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Previous Year Topic Wise Questions With Solutions: Mathematical Operations | CSAT Preparation - UPSC PDF Download
Q1. What is the number of fives used in numbering a 260-page book? (2024)
(a) 55
(b) 56
(c) 57
(d) 60
View Answer 
Ans: (b)
From 1 to 100, 5 comes 20 times.
Similarly, from 101 to 200, 5 comes 20 times.
Similarly, from 201 to 300, 5 comes 20 times.
So, we just need to check the numbers after 260. Such numbers having 5 are 265, 275, 285, 295 i.e. 4 numbers.
So, the number of 5’s used from 1 to 260 = (20 + 20 + 20) - 4 = 56
Q2. Three numbers x, y, z are selected from the set of the first seven natural numbers such that x > 2y > 3z. How many such distinct triplets (x, y, z) are possible? (2024)
(a) One triplet
(b) Two triplets
(c) Three triplets
(d) Four triplets
View Answer Ans: (d)
4 triplets satisfying the given conditions are: (5,2,1), (6,2,1), (7,2,1) and (7,3,1)
Q3. Let x be a positive integer such that 7x + 96 is divisible by x. How many values of x are possible? (2023)
(a) 10
(b) 11
(c) 12
(d) Infinitely many
View Answer Ans: (c)
7x + 96 is divisible by x. It means that 96 is divisible by x, or x is a factor of 96.
96 = 25 × 3
So, x can be 1, 3, 2, 4, 8, 16, 32, 6, 12, 24, 48, and 96. So, a total of 12 possible values.
Hence, option (c) is correct.
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FAQs on Previous Year Topic Wise Questions With Solutions: Mathematical Operations - CSAT Preparation - UPSC
| 1. What are mathematical operations, and why are they important for UPSC preparation? |  |
Ans. Mathematical operations refer to the basic processes of addition, subtraction, multiplication, and division. These operations are fundamental to solving mathematical problems and are essential for various subjects in the UPSC examination, including quantitative aptitude, reasoning, and data interpretation. Mastery of these operations helps candidates efficiently solve complex problems, manage time during the exam, and improve overall analytical skills.
| 2. How can candidates effectively practice mathematical operations for the UPSC exam? | |
Ans. Candidates can effectively practice mathematical operations by using a variety of resources such as textbooks, online tutorials, and mock tests specifically designed for UPSC preparation. Regular practice through solving previous years' question papers, taking timed quizzes, and working on sample problems can enhance proficiency. Additionally, studying shortcuts and techniques for quick calculations is beneficial for improving speed and accuracy during the exam.
| 3. What type of mathematical problems can be expected in the UPSC examination? | |
Ans. The UPSC examination typically includes a range of mathematical problems such as arithmetic operations, algebra, geometry, statistics, and data interpretation. Candidates may encounter questions that require the application of mathematical operations in real-life scenarios, such as calculating percentages, ratios, and averages, as well as solving word problems and interpreting graphical data.
| 4. Are there any specific mathematical rules or shortcuts that candidates should learn for UPSC? | |
Ans. Yes, candidates should learn various mathematical rules and shortcuts to enhance their problem-solving speed. These include multiplication tricks, percentage and ratio conversions, the use of Vedic mathematics for mental calculations, and understanding properties of numbers (like divisibility rules). Familiarity with these techniques can significantly reduce the time taken to solve problems during the examination.
| 5. How important is accuracy in mathematical operations for the UPSC exam? | |
Ans. Accuracy in mathematical operations is crucial for the UPSC exam as incorrect calculations can lead to wrong answers, affecting the overall score. Since the exam has a negative marking scheme, a wrong answer can deduct marks, making it vital for candidates to double-check their calculations and ensure precision. Practicing regularly can help improve both speed and accuracy, which are essential for success in the quantitative sections of the exam.
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