UKPSC 2012 Paper VII

Points to Remember: The area of a triangle with coordinates (x1, y1), (x2, y2), (x3, y3) is given by: 0.5 * |x1(y2 – y3) + x2(y3 – y1) + x3(y1 – y2)| The equation of a line is given. We need to find a point on this line that satisfies the area constraint. Introduction: This … Read more The coordinates of the vertices B and C of a triangle ABC are (1, –2) and (2, 3), respectively. Third vertex A lies on the line 2x + y – 2 = 0. The area of the triangle is 8 square units. Find the coordinates of vertex A.

Points to Remember: Understanding of set theory and probability. Application of Venn diagrams to solve probability problems. Accurate calculation of probabilities. Introduction: This question involves calculating conditional probability using a Venn diagram. We are given the number of students studying different subjects (Maths, French, Business Studies) in a class of 400 students, along with information … Read more There are 400 students in a class. Of these, 270 study Maths, 300 French, and 50 Business Studies. All those who study Maths also study French. 20 study Maths and Business Studies. 35 study French and Business Studies. A student is selected at random. Find the probability that the selected student studies French but neither Maths nor Business Studies. Use a Venn diagram only.

Keywords: Work, days, individual rates, combined work, simultaneous work. Required Approach: Factual and Analytical. This question requires a mathematical approach to solve for an unknown variable (the number of days C takes to complete the work alone). Points to Remember: Individual work rates are inversely proportional to the number of days taken to complete the … Read more A and B alone can complete a piece of work in 7 and 14 days, respectively. A and B work together for 2 days, after which C joins them. Now, the work is completed in one day. In how many days can C alone do that work?

Points to Remember: Profit is calculated as Selling Price (SP) – Cost Price (CP). Profit percentage is calculated as (Profit/Cost Price) * 100. The problem involves a direct relationship between cost price and selling price. Introduction: This question is a basic profit and loss problem in mathematics. Profit and loss calculations are fundamental to understanding … Read more If the cost price of 150 shirts is equal to the selling price of 120 shirts, find the profit in percentage.

Points to Remember: This is a word problem requiring the application of averages. We need to solve for the original number of students in the class. The problem involves calculating weighted averages. Introduction: This question is a classic example of a weighted average problem. Weighted averages are used when different groups have different sizes and … Read more The average age of a class was 15 years. When 5 more boys, whose average age was 12 years 6 months were admitted in the class, the average age of the whole class was reduced by 6 months. How many students were there in the class originally?

Points to Remember: The volumes of a cone, hemisphere, and cylinder with the same circular base and height are related through simple formulas. The ratio will be a constant regardless of the specific dimensions of the base and height. Understanding the formulas for the volume of each 3D shape is crucial. Introduction: This question requires … Read more Find the ratio of the volumes of a cone, hemisphere, and cylinder which are made with the same circular base and height.

Points to Remember: Median: The middle value in a dataset when arranged in ascending order. If there’s an even number of data points, the median is the average of the two middle values. Mode: The value that appears most frequently in a dataset. A dataset can have one mode (unimodal), more than one mode (multimodal), … Read more Find the difference between the median and mode of the following data: 25, 33, 72, 65, 29, 60, 30, 54, 32, 53, 42, 52, 42, 51, 42, 48, 45, 47, 46, 33

Points to Remember: Moral attitude encompasses beliefs, values, and dispositions towards ethical conduct. It influences decision-making and behavior in various contexts. Moral attitudes are shaped by individual experiences, societal norms, and cultural influences. Understanding moral attitudes is crucial for fostering ethical behavior and social harmony. Introduction: Moral attitude refers to an individual’s consistent pattern of … Read more Describe moral attitude.

Points to Remember: Definition and components of emotional intelligence (EQ). Relationship between EQ and other personality traits. Benefits and drawbacks of high EQ. Measurement and development of EQ. EQ’s role in various life domains (work, relationships, etc.). Introduction: Emotional intelligence (EQ), also known as emotional quotient, is a set of emotional and social skills that … Read more Discuss ‘Emotional Intelligence’ as a trait of human personality.

Points to Remember: Definition and importance of corporate governance. Key principles of corporate governance (transparency, accountability, responsibility, fairness). Role of stakeholders (shareholders, directors, employees, creditors, customers, government). Mechanisms for ensuring good corporate governance (audits, regulations, codes of conduct). Challenges and failures in corporate governance. Best practices and future trends. Introduction: Corporate governance refers to the … Read more Write a note on Corporate Governance.