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Delhi Pharmaceutical Sciences and Research University offers admission in a BSc course on a merit-basis. The applicants performance in the last qualifying examination is evaluated for selection. There is no entrance exam score requirement for admission. Apart from this, it is crucial that the aspirants must meet the course-specific eligibility requirements. 

Minimize and Maximise $z=5x+10y$

Subject to $x+2y\le 120,x+y\ge 60,x-2y\ge 0,x,y\ge 0$

The corresponding equation of the given inequalities are

$\begin{array}{l}x+2y=120\\ x+y=60\\ x-2y=0\\ x,y=0\end{array}$

$\Rightarrow \frac{x}{120}+\frac{y}{60}=120$

$\begin{array}{l}\frac{x}{60}+\frac{y}{60}=1\\ x=2y\\ x,y=0\end{array}$

The graph of the inequalities in shown.

The shaded founded region ABCD is the feasible region with the corner points $A\left(60,0\right),B\left(120,0\right),C\left(60,30\right)\&D\left(40,20\right)$

The value of Z a these corner points are

The minimum value of Z is 300 at (60,0) and the maximum value of Z is 600 at all the points on the line segment joining B (120,0) and C (60,30).

If candidates find error in their KLEE admit card 2026, contact the exam authorities for the correction. Candidates can contact the helpline numbers: 0471 – 2525300, 2332120, 2338487

According to Times Higher Education (THE) Computer Science subject rankings for 2025, Yale University ranks at #24 in the World subject rankings. The university are scored in areas such as Teaching, International Outlook, and Research. The duration of Yale MS in Computer Science is 1 year or 2 years. The acceptance rate for this course is around 15%. This means that the university is very selective at the time of granting admissions.

Students or professionals with 3+ years of experience can take admission in an MBA in Ireland under various specializations. Some of the top specializations with more popularity and high ROI are listed below:

• Finance
• Marketing
• International Business
• Entrepreneurship
• Strategy
• HRM (Human Resource Management)
• Business Analytics
• Supply Chain Management
• Technology Management

Minimize $z=x+2y$

Subject to $2x+y\ge 3,x+2y\ge 6,x,y\ge 0$

The corresponding equation of the given inequalities are

$\begin{array}{l}2x+y=3\\ x+2y=6\\ x,y\ge 0\end{array}$

$\Rightarrow \frac{x}{\frac{3}{2}}+\frac{y}{3}=1$

$\frac{x}{6}+\frac{y}{3}=1$

$x,y\ge 0$

The feasible region is unbounded the corner point are A (6,0), B (0,3)

The value of Z at these corner points are follows.

Since, the feasible region is unbounded, a graph of $x+2y<6$ is drawn.

Also since there is no point common in feasible region and region $x+2y<6$ .

$z=6$ is maximum on all points joining line (0,3), (6,0)

i.e,  $z=6$ will be minimum on $x+2y=6$ 

To get into Yale Law School (LLM) course, the applicants must have earned their law degree. The applicants should have a strong academic record. LSAT and GRE scores are not required for admission. Additionally, the Admission Committee looks for a TOEFL minimum score of 100 in iBT and 25 in each category: Reading, Writing, Listening, and Speaking. Additionally, submit two letters of recommendation, two separate essays, and academic transcripts along with the application.

Students can take admission in MBA without work experience in some universities. Some universities mandate having 3+ years of work experience. The basic eligibility required for each university is holding a bachelor's degree from a recognised university or equivalent, with a minimum of 60%-70%.

Universities that allow pursuing an MBA without work experience are:

• Dublin Business School
• Griffith College
• IBAT College Dublin
• Technological University Dublin

Maximum $z=3x+2y$

Subject to $x+2y\le 10,3x+y=\le 15,x,y\ge 0$

The corresponding equation of the given inequalities are :

$\begin{array}{l}x+2y=10\\ 3x+y=15\\ x,y=0\end{array}$

$\Rightarrow \frac{x}{10}+\frac{y}{5}=1$

$\begin{array}{l}\frac{x}{5}+\frac{y}{5}=1\\ x,y=0\end{array}$

The graph of the given inequalities

The shaded bounded region OABC in the feasible region with the corner points

$O(0,0),A(5,0),B(4,3),C(0,5)$

The value of Z at these points are given below.

Therefore, the maximum value of Z is 18 at point (4,3).

Minimize $z=3x+5y$

Such that $x+3y\ge 3,x+y\ge 2,x,y\ge 0$

The corresponding equation of the given inequalities are

$\begin{array}{l}x+3y=3\\ x+y=2\\ x,y=0\end{array}$

$\begin{array}{l}\Rightarrow \frac{x}{3}+\frac{y}{1}=1\\ \frac{x}{2}+\frac{y}{2}=1\\ x,y=0\end{array}$

The graph of the given inequalities is

The feasible region is unbounded. The corner points are $A\left(3,0\right),B\left(\frac{3}{2},\frac{1}{2}\right)\&C\left(0,2\right)$

The values of Z at these corner points as follows.

As the feasible region is unbounded, 7 may or may not be minimum value of Z.

We draw the graph of inequality $3x+5y<7$ .

The feasible region has no common point with $3x+5y<7$ .

Therefore minimum value of Z in 7 at $B\left(\frac{3}{2},\frac{1}{2}\right)$

Yes, in order to help the students of reserved categories, S. S. Jain Subodh Management Institute offers scholarships to students belonging to the SC/ST/OBC and TFWS categories. Students who fulfil the eligibility criteria and are able to furnish required proofs are awarded scholarships as per the norms set by the Government of India.

IIT Patna offers several BS, BTech and BTech Integrated courses via JEE Advanced exam. Considering the IIT Patna JEE Advanced cutoff 2024, the needed rank to get into the institute for candidates belonging to PWD AI quota stood between 108 and 180 while consdering the last-round cutoffs. Similarly, for the candidates belonging to EWS AI quota, the cutoff varied from 445 to 2461. Among both categories, the most competitive course was BTech in Computer Science and Engineering.

Maximise $z=5x+3y$

Subject to $2x+5y\le 15,5x+2y\le 10,x\ge 0,y\ge 0$

The corresponding equation of the above linear inequalities are

$\begin{array}{l}3x+5y=15\\ 5x+2y=10\&x=0,y=0\end{array}$

$\Rightarrow \frac{x}{5}+\frac{y}{3}=1$

$\begin{array}{l}\frac{x}{2}+\frac{y}{5}=1\\ x=0,y=0\end{array}$

The graph of its given inequalities.

The shaded region OABC is the feasible region which is bounded with the corner points

$O\left(0,0\right),A\left(2,0\right),B\left(\frac{20}{19},\frac{45}{19}\right)\&C\left(0,3\right)$

The values of Z at these points are

Therefore the maximum value of Z is $\frac{235}{19}at,B\left(\frac{20}{19},\frac{45}{19}\right)$

The BCom course at Rajiv Academy for Technology and Management is provided in a single specialisation which is e-Commerce. Students wanting to study this specialisation and develop a career path ahead in this field must consider Rajiv Academy, Mathura for the admission purpose.

Minimize $z=-3x+4y$

Subject to $x+2y\le 8,3x+2y\le 12,x\ge 0,y\ge 0$

The corresponding equation of the given inequalities are

$\begin{array}{l}x+2y=8\\ 3x+2y=12\\ x=0,y=0\end{array}$

$\Rightarrow \frac{x}{8}+\frac{y}{4}=1$

$\begin{array}{l}\frac{x}{4}+\frac{y}{6}=1\\ x=0,y=0\end{array}$

The graph is shown below.

The bounded region OABC is the feasible region with the corner points O (0,0), A (4,0), B (2,3), and C (0,4

The value of Z at these points are

Therefore, the minimum value of Z is -12 at (4,0).

Generally, for an accommodation in Ireland, the average rent is around €1,200 - €1,500 per month. This will vary as per the chosen accommodation. Othere expenses that students have to bear are: 

• Mobile phone monthly plan: €20.73
• Personal expenses: €200 - €300
• Food: €280 - €400
• Utilities: €200 - €225
• Travel: €160 (Monthly bus ticket)
• Textbook & materials: €75

Maximise $z=3x+4y$

Subject to the constraints: $x+y\le 4,x\ge 0,y\ge 0$

The corresponding equation of the above inequality are

$\begin{array}{l}x+y=4\\ x=0,y=0\end{array}$

$\Rightarrow \frac{x}{4}+\frac{y}{4}=1$

$x=0,y=0$

The graph of the given inequalities.

The shaded region OAB is the feasible region which is bounded.

The corresponding of the corner point of the feasible region are O (0,0), A (4,0), and B (0,4).

The value of Z at these points are as follows,

Corner point $z=3x+4y$

O (0,0) 0

A (4,0) 12

B (0,4) 16

Therefore the maximum value of Z is 16 at the point B (0,4).

The first-year expense is between INR 25 L and INR 48 L for international students, including tuition and living costs. The universities like Trinity College Dublin and Dublin City University charge between INR 33 and INR 35 L and from INR 20 L to INR 21 L respectively. Students can check the estimated tuition cost of popular universities in Ireland below: