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$l={\displaystyle \underset{0}{\overset{1}{\int }}\frac{\sqrt[]{x}dx}{\left(1+x\right)\left(1+3x\right)\left(3+x\right)}}$

Put x = t² then dx = 2tdt

$l={\displaystyle \underset{0}{\overset{1}{\int }}\frac{dt}{\left(1+t^2\right)\left(3+t^2\right)}-{\displaystyle \underset{0}{\overset{1}{\int }}\frac{dt}{\left(1+3t^2\right)\left(3+t^2\right)}}}$

$=\frac{1}{2}{\left(ta{n}^{-1}t\right)}_0^1-\frac{3}{8\sqrt[]{3}}{\left(ta{n}^{-1}\frac{t}{\sqrt[]{3}}\right)}_0^1-\frac{8}{8\sqrt[]{3}}{\left(ta{n}^{-1}\sqrt[]{3}t\right)}_0^1$

$=\frac{\pi }{8}\left(1-\frac{\sqrt[]{3}}{2}\right)$      

$r=\sqrt[]{{\left(\frac{p}{2}\right)}^2+{\left(\frac{1-p}{2}\right)}^2-5}=\sqrt[]{\frac{p^2+1+p^2-2p-20}{4}}=\sqrt[]{\frac{2p^2-2p-19}{2}}$

Since $r\in \left(0,5\right)so0<\sqrt[]{2p^2-2p-19}<10$

$\Rightarrow 2p^2-2p-19>0\&2p^2-2p-19<100$     

$P\in \left[\frac{1-\sqrt[]{239}}{2},\frac{1-\sqrt[]{39}}{2}\right)\cup \left(\frac{1+\sqrt[]{39}}{2},\frac{1+\sqrt[]{239}}{2}\right]$

So number of integral values of P² is 61.

The admission fee for Kumaraguru College of Liberal Arts and Science (KCLAS) is INR 1,700. The first-year fees for the BA programme is INR 1,50,000, and the total tuition fees for the entire programme is INR 4.5 lakhs. Here's a breakdown of what you can expect to pay:

- *Admission Fee*: INR 1,700

- *First-Year Fees*: INR 1,50,000

- *Total Tuition Fees*: INR 4.5 Lacs (for the entire 3-year program)

Additionally, you may need to consider other expenses such as:

- *Hostel Fees*: INR 84,000 (according to some sources)

- *Mess Fees*: INR 30,000 to 60,000 per annum (depending on the quality and variety of food offered).

Candidates applying for admission at MIT School of Distance Education need to upload a self-attested copy of an id proof. Below are the documents that can go as id proof for filling out the application form:

• Aadhaar Card
• PAN Card
• Driving License

The requirement of work experience varies course-wise. Aspirants who have applied for Executive PGDM need to have more than five years of experience. Hence, such candidates have to upload work experience certificate along with other specified documents.

  $\left|x-2\right|>1givesx-2<-1orx-2>1$ $$

i.e. x < 1 or x > 3 . (i) represent set A

$\sqrt[]{x^2-3}>1gives{x}^2-3>1or{x}^2-4>0$

x < 2 or x > 2 . (ii) represent set B

$\left|x-4\right|\ge 2givesx-4\le -2orx-4\ge 2$

$$  $x\le 2orx\ge 6$ . (iii)respect set C

so number of subset = 28 = 256

Yes, candidates can fill out the application form for MIT School of Distance Education online. Aspirants must fulfill the eligibility requirements to apply for admission. Below are the steps to follow:

Step 1: Visit the official website of MITSDE.

Step 2: Click on 'Apply Now' on the Home page.

Step 3: Fill out the details and pay the fee to submit it.

Change in oxidation number = 2

$\Delta G°=-n{E}_{cell}^{o}F$

$\Delta G°=-n{E}_{cell}^{o}F$

=-2 × 4.315 × 96487 Jmol^-1

^{$\therefore \Delta G°=\Delta H°-T\Delta S°$}

^{$\Delta S°=\frac{\Delta H°-\Delta G°}{T}$}

$=\frac{-825.2\times 1000-\left(-2\times 4.315\times 96487\right)}{298.15}J{K}^{-1}$

$=\frac{7482.81}{298.15}=25.09J{K}^{-1}$

$\approx$ 25.1 JK^-1

Ans. = 25

P1 is living in white house and earning low salary.

Some books for Bihar B.Ed CET preparation are mentioned here:

• For Mental Ability, candidates can refer to the "A Modern Approach to Verbal & Non-Verbal Reasoning" by R.S. Aggarwal.
• For Teaching Aptitude subject, students can rely on : "Teaching Aptitude & Attitude Test" by Arihant Publications.
• For General Awareness, you can refer to : "Lucent's General Knowledge" and newspapers like The Hindu.
• For Language Proficiency, this is some book you can: "English Grammar & Composition" by Wren & Martin or Lucent General English.

Also refer to the online study materials, solve past year question papers and give mock tests when the exam is near.

MIT School of Distance Education admissions are open. The school has not specified the admission deadline for now. However, aspirants must fill out the application form for the preferred course online. Admission to all the offered programmes is based on merit of the candidates in the last qualifying exam.

Given $2\mathcal{l}+2m-n=0........\left(i\right)$

$mn+n\mathcal{l}+\mathcal{l}m=0...........\left(ii\right)$

$\&wehave{\mathcal{l}}^2+m^2+n^2=1..........\left(iii\right)$

$\left(i\right)\Rightarrow 2\left(\mathcal{l}+m\right)=n$  

  $\left(ii\right)\Rightarrow \mathcal{l}m+n\left(\mathcal{l}+m\right)=0$

$2{\mathcal{l}}^2+2m^2+5\mathcal{l}m=0$             

(a) $\frac{\mathcal{l}}{m}=-2$  

(i) $\Rightarrow \frac{2\mathcal{l}}{m}+2-\frac{n}{m}=0$  

$\frac{n}{m}=-2$  

$So,\left(\mathcal{l},m,n\right)=\left(-2m,m,-2m\right)$  

= (-2, 1, -2)

(b)   $\frac{\mathcal{l}}{m}=\frac{-1}{2}givesn=-2\mathcal{l}$

$\left(\mathcal{l},m,n\right)=\left(\mathcal{l},-2\mathcal{l},-2\mathcal{l}\right)=\left(1,-2,-2\right)$

$Now,cos\theta =\frac{-2-2+4}{3\times 3}=0$

$\Rightarrow \theta =\frac{\pi }{2}$  

Almost all of the colleges offering BTech Aerospace Engineering follow a balanced approach where the theory-based subjects are assessed through semester exams that are conducted after every 6 months, along with individual and group research projects and class assignments. The division may vary with more weightage being given to the semester exams, around 60 to 70%, and the remainder to the practical component.

know more about -

Aerospace Engineering Courses

Aspirants do not require passing an entrance exam for admission to MIT School of Distance Education. The school shortlists aspirants for admission based on their merit in the last qualifying exam. Except professional certificate courses, the selection to all other programmes is based on graduation marks of the candidates.

Yes. It is a mix of internships, project work and practical training so that you can get knowledge of the aerospace field, learn new skills and sharpen your problem solving abilities. You can also join small or large projects to get familiar with the work environment and expectations in aerospace companies.

It improves your chances of landing high-paying jobs, skill development scope, and networking opportunities, leading to a better career graph in the future.

Absolutely, anyone candidate preparing for the Bihar BEd CET exam must use previous year papers; atleast of five years to prepare for the examination. It will help you understand the exam pattern and find important questions. There is a high probability that some of the questions main reoccur in the upcoming exam.

MIT School of Distance Education offers admission to candidates based on their merit. The school reviews the application form of the candidates to confirm eligibility. Those who fulfill the eligibility requirements for the applied course are offered admission. Once selected, aspirants have to confirm their seat by paying the course fee.

You can surely get admission to the BTech Aerospace Engineering course without giving the entrance exam but it depends on the college you're targeting. While top colleges like the IITs and some other private colleges strictly ask for valid entrance exam scores, there are around 30 colleges that consider Class 12 board exam marks in the Science stream and may take extra rounds like the GD or PI for admission to BTech Aerospace Engineering.

So, you should go to the official college websites to check their BTech Aerospace Engineering eligibility and admission requirements and then prepare accordingly.