Free mock test · MPSO / ASO
TGPSC ASO Paper II Mock 1 with answers
- 150 questions
- 150 minutes
- +1 right · 0 wrong
Try each question first. Then tap Show answer.
Topics in this test (8)
Questions and answers
- Q1 Introduction to Statistics
In a pilot survey, 30 households took 45 enumerator-hours. At the same rate, how many enumerator-hours will the main survey of 2,400 households need?
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Answer C. 3,600
The pilot gives 45 ÷ 30 = 1.5 hours per household. Main survey = 2,400 × 1.5 = 3,600 enumerator-hours. Estimating time and cost is one use of a pilot survey.
Source: Standard concept (BRAOU Sem1 Descriptive Statistics & Probability, Unit 1: collection and editing of primary data); answer and every option computed in Python
- Q2 Introduction to Statistics
The class marks of four continuous classes are 5, 15, 30 and 55, and the first class starts at 0. What are the limits of the last class?
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Answer D. 40–70
Each upper limit = 2 × class mark − lower limit: 0–10, 10–20, 20–40, 40–70. The last class is 40–70.
Source: Standard concept (BRAOU Sem1 Descriptive Statistics & Probability, Unit 3: classification and tabulation); answer and every option computed in Python
- Q3 Introduction to Statistics
A census of 20,000 households would cost ₹60 per household. Instead, a 4% sample is surveyed at ₹150 per household because more detailed questions are asked. How much money is saved?
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Answer B. ₹10,80,000
Census cost = 20,000 × 60 = ₹12,00,000. Sample cost = 800 × 150 = ₹1,20,000. Saving = ₹10,80,000.
Source: Standard concept (S.P. Gupta, Statistical Methods, chapter on sampling; BRAOU Sem1 Block I); answer and every option computed in Python
- Q4 Introduction to Statistics
Consider the following statements about ogives:
1. A 'less than' ogive is drawn by plotting cumulative frequencies against the upper limits of the classes.
2. A 'more than' ogive is a rising curve.
3. The 'less than' and 'more than' ogives intersect at the median.
Which of the statements given above is/are correct?
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Answer C. 1 and 3 only
Less-than c.f. are plotted at upper limits and rise; more-than c.f. are plotted at lower limits and fall; the two curves meet at the median.
Source: NCERT Class 11 Statistics for Economics, Organisation and Presentation of Data
- Q5 Introduction to Statistics
Consider the following statements about judgement (purposive) sampling:
1. It can be useful when the sample is very small and the investigator knows the population well.
2. Its sampling error can be measured by the theory of probability.
Which of the statements given above is/are correct?
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Answer A. 1 only
Judgement sampling is quick and handy for small samples chosen by an expert, but the selection is not random, so the probability of selection is unknown and the sampling error cannot be estimated; the investigator's bias may enter.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q6 Introduction to Statistics
For the classes 10–20, 20–30, 30–40, 40–50 and 50–60 with total frequency 90, what is the first point plotted for the 'more than' ogive?
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Answer D. (10, 90)
A 'more than' ogive plots cumulative frequencies against lower limits. All 90 values are 10 or more, so the first point is (10, 90).
Source: Standard concept (S.P. Gupta, Statistical Methods, chapters on diagrams and graphs); answer and every option computed in Python
- Q7 Introduction to Statistics
Match List I (event in the history of the Indian census) with List II (year):
List I:
A. First census, taken non-synchronously in different parts of the country
B. First synchronous census
C. Census Act passed
D. First census after independence
List II:
1. 1948
2. 1881
3. 1951
4. 1872
Select the correct answer using the code given below.
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Answer C. A-4, B-2, C-1, D-3
The 1872 census was non-synchronous; 1881 was the first synchronous census; the Census Act was passed in 1948; the 1951 census was the first after independence.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q8 Introduction to Statistics
Which of the following pairs of diagram and its type is NOT correctly matched?
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Answer D. Square diagram : one-dimensional
A square diagram is two-dimensional because its area shows the value. The other pairs are correct.
Source: Standard concept (S.P. Gupta, Statistical Methods, chapters on diagrams and graphs)
- Q9 Introduction to Statistics
Match List I (source of secondary data) with List II (type of source):
List I:
A. Census of India reports
B. Reports of a municipal corporation
C. Records kept in a private firm's office for its own use
D. Reports of the International Monetary Fund
List II:
1. Unpublished source
2. International publication
3. Official publication of the government
4. Semi-official publication
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Answer C. A-3, B-4, C-1, D-2
A-3, B-4, C-1, D-2. Census reports are official, municipal reports semi-official, private office records unpublished and IMF reports international publications.
Source: Standard concept (BRAOU Sem1 Descriptive Statistics & Probability, Unit 2: collection and editing of secondary data)
- Q10 Introduction to Statistics
Consider the following statements:
1. Classification is done before tabulation.
2. In a statistical table, the source note states the agency or publication from which the data were taken.
Which of the statements given above is/are correct?
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Answer C. Both 1 and 2
Tabulation follows classification and presents the classified data in rows and columns. The source note at the foot of a table names the source of the data, so that it can be checked.
Source: Telugu Akademi B.Com/B.A. Statistics, Classification, Tabulation and Diagrammatic Presentation
- Q11 Introduction to Statistics
Consider the following statements:
1. Figures taken by a research scholar from an RBI publication are secondary data for that scholar.
2. Primary data are generally more costly and time-consuming to collect than secondary data.
Which of the statements given above is/are correct?
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Answer C. Both 1 and 2
Data are primary for the agency that collects them and secondary for anyone who later uses them. Collecting original data needs field work, so it costs more time and money than using published data.
Source: S.P. Gupta, Statistical Methods; Telugu Akademi B.Com Business Statistics
- Q12 Introduction to Statistics
Consider the following statements about bar diagrams:
1. Bars may be drawn vertically or horizontally.
2. Horizontal bars are generally preferred for time series data.
Which of the statements given above is/are correct?
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Answer A. 1 only
Only statement 1 is correct. Bars can be vertical or horizontal; vertical bars are usual for time series and horizontal bars for categories.
