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

Sol:

$\begin{array}{l}Giventhatf\left(x\right)=log\left(x^2+2\right)-log3in\left[-1,1\right]\\ \left(i\right)f\left(x\right)=log\left(x^2+2\right)-log3,beingalogarithmfunctions,f\left(x\right)iscontinuousin\left[-1,1\right].\\ \left(ii\right)f^{\text{'}}\left(x\right)=\frac{1}{x^2+2}.2x-0=\frac{2x}{x^2+2}whichexistsin\left(-1,1\right)\\ Sof\left(x\right)isdifferentiablein\left(-1,1\right).\\ \left(iii\right)f\left(-1\right)=log\left(1+2\right)-log3\Rightarrow log3-log3=0\\ f\left(1\right)=log\left(1+2\right)-log3\Rightarrow log3-log3=0\\ \therefore f\left(-1\right)=f\left(1\right)=0\\ Astheaboveconditionsaresatisfied,thentheremustexistatleastonepoint\\ c\in \left(-1,1\right)suchthat{f}^{\text{'}}\left(c\right)=0\\ \therefore \frac{2c}{c^2+2}=0\Rightarrow 2c=0\Rightarrow c=0\in \left(-1,1\right)\\ Hence,Rolle\text{'}sTheoremisverified.\end{array}$

The library at Mohamed Sathak A.J. College of Nursing offers several facilities to support BSc students, including a book bank, photocopying services, internet access, OPAC/indexing tools, and access to online journals. A spacious reading hall is also available for students to study in a quiet and focused environment. These resources enhance the academic experience for BSc Nursing students.

The University of Delhi, along with regular courses, offeres elective courses to students. It includes subjects outside their core discipline. These courses allows students to learn about subjects unrelated to their core subjects, increasing their academic knowledge.

Mohamed Sathak A.J. College of Nursing provides BSc students with extensive clinical exposure through tie-ups with leading hospitals, including Chennai Port Trust Hospital, Sri Sathya Sai Medical College, Global Health City, and Bharathi Raja Hospital. Students also gain hands-on training at urban and rural health posts, mental health institutions, and specialised hospitals, ensuring comprehensive practical experience in various healthcare settings.

Following entrance exams includes the questions on parajumbles

• SSC CGL
• NDA
• MBA National Entrance Exams
• BBA National Entrance Exams
• UPSC
• CUET UG
• CUET PG

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

Sol:

$\begin{array}{l}Giventhatf\left(x\right)=si{n}^{4}x+co{s}^{4}xin\left[0,\frac{\pi }{2}\right]\\ \left(i\right)f\left(x\right)=si{n}^{4}x+co{s}^{4}x,beingsineandcosinefunctions,f\left(x\right)iscontinuousin\left[0,\frac{\pi }{2}\right].\\ \left(ii\right)f^{\text{'}}\left(x\right)=4si{n}^{3}x.cosx+4co{s}^{3}x\left(-sinx\right)\\ =4si{n}^{3}x.cosx-4sinxco{s}^{3}x\\ =4sinx.cosx\left(si{n}^{2}x-co{s}^{2}x\right)\\ =-4sinx.cosx\left(co{s}^{2}x-si{n}^{2}x\right)\\ =-2.2sinx.cosxcos2x\left[\begin{array}{l}?cos2x=co{s}^{2}x-si{n}^{2}x\\ sin2x=2sinxcosx\end{array}\right]\\ =-2sin2x.cos2x=-sin4xwhichexistsin\left(0,\frac{\pi }{2}\right)\\ Sof\left(x\right)isdifferentiablein\left(0,\frac{\pi }{2}\right).\\ \left(iii\right)f\left(0\right)=si{n}^4\left(0\right)+co{s}^4\left(0\right)=1\\ f\left(\frac{\pi }{2}\right)=si{n}^4\left(\frac{\pi }{2}\right)+co{s}^4\left(\frac{\pi }{2}\right)=1\\ \therefore f\left(0\right)=f\left(\frac{\pi }{2}\right)=1\\ Astheaboveconditionsaresatisfied,thentheremustexistatleastonepoint\\ c\in \left(0,\frac{\pi }{2}\right)suchthat{f}^{\text{'}}\left(c\right)=0\\ \therefore f^{\text{'}}\left(c\right)=0\Rightarrow -sin4c=0\Rightarrow sin4c=0\\ \Rightarrow sin4c=sin0\Rightarrow 4c=n\pi \\ \therefore c=\frac{n\pi }{4},n\in I\\ Forn=1,c=\frac{\pi }{4}\in \left(0,\frac{\pi }{2}\right)\\ Hence,Rolle\text{'}sTheoremisverified.\end{array}$

Identifying the first sentence of the para jumble is easy and most important steps to form a sentence. Students must identify the noun, or an opening words like- Nowadays, The, A, An.

