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To learn the simple English words for daily use, start with words for common actions (eat, go, sleep), objects (book, car, phone), and emotions (happy, tired, sad).

To speak basic English in daily life, about 1000 to 1500 words are enough to handle most everyday conversations in English.

Risali Institute of Management offers a wide range of BSc specialisations, including Sound Engineering, Psychology, Hotel Management, Film Making, and Visual Communication, among others. These industry-relevant options allow students to choose a field aligned with their interests and future goals.

The average package offered to BTech CSE students in 2025 was 18.87 LPA. MTech CSE and CSE Analytics average package recorded during placements 2025 was 7.07 LPA and 8.78 LPA.

MBA degree is indeed very sought after by professionals and employers. And generally it offers excellent job prospects. The degree prepares students for leadership and management roles across diverse industries. Students looking for a job can pursue roles like Project Manager, Business Analyst, Marketing Manager, Financial Analyst, or Consultant.

Professor Kevin Ball, adjunct law professor at Monash, attended & graduated with a Bachelor of Law degree in 1980.

Kevin is notable for being the former director of the Castan Centre for Human Rights Law, having also served as a Commissioner on Victoria's YooRrook Justice Commission from 2021-23.

BSc programme at Risali Institute of Management is offered in full-time mode with a duration of three years. It is designed to provide in-depth theoretical and practical knowledge across various specialisations, preparing students for both higher studies and career opportunities in their chosen field.

Yes, to be eligible for BBA admissions at Mangalayatan University, candidates are only required to complete their class 12 board examination. As long as candidates pass their Class 12 board examniations from a recognised board like CBSE, they will be eligible to apply at Mangalayatan University BBA courses regardless of their chosen stream.  

The institute has trained multiple supreme court justices over its 60+ year history, including Hon Justice Elizabeth Fullerton (Supreme Court Justice in New South Wales) & Hon Justice Anne Ferguson (Supreme Court Justice in Victoria), are among such individuals.

While Fullerton graduated with a BA in 1980, Ferguson did so with an Arts & Law degree in 1982.

In terms of placement rate, BTech CSE received the best placement in 2025. The placement percentage recorded was 100%. In BTech ECE and EEE, placement percentage was 68.62% and 85.71%.

Branch-wise MTech placement percentage recorded in 2025 is mentioned below:

Patanjali University is yet to release the official placement data for BA courses. In the meantime, students can take a look at the NIRF report 2023. According to the report, the median package secured by UG 3-year during the placement drive held in 2022 was INR 3 LPA. Other than this, as per the report, the total number of students placed during the same placement drive was 22.

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

Sol:

$\begin{array}{l}Givenf\left(x\right)=\{\begin{array}{cc}\hfill \frac{kcosx}{\pi -2x} \hfill & \hfill when x\ne \frac{\pi }{2},\hfill \\ \hfill 3\hfill & \hfill when x=\frac{\pi }{2}\hfill \end{array}\\ LHLf\left(x\right)=\underset{x\to {\frac{\pi }{2}}^{-}}{lim}\frac{kcosx}{\pi -2x}=\underset{h\to 0}{lim}\frac{kcos\left(\frac{\pi }{2}-h\right)}{\pi -2\left(\frac{\pi }{2}-h\right)}\\ =\underset{h\to 0}{lim}\frac{ksinh}{\pi -\pi +2h}=\underset{h\to 0}{lim}\frac{ksinh}{2h}=\frac{k}{2}.1=\frac{k}{2}\left[?\underset{x\to 0}{lim}\frac{sinx}{x}=1\right]\\ RHLf\left(x\right)=\underset{x\to {\frac{\pi }{2}}^{+}}{lim}\frac{kcosx}{\pi -2x}=\underset{h\to 0}{lim}\frac{kcos\left(\frac{\pi }{2}+h\right)}{\pi -2\left(\frac{\pi }{2}+h\right)}\\ =\underset{h\to 0}{lim}\frac{-ksinh}{\pi -\pi -2h}=\underset{h\to 0}{lim}\frac{-ksinh}{-2h}=\frac{k}{2}\left[?\underset{x\to 0}{lim}\frac{sinx}{x}=1\right]\\ Wearegiventhat\underset{x\to \frac{\pi }{2}}{lim}f\left(x\right)=3\\ So,\frac{k}{2}=3\Rightarrow k=6\end{array}$

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

Sol:

$\begin{array}{l}Given\underset{x\to 4}{lim}\frac{\left|x-4\right|}{x-4}\\ LHL=\underset{x\to 4^{-}}{lim}\frac{-\left(x-4\right)}{x-4}=-1\left[?\left|x-4\right|=-\left(x-4\right)ifx<4\right]\\ RHL=\underset{x\to 4^{+}}{lim}\frac{\left(x-4\right)}{x-4}=1\left[?\left|x-4\right|=\left(x-4\right)ifx>4\right]\\ LHL\ne RHL\\ Hence,the\text{\hspace{0.17em}limit}doesnotexist.\end{array}$

Patanjali University offers 235 seats under the BA program. These seats are spread across the different specialisations offered with the program. Moreover, getting a BA seat at Patanjali University is fairly easy. To get a seat, students must apply for the course and show their interest in the program. Next, applicants are reviewed and allocated a seat based on marks obtained in the qualifying examination.

The MBA programme conducted by the GIET Engineering College (Godavari Global University) is offered in a full-time mode for the enrolled students. The MBA programme spans for two years. For every year the curriculum is divided into two semesters. Therefore, the total number of semsters during the course period is four.

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

Sol:

$\begin{array}{l}Giventhat\underset{x\to \pi }{lim}\frac{1-sin\frac{x}{2}}{cos\frac{x}{2}\left(cos\frac{x}{4}-sin\frac{x}{4}\right)}\\ =\underset{x\to \pi }{lim}\frac{co{s}^2\frac{x}{4}+si{n}^2\frac{x}{4}-2sin\frac{x}{4}.cos\frac{x}{4}}{\left(co{s}^2\frac{x}{4}-si{n}^2\frac{x}{4}\right)\left(cos\frac{x}{4}-sin\frac{x}{4}\right)}\left[\begin{array}{l}?cos2x=co{s}^{2}x-si{n}^{2}x\\ si{n}^{2}x+co{s}^{2}x=1\end{array}\right]\\ =\underset{x\to \pi }{lim}\frac{{\left(cos\frac{x}{4}-sin\frac{x}{4}\right)}^2}{\left(cos\frac{x}{4}-sin\frac{x}{4}\right)\left(cos\frac{x}{4}+sin\frac{x}{4}\right)\left(cos\frac{x}{4}-sin\frac{x}{4}\right)}\\ =\underset{x\to \pi }{lim}\frac{1}{\left(cos\frac{x}{4}+sin\frac{x}{4}\right)}\\ Taking\text{\hspace{0.17em}limit}wehave\\ =\frac{1}{cos\frac{\pi }{4}+sin\frac{\pi }{4}}=\frac{1}{\frac{1}{\sqrt[]{2}}+\frac{1}{\sqrt[]{2}}}=\frac{1}{\frac{2}{\sqrt[]{2}}}=\frac{1}{\sqrt[]{2}}.\end{array}$

No, not all US universities are test-optional for undergraduate admissions. One of the popular Ivy League school - Princeton University does require an SAT or ACT score. Yale University also does not accept it until Fall 2025 intake.  There are universities like Columbia University which have officially announced the scrapping of SAT and ACT scores for undergraduate admissions. Some US universities may require SAT or ACT scores based on admission to a specific course. Applicants are required to check the test optionality option if it is available or not. Check out SAT Accepting Colleges in USA.

To get a BA seat at Patanjali University, students must follow the below-mentioned steps:

1. Eligibility check: Ensure that you fulfil the eligibility criteria.

2. Application process: Fill out the application form for the preferred BA course.

3. Merit list check: Stay updated with the merit list. If shortlisted, you move to the next stage.

4. Reporting: Report to the institute for verification of documents.

5. Fee payment: Pay the admission fees to secure the seat.

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

Sol:

$\begin{array}{l}Giventhat\underset{x\to \frac{\pi }{4}}{lim}\frac{tan{ }^{3}x-tanx}{cos \left(x+\frac{\pi }{4}\right)}\\ =\underset{x\to \frac{\pi }{4}}{lim}\frac{tanx\left(tan{ }^{2}x-1\right)}{cos \left(x+\frac{\pi }{4}\right)}=\underset{x\to \frac{\pi }{4}}{lim}tanx.\underset{x\to \frac{\pi }{4}}{lim}\left[\frac{-\left(1-tan{ }^{2}x\right)}{cos \left(x+\frac{\pi }{4}\right)}\right]\\ =-1\times \underset{x\to \frac{\pi }{4}}{lim}\frac{\left(1-tanx\right)\left(1+tanx\right)}{cos \left(x+\frac{\pi }{4}\right)}\\ =\underset{x\to \frac{\pi }{4}}{lim}-\left(1+tanx\right)\times \underset{x\to \frac{\pi }{4}}{lim}\left[\frac{1-tanx}{cos \left(x+\frac{\pi }{4}\right)}\right]\\ =-\left(1+1\right)\times \underset{x\to \frac{\pi }{4}}{lim}\frac{\left(cosx-sinx\right)}{cosx.cos \left(x+\frac{\pi }{4}\right)}=-2\times \underset{x\to \frac{\pi }{4}}{lim}\frac{\sqrt[]{2}\left(\frac{1}{\sqrt[]{2}}cosx-\frac{1}{\sqrt[]{2}}sinx\right)}{cosx.cos \left(x+\frac{\pi }{4}\right)}\\ =-2\sqrt[]{2}\times \underset{x\to \frac{\pi }{4}}{lim}\frac{\left(cos\frac{\pi }{4}.cosx-sin\frac{\pi }{4}.sinx\right)}{cosx.cos \left(x+\frac{\pi }{4}\right)}\\ =-2\sqrt[]{2}\times \underset{x\to \frac{\pi }{4}}{lim}\frac{cos \left(x+\frac{\pi }{4}\right)}{cosx.cos \left(x+\frac{\pi }{4}\right)}=-2\sqrt[]{2}\times \underset{x\to \frac{\pi }{4}}{lim}\frac{1}{cosx}\\ Taking\text{\hspace{0.17em}limit}wehave\\ =\frac{-2\sqrt[]{2}}{cos\frac{\pi }{4}}=\frac{-2\sqrt[]{2}}{\frac{1}{\sqrt[]{2}}}=-2\times 2=-4.\end{array}$