal to 1x <unk>2 less than 1.

[01:37:21]Same question. Another question.

[01:37:32]Same answer without solving. Don't decide.

[01:37:49]Okay.

[01:38:00]X is greater than= 1x<unk>2 less than 1usion.

[01:38:12]Y = sin inverse of 2x roo<unk> 1 - x² x= 1x<unk>2 less than 1 prim x= cos xrim able to respond.

[01:38:52]Just cos x= cos x that implies sorry x cos theta x = cos theta that implies theta is equal to cos inverse x same.

[01:39:11]So y = sin inverse of 2 of cos theta into sin theta.

[01:39:24]So y = sin inverse of 2 sin theta into cos theta can be written as sin 2 theta.

[01:39:30]So again sin inverse of sin 2a 2 theta can be written as 2 theta.

[01:39:36]So y = 2 theta is nothing but cos inverse x here theta is nothing but cos inverse x differentiate with respect to x on both side dy by dx X which is equal to 2 into differentiation of cos inverse X is - 1 by roo<unk> 1 - x² differentiation of cos inverse x is - 1x roo<unk> 1 - x square that's why 2 / roo<unk> 1 - x² So previous answer 2 - x square but here negative sign is there dy by dx which is equal to - 2 roo<unk> 1 - x² you get both answers are sameus right okay is there any doubt Is there any doubt?

[01:41:15]Okay.

[01:41:16]Okay.

[01:41:39]Okay.

[01:41:40]Well, thank you. Next class will continue.

[01:44:05]So good afternoon dear students.

[01:44:12]Please update your attendance online.

[01:44:18]All of you please update your attendance as soon as possible.

[01:44:27]So we'll be starting with the classes biology class Suraj Rakita Gusuma Sonali Nitamita Jesus. Thank you Raui.

[01:44:46]Yes.

[01:44:49]So I have I hope all of you have joined.

[01:44:54]So we'll be starting with the chapter that is organisms and populations under the unit ecology.

[01:45:16]Yes. So shall we start?

[01:45:24]Am I audible all of you?

[01:45:27]Am I visible for for you? Please give me a thumbs up.

[01:45:43]Okay.

[01:45:46]Okay. Okay. Thank you. So, we'll start with the unit. So, I've completed the introduction part. Okay. The unit introduction as well as uh I also have completed the scientist introduction. Okay. The scientist introduction has been completed. Now, we'll go through the actual chapter. Okay. The organisms and populations. As I told you organisms and populations also although it is mentioned in your headings but actually you don't have the organism part okay organism part is not there for you okay just it is mentioned as a heading you can go through the old NCRT if you need but I don't recommend you to do so because if you see the need paper of this year also they have never not asked any question out of the old NCERT or from the organisms part. Okay. So, hence we'll be dealing with populations itself. Okay. Moreover, we'll be dealing with populations itself.

[01:47:00]So to start with to begin with so you know this chapter comes under the unit ecology. If you break the word ecology so it comes out to be echo and logi.

[01:47:15]Okay echo and logi. So what is it? I mean these words are taken from Greek language and echo comes from the word oos. Okay. Oos.

[01:47:30]Okay. So it comes out from the word oos.

[01:47:34]Oos means the meaning is home. Okay. Oos means home. And uh the logi logi means it comes out from the word logus. You know it is to study. The study of your home you call it as ecology. I've discussed it already. So now your NCERTT as a starting introduction it mentions that our living world is fascinatingly diverse and amazingly complex. Okay, fascinatingly diverse and amazingly complex. So you have lot of diversity. Okay, different species of plants are present and different species of animals are present in case of your uh in the living world. Okay, in the we have lot of biodiversity that is what I mean to tell you and in that it is already I mean a lot of diverse and you can see that it is very complex also it is not very simple okay lot of organisms are present different at different complexities you can find the organisms okay now how to study this one okay how to study this one for that you have something called as levels of biological organization. Okay, you have to know what is the levels of biological organization. Okay, so on this basis you are going to study how diverse is our uh system. I mean the organisms, how diverse are the organisms that is plants and animals. So on what basis you you can study that on the levels of biological organization. Okay. And if you see the biological organization it as a starting point of uh this one you can start with a cell. Okay. Wherein you call this what is a cell?

[01:49:42]So what is a cell? So cell is a basic structural and functional unit of life.

[01:49:48]Okay. on which it is a basic level of biological organization. Okay, very a starting point of biological organization and before that it comes to be the cells are made from many molecules. Okay, so molecules such as proteins such as you know that carbohydrates, minerals so all those things together constitute the cell.

[01:50:12]Okay, the macroolelecules we call them as we call them as macro molecules or the large molecules. Okay, macro means large and molecules are the uh components. Okay, the molecules the very large molecules make up your cell that is uh like your carbohydrates that is sugars and then you have the proteins and then lot of vitamins, minerals, you have lot of fatty acids. Okay, lipids.

[01:50:42]So all those things together forms a macroolelecules and these macroolelecules constitute a cell and cell forms the basic structural and functional unit of life that you know and together if you group a uh certain types of cells okay many types of cells are are grouped in a to perform a specific function you can call it as what the group of cells What do you call group of cells?

[01:51:16]You can call group of cells as tissue.

[01:51:20]Okay. So group of cells can be called as tissues. And so group of tissues will form together. It can be formed into a group of tissues can form into a organ.

[01:51:33]Okay. So a specific type of organ can be formed from a group of tissues. Okay. So then many organs say for example you have many organs such as uh your esophagus you have stomach you have small intestine you have large intestine and all these organs or say for example lungs you have kidney you have brain you have and then these organs together constitute your organ system. Okay it constitute into a organ system. Say you have uh the organ systems okay different organ systems you have in your body okay that is called as say for example you have digestive system you have respiratory system you have circulatory system different uh systems you have in your body okay that is called as organ system and these organ systems together all these organ systems will constitute an organism okay will constitute an organism okay we are talking about a individual organism. Okay, individual organism develop that is what happens in case of an individual organism and then comes out and then comes out here these organisms tend to live in a specific group. Okay, in a specific group you can call this group as population. Okay, that is what you can call it as a population. So what is population? So it is a group of organisms. Okay. Group of organisms in a in a specific geographical area.

[01:53:19]Okay. In a specific geographical area or a region. Okay. Or a region you can call them or you can call it as a population. So group of organisms I tell you. So these organisms belong to a same species. Okay. So these organisms are belonging to the same species not different species. Okay. Only say for example you have human population. So human population you will find only homo sapiens. The species are human beings or monkeys. Say population of monkeys. It is only restricted to monkeys. Okay.

[01:54:02]Then this population together many different populations. Okay. Say for example uh you have monkey population, you have squirrel population, you have bird population.

[01:54:14]Together it is uh going to be present at in a specific region. Okay. In a specific region you can call them as a community. Can call them as a community.

[01:54:26]Say for example you have squirrels as I told you or the birds which is present on a tree. Okay the birds which are present on a tree. So you have different species. So different organisms belonging to different species are present in a same region. Okay that region you can call it as a say for example you have a tree. Okay in a tree different species or different populations are present together. You can call such a organization level as community. Okay.

[01:55:00]So what is that? A group of different organisms. Okay. Group of different organisms belonging to different species. Okay.

[01:55:14]I'm telling you this is different organism means different species. Okay.

[01:55:18]A group of different species that is present in a specific in a specific area. Okay. In a specific area you can call it as a community.

[01:55:32]Okay. Then if you go further if you go further from a community you have a higher level that is ecosystem. Okay.

[01:55:42]That is your ecosystem. So after community you have a larger space in which there will be there is going to be interactions. Okay, interactions are taking place. So interactions are taking place between the organisms. Okay, between the organisms in a area. Okay, in a given area there are lot of interactions that are going on between the organisms as well as between the physical environment. You can call that such a level you can call it as a ecosystem. Okay. So wherein lot of interactions are going to be happening.

[01:56:22]Okay. So ecosystem sanskari. Next you can if a larger ecosystem. Okay. Larger ecosystem you can call it as a biome.

[01:56:34]Okay. So here it is a large area. Okay.

[01:56:38]You have a large area. talking about a very large area like a tropical rainforest or evergreen forest large area and then in which you have which you have it has a specific vegetation. Okay, it has got a specific vegetation in it. And what do you mean by vegetation here? Vegetation means So vegetation means the flora or the plants. Okay, plants flora.

[01:57:20]So you have a specific vegetation. this specific vegetation. Okay, this specific vegetation is going to decide decide the animals that are present. Okay, that is your fauna. Okay, the animals which plants are sorry which animals should be present in that area that is going to be decided on the basis of the specific vegetation that is present in that area.

[01:57:49]Okay. So such an area you can call it as a biome. So for example for your example you have you can write a type different types of forest. Okay say for example you have tropical rainforest. Okay tropical rainforest can be an example for biome or you can give desert ecosystem. Okay desert can be an example for biome. Okay different biomes are present. Now this on what basis here you have different types of I mean biomes. Okay. Different types of biomes.

[01:58:28]It is on the basis of temperature. Okay. It is on the basis of the first thing is temperature. So what is the temperature in a tropical rainforest and what is the temperature in a desert? So desert has got very high temperature comparatively to the tropical rainforest. Okay, that is what you have. And then uh you can give other examples like other factors uh you can give that is your precipitation.

[01:58:58]So precipitation means not your chemistry precipitation. Okay, it is we are talking about ecology perspective that is rain. Okay, rain. So amount of rain. So amount of rain is going to decide which type of biome is going to be present. Okay, amount of rain that is going to decide the different type of biome. Say for example tropical rainforest has got more precipitation and rather than desert you know in a desert ecosystem or in a desert biome the precipitation level is very less.

[01:59:32]Okay. Then uh the other thing is you can go for snow also. Snow can be a deciding factor. So in a Himalayan forest okay or a deciduous forest you can find a pine forest. So in that you'll see usually you can see snowfall. Snowfall is a factor for deciding a biome.

[01:59:54]Okay. So that's all about different levels of ecosystem. We started with macroolecules then came to cell then you have tissues then organ organ system then the organism okay then you have organism From organism you have population.

[02:00:38]Then comes community.

[02:00:45]Then it is ecosystem. Okay. Ecosystem.

[02:00:50]And finally we reached biome. Okay. And all the biomes together you can call it as a biosphere also. The highest level can call it as a biosphere means nothing but your earth the entire earth can be considered as a total ecosystem. So we in this unit in the ecology you will be studying all these four different levels of organization. Okay, different levels of organization you will be studying starting from organism and then going with population and then community and ecosystems. This will be dealt in the next chapter that is in ecosystem and very less is given about biome.

[02:01:38]Okay, biome is very less discussion that you have in your textbook. So we'll be largely on a large scale in the next chapter we'll be discussing about ecosystem as well as the community and what are the interactions and all we'll be discussing in the next chapter and in this chapter as the name suggest you have organisms and population. So we'll be concentrating more on population in this chapter. Okay. In this chapter we'll be concentrating more on population level not on the organism level. Okay. So without delay we'll start with the populations. Okay.

[02:02:24]Populations as I've given the definition for you. It is nothing but the group of same species that is present in a definite geographical region. Okay. Definite geographical region.

[02:02:39]you can call it as a population. Okay.

[02:02:42]So now this is your just I'll go through the slides. Okay. Please uh go through this one. Please see to it.

[02:02:49]You have the basic level that is it starts from individual. Okay.

[02:02:55]Individual. Then population. Then comes the higher level that is community.

[02:03:01]Okay. Then you have ecosystem biomes and the largest one is biosphere.

[02:03:08]Okay. So the basic unit of ecology okay it is the basic unit of ecology is your individual okay basic unit of ecology is nothing but the individual then comes group of individuals together forms a population then different species forms a community and then comes your ecosystem and then lastly your biome okay this is what the levels of uh organization ation. Now, so they have given to explain this ecology they have given an example very interesting example of bullbull. Okay, the bird which is singing. Okay, so at any level of biological organization we can ask two types of questions. Okay, so you can ask two different types of questions in ecology. So what is that? How and why type. Okay, how type and why type question. Okay. So for example, when we hear the bullbull singing early morning in the garden, okay, we may ask how does the bird sing, the bird is singing, how does it sings? That is the first question, a primary question that you can ask. Okay, then or you can ask why does the bird sing? Okay, out of curiosity, why it is singing?

[02:04:30]The how type questions seek a mechanism behind the process. Okay. How type questions will tell you what is the mechanism behind it? How it is going to sing? So what is the principle behind it? So how it is producing sound. Okay.

[02:04:45]By with the help of they have given the voice box. Okay. Or sirenings. Sireni that is your voice box. So vibrations in the bones will create a sound. Okay.

[02:04:57]That is from the sirens. So that is why that is how it is going to sing. That is the first question. And the next question, the second question, for the second question, what is that? Why the bird is singing?

[02:05:13]It is to communicate with its mate during the breeding season. Okay? Is to communicate with a bird during mating season. That is why 1 minute students.

[02:06:33]Okay.

[02:06:38]Okay. So the the second question is why type question. Okay. What is the mechanism? I mean the first question is what is the mechanism and how it is going to sing and the second question is why it is singing okay why the bird the bullw is singing so in order to communicate with its mate during the breeding season. So breeding season means the reproductive phase. Okay, reproduction reproductive phase you have to the bird the male bird has to impress the female bird. So hence uh there is breeding therefore it will be allowed for breeding otherwise hence it is going to sing or to communicate with its mate that is the female bird. So that is why it is going to sing. Now when you observe the nature around you with a scientific frame of mind you will certainly come up with many interesting questions. Okay many interesting questions you can find like this not only bull singing you can have many questions. See many examples are given in your NCERT itself. Say for example you have night blooming flowers are generally white in color. Okay. So night blooming flowers are white in color. Why why it is white in color? Okay. They're asking white type question. So white is white in color. Can anyone answer this?

[02:08:05]Why the night blooming night blooming flowers are generally white? Okay, because in order to attract, okay, so remember in order to attract nocturnal pollinators, okay, nocturnal means those organisms which are active at the night. Okay, nocturnal pollinators attract they are white in color. Okay, because at the night time it is the moon's light will be reflected by the white color.

[02:08:40]Okay. So, white color flies are present in order to attract nocturnal pollinators. Okay. Remember that because hence the night blooming flowers are generally white in color and you know it will save its energy to synthesize the pigments. So different pigments are required for colors. So colors different pigments. So that energy is saved and that energy is transformed into uh your to create orders. Okay. to I mean orders means the smell okay smell to attract the pollinators they will rather than producing the pigments they will invest their energy in order to bring out the different smells okay so that is why it is going to be produced into white color and how does the bee know which flower has nectar so bees are you know bees main uh function is to pick the nectar from from the flowers and what so how does the bee know which flour has nectar and which does not have. So many flowers will not have nectars but many of them offer nectars.

[02:09:45]Okay, that you have studied in your first chapter itself. Pollination when the sexual reproduction in claring plants. So how does the bee know where on which flowers have nectar?

[02:09:59]These bees have a okay sensors. Okay, they have a sensors, neurological sensors that can attract that can get attracted towards the nectar which is present. Okay. And their vision is also like that. So the vision of these organisms the pollinators will be in such a way that it can see through the nectars. Yeah. And one more thing is through the smell also. Okay. through the smell also it can it can get a note of the flower which has got nectar in it. Okay. Then why does cactus have so many thorns? Okay.

[02:10:42]Cactus cactus plant you will find the thorns.

[02:10:47]What is the purpose of this thorns? So basically it is for defense purpose.

[02:10:53]Okay. Defense from the herbivores. So our viewers will eat away all the plants mean the cactus. So in order to avoid that it will produce thorns as a defense mechanism and also to reduce transpiration. Okay transpiration the loss of water you can call it as transpiration. So to reduce the transpiration you can go for I mean the cactus have got thorns. Okay that is the questions. And how does the chick spurse recognize its own mother? Okay, her own mother. How it is going to recognize? So recognize it is through through behavioral imprints. Okay. Through behavioral imprints. So what is that?

[02:11:45]So as soon as the uh chick comes out or hatches from the egg, okay, it hatches from the egg.

[02:11:55]So what happens? It interacts with a object which is going to be near to it and it is going to be move. Okay. So it interacts with the objects which is moving.

[02:12:10]interact.

[02:12:12]So which is going to move and that is your the mother hen is going to be staying near the chicks and it is going to be taking care of that organism. Okay, it baby that is its chick. So the mother hen is going to take care the chick. So hence it knows the hen mother hen is the protector.

[02:12:37]Okay, it is going to feed it or it is going to take care of it. Hence the chicks will identify that it is a protector. Okay, not as a mother but moreover it is a protector of themselves and they identify mother. That is how the chicks are the chicks identifies or recognizes its own mother.

[02:12:59]Okay. Then uh you have we'll come to the population that's all about uh the introduction part. Then you have the populations. So what you mean by populations? Many times uh I have discussed uh the definitions already.

[02:13:17]Can you tell me what you what do you mean by populations?

[02:13:24]Yes. What do you mean by populations?

[02:13:29]I've told you the definition already.

[02:13:35]So, populations are nothing but a group of group of wait. Okay. group of similar organisms belonging to belonging to a similar species. Okay. Or a belonging to a specific species. Okay. belonging to a specific species where it is going to share or compete. Okay, it is going to share or compete for resources. Okay, remember it is going to share or compete for resources and they can interbreed. Okay, they can interbreed between themselves. Okay, they can interbreed between themselves. That is your actual definition of a population.

[02:15:00]So it is nothing but a group of similar organisms belonging to the same species or specific species and they share or compete share or compete. They can share the resources or they can compete for the resources. Okay, they are see for example human beings we share the resources and we'll live in a social group. Okay, so we are going to live in a group itself but we share at the same time we share the uh resources and also we fight for the resources. See sometimes people won't get the food.

[02:15:37]Okay, then the family cannot provide food for all the individuals. So hence there will be computation for resources.

[02:15:45]Okay, computations will be present for resources that you can see in case of a population and then they can interbreed between themselves. Okay, they can interbreed. So interbreed the meaning is they can have or undergo sexual reproduction only sexual reproduction not asexual reproduction. So when in the context of ecology you have to talk about only sexual reproduction not about a asexual reproduction. Okay. So that is what here you have a group of similar organisms belonging to a same species or specific species share or compete for resources and they can interbreed with themselves. Okay. Or within themselves or between themselves you call it as a species uh sorry a population. Okay. So remember the definition of population anyways you will not be asked a direct definition but you have to know what is meant by uh population.

[02:16:45]Okay. So that is what you have in case of population and after that you have to know something called as population attributes. Okay. Population attributes.

[02:16:56]What do you mean by attributes?

[02:16:57]Attributes and attributes are nothing but the features. Okay, attributes are nothing but features.

[02:17:14]Okay, they are okay. Many of you are typing the definitions. Group of organisms of same species. Yeah, specific geographical area. Yeah, you can write that.

[02:17:27]You have to mention about the resources also. Okay, that is what in depth you have to understand about the populations you have to mention the in the definitions you have to mention that it is going to compete for it is going to share the resources. Okay, you have to mention that point as well dan.

[02:17:48]So you have not included in that in your definition. You please add that also.

[02:17:53]Okay, now coming to population attributes. Attributes are nothing but the features or you can call it as a characters. So how you can study population on basis of your population attributes. Okay. On the basis of population attributes itself you're going to study or you can study the populations. Okay.

[02:18:15]So populations attributes are of different uh things like different varieties you have that is starting with birth rates and then you have death rates then you have sex ratio age pyramids and then population density. So each one of uh this one you have to study in detail. Okay each one of them you have to study in detail. So what what are the examples? Can you give some examples for populations?

[02:18:44]give some examples for populations.

[02:18:47]NCIT mentions you about corants. Okay, there are something organisms called as cormerants. These or these corarans are nothing but fish eating birds. Okay, fish eating birds. You can call them as cormerants. It is belonging to a specific species. Okay, specific species and it is present in a area a single area say for example in a lake. Okay. A group of or a population of cormanents.

[02:19:15]A group of cormanants present in a lake.

[02:19:18]You can call it as a a population. Okay.

[02:19:20]You can call it as a population or you can call the rats or rodents. Rats or rodents can be called as mean present in a leftover area. Okay. That you can also call it call them the rats as a specific population. Okay. Or and other examples.

[02:19:41]You have other examples that is tewood.

[02:19:44]Okay, teakwood present in a plantation.

[02:19:47]Okay, in a plantation you have teak plants only plants are present. So hence you can consider it also as a example for that is your population. Okay, these are some of the examples. You can g give a number of examples. Okay, if you want you can give a number of examples. I've mentioned only those examples which are present as per your NCERTT. Okay. Then also not only this is in uh in a large scale. Okay. You have a small scale under very micro level you can give the microorganisms that is or say for example you have the bacteria. Bacteria which is present in a culture.

