UKPSC 2016 Paper VII

Points to Remember: The area covered by the minute hand represents a sector of a circle. The formula for the area of a sector is (θ/360) * πr², where θ is the central angle in degrees and r is the radius. The minute hand completes a full circle (360°) in 60 minutes. Introduction: This question … Read more The length of the minute hand of a clock is 14 cm. Find the area covered by it in 5 minutes.

Points to Remember: Understanding set theory and Venn diagrams is crucial. The principle of inclusion-exclusion is vital for solving this problem. Careful calculation and attention to detail are necessary to avoid errors. Introduction: This question involves the application of set theory to determine the number of students playing only one sport out of three offered: … Read more Out of a group of 60 students, 25 play cricket, 30 play football, and 24 play hockey. 10 students play both cricket and football, 9 play both cricket and hockey, 12 play both hockey and football, and 5 play all three games. Using a Venn diagram, find the number of students who play only one game.

Points to Remember: This is a mathematical word problem requiring a step-by-step solution. The problem involves calculating percentages, simple interest, and working backward from a final amount. Introduction: This question is a mathematical word problem that tests the ability to solve multi-step problems involving percentages and simple interest. The problem presents a scenario where an … Read more A person loses 12.5% of his money and spends 60% of the remaining money. The part of his total money, now left with him, if deposited in a bank for 2 years at 8% annual simple interest, gives ₹2,030 after 2 years. What was the total initial amount of money with the person?

Points to Remember: Simple interest is calculated only on the principal amount. Compound interest is calculated on the principal amount plus accumulated interest. The difference between compound interest and simple interest increases with time and interest rate. Introduction: Interest is the cost of borrowing money or the return on an investment. Simple interest is calculated … Read more The difference between compound interest and simple interest on an amount of ₹15,000 for 2 years is ₹96. Find the rate of interest per annum.

Points to Remember: Simplify each term within the parentheses. Express each term as a multiple of √3. Combine like terms to obtain a simplified expression in the form a + b√3. Identify the rational numbers ‘a’ and ‘b’. Introduction: This question requires simplifying a mathematical expression involving square roots. The expression (−5√3 + 3√12 + … Read more Find the value of (−5√3 + 3√12 + 2√75) in the form of (a + b√3), where a and b are rational numbers.

Points to Remember: Average speed is calculated by total distance divided by total time. Time taken for each segment of the journey needs to be calculated individually. Units must be consistent throughout the calculation. Introduction: This question requires a factual and analytical approach to calculate the average speed of a car given varying speeds over … Read more A car runs at the rate of 20 km/hour for the first 30 km, at 25 km/hour for the next 30 km, and at 30 km/hour for the last 30 km. Calculate the average speed of the car.

Points to Remember: Definition and core tenets of Satyagraha. Gandhi’s motivations for employing Satyagraha. Political efficacy of Satyagraha in the Indian context. Alternative interpretations of Satyagraha’s purpose. Assessment of Satyagraha’s broader impact beyond political strategy. Introduction: Mahatma Gandhi’s Satyagraha, often translated as “truth force” or “soul force,” was a potent philosophy and methodology of nonviolent … Read more Explain Gandhi’s concept of Satyagraha. Do you think that Gandhi adopted it only as a political strategy since India was not in a position to fight the mighty British Empire?

Points to Remember: Geometric mean is a type of average that indicates the central tendency or typical value of a set of numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum). It’s particularly useful for data sets representing rates of change or growth over time. The … Read more Calculate the geometric mean of the numbers 3, 6, 24, and 48.

Points to Remember: This is a mathematical word problem requiring an algebraic approach to solve. The core concept involves setting up equations based on ratios and solving for the unknowns. We need to find the total number of members in the assembly. Introduction: This question involves a classic ratio problem often encountered in algebra. It … Read more In a legislative assembly, the ratio of the members of the ruling party to the members of the opposition party was 7:3. Eighteen members of the ruling party left their party and joined the opposition, making the ratio 3:2. Find the total number of members in the assembly.

Points to Remember: Higher values are abstract principles guiding human behavior and societal structures. Their nature is multifaceted, encompassing both individual and collective dimensions. They are often contested and evolve over time. They form the basis of ethical frameworks and legal systems. Introduction: The concept of “higher values” lacks a universally agreed-upon definition. However, it … Read more What do you understand by Higher values? What is the nature of higher values?