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Given hyperbola :

$\frac{x^2}{a^2}-\frac{y^2}{9}=1$

$$ $?$  it passes through

$\left(8,3\sqrt[]{3}\right)$

$?\frac{64}{a^2}-\frac{27}{9}=1\Rightarrow a^2=16$

Now, equation of normal to hyperbola

$\frac{16x}{8}+\frac{9y}{3\sqrt[]{3}}=16+9$

$\text{exception 25:}$ $\left(-1,9\sqrt[]{3}\right)$  satisfied

According to the data available for Garden CIty University MBA fees and its competitors, it seems Garden CIty University MBA fees is either lower or on point with other similar institutes. The Garden City University MBA fees is around INR 5.42 Lacs while the fee for an MBA course sits at around 7 lakh. This means that Garden City University is a good choice for pursuing MBA courses.

A Product Portfolio is a showcase of your work, case studies or product thinking which is  crucial for cracking PM roles and interviews, especially as a fresher.

Your portfolio may include:

• Case study on improving a known app (e.g., Uber, Zomato)
• A product you built (app, website, or feature mockup)
• Go to market (GTM) strategy for a fictional product
• Product teardown of a competitor
• A deck explaining how you'd solve a real world user problem

Below are the examples of some tools to build it:

1. Notion (best for organized portfolios)
2. Google Slides / Docs
3. Figma (for product mockups)

Pro tip: Link your portfolio in your resume and LinkedIn!

Yes, Medicaps University provides hostel facilities to students who wish to reside in hostel facilities and are pursuing a course offered by the university. As per official sources, the university has separate hostels for boys and girls. Each hostel is equipped with amenities, such as spacious rooms, a mess, recreational areas, and more. Moreover, on average, the hostel at Medicaps University ranges from INR 2.4 Lacs to INR 4.75 lakh.

Note: The above-mentioned fee is as per the official sources. However, it is indicative and subject to change.

  $E:\frac{x^2}{4}+\frac{y^2}{2}=1$

any pt on it is P  $\left(2cos\theta ,\sqrt[]{2}sin\theta \right)$

$\therefore$ M (h, k) be mid point of P & A (4, 3)

$\Rightarrow {\left(h-2\right)}^2+{\left(\frac{2k-3}{\sqrt[]{2}}\right)}^2=1$        

Required locus (x – 2)² +   $\frac{{\left(y-\frac{3}{2}\right)}^2}{\frac{1}{2}}=1$

$\therefore e=\sqrt[]{1-\frac{1}{2}}=\frac{1}{\sqrt[]{2}}$

The minimum eligibility criteria for admission to the PGPM/ MBA course at ISME Bangalore and Athena School of Management are almost similar, in which candidates must complete their graduation with decent scores. Moreover, for the selection process, the accepted entrance varies from college to college:

• Accepted Entrance Exam for PGPM at Athena School of Management: GMAT/ NMAT by GMAC/ CAT/ Athena Scholastic Ability Test. 
• Accepted Entrance Exam for MBA at ISME Bangalore: CAT/ XAT/ MAT/ CMAT/ ATMA/ Other. 

Further, GD&PI are common selection processes at both colleges. 

Yes, it has been released on July 22–23, 2025, by Jharkhand's examination board.

Temple Uni is one of best universities in US. Temple has vast alumni network which includes more than 378000 alumni members from all world. UTemple alumni are working worldwide and making university proud of them. Temple Uni graduates are working in top sector such as Business Development IT Engineering Finance Marketing Research etc. Some famous personalities that are part of UTemple alumni network are -

Robert Prosky
Patricia Wettig
Tim Heidecker
Veronica Hamel
Jimmy Pop
Richard Brooks
Irvin Kershner
Marc Lamont Hill
Joe Klecko
Mark Levin
Jill Scott

Yes, Medicaps University does provide a refund in case of withdrawal of admission. However, the refund is subject to the fulfilment of certain conditions. Tabulated below are the guidelines to be followed as per the fee refund policy of the university:

The registrations for BCom at RUHS may open soon. Candidates shall ensure that they submit their applications on or before the prescribed deadline. The application forms shall be made available online on the official website.

Temple University has big alumni network of 378,000+ members. Temple University has various famous personalities such as Actors, Comedians, Athletes, Novelists, etc. Some famous people of Temple university include Bill Cosby, Tom Sizemore, David Brenner, Mark Margolis, Kim Rhodes, Norman Fell, Robert Prosky, etc. Temple graduates work for top companies such as Vanguard, Amazon, GSK, SAP, Microsoft, etc. Temple graduates work for big sectors such as Business Development, Education, Operations, Sales, etc. Temple University graduates get skilled in Business Development, Marketing, Sales, Project Management, etc.

Equation of any tangent to   $\frac{x^2}{16}+\frac{y^2}{9}=1$

is y = mx + $\sqrt[]{16m^2+9}$  if this line is also tangent to x² + y² = 12

then  $\sqrt[]{12}$ =   $\left|\frac{\sqrt[]{16m^2+9}}{\sqrt[]{1+m^2}}\right|$

^{$\Rightarrow 12+12m^2=16m^2+9$}

$\Rightarrow 12m^2=9$        

IIEST Shibpur has a decent record of placements for its UG and PG courses like BTech, MTech, BArch, MBA, etc. Check out the key highlights of IIEST Shibpur placement for the overall Class of 2024 and 2025 in the table below:

To begin, candidates seeking Medicaps University BBA admission are required to submit an online application form available on the official website of the university. Next, students must appear for the MUSAT exam on the scheduled date and time. After the announcement of the test results, the university prepares a rank list based on applicants scores in the MUSAT exam. Based on this list, the university conducts the seat allotment process. Students who get a seat must report to the institute for verification of documents and payment of fees. A successful fee payment completes the admission process.

The total tuition fee for the PGPM course offered at Athena School of Management is INR 13.5 lakh. On the other hand, the total tuition fee for the MBA course at ITM Navi Mumbai is INR 12.4 lakh. Therefore, the tuition fee at ITM Navi Mumbai is more affordable than at Athena School of Management. Candidates can compare these two colleges on other parameters too, such as placement packages, accreditation, affiliation, offered seats, cutoff, etc. 

  $?\frac{dy}{dx}+e^x\left(x^2-2\right)y=\left(x^2-2x\right)\left(x^2-2\right)e^{2x}$ $\frac{}{}{}^{}{}^{}{}^{}{}^{}{}^{}$

Here, I.F.

$=e^{{\displaystyle \int e^x\left(x^2-2\right)dx}}$

$=e^{\left(x^2-2x\right)e^x}$

$$ $\therefore$  Solution of the differential equation is

$y.e^{\left(x^2-2x\right)e^x}=\left(x^2-2x-1\right)e^{\left(x^2-2x\right)e^x}$

$$ $\therefore$  y(0) = 0

$\therefore c=1$

$\therefore y\left(2\right)=-1+1=0$

RM = $\left|\frac{3+7-5}{\sqrt[]{2}}\right|=\frac{5}{\sqrt[]{2}}$

$\mathcal{l}sin60°=\frac{5}{\sqrt[]{2}}\Rightarrow \mathcal{l}=5\sqrt[]{\frac{2}{3}}$

$\therefore Areaof\Delta PQR=\frac{\text{exception 25:}}{4}{\mathcal{l}}^2=$=25/2√3

  $x\frac{dy}{dx}+2y=x{e}^x$ $\frac{}{}{}^{}$

$\frac{dy}{dx}+\frac{2y}{x}=e^x$

$\frac{dz}{dx}=e^x.2\left(x-1\right)+e^x{\left(x-1\right)}^2=0$

$e^x\left(x-1\right)\left(2+x-1\right)=0$

$x=-1,1$

x = 1 local maxima. Then maximum value is

$z\left(-1\right)=\frac{4}{e}-e$

IIMs participants In IPMAT counselling are mentioned below:

IIM Indore

IIM Ranchi 

IIM Amritsar (recently launched IPM)

IM Shillong 

IIM Sirmaur.

Candidates who have Class 12 in any stream can apply for the SVIHMT for BHM programme. The selection criteria are merit-based.  Hotel Management courses teach candidates how to run and manage hotels, restaurants, resorts, and other hospitality services. Hotel Management courses also cover business skills like marketing, budgeting, and staff management.