[02:20:29]Bacteria that is present in a culture can also be called as a population. The bacterial population can be called as a population as well. Okay. Although it is very minute, very microorganism, you can give that example for your population.

[02:20:43]Okay. Like many examples you can give the human beings can be a good example for population and the lotus plants in a pond. You can give as an example. You can give any number of examples for the populations. So population attributes.

[02:21:00]Okay, we'll come to population attributes. So whenever you are considering population or population attributes you have to compare okay we'll be comparing with the organism level and the population level organism level and population level uh say for example you have at the population level say first one okay first one birth rate okay birth Example, birth is for individual. Okay, birth is for individual level.

[02:21:40]And when you consider for population level, population level only consider m is birth, it becomes birth rate. Okay, becomes birth rate. Or if you consider death at a individual level, it becomes death rate at a population level. At a population level, it is death rate and sex ratio. Okay, you have the next attribute as sex ratio. At the individual level, we have different sex.

[02:22:12]Okay, you have the male as well as you have the female individual. But at a population level, we'll be talking about sex ratio. Okay, we'll be talking about sex ratio. And then uh what else? You have other things like you have age pyramids.

[02:22:31]Okay, age pyramids means individually we have different ages. Okay, so individuals we have say for example starting from a baby. Okay. One year old baby you have individual level and the adult you have 18 years for example you have you are uh around 16 to 17 years of age. Okay. So and other people and for example myself we are having more age than you. Okay. So individual level we are talking about age. Okay. But at a population level we will compare it in a larger level. Okay. We'll have three categories of uh ages. Okay, we'll we'll talk about these categories later on.

[02:23:15]Okay, when we come to in detail about uh this age and age pyramids and at these three categories are made on the basis of age pyramids. Okay, we have something called as age pyramids and then at the last you have something called as population density. Okay, population density. So population at the individual level if you talk you have number of individuals what number of individuals.

[02:23:47]So we'll talk about the same thing at a population level you call it as population density.

[02:23:55]Okay, population size or population density can call it as population size or population density as well. Okay, these are the things we'll be discussing in the uh next slides. Okay, the first one the key attributes of population is your birth rate. Okay, birth rate. So per thousand people you're talking per year. So how many uh children or how many individuals are born per thousand people per year you can call it as you can call it as birth rate okay thousand people so per thousand your people how many of them are born the number of live births okay we are talking about number of live births per thousand people in a population over a given period. Okay, over a given period usually we record it as a year. Okay, one year per year how many how much increase in the population you will be discussing about that. Okay, then you have death rate. Okay, death rate is per thousand people per year. So how many of them are dead per year? The number of deaths per thousand people in a population over a given period. over a given period again the period the time period we consider it as one year itself not less okay one year I mean uh we will not consider it as a smaller intervals like say 1 week 1 month and consider model so we are considering it as usually as one year as per when you consider human beings okay human beings in pictures then you have sex ratio okay sex ratio ratio of males and females so sex means you have male and female sex so what is the ratio For how many males you have? How many females? So for say for thousand in a population of thousand.

[02:25:55]So how many are males or how many are females? Okay. What is the ratio between them? So how many females are present for a how many males? You can call it as a sex ratio. Here 51% and 49%. It is the real time value of India. Okay. They have given 59% male and 49% is a female.

[02:26:17]Now it is it will change. Okay, it is dynamic. It is going to change the ratio of males to females in a population over often expressed as males per th 100 females. Okay, so how many males are present per 100 females? Okay, 100 females to males.

[02:26:35]Next you have age distribution. So age distribution in by using age distribution you will plot a graph. Okay that graph you can call it as age pyramids. Okay it will come out to be age pyramids. So what do you mean by that age pyramid? The population of a the population of the populations within different age group. Okay within the different age groups what is the population that is present? Say for example below 18. So how many people are present in the age group below 18 and above 18 and below 60 how many people are present that is one uh category you can make and above 60 okay above 60 the old age people okay how many of them are above 60 that is different uh groups that you can make and which are critical for future growth projections about if you know this range okay if you know this range you can definitely uh predict what will be the future population uh distribution or age distribution that is present in a population. And lastly the population density. Okay, population density is very important. So you know what is density? Density means number of individuals. Okay. Number ofology perspective number of atoms number of particles in physics present in a given area you can call it as density. But here population density the number of individual organisms. Okay.

[02:28:14]Number of individual organisms that is present in a unit area. Okay. In a unit area that unit area may be square kilometer. Okay. The number of people present in one square kilometer. Okay.

[02:28:28]Or per square kilometer. How many individuals are present in a given area?

[02:28:32]Say for example in Oda. So how many individuals are present per square kilometer? You can tell or you can give that population density. Okay. So here you can see in this graph there is high density means more individuals are present in this region. And here you can see there is low density. Okay. low density is present in this region. So that is what you can measure. So the on the basis of density you can measure the population you can you can get a brief idea about population. So starting with the first one birth rate and death rate.

[02:29:09]So birth rate and death rate is nothing but we are talking about we are talking about the per capita per capita births or deaths.

[02:29:30]Okay. per capita growth in the births as well or the births and deaths you are talking about that is given as a birth rate or the death rate. The number of individuals born you can call it as birth rate. The number of individuals death dead in a given time period you can call it as death rate. Okay. So we as per individual level you have births and deaths. Okay. But at a population level you are you are talking about rates.

[02:30:02]Okay. In a given time period how many uh births are happening or how many death is going to be happening. Okay. So you have to calculate that uh I'll give you an example. Say for example in uh for birth rate okay for birth rate I'll give you an example. So okay we have a pond. Okay we have a pond. So in that pond you have uh many lotus okay lotus species are present in a pond. Say you are initially okay at the beginning of a year say in 2024.

[02:30:40]So 2024 it had got 20 lotus. Okay a simple idea. Okay, it's a for example in 2024 you had 20 lotus and when we saw it in the next year that next coming year it was grown into 28 lotus. There was a population of 28 lotus. So what is the growth? So how much have been added to this population of lotus? That is your birth rate. Okay. How many births have happened in this lotus population? That is your uh birth rate. Okay. Birth rate.

[02:31:22]So how many lotus is present or it is grown in this population? I mean in this pond.

[02:31:33]So 20 to 28 you have eight lotus. So eight lotus plants have added to this initial population. So initial population was 20 lotus and later on it became 28. This 2025 you can call it as final population. Okay. Final population and 2024 initial population.

[02:32:03]Okay. Initial population. Okay. You can call this as initial population. So initial and final population you'll get the difference. So you'll get the difference that is final minus initial. Okay final minus initial population is your difference you'll get that difference is nothing but you can call this difference as delta n. Okay, where n is number of organisms. Okay, number of organisms and then you have the formula to calculate the birth rate you have that is birth rate is equal to delta n by n deltat t. Okay, birth rate is equal to delta n by n delta t. So what is delta n? the change in population. Okay, delta n is nothing but change in population.

[02:33:09]Okay, that is what is the formula for this? Final minus final minus initial population. Final minus initial population will give you delta n. Okay. And n is again number of species. What is this? Delta t is change in time. Okay. So this is nothing but your change in time. So change in time.

[02:33:38]Now what I mean according to this values can you calculate this one? What will be the values? Delta n is we have already calculated it is comes out to be eight.

[02:33:48]N is what?

[02:33:51]N is what? N is nothing but number of individuals. Okay. Number of individuals present at the starting. Okay. presented the initial time. So that you can call it as n that was 20. Okay. 20. Uh so how many I mean uh what is the time change in time is what? 2024 to 2025.

[02:34:16]How many years that is 1 year. Okay. Per year 20 into 1.

[02:34:23]So per year means 1 year. So can calculate this one. What will be the value?

[02:34:31]comes out to be 8 by 20. 8 by 20 in divide by the value will be 4. Okay. 0.4 will be the value. Okay. 0.4 will be the value 0.4 of springs. Yeah. We have to answer this mean 0.4 offsprings per lotus. Okay. Per lotus per year. Per lotus per year. So 0.4 is the birth rate increase in the growth rate of this population is nothing but your 04. Okay.

[02:35:19]So 04 offsprings per lotus per year has been increased in this lotus population present in a lake. Done. That is how you calculate birth rate. Okay. And uh in the next one we'll uh same logic please apply for death rate also.

[02:35:39]Death rate same formula is same delta n by n delta t. Okay. The example you have I'll give you a different example. Say for example in a in a lab okay in a lab you have 40 fruit flies. Okay there are 40 fruit flies.

[02:36:03]So out of this 40 fruit flies four will be dead or four died in a week.

[02:36:20]So that is the data that you have. So what is the final population now? So this is this becomes initial population.

[02:36:27]Final population is so 40 minus 4 after a week it will become 36. So 36 will be your final population.

[02:36:41]So final population will be 36 and initial population will be 40. Now what you have to calculate delta n by n delta t that gives you death rate. Okay, death rate. What is the change in this number? I mean change in the number of individuals is four by n is initial that is 40. So 40 becomes initial death rate.

[02:37:11]40 becomes initial thing. Then 4x 40 into 1. Okay. One week.

[02:37:23]What is 4x40?

[02:37:28]Very simple calculation.

[02:37:35]1. Okay. 0.1 will be the answer. Okay, that is correct.

[02:37:42]Yeah.

[02:37:45]So 0.1 will be your answer for death rate. That is all about your uh birth rate and death rate. So this was very uh useful during the measurement of the death rates and death rates during COVID. Okay. So where we have we were having the corona virus. Okay. in the last before last year like 2020. So at 2020 we were having it was shown in the news and all the death rate. So this is the death rate that the the death rate has been increasing due to the covid viruses. Okay, it was in news and there may be this there may be increase or decrease. Okay, increase number if the number of individuals decreased we can call it as death rates. Okay, that is the difference you have to understand and yeah it is always given in per capita. Okay, per capita death rate per capita birth consider okay that is what you have in case of birth rate and death rate. Next one is sex ratio.

[02:38:52]I'll complete it and I'll stop here itself. So sex ratio is nothing but at the individual level you have male and female sex. male sex and female sex and but at a population level you are talking about sex ratios. Now that is nothing but how many males are present for females say 100 females. So 100 females you get is to males this ratio is nothing but your sex ratio. Okay, say for example you have in a population you have 60% females, 60% females and what will be the males? How much percentage will be the males? Males will be 40% males.

[02:39:35]Okay. So if you're asked what is the ratio for example in this you have thousand individuals. Okay. We'll take an example that is there are thousand people. So out of this thousand people we'll take the same data 60% are females 40% are males. So can you tell me what will be the ratio? What will be the ratio? How you can find it out? So out of thousand people 60% are females and 40% are males.

[02:40:06]So 60% females. I'll go with 600. 60% of,000 people is nothing but 600. and 40% of thousand people is 400.

[02:40:18]So now calculate this one 0 0 cancel and 2 3's are 2 2's are okay then 3 is to 2 or 3x2 3 is to2 will be your answer okay so 2 is mean yeah 3 is to2 or 2 is to 3 so that is female is to male okay female is to male so when here I'm asking male is to female and 2 is three. So whatever so females there two I mean females is three and males are two. So 2 is to 3 is the ratio. So that is male to female ratio. Now what you have to understand is if this difference is more. Okay, if remember if the difference is more then it shows that it shows that the population is unhealthy.

[02:41:32]Okay, there is a unhealthy population that is present in case of this ratio.

[02:41:39]If the ratio I mean population ratio or sex ratio if you know if there is difference more difference in the sex ratio we'll tell you that the population is unhealthy. Say for example in India say we have for every thousand males there is 950 around the 900 females.

[02:41:57]Okay around 900 females are present in India. But if the difference is more say for every thousand males you have only 500 females that is a big problem. Okay it was the situation back in 1960s and all where wherein there was lot of female feticides. So female ficides female population the male population was given much preference and was and there was there was much more population in case of males. Okay, that creates that creates a imbalance in the society. That is what the population becomes imbalanced and the uh it shows that it is unhealthy population. So this ratio if it is very close enough then it tells you that the we have a healthy population ratio.

[02:42:48]Okay, that is the population is good.

[02:42:51]So that is what you can come to know about uh the population by using this different attributes. Next you have age pyramids that we will continue in the next class. So that's all for today. See if you have any doubts please comment.

[02:43:10]So we'll be winding up the class now.

[02:43:16]It's already time.

[02:43:25]So that's all students for today. We'll catch you tomorrow for the next class.

[02:43:31]So thank you all.