Day 24 - CRACK SSC MATHS by DEO, Nizamabad Sri P.Ashok garu

本站添加: 2026-05-25

[00:06:07]Good morning, sir.

[00:06:22]Good morning, sir.

[00:08:15]What the hell?

[00:08:45]I can't see.

[00:10:14]Amazing.

[00:10:35]>> Amazing.

[00:11:55]Can you hear me now?

[00:11:58]>> Yes sir.

[00:11:58]>> Yes sir.

[00:12:00]>> Good morning sir.

[00:12:01]>> Good morning. Tell first one. What is sin plus theta?

[00:12:07]>> cos theta.

[00:12:10]>> Which quadrant? Second quadant. Second quadant s is positive. Right?

[00:12:13]>> Uh yes sir. It is 1 + >> 1 into 90 + theta.

[00:12:18]>> Oh 1 is odd number change function. Next >> theta. Which quadrant?

[00:12:26]>> Third quadant. Third quadrant.

[00:12:30]>> Third quadrant cos is >> sin theta.

[00:12:38]>> Sin theta.

[00:12:39]>> Sin theta.

[00:12:41]>> Yes sir. This is 2 into 90 + >> 2 into 90 + theta.

[00:12:45]>> Which quadrant?

[00:12:46]>> Third quadrant.

[00:12:47]>> Third quadrant.

[00:12:48]>> Third quadrant.

[00:12:51]>> Tan is plus >> uh tan is >> positive siritan tan theta.

[00:12:58]>> Tan theta >> 2 is even number >> even number. So same function.

[00:13:05]This is >> Yes sir.

[00:13:07]4 into 90us theta quadrant sir >> fourth quadant quadrantus theta minus theta co theta >> co theta right >> yes sir >> first quadrant sir >> 1 into 90 >> 1 into 90us theta >> first quadant first quadrant plus cosec theta.

[00:13:42]>> Yes, sir.

[00:13:44]Yes. Yes sir.

[00:13:47]>> 2 90us theta second quadrant quadrant is evensea function cosec theta right.

[00:13:59]>> Yes sir. Yes sir.

[00:14:04]So some problems.

[00:14:22]>> Yes. One more result also have to tell.

[00:14:32]Hey, I'll do it.

[00:14:56]S of minus theta.

[00:15:02]>> Suppose this is theta.

[00:15:06]>> It is in anticlockwise direction.

[00:15:10]Minus theta means you have to take in clockwise direction with same angle.

[00:15:22]Right.

[00:15:24]>> Yes sir.

[00:15:26]>> Angle theta is in first quadrant minus theta is in fourth quadrant. Right.

[00:15:32]>> Yes sir.

[00:15:34]>> In fourth quadrant which are positive which are negative.

[00:15:39]Second remaining are negative we can write as 0 into 90 minus theta right? Yes sir. Z is even number >> function same function same or different same function >> but quadrant is which quadrant fourth quadrant >> fourth quadrant >> fourth quadrant which are positive >> cos theta >> remaining all are >> negative >> sin of minus theta is >> minus sin theta >> sus of minus theta is >> cos theta tan tan theta.

[00:16:34]>> Yes sir.

[00:16:35]>> This is the sixth set of results.

[00:16:40]>> Sin of minus theta is sinus theta. Cos of minus theta is >> plus cos theta. tan of minus theta is theta of minus theta is theta of minus theta is >> theta >> coseant of minus theta is >> theta >> right? Yes sir.

[00:17:23]33 36 - 0.

[00:17:48]S of - 660° >> s of - 660° of,50 of - 450 by cos of 225 into cose 315 into cos 510 10us 660 means - 6.

[00:18:18]>> Yes sir.

[00:18:19]>> Right.

[00:18:20]>> Yes. Yes sir. Yes sir.

[00:18:25]>> S of 6ide with what angle? 90° 90 360 >> First of all 1 minute that is equal to sin of minus 660 you can write as minus sin 660 right >> yes >> yes sir >> into50 rightus USUS plus theta plus theta is what? Seeant of minus theta is >> yes >> plus second theta >> plus second just fourth quadrant minus theta is in fourth quadrant just that's that's you remember right and second are positive right >> yes sir >> 225 >> cosec 35 >> 350 >> cos 5 10 >> this will become minus >> sin 660 16 >> 60 cos 2° cos 5° cos 5 >> equation 6 into 90 + 30 >> 90 + 30. Yes.

[00:20:06]Quadrant.

[00:20:07]Quadrant.

[00:20:09]Eight quadrant. Fourth quadrant.

[00:20:11]>> Yes sir. 1 2 3 4 5 6 >> 5 6 7 8 >> 8. Fourth quadrant. Right.

[00:20:18]>> Fourth quadrant. Yes sir.

[00:20:20]>> Fourth quadrant. Which are positive? Cos are positive.

[00:20:27]>> Negative. Yes sir.

[00:20:28]>> Symbol negative.

[00:20:32]>> Minus. Huh? Minus what? 7 is what number?

[00:20:37]>> Yes sir.

[00:20:38]>> 30°us 30 - <unk>2 by<unk> 3 by 2<unk>3.

[00:20:46]>> Yes sir. Roo<unk>3 by 2<unk>3 by >> two >> right.

[00:20:52]>> Yes sir. Next.

[00:20:59]>> 50°.

[00:21:05]>> How do you get 10,50?

[00:21:08]Set divide with 90 >> 90 1 90 >> 11 into 90 + 60 >> 600 quadrant 12th quadrant 12th quadant 12th quadant quadant quadrant yes sir 12th quadrant Yes, sir.

[00:21:46]60° 1 - 1 by <unk>3 >> - 1 by <unk>3 right?

[00:21:54]>> Yes.

[00:21:54]>> Yes sir.

[00:21:58]>> Take 420.

[00:22:00]Second >> 420 420 360 >> 360 + 60° right?

[00:22:12]>> Yes sir. Yes sir.

[00:22:14]>> Yes sir.

[00:22:15]>> 10th quadrant. Fifth quadrant.

[00:22:17]>> Fifth quadrant.

[00:22:17]>> Fifth quadrant first quadrant. First quadrant all are positive. positive positive 60° pass 60 1 by 2 reciproal 2 by 1.

[00:22:37]>> Yes sir.

[00:22:40]That's it. Next.

[00:22:44]>> Cost 225.

[00:22:57]into 90°.

[00:23:00]>> Oh, third quadrant.

[00:23:02]>> Third quadrant. Third >> quadrant quadrant.

[00:23:05]>> Third quadrantus.

[00:23:09]So sus 45 cos 45° 1 - 1 by<unk> - 1 by<unk>2<unk>3 <unk>2 >> next cos 510 315 cose >> 35° right >> yes sir 2 into 90 >> 3 into 90 Yes. 45.

[00:23:40]>> Fourth quadant.

[00:23:43]>> Fourth.

[00:23:44]>> Fourth quadrant.

[00:23:51]>> Function 452.

[00:23:56]Second 45 <unk>2. Right. Yes sir.

[00:24:00]45 reciprocal. Second cos 45 1 by <unk>2. Second part is <unk>2 right >> <unk>2 cos 10° >> cos 10° >> cos 5 into 90 >> plus 60° right?

[00:24:30]>> Yeah.

[00:24:30]>> Yes sir.

[00:24:32]>> Sixth quadrant. The second quadant >> sixth quadrant quadrant >> second quadrant cos is sus 60° by 2<unk>us roo<unk>3 by 2<unk>3 sortus Similar us - <unk>3 by 2 into >> - 1 by <unk>3 - 1 by <unk>3 Sir, somebody's making noise. Sir, >> please note your >> 5 - 1 by <unk>2. Next cos 225 225 is >> - 1 - 1 by <unk>2 35°us <unk>2us roo<unk>3 - <unk>3 by 2us right?

[00:26:04]>> Yes sir.

[00:26:06]>> What happens here?

[00:26:13]>> Right.

[00:26:14]>> Yes sir. Here first of all symbols you multiply symbols minus into minus plus >> 1 by <unk>3 >> this is 2 by<unk> 1 into 2 mean 2 2 by<unk> sus <unk>32 by <unk>2 >> yes sir >> this is what happens this will become <unk>2 by roo<unk>2 means one >> one yes sir Yes sir. 2 by<unk>3 2 by<unk>3.

[00:26:48]>> Got it.

[00:26:48]>> Yes sir.

[00:26:49]>> Yes sir.

[00:26:50]>> Yes sir.

[00:26:51]>> What is this one sir?

[00:26:53]>> 2x 2 by <unk>3 by roo<unk>3. Got it?

[00:26:57]>> Yes sir.

[00:26:57]>> Yes sir.

[00:27:21]How many members understood? Please raise your hand.

[00:27:45]Okay.

[00:27:52]Okay. Good.

[00:28:23]seriously just not there. You're trying to draw wedge between my I this problem.

[00:29:06]Take this problem.

[00:29:33]Now the Oh yeah.

[00:30:11]There you go.

[00:31:29]us.

[00:32:05]What did I say?

[00:32:29]Please tell the answers.

[00:32:32]Got it.

[00:32:35]Okay.

[00:32:37]H please respond anybodyus cos theta into cos theta into cos theta by >> 1 minute >> direct directly you're right yes what is this what is this one it is equal to >> minus cos theta >> cos of 180 minus theta >> minus cos theta Right. Next.

[00:33:09]>> Ofus sin theta.

[00:33:11]>> Minus sin theta.

[00:33:13]>> Right. Next.

[00:33:16]>> Cos of minus theta is cos theta.

[00:33:29]>> Sin theta.

[00:33:31]>> Sin theta. Right.

[00:33:34]>> Yes.

[00:33:35]First multiply the symbol minus into minus plus right.

[00:33:38]>> Yes sir.

[00:33:41]Uh cos theta into sin theta into sin theta into cos theta minus into minus >> plus plus >> plus tan theta into cos theta sin theta theta sin theta sin theta cancels the cos theta theta sin theta by cos theta cos theta by sin theta sin theta >> cos theta cos theta sin theta sin theta gets cancel >> get cancel >> cos square theta >> cos theta cos >> square theta but not there in the option >> yes sir >> there we did mistake anywhere we did mistake please check of 180us theta minus cos theta correct cos of 90 plus theta minus sin theta minus sin cos of minus theta is cos this is 18 cos theta 27us theta correct it is sine of 360us correct okay I think I may give some problem hospitaliz.

[00:35:25]Okay, I have given wrong question. It is not fast. This is C.

[00:35:33]If it is there is then you will get to keep it as is no problem.

[00:35:40]minus standard question right okay no problem next problem what this higher angles to Got it. All of you right?

[00:36:13]>> Yes sir. You were instructor.

[00:36:16]>> Hello.

[00:36:17]>> Okay.

[00:36:19]Let me see.

[00:36:21]>> Okay. Wi-Fi is gone somewhat. It is very poor connection.

[00:36:31]Not audible.

[00:36:33]Audible. Audible. Okay. Right.

[00:36:49]>> I know.

[00:37:09]Read the questions square 1° cos² plus dash + 90° >> cos square 9° cos square 1° cos square 2° cos square 90° up to what square >> 90° >> 90° >> spring you have only s of 90us theta and s of 90 plus theta that only you have okay okay cos square 1° plus cos square 2° plus cos square 90° how to write this one see this cos square 1° + cos square 2° + 1 up to cos² 45° can we write?

[00:38:10]>> Yes sir.

[00:38:11]>> Yes sir.

[00:38:12]>> 44° plus cos² 45° right?

[00:38:18]>> Yes sir.

[00:38:20]>> Next after cos square 45 what you will get?

[00:38:24]square 46° right?

[00:38:27]>> Yes sir.

[00:38:27]>> Yes sir.

[00:38:29]>> Come in this direction. 46.

[00:38:33]>> 47.

[00:38:36]>> Yes sir. 47.

[00:38:38]>> Here you will write cos square >> 47.

[00:38:43]>> 1 minute. Cos square 89 cos square >> 90 >> 88 plus cos square 90. Yeah. Yes sir.

[00:38:55]>> Right. Both all of them are same or not.

[00:38:58]Once again I'm rewriting I'm rewriting once again cos square 1° plus cos square 2° + up to cos² 44° + cos² 45° >> 6° 46° >> 46° >> 47° up to 8° 88 89 12 >> right?

[00:39:35]>> Yes sir.

[00:39:36]>> Yes sir.

[00:39:37]>> Yes sir.

[00:39:39]>> Yeah. See this I am regrouping it.

[00:39:42]Square 1 + cos square 89. Can we write cos square 1 + cos square 89?

[00:39:49]>> That is one set.

[00:39:50]>> Yes sir. cos square 2 + cos square >> cos square 88 >> same right?

[00:39:59]>> Yes sir. Plus next one.

[00:40:07]Yes.

[00:40:08]>> Plus cos square 44 + >> 4 5 >> 46.

[00:40:18]>> So uh 46 >> 46 right?

[00:40:22]>> 89 + 190 89 + 190 88 + 290 87 + 390. For you have 464 is left over 47 square 90 is left over right >> but what about this one cos square 89 how to write it? Yeah. 8 plus 1 minute. 1 minute. Cos 89. How to write cos 89?

[00:41:01]You can write cos of 90 - 1°.

[00:41:05]>> Yes sir.

[00:41:06]>> Yes sir.

[00:41:07]>> C of 90us theta formula is what?

[00:41:11]>> Which quadrant it is?

[00:41:19]>> First all are positive right?

[00:41:22]>> Yes. Yes.

[00:41:24]one is right side. Therefore, Daddy, watch.

[00:42:39]It's Hello.

[00:43:20]>> Can you hear me now?

[00:43:21]>> Yes, sir.

[00:43:22]>> Yes, sir.

[00:43:29]cos 8° right?

[00:43:32]>> Yes. Yes sir.

[00:43:35]Therefore cos square 89 you can write as >> sin sin square 1.

[00:43:45]>> Yes sir.

[00:43:46]>> Is it clear?

[00:43:47]>> Yeah.

[00:43:48]>> Yes sir.

[00:43:51]Square 1 + cos square 1g sin square 1g.

[00:43:54]This is equal to becomes one. Right.

[00:43:56]Yes sir.

[00:43:57]>> Yes sir.

[00:43:59]>> What is cos square 88? You can write as cos 88. You can write as what? Cos of 90° >> mean sin 2° right?

[00:44:12]>> Sin 2°.

[00:44:15]Therefore 828 sin square two >> sin square 2° right? Yes sir.

[00:44:26]>> Therefore, how to write this one? cos square 1° + cos square 89° plus cos square 2° + cos square 88° plus so on up to cos square 44° plus cos square 46° plus cos² >> square + cos square 90 >> square 90° >> this is equal you can write as cos square 1° + >> sin square 1 >> sin square 1 right >> yes cos square 1° >> cos 2 + sin square 2 >> + 1 up to >> square 45 446 >> plus sin square 46 cos square 46 nothing but cos square 46 is nothing but what sin square 44 right >> yes sir >> is it clear cos square 46 is nothing but square right 46 + 44 is 90 right >> yes sir >> yes sir plus 1 by <unk>2² + 0² cos 90 Zero >> zero. Yes sir. Right.

[00:46:01]>> Yes. Yes sir.

[00:46:02]>> This is equal to 1 + 1 + 1 + repeated how many times?

[00:46:09]>> 44 times.

[00:46:11]>> Four times.

[00:46:12]>> Right.

[00:46:13]>> Yes.

[00:46:14]>> 44. Right. 1 2 3 4 1 up to 44 times. One is repeated added. Right.

[00:46:20]>> Yes sir. Yes sir.

[00:46:23]Plus plus 1 by <unk>2.

[00:46:35]>> Yes sir.

[00:46:37]>> 44 + 1 by 2 8 + 1 by 2.

[00:46:44]What is the answer?

[00:46:46]>> 89 by 2.

[00:46:50]89 by >> two.

[00:46:55]>> Got it.

[00:46:56]>> Yes sir.

[00:46:57]>> Yes sir.

[00:46:59]>> Yes.

[00:47:00]>> Understood?

[00:47:02]>> Yes sir.

[00:47:03]>> Yes sir.

[00:47:04]>> Right.

[00:47:05]>> Yes sir.

[00:47:07]>> Right. Note >> alpha plus beta = 90 by 2 by2 please.

[00:47:21]>> Yes. This is a symbol pi represents 180°.

[00:47:27]>> Got it.

[00:47:28]>> Yes sir.

[00:47:30]This symbol is called as pi repres.

[00:47:42]>> If alpha comma beta or compliment angles compliment angles means what?

[00:47:54]>> 180° by is 180° >> not 180° >> 90° >> supplementary is 180.

[00:48:08]>> Uh what is alpha? Alpha equal to<unk> by 2 minus beta. Right?

[00:48:13]>> Yes sir.

[00:48:15]>> Yes sir.

[00:48:17]>> What is sin alpha? Sin alpha = sin of<unk> by 2 minus beta means what? Sin of 1 into 90us beta.

[00:48:32]Do you know these symbols alpha and beta?

[00:48:35]>> Yes sir. Yes sir.

[00:48:38]>> Do you know these symbols?

[00:48:40]>> Yes sir.

[00:48:42]>> Sir no. Alpha beta gamma. Yes sir.

[00:48:55]Yes. Yes. Alpha, beta, gamma, >> I think it might be.

[00:49:00]>> Yes sir.

[00:49:03]X Y Z. This is also simp right.

[00:49:11]>> Uh okay. One minute please.

[00:49:16]Alpha beta are complement angles. Alpha plus beta is 90°. Alpha equal 90 - beta.

[00:49:21]Sin alpha is equal to sin of 90us beta sin of 90us beta becomes >> 90 sin becomes cos right first quadrant >> sir cos >> yes sir cos beta >> yes sir sin alpha is same as what cos >> beta >> beta >> beta >> cos alpha means cos of 90 minus beta cos of 1 into 90us beta cos of 90us beta means sin beta first quadrant all are positive right >> beta >> yes sir >> alpha beta are supplement complimentary angles alpha beta compliment angles sin alpha is same as cos cos beta and cos alpha is same as sin beta.

[00:50:25]>> Got it?

[00:50:27]>> Yes sir.

[00:50:28]>> Yes sir.

[00:50:30]>> Sin 30° is equal to cos 60.

[00:50:35]>> Yes sir.

[00:50:36]>> 60 sin 60 cos 30= cos 30= >> Yes sir. cos 30 = what? Sin 60.

[00:50:47]>> Sin 60.

[00:50:49]>> Similarly, >> 60 is same as 30, >> right?

[00:51:08]>> Yes. Yes. 30 same assembal to >> cos 40 >> cos ah Sorry sir. 70 sir >> 20 compliment angle is what?

[00:51:44]>> 70 sir >> 70 right? cos 50 equal to >> 40 sin 40 right >> yes sir sir >> tan 42° equal to >> sir 48 >> 48 48 >> 48 48 >> 48 How to prove you can prove like this one tan 42° 190us, >> right?

[00:52:25]>> Yes sir.

[00:52:25]>> 48.

[00:52:26]>> 48. Right.

[00:52:28]>> First quadrant. First quadrant all are positive. Right.

[00:52:32]>> Yes. Yes sir.

[00:52:34]>> First quadrant all are positive. One is our number.

[00:52:39]>> Right.

[00:52:41]>> Yes.

[00:52:43]>> Yes sir.

[00:52:44]>> Yes.

[00:52:46]22° equal to cos 22 and degrees is equal to sin 67 and half° right?

[00:53:02]>> Yes sir.

[00:53:04]>> Is it clear?

[00:53:05]>> Yes sir.

[00:53:07]Check this sin 30 1x2 cos 60 1x2 same right tan 30 1x roo<unk>3 cos 60 also 1x roo<unk>3 check right >> okay sir >> that is that is one concept if alpha come okay sir got it Yes, sir.

[00:54:06]>> Thank you.

[00:54:27]Next.

[00:54:33]>> Yeah.

[00:54:37]Okay.

[00:54:41]>> If alpha, comma, beta are supplementary angles. Supplementary supplementary angles.

[00:54:48]>> Yes.

[00:54:55]Cos square alpha plus square beta equal to >> 18.

[00:55:05]Supplement triangles means what?

[00:55:08]The sum of all right >> 180 >> 180us >> 180us beta= 180us beta right >> 180 minus beta >> yes sir >> 180 minus >> beta 90us beta.

[00:55:49]>> Yes.

[00:55:50]>> Second quadrant it is minus.

[00:55:52]>> Yes sir. 2 beta minus beta right cosal >> cos square alpha is equal to - cos beta square alpha is same as cos² beta right?

[00:56:18]>> Yes sir.

[00:56:20]Therefore cos square + sin square beta is equal to cos square beta + sin square beta.

[00:56:27]Right?

[00:56:31]>> Sin square beta cos square beta plus sin square beta is equal to what?

[00:56:38]>> One square beta + sin square beta is equal to >> one >> one >> one. Right?

[00:56:46]>> Yes sir sir.

[00:56:46]>> Is it clear?

[00:56:49]Yes, sir.

[00:57:09]>> Let's find this problem next.

[00:58:07]Right. Read this question.

[00:58:10]Sin of 15 by 9 into 4 into by 3 - 7 7 by 3 of - 3<unk> by 4 into cos of 7 by 6 into cosec of - 7 by 4.

[00:58:37]Right.

[00:58:49]First one of this you can write it as sin of 15 by 9 into tan of 4<unk> by 3 of minus theta is secant theta right >> yes >> seeant of minus - second theta right?

[00:59:10]>> Yes sir.

[00:59:11]>> Yes sir.

[00:59:11]>> This is this is - 3<unk> by 4 >> right?

[00:59:18]>> Yes sir.

[00:59:21]>> 7us 4 >> minus into minus becomes plus right?

[00:59:33]>> Yes sir. This is s of 15 into 180 by 9 into 180 by 4 into 180 by 3 into secant of 7 into 180 by 3 into 180 by 4 >> into 6 7 into 18 by 6 9 goes 20 300° >> Yes sir. 15 into 2300 >> 640° >> Yes sir.

[01:00:30]Second, >> 60 42° right?

[01:00:38]>> Yes sir.

[01:00:39]>> 20 times, sir?

[01:00:41]>> 60.

[01:00:43]>> How many times?

[01:00:45]>> 4 20 16 45 times, right?

[01:00:51]>> Yes.

[01:00:52]>> Sir, it is 180.

[01:00:57]>> 180.

[01:00:58]>> Okay, sir. Okay. 180 180.

[01:01:01]>> Yes sir.

[01:01:02]>> 45 times.

[01:01:03]>> Yeah. 45° 135° >> 135° >> * 30 * 3 * 45 into 7 35° Right.

[01:01:34]>> Yes.

[01:01:38]>> Is it clear?

[01:01:39]>> Yes, sir.

[01:01:40]>> Yes.

[01:01:41]>> Later you can do it.

[01:01:43]>> Okay.

[01:01:46]>> 10,000 to this 310,000 >> 3 into 90 + 30.

[01:02:02]is equals to >> okay you can do it later >> okay >> okay sir >> sir okay yourself please later you can do Right. Next problem.

[01:02:36]and triangle ABC + B by 2 into a + b by 2 into tan c2= first option sin 2 Okay. Second option one.

[01:03:08]Third option 2 A.

[01:03:11]Fourth option B.

[01:03:17]Yes, please.

[01:03:21]What is A + B plus? A + B +al.

[01:03:30]What is A + B?

[01:03:34]180 - 180US 3 >> A + B / 2 is >> 180 - C by 2, right?

[01:03:45]>> Yes, sir. Yes, sir. B2 is equal to 90us C >> 90us C by 2, right?

[01:03:54]>> Yes, sir. Yes, sir.

[01:03:57]>> We want what? We want tan of A + B / 2, right?

[01:04:00]>> Yes, sir. Okay.

[01:04:04]tan a + b by 2 = tanus by 2 >> this is equal to 1 into 90 1 quadrant all are positive right >> yes it is 1 into 90 is odd number means c by 2 right yes B2 by 2 A + B by 2 = C by2 right?

[01:04:39]>> Yes sir.

[01:04:39]>> Yes sir.

[01:04:40]>> Yes sir.

[01:04:41]>> Therefore tan of A + B / 2 into tan C by 2 equal to C by 2 into tan C by2 right?

[01:04:52]>> Yes sir.

[01:04:53]>> Yes sir.

[01:04:56]>> C and tan are what? Transal or not?

[01:04:59]Yes sir sir question their product is equal to one right?

[01:05:06]>> Yes sir.

[01:05:07]>> Answer is >> C by2 consider as theta co theta equal to 1 by tan theta tan theta tan theta gets cancelled right?

[01:05:14]>> Yes sir.

[01:05:16]>> Tan and quarter angle is same C by2 C by2 same angle or not?

[01:05:20]>> Yes sir.

[01:05:20]>> Yes sir. Same angle.

[01:05:22]>> Therefore tan theta into the equal to what? One >> one.

[01:05:27]>> Yes.

[01:05:30]Yes, sir.

[01:05:30]>> Right.

[01:05:34]>> Okay.

[01:05:40]Okay. This I will post one worksheet to try those problems.

[01:05:44]Okay.

[01:05:45]>> Okay, sir.

[01:05:46]>> Monday test is postponed. I will tell you later.

[01:05:51]Okay, sir.

[01:06:01]I'll be >> right.

[01:06:05]>> Okay.

[01:06:06]>> I will I will put one worksheet. You try it. Try those problems.

[01:06:10]>> Okay sir. Okay sir.

[01:06:13]>> Bye. Okay.

[01:06:14]>> Bye.

[01:06:16]>> Thank you.

[01:06:18]>> Thank you sir.

[01:06:20]>> Thank you sir.

[01:06:22]>> Right.