To enroll in a B.Com course at DU, students must meet the following eligibility criteria:

1. Academic Qualifications: The candidate should have passed the Class 12 examination from a recognised board with a minimum 50% aggregate.
2. Admission Process: Admission is done based on the Common University Entrance Test (CUET) scores in regular colleges and Class 12 marks in SOL.

To solve the Para Jumbles correctly, students must:

• Read all the sentences provided in a question
• Identify the first sentence of the paragraph by applying the Para Jumbles rules
• Try finding link between the sentences
• Pay attention to nouns and pronouns to identify the following sentences
• Form a structured sentence and read again to create a meaning

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

Sol:

$\begin{array}{l}Giventhatf\left(x\right)=x{\left(x-1\right)}^{2}in\left[0,1\right]\\ \left(i\right)f\left(x\right)=x{\left(x-1\right)}^2,beinganalgebraicpolynomial,iscontinuousin\left[0,1\right].\\ \left(ii\right)f^{\text{'}}\left(x\right)=x.2\left(x-1\right)+{\left(x-1\right)}^2.1\\ =2x^2-2x+x^2+1-2x\\ =3x^2-4x+1whichexistsin\left(0,1\right)\\ \left(iii\right)f\left(x\right)=x{\left(x-1\right)}^2\\ =0{\left(0-1\right)}^2=0;f\left(1\right)=1{\left(1-1\right)}^2=0\\ \Rightarrow f\left(0\right)=f\left(1\right)=0\\ Astheaboveconditionsaresatisfied,thentheremustexistatleastonepoint\\ c\in \left(0,1\right)suchthat{f}^{\text{'}}\left(c\right)=0\\ \therefore f^{\text{'}}\left(c\right)=3c^2-4c+1=0\Rightarrow 3c^2-3c-c+1=0\\ \Rightarrow 3c\left(c-1\right)-1\left(c-1\right)=0\Rightarrow \left(c-1\right)\left(3c-1\right)=0\\ c-1=0\Rightarrow c=1\\ 3c-1=0\Rightarrow 3c=1\therefore c=\frac{1}{3}\in \left(0,1\right)\\ Hence,Rolle\text{'}sTheoremisverified.\end{array}$

Yes, the GMAT syllabus is the same for GMAT online and GMAT at a test centre. The format is the same, applicants can attempt the exam based on their preferred sectional order. The duration of GMAT is also the same for both formats, exceptions for those with accommodations also apply. 

The questions on English Para Jumbles in CAT exam are approximately four to five questions. The difficulty level of the questions in CAT exam is moderate. Candidates must practice questions to master the trick of arranging sentences in coherent paragraph.

The TOEFL iBT Home Edition is the same test as the one in the test center, but you take it from your home. It is safe, official, and accepted by over 13,000+ universities and colleges.

Candidates seeking MBA admission at Chennais Amirta International IHM must begin with the online application process. To apply, candidates can visit the institute's official website. The application form available on the official website must be carefully filled and submitted online. The form includes the candidates' personal details, such as their name, Aadhar Number, parents' names, address and qualification. Before applying, candidates must ensure that they meet the eligibility requirements set by the institute. 

Yes. Candidates can choose between the June and December CMA Final exam terms based on their preparation level. The Institute of Cost Accountants of India conducts the Final exam twice yearly. CMA students have the flexibility of choosing between two terms based on their preparation level.

Eligible candidates are allowed to enroll in either session. Candidates who wish to apply for the exam in any of the term must keep the application cutoff date in mind.

It is better to book your TOEFL test at least 2 to 3 months before your university deadline. That gives enough time to get your TOEFL scores, which usually come in 4 to 8 days.

Sri Krishna Arts and Science College offered the highest placement package of INR 4.5 LPA and the top recruiters include Wipro, TCS, HCL, Tommy Hilfiger, Amazon, Concentrix, etc.

Listed below are the top ranked Arts colleges in Coimbatore along with their average placement package and the top recruiters:

Source: Official site and may vary.