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The NLU Kolkata BA LLB (H) tuition fee is charged on an annual basis. For a five-year course duration, the total tuition fee amounts to INR 3.66 lakh. Other than this, the fee structure includes other charges such as admission fees, hostel fees, one-time fees, etc. Candidates who wish to know the complete fee structure can visit the official website of the West Bengal National University of Juridical Sciences.

This is a Objective Type Questions as classified in NCERT Exemplar

Sol: 

$\begin{array}{l}Wehavey=4x^2+2x-8\dots \left(i\right)\\ andy=x^3-x+13\dots \left(ii\right)\\ Differentiatingeq.\left(i\right)w.r.t.x,wehave\\ \frac{dy}{dx}=8x+2\Rightarrow m_1=8x+2\left[m_{1}isslopeofcurve\left(i\right)\right]\\ Differentiatingeq.\left(ii\right)w.r.t.x,weget\\ \frac{dy}{dx}=3x^2-1\Rightarrow m_2=3x^2-1\left[m_{2}isslopeofcurve\left(ii\right)\right]\\ Ifthetwocurvestoucheachother,then{m}_1=m_2\\ \therefore 8x+2=3x^2-1\\ \Rightarrow 3x^2-8x-3=0\Rightarrow 3x^2-9x+x-3=0\\ \Rightarrow 3x\left(x-3\right)+1\left(x-3\right)=0\Rightarrow \left(x-3\right)\left(3x+1\right)=0\\ \therefore x=3,\frac{-1}{3}\\ Puttingx=3ineq\left(i\right),weget\\ y=4{\left(3\right)}^2+2\left(3\right)-8=36+6-8=34\\ So,therequiredpointis\left(3,34\right)\\ Nowforx=\frac{-1}{3}\\ y=4{\left(\frac{-1}{3}\right)}^2+2\left(\frac{-1}{3}\right)-8=4\times \frac{1}{9}-\frac{2}{3}-8\\ =\frac{4}{9}-\frac{2}{3}-8=\frac{4-6-72}{9}=\frac{-74}{9}\\ \therefore Otherrequiredpointis\left(\frac{-1}{3},\frac{-74}{9}\right).\\ Hence,there\end{array}$

Once you finish learning with the Maharashtra HSc syllabus, you can start solving the Maharashtra Class 12 sample papers and previous year question papers. You can solve the question papers and understand your weaknesses. Thus you can concentrate more on the topics on which you are weak.

Students are placed across various companies and in various fields after completing their education in the Arts. Some of the top recruiters for Arts graduates from colleges in Kolkata have been mentioned below, along with their average placement salary.

Note: This information is sourced from the web and may vary.

The fee for the courses at GS College Wardha are as follows: 

Candidates are required to follow the admission process to get the admission offer and become eligible to pay the course fee. 

This is a Objective Type Questions as classified in NCERT Exemplar

Sol: 

$\begin{array}{l}Wehavef\left(x\right)={\left(\frac{1}{x}\right)}^x\\ Takinglogofbothsides,wehave\\ logf\left(x\right)=xlog\frac{1}{x}\\ logf\left(x\right)=xlog{x}^{-1}\Rightarrow log\left[f\left(x\right)\right]=-\left[xlogx\right]\\ Differentiatingbothsidesw.r.t.x,weget\\ \frac{1}{f\left(x\right)}{f}^{\text{'}}\left(x\right)=-\left[x.\frac{1}{x}+logx.1\right]\\ \Rightarrow f^{\text{'}}\left(x\right)=-f\left(x\right)\left[1+logx\right]=-{\left(\frac{1}{x}\right)}^x\left[1+logx\right]\\ Forlocalmaximaandlocalminima{f}^{\text{'}}\left(x\right)=0\\ -{\left(\frac{1}{x}\right)}^x\left[1+logx\right]=0\Rightarrow {\left(\frac{1}{x}\right)}^x\left[1+logx\right]=0\\ {\left(\frac{1}{x}\right)}^x\ne 0\therefore 1+logx=0\\ \Rightarrow logx=-1\Rightarrow x=e^{-1}\Rightarrow x=\frac{1}{e}\\ So,x=\frac{1}{e}isthestationarypoint.\\ Now,f^{\text{'}}\left(x\right)=-{\left(\frac{1}{x}\right)}^x\left[1+logx\right]\\ f^{\text{'}\text{'}}\left(x\right)=-\left[{\left(\frac{1}{x}\right)}^x\left(\frac{1}{x}\right)+\left(1+logx\right).\frac{d}{dx}{\left(x\right)}^x\right]\\ f^{\text{'}\text{'}}\left(x\right)=-\left[{\left(e\right)}^{1/e}\left(e\right)+\left(1+log\frac{1}{e}\right)\frac{d}{dx}{\left(\frac{1}{e}\right)}^{1/e}\right]\\ x=\frac{1}{e}=-e^{\frac{1}{e}+1}<0maxima\\ \therefore Maximumvalueofthefunctionatx=\frac{1}{e}is\\ f\left(\frac{1}{e}\right)={\left(\frac{1}{1/e}\right)}^{1/e}\\ Hence,thecorrectoptionis\left(c\right).\end{array}$

Maharaja Ganga Singh University is a State University established by the University of Bikaner Act 2003. The University is approved by University Grants Commission (UGC). UGC is a statutory body that is responsible for the coordination, determination, and maintenance of higher educational institutions in India. The university is also approved by the Bar Council of India (BCI). MGSU is also a member of the Association of Indian Universities (AIU). Additionally, Maharaja Ganga Singh University is NAAC accredited.

Top Arts colleges in Kolkata often admit students through direct admissions based on merits.

Direct Admission Based on Merit

1. Eligibility: Complete 10+2 from a recognised board with the required percentage.
2. Application: Apply online or offline, submit documents (mark sheets, ID proof), and wait for the merit list.
3. Selection: If shortlisted, verify documents and pay the fees.

This is a Objective Type Questions as classified in NCERT Exemplar

Sol.

$\begin{array}{l}Wehavef\left(x\right)=x^x\\ Takinglogofbothsides,wehave\\ logf\left(x\right)=xlogx\\ Differentiatingbothsidesw.r.t.x,weget\\ \frac{1}{f\left(x\right)}{f}^{\text{'}}\left(x\right)=x.\frac{1}{x}+logx.1\\ \Rightarrow f^{\text{'}}\left(x\right)=f\left(x\right)\left[1+logx\right]=x^x\left[1+logx\right]\\ Tofindstationarypoint,f^{\text{'}}\left(x\right)=0\\ \therefore x^x\left[1+logx\right]=0\\ x^x\ne 0\therefore 1+logx=0\\ \Rightarrow logx=-1\Rightarrow x=e^{-1}\Rightarrow x=\frac{1}{e}\\ Hence,thecorrectoptionis\left(b\right).\end{array}$

Students must ensure to solve atleast one previous year Maharashtra 12th Mathematics question paper every day to efficiently prepare for the Maharashtra 12th Mathematics board exam. Make sure to practice the question papers during the last month of the preparation. 

The following are the steps that make up GS College Wardha's admissions process: 

Step 1: Candidates must go over the prerequisites for the courses. 

Step 2: Apply for the programme by completing the online application form. 

Step 3: Pay the application fee and appear for the required entrance. 

Step 4: Confirm admission by paying the course fee is the final admission offer has been received. 

This is a Objective Type Questions as classified in NCERT Exemplar

Sol: 

$\begin{array}{l}Giventhaty=-x^3+3x^2+9x-27\\ So,\frac{dy}{dx}=-3x^2+6x+9\\ \therefore Slopeofthegivencurve,\\ m=-3x^2+6x+9\\ \frac{dm}{dx}=-6x+6\\ Forlocal\text{?}\text{?}\text{?}maximaandlocalminima,\frac{dm}{dx}=0\\ \therefore -6x+6=0\Rightarrow x=1\\ Now\frac{d^{2}m}{d{x}^2}=-6<0maxima\\ \therefore Maximumvalueoftheslopeatx=1is\\ m_{x=1}=-3{\left(1\right)}^2+6\left(1\right)+9=-3+6+9=12\\ Hence,thecorrectoptionis\left(b\right).\end{array}$

Students can check the India Today and Outlook Ranking 2024 for the top Arts colleges in Kolkata, mentioned in the table below:

Note: The rankings mentioned above have been taken from India Today and Outlook Rankings 2024.

Yes, NLU Kolkata offers a BA LLB Hons course. It is a dual degree programme offered in full-time mode. Moreover, it runs for a duration of five years. During the duration, students study various facets of Law and Arts. To enroll into this course, students must appear for CLAT and the subsequent counselling process. The total fees to pursue this course amount to INR 5.4 lakh. This fee is as per official sources. However, it is subject to change.

This is a Objective Type Questions as classified in NCERT Exemplar

Sol: 

$\begin{array}{l}Wehavef\left(x\right)=2sin3x+3cos3x\\ So,f^{\text{'}}\left(x\right)=2cos3x.3-3sin3x.3=6cos3x-9sin3x\\ f^{\text{'}\text{'}}\left(x\right)=-6sin3x.3-9cos3x.3\\ =-18sin3x-27cos3x\\ Now{f}^{\text{'}\text{'}}\left(\frac{5\pi }{6}\right)=-18sin3\left(\frac{5\pi }{6}\right)-27cos3\left(\frac{5\pi }{6}\right)\\ =-18sin\left(\frac{5\pi }{2}\right)-27cos\left(\frac{5\pi }{2}\right)\\ =-18sin\left(2\pi +\frac{\pi }{2}\right)-27cos\left(2\pi +\frac{\pi }{2}\right)\\ =-18sin\frac{\pi }{2}-27cos\frac{\pi }{2}=-18.1-27.0\\ =-18<0maxima\\ Maximumvalueoff\left(x\right)atx=\frac{5\pi }{6}\\ f\left(\frac{5\pi }{6}\right)=2sin3\left(\frac{5\pi }{6}\right)+3cos3\left(\frac{5\pi }{6}\right)=2sin\left(\frac{5\pi }{2}\right)+3cos\left(\frac{5\pi }{2}\right)\\ =2sin\left(2\pi +\frac{\pi }{2}\right)+3cos\left(2\pi +\frac{\pi }{2}\right)=2sin\frac{\pi }{2}+3cos\frac{\pi }{2}=2\\ Hence,thecorrectoptionis\left(a\right).\end{array}$