Mathematics - MOST IMPORTANT UPSC CSE Previous Year Questions
Practice real questions from previous year exams of UPSC CSE.
📘 Bar Graph - Single and Grouped Bars📚 Misc
Q1
Consider the four age pyramids given below namely A, B, C and D representing four different countries (vertical axis: Age; horizontal axis: Percent in age class). Which one of them indicates the declining population?
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📘 Line Graph - Single Entity Time Series📚 Misc
Q2
The following figure has four curves namely A, B, C and D (Population in billions versus Year from AD 200 to 2000). Study the figure and answer the item that follows. Which curve indicates the exponential growth?
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📘 Pie Chart - Multiple Pie Charts📚 Comparing Same Categories with Different Totals
Q3
The following pie charts show the break-up of disease categories recorded in the patients from two towns, Town A and Town B. Pie charts plot the disease categories as percentage of the total number of patients. (Town A: Diabetes 18%, High BP 13%, Heart Disease 22%, Obesity 34%, Others 13%; Town B: Diabetes 24%, High B.P. 19%, Heart Disease 30%, Obesity 28%, Others 20%.) Which of the two towns has a higher number of persons with Diabetes?
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📘 Pie Chart - Multiple Pie Charts📚 Combined Total and Combined Category Calculations
Q4
The following pie charts show the break-up of disease categories recorded in the patients from two towns, Town A and Town B, as percentage of the total number of patients. (Town A: Diabetes 18%, High BP 13%, Heart Disease 22%, Obesity 34%, Others 13%; Town B: Diabetes 24%, High B.P. 19%, Heart Disease 30%, Obesity 28%, Others 20%.) What can we say about persons with more than one disease from these graphs?
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📘 Line Graph - Multiple Entity Comparison📚 Intersection or Crossover Analysis
Q5
Consider the following Velocity-Time Graph. It shows two trains starting simultaneously on parallel tracks (Train A's graph is a straight line; Train B's graph is a curve lying above Train A and both meet at time $T_0$). With reference to the above graph, which one of the following statements is not correct?
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📘 Line Graph - Multiple Entity Comparison📚 Intersection or Crossover Analysis
Q6
Consider the following distance-time graph. The graph shows three athletes A, B and C running side by side for a 30 km race (vertical axis: Time in minutes; horizontal axis: Distance in km). With reference to the above graph, consider the following statements:
1. The race was won by A.
2. B was ahead of A up to 25 km mark.
3. C ran very slowly from the beginning.
Which of the statements given above is/are correct?
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📘 Miscellaneous Counting Problems📚 Shortest Path and Grid Problems
Q7
Study the following figure: a rectangular grid of 2 rows and 2 columns of squares with corner A at the top-left and corner B at the bottom-right. A person goes from A to B always moving to the right or downwards along the lines. How many different routes can he adopt?
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📘 Line Graph - Single Entity Time Series📚 Misc
Q8
During a party, a person was exposed to contaminated water. A few days later, he developed fever and loose motions. He suffered for some days before going to a doctor for treatment. On starting the treatment, he soon became better and recovered completely a few days later. The following graph (Number of Bacteria versus Time) shows different phases of the person's disease condition as regions A, B, C, D and E of the curve. Which region/regions of the curve correspond/corresponds to the incubation phase of the infection?
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📘 Line Graph - Single Entity Time Series📚 Misc
Q9
During a party, a person was exposed to contaminated water. A few days later, he developed fever and loose motions. He suffered for some days before going to a doctor for treatment. On starting the treatment, he soon became better and recovered completely a few days later. The following graph (Number of Bacteria versus Time) shows different phases of the person's disease condition as regions A, B, C, D and E of the curve. Which region of the curve indicates that the person began showing the symptoms of infection?
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📘 Line Graph - Single Entity Time Series📚 Misc
Q10
During a party, a person was exposed to contaminated water. A few days later, he developed fever and loose motions. He suffered for some days before going to a doctor for treatment. On starting the treatment, he soon became better and recovered completely a few days later. The following graph (Number of Bacteria versus Time) shows different phases of the person's disease condition as regions A, B, C, D and E of the curve. Which region of the curve indicates that the treatment yielded effective relief?
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📘 Basic nPr, nCr, and Factorial Computations📚 Fundamental Counting Principle
Q11
There are four routes to travel from city A to city B and six routes from city B to city C. How many routes are possible to travel from city A to city C?
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📘 AP-based Word Problems📚 Real-life Increasing or Decreasing Quantity Problems
Q12
A contract on a construction job specifies a penalty for delay in completion of the work beyond a certain date as follows: Rs. 200 for the first day, Rs. 250 for the second day, Rs. 300 for the third day etc., the penalty for each succeeding day being Rs. 50 more than that of the preceding day. How much penalty should the contractor pay if he delays the work by 10 days?
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📘 Composite Figure and Mixed Geometry Problems📚 Reflection and Symmetry Based Angle Problems
Q13
Consider the figure given below: $OP_1$ and $OP_2$ are two plane mirrors kept perpendicular to each other (one horizontal, one vertical). S is the direction of a beam of light falling on the mirror $OP_1$. The direction of the reflected beam of light from the mirror $OP_2$ will be
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📘 Miscellaneous Counting Problems📚 Misc
Q14
Consider the following figure: three concentric circular rings (with a small circle at the centre) divided by radial line segments into several regions. What is the minimum number of different colours required to paint the figure such that no two adjacent regions have the same colour?
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📘 Square📚 Side from Area or Perimeter
Q15
Consider the following figure: a square is divided into four rectangles as shown (one vertical cut and one horizontal cut; the areas of two rectangles are indicated as 15 for the smaller top rectangle and 48 for the larger bottom rectangle). The lengths of the sides of the rectangles are natural numbers. What is the length of each side of the square?
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📘 Word Problems with One Variable📚 Money and Denomination Problems
Q16
A person has only Rs. 1 and Rs. 2 coins with her. If the total number of coins that she has is 50 and the amount of money with her is Rs. 75, then the number of Rs. 1 and Rs. 2 coins are, respectively.
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📘 Real-life Application Problems📚 Coinciding Events
Q17
Three persons start walking together and their steps measure 40 cm, 42 cm and 45 cm respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps?
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📘 Basic TSD Formula Applications📚 Speed Ratio and Distance Ratio Problems
Q18
If a bus travels 160 km in 4 hours and a train travels 320 km in 5 hours at uniform speeds, then what is the ratio of the distances traveled by them in one hour?
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📘 Three Dimensional Cost and Application Problems📚 Capacity and Filling Time Problems
Q19
A village having a population of 4000 requires 150 litres of water per head per day. It has a tank measuring $20\text{ m} \times 15\text{ m} \times 6\text{ m}$. The water of this tank will last for
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📘 Person Inclusion and Exclusion📚 Member Added of Known Value, Find Original or New Average
Q20
A student on her first 3 tests received an average score of N points. If she exceeds her previous average score by 20 points on her fourth test, then what is the average score for the first 4 tests?
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