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Candidates willing to take admission in the BSc course at the Gujarat Technical University should check for the admission criteria. The admission is primarily granted on the basis of Class 12 exam under the guildlines of Gujarat Common Admission Service (GCAS). Therefore, appearing for CUET examis not necessary for the getting admission into BSc at GTU.

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

Sol:

$\begin{array}{l}Giventhatf\left(x\right)=x^3-2x^2-x+3in\left[0,1\right]\\ \left(i\right)f\left(x\right)isanfunction,soitiscontinuousin\left[0,1\right].\\ \left(ii\right)f^{\text{'}}\left(x\right)=3x^2-4x-1whichexistsin\left(0,1\right)\\ So,f\left(x\right)isdifferentiable.\\ Astheaboveconditionsaresatisfied,thentheremustexistatleastone\in \left(0,1\right)suchthat\\ f^{\text{'}}\left(c\right)=\frac{f\left(b\right)-f\left(a\right)}{b-a}\\ \Rightarrow 3c^2-4c-1=\frac{\left[{\left(1\right)}^3-2{\left(1\right)}^2-\left(1\right)+3\right]-\left[0-0-0-3\right]}{1-0}\\ \Rightarrow 3c^2-4c-1=\frac{\left(1-2-1+3\right)-\left(3\right)}{1}\\ \Rightarrow 3c^2-4c-1=1-3\Rightarrow 3c^2-4c-1=-2\\ \Rightarrow 3c^2-4c+1=0\Rightarrow 3c^2-3c-c+1=0\\ \Rightarrow 3c\left(c-1\right)-1\left(c-1\right)=0\Rightarrow \left(c-1\right)\left(3c-1\right)=0\\ \Rightarrow c-1=0\therefore c=1\\ 3c-1=0\therefore c=\frac{1}{3}\in \left(0,1\right)\\ Hence,MeanValueTheoremisverified.\end{array}$

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

Sol:

The admission process begins with the form filling. Aspirants who fulfil the course-specific eligibility criteria can register and apply. The received applications are scanned by the selection committee of Sant Baba Bhag Singh University. Admission selection is done based on performance in the last qualifying examination, i.e., Class 12 or equivalent. After selection, students need to get their documents verified and pay the required admission fee amount for the admission confirmation. 

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

Sol:

$\begin{array}{l}Giventhaty=x\left(x-4\right),x\in \left[0,4\right]\\ Letf\left(x\right)=x\left(x-4\right),x\in \left[0,4\right]\\ \left(i\right)f\left(x\right)beinganalgebraicpolynomialiscontinuousfunctioneverywhere.\\ So,f\left(x\right)=x\left(x-4\right)iscontinuousxin\left[0,4\right].\\ \left(ii\right)f^{\text{'}}\left(x\right)=2x-4whichexistsin\left(0,4\right)\\ So,f\left(x\right)isdifferentiable.\\ \left(iii\right)f\left(0\right)=0\left(0-4\right)=0\\ f\left(4\right)=0\left(4-4\right)=0\\ \therefore f\left(0\right)=f\left(4\right)=0\\ Astheaboveconditionsaresatisfied,thentheremustexistatleastonepointc\in \left(0,4\right)suchthat{f}^{\text{'}}\left(c\right)=0\\ \therefore 2c-4=0\Rightarrow c=2\in \left(0,4\right)\\ Hence,c=2isthepointin\left(0,4\right)onthegivencurveatwhichthetangentisparalleltothex-axis.\end{array}$

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

Sol:

$\begin{array}{l}Giventhaty=cosx-1on\left[0,2\pi \right]\\ Firstly,wehavetofindapointconthegivencurvey=cosx-1on\left[0,2\pi \right]suchthatthetangentat\\ c=0\in \left[0,2\pi \right]isparalleltox-axisi.e.,f^{\text{'}}\left(c\right)=0where{f}^{\text{'}}\left(c\right)istheslopeofthetangent.\\ So,wehavetoverifytheRolle\text{'}sTheorem.\\ \left(i\right)y=cosx-1,isthecombinationofcosineandconstantfunctions.So,itiscontinuouson\left[0,2\pi \right].\\ \left(ii\right)\frac{dy}{dx}=-sinxwhichexistsin\left(0,2\pi \right)\\ Soitisdifferentiableon\left(0,2\pi \right).\\ \left(iii\right)Letf\left(x\right)=cosx-1\\ f\left(0\right)=cos0-1\Rightarrow 1-1=0\\ f\left(2\pi \right)=cos2\pi -1\Rightarrow 1-1=0\\ \therefore f\left(0\right)=f\left(2\pi \right)=0\\ Astheaboveconditionsaresatisfied,thenthereliesapointc\in \left(0,2\pi \right)suchthat{f}^{\text{'}}\left(c\right)=0\\ \therefore -sinc=0\Rightarrow sinc=0\\ \therefore c=n\pi ,n\in I\\ \Rightarrow c=\pi \in \left(0,2\pi \right)\\ Hence,c=\pi isthepointonthecurvein\left(0,2\pi \right)atwhichthetangentisparalleltox-axis.\end{array}$

Lawrence Technological University offers one of the best master's programs in Business Data Analytics for international students. The curriculum includes Statistics for Data Analytics and Visualization, Management Information Systems, Database Management Systems, Machine Learning, Social Media Data Analytics, Visual Analytics, and more. Students must hold a bachelor's degree or equivalent, an academic GPA of min 3 or above, a goal statement, academic transcripts, and English language requirements to apply for the curriculum. The scope of becoming a Data Analytics expert is increasing in nearly every industry.

Sant Baba Bhag Singh University is currently accepting applications for its BA programme. The eligible students can go to the official website or contact the admission office to access the form and submit it. There is no application deadline available as of now. Hence, it is advisable to apply as soon as possible.

Yes, candidates passing out with an MBA degree from CAIIHM Chennai are eligible for a range of career opportunities in the government sector. The institute offers an MBA in Hospitality Management. After completing the programme, candiates can join the following organisations and departments:

• IRCTC
• Ministry of Tourism
• State Tourism Department Corporations
• AAI
• PSUs
• FSSAI
• Government Educational Institutes

As per the ICMAI CMA application cutoff dates, the last date to enrol for the CMA Final June term exam is January 31. Candidates enrolling on or before this date are eligible to appear for the ICMAI CMA Final exam held in the June session. If the candidates miss the deadline, they can apply to appear for the exam in the next term, that is December.

This application cutoff date refers to the enrolment deadline, those who have enrolled in the course before the cutoff date for the specific term will have to fill the CMA exam form. CMA exam form submission facility is typically made available along with the notification for the exam dates.

Students willing to study BSc Biotechnology (Hons) at Gujarat Technological University should expect an expenditure of over seventy thousand. The detailed fee information is mentioned in the following table:

The information regarding fees is taken from the official website. This could be subject to revision.

In order to get admission at Bunts Sangha's Ramanath Payyade College of Hospitality Management Studies candidates must keep certain documents ready. Student can check the list of documents below:

• Scanned Class 10, Class 12 and graduation marksheet
• Leaving Certificate
• Aadhaar Card
• Passport-size photograph
• Signature

Note: The list of documents mentioned above is a general documents. For more details, visit the official website.

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

Sol:

$\begin{array}{l}\left(i\right)f\left(x\right)beinganalgebraicpolynomialiscontinuouseverywhere.\\ \left(ii\right)f\left(x\right)mustbedifferentiableatx=1\\ L.H.L.=\underset{x\to 1^{-}}{lim}\frac{f\left(x\right)-f\left(1\right)}{x-1}\\ =\underset{x\to 1^{-}}{lim}\frac{\left(x^2+1\right)-\left(1+1\right)}{x-1}\\ =\underset{x\to 1^{-}}{lim}\frac{x^2+1-2}{x-1}=\underset{x\to 1^{-}}{lim}\frac{x^2-1}{x-1}\\ =\underset{x\to 1^{-}}{lim}\frac{\left(x-1\right)\left(x+1\right)}{x-1}=\underset{x\to 1^{-}}{lim}\left(x+1\right)=\left(1+1\right)=2\\ R.H.L.=\underset{x\to 1^{+}}{lim}\frac{f\left(x\right)-f\left(1\right)}{x-1}\\ =\underset{x\to 1^{-}}{lim}\frac{\left(3-x\right)-\left(1+1\right)}{x-1}\\ =\underset{x\to 1^{-}}{lim}\frac{\left(3-x\right)-2}{x-1}=\underset{x\to 1^{-}}{lim}\frac{1-x}{x-1}=-1\\ \therefore L.H.L.\ne R.H.L.\\ So,f\left(x\right)isnotdifferentiableatx=1.\\ Hence,Rolle\text{'}sTheoremisnotapplicablein\left[0,2\right].\end{array}$

Yes, many students take TOEFL in final year of graduation. Just check your college deadlines, and take the test at least 2 months before that.

Yes, students can pursue a BSc in Nursing from Mohamed Sathak A.J. College of Nursing, provided they meet the eligibility criteria. Applicants must have passed Class 12 or an equivalent examination with subjects like Physics, Chemistry, and Biology (or Botany and Zoology). Admission is based on academic merit, and the college offers 50 seats annually. Interested candidates should apply through the official website and follow the admission process carefully.

Yes, Sant Baba Bhag Singh University offers a three-year long BA programme. Its mode of study is full-time. SBBS University BA admission is merit-based. Candidates who are Class 12 pass in any stream can apply for the course admission. Moreover, the applications are accepted in both online and offline modes by the university.