Source: Standard concept (S.P. Gupta, Statistical Methods, chapters on diagrams and graphs)
- Q13 Introduction to Statistics
Consider the following statements:
1. Data collected by a firm through its own survey of its customers are primary data for that firm.
2. Secondary data are always more accurate than primary data because they come from official agencies.
Which of the statements given above is/are correct?
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Answer A. 1 only
Data collected first-hand by the user for its own purpose are primary data. Secondary data must be checked for reliability, suitability and adequacy before use; they are not automatically more accurate than primary data.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q14 Introduction to Statistics
Which of the following are objectives of tabulation?
1. To simplify complex data
2. To make comparison easy
3. To show the trend or pattern in the data
4. To remove the need for any further analysis
Select the correct answer:
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Answer B. 1, 2 and 3 only
Tabulation simplifies data, eases comparison and shows patterns. It prepares data for analysis but does not replace it.
Source: Standard concept (BRAOU Sem1 Descriptive Statistics & Probability, Unit 3: classification and tabulation)
- Q15 Introduction to Statistics
Consider the following statements:
1. Statistics is a science because it has systematic methods for collecting and analysing data.
2. Statistics is also an art because applying these methods to real problems needs skill and judgement.
Which of the statements given above is/are correct?
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Answer C. Both 1 and 2
Both statements are correct. Statistics is a science (systematic methods) and also an art (skilful use of those methods).
Source: Standard concept (S.P. Gupta, Statistical Methods; BRAOU Sem1 Descriptive Statistics & Probability, Block I)
- Q16 Introduction to Statistics
Consider the following statements:
1. Diagrams are usually drawn on plain paper, while graphs are drawn on graph paper.
2. Graphs such as ogives can be used to locate the median and quartiles.
Which of the statements given above is/are correct?
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Answer C. Both 1 and 2
Both statements are correct. Diagrams are drawn on plain paper for comparison; graphs on graph paper also help locate values such as the median.
Source: Standard concept (S.P. Gupta, Statistical Methods, chapters on diagrams and graphs)
- Q17 Introduction to Statistics
Data collected by an investigator for the first time, for the purpose of his own enquiry, are called
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Answer C. Primary data
Primary data are original data collected afresh by the investigator for the purpose in hand; secondary data are already collected by someone else and used again.
Source: S.P. Gupta, Statistical Methods; Telugu Akademi B.Com Business Statistics
- Q18 Introduction to Statistics
In a sub-divided bar diagram, the small box that explains which shade or colour stands for which component is called the
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Answer D. key (index)
The key (index) of a diagram explains what each shade, colour or pattern stands for.
Source: Standard concept (S.P. Gupta, Statistical Methods, chapters on diagrams and graphs)
- Q19 Central Tendency, Dispersion, Skewness & Kurtosis
The mean of 20 observations was found to be 15. Later it was found that one observation, 52, had been recorded as 25, and that another observation, 30, should not have been included at all. What is the correct mean of the remaining observations?
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Answer B. 15.63
Correct total = 300 − 25 + 52 − 30 = 297 for 19 observations, so the mean = 297 / 19 ≈ 15.63.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q20 Central Tendency, Dispersion, Skewness & Kurtosis
For the distribution below, find the mean and the median, and then estimate the mode by the empirical relation.
Class: 0–10, 10–20, 20–30, 30–40, 40–50
Frequency: 4, 10, 16, 12, 8
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Answer B. 26.625
Mean = Σfx/N = 1350/50 = 27. Median: N/2 = 25 in 20–30, = 20 + (25 − 14)/16 × 10 = 26.875. Mode ≈ 3 × 26.875 − 2 × 27 = 26.625.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q21 Central Tendency, Dispersion, Skewness & Kurtosis
The mean and standard deviation of 20 observations were found to be 40 and 5. It was later found that one observation 35 had been wrongly copied as 53. What is the correct standard deviation?
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Answer A. 4.12
Σx = 800 → corrected 800 − 53 + 35 = 782, mean = 39.1. Σx² = 20(5² + 40²) = 32500 → corrected 32500 − 2809 + 1225 = 30916. σ² = 30916/20 − 39.1² = 1545.8 − 1528.81 = 16.99, so σ ≈ 4.12.
Source: Standard method; answer and every option computed and checked in Python
- Q22 Central Tendency, Dispersion, Skewness & Kurtosis
Karl Pearson's coefficient of skewness of X is 0.8 and β₂ of X is 3.6. If Y = 5 − 2X, the coefficient of skewness and β₂ of Y are
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Answer B. Skewness changes sign to −0.8; β₂ stays 3.6
Origin changes cancel. Multiplying by −2 multiplies Mean − Mode by −2 and σ by |−2| = 2, so Sk changes sign: −0.8. β₂ = μ₄/μ₂² has the scale factor 2⁴ in both parts and stays 3.6.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q23 Central Tendency, Dispersion, Skewness & Kurtosis
Consider the following statements about the geometric mean (GM) of positive values:
1. The logarithm of the GM equals the arithmetic mean of the logarithms of the observations.
2. The GM of the ratios x/y of paired values equals the ratio of the GM of x to the GM of y.
3. The GM of a set of values is never smaller than their arithmetic mean.
Which of the statements given above is/are correct?
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Answer A. 1 and 2 only
log GM = Σ log x / n by definition. Since Π(x/y) = Πx / Πy, the n-th root gives GM(x/y) = GM(x)/GM(y), which is why the GM suits ratios and index numbers. The GM is never larger than the AM, so statement 3 is false.
Source: Standard method; answer and every option computed and checked in Python
- Q24 Central Tendency, Dispersion, Skewness & Kurtosis
Consider the following statements:
1. For a grouped distribution with unequal class intervals, the frequencies should be adjusted to a common class width before the mode is calculated by the formula.
2. For a grouped distribution with unequal class intervals, the classes must be made equal before the median can be calculated by the formula.
Which of the statements given above is/are correct?
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Answer A. 1 only
The interpolation formula for the mode compares the modal class frequency with those of the adjoining classes, so with unequal widths the frequencies (or frequency densities) must first be adjusted. The median formula L + (N/2 − cf)/f × h needs only cumulative frequencies and the width of the median class, so equal classes are not required.
Source: Telugu Akademi / APSCHE B.Com Business Statistics, Measures of Central Tendency
- Q25 Central Tendency, Dispersion, Skewness & Kurtosis
What is the arithmetic mean of the squares of the first 10 natural numbers, 1², 2², …, 10²?
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Answer B. 38.5
Σk² = n(n + 1)(2n + 1)/6 = 385 for n = 10, so the mean is 385/10 = 38.5.
Source: Standard method (BRAOU Sem1 Descriptive Statistics & Probability, unit on measures of central tendency); answer and every option computed in Python
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Start free - Q26 Central Tendency, Dispersion, Skewness & Kurtosis
Find the median daily wage (₹) of the following workers.
Daily wage: Below 200, 200–300, 300–400, 400–500, 500 and above
No. of workers: 10, 18, 32, 25, 15
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Answer C. 368.75
The open ends do not matter for the median. N = 100, N/2 = 50; c.f.: 10, 28, 60, 85, 100, so the median class is 300–400. Median = 300 + (50 − 28)/32 × 100 = ₹368.75.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q27 Central Tendency, Dispersion, Skewness & Kurtosis
What is the coefficient of variation of 12, 15, 18, 21 and 24?
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Answer A. 23.57%
Mean = 18; squared deviations 36, 9, 0, 9, 36 sum to 90; σ = √(90/5) = √18 = 4.24; CV = 4.24/18 × 100 = 23.57%.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q28 Central Tendency, Dispersion, Skewness & Kurtosis
Assertion (A): Two distributions can have the same mean, the same standard deviation and the same skewness, and yet differ in shape.
Reason (R): Kurtosis, which depends on the fourth moment, describes peakedness that the first three moments do not fix.
Select the correct answer using the code given below.
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Answer A. Both A and R are true, and R is the correct explanation of A
Both are true and R explains A. Mean, SD and skewness use the first three moments; peakedness depends on μ4.
Source: Standard definition (BRAOU Sem1 Descriptive Statistics & Probability, unit on moments, skewness and kurtosis)
- Q29 Central Tendency, Dispersion, Skewness & Kurtosis
Match List I (average) with List II (most suitable use):
List I:
A. Arithmetic mean
B. Geometric mean
C. Harmonic mean
D. Weighted arithmetic mean
List II:
1. Average speed when equal distances are covered at different speeds
2. Average rate of growth of population over several years
3. Average of items of unequal importance, such as a cost of living index
4. Average marks of students in a class
Select the correct answer using the code given below.
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Answer D. A-4, B-2, C-1, D-3
AM is the everyday average (marks); GM averages growth rates; HM averages speeds over equal distances; the weighted AM gives items importance weights, as in a cost of living index.
Source: Telugu Akademi B.Com/B.A. Statistics, Measures of Central Tendency (AM, GM, HM)
- Q30 Central Tendency, Dispersion, Skewness & Kurtosis
For the observations 2, 5, 9, 14 and 20, the sum Σ|x − a| is the least for which value of a?
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Answer C. 9
Σ|x − a| is least when a is the median. The median of 2, 5, 9, 14, 20 is 9 (Σ|x − 9| = 27, while Σ|x − 10| = 28).
Source: Standard method (BRAOU Sem1 Descriptive Statistics & Probability, unit on median, mode and partition values); answer and every option computed in Python
- Q31 Central Tendency, Dispersion, Skewness & Kurtosis
Consider the following statements about measures of dispersion:
1. Absolute measures are expressed in the units of the data.
2. Relative measures are pure numbers and can compare series in different units.
3. The coefficient of variation is an absolute measure.
Which of the above are correct?
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Answer C. 1 and 2 only
Absolute measures (range, QD, MD, SD) carry the data's units; relative measures (coefficients, CV) are unit-free ratios. CV is relative, so 3 is false.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q32 Central Tendency, Dispersion, Skewness & Kurtosis
For 10 observations Σx = 500 and Σx² = 25,160. The mode is 47. What is Karl Pearson's coefficient of skewness?
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Answer C. 0.75
x̄ = 500/10 = 50. σ² = 25160/10 − 50² = 16, so σ = 4. Sk = (Mean − Mode)/σ = 3/4 = 0.75.
Source: Standard method (BRAOU Sem1 Descriptive Statistics & Probability, unit on moments, skewness and kurtosis); answer and every option computed in Python
- Q33 Central Tendency, Dispersion, Skewness & Kurtosis
The geometric mean of a set of positive observations is 6. If every observation is squared, what is the geometric mean of the new set?
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Answer D. 36
(Π x²)^(1/n) = ((Π x)^(1/n))² = 6² = 36.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q34 Central Tendency, Dispersion, Skewness & Kurtosis
Which of the following are merits of the median?
1. It can be found for a distribution with open-end classes.
2. It can be located graphically.
3. It is based on all the observations.
4. It is well suited to further algebraic treatment.
Select the correct answer using the code given below.
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Answer D. 1 and 2 only
1 and 2. The median works with open-end classes and can be read from ogives, but it ignores most values and is not suited to algebra.
Source: Standard definition (BRAOU Sem1 Descriptive Statistics & Probability, unit on median, mode and partition values)
- Q35 Central Tendency, Dispersion, Skewness & Kurtosis
A series has mean 20 and SD 4. Every observation is multiplied by 3 and then 5 is added. What is the coefficient of variation of the new series?
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Answer B. 18.46%
New mean = 3 × 20 + 5 = 65; new SD = 3 × 4 = 12; CV = 12/65 × 100 = 18.46%.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q36 Central Tendency, Dispersion, Skewness & Kurtosis
Consider the following statements about Sheppard's corrections:
1. They apply to grouped continuous distributions whose frequencies taper off to zero at both ends.
2. The third central moment μ₃ needs no correction.
Which of the statements given above is/are correct?
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Answer C. Both 1 and 2
Sheppard's corrections remove the grouping error under exactly those conditions; μ₂ and μ₄ are corrected, while μ₁ and μ₃ need none because the errors cancel.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q37 Central Tendency, Dispersion, Skewness & Kurtosis
A car travels from A to B at 40 km/h and returns over the same distance at 60 km/h. What is its average speed for the whole journey?
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Answer D. 48
Equal distances are covered at different speeds, so the harmonic mean applies: 2 × 40 × 60 / (40 + 60) = 4800 / 100 = 48 km/h.
Source: Standard method; answer and every option computed and checked in Python
- Q38 Central Tendency, Dispersion, Skewness & Kurtosis
Consider the following statements:
1. The geometric mean is the appropriate average for averaging rates of growth and ratios.
2. The harmonic mean is the appropriate average of speeds when equal distances are covered at different speeds.
Which of the statements given above is/are correct?
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Answer C. Both 1 and 2
GM suits relative changes such as growth rates and ratios (and is used in index numbers); HM suits rates such as speed when the numerator quantity (distance) is fixed.
Source: Telugu Akademi B.Com/B.A. Statistics, Measures of Central Tendency (AM, GM, HM)
- Q39 Central Tendency, Dispersion, Skewness & Kurtosis
Find the median of the following discrete frequency distribution.
x: 10, 20, 30, 40, 50, 60
f: 12, 9, 8, 10, 6, 5
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Answer D. 30
N = 50, (N + 1)/2 = 25.50. Cumulative frequencies: 12, 21, 29, 39, 45, 50. The first c.f. ≥ 25.50 is 29, against x = 30. Median = 30.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q40 Central Tendency, Dispersion, Skewness & Kurtosis
Which of the following are relative measures of dispersion?
1. Coefficient of quartile deviation
2. Standard deviation
3. Coefficient of variation
4. Mean deviation
Select the correct answer using the code given below.
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Answer A. 1 and 3 only
Relative measures are pure numbers (coefficients). SD and MD are absolute measures expressed in the units of the data.
Source: NCERT Class 11 Statistics for Economics, Measures of Dispersion
- Q41 Central Tendency, Dispersion, Skewness & Kurtosis
Match List I (central moment) with List II (what it gives):
List I:
A. First central moment μ1
B. Second central moment μ2
C. Third central moment μ3
D. Fourth central moment μ4
List II:
1. Basis of kurtosis (β2)
2. Always zero
3. Variance
4. Basis of skewness (β1)
Select the correct answer using the code given below.
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Answer C. A-2, B-3, C-4, D-1
The first moment about the mean is always zero; μ2 is the variance; β1 = μ3² / μ2³ measures skewness; β2 = μ4 / μ2² measures kurtosis.
Source: S.C. Gupta & V.K. Kapoor, Fundamentals of Mathematical Statistics, Moments, Skewness and Kurtosis
- Q42 Central Tendency, Dispersion, Skewness & Kurtosis
Consider the following statements about the arithmetic mean x̄ of a set of observations:
1. x̄ always lies between the smallest and the largest observation (both included).
2. The sum of the deviations Σ(x − x̄) is zero only when the distribution is symmetrical.
Which of the statements given above is/are correct?
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Answer A. 1 only
Only 1. The mean always lies between the extreme values. The sum of deviations from the mean is zero for all data, symmetrical or not.
Source: Standard definition (BRAOU Sem1 Descriptive Statistics & Probability, unit on measures of central tendency)
- Q43 Central Tendency, Dispersion, Skewness & Kurtosis
Consider the following statements:
1. The second quartile, the fifth decile and the fiftieth percentile of a distribution are all equal to the median.
2. The seventh decile of a distribution is the same as its seventy-fifth percentile.
Which of the statements given above is/are correct?
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Answer A. 1 only
Quartiles divide the data into 4 parts, deciles into 10 and percentiles into 100. So Q2 = D5 = P50 = median. D7 cuts off 70% of the items, so D7 = P70; P75 equals Q3.
Source: Telugu Akademi / APSCHE B.Com Business Statistics, Measures of Central Tendency
- Q44 Central Tendency, Dispersion, Skewness & Kurtosis
Consider the following statements:
1. Standard deviation is independent of change of origin.
2. Standard deviation is independent of change of scale.
Which of the statements given above is/are correct?
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Answer A. 1 only
If u = (x − A)/h, then σₓ = |h| σᵤ: shifting the origin A has no effect, but dividing or multiplying by h changes the SD.
Source: Gupta, S.C. & Kapoor, V.K., Fundamentals of Mathematical Statistics, Measures of Dispersion
- Q45 Central Tendency, Dispersion, Skewness & Kurtosis
Match List I (value) with List II (shape of the distribution):
List I:
A. γ1 = 0
B. γ2 > 0
C. γ1 < 0
D. γ2 < 0
List II:
1. Platykurtic
2. Negatively skewed
3. Leptokurtic
4. Symmetrical
Select the correct answer using the code given below.
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Answer C. A-4, B-3, C-2, D-1
A-4, B-3, C-2, D-1. γ1 gives skewness (0 symmetrical, negative = negative skew); γ2 = β2 − 3 gives kurtosis (> 0 lepto, < 0 platy).
Source: Standard definition (BRAOU Sem1 Descriptive Statistics & Probability, unit on moments, skewness and kurtosis)
- Q46 Central Tendency, Dispersion, Skewness & Kurtosis
A constant 5 is added to every one of a set of positive observations. Which of the following averages increases by exactly 5?
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Answer D. The arithmetic mean only
Only the arithmetic mean. For example, for 1 and 9 the GM is 3, but for 6 and 14 it is √84 ≈ 9.17, not 8.
Source: Standard definition (BRAOU Sem1 Descriptive Statistics & Probability, unit on measures of central tendency)
- Q47 Central Tendency, Dispersion, Skewness & Kurtosis
Match List I (measure for grouped data) with List II (formula). L = lower boundary, f = frequency and h = width of the class concerned; c = c.f. of the class before it; f1, f0, f2 = frequencies of the modal class and of the classes before and after it.
List I:
A. Mode
B. Median
C. Third quartile
D. Seventh decile
List II:
1. L + (7N/10 − c)/f × h
2. L + (f1 − f0)/(2f1 − f0 − f2) × h
3. L + (3N/4 − c)/f × h
4. L + (N/2 − c)/f × h
Select the correct answer using the code given below.
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Answer C. A-2, B-4, C-3, D-1
The mode uses the frequencies on either side of the modal class (2). Every partition value is L + (position − c)/f × h with its own position: median N/2 (4), Q3 3N/4 (3), D7 7N/10 (1).
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q48 Central Tendency, Dispersion, Skewness & Kurtosis
To compare the variability of the heights (in cm) and weights (in kg) of a group of students, the most suitable measure is the:
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Answer B. Coefficient of variation
Heights and weights are in different units. The coefficient of variation (σ/x̄ × 100) is a unit-free relative measure, so it can compare them.
Source: Gupta, S.C. & Kapoor, V.K., Fundamentals of Mathematical Statistics, Measures of Dispersion
- Q49 Probability
A die is thrown once. Which of the following collections of events are exhaustive?
1. {1, 2, 3} and {4, 5, 6}
2. {2, 4, 6} and {2, 3, 5}
3. {1, 2, 3, 4} and {3, 4, 5, 6}
4. {1, 2}, {3, 4} and {5, 6}
Select the correct answer using the code given below.
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Answer B. 1, 3 and 4 only
Collections 1, 3 and 4 cover every face. Collection 2 misses the face 1. Exhaustive events may overlap, as in 3.
Source: Standard definition (BRAOU Sem1 Descriptive Statistics & Probability, unit on basic concepts and definitions of probability)
- Q50 Probability
A and B throw a fair die alternately, A throwing first. The first to throw a six wins. What is the probability that A wins?
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Answer D. 6/11
A wins on throw 1, 3, 5, ...; these cases are mutually exclusive. Each needs earlier failures (multiplication theorem). Sum = (1/6)/(1 − 25/36) = 6/11.
Source: Standard method (BRAOU Sem1 Descriptive Statistics & Probability); answer and every option computed in Python
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Start free - Q51 Probability
In a college, 60% of students study Mathematics, 40% study Statistics and 25% study both. A student chosen at random does not study Statistics. What is the probability that the student studies Mathematics?
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Answer B. 7/12
P(M | S') = P(M ∩ S')/P(S') = (0.6 − 0.25)/(1 − 0.4) = 0.35/0.6 = 7/12.
Source: Standard method (BRAOU Sem1 Descriptive Statistics & Probability); answer and every option computed in Python
- Q52 Probability
A disease affects 10% of a population. A test is positive for 90% of people with the disease and negative for 90% of people without it. A person tests NEGATIVE. What is the probability that the person still has the disease?
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Answer B. 1/82
P(− | D) = 0.1, P(− | D′) = 0.9. P(D ∩ −) = 0.1 × 0.1 = 0.01; P(D′ ∩ −) = 0.9 × 0.9 = 0.81. P(D | −) = 0.01/0.82 = 1/82.
Source: Standard method (BRAOU Sem1 Descriptive Statistics & Probability, unit on Bayes' theorem); answer and every option computed in Python
- Q53 Probability
A sample space is S = {a, b, c, d} with P(a) = 0.1, P(b) = 0.3 and P(c) = 2P(d). What is P(c)?
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Answer C. 0.4
P(c) + P(d) = 1 − 0.1 − 0.3 = 0.6. With P(c) = 2P(d), 3P(d) = 0.6, so P(d) = 0.2 and P(c) = 0.4.
Source: Standard method (BRAOU Sem1 Descriptive Statistics & Probability, unit on basic concepts of probability); answer and every option computed in Python
- Q54 Probability
Events E₁, E₂ and E₃ are mutually exclusive and exhaustive. Which of the following are necessarily true?
1. P(E₁) + P(E₂) + P(E₃) = 1
2. P(E₁ ∩ E₂) = 0
3. P(E₁) = P(E₂) = P(E₃) = 1/3
Select the correct answer using the code given below.
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Answer B. 1 and 2 only
Mutually exclusive and exhaustive events form a partition: their probabilities add to 1 and their pairwise intersections have probability 0. Their individual values can differ.
Source: Standard result (BRAOU Sem1 Descriptive Statistics & Probability, unit on the addition theorem)
- Q55 Probability
For events A and B, P(A) = 0.5, P(B) = 0.4 and P(A | B) = 0.6. What is P(B | A)?
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Answer B. 0.48
Multiplication theorem: P(A ∩ B) = P(B)P(A | B) = 0.24. Then P(B | A) = 0.24/0.5 = 0.48.
Source: Standard method (BRAOU Sem1 Descriptive Statistics & Probability); answer and every option computed in Python
- Q56 Probability
A coin is picked at random from a bag holding one fair coin and one double-headed coin, and tossed. Consider the following statements:
1. If the toss gives a tail, the coin is certainly the fair coin.
2. If the toss gives a head, the coin is more likely to be the fair coin.
Which of the statements given above is/are correct?
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Answer A. 1 only
Statement 1 is true: P(tail | double-headed) = 0, so the posterior for the fair coin is 1. Statement 2 is false: P(fair | head) = (1/4)/(3/4) = 1/3, so the double-headed coin is more likely.
Source: Standard definition (BRAOU Sem1 Descriptive Statistics & Probability, unit on Bayes' theorem)
- Q57 Probability
Consider the following statements about two events A and B:
1. If A and B are independent, then A and B' (complement of B) are also independent.
2. If A and B are independent, then P(A ∩ B) = P(A) + P(B).
Which of the statements given above is/are correct?
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Answer A. 1 only
P(A ∩ B') = P(A) − P(A ∩ B) = P(A) − P(A)P(B) = P(A)P(B'), so A and B' are independent. For independent events P(A ∩ B) = P(A)P(B), a product, not a sum.
Source: Gupta and Kapoor, Fundamentals of Mathematical Statistics, Theory of Probability
- Q58 Probability
A box contains 10 bulbs, of which 3 are defective. Two bulbs are picked one after another without replacement. What is the probability that at least one of them is defective?
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Answer A. 8/15
P(no defective) = (7/10)(6/9) = 42/90 = 7/15. So P(at least one defective) = 1 − 7/15 = 8/15.
Source: Standard method (BRAOU Sem1 Descriptive Statistics & Probability); answer and every option computed in Python
- Q59 Probability
A and B are independent events. Which of the following pairs of events is NOT necessarily independent?
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Answer D. A and A ∪ B
Independence of A and B carries over to A and B', A' and B, and A' and B'. But A ⊂ A ∪ B, so knowing A occurred makes A ∪ B certain; A and A ∪ B are generally dependent.
Source: Standard definition (BRAOU Sem1 Descriptive Statistics & Probability, unit on independent events)
- Q60 Probability
In a town it rains on 1 day in 5. A weather forecaster predicts rain on 80% of the days that turn out rainy and on 10% of the days that turn out dry. Rain is predicted for tomorrow. What is the probability that it will rain?
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Answer C. 2/3
P(R ∩ F) = 0.2 × 0.8 = 0.16; P(R′ ∩ F) = 0.8 × 0.1 = 0.08. P(R | F) = 0.16/0.24 = 2/3.
Source: Standard method (BRAOU Sem1 Descriptive Statistics & Probability, unit on Bayes' theorem); answer and every option computed in Python
- Q61 Probability
Assertion (A): When a fair die is thrown, the events 'getting an odd number' and 'getting a number greater than 4' are not mutually exclusive.
Reason (R): Both events contain the outcome 5.
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Answer A. Both (A) and (R) are true and (R) is the correct explanation of (A)
Both are true. The events are {1, 3, 5} and {5, 6}; they share 5, so they can happen together. R gives the reason.
Source: Standard definition (BRAOU Sem1 Descriptive Statistics & Probability, unit on basic concepts and definitions of probability)
- Q62 Probability
A die is thrown once. Which of the following pairs of events are NOT mutually exclusive?
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Answer B. 'A prime number' and 'an even number'
Primes on a die are {2, 3, 5} and evens are {2, 4, 6}; they share 2, so they are not mutually exclusive.
Source: Standard definition (BRAOU Sem1 Descriptive Statistics & Probability, unit on events and algebra of events)
- Q63 Probability
A fair die is thrown twice. Given that the first throw shows 4, what is the probability that the sum of the two throws is at least 9?
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Answer C. 1/3
Given the first throw is 4, a sum of at least 9 needs 5 or 6 on the second throw: P = 2/6 = 1/3.
Source: Standard method (BRAOU Sem1 Descriptive Statistics & Probability); answer and every option computed in Python
- Q64 Probability
Which of the following problems are usually solved with Bayes' theorem?
1. Finding which machine most likely produced a defective item
2. Finding the chance that a person who tested positive actually has the disease
3. Finding the arithmetic mean of a frequency distribution
4. Finding which urn a ball of a known colour came from
Select the correct answer using the code given below.
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Answer D. 1, 2 and 4 only
Statements 1, 2 and 4 all ask for the probability of a cause after an effect is seen, which is Bayes' theorem; finding a mean is not.
Source: Standard definition (BRAOU Sem1 Descriptive Statistics & Probability, unit on Bayes' theorem)
- Q65 Probability
Consider the following statements about the relative frequency (statistical) definition of probability:
1. It defines P(A) as the limit of the relative frequency m/n of A as the number of trials n increases indefinitely.
2. It requires the outcomes of the experiment to be equally likely.
Which of the statements given above is/are correct?
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Answer A. 1 only
The statistical (von Mises) definition is P(A) = lim (n→∞) m/n, where the trials are repeated under identical conditions. It does not need equally likely outcomes; that is a condition of the classical definition.
Source: Gupta and Kapoor, Fundamentals of Mathematical Statistics, Theory of Probability
- Q66 Probability
Consider the following statements:
1. For any two events A and B, P(A ∪ B) ≥ P(A).
2. For any two events A and B, P(A ∪ B) = P(A) + P(B).
Which of the statements given above is/are correct?
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Answer A. 1 only
Statement 1 holds because A ⊂ A ∪ B. Statement 2 is the special case for mutually exclusive events only.
Source: Standard definition (BRAOU Sem1 Descriptive Statistics & Probability, units on probability)
- Q67 Random Variables, Distributions & Inference
For a random variable X, E(X) = 2 and E(X²) = 8. Find Var(2X + 1).
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Answer C. 16
Var(X) = 8 − 2² = 4, so Var(2X + 1) = 2² × 4 = 16.
Source: Standard result (BRAOU Sem2 Mathematical Expectation, units on random variables and expectation); answer and every option computed in Python
- Q68 Random Variables, Distributions & Inference
X ~ B(6, p) and 9 P(X = 4) = P(X = 2). Find p.
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Answer B. 1/4
9 × 15 p⁴q² = 15 p²q⁴ gives 9p² = q², so q = 3p, 4p = 1 and p = 1/4.
Source: Standard result (BRAOU Sem3 Discrete Distributions, unit on Bernoulli and binomial distributions); answer and every option computed in Python
- Q69 Random Variables, Distributions & Inference
For a Poisson distribution with λ = 4, consider:
1. The mean is 4.
2. The standard deviation is 2.
3. P(X = 3) = P(X = 4).
4. The only mode is 4.
Which of the statements given above are correct?
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Answer D. 1, 2 and 3 only
Statements 1, 2 and 3 are correct. The distribution has two modes, 3 and 4.
Source: Standard definition (BRAOU Sem3 Discrete Distributions, unit on the Poisson distribution)
- Q70 Random Variables, Distributions & Inference
A population has mean 50 and SD 10. For a random sample of 25, find P(x̄ > 52). (Area from 0 to z: z = 0.2 → 0.0793, z = 1 → 0.3413)
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Answer A. 0.1587
x̄ ~ N(50, 10²/25), SE = 2. z = (52 − 50)/2 = 1. P = 0.5 − 0.3413 = 0.1587.
Source: Standard result (BRAOU Sem4 Continuous Distributions, unit on the normal distribution); answer and every option computed in Python
- Q71 Random Variables, Distributions & Inference
Consider the following statements about the Cramér–Rao lower bound:
1. An unbiased estimator that attains the bound is a minimum variance unbiased estimator.
2. Every unbiased estimator attains the bound.
3. The bound is derived under regularity conditions, such as the range of the variable not depending on θ.
Which of the statements given above are correct?
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Answer A. 1 and 3 only
Statements 1 and 3 are correct. Attaining the bound makes an estimator the MVUE, but not every unbiased estimator attains it, and the bound needs regularity conditions.
Source: Standard result (BRAOU Sem6 Estimation & Testing of Hypothesis, Block I unit 2: sufficiency, Fisher–Neyman factorisation, MVUE)
- Q72 Random Variables, Distributions & Inference
Consider the following statements about a continuous random variable X with pdf f(x):
1. f(x) can be greater than 1 for some values of x.
2. P(a < X < b) = P(a ≤ X ≤ b).
Which of the above is/are correct?
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Answer B. Both 1 and 2
A density only needs to be non-negative with total area 1, so it can exceed 1. Endpoints have zero probability, so including them changes nothing.
Source: Standard definition (BRAOU Sem2 Mathematical Expectation, units on random variables, pmf, pdf and distribution function)
- Q73 Random Variables, Distributions & Inference
X ~ B(6, 1/3). Using the recurrence relation, P(X = 3) = k × P(X = 2). Find k.
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Answer B. 2/3
P(x + 1)/P(x) = [(n − x)/(x + 1)] × (p/q) = (4/3) × (1/2) = 2/3.
Source: Standard result (BRAOU Sem3 Discrete Distributions, unit on Bernoulli and binomial distributions); answer and every option computed in Python
- Q74 Random Variables, Distributions & Inference
Assertion (A): For a Poisson distribution, the mean and the variance are equal.
Reason (R): The Poisson is the limit of a binomial with p → 0, so q → 1 and the binomial variance npq approaches the mean np.
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Answer A. Both A and R are true, and R is the correct explanation of A
Mean = variance = λ for the Poisson. As p → 0, q → 1 and npq → np = λ, which is why the two become equal.
Source: Standard definition (BRAOU Sem3 Discrete Distributions, unit on the Poisson distribution)
- Q75 Random Variables, Distributions & Inference
Kiran scores 70 in a test with mean 60 and SD 5. Ravi scores 80 in another test with mean 65 and SD 10. Both tests have normal scores. Who did relatively better?
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Answer B. Kiran, with z = 2 against Ravi's 1.5
z = (x − μ)/σ: Kiran (70 − 60)/5 = 2; Ravi (80 − 65)/10 = 1.5. Kiran stands higher relative to his group.
Source: Standard result (BRAOU Sem4 Continuous Distributions, unit on the normal distribution); answer and every option computed in Python
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Start free - Q76 Random Variables, Distributions & Inference
For a sample of size 9 from a population with mean μ = 50, the estimator T = Σx/(n + 1) is used. What is the bias of T?
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Answer B. −5
E(T) = 9 × 50/10 = 45, so bias = 45 − 50 = −5.
Source: Standard result (BRAOU Sem6 Estimation & Testing of Hypothesis, Block I unit 1: consistency, unbiasedness, efficiency); answer and every option computed in Python
- Q77 Random Variables, Distributions & Inference
Which one of the following pairs is NOT correctly matched?
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Answer B. F-test : named after 'Student'
The F-distribution is named after Fisher (by Snedecor); 'Student' is Gosset's pen-name for t.
Source: Standard definition (BRAOU Sem 6 Estimation & Testing of Hypothesis, Unit 9 F-test and chi-square test)
- Q78 Random Variables, Distributions & Inference
f(x) = kx(1 − x) for 0 ≤ x ≤ 1 (and 0 elsewhere) is a pdf. Find k.
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Answer D. 6
The integral of x − x² from 0 to 1 is 1/2 − 1/3 = 1/6, so k/6 = 1 and k = 6.
Source: Standard result (BRAOU Sem2 Mathematical Expectation, units on random variables and expectation); answer and every option computed in Python
- Q79 Random Variables, Distributions & Inference
X ~ B(5, 1/2). Find P(X ≤ 1).
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Answer C. 3/16
P(X ≤ 1) = (1 + 5)/32 = 6/32 = 3/16.
Source: Standard result (BRAOU Sem3 Discrete Distributions, unit on Bernoulli and binomial distributions); answer and every option computed in Python
- Q80 Random Variables, Distributions & Inference
Which of the following pairs about the Poisson distribution is NOT correctly matched?
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Answer A. Mode when λ is a whole number : a single mode at λ
For a whole-number λ, P(λ − 1) = P(λ), so the distribution is bimodal at λ − 1 and λ.
Source: Standard definition (BRAOU Sem3 Discrete Distributions, unit on the Poisson distribution)
- Q81 Random Variables, Distributions & Inference
Assertion (A): The normal approximation to the binomial works well when n is large and p is close to 0.5.
Reason (R): For a normal distribution, the mean, median and mode coincide.
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Answer B. Both A and R are true, but R is not the correct explanation of A
With p near 0.5 the binomial is nearly symmetrical, so the normal fits it well even for moderate n. R is a true property of the normal, but it does not say why the binomial approaches it.
Source: Standard definition (BRAOU Sem4 Continuous Distributions, unit on the normal distribution)
- Q82 Random Variables, Distributions & Inference
Consider the following statements about S² = Σ(x − x̄)²/n as an estimator of σ²:
1. It is a negatively biased estimator of σ².
2. Its bias tends to zero as n tends to infinity.
Which of the statements given above is/are correct?
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Answer C. Both 1 and 2
Both are correct. E(S²) = (n − 1)σ²/n, so the bias −σ²/n is negative and tends to zero as n → ∞.
Source: Standard result (BRAOU Sem6 Estimation & Testing of Hypothesis, Block I unit 1: consistency, unbiasedness, efficiency)
- Q83 Random Variables, Distributions & Inference
Which of the following pairs of a random variable and its type is NOT correctly matched?
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Answer A. Number of goals scored in a football match : Continuous
The number of goals is a count (0, 1, 2, …), so it is a discrete random variable, not continuous.
Source: Standard definition (BRAOU Sem2 Mathematical Expectation, units on random variables, pmf, pdf and distribution function)
- Q84 Random Variables, Distributions & Inference
Match List I with List II:
List I:
A. Mean of a Bernoulli distribution
B. Variance of a Bernoulli distribution
C. Mean of a binomial distribution
D. Variance of a binomial distribution
List II:
1. npq
2. p
3. np
4. pq
Choose the correct answer:
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Answer D. A-2, B-4, C-3, D-1
Bernoulli: mean p, variance pq. Binomial (n trials): mean np, variance npq.
Source: Standard definition (BRAOU Sem3 Discrete Distributions, unit on Bernoulli and binomial distributions)
- Q85 Random Variables, Distributions & Inference
Which of the following are typical Poisson situations?
1. The number of accidents per day at a road crossing
2. The number of defects per metre of cloth
3. The marks obtained by students in an examination
4. The number of telephone calls received per minute
Which of the statements given above are correct?
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Answer D. 1, 2 and 4 only
Statements 1, 2 and 4 are correct. Marks are measurements with an upper limit, not counts of rare events.
Source: Standard definition (BRAOU Sem3 Discrete Distributions, unit on the Poisson distribution)
- Q86 Random Variables, Distributions & Inference
For a normal distribution, consider:
1. The area between μ and μ + σ equals the area between μ + σ and μ + 2σ.
2. The total area under the normal curve is 1.
Which of the statements given above is/are correct?
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Answer B. 2 only
The first area is about 34.13%, the second only about 13.59%. The density integrates to 1 over −∞ to ∞.
Source: Standard definition (BRAOU Sem4 Continuous Distributions, unit on the normal distribution)
- Q87 Random Variables, Distributions & Inference
Consider the following statements:
1. A statistic is a random variable because its value changes from sample to sample.
2. A parameter is a random variable because it is unknown.
Which of the statements given above is/are correct?
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Answer A. Only 1
Only statement 1 is correct. A statistic varies from sample to sample and has a sampling distribution; a parameter is a fixed population constant.
Source: Standard definition (BRAOU Sem6 Estimation & Testing of Hypothesis, Block I unit 1: basic terminology)
- Q88 Random Variables, Distributions & Inference
Consider the following statements about large sample tests.
1. Under H0, Z = (t − E(t))/SE(t) is approximately a standard normal variate when n is large.
2. At a given level of significance, the critical value of Z does not depend on the sample size n.
Which of the statements given above is/are correct?
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Answer C. Both 1 and 2
For large n, Z = (t − E(t))/SE(t) is approximately N(0, 1) under H0, and its critical values (such as 1.96 at 5%, two-tailed) depend only on α and the tails, not on n.
Source: Standard definition (BRAOU Sem 6 Estimation & Testing of Hypothesis, Unit 6 tests for single mean and proportion)
- Q89 Random Variables, Distributions & Inference
Match List I with List II:
List I:
A. Probability mass function
B. Probability density function
C. Distribution function
D. Mathematical expectation of X
List II:
1. Σ x p(x)
2. P(X ≤ x)
3. Point probabilities of a discrete variable that add to 1
4. Area under its curve over an interval gives a probability
Choose the correct answer:
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Answer A. A-3, B-4, C-2, D-1
A pmf gives point probabilities that add to 1; a pdf gives probabilities as areas; F(x) = P(X ≤ x); E(X) = Σ x p(x).
Source: Standard definition (BRAOU Sem2 Mathematical Expectation, units on random variables, pmf, pdf and distribution function)
- Q90 Random Variables, Distributions & Inference
A test has 8 questions, each with 4 options of which one is correct. A student guesses every answer. What is the expected number of correct answers?
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Answer B. 2
X ~ B(8, 1/4), so E(X) = np = 8 × 1/4 = 2.
Source: Standard result (BRAOU Sem3 Discrete Distributions, unit on Bernoulli and binomial distributions); answer and every option computed in Python
- Q91 Correlation & Regression
Find Spearman's rank correlation coefficient, corrected for ties (to three decimals):
X: 53, 40, 40, 58, 60, 50, 40
Y: 63, 41, 50, 66, 64, 59, 64
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Answer A. 0.625
Ranks X: 3, 6, 6, 2, 1, 4, 6; Y: 4, 7, 6, 1, 2.5, 5, 2.5. Σd² = 18.5. Ties: 40 three times in X, 3(3² − 1)/12 = 2; 64 twice in Y, 2(2² − 1)/12 = 0.5. R = 1 − 6 × 21/(7 × 48) = 0.625.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q92 Correlation & Regression
The regression line of Y on X is y = 0.5x + 4 and the regression line of X on Y is x = 0.5y + 2.5. Which of the following is correct?
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Answer A. x̄ = 6, ȳ = 7, r = 0.5
Substituting y: x = 0.5(0.5x + 4) + 2.5, so 0.75x = 4.5, x̄ = 6 and ȳ = 7. r = √(0.5 × 0.5) = 0.5, positive like the coefficients.
Source: Standard result (BRAOU Sem5 Correlation, Regression & Sampling, Unit 4 Simple Linear Regression); answer and every option computed in Python
- Q93 Correlation & Regression
The coefficient of correlation between X and Y is 0.6. If U = (X − 5)/2 and V = (Y − 10)/(−3), what is the coefficient of correlation between U and V?
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Answer C. −0.6
r is unaffected by change of origin and by change of scale in magnitude, but its sign reverses when the two scale factors have opposite signs. Here h = 2 and k = −3, so r(U, V) = −0.6.
Source: S.P. Gupta, Statistical Methods, Correlation Analysis
- Q94 Correlation & Regression
If byx = 1.6 and bxy = 0.4, what is the ratio σy/σx?
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Answer D. 2
byx/bxy = (r σy/σx)/(r σx/σy) = σy²/σx² = 4, so σy/σx = 2. (Also r = √(1.6 × 0.4) = 0.8.)
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q95 Correlation & Regression
The regression coefficient of weight (Y, in kg) on age (X, in years) is 0.4. If weight is recorded in grams instead, the new regression coefficient is
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Answer D. 400
Every Y is multiplied by 1000, so byx (units of Y per unit of X) is also multiplied by 1000: 0.4 × 1000 = 400 g per year.
Source: Standard result (BRAOU Sem5 Correlation, Regression & Sampling, Unit 4 Simple Linear Regression); answer and every option computed in Python
- Q96 Correlation & Regression
If Cov(X, Y) = 6, Var(X) = 9 and the coefficient of correlation is 0.5, what is Var(Y)?
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Answer D. 16
σx = 3. r = Cov/(σx σy) ⇒ σy = Cov/(r σx) = 6/(0.5 × 3) = 4, so Var(Y) = 16.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q97 Correlation & Regression
Assertion (A): The correlation coefficient is independent of change of scale.
Reason (R): Regression coefficients are independent of change of scale.
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Answer C. A is true, but R is false
r is unchanged by a positive change of scale, but regression coefficients change with scