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Yes, once you have completed D Pharma and registered with the State Pharmacy Council, you can establish and run a medical store in India.

You will obtain a pharmacists registration number which is required for applying for a retail drug license. The retail drug license enables you to purchase, stock and sell prescription medicines and over the counter (OTC) drugs legally.

This is a Matching Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}\left(a\right)Let{S}_n=1^2+2^2+3^2+\dots +n^2\\ K^3-{\left(K-1\right)}^3=3K^2-3K+1\\ ForK=1,1^3-0^3=3{\left(1\right)}^2-3\left(1\right)+1\\ ForK=2,2^3-1^3=3{\left(2\right)}^2-3\left(2\right)+1\\ ForK=3,3^3-2^3=3{\left(3\right)}^2-3\left(3\right)+1\\ \dots \dots \dots \\ ForK=n,n^3-{\left(n-1\right)}^3=3{\left(n\right)}^2-3\left(n\right)+1\\ AddingColumnwise,weget\\ n^3-0^3=3\left(1^2+2^2+3^2+\dots +n^2\right)-3\left(1+2+3+\dots +n\right)+n\\ \Rightarrow n^3=3.S_n-\frac{3n\left(n+1\right)}{2}+n\\ \Rightarrow n^3+\frac{3n\left(n+1\right)}{2}-n=3.S_n\\ \Rightarrow \frac{2n^3+3n^2+3n-2n}{2}=3.S_n\\ \Rightarrow 6.S_n=2n^3+3n^2+n\\ \Rightarrow 6.S_n=n\left(2n^2+3n+1\right)\\ \Rightarrow 6.S_n=n\left[2n^2+2n+n+1\right]\\ \Rightarrow 6.S_n=n\left(n+1\right)\left(2n+1\right)\\ \Rightarrow S_n=\frac{n\left(n+1\right)\left(2n+1\right)}{6}\\ Here,\left(a\right)\leftrightarrow \left(iii\right)\\ \left(b\right)Let{S}_n=1^3+2^3+3^3+\dots +n^3\\ K^4-{\left(K-1\right)}^4=4K^3-6K^2+4K-1\\ ForK=1,1^4-0^4=4{\left(1\right)}^3-6{\left(1\right)}^2+4\left(1\right)-1\\ ForK=2,2^4-1^4=4{\left(2\right)}^3-6{\left(2\right)}^2+4\left(2\right)-1\\ ForK=3,3^4-2^4=4{\left(3\right)}^3-6{\left(3\right)}^2+4\left(3\right)-1\\ \dots \dots \dots \\ ForK=n,n^4-{\left(n-1\right)}^4=4{\left(n\right)}^3-6{\left(n\right)}^2+4\left(3\right)-1\\ AddingColumnwise,weget\\ n^4-0^4=4\left(1^3+2^3+3^3+\dots +n^3\right)-6\left(1^2+2^2+3^2+\dots +n^2\right)+4\left(1+2+3+\dots +n\right)-n\\ \Rightarrow n^4=4.S_n-n\left(n+1\right)\left(2n+1\right)+2n\left(n+1\right)-n\\ \Rightarrow n^4+n\left(n+1\right)\left(2n+1\right)-2n\left(n+1\right)+n=4.S_n\\ \Rightarrow n\left[n^3+\left(n+1\right)\left(2n+1\right)-2n-2+1\right]=4.S_n\\ \Rightarrow n\left[n^3+2n^2+3n+1-2n-1\right]=4.S_n\\ \Rightarrow n\left[n^3+2n^2+n\right]=4.S_n\end{array}$

$\begin{array}{l}\Rightarrow \frac{n^2\left(n^2+2n+1\right)}{4}=S_n\\ \Rightarrow \frac{n^2{\left(n+1\right)}^2}{4}=S_n\\ \therefore S_n={\left[\frac{n\left(n+1\right)}{2}\right]}^2\\ Here,\left(b\right)\leftrightarrow \left(i\right)\\ \left(c\right)Let{S}_n=2+4+6+\dots +2n\\ =2\left(1+2+3+\dots +n\right)\\ =2\frac{n\left(n+1\right)}{2}=n\left(n+1\right)\\ Here,\left(c\right)\leftrightarrow \left(ii\right)\\ \left(d\right)Let{S}_n=1+2+3+\dots +n=\frac{n\left(n+1\right)}{2}\\ Here,\left(d\right)\leftrightarrow \left(iv\right)\end{array}$

This is a Matching Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}\left(a\right)4,1,\frac{1}{4},\frac{1}{16}\\ Here,\frac{a_2}{a_1}=\frac{1}{4},\frac{a_3}{a_2}=\frac{1/4}{1}=\frac{1}{4}and\frac{a_4}{a_3}=\frac{1/16}{1/4}=\frac{1}{4}\\ Hence,itisG.P\\ \therefore \left(a\right)\leftrightarrow \left(iii\right)\\ \left(b\right)2,3,5,7\\ Here,a_2-a_1=3-2=1\\ a_3-a_2=5-3=2\\ a_2-a_1\ne a_3-a_2\\ HenceitisnotA.P\\ \frac{a_2}{a_1}=\frac{3}{2},\frac{a_3}{a_2}=\frac{5}{3}\\ So,\frac{3}{2}\ne \frac{5}{3}\\ So,itisnotG.P\\ Hence,itissequence\\ \therefore \left(b\right)\leftrightarrow \left(ii\right)\\ \left(c\right)13,8,3,-2,-7\\ Here,a_2-a_1=8-13=-5\\ a_3-a_2=3-8=-5\\ a_2-a_1=a_3-a_2\\ So,itisanA.P\\ \therefore \left(c\right)\leftrightarrow \left(i\right)\end{array}$

For SUCET registration, candidates have to use their full name, email address, mobile number, city, state, course and specialisation. All provided details for registration has to be correct. After completing registration, login details will be available.

Candidates who wish to enrol in the MBA courses at Mangalyatan University can do so after the release of the CUET-PG exam results. The scorecard for the CUET-PG exam is an important document that will be attached to the registration form for Mangalyatan University MBA courses.

The CUET-PG exam 2026 was conducted in March. Once the results have been announced, candidates can start to apply for MBA courses at Mangalayatan University.

The last date for applications to the CUET-PG exam 2025 was 8 February. Candidates can start to register for the CUET-PG exam from 2 January. The date mentioned here hasalready passed at this point of time. Candidates who had appeared for the CUET-PG exam can download the results from the official website of the NTA. The dates for the CUET-PG 2026 exam will be announced soon.

The key highlights of IIM Ranchi placements 2025 for MBA, MBA BA and MBA HR programs are presented below:

After completing an MBA course at Mangalyatan University, students have a wide range of career options open to them across many industries. Some of the noteworthy career options open to students are Finance Analyst, HR Analyst, Sales Executive, Marketing Executive, Business Development Executive, etc.

There are seven specialisations of MBA that are available at Mangalayatan University. All of these courses are full-time and allow students to choose different subjects throughout the curriculum depending on the specialisation chosen by the candidate.

While filling out the SUCET application form, candidates have to upload their photograph and signature. Scanned documents should be according to official notification. If required specifications are not met, then the documents will not be uploaded in the SUCET application form. Students have to check carefully before uploading the documents.

The required rank need for IIT Hyderabad admission would depend entirely on the IIT Hyderabad BTech cutoff 2025 for a particular category and round. For the General AI category, the overall cutoff varied between 667 and 10043. Therefore, students who belong to this category need to attain a rank between this range.

Students can refer to the table below to know the overall cutoff range for other All India categories. 

Candidates looking for admission into the MBA courses at Mangalayatan University need to clear the CUET-PG exam with an appropriate rank. Candidates who secured an appropriate rank in the CUET-PG exam can then apply for the personal interview round.

Before filling SUCET application form, candidates should keep important information and documents ready so that registration is completed quickly. Candidates should keep their basic details ready with their scanned photograph and signature. Payment details should also be ready.

The last date to apply for the MUJEE 2025 exam is 4 July. Candidates can apply for the MUJEE exam by filling out the registration form on the official website of Mangalayatan University.

The domain-wise average package received during IIM Ranchi placements 2025 is presented below:

Yes, admission is possible with a rank of 8000, considering the IIT Hyderabad JEE Advanced cutoff 2025 for the General AI category. For this category, the overall closing cutoff ranged from 667 to 10043. Hence, a rank of 8K will make a student eligible for IIT Hyderabad admission, if they belong to the General AI category. 

Please note that other categories, rounds, etc., will have different qualifying cutoffs accordingly, and that admission is based on various factors, like total number of seats, difficulty level of exam, etc. 

The course-wise average salary trend witnessed during IIM Ranchi placements over the past three years is presented below: