Mathematics for Physics | Practice Session | Target JEE NEET 2028

追加: 2026-05-18

[00:00:18]Hello. Hello.

[00:00:21]Hello everyone.

[00:00:24]Good morning.

[00:00:33]Hello.

[00:00:42]Hello. Hello.

[00:00:48]Shurukury kids practice session uh for basic mathematics.

[00:00:56]Ch. This is the first question from logarithm answer.

[00:01:04]Uh if log x base 2 plus log x base 4 + log x base 8 is 11 then you have to find the value of x. Okay. You have to find the value of x. Sound if the sound is coming or not.

[00:01:24]Sound is coming or not?

[00:01:27]Sound is okay or not?

[00:01:37]Sir, but sir option is action already.

[00:01:49]Okay. Sound is coming. Okay. Okay.

[00:01:55]Okay.

[00:02:02]2 power. This is also power of two. That means log we can write this is x base 2 plus we can write log x base 2² plus log x base 2 cube until and unless the bases are same. We can't do anything in logarithm. So log x 2 1 by 2 log x base 2 + 1 by 3 log x base 2 log x base 2 common. So log x base 2 assume y. So this would be y + y by 2 + y by 3 should be y 11. So you just have to solve this now.

[00:03:01]Option A solable option A. Yes.

[00:03:10]Simplify 6. This will be 6 y 3 y + 2 y = 11. So 6 + 3 is 9. 9 + 2 is 11. So 11 y by 6 = to 11. So we can write 11 11 cancelled out.

[00:03:28]So it would be y = to only 6. So y = to 6 means this is y that means this is 6 log x base 2 becomes 6. So x = to 2 ^ 6.

[00:03:43]Very easy question. This is the solution of the first question. Now we'll go for the question number two.

[00:03:51]If log x base 5 = to 2 log y x = to 3, then log y base 5.

[00:04:03]Another question from logarithm sir. What are the questions about conic section? section log x base 5 = to 2 log y x = 3 then log y 5 b 6 okay I'm qu log x base 5 is 2 log log y base x is 3. You have to find log y base 5 below. So this is from base change rule.

[00:04:52]Actually this question is from base change rule. Very easy question. See log x base 5 into log y base x = to 3.

[00:05:03]This will be 2 into you want to you have to multiply this with this question y base with with the help of base change this will be six very easy questions Change the sum of this series.

[00:05:35]The sum of this series you have to identify which series it is. Which series it is?

[00:05:44]Up to which term only dot dot dot is given here.

[00:05:49]dot dot dot answer.

[00:06:06]Anyone to have answer is sir answer is three by answer option opt Option just option say the option option I guess option I guess so exactly exactly GP series yes this is geometric progression and this is an infinite GP as the nth term is not given this is actually we have to assume this is an infinite GP GP. So in this infinite GP if you want to solve this roo<unk>3 + 1 + 1 by roo<unk>3 + 1 by3 plus dot dot dot infinity this is the GP this is the GP okay everyone is saying B so first term is A we can say A1 also root3 and how much is A2 today a2 is 1. So the common ratio we can find a2 by a1 that is 1 by <unk>3 and this is less than one. So this is a decreasing GP. In case of decreasing GP s infinity becomes a by 1 - r. How much is a? A is the first term. First term you can easily see this is roo<unk>3. So roo<unk>3 okay roo<unk>3 upon 1 - r r to 1 by <unk>3. So <unk>3 by <unk>3 -1 by <unk>3. So 3 by <unk>3 - 1 3 by <unk>3 - 1. So there is some mistake in option B I guess.

[00:08:31]So 3 by <unk>3 - 1 will be the answer.

[00:08:35]3x roo<unk>3 - 1. This will be the answer.

[00:08:40]This will be the answer. Okay. Ch.

[00:08:44]Let's go for the next question.

[00:08:48]Let's go for the next question. Yes.

[00:08:59]Ch.

[00:09:01]If the minimum value uh if the minimum value um you have to find the minimum value actually find the minimum value of 3 sin theta + 4 cos theta + 5. You have to find the minimum value of this expression.

