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BBA Applicants typically need to upload their Class 10 and 12 mark sheets, a recent passport-sized photograph, identity proof (like Aadhaar or PAN card), and any other documents requested during the process. It's important to cross-check the NIILM university's instructions to ensure all required files are included and in the correct format.

80. Given, xy + yx = 1

Let 4 = xy and v =., we have,

u + v = 1.

$\Rightarrow \frac{dy}{dx}+\frac{dv}{dy}=0$ ___ (1)

So, u = xy

= log u = y log x(taking log)

Now, differentiating w r t ‘x’,

$\frac{1}{4}\frac{dy}{dx}=y\frac{d}{dx}logx+logx\frac{dy}{dx}.$

$\frac{dy}{dx}=4\left[\frac{y}{x}+logx\frac{dy}{dx}\right]$

$\Rightarrow x^y·\frac{y}{x}+x^{y}logx·\frac{dy}{dx}$

= xy- 1y + xy log x $\frac{dy}{dx}.$

And v = yx.

log v = x log y.

Differentiating w r t ‘x’,

$\Rightarrow \frac{1}{v}\frac{dv}{dx}=x\frac{d}{dx}logy+logy\frac{dx}{dx}$

$=\frac{x}{y}\frac{dy}{dx}+logy$

$\Rightarrow \frac{dv}{dx}=v\left[\frac{x}{y}\frac{dy}{dx}+logy\right]$

$=y^x·\frac{x}{y}·\frac{dy}{dx}+y^{x}log·y$

= yx- 1. $x\frac{dy}{dx}$ + yx log y.

So, eqn (1) becomes

xy- 1y + xy log x $\frac{dy}{dx}$ + yx - 1 $\frac{dy}{dx}$ + yx log y = 0

$\Rightarrow \frac{dy}{dx}\left(x^{y}logx+y^{x+1}·x\right)$ = - (xy- 1y + yx log y)

$\Rightarrow \frac{dy}{dx}=\frac{-\left(x^{y-1}·y+y^{x}logy\right)}{\left(x^{y}logx+y^{x-1}·x\right).}$

Having houses two Noble Prize winners, the Stevens Institute of Technology is often considered among the top private universities in the U.S, ranking #140 among Best Colleges in America and #3 in New Jersey. 

Furthermore, it ranked 701-710th in the World University Rankings 2025, #76 in the National Universities ranking list and #63 in the Best Value Schools rankings. Stevens is renowned for its courses in engineering, technology and business. Also check popular courses at Stevens Institute of Technology.

The following is a list of few top recruiters who were part of NIT Trichy MBA placements in recent years:

The NUSRL Ranchi LLM cutoff list is prepared based on applicants' Common Law Admission Test (CLAT) scores. The consortium of NLUs releases the cutoff lists for counselling rounds. Recently, the Round 1 seat allomtent has been released for All India and Home State quotas. According to the NLU Ranchi CLAT cutoff 2025 for the needed rank to get admission to for the BA LLB (Hons.) and B.B.A., LL.B. (Hons.) course is 1476 and 1504 for the students belonging to the General AI category. The NLU Ranchi accepts CLAT entrance exam, followed by the counselling rounds for admitting students to its law courses.

78. Let y = x^x cos x  $\frac{a^2+1}{x^2-1}$

Putting  4 = x^x cos x and v = $\frac{x^2+1}{x^2-1}$ we have,

y = u + v

$\Rightarrow \frac{dy}{dx}=\frac{dy}{dx}+\frac{dv}{dx}$ ____ (1)

As u $\left|=\right|$ x^x cos x.

Taking log,

Log u = x cos x log x

Differentiating w r t ‘x’,

$\frac{1}{u}\frac{dy}{dx}=x\frac{d}{dx}$ [cos x log x] + cos x log x $\frac{dx}{dx}$

= x $\left\{cotx\frac{d}{dx}logx+logx\frac{d}{dx}cosx\right\}$ + cos x log x.

$=x\left\{cosx·\frac{1}{x}-sinx·logx\right\}$ + cos x log x.

= cos x- sin x. log x + cos x log x.

$\frac{dy}{dx}=u$ [cosx + cos x log x- sin x log x]

= x^x cos x [cos x + cos x log x-x sin x log x]

And v = $\frac{x^2+1}{x^2-1}$

So, $\frac{dv}{dx}=\frac{\left(x^2-1\right)\frac{d}{dx}\left(x^2+1\right)-\left(x^2+1\right)\frac{d}{dx}(x-1)}{{\left(x^2-1\right)}^2}$

$=\frac{\left(x^2-1\right)(2x)-\left(x^2+1\right)(2x)}{{\left(x^2-1\right)}^2}$

$=\frac{2x^3-2x-2x^3-2x}{{\left(x^2-1\right)}^2}$

$=\frac{-4x}{{\left(x^2-1\right)}^2}.$

Hence, eqn (1) becomes,

$\frac{dy}{dx}$ x^{xcos x} [cos x + cos x log x-x sin x log x] $\frac{-4x}{{\left(x^2-1\right)}^2}$

To apply for BBA, head to NIILM University admission portal. Choose your course, fill in accurate personal and academic details, upload necessary documents, and pay the application fee. Once submitted, your application will be reviewed for eligibility and further admission steps.

Upon completion of the BPharm from CHARUSAT, there are various career opportunities for graduates in pharmacy. Aspirants can choose to be a medical representative, hospital pharmacist, quality control analyst, pharmacologist, etc. Some of the most popular careers after BPharm for CHARUSAT students are mentioned below:

If any student is unable to clear the JKBOSE 12th exams, they can appear for the JK Board 12th supplementary exam which will be held in June 2026. The JKBOSE 12th Supplementary result 2026 will be out in July 2026 tentatively.

These exams will save an academic year of students thus, they must study hard to clear them. It is important that they go through the entire syllabus and cover all the topics, they must also know the exam pattern and solve the sample papers and previous years' question papers for better preparation. 

Yes, Charotar University of Science and Technology provides a full-time BPharm course at the UG level. It is four years long. Admission is granted to students who satisfy the course-wise eligibility and selection criteria. Applicants can refer some major highlights from the table mentioned below:

NOTE:  The mentioned seat intake is taken from the official website/ sanctioning body. It is still subject to change and, hence, is indicative.

17. Kindly go through the solution

A few factors that may be responsible in deciding where to study at IIM or London Business School include particular course availability, academic reputation, quality of faculty, location, etc. A comparison between these two are given below:

Stevens Institute of Technology is a private research institution and has one main campus based in Hoboken, New Jersey, directly across the Hudson River from Manhattan, spanning across 55 acres.

Stevens was founded in 1870 and is considered one of the oldest technological universities of the U.S. It has 17 academic buildings and also provides on-campus housing facilities to its students across seven unique residence halls.

16. Kindly go through the solution

Yes, the Charotar University of Science and Technology accepts the GUJCET entrance exam for BPharm admission. Those who scored well in the GUJCET are eligible to enroll in the BPharm programme. However, it is crucial for candidates to meet the requisite eligibility criteria and submit the relevant documents along with the application fee to confirm their admission.

Hidayatullah National Law University accepts the CLAT entrance exam for admission to its B.A. LLB(Hons) course at the undergraduate level. HNLU Raipur CLAT cutoff 2026 for Round 1 is out for different categories of students in the All India and Home State quotas. For the AI quota, the CLAT first round cutoff 2026 for BA LLB (Hons) programme stood at 736. For the HS quota, the cutoff rank for the same course was 3781. Candidates can refer to the table below to view the category-wise CLAT first round closing ranks for BA LLB (Hons) programme.