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As per CHARUSAT's admission criteria for its BPharm programme, the selection of candidates is based on the scores obtained in the accepted GUJCET entrance exam. Therefore, candidates cannot get direct admission for BPharm. Those who are selected must pay the applicable course fee to confirm their enrollment.

76. Kindly go through the solution

The CHARUSAT BPharm tuition fee for the entire course duration is INR 6.2 lakh. However, the total tuition fee may include various other fee elements, such as the tuition fee, admission fee, security charges, and other one-time fees. It must be noted that the mentioned fee is taken from the official website. It is still subject to change and, hence, is indicative.

75. Let y = (log x)^x + x ^{log x}.

Putting u = log x^x and v = x log x we get,

y = u + v

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

As u = log x^x

Taking log,

Þlog u = x [log(log x)]

Differentiating w r t x we get,

$\Rightarrow \frac{1}{y}\frac{dy}{dx}=x\frac{d}{dx}$ log (log x) + log (log x)  $\frac{dx}{dx}$

= $x\times \frac{1}{logx}\frac{dlogx}{dx}$ + log (log x)

= $\frac{x}{logx}\times \frac{1}{x}+log1(logx)$

$\Rightarrow \frac{dy}{dx}=\mu \left[\frac{1}{logx}+log(logx)\right]$

$\frac{dy}{dx}={(logx)}^x{\left[\frac{1}{logx}+log(logx)\right]}_{.}$

= (log x)^x$\left[\frac{1+logx.log(logx)}{logx}\right]$

= (log x)^{x- 1} [1 + log ´. log (log x)]

And v = log x

Taking log,

Log v = log x log x. = (log x)².

Differentiating w r t ‘x’ we get,

$\Rightarrow \frac{1}{v}\frac{dv}{dx}=2logx\frac{d}{dx}logx$

$\Rightarrow \frac{dv}{dx}$ = 2v log x$\frac{1}{x}$

= 2. x log x. $\frac{logx}{x}$

= 2 x log x- 1 log x.

Hence eqⁿ becomes

$\frac{dy}{dx}$= (log x) x- 1[1 + log x log (log x)] + 2x ^{log x- 1} log x

15. Kindly go through the solution

Yes, NLU Odisha have a state domicile reservation for the candidates belonging to various categories under Home State. Unlike many NLUs, it has released its CLAT cutoff 2025 for both All India and Home State quotas. In relation to that, the NLU Odisha cutoff 2025 for BA LLB Hons. and BBA LLB Hons. courses under General Home State quota stood at 1913 and 3066, respectively. Moreover, for the aforementioned courses, the General AI quota cutoff stood at 943 and 1034, respectively.

The official application deadline for NIILM University BBA programme 2025 is yet to be announced. Interested students should stay connected with the university official website or get in touch with the admissions office for the latest information. Keeping track of updates will help avoid missing out on key dates related to the BBA admission process.

Candidates seeking admission to BBA course of IBS Hyderabad must meet the prescribed eligibility criteria. Students who are Class 12 or equivalent pass with a minimum of 50% aggregate can apply. The eligible students can go to the official website or collect the form by visiting the admission office in person. At the time of form filling and admissio, aspirants must hold the relevant documents for verification purposes. 

Yes, admissions for the BBA programme at NIILM University for the 2025 academic session are currently open. Students who meet the eligibility criteria, including passing Class 12 from a recognised board, can apply. For the most accurate and updated information on the application process, candidates are encouraged to visit the official university website regularly.

To download the admit card of TS PECET candidates will have to follow the steps mentioned below -

• Visit the official website of the exam body.
• On the home page click on the link titled "Download hall ticket" and credentials such as the registration number and date of birth.
• Once the admit card is available candidates need to check all the details mentioned on it such as their name, roll number, exam date, and exam center.
• If they find any discrepancies they will have to immediately contact the exam authorities for correction.

The institute has not released its course wise data yet. However, NIRF Report for 2025 is out. According to the NIRF report 185 PG 2-year students were placed during Manonmaniam Sundaranar University placements. Refer to the table below to know more:

Note: The data provided above is taken from NIRF report 2025

Candidates must carry the following documents to the exam centre:

- Printed copy of the TS PECET Admit Card

- Valid photo ID proof (Aadhaar card, Driving License, Passport, PAN card, Voter ID)

- Passport-size photograph (same as the one uploaded in the application)

Candidates who fail to carry any of the above documents will not be allowed. It is also advisable to carry a copy of the application form printout and arrive at the centre well before reporting time. Ensure the photo and signature on the ID match those on the admit card.

The total fee for the BBA programme of IBS Hyderabad is sum of various components. Some of the components included in the fee structure are tuition fee, admission fee, security deposit, etc. IBS Hyderabad BBA tuition fee is INR 11.2 lakh and the one-time fee is INR 30,000. Students have to submit the first semester or the admission fee amount to lock their seats. It must be noted that the mentioned intake is as per the official website/ sanctioning body. It is however still subject to changes and hence, is indicative.

74 . Let y = ${\left(x+\frac{1}{x}\right)}^x$ + ${\left(1+\frac{1}{x}\right)}^x$

Putting u = ${\left(x+\frac{1}{x}\right)}^x$ and v = ${\left(1+\frac{1}{x}\right)}^x$ we get,

y = u + v

$\therefore \frac{dy}{dx}=\frac{du}{dx}+\frac{dv}{dx}$ _____ (1)

As u = ${\left(x+\frac{1}{x}\right)}^x$

Taking log,

= log u = x log $\left(x+\frac{1}{x}\right)$

Differentiating w r t ‘x’ we get,

$\frac{1}{4}\frac{dy}{dx}=x\frac{d}{dx}log$ $\left(x+\frac{1}{x}\right)+log\left(x+\frac{1}{x}\right)\frac{dx}{dx}$

$=x\frac{1}{\left(x+\frac{1}{x}\right)}\frac{d}{dx}\left(x+\frac{1}{x}\right)$ + log $\left(x+\frac{1}{x}\right)$ 1.

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

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

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

$\Rightarrow \frac{du}{dx}=u\left[\frac{x^2-1}{x^2+1}+log\left(x+\frac{1}{x}\right)\right]$

$={\left(x+\frac{1}{x}\right)}^x{\left[\frac{x^2-1}{x^2+1}+log\left(x+\frac{1}{x}\right)\right]}_{.}$

And v = x $\left(1+\frac{1}{x}\right)$

Taking log, log v = $\left(1+\frac{1}{x}\right)$ log x

Differentiating W r t ‘x’,

$\frac{1}{v}\frac{dv}{dx}=\left(1+\frac{1}{x}\right)\frac{d}{dx}$ log x + log x $\frac{d}{dx}{\left(1+\frac{1}{x}\right)}_{.}$

$\left(1+\frac{1}{x}\right)\times \frac{1}{x}$ + log x ${\left(0-\frac{1}{x^2}\right)}_{.}$

$\frac{dv}{dx}$ = v $\left[\frac{1}{x}\left(1+\frac{1}{x}\right)-\frac{logx}{x^2}\right]$ = $x^{\left(1+\frac{1}{x}\right)}\left[\frac{1}{x}\left(1+\frac{1}{x}\right)-\frac{logx}{x^2}\right]$

Hence, eqn (1) becomes,

$\frac{dy}{dx}={\left(x+\frac{1}{x}\right)}^x{\left[\frac{x^2-1}{x^2+1}+log\left(x+\frac{1}{x}\right)\right]}_{.}$ $+x^{\left(1+\frac{1}{x}\right)}\left[\frac{1}{x}\left(1+\frac{1}{x}\right)-\frac{logx}{x^2}\right]$

The distribution of BA seats offered by Sambalpur University is done as per the university's admission policy. According to the policy, students must first apply for the programme on the university's official website. After applying, they must stay updated with the release of the merit list. Students whose names appear on the merit list must report to the allocated institute for verification and payment of fees.