Ask & Answer: India's Largest Education Community

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

Sol:

BITS Pilani Dubai offers merit-based scholarships. The scores required for a student to be eligible for a scholarship are mentioned below:

There are various entrance exam accepted by the University, such as CMAT, NEET, GUJCET, etc. The university also offers seats on the basis of merit too for some courses. For more  in-depth detail, click here, and here. 

There are several events arranged by IIT Jammu students and the faculty members. The below-mentioned are the events that the college has conducted in the past:

• INAE-SERB Workshop
• Student Research Conclave
• Celebrating Democracy Through Art!
• GIAN course on 'AI Hardware: Architectures and Design' and others. 

For BCom admission at NGBU, CUET plays a key role in the selection process. The application process was held from March 1 to March 24, 2025. The exam took place between May 13 and June 3, 2025, and results are tentatively expected in July 2025. Applicants should regularly check the official site for result updates.

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

Sol. 

$\begin{array}{l}Giventhaty=-x^3+3x^2+9x-27\\ Differentiatingbothsidesw.r.t.x,weget\\ \frac{dy}{dx}=-3x^2+6x+9\\ Letslopeofthecurve\frac{dy}{dx}=Z\\ \therefore z=-3x^2+6x+9\\ Differentiatingbothsidesw.r.t.x,weget\frac{dz}{dx}=-6x+6\\ Forlocalmaximaandlocalminima,\frac{dz}{dx}=0\\ \therefore -6x+6=0\Rightarrow x=1\\ \Rightarrow \frac{d^{2}z}{d{x}^2}=-6<0Maxima\\ Putx=1inequationofthecurvey={\left(-1\right)}^3+3{\left(1\right)}^2+9\left(1\right)-27\\ =-1+3+9-27=-16\\ Maximumslope=-3{\left(1\right)}^2+6\left(1\right)+9=12\\ Hence,\left(1,-16\right)isthepointatwhichtheslopeofthegivencurveismaximumand\\ Maximumslope=12\end{array}$

Yes, admissions for the BCom programme at Nehru Gram Bharati University Kotwa, for the 2025 academic session are currently open. Interested students should visit the official website to check eligibility, submit their application, and stay updated on important deadlines and announcements.

The primary eligibility criteria required for admission to the MA course at Dr. Shantilal K. Somaiya School of Art is that candidates must complete their graduation from any stream with decent scores. Additionally, for the admission process, the school/university releases the merit of selected candidates according to their scores achieved in their last qualifying examination (graduation). 

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

Sol: 

$\begin{array}{l}Giventhatf\left(x\right)=ta{n}^{-1}\left(sinx+cosx\right)in\left(0,\frac{\pi }{4}\right)\\ Differentiatingbothsidesw.r.t.x,weget\\ f^{\text{'}}\left(x\right)=\frac{1}{1+{\left(sinx+cosx\right)}^2}.\frac{d}{dx}\left(sinx+cosx\right)\\ \Rightarrow f^{\text{'}}\left(x\right)=\frac{1\times \left(cosx-sinx\right)}{1+{\left(sinx+cosx\right)}^2}\\ \Rightarrow f^{\text{'}}\left(x\right)=\frac{\left(cosx-sinx\right)}{1+si{n}^{2}x+co{s}^{2}x+2sinxcosx}\\ \Rightarrow f^{\text{'}}\left(x\right)=\frac{\left(cosx-sinx\right)}{1+1+2sinxcosx}\Rightarrow f^{\text{'}}\left(x\right)=\frac{cosx-sinx}{2+2sinxcosx}\\ Foranincreasingfunction,f^{\text{'}}\left(x\right)\ge 0\\ \therefore \frac{cosx-sinx}{2+2sinxcosx}\ge 0\\ \Rightarrow cosx-sinx\ge 0\left[?\left(2+sin2x\right)\ge 0in\left(0,\frac{\pi }{4}\right)\right]\\ \Rightarrow cos\ge sinx,whichistruefor\left(0,\frac{\pi }{4}\right)\\ Hence,thegivenfunctionf\left(x\right)isanincreasingfunctionin\left(0,\frac{\pi }{4}\right).\end{array}$

The University of Florida offers accommodation in the form of suites, apartements & traditional bedrooms, with the option of double & triple beds. 