[00:09:16]A expression minimum value find.

[00:09:19]You have to find the minimum value of this expression. Very easy question. It is in the form of K a sin theta. It is in the form of a sin theta plus b cos theta. So you know this expression actually lies between key root under a² + b² minus 2.

[00:09:46]If this is x, this x should lie between these two values.

[00:09:52]Okay. Now when this is minimum, this part should be minimum because this part is having key variable key theta and theta. This five is constant. You can't change this five.

[00:10:07]Option A. Everyone is saying option A min sin theta + 4 cos theta. This would be minimum when this becomes minimum. So minimum 3 sin theta + 4 cos theta minimum value is minus root under a². How much is a a 3. So it is 3² + 4 squared.

[00:10:36]So it is - 5 it is - 5. So this whole part is min -5 and there is another key + 5 with this. So it would be zero. So the answer is a option a very easy question.

[00:10:52]Option A.

[00:10:59]Chi.

[00:11:02]Next.

[00:11:04]The value of cos 240°.

[00:11:08]Value of cos 240°.

[00:11:11]Question number five. Very easy question.

[00:11:17]Cos 240° value.

[00:11:25]cos 240° value of cos 240°.

[00:11:47]So I will say B. Okay. So cos 240° it can be written as cos 2 into 90 plus 60°.

[00:12:00]So this is even number so you can't change cos will be as it is cos 60 but the quadrant is quadrant is 1 into 90 2 into 90 + 60 that is third quadrant. In third quadrant only 10 and cot are positive. So cos is negative. So it is minus half. So option is B. Option B not D it's B. Option B minus/ okay.

[00:12:32]Next.

[00:12:34]The line kx + it's from straight line.

[00:12:38]The line kx + 3 y + 9 has a slope minus2. Find the value of K. If this straight line is having slope, if this straight line is having some slope, If this straight line is having sl some slope minus 2, you have to find the value of you have to find the value of K to K value. You have to find the value of K bom K value.

[00:13:34]So I will say B everyone is saying B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B six.

[00:13:40]So find you have to convert this equation into Y = MX + C form. Convert this equation into Y = to MX + C form. So it is kx + 3 y + 9 is equal to 0. So 3 y + 3 y is equal to x and c. These two part should be in right side. So - kx - 9.

[00:14:08]So y = - kx by 3 - 9 by 3. Okay. So slope is this part. Actually if you compare this with y = mx + c minus k by 3 is slope this m actually so - k by3 we can write minus2 so k will be six very easy question k will be six it's b not min - 6 it will be six so go for the next question the points this this and this are collinear Then K is collinear point collinear.

[00:14:52]Collinear means what do you mean by collinear?

[00:14:57]Collinear means lie on same line.

[00:15:02]They all lie on same line. Same linear.

[00:15:09]These three points are collinear. Then you have to find the value of k.

[00:15:14]Collinear means lying on same line.

[00:15:16]Anyone C versus C.

[00:15:39]C.

[00:15:41]Okay.

[00:15:48]Three points 1 comma 2 3 3a 6 5A K. These three points are colinear.

[00:15:58]Collinear means they all lie on same plane. And for any straight line, for any straight line, this is one information. Slope is constant.

[00:16:07]Slope is constant. As the slope is constant, you can find slope with taking any two points. Okay.

[00:16:20]That slope would be same. Yes, slopes are same. Yes, slope same.

[00:16:27]6 - 2 y - y1 by x2 - x1 3 - 1.

[00:16:37]So k - 2 k - 2 by it will be 5 - 1 it is 5 - 1 okay so it will be 4 by 2 = k - 2 by 4 16 = 2k - 4 so 2k = 20 that is k = 10 ultimately so K value will be 10.

[00:17:11]It is C.

[00:17:14]Same slope. Yes. Same slope. Slope. Same way to change.

[00:17:21]If the line passing through this and this is parallel to this line, the value of k is a d to point straight line to this straight line is parallel to par to this line. Then you have to find the value of k. This ko Answer.

[00:18:02]Answer line.

[00:18:21]That means this line this line is containing 2a k as well as -4a 7 this should be parallel to this line this given line option a a a 16 answer 16 answer.

[00:18:57]Everyone is saying it's 16axis.

[00:19:18]This is x-axis. This is our x-axis. If the lines are parallel, then their angle of inclination should be same. Tan theta same 10 slope also same. Wow. A slope same slopes are same. So what will be the slope? k - 7 y2 - y1 by x2 - x1 2 - 4 2 - 4 = to it should be converted into y = mx + c form so - 2 y = - 3x - 5 so y can be written as - 3x - 2 - 5 by - 2 so this would be 3x 2 into x + 5x2 2. So 3x2 is the slope here.

[00:20:21]Okay, this is y = to mx + c form. So m is the slope. 3x2 is the slope. So it is equal to 3x2. You just have to calculate the value of k from this equation. Both have same slope. Yes, both are having same slope.

[00:20:39]Option A. Yes.

[00:20:43]Ch. We'll go for the next question now.

[00:20:52]If y = to 3x² + 5 the^ 7 then dy dxis derivative questions from derivative which one is the correct answer correct answer 2 - - 4 oh 2 + 4. Yes 2 - - 4 is 2 + 4. Next ho if y = 3x² + 5 all ^ 7 derivative d b d a different Secondary different a a don this is y. So if you do dy dx if you do dy dx this is variable variable power there is constant. So first formula will be constant or variable power 3x² + 5 a 6. Then you have to differentiate this part again according to chain rule dx 7 into 7 into 3x² + 5 all the power 6.

[00:22:33]This would be d of 3x² dx + d5 dx.

[00:22:42]Okay. So solve 7 into 3x² + 5 all ^ 6.

[00:22:49]It would be 3 x² derivative is 2x dative to 0. So it would be 3 2 6 42x into 3x² + 5 all ^ 6.

[00:23:04]So answer will be option number A. It is option A.

[00:23:10]B C option number A.

[00:23:14]Option A is the correct answer.

[00:23:20]Ch option A is the correct answer.

[00:23:27]Ch. Next question. We'll go for the next question.

[00:23:31]Then find dy dx in this case. Very easy question. Uh it is from log ln. ln is given. So log base e is given.

[00:23:48]Sir question.

[00:24:12]A B A A A A Max.

[00:24:20]Answer key A B. Option A. Answer sir. A a A a.

[00:24:30]Okay.

[00:24:32]Option.

[00:24:35]This is Y. So if you differentiate this y so first of all there is log. So log at derivative is 1x derivative of log x is 1x. So it would be first of all 1x 2x cq + 5x. Then again you have to differentiate this 2x cq + 5x with respect to x.

[00:24:59]So this is 1x 2x cq + 5x 2 x cub derivative is 3x² x cub derivative is 3x² + 5 x derivative is 1. So you don't have to write anything. So it would be 6 x² + 5 by 2x cq + 5x. Now you can see which one is the answer. Yes, option number A is the correct answer. 6x² + 5 very easy derivative sir.

[00:25:35]Easy. Yes.

[00:25:39]Ch very easy derivative change y = 10 rootter.

[00:25:50]Okay.

[00:25:53]This is root because bracket you have to differentiate y = 10 root x² + 1 then dy dx dy dx find sir where are you class you have to find the derivative Leave B C. Wow. Different different s B.

[00:26:56]Okay.

[00:27:02]First function 10ative is sec square. So it is sec square root x² + 1 this is square root derivative of roo<unk>x we know it is 1x 2<unk>x 1 by 2<unk> x² + 1 you have to do x² + 1 derivative again.

[00:27:37]So x² derivative is 2x and 1 derivative is 0. So this is the correct answer. So they contrast 22 will be cancelled out.

[00:27:47]So x se² root under x² + 1 by roo<unk> under x² + 1. This is the correct answer. So correct answer x x² this by root under this. Option B is the correct answer.

[00:28:06]Yes, everyone is saying option B. Very good. Very good everyone.

[00:28:10]Option B also show. So this is correct answer.

[00:28:16]Change quy.

[00:28:18]Should we change?

[00:28:22]Change quy.

[00:28:25]Now this derivative this is very easy derivative.

[00:28:28]It is y = sin² bracket bracket to x cube. So you have to differentiate this with respect to x. y = sin² x cative sin² x cube answer.

[00:28:57]y = sin² x cube.

[00:29:01]First, first you have to do it very fast.

[00:29:16]C A C C C C C C C C C C C C C C C C C C C C C C Max A C A C A R Next 2.3 2.4 Middle 100 Awami.

[00:30:11]First in this form sin x² this can also be written as in this form sin square x.

[00:30:29]So first variable power constant. So constant will come in front two or sin x cq constant power one decrease variable power one decrease. Then you have to differentiate sine again. This sign sine will be cos x cq. Okay. Then you have to differentiate this x cube again. So xubative is 3 x² because x 3.

[00:31:04]So it will be 3x². So answer 3 2 6 this 3 2 6 x² then it would be sin it would be sin x cq and shat it will be cos x cq. So answer is I guess option A. Option A is the correct answer. Option A is the correct answer.

[00:31:30]Correct. C. So what is the meaning of the word? Which word?

[00:31:35]Which word? Which is the meaning of the word?

[00:31:46]Which word?

[00:31:48]word.

[00:31:54]Next, if y ln y = to ln sin² x + cos² x then dy dx is how much is dy dx dy dx value a dy dx value in this question how much is the value of dy dx X option A one.

[00:32:26]Sh say option A. Is it A?

[00:32:30]A A A.

[00:32:43]B.

[00:32:45]Okay. There is fight between A and B.

[00:32:52]B 0 0 B for ball for ball zero. Okay. See very very easy question.

[00:33:03]Very easy question.

[00:33:08]B² X + cos² X this is actually one this is always one this is not actually variable a part this part is not variable this is not variable okay this whole part is actually it is constant it is a big constant and this is equals to 1 say to y = ln 1. So it is derivative of ln 1 is ln 1 is a constant. So derivative of this is zero. It is B.

[00:33:46]Option B.

[00:33:48]Option B. You don't have to do anything here.

[00:33:52]Question.

[00:33:58]Question number 14.

[00:34:01]The function has minimum value. A value function minimum value. Which one is the minimum value of the function?

[00:34:10]Minimum value of the function. A function minimum value to this is the given function up to 11.

[00:34:24]You have to find the minimum value of this function.

[00:34:34]Minimum value So B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C B C min how to find minimum value B now B and C minimum value to find minimum or maximum value of any function we have to use maximum minima principle uh to use maximum principle we have to differentiate the given I'm assuming this is y = 2x² - 8x + 11 different first should be zero so 2x dative is 2 into 2x dative is 2x X and X derivative is 1 so - 8 and 11 dative is 0 so it would be zero so 4x - 8 =0 so x = 8 by 4= to 2 answer never two is not the answer maximum what will be the minimum minimum value of this function this is the value of X this is not minimum value of function not minimum value X = to 2 minimum value P actually we get the minimum value of this function at X = 2.

[00:36:21]So we have to find the minimum value. So minimum value will be now y when x = to 2. So 2 put 2 x² x x square it is 2² - 8 x - 8 into 2 + 11. So it would be 2 into 2² that is 8 - 16 + 11. So uh it is um uh 19 - 16 that is three. So three is the correct answer. Three is the correct answer. You have to find the y minimum not x value. You have to find the value of f of x or y minimum value.

[00:37:05]So answer C.

[00:37:09]Answer C is the correct answer.

[00:37:14]C is the correct answer.

[00:37:19]C is correct. Yes, C is the correct answer. Confused. You have to be very clear.

[00:37:32]Question number 15. The radius of a circle is decreasing at the rate of 3 cm/s when the radius is 5 cm. Radius of a circle is decreasing 3 cm/s rate and the when the radius is 5 cm the rate of change of area rate of change of area you have to find very easy question answer which one is the Sir answer B. Everyone is saying B is the correct answer.

[00:38:35]B correct answer B it is decreasing and radius change. So radius change rate drdt and it is negative minus 3 when the radius is five. When the radius is five you have to find the rate of change of area to p<unk> r². So d a dt can be written as d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d can be written as d pi r² dt. So pi the constant various way. So d r² dt. So it would be pi r² is 2 r but with respect to t we are differentiating. So this will be d r dt again.

[00:39:17]So p<unk> into p<unk> into 2 r how much is r? R is five and how much is DRD? DRD is minus 3 minus 30 pi cm² per second because this is the rate of change of area. So how much will be the answer? Option B change very easy question 16 number a circular balloon is inflated so that its radius increases at the rate of 0.5 cm/s when the radius is 10 cm its area is increasing at the rate of ballooner area ballooner area go sir how many questions will be the in the test uh 50 questions total 50 questions 1.5 hours time means 1 hour 30 minutes sir Please answer the questions in the test.

[00:40:52]Option B. It is very easy question actually.

[00:41:02]Okay.

[00:41:04]to it is 4 pi r² is the area say so and rate of radius to radius change rate dt is 0 5 and when radius is 10 you have to find this rate da dt so dt can be written as da dt can be written as d 4 pi r² dt. So 4 pi d r² dt. So 4 pi into 2 r d r dt. So 8 pi rl value is 10. RL value is 10 and DRD is 0.5 it is 0.5 question pattern for those are easy or tough easy everything is easyt Because 16.

[00:42:38]Okay.

[00:42:42]Circular spherical.

[00:42:47]The algebraic area under the y = to sinx from x =0 to x= to area. How to find area?

[00:42:57]How to find area?

[00:43:06]Y = from x =0 to from x =0 to x = to p<unk> x = to0 to x = to pi h.

[00:43:28]So, how many sets of questions set?

[00:43:41]Yes. Integration. Yes. Area find integration. Algebraic area means positive area. Actually, you have to find actually area means you have to use integration.

[00:44:00]You have to use integration.

[00:44:30]B Craft Sin x is like this.

[00:45:00]This is<unk> by 2 that is sin 90 is 1.

[00:45:02]This is pi.

[00:45:13]So integration limit will be 0.

[00:45:20]Okay.

[00:45:22]Integration y dx that is integration sin x dx limit from 0 to 0 to pi sin x integration is minus cos x and the limit would be 0 to pi. So first up limit. So upper limit is cos pi minus cos 0 cos pi means cos 180° cos 180°us 1 or cos 0 to minus one or cos 0 1 - 1 it would be 2.

[00:46:13]Sorry advanc class will be there today.

[00:46:15]Yes advanc class will be there. Advanc class to hobby. Advanc advanc class hobby. There will be advanc class.

[00:46:26]Advanc class hobby.

[00:46:36]Sir, how to know which one is upper limit and which one is lower limit?

[00:46:42]Lower limit.

[00:46:44]Lower limit. Upper limit. Startation is lower obviously dx that is upper limit the value of it is 0 to<unk> by 2 cos² x dx.

[00:47:20]You have to do this integration.

[00:47:27]Cor you have to do this integration.

[00:47:37]Integration cos² x dx 0 to p<unk> by 2.

[00:47:41]Integration cos² x dx 0 to<unk> by2 Follow D.

[00:48:20]Everyone is saying it's D.

[00:48:32]squareation possible. So convert it into linear quantity.

[00:48:37]So linearity linear quantity convert.

[00:48:45]So I will say D.

[00:48:51]Say DH D okay cos square x cos square x for 1 + cos 2 theta = 2 cos² theta so 1 + cos 2x 1 + cos 2x this can be written as 2 cos² x so cos² x can be written as cos² x can be written as 1 + cos 2 theta or 1 + cos 2x by 2. So we just have to put this because so you have to use this here. So integration 0 to<unk> by 2 1 + cos 2x by 2 dx.

[00:49:46]So 2 constant.

[00:49:49]So it will be half. Now there are two integrations. See one integration is integration 0 to<unk> by 2 only dx 0 to<unk> by 2 cos 2x dx.

[00:50:08]So then dx integration will be dx integration will be only x and limits are will be as usual 0 to<unk> by 2.

[00:50:29]Then cos 2x cos 2x means cos 2x integration sin 2x and x divide so by 2 and limits will be as usual 0 to by 2 limit lower answer to the multiply to the divide uh divide Answer 1 by 2<unk> by 2 upper limit lower limit minus minus lower limit plus sin 2 into<unk> by2 that is sin pi US sin sin 0 by 2 into 2<unk> by 4. So answer B option B is the correct answer.

[00:51:43]Okay. So this is the correct answer.

[00:51:48]Ch next question.

[00:51:51]We'll go for the next question.

[00:51:58]A question.

[00:52:00]If x² + y² = 2x y then divide dx x² + y square option a check option. Act option. Act option option.

[00:52:18]Answer x² + y² = given as 2xy. Find a dy dx.

[00:52:27]This is given. x² + y² = 2xy. This is the given question.

[00:52:42]Answer key.

[00:52:46]You have to find dy dx.

[00:53:20]question. This is a very good question.

[00:53:41]A you have to Check answer one.

[00:53:53]So connect A a A first d of x² + y² dx = to d 2xy dx.

[00:54:45]It would be dx² dx + d y² dx + 2 uh sorry 2 d xy dx square derivative is 2x y square derivative is 2 y but y respect. So this would be dy dx equals to 2 x into y x into y. So x into y means you have to do u v rule. U into v rule u into v rule. Okay.

[00:55:28]So u that is dx dx then x y dy dx dy dx 2 2 will be cancel out. So x + y into dy dx a dy dx dy dx I assuming it is a. So here it will be it will be x y plus it will be x into a so y a - x a = y - x so a common now y - x = y - x ultimately okay so it sorry Okay.

[00:56:31]From this will be equal to y - x by y - x. So option correct answer if x is not equal to y one option most probably. So first option is the correct answer. y - x by y - x numerator and denominator will cancel out. Denominator is denominator.

[00:57:08]Denominator is denominator. Denom is denom. Wow.

[00:57:13]Very good.

[00:57:16]Nice.

[00:57:21]Next.

[00:57:26]If x + y² = to x + xy + 1, then dy dx dy dx. You have to find dy dx here.

[00:57:48]Mish rocks.

[00:57:51]If x + y² = to x y + 1 then dy dx.

[00:58:10]So whole square is empty. Huh?

[00:58:13]Whole square is empty.

[00:58:15]What? Empty.

[00:58:29]App is not helping me. Who? Break up, sir. Break up.

[00:58:37]Break up.

[00:58:45]answer. Better question.

[00:59:05]Ch B or B should Hi sir. Hi. Hi.

[00:59:42]CC C.

[00:59:55]Anyone else?

[00:59:59]A key baba square strike to x² + y square x + y whole square x² + y² + 2xy = xy + 1 x² x x x² + y² x square 2x y - x y + x y = 1. Now you can differentiate easily differentiate. So differentiate d x² + y² + xy with respect to x = 1 uh equals to derivative of 1.

[01:00:52]Derivative of one becomes zero as it is a constant quantity. Now in this side it will be dx² dx plus d y² dx plus this would be dxy dx.

[01:01:07]So different x² derivative is 2x actually and y square dative is 2 y but you you are differentiating y with respect to x that's why it will be dy dx y dative dy dx will be there according to chain rule. So now xy xy first u rule again. So first y x derivative plus x y derivative this would be zero.

[01:01:48]So uh 2x + 2 y a plus dy dx dx is 1. So y + a into x = 0.

[01:02:05]Now you have to find the value of a only 2x + 2 y a + y + x a= to0. So so y a common a you have to take common. So it will be 2 y + x these two 2x and y. So it would be minus of y + or 2x + y. So a will be ultimately - 2x + y by x + 2 y.

[01:02:46]So I think option B is the correct answer. Yes, option B is the correct answer. So what will be the duration of the practice session? Sham, this is the last question.

[01:03:08]take.

[01:03:13]Thank you.