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This is a multiple choice answer as classified in NCERT Exemplar

Option (C)

Explanation: PHBV (Poly beta-hydroxybutyrate co-beta-hydroxy valerate) is a biodegradable polymer. It undergoes bacterial degradation in the environment. The structure is shown as,

The top employers for Brown University MSc in Data Science are:

• Accenture
• Amazon
• Google
• IBM
• Capital One
• Zest AI
• Oracle
• Meta
• LinkedIn

Many of the Brown University MSc in CS graduates have been hired by top-notch companies such as Amazon, Meta, Bloomberg, Goldman Sachs, Tesla, Uber, Spotify, etc. The graduates of this course are working on varied job roles such as Senior Software Developers, Data Scientists, Product Engineers, ML / AI engineers, etc.

This is a Long Answer Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}Let\text{?}\text{?}\text{?}\text{?}I={\displaystyle ?\underset{II}{e^{?3x}}}\underset{I}{co{s}^{3}x}dx\\ \text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}=co{s}^{3}x.{\displaystyle ?e^{?3x}\text{?}dx}?{\displaystyle ?\left(D\left(co{s}^{3}x\right).{\displaystyle ?e^{?3x}\text{?}dx}\right)dx}\\ \text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}=co{s}^{3}x.\frac{e^{?3x}}{?3}?{\displaystyle ?\left(3co{s}^{2}x\left(?sinx\right).\frac{e^{?3x}}{?3}\right)dx}\\ \text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}=?\frac{1}{3}{e}^{?3x}co{s}^{3}x?{\displaystyle ?co{s}^{2}xsinx.}{e}^{?3x}dx\\ \text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}=?\frac{1}{3}{e}^{?3x}co{s}^{3}x?{\displaystyle ?\left(1?si{n}^{2}x\right)sinx.}{e}^{?3x}dx\\ \text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}=?\frac{1}{3}{e}^{?3x}co{s}^{3}x?{\displaystyle ?sinx.e^{?3x}dx}+{\displaystyle ?\underset{I}{si{n}^{3}x}}.\underset{II}{e^{?3x}}dx\\ \text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}=?\frac{1}{3}{e}^{?3x}co{s}^{3}x?{\displaystyle ?sinx.e^{?3x}dx}+si{n}^{3}x{\displaystyle ?e^{?3x}dx?{\displaystyle ?\left(D\left(si{n}^{3}x\right).{\displaystyle ?e^{?3x}\text{?}dx}\right)dx}}\\ \text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}=?\frac{1}{3}{e}^{?3x}co{s}^{3}x?{\displaystyle ?sinx.e^{?3x}dx}+si{n}^{3}x.\frac{e^{?3x}}{?3}?{\displaystyle ?\left(3si{n}^{2}x.cosx.\frac{e^{?3x}}{?3}\right)dx}\\ \text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}=?\frac{1}{3}{e}^{?3x}co{s}^{3}x?{\displaystyle ?sinx.e^{?3x}dx}?\frac{1}{3}{e}^{?3x}si{n}^{3}x+{\displaystyle ?si{n}^{2}xcosx.}{e}^{?3x}dx\\ \text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}=?\frac{1}{3}{e}^{?3x}co{s}^{3}x?{\displaystyle ?sinx.e^{?3x}dx}?\frac{1}{3}{e}^{?3x}si{n}^{3}x+{\displaystyle ?\left(1?co{s}^{2}x\right)cosx.}{e}^{?3x}dx\\ \text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}I=?\frac{1}{3}{e}^{?3x}co{s}^{3}x?\left[sinx.\frac{e^{?3x}}{?3}?{\displaystyle ?cosx.\frac{e^{?3x}}{?3}dx}\right]?\frac{1}{3}{e}^{?3x}si{n}^{3}x+{\displaystyle ?cosx.e^{?3x}}dx?{\displaystyle ?co{s}^{3}x.e^{?3x}dx}\\ \text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}=?\frac{1}{3}{e}^{?3x}co{s}^{3}x+sinx.\frac{e^{?3x}}{3}?{\displaystyle ?cosx.\frac{e^{?3x}}{?3}dx}?\frac{1}{3}{e}^{?3x}si{n}^{3}x+{\displaystyle ?cosx.e^{?3x}}dx?I\\ \text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}2I=\frac{e^{?3x}}{?3}\left[co{s}^{3}x+si{n}^{3}x\right]?\left[sinx.\frac{e^{?3x}}{3}?{\displaystyle ?cosx.\frac{e^{?3x}}{?3}dx}\right]+{\displaystyle ?cosx.e^{?3x}}dx\\ \text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}=\frac{e^{?3x}}{?3}\left[co{s}^{3}x+si{n}^{3}x\right]+\frac{1}{3}sinx.e^{?3x}?\frac{1}{3}{\displaystyle ?cosx.e^{?3x}}dx+{\displaystyle ?cosx.e^{?3x}}dx\\ ?\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}2I=\frac{e^{?3x}}{?3}\left[co{s}^{3}x+si{n}^{3}x\right]+\frac{1}{3}sinx.e^{?3x}+\frac{2}{3}{\displaystyle ?cosx.e^{?3x}}dx\\ Now,\text{?}{I}_1=\frac{2}{3}{\displaystyle ?\underset{I}{cosx}}.\underset{II}{e^{?3x}}dx\\ \text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}=\frac{2}{3}\left[cosx.{\displaystyle ?e^{?3x}dx}?{\displaystyle ?\left(D\left(cosx\right).{\displaystyle ?e^{?3x}\text{?}dx}\right)dx}\right]\\ \text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}=\frac{2}{3}\left[cosx.\frac{e^{?3x}}{?3}?{\displaystyle ??sinx.\frac{e^{?3x}}{?3}dx}\right]\\ \text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}=\frac{2}{3}\left[cosx.\frac{e^{?3x}}{?3}?\frac{1}{3}{\displaystyle ?sinx.e^{?3x}dx}\right]\end{array}$

Both ISB&M COC and Indira College of Commerce and Science are popular institutes offering the BBA programme to students in Pune. The key comparisons are done below: 

Rankings: ISB&M was ranked #3 by GHRDC BBA College Survey 2022, while ICCS has been ranked at the 84th spot by India Today, 2024.

Tuition Fees: The total tuition fees is INR 3.63 Lakhs - 5.73 Lakhs. On the other hand, the tuition fees at ICCS is INR 1.56 Lakhs - 1.8 Lakhs.

Placements: The average package is INR 4.60 LPA, while the median salary at Indira College of Commerce and Science is INR 3.41 LPA.

Students with valid F1 status can work part-time while studying at Brown University. However, note that F1 students must make sure they have the appropriate work authorization prior to pursuing any type of employment activity, paid or unpaid. For on-campus employment, students can work up to 20 hours per week when the classes are in session. They can work over 20 hours per week during the summer and winter breaks. Also Check: Popular Part-Time Jobs in USA

For students belonging to the General AI quota, the IIT Delhi CSE cutoff 2025 ranged between 125 and 126. However, please note that the cutoff ranks vary for different rounds and categories. Therefore, aspirants can refer to the table below to view the category-wise CSE cutoff ranks in 2025 for the last round. 

The weightage distribution of the tests and interview components in the IICD entrance exam is given below.

A. General Awareness, Creativity & Perception Test - 35%
B. Material, Color & Conceptual Test - 45%
C. Personal Interview - 20%

Yes, the course is tailored to cater the needs of working professionals wanting to make a career in the field of Management. The curriculum is aligned to cover the essential management specialisations. Candidates seeking admission must check out the eligibility and selectio requirements. 

Maya Academy of Advanced Cinematics is a well-known institution for education situated at South Ex 1 in Delhi. The institute gives distinct Certificate and Diploma programmes at UG and Certificate levels. Students can check some of the course streams below:

• Animation
• Architecture & Planning
• Arts 
• Design
• IT & Software
• Mass Communication & Media

UPES School of Design offers courses at the UG and PG level. The school offers courses such as BDes and MDes for the duration of 2 years and 4 years. The admission process for the respective courses includes various qualification rounds, starting with entrance based shortlisting. The school offers respective courses with the total tuition fees ranging from INR 13.15 Lacs to INR 43.74 Lakh.

Since the acceptance rate at Brown Uni is very low which means Indian applicants must have a good academic record to take admission also for the Class of 2029 Brown University acceptance rate is 5.65% and to take admission to this university the applicants must aim to maintain a strong academic record, provide good standardized test scores if applicable, provide English proficiency proof, have a subject history thats in alignment with the open curriculum and craft compelling essays

Jagannath Institute of Management Sciences (JIMS) Vasant Kunj - II is an institute with a national as well as international reputation. It is ranked by various prominent ranking agencies such as the NIRF, India Today, and others. JIMS Vasant Kunj is ranked among the top 201-300 institutions under the 'College' category in India, according to the National Institutional Ranking Framework (NIRF) 2024. 

UG international students must have proof of the completion of high school (secondary school) or equivalent. On the other hand, Indian students who want to study Graduate courses, students are required to have a Bachelor's degree. Additionally, students must submit the English language proficiency scores and documents as required such academic transcripts, resume, financial documents, standardized test scores, etc.

This is a multiple choice answer as classified in NCERT Exemplar

Option (B)

Explanation: Polyacrylonitrile is used as a wool substitute in the manufacture of commercial fibers such as orlon or acrilan.

The application deadlines for Brown University UG programs are given below:

For PG, deadlines vary as per the programs. 

MAAC, South Extension application forms are also available online. Students satisfying the eligibility criteria can apply for the chosen course. Below are the guide to apply for admission-

1- Go to the verified website of the MAAC, South Extension, maacdelhi.com/contact

2- Fill out the form.

3- Complete the form and submit it.

Yes, international applicants at the UG level can apply via Common App. Enter the particular questions in the application and submit the documents as required. Brown University application fee is USD 80 (Around INR 7.2 K). To apply, the applicants are required to submit the following documents:

• Academic transcript
• TOEFL or any other equivalent test score
• Letters of reference
• Financial documents
• Any other document (as required)
• Mid-year school report
• Two teacher recommendations
• Final school report and transcript
• SAT / ACT score

A TOEFL score of 105 on iBT / IELTS with 8.0 / Duolingo with 130 / PTE score of 75 is accepted.

1 USD = INR 90.25