The cost of accommodation depends on the type & the timing of applying for accommodation.

Listed below is a detailed description of the University of Florida accommodation costs at the Beaty Towers, Broward & Buckman Halls:

1 USD = INR 86.48

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

Sol: 

$\begin{array}{l}Giventhatf\left(x\right)=sinx-cosx-2ax+b,a\ge 1\\ Differentiatingbothsidesw.r.t.x,weget\\ f^{\text{'}}\left(x\right)=cosx+sinx-2a\\ Fordecreasingfunction,f^{\text{'}}\left(x\right)<0\\ \therefore cosx+sinx-2a<0\\ \Rightarrow 2\left(\frac{}{2}cosx+\frac{1}{2}sinx\right)-2a<0\\ \Rightarrow \frac{}{2}cosx+\frac{1}{2}sinx-a<0\\ \Rightarrow \left(cos\frac{\pi }{6}cosx+sin\frac{\pi }{6}sinx\right)-a<0\\ \Rightarrow cos\left(x-\frac{\pi }{6}\right)-a<0\\ Sincecosx\in \left[-1,1\right]anda\ge 1\\ \therefore f^{\text{'}}\left(x\right)<0\\ Hence,thegivenfunctionisdecreasingfunctioninR.\end{array}$

No, direct admission is not available for courses at  GITAM School of Pharmacy, Visakhapatnam . To be accepted into the programs, candidates must finish the admissions process and take entrance exams like the GITAM GAT. 
Candidates who fulfill the minimal eligibility requirements are granted the opportunity to participate in the admission process . To be considered for a shortlist, candidates need to review the selection criteria for the course. 

Yes, Dr. Shantilal K. Somaiya School of Art does offer MA courses for the duration of two years. Moreover, the school offers an MA in two very rare specialisations i.e., an MA in Writing Art & Criticism and an MA in Arts & Visual Studies. The eligibility requirements and admission process for both of the offered specialisations is almost similar. 

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

Sol. 

$\begin{array}{l}Giventhatf\left(x\right)=2x+co{t}^{-1}x+log\left(-x\right)\\ Differentiatingbothsidesw.r.t.x,weget\\ f^{\text{'}}\left(x\right)=2-\frac{1}{1+x^2}+\frac{1}{-1}\times \frac{d}{dx}\left(-x\right)\\ =2-\frac{1}{1+x^2}+\frac{\left(\frac{1}{2}\times \left(2x-1\right)\right)}{-1}\\ =2-\frac{1}{1+x^2}+\frac{x-}{\left(-x\right)}\\ =2-\frac{1}{1+x^2}-\frac{-x}{\left(-x\right)}\\ =2-\frac{1}{1+x^2}-\frac{1}{}\\ Forincreasingfunction,f^{\text{'}}\left(x\right)\ge 0\\ \therefore 2-\frac{1}{1+x^2}-\frac{1}{}\ge 0\\ \Rightarrow \frac{2\left(1+x^2\right)-1+}{1+x^2}\ge 0\Rightarrow 2+2x^2-1+\ge 0\\ \Rightarrow 2x^2+1+\ge 02x^2+1\ge -\\ Squaringbothsides,weget4x^4+1+4x^2\ge 1+x^2\\ \Rightarrow 4x^4+4x^2-x^2\ge 0\Rightarrow 4x^4+3x^2\ge 0\Rightarrow x^2\left(4x^2+3\right)\ge 0\\ whichistrueforanyvalueofx\in R\\ Hence,thegivenfunctionisanincreasingfunctionoverR.\end{array}$

There are 63 countries which accept SAT scores for admission and use them to assess applicants. These countries are as follows: