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Stats I · Most repeated questions

BSMA1002 · 131 questions · 355 marks · 13 papers · 40 question types

Answer key

Indian Institute of Technology Madras

BS Degree Programme · Examination & Study Paper

BSMA1002 · Statistics for Data Science I

Most repeated questions

Official Paper

Examination Instructions & Guidelines

Solve on notebook/paper first before checking solutions.
MCQ: Exactly 1 option is correct. Negative marking applies.
MSQ: One or more options correct. Select all to score.
NAT: Numerical response. No negative marking.
Scientific calculator allowed for all calculations.
Official answer key is sealed at the end of this sheet.

Type 1 · asked 6 times · Types of data & scales of measurement

Identify the scale of measurement or type of given variables

Read the passage below, then answer Q1
Based on the given data in the Table 3 , answer the subquestions.
Q1MCQ2 Marks·Choose one option
Qualifier · May 2023Key ↓
What is the scale of measurement of “Category”?
1. AOrdinal Scale.
2. BRatio Scale.
3. CNominal Scale.
4. DInterval Scale.
Q2MSQ2 Marks·Choose all correct options
Qualifier · September 2023Key ↓
Which of the following statement(s) is(are) true?
1. AEye colour of a person has ordinal scale of measurement.
2. BRecording the price of bitcoin every hour for 3 days is a time-series data.
3. CNumber of students present in a class is a discrete variable.
4. DAmount of milk (in litres) is a categorical variable.
Q3MSQ2 Marks·Choose all correct options
Qualifier · January 2024Key ↓
Which of the following statement(s) is/are true?
1. AThe gross annual income for each of 1000 randomly chosen households in New York City for the year 2000 is a time series data.
2. BPassenger Name Record (PNR) number has an ordinal scale of measurement.
3. CRevenue generated by India through tea exports to 10 different countries in year 2010 is a cross-sectional data.
4. DShirt size is a categorical variable.
Q4MSQ3 Marks·Choose all correct options
Qualifier · January 2024Key ↓
1. APurchase and Region are categorical variables.
2. BIncome Range has nominal scale of measurement.
3. CAge has a ratio scale of measurement.
4. DHousehold size is a discrete numerical variable.
5. EPurchase has an ordinal scale of measurement.
Q5MCQ3 Marks·Choose one option
Qualifier · May 2024Key ↓
Consider the following three statements: Statement 1 : Election symbol is a categorical variable. Statement 2 : Election symbol has a nominal scale of measurement. Statement 3 : Number of votes received by a candidate is a continuous variable. Choose the correct option from the following:
1. AStatement-2 and statement-3 both are correct.
2. BStatement-1 and statement-3 both are correct.
3. CStatement-1 and statement-2 both are correct.
4. DAll statements are correct.
Q6MSQ2 Marks·Choose all correct options
End Term · 31 Aug 2025 (AN)Key ↓
Which of the following statement(s) is/are incorrect?
1. AThe annual income of 1000 individuals surveyed for year 2024 is an example of time-series data.
2. BThe brand of a smartphone used by students is a categorical variable.
3. CEducational qualifications such as elementary, secondary, and higher secondary has an ordinal scale of measurement.
4. DMaking predictions about population behavior based on sample data is a part of Descriptive Statistics.

Type 2 · asked 6 times · Describing categorical data

Read a pie chart to find the amount in a category or the difference

Read the passage below, then answer Q7
Figure Q.1 represents the placement report of an engineering college for the academic year 2021-22.
Based on the information, answer the given subquestions.
Q7NAT3 Marks·Write the number
Qualifier · January 2023Key ↓
If 1200 students are placed during the placement season of 2021-22, then find the number of students placed in core companies?
Your answer:
Read the passage below, then answer Q8
Q8NAT2 Marks·Write the number
Qualifier · September 2023Key ↓
If a total of 500 fruits are sold on a given day, then find the number of mangoes sold.
Your answer:
Read the passage below, then answer Q9–Q10
Based on the above data answer the given subquestions.
Q9MCQ3 Marks·Choose one option
End Term · 22 Dec 2024 (AN)Key ↓
What is the difference between the expenditure on Groceries and Utilities?
1. A₹20000
2. B₹12500
3. C₹15000
4. D₹27000
Q10MCQ2 Marks·Choose one option
End Term · 22 Dec 2024 (AN)Key ↓
How much money does the family spend on Rent and Utilities combined?
1. A₹25,000
2. B₹27,500
3. C₹27,000
4. D₹28,000
Read the passage below, then answer Q11–Q12
Based on the above data answer the given subquestions.
Q11MCQ3 Marks·Choose one option
End Term · 22 Dec 2024 (FN)Key ↓
What is the difference between the expenditure on Rent and Groceries?
1. A₹2000
2. B₹2500
3. C₹1500
4. D₹2700
Q12MCQ2 Marks·Choose one option
End Term · 22 Dec 2024 (FN)Key ↓
How much money does the family spend on Utilities and Entertainment combined?
1. A₹12,000
2. B₹12,500
3. C₹15,000
4. D₹15,200

Type 3 · asked 5 times · Types of data & scales of measurement

Check true/false properties of nominal, ordinal, interval and ratio scales

Q13MSQ3 Marks·Choose all correct options
Qualifier · January 2023Key ↓
Choose the correct statement/s ?
1. AA nominal scale has the property of labelling the categories and it does not involve the ranking of data.
2. BAn ordinal scale has all the properties of nominal scale and it involves the ranking of data.
3. CAn Interval scale has all the properties of ordinal scale and it satisfies the absolute zero property.
4. DA ratio scale has all the properties of interval scale and it does not satisfy the absolute zero property.
Q14MSQ2 Marks·Choose all correct options
End Term · 22 Dec 2024 (AN)Key ↓
Which of the following options is/are incorrect for a variable having ratio scale of measurement?
1. ADifference between the values of a variable can not be evaluated.
2. BOrder of the data is meaningful.
3. CMultiplication and division of values of a variable is possible.
4. DIt does not have an absolute zero.
Q15MSQ2 Marks·Choose all correct options
End Term · 22 Dec 2024 (FN)Key ↓
Which of the following options is/are incorrect for a variable having ratio scale of measurement?
1. ADifference between the values of a variable can not be evaluated.
2. BOrder of the data is meaningful.
3. CMultiplication and division of values of a variable is possible.
4. DIt does not have an absolute zero.
Q16MSQ2 Marks·Choose all correct options
End Term · 13 Apr 2025 (FN)Key ↓
Which of the following option(s) is/are correct for a variable with an ordinal scale of measurement?
1. AThe data can be arranged in a meaningful order.
2. BArithmetic operations like addition and subtraction are valid.
3. CThe intervals between values are equal and meaningful.
4. DThe mode and median can be determined, but not the mean.
Q17MSQ2 Marks·Choose all correct options
Quiz 1 · 26 Oct 2025 (AN)Key ↓
If addition and subtraction are meaningful operation for a variable, then the scale(s) of measurement of the variable could be:
1. ARatio
2. BNominal
3. COrdinal
4. DInterval

Type 4 · asked 5 times · Describing categorical data

Find missing frequencies or relative frequencies in a frequency table

Read the passage below, then answer Q18
Table 2 represents the movies released in 2022 on the OTT platform.
Based on the information, answer the given subquestions.
Q18NAT3 Marks·Write the number
Qualifier · May 2023Key ↓
Calculate a + b. (Enter the answer correct to three decimal accuracy)
Your answer:
Read the passage below, then answer Q19
Table Q.1 represents the number of books read by five students in a year.
Based on the above data, answer the given subquestions
Q19NAT2 Marks·Write the number
Qualifier · May 2024Key ↓
What is the value of x? Enter the answer correct to two decimal places.
Your answer:
Q20NAT3 Marks·Write the number
End Term · 31 Aug 2025 (FN)Key ↓
Your answer:
Q21MCQ2 Marks·Choose one option
Quiz 1 · 26 Oct 2025 (AN)Key ↓
1. A7
2. B9
3. C8
4. D6
Q22NAT3 Marks·Write the number
Quiz 1 · 26 Oct 2025 (AN)Key ↓
Your answer:

Type 5 · asked 5 times · Mean, median & mode

Find a missing observation or group mean from given group averages

Q23NAT3 Marks·Write the number
Qualifier · May 2024Key ↓
Your answer:
Q24NAT4 Marks·Write the number
End Term · 22 Dec 2024 (AN)Key ↓
The average of 15 observations is 45. If the average of the first 8 observations is 41 and the average of the last 8 observations is 53, what is the value of the 8th observation?
Your answer:
Q25NAT4 Marks·Write the number
End Term · 22 Dec 2024 (FN)Key ↓
The average of 15 observations is 48. If the average of the first 8 observations is 42 and the average of the last 8 observations is 54, what is the value of the 8th observation?
Your answer:
Q26NAT3 Marks·Write the number
End Term · 13 Apr 2025 (AN)Key ↓
The total number of observations in a dataset is 8. If the mean of first 4 observations is 12 and the mean of all 8 observations is 18, then find the mean of last 4 observations.
Your answer:
Q27MCQ3 Marks·Choose one option
Quiz 1 · 26 Oct 2025 (AN)Key ↓
1. A
2. B
3. C
4. D

Type 6 · asked 5 times · Discrete random variables

Find E[g(X)] from a given distribution

Read the passage below, then answer Q28
Based on the above data answer the given subquestions.
Q28MCQ4 Marks·Choose one option
End Term · 22 Dec 2024 (AN)Key ↓
1. A15
2. B10
3. C20
4. D12
Read the passage below, then answer Q29
Based on the above data answer the given subquestions.
Q29MCQ4 Marks·Choose one option
End Term · 22 Dec 2024 (FN)Key ↓
1. A15
2. B10
3. C20
4. D12
Read the passage below, then answer Q30
The probability mass function of a discrete random variable X is given by,
Based on the above data, answer the given subquestions.
Q30MCQ2 Marks·Choose one option
End Term · 13 Apr 2025 (AN)Key ↓
Find the value of E(6X − 2).
1. A1
2. B4
3. C6
4. D8
Read the passage below, then answer Q31
Based on the above data, answer the given subquestions.
Q31NAT3 Marks·Write the number
End Term · 13 Apr 2025 (FN)Key ↓
Your answer:
Read the passage below, then answer Q32
Based on the above data, answer the given subquestions.
Q32NAT3 Marks·Write the number
End Term · 31 Aug 2025 (FN)Key ↓
Your answer:

Type 7 · asked 4 times · Types of data & scales of measurement

Classify an analysis as descriptive or inferential statistics

Read the passage below, then answer Q33
An analyst want to analyse the salary of employees in different organizations in a city. To analyse this, he has selected an organization and the data of salaries is tabulated as shown in Table Q.2.
Based on the given information, answer the subquestions.
Q33MCQ2 Marks·Choose one option
Qualifier · January 2023Key ↓
Based on the data collected from an organisation, analyst made a statement that the average salary of an employee is 50,000 rupees in different organizations in the city. The given statement of analyst is based on which kind of statistical analysis ?
1. ADescriptive statistics
2. BInferential statistics
Q34MCQ2 Marks·Choose one option
Qualifier · May 2023Key ↓
A researcher wants to investigate the relationship between studying hours and exam scores. He collects the data on studying hours and exam scores from a sample of 100 students and perform a correlation analysis. Which branch of statistics does this analysis belong to?
1. ADescriptive Statistics.
2. BInferential Statistics.
3. CBoth Descriptive and Inferential Statistics.
4. DNeither Descriptive nor Inferential Statistics.
Q35MCQ2 Marks·Choose one option
Qualifier · May 2024Key ↓
Choose the correct statement from the following:
1. ADescriptive statistics is concerned with drawing of conclusions from the sample data.
2. BInferential statistics is concerned with describing and summarizing the data.
3. CInferential statistics doesn’t require sample data.
4. DAll statements are incorrect.
Q36MSQ2 Marks·Choose all correct options
Quiz 1 · 26 Oct 2025 (AN)Key ↓
Which of the following statements correctly describe Descriptive and Inferential Statistics?
1. ADescriptive statistics uses probability theory to draw conclusions, while inferential statistics is represented through tables, charts, and graphs.
2. BInferential statistics involves using sample data to make generalizations or predictions about a population.
3. CBoth descriptive and inferential statistics only deal with numerical data, not categorical data.
4. DDescriptive statistics involves summarizing data using measures such as mean, median,and standard deviation.

Type 8 · asked 4 times · Describing categorical data

Find the mode and median of categorical (ordinal) data

Q37MSQ2 Marks·Choose all correct options
Qualifier · September 2023Key ↓
Sunidhi purchased 5 t-shirts of sizes M, L, S, XL, S for her cousins. Later she purchased one more t-shirt of size M, then choose the correct option(s) from the following:
1. AMedian of the new data is same as of old data.
2. BNew data will be bimodal.
3. CMedian of the new data will change.
4. DNew data will be unimodal.
Read the passage below, then answer Q38–Q39
An analyst conducted a survey to understand the opinions of college students regarding the quality of education at their institution. He collected the data from 10 students as:
“Fair”, “Fair”, ”Excellent”, “Poor”, “Fair”, “Excellent”, “Poor”, “Poor”, “Excellent”, and “Poor”.
Based on the above data, answer the given subquestions.
Q38MCQ1 Mark·Choose one option
Qualifier · January 2024Key ↓
What is the mode of the given data?
1. AExcellent
2. BPoor
3. CFair
4. DMode is not defined for the given data
Q39MCQ2 Marks·Choose one option
Qualifier · January 2024Key ↓
What is the median of the given data?
1. APoor
2. BFair
3. CExcellent
4. DMedian is not defined for given data
Q40MSQ2 Marks·Choose all correct options
Qualifier · May 2024Key ↓
Figure Q.1 shows the sales distribution of the number of bottles of different types of soft drinks in a shop on a particular day. Which of the following option(s) is/are true?
1. AMedian of the data will be either “Mountain Dew” or “Mirinda”.
2. BThe data is bimodal.
3. CMode is not defined for the given data.
4. DMedian is not defined for the given data.

Type 9 · asked 4 times · Mean, median & mode

Find mean, median or mode after a linear change of every observation

Q41NAT3 Marks·Write the number
Qualifier · January 2023Key ↓
The mean and sample variance of the marks (out of 50) scored by the students in the Statistics course are 40 and 25 respectively. If 5 is subtracted from the marks of each student and then multiplied by 2. Find the mean of the modified marks.
Your answer:
Read the passage below, then answer Q42
Q42NAT3 Marks·Write the number
Qualifier · September 2023Key ↓
What is the average annual package of the students if each observation is doubled after subtracting 5 from it?
Your answer:
Read the passage below, then answer Q43
The marks (out of 100) scored by Manoj in a semester exam are given as 60, 70, 65, 75, 80. If Nitin has scored 5 marks more than Manoj in each subject.
Based on the given information, answer the subquestions.
Q43NAT2 Marks·Write the number
Qualifier · May 2024Key ↓
Find the mean of the marks scored by Nitin.
Your answer:
Q44NAT1 Mark·Write the number
Qualifier · May 2024Key ↓
Your answer:

Type 10 · asked 4 times · Variance, percentiles & outliers

Find the variance after shifting or scaling every observation

Read the passage below, then answer Q45
Q45MCQ4 Marks·Choose one option
Qualifier · September 2023Key ↓
What is the population variance of the given data if 5 is subtracted from each observations?
1. A78.6
2. B83.6
3. C88.6
4. D93.6
Read the passage below, then answer Q46
The marks (out of 100) scored by Manoj in a semester exam are given as 60, 70, 65, 75, 80. If Nitin has scored 5 marks more than Manoj in each subject.
Based on the given information, answer the subquestions.
Q46MCQ4 Marks·Choose one option
Qualifier · May 2024Key ↓
1. A25
2. B50
3. C12.5
4. DCannot determine
Q47MCQ2 Marks·Choose one option
End Term · 13 Apr 2025 (FN)Key ↓
1. A64
2. B18
3. C16
4. D32
Read the passage below, then answer Q48
Based on the above data, answer the given subquestions.
Q48NAT2 Marks·Write the number
Quiz 1 · 26 Oct 2025 (AN)Key ↓
Your answer:

Type 11 · asked 4 times · Variance, percentiles & outliers

Find a percentile or IQR after shifting or scaling the data

Read the passage below, then answer Q49–Q50
Consider a dataset such as 8, 12, 16, 24, and 20. Suppose we multiply all observations by 3. Based on the given information answer the subquestions.
Q49NAT2 Marks·Write the number
End Term · 13 Apr 2025 (FN)Key ↓
What will be the 25th percentile of the new dataset?
Your answer:
Q50NAT2 Marks·Write the number
End Term · 13 Apr 2025 (FN)Key ↓
Find IQR of the new dataset.
Your answer:
Q51NAT3 Marks·Write the number
End Term · 31 Aug 2025 (AN)Key ↓
Consider the dataset 10, 27, 32, 15 and 22. If we subtract 3 from all observations, find the difference between IQR of the new dataset and the old dataset.
Your answer:
Q52MCQ3 Marks·Choose one option
End Term · 31 Aug 2025 (FN)Key ↓
Consider the dataset 10, 27, 32, 15 and 22. A new dataset is obtained by subtracting 3 from every observation. Compute the value of (70th percentile of new dataset) - (30th percentile of the old dataset).
1. A-3
2. B9
3. C3
4. D-9

Type 12 · asked 4 times · Association between two variables

Decide association from row/column relative frequencies of a contingency table

Q53MSQ4 Marks·Choose all correct options
Qualifier · January 2023Key ↓
An analyst did a survey to know whether literacy rate affects voting rate among adults in villages. He collected the data from a village and the results are tabulated in Table Q.1. Choose the correct option/s?
1. AOf all the literate adults, 25% do not participate in voting.
2. BOf all the illiterate adults, 72.73% participate in voting.
3. CIf all row relative frequencies are similar within each column then, it implies that all column relative frequencies will also be similar within each row.
4. DIf all column relative frequencies are similar within each row then, it does not imply that all row relative frequencies will also be similar within each column.
5. EThere is no association between literacy and voting participation.
6. FThere is an association between literacy and voting participation.
Q54MCQ2 Marks·Choose one option
Qualifier · January 2024Key ↓
1. AThere is an association between “Gender” and “Willingness” as row relative frequencies will be approximately same for all rows.
2. BThere is no association between “Gender” and “Willingness” as row relative frequencies will be approximately same for all rows.
3. CThere is an association between “Gender” and “Willingness” as row relative frequencies will be different for all rows.
4. DThere is no association between “Gender” and “Willingness” as row relative frequencies will be different for all rows.
Q55MSQ5 Marks·Choose all correct options
Qualifier · January 2024Key ↓
1. AOf all the shirts with Polo style, there are 26.67% shirts of Medium size.
2. BOf all the shirts with Small size, there are 25% shirts of Small Print style.
3. CThere is no association between the size and style of shirts.
4. DThere is an association between the size and style of shirts.
Q56MCQ3 Marks·Choose one option
Quiz 1 · 26 Oct 2025 (AN)Key ↓
1. AYes
2. BNo

Type 13 · asked 4 times · Association between two variables

Compute the covariance between X and Y from a table

Read the passage below, then answer Q57
Table 5 represents the data set about Advertising Expenditure and the Sales Revenue of a company. An analyst wants to investigate the relationship between the Advertising Expenditure (in Lakhs of rupees) and the monthly Sales Revenue (in Lakhs of rupees) of a company over a period of 6 months.
Based on the information, answer the given subquestions.
Q57NAT4 Marks·Write the number
Qualifier · May 2023Key ↓
What is the sample covariance between the Sales Revenue and Advertising Expenses?(Enter the answer correct to one decimal accuracy)
Your answer:
Q58NAT4 Marks·Write the number
Qualifier · January 2024Key ↓
Your answer:
Q59NAT3 Marks·Write the number
Qualifier · May 2024Key ↓
Find the population covariance between X and Y for the dataset given in Table Q.2.
Your answer:
Q60NAT4 Marks·Write the number
Quiz 1 · 26 Oct 2025 (AN)Key ↓
Your answer:

Type 14 · asked 4 times · Permutations & combinations

Count teams when particular people must or must not be included

Read the passage below, then answer Q61–Q62
A university needs to form a research team of 4 students out of total 9 students.
Based on the above data answer the given subquestions.
Q61NAT2 Marks·Write the number
End Term · 22 Dec 2024 (AN)Key ↓
In how many ways can the team be formed if two particular students must be included?
Your answer:
Q62NAT2 Marks·Write the number
End Term · 22 Dec 2024 (AN)Key ↓
In how many ways can the team be formed if two particular students must not be included?
Your answer:
Read the passage below, then answer Q63–Q64
A university needs to form a research team of 4 students out of total 8 students.
Based on the above data answer the given subquestions.
Q63NAT2 Marks·Write the number
End Term · 22 Dec 2024 (FN)Key ↓
In how many ways can the team be formed if two particular students must be included?
Your answer:
Q64NAT2 Marks·Write the number
End Term · 22 Dec 2024 (FN)Key ↓
In how many ways can the team be formed if two particular students must not be included?
Your answer:

Type 15 · asked 4 times · Discrete random variables

Find Var(X) or Var(aX+b) from a given PMF

Read the passage below, then answer Q65
Based on the above data answer the given subquestions.
Q65NAT2 Marks·Write the number
End Term · 22 Dec 2024 (AN)Key ↓
Your answer:
Read the passage below, then answer Q66
Based on the above data answer the given subquestions.
Q66NAT2 Marks·Write the number
End Term · 22 Dec 2024 (FN)Key ↓
Your answer:
Read the passage below, then answer Q67
The probability mass function of a discrete random variable X is given by,
Based on the above data, answer the given subquestions.
Q67NAT2 Marks·Write the number
End Term · 13 Apr 2025 (AN)Key ↓
Find the value of V (3X − 4).
Your answer:
Read the passage below, then answer Q68
Based on the above data, answer the given subquestions.
Q68NAT3 Marks·Write the number
End Term · 31 Aug 2025 (FN)Key ↓
Find the value of Var(X). Enter the answer correct to two decimal places.
Your answer:

Type 16 · asked 4 times · Binomial, Poisson & hypergeometric

Poisson probability after scaling the rate to a new time interval

Q69MCQ4 Marks·Choose one option
End Term · 22 Dec 2024 (AN)Key ↓
The number of customers entering in a store follows a Poisson distribution with an average rate of 8 customers per hour. What is the probability that exactly 5 customers will enter the store in a 15- minute period?
1. A
2. B
3. C
4. D
Q70MCQ4 Marks·Choose one option
End Term · 22 Dec 2024 (FN)Key ↓
The number of customers entering in a store follows a Poisson distribution with an average rate of 12 customers per hour. What is the probability that exactly 5 customers will enter the store in a 15- minute period?
1. A
2. B
3. C
4. D
Q71NAT3 Marks·Write the number
End Term · 13 Apr 2025 (FN)Key ↓
A call center receives customer calls and the number of calls received per hour follows a Poisson distribution with a mean rate of 6 calls per hour. What is the probability that at most 2 calls are received in 30 minutes? Enter the answer correct to two decimal places.
Your answer:
Q72NAT3 Marks·Write the number
End Term · 31 Aug 2025 (AN)Key ↓
The number of vehicles passing through a highway toll booth in a minute follows a Poisson distribution with mean λ = 4. Find the probability that at most two vehicle pass through highway toll booth in a minute. Enter the answer correct to two decimal places. (Use : e^4 = 54.60, e^(1/4) = 1.28, e^(-4) = 0.02, e^(-1/4) = 0.78)
Your answer:

Type 17 · asked 4 times · Uniform, exponential & normal

Uniform distribution probability, including conditional waiting time

Q73MCQ4 Marks·Choose one option
End Term · 22 Dec 2024 (AN)Key ↓
Metros on a certain station arrives uniformly after every 10 minutes. If a person arrives at the metro station at random, then what is the probability that he has to wait at least 4 minutes?
1. A
2. B
3. C
4. D
Q74MCQ4 Marks·Choose one option
End Term · 22 Dec 2024 (FN)Key ↓
Metros on a certain station arrives uniformly after every 5 minutes. If a person arrives at the metro station at random, then what is the probability that he has to wait at least 3 minutes?
1. A
2. B
3. C
4. D
Read the passage below, then answer Q75
Let X represent the time a student takes to complete a test, which follows a uniform distribution between 45 and 75 minutes. Using this information, answer the given subquestions.
Q75MCQ3 Marks·Choose one option
End Term · 13 Apr 2025 (AN)Key ↓
Given that a student has already spent 60 minutes on the test, what is the probability that they will take more than 65 minutes to complete it?
1. A
2. B
3. C
4. D
Read the passage below, then answer Q76
The time taken by a coffee machine to brew a cup of coffee is uniformly distributed between 2 and b minutes. Based on this information, answer the given subquestions:
Q76MCQ3 Marks·Choose one option
End Term · 13 Apr 2025 (FN)Key ↓
If the coffee machine has been brewing for more than 6 minutes, what is the probability that it will finish brewing between 6 and 10 minutes?
1. A
2. B
3. C
4. D

Type 18 · asked 3 times · Types of data & scales of measurement

Identify cross-sectional vs time-series (and structured) data

Q77MSQ3 Marks·Choose all correct options
Qualifier · January 2023Key ↓
Which of the following represent(s) cross sectional data?
1. ACensus of tigers estimated in four different countries in 2021.
2. BYearly irrigation report released by a government over the period of ten years.
3. CRevenue generated by a company in four different states in 2022.
4. DMonthly expenditure of a family in 2020.
Q78MSQ2 Marks·Choose all correct options
Qualifier · May 2023Key ↓
1. AIt is a time series Data.
2. BIt is a cross sectional Data.
3. CIt is a structured Data.
4. DIt is an unstructured Data.
Q79MSQ2 Marks·Choose all correct options
End Term · 13 Apr 2025 (AN)Key ↓
A surveyor collects data on the electricity bills of 100 randomly selected households in a particular month. Which of the following statements about this data is/are correct?
1. AThe electricity bill in rupees is a continuous variable.
2. BThe data collected represents cross-sectional data.
3. CThe electricity bill in rupees is a categorical variable.
4. DThe data collected represents time-series data.

Type 19 · asked 3 times · Mean, median & mode

Find the median or mode from a stem-and-leaf plot

Read the passage below, then answer Q80–Q81
The heights (in cm) of ten athletes are represented by a stem and leaf plot in Figure Q.2.
Based on the above information, answer the given subquestions
Q80NAT3 Marks·Write the number
Qualifier · January 2023Key ↓
What is the median height(in cm) of an athlete?
Your answer:
Q81NAT3 Marks·Write the number
Qualifier · January 2023Key ↓
What is the mode of the heights (in cm) of athletes?
Your answer:
Read the passage below, then answer Q82
Based on the above data, answer the given subquestions
Q82NAT2 Marks·Write the number
Qualifier · May 2024Key ↓
What will be the median age for this group?
Your answer:

Type 20 · asked 3 times · Variance, percentiles & outliers

Find quartiles and IQR of a small data set

Read the passage below, then answer Q83–Q84
A clothe retailer wants to analyze the prices of different brands of t-shirts in his store. He randomly collected 10 t-shirts and prices (in rupees) of the t-shirts are 150, 550, 700, 240, 300, 750, 200, 180, 320, 420 respectively.
Based on the information, answer the given subquestions.
Q83MSQ3 Marks·Choose all correct options
Qualifier · May 2023Key ↓
Price below which 25% of the t-shirts fall.
1. AIt is a measure of Q₁.
2. B200 Rs.
3. CIt is a measure of Q₃.
4. D550 Rs.
Q84MSQ3 Marks·Choose all correct options
Qualifier · May 2023Key ↓
Price of the t-shirt that separates price of the highest 25% of the data from the lower 75%.
1. AIt is a measure of Q₂
2. B550 Rupees
3. CIt is a measure of Q₃
4. D310 Rupees
Q85NAT2 Marks·Write the number
Qualifier · September 2023Key ↓
Find the IQR (Interquartile range) of the data 14, 20, 40, 23 and 18.
Your answer:

Type 21 · asked 3 times · Variance, percentiles & outliers

Count outliers using the 1.5 x IQR rule

Q86MCQ4 Marks·Choose one option
Qualifier · January 2023Key ↓
Suppose the number of cars sold by a car dealer in five months are 12, 8, 9, 20, 40. Which of the following is/are outliers?
1. A-8
2. B20
3. C40
4. D8
Read the passage below, then answer Q87
A clothe retailer wants to analyze the prices of different brands of t-shirts in his store. He randomly collected 10 t-shirts and prices (in rupees) of the t-shirts are 150, 550, 700, 240, 300, 750, 200, 180, 320, 420 respectively.
Based on the information, answer the given subquestions.
Q87MCQ3 Marks·Choose one option
Qualifier · May 2023Key ↓
How many outliers are in the given data set?
1. A0
2. B1
3. C2
4. DCan’t determined.
Q88NAT4 Marks·Write the number
Quiz 1 · 26 Oct 2025 (AN)Key ↓
Your answer:

Type 22 · asked 3 times · Permutations & combinations

Arrange letters of a word so that vowels always come together

Q89NAT3 Marks·Write the number
End Term · 22 Dec 2024 (AN)Key ↓
In how many different ways can the letters of the word “READING” be arranged such that the vowels always come together?
Your answer:
Q90NAT3 Marks·Write the number
End Term · 22 Dec 2024 (FN)Key ↓
In how many different ways can the letters of the word “LEADING” be arranged such that the vowels always come together?
Your answer:
Q91NAT3 Marks·Write the number
Quiz 2 · 3 Aug 2025 (AN)Key ↓
In how many different ways can the letters of the word ‘ARTICLE’ be arranged such that all the vowels always come together?
Your answer:

Type 23 · asked 3 times · Probability and conditional probability

Use the addition rule for two overlapping preferences (tea/coffee type)

Q92NAT2 Marks·Write the number
End Term · 22 Dec 2024 (AN)Key ↓
In a survey of 120 people, 70 like tea, 50 like coffee, and 30 like both tea and coffee. What is the probability that a person chosen at random likes either tea or coffee? [Enter the correct answer up to 1 decimal place]
Your answer:
Q93NAT2 Marks·Write the number
End Term · 22 Dec 2024 (FN)Key ↓
In a survey of 100 people, 60 like tea, 40 like coffee, and 20 like both tea and coffee. What is the probability that a person chosen at random likes either tea or coffee? [Enter the correct answer up to 1 decimal place]
Your answer:
Q94MCQ3 Marks·Choose one option
Quiz 2 · 3 Aug 2025 (AN)Key ↓
A survey of 800 students shows that 65% like reading and 50% like painting. If each student likes at least one of the two activities, how many students like painting but not reading?
1. A240
2. B400
3. C280
4. D120

Type 24 · asked 3 times · Probability and conditional probability

Total probability rule with categories and conditional rates

Q95NAT3 Marks·Write the number
End Term · 13 Apr 2025 (AN)Key ↓
At a university, 60% of the students are enrolled in science programs, while 40% are enrolled in arts programs. Among science students, 25% participate in research projects, whereas 15% of arts students participate in research project. If a student is chosen at random, what is the probability that he/she participates in a research project? Enter the answer correct to two decimal places.
Your answer:
Q96NAT2 Marks·Write the number
End Term · 13 Apr 2025 (FN)Key ↓
Your answer:
Q97NAT3 Marks·Write the number
Quiz 2 · 3 Aug 2025 (AN)Key ↓
A box C contains 3 white balls and 2 black balls, while box D contains 4 white balls and 3 black balls. One ball is randomly selected from box C and transferred to box D. After the transfer, one ball is drawn at random from box D. What is the probability that the ball drawn from box D is black? Enter the answer correct to three decimal places.
Your answer:

Type 25 · asked 3 times · Discrete random variables

Find probabilities or an unknown from a discrete CDF

Q98MCQ3 Marks·Choose one option
End Term · 13 Apr 2025 (AN)Key ↓
1. A0.15
2. B0.25
3. C0.75
4. D0.10
Q99NAT2 Marks·Write the number
End Term · 13 Apr 2025 (AN)Key ↓
Your answer:
Q100MCQ2 Marks·Choose one option
End Term · 31 Aug 2025 (AN)Key ↓
1. A0.6
2. B0.8
3. C0.2
4. D1

Type 26 · asked 3 times · Binomial, Poisson & hypergeometric

Binomial probability of at least / exactly k successes

Q101MCQ3 Marks·Choose one option
End Term · 22 Dec 2024 (AN)Key ↓
If the Indian cricket team has a 65% chance of winning a match, and they play a 5-match series with each match being independent of the others, what is the probability that the team will win at least 4 matches?
1. A0.31
2. B0.12
3. C0.43
4. D0.57
Q102MCQ3 Marks·Choose one option
End Term · 22 Dec 2024 (FN)Key ↓
If the Indian cricket team has a 60% chance of winning a match, and they play a 5-match series with each match being independent of the others, what is the probability that the team will win at least 4 matches?
1. A0.26
2. B0.078
3. C0.34
4. D0.68
Read the passage below, then answer Q103
A small game involves spinning a wheel that has an equal chance of landing on one of four colors: Red, Blue, Green, or Yellow. Let the random variable X represent the number of times the wheel lands on Red in three independent spins.
Based on the above data, answer the given subquestions.
Q103MCQ3 Marks·Choose one option
End Term · 13 Apr 2025 (AN)Key ↓
Find probability that the wheel lands on red exactly 2 times out of the three spins.
1. A
2. B
3. C
4. D

Type 27 · asked 2 times · Describing categorical data

True/false statements on mean, median, mode and relative frequency

Q104MSQ2 Marks·Choose all correct options
Qualifier · May 2023Key ↓
Which of the following is/are correct?
1. AMean and Mode can only be defined for a numerical data.
2. BMode can be defined for a categorical data.
3. CThere can be more than one mode for a data.
4. DMedian can be measured for a categorical variable only if the variable is nominal.
5. EThe sum of relative frequencies of all the observations in a given data set is always equal to 1.
Q105MSQ1 Mark·Choose all correct options
End Term · 31 Aug 2025 (FN)Key ↓
Which of the following statements is/are true?
1. AMedian can be measured for a categorical variable only if the variable is nominal.
2. BMode can not be defined for categorical data.
3. CThere can be more than one mode for a data.
4. DThe sum of relative frequencies of all the observations in a given data set is always equal to 1.

Type 28 · asked 2 times · Mean, median & mode

Find an unknown in a frequency table when the mean is given

Q106NAT4 Marks·Write the number
Qualifier · May 2023Key ↓
Your answer:
Q107NAT4 Marks·Write the number
Qualifier · January 2024Key ↓
Your answer:

Type 29 · asked 2 times · Association between two variables

Compute the correlation coefficient between two variables

Q108NAT4 Marks·Write the number
Qualifier · September 2023Key ↓
Your answer:
Q109NAT2 Marks·Write the number
Quiz 1 · 26 Oct 2025 (AN)Key ↓
Your answer:

Type 30 · asked 2 times · Association between two variables

Correlation between X and a linear function of X

Q110MCQ3 Marks·Choose one option
Qualifier · January 2023Key ↓
Let X and Y represent the total marks of Mayur and Deepak in 5 subjects respectively. If the marks scored by Deepak is twice the marks scored by Mayur in each subject, then which of the following statement is correct?
1. AThere is no correlation between X and Y .
2. BThere is a weak positive correlation between X and Y .
3. CThere is a strong positive correlation between X and Y .
4. DInsufficient information.
Read the passage below, then answer Q111
The marks (out of 100) scored by Manoj in a semester exam are given as 60, 70, 65, 75, 80. If Nitin has scored 5 marks more than Manoj in each subject.
Based on the given information, answer the subquestions.
Q111NAT2 Marks·Write the number
Qualifier · May 2024Key ↓
Calculate the correlation coefficient between the marks scored by Manoj and Nitin.
Your answer:

Type 31 · asked 2 times · Permutations & combinations

Seat people in a row with some persons not adjacent

Q112NAT3 Marks·Write the number
End Term · 13 Apr 2025 (AN)Key ↓
A group of 7 people (A, B, C, D, E, F, G) is to be seated in a row for a photograph. The following conditions must be satisfied: • A and B must always sit next to each other. • D and E cannot sit next to each other. What is the total number of valid arrangements under these conditions?
Your answer:
Q113MCQ3 Marks·Choose one option
End Term · 13 Apr 2025 (FN)Key ↓
A group of 7 people (A, B, C, D, E, F, G) is to be seated in a row for a photograph. Find the number of possible arrangements such that D and E cannot sit next to each other.
1. A3600
2. B4320
3. C5040
4. D720

Type 32 · asked 2 times · Probability and conditional probability

Statements on events A, B when drawing two balls without replacement

Q114MSQ3 Marks·Choose all correct options
End Term · 22 Dec 2024 (AN)Key ↓
A jar contains 6 red balls and 8 blue balls. Two balls are drawn without replacement. Let event A be the event that the first ball drawn is red, and event B be the event that the second ball drawn is blue. Which of the following statement(s) is(are) true?
1. A
2. B
3. C
4. D
Q115MSQ3 Marks·Choose all correct options
End Term · 22 Dec 2024 (FN)Key ↓
A jar contains 5 red balls and 7 blue balls. Two balls are drawn without replacement. Let event A be the event that the first ball drawn is red, and event B be the event that the second ball drawn is blue. Which of the following statement(s) is(are) true?
1. A
2. B
3. C
4. D

Type 33 · asked 2 times · Discrete random variables

Find the constant c or a that makes a PMF valid

Read the passage below, then answer Q116
Based on the above data, answer the given subquestions.
Q116NAT2 Marks·Write the number
End Term · 13 Apr 2025 (FN)Key ↓
If the probability that the vendor sells exactly 2 items in a day is 0.30, then find the value of a. Enter the answer correct to two decimal places.
Your answer:
Read the passage below, then answer Q117
Based on the above data, answer the given subquestions.
Q117NAT2 Marks·Write the number
End Term · 31 Aug 2025 (FN)Key ↓
Find the value of c such that X has a valid pmf. Enter the answer correct to one decimal place.
Your answer:

Type 34 · asked 2 times · Binomial, Poisson & hypergeometric

Variance of a linear combination of independent random variables

Q118MCQ2 Marks·Choose one option
End Term · 13 Apr 2025 (AN)Key ↓
1. A21.5
2. B20
3. C5.38
4. D5
Q119NAT2 Marks·Write the number
End Term · 13 Apr 2025 (FN)Key ↓
Your answer:

Type 35 · asked 2 times · Binomial, Poisson & hypergeometric

Expected value of a binomial random variable

Read the passage below, then answer Q120
A small game involves spinning a wheel that has an equal chance of landing on one of four colors: Red, Blue, Green, or Yellow. Let the random variable X represent the number of times the wheel lands on Red in three independent spins.
Based on the above data, answer the given subquestions.
Q120NAT2 Marks·Write the number
End Term · 13 Apr 2025 (AN)Key ↓
Find the value of E(X). Enter the answer correct to two decimal places.
Your answer:
Read the passage below, then answer Q121
Based on the above data, answer the given subquestions.
Q121NAT2 Marks·Write the number
End Term · 31 Aug 2025 (FN)Key ↓
Your answer:

Type 36 · asked 2 times · Binomial, Poisson & hypergeometric

Find the range of a hypergeometric random variable

Q122MCQ3 Marks·Choose one option
End Term · 22 Dec 2024 (AN)Key ↓
1. A{0,1,2,3,4}
2. B{0,1,2,3}
3. C{0,1,2}
4. D{0,1,2,3,4,5}
Q123MCQ3 Marks·Choose one option
End Term · 22 Dec 2024 (FN)Key ↓
1. A{0,1,2,3,4}
2. B{0,1,2,3}
3. C{0,1,2}
4. D{0,1,2,3,4,5}

Type 37 · asked 2 times · Uniform, exponential & normal

Exponential lifetime: memoryless conditional probability

Q124NAT4 Marks·Write the number
End Term · 22 Dec 2024 (AN)Key ↓
A certain type of electronic device has a lifetime that follows an exponential distribution with a mean of 500 hours. If the device has already worked for 400 hours without failing, what is the probability that it will continue to function for at least another 100 hours? (Enter the answer correct to 2 decimal accuracy.)
Your answer:
Q125NAT4 Marks·Write the number
End Term · 22 Dec 2024 (FN)Key ↓
A certain type of electronic device has a lifetime that follows an exponential distribution with a mean of 500 hours. If the device has already worked for 300 hours without failing, what is the probability that it will continue to function for at least another 200 hours? (Enter the answer correct to 2 decimal accuracy.)
Your answer:

Type 38 · asked 2 times · Uniform, exponential & normal

True/false statements about an exponential distribution

Q126MSQ3 Marks·Choose all correct options
End Term · 13 Apr 2025 (AN)Key ↓
A customer support center tracks the time agents take to resolve customer queries. Let X (in minutes) represent the resolution time, which follows an exponential distribution with an average resolution time of 2 minutes. Which of the following option(s) is/are true?
1. A
2. B
3. C
4. D
Q127MSQ2 Marks·Choose all correct options
End Term · 31 Aug 2025 (AN)Key ↓
1. A
2. B
3. C
4. D

Type 39 · asked 2 times · Uniform, exponential & normal

Statements on a normal distribution with given mean and variance

Q128MSQ3 Marks·Choose all correct options
End Term · 22 Dec 2024 (AN)Key ↓
1. A
2. B
3. C
4. D
Q129MSQ3 Marks·Choose all correct options
End Term · 22 Dec 2024 (FN)Key ↓
1. A
2. B
3. C
4. D

Type 40 · asked 2 times · Types of data & scales of measurement

Is the selected sample a good representation of the population?

Read the passage below, then answer Q130
The Head of the transportation facility at the IIT Madras campus wants to conduct a survey to rate the bus services offered to all the students. He randomly selects 100 final year students from the campus. Based on the given information, answer the subquestions
Q130MCQ2 Marks·Choose one option
Qualifier · September 2023Key ↓
Identify the correct statement from the following.
1. ASelected sample is a good representation of the population.
2. BSelected sample is not a good representation of the population.
Q131MSQ2 Marks·Choose all correct options
Qualifier · January 2024Key ↓
To ensure the accuracy of conclusions drawn through inferential statistics, which of the following statement(s) must be true?
1. ASample should not be randomly selected.
2. BSample should be randomly selected.
3. CSample should be a good representative of the population.
4. DSample should not be representative of the population.

Official Key

Master Answer Key & Explanations

Official answer keys from IIT Madras BS past papers. Click any question to review.

Reveal Key

Q1C

Q2B, C

Q3C, D

Q4A, C, D

Q5C

Q6A, D

Q7300

Q8125

Q9B

Q10B

Q11B

Q12B

Q13A, B

Q14A, D

Q15A, D

Q16A, D

Q17A, D

Q180.542 to 0.548

Q190.23 to 0.27

Q200.5 to 0.7

Q21B

Q2272

Q239.9 to 9.96

Q2477

Q2548

Q2624

Q27D

Q28B

Q29B

Q30B

Q3134

Q3222

Q33B

Q34A

Q35D

Q36B, D

Q37A, B

Q38B

Q39B

Q40B, D

Q4170

Q4240

Q4375

Q4490

Q45C

Q46C

Q47A

Q48256

Q4936

Q5024

Q510

Q52B

Q53A, B, C, E

Q54B

Q55A, D

Q56A

Q5718.6 to 19.2

Q5870

Q590

Q60175

Q6121

Q6235

Q6315

Q6415

Q651.01 to 1.07

Q661.01 to 1.07

Q6718

Q680.73 to 0.79

Q69D

Q70D

Q710.39 to 0.45

Q720.26

Q73B

Q74B

Q75B

Q76A

Q77A, C

Q78A, C

Q79A, B

Q80175

Q81175

Q8231

Q83A, B

Q84B, C

Q855

Q86C

Q87A

Q880

Q89720

Q90720

Q91720

Q920.72 to 0.78

Q930.8

Q94C

Q950.18 to 0.24

Q960.51 to 0.57

Q970.422 to 0.428

Q98D

Q9935

Q104B, C, E

Q105C, D

Q1065

Q10739

Q1080.29 to 0.35

Q1090.8

Q110C

Q1111

Q112960

Q113A

Q114A, C

Q115A, C

Q1160.43 to 0.47

Q1170.2

Q118D

Q1193.64 to 3.7

Q1200.73 to 0.77

Q1212

Q122A

Q123A

Q1240.79 to 0.85

Q1250.64 to 0.7

Q126A, B, D

Q127B, C

Q128A, D

Q129A, D

Q130B

Q131B, C

Questions and answer keys are reproduced from the official IIT Madras BS papers. Topics and repeated question types are BTechi’s own grouping. BTechi is not affiliated with IIT Madras.