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 $l={\displaystyle \underset{0}{\overset{20\pi }{\int }}{\left(\left|sinx\right|+\left|cosx\right|\right)}^{2}dx=20{\displaystyle \underset{0}{\overset{\pi }{\int }}\left(1+\left|sin2x\right|\right)dx=40{\displaystyle \underset{0}{\overset{\frac{\pi }{2}}{\int }}\left(1+\left|sin2x\right|\right)dx=40{\left(x-\frac{cos2x}{2}\right)}_0^{\frac{\pi }{2}}}}}$

$=40\left(\frac{\pi }{2}+\frac{1}{2}+\frac{1}{2}\right)$ = 20 (p + 2)

CENTAC conducted the registration process for CENTAC MBBS admission or the NEET counselling from July 5 to July 16, 2025. CENTAC NEET 2025 merit lists are released within a few days after the conclusion of the registration process. The merit list will include the names of the candidates along with their exam details. Only those whose names would be included in the CENTAC NEET 2025 merit list will be considered eligible to participate in the counselling process. However, candidates will be given the opportunity to submit grievances or challenges, after which the final merit list will be released.  

f (3x)- f (x) = x

Replace $x\to \frac{x}{3}\Rightarrow f\left(x\right)-f\left(\frac{x}{3}\right)=\frac{x}{3}$

Again replace $x\to \frac{x}{3}\Rightarrow f\left(\frac{x}{3}\right)-f\left(\frac{x}{3^2}\right)-f\left(\frac{x}{3^2}\right)=\frac{x}{3^2}$

$\Rightarrow f\left(3x\right)-f\left(0\right)=\frac{3x}{2}puttingx=\frac{8}{3}\Rightarrow f\left(8\right)-f\left(0\right)=4\therefore f\left(0\right)=3$

Also putting x = $\frac{14}{3}$ in f (3x) – 3 = $\frac{3x}{2}\Rightarrow$ F (14) – 3 = 7 f (14) = 10

The mode of TSSM Narhe course admissions is online. Admission to various courses is based on entrance exam scores and merit. The accepted entrance exams are JEE Main,  MHT CET, and others. Candidates willing to get admission must first visit the official website. Then, click on the Apply Now tab. Then, select the required course. Then, pay the application fee. Then, fill out and submit the application form with required information. 

School of Law, Pandit Deendayal Energy University admissions are completely entrance-based. Candidates who meet the course-specific eligibility criteria can apply for admission to the School of Law, Pandit Deendayal Energy University courses. Candidates must pass Class 12 for the BA LLB and graduation for the LLB course.

The mode of JEE Narhe course admissions is online. Admission to various courses is based on entrance exam scores and merit. The accepted entrance exams are JEE Main,  MHT CET, and others. Candidates willing to get admission must first visit the official website. Then, click on the Apply Now tab. Then, select the required course. Then, pay the application fee. Then, fill out and submit the application form with required information.

Vijayanagara Sri Krishnadevaraya University offers various courses for candidates. To apply to these courses candidates are required to keep the following list of documents handy: 

• Class 10 marksheet
• Class 12 marksheet
• Graduation marksheet for PG courses
• TC
• Government-authorized ID

Candidates with the following list of documents can successfully apply to the courses. 

 $Letf\left(x\right)=lo{g}_{cosx}cosecx=\frac{logcosecx}{logcosx}$

$f\text{'}\left(x\right)=\frac{logcosx.sinx\left(-cosecxcotx-\left(logcosecx\right)\frac{1}{cosx}.\left(sinx\right)\right)}{{\left(logcosx\right)}^2}$

$Atx=\frac{\pi }{4}f\text{'}\left(\frac{\pi }{4}\right)=\frac{-log\left(\frac{1}{\sqrt[]{2}}\right)+log\sqrt[]{2}}{{\left(log\frac{1}{\sqrt[]{2}}\right)}^2}=\frac{2}{log\sqrt[]{2}}\therefore atx=\frac{\pi }{4},lo{g}_e\left(2f\text{'}\left(x\right)\right)=4$

Survival at TSSM College of Engineering Pune is quite easy as the college believes in providing equal education to everyone. For getting admission in this college, students must follow the application process mentioned below:

Step 1: Visit the official website of TSSM College of Engineering Pune.

Step 2: Select the required course.

Step 3: Pay the application fee.

Step 4: Fill out and submit the application form with required information.

The total nuber of seats that are available for BTech courses at IIIT Ranchi is 320. Keep in mind that this figure represents the overall number of seats available in 2025. The actual available seat for your chosen BTech course will be lower than the aforementioned number.

Teesside university usually accepts IELTS as an English proficiency score. Students are required to submit a minimum score of 6.0 with 4.5 in each band for a 12 week online and a minimum score of 5.0 for a 6 week online for on-campus program. 

Yes, currently, admissions are open at the School of Law, Pandit Deendayal Energy University. SOL, PDEU admissions are currently open for all courses. Candidates are selected for courses based on entrance exam scores. Aspirants can apply online. Interested candidates meeting the eligibility criteria can fill out the form. 

The total seat intake for B.Tech. in Electronics and Communication Engineering (Embedded Systems and Internet of Things) is 30. Seat intake for various courses across IIIT Ranchi is always subject to change. Candidates are advised to confim the availableseats on the official website for IIIT Ranchi.

School of Law, Pandit Deendayal Energy University, admits students based on entrance exam scores. The institute offers BA LLB and LLB courses. Candidates willing to seek admission can fill out the application form online through the official website. The admission is done based on entrance exam.

School of Law, Pandit Deendayal Energy University 2025 are open online. The application will close on 20 July, 2025. Since the admission is open, candidates can apply. To get admission to the SOL,  candidates must meet the eligibility criteria set by the college. The application process at the SOL, PDEU is conducted online.

At IIIT Ranchi, the total available seats for the course B.Tech. in Computer Science and Engineering (Data Science and Artificial Intelligence) is 30. Candidates are advised to be cautious as it is easy to confuse B.Tech. in Computer Science and Engineering (Data Science and Artificial Intelligence) with B.Tech. in Computer Science and Engineering offered by IIT Ranchi which is a different course and has different seat intake.

The Master's in Business Analytics is one of the best courses among Indians seeking or aiming a career in fields such as Consulting, Decision Making, and Analytical Leadership. The course is available in Melbourne Business School and provides Cohort-based learning and collaboration in companies like Accenture, Telstra, NAB, and PwC. To opt for this course, students must hold a bachelor's degree and backgrounds in fields like Engineering, Economics, and Math, CS, with 2-3 years of work experience.

The Master's in Information Technology programme at the University of Melbourne is ideal for Indian students seeking a career in fields like Software Development, Cybersecurity, IT consulting, or AI. The students can choose any specializations including Artificial Intelligence, Cybersecurity, Distributed Computing, Spatial Information, and more. The MS in Information Technology course helps students to take project-based learning and an internship opportunity with Australian Tech companies.