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In order to be considered for scholarships in IBS Mumbai, the candidates should appear for and pass in IBSAT 2025. Scholarships are provided to top rankers of IBSAT, alumni wards of IBS, physically challenged applicants, and defence personnel wards. The applicants who are eligible should proceed with the admission process, pay the admission fee, and register on the date given. The scholarship will be offset only against the programme fee.

Given f(x) =   _{${\displaystyle {\int }_e^x{e}^{t}f\left(t\right)dt+e^x..........\left(i\right)}$}

using Leibniz rule then

f’(x) = e^xf(x) + e^x

_{$\Rightarrow \frac{dy}{dx}=e^{x}y+e^{x}wherey=f\left(x\right)then\frac{dy}{dx}=f\text{'}\left(x\right)$}            

P = -e^x, Q = e^x

Solution be y. (I.F.) =  ${\displaystyle \int Q\left(I.F.\right)dx+c}$

I. f. =  $e^{{\displaystyle \int -e^{x}dx}=e^{-e^x}}$

$\Rightarrow y.\left(e^{-e^x}\right)={\displaystyle \int e^x.e^{-e^x}dx+c}$   

$y.e^{-e^x}=-{\displaystyle \int dt+c=-t+c=-e^{-e^x}+c..........\left(ii\right)}$

Put x = 0 , in (i) f (0) = 1

$From\left(ii\right),\frac{1}{e}=-\frac{1}{e}+cgivenc=\frac{2}{e}$   

Hence f(x) = 2. $e^{\left(e^x-1\right)}-1$

  $v=\frac{1}{\sqrt[]{\epsilon \mu }}=\frac{1}{\sqrt[]{2{\epsilon }_0.2{\mu }_0}}=\frac{1}{2\sqrt[]{{\epsilon }_0{\mu }_0}}=\frac{c}{2}=15\times 10^{7}m/s.$

Yes, Mysore University Library is known to be the largest and most historical library in South India. The library is developed into a multi-branch system with a main library in the Manasagangotri campus and other libraries spread across the campus. With books comprising Mysore's history, art, architecture, and culture, the library has a huge collection of books, journals, theses, government publications, manuscripts, and other documents. Besides, the library offers access to extensive e-resources that enable students and researchers to access information anytime, anywhere. 

The tuition fee structure at DSEU BSc courses is currently not available. Generally, the tuition fee structure of BSc courses is a per semester model which divides the tuition fee for BSc courses into 6-8 instalments. Candidates can visit the official website of the university and check the tuition fee structure as well as the constituents of the tuition fee for BSc courses at DSEU.

IBSAT entrance test for IBS Mumbai testing verbal ability, reading comprehension, quantitative aptitude, and data interpretation. Difficulty is medium relative to other MBA entrance exams. Sufficient preparation can assist in achieving a good score.

No, the admission in IBS Mumbai is on the basis of graduation marks and entrance test performance, not Class 12 marks. Aspirants should have a bachelor's degree with at least 50% aggregate. Selection tests such as IBSAT, CAT, GMAT, or NMAT are required.

For the holistic development of the students, the university has a separate cell called the Directorate of Physical Education, which looks after the sports-related events. The University of Mysore sports facilities include three cricket grounds, four tennis courts, a cinder track, three basketball courts, etc. It also has Nalwadi Krishnaraja Wadiyar, Gangotri Glades, and three indoor stadiums. A well-equipped large gymnasium and a well-maintained swimming pool are also available for the students to focus on their physical health. 

The last date to apply for courses is ongoing. All Candidates must apply through the website and have to appear for the entrance exam as per the course requirements. Applicants are advised to seek proper updates from the university website about any change in the said date.

Yes, IBS Mumbai offers several research opportunities throughout the PhD programme, which include a 3-month summer research project in the student's field of specialisation. This is guided by a mentor and ends with a research seminar presentation prior to the PhD qualifying exam. The goal is to get research writing skills that can culminate in publication. Students are also linked with senior faculty for teaching and consultancy guidance.

DPG Institute of Technology and Management offers UG and PG courses. The selection criteria are based on entrance-exam scores. The application process at the DPG Institute of Technology and Management is conducted online. To secure a seat, students can follow the steps presented below:

1. Visit the official website and complete the online application process. 
2. Ensure eligibility and selection criteria for all programmes.
3. The selection criteria are based on the entrance exam score.
4. Upon selection, pay the specified fee to confirm and secure your seat.

For the IBS Mumbai PhD program, MBA degree holders can go directly into doctoral courses. Holders of a postgraduate qualification in allied fields need to complete first-year MBA courses as a prerequisite. This is to ensure that all applicants have a solid management foundation prior to embarking on doctoral research. The programme is meant for those who aspire for careers in teaching, research, and consultancy.

Candidates seeking admission to the BTech programme can enrol for admission with Class 12 marks. Candidates must complete Class 12 to enrol for the BTech course. The college offers only one UG course, i.e., BTech. DPG Institute of Technology and Management admissions are based on the entrance exam.

The four-year PhD programme offered at IBS Mumbai involves five stages. These include courses, research workshops and projects, PhD qualifying examination, progress seminars, thesis proposal, and thesis work. During the first year, eight courses on seminars, interdisciplinary studies, and research methodology are undertaken by students. Ongoing assessment is carried out at each stage to monitor academic development.

Kirori Mal College provides the flagship programme of Bachelor of Arts (BA), which is a popular choice for students in Humanities. The tuition fees for Kirori Mal College BA costs around INR 38.92 K - 50.45 K. Kirori Mal College BA admissions are held on the basis of entrance test, and accepted exam is CUET. Interested candidates can visit the official website and begin the application process for Kirori Mal College BA.

DPG Institute of Technology and Management admissions are currently open. Candidates are selected for courses based on the entrance exam, i.e., JEE Main, GATE, as per the course requirements. Candidates are selected based on these entrance exam scores. The institute offers UG and PG courses. 

Adichunchanagiri University offers a total of 240 seats. These seats are distributed across various specialisations. Popular speiclisations including BSc Nursing have 60 seats, in total. Seat allocation is based on merit in Class 12 or a valid KCET score, depending on the specialisation. 

  $\frac{N{}_p}{N_s}=\frac{V_p}{V_s}\Rightarrow N_p=\frac{V_p}{V_s}\times N_s=\frac{220}{12}\times 24=440$