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For equilibrium,

$\frac{dU}{dr}=0\Rightarrow \frac{-10\alpha }{r^{11}}+\frac{5\beta }{r^6}=0\Rightarrow r={\left(\frac{2\alpha }{\beta }\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$5$}\right.}$

$A_1+A_2={\displaystyle {\int }_0^{\pi /2}cosxdx}$           

$={\left(Sinx\right)}_0^{\pi /2}=1$           

$A_1={\displaystyle {\int }_0^{\pi /4}\left(cosx-sinx\right)dx={\left(sinx+cosx\right)}_0^{\pi /4}}$           

$=\frac{2}{\sqrt[]{2}}-1=\sqrt[]{2}-1$

$So{A}_2=1-\left(\sqrt[]{2}-1\right)=2-\sqrt[]{2}=\sqrt[]{2}\left(\sqrt[]{2}-1\right)$

$Now\frac{A_1}{A_2}=\frac{1}{\sqrt[]{2}}$

Alliance Manchester is located in the heart of the vibrant city of Manchester.The university's Business school campus is surrounded by some major tourist attractions. There are many things to explore around the campus area, such as historical architectures, media centers, museums, parks, iconic sports stadiums, etc. 
 
Listed below are some top attractions for students to explore near Alliance Manchester B-school: 
 
· John Rylands Library 
 
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$L\frac{di}{dt}=V\Rightarrow 2di=3tdt\Rightarrow 2{\displaystyle \underset{0}{\overset{i}{\int }}di=3}{\displaystyle \underset{0}{\overset{4}{\int }}tdt\Rightarrow i=12A}$

$U=\frac{1}{2}L{i}^2=\frac{1}{2}\times 2\times 12^2=144J$

For JEE Main exam, the Electric Charges and Fields is an important chapter. It is a part of Electrostatics unit. The weightage of this unit is around 6-9% of the total Physics section. You should expect around 3-5 questions in this unit including the questions from the class 12 physics chapter 1.

As per the exam day guidelines - 

• Candidates need to reach the exam centre atleast 30-40 minutes before the reporting time.
• They must co-operate with the exam centre officials to ensure a smooth functioning of the frisking process.
• Candidates must avoid carrying electronic devices, and wear flashy jewellery.
• Not involve in mischeavous activities at the centre.

$L\frac{di}{dt}=V?2di=3tdt?2{\displaystyle \underset{0}{\overset{i}{?}}di=3}{\displaystyle \underset{0}{\overset{4}{?}}tdt?i=12A}$

$U=\frac{1}{2}L{i}^2=\frac{1}{2}*2*12^2=144J$

$P{A}^2+P{B}^2=co{s}^2\theta +{\left(sin\theta -3\right)}^2+co{s}^2\theta +{\left(sin\theta +6\right)}^2$       

= 2 cos² θ + 2 sin² θ + 6 sin θ + 45

= 6 sin θ + 47

for maximum of PA² + PB², sin q = 1

then P (1, 2)

Hence P, A & B will lie on a straight line.

Let the charge of on each drop be q and radius of each drop be r.

  $\frac{kq}{r}=2$

When all drops are joined, radius,

$r\text{'}={\left(512\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}r=8r$

Potential of the new drop,

$V=\frac{k.512q}{8r}=64\frac{kq}{r}=128V$

Indeed, it is an easy chapter of Class 12 Physics. In this chapter, you will learn about the foundational concepts like Gauss's law and electric fields.

No, the exam body doesn't sent the hall ticket by post, candidates can only download the VSAT hall ticket from its official website in online mode.

It is not necessary to mention about your backlogs in the SOP. Sometimes, universities provide a separate space in the application for explaining any gap or inconsistency in the academic record. However, in case no such space for justification is provided in the application, you can use SOP to justify the reasons for such inconsistency in your record.  You must mention about them briefly and explain well with the genuine reasons that led to these backlogs. Mentioning about backlogs with our explanation must be avoided.

Flux through the 6 sides of square (i.e. cube)

${?}_T=\frac{q_{in}}{{\epsilon }_0}=\frac{12\times 10^{-6}C}{{\epsilon }_0}$   

Flux through a square

$?=\frac{{?}_T}{6}=\frac{12\times 10^{-6}}{{\epsilon }_0\times 6}=\frac{2\times 10^{-6}}{{\epsilon }_0}$

$\Rightarrow ?=225.98\times 10^{3}N{m}^2/C?226N{m}^2/C$     

An SOP is typically two pages long and should be written in concise paragraphs, much like an essay. A general declaration of your aims should come first in the statement of purpose, followed by a justification for why you are pursuing those goals. It should also cover your grasp of the selected topic of study, any relevant experience you may have, as well as your long-term objectives and how they relate to it. Provide a summary of your objectives and a brief restatement of your qualifications for the programme in your conclusion.

Given $\left(x\right)=\{\begin{array}{l}2sin\left(\frac{-\pi x}{2}\right),x<-1\\ \left|a{x}^2+x+b\right|,-1\le x\le 1\\ sin\pi x,x>1\end{array}$

If f (x) is continuous for all $x\in R$ then it should be continuous at x = 1 & x = -1

At x = -1, L.H.L = R.H.L. Þ 2 = |a + b - 1|

->a + b – 3 = 0  OR  a + b + 1 = 0 . (i)

-> a + b + 1 = 0 . (ii)

(i) & (ii), a + b =-1

The main ideas covered in the essay should be summarised in the statement of purpose conclusion. In order to leave the reader with a lasting impression, it should briefly reiterate the thesis statement and offer a concluding idea or argument. The conclusion should be succinct, but it also has to be interesting and convincing. Moreover, the conclusion should be able to convince the Ad Com about your candidature for the programme. You can read a sample sop for MS in project management to understand how the conclusion should be written.

It is crucial to start your statement of purpose for project management with a clear explanation of why you want to pursue the degree in the first place. The reasons behind your interest in project management, should be included in your SOP. You can mention about a recent anecdote that made you decide about this programme. It is also critical to show that you are committed to overcoming the problems involved in project management and that you are aware of them. Ultimately, it is crucial to show that you have a thorough grasp of the particular programme you are applying for and to justify your decision.

$T=27°C,P=1atm=10^{5}N/m^2,V_{rms}=200m/s$

As we know

$v_{rms}=\sqrt[]{\frac{3RT}{M}}\Rightarrow \frac{v_{rms}}{v{\text{'}}_{rms}}=\frac{\sqrt[]{\frac{3RT}{M}}}{\sqrt[]{\frac{3RT\text{'}}{M}}}$

$V{\text{'}}_{rms}=200\times \frac{2}{\sqrt[]{3}}=\frac{x}{\sqrt[]{3}}$

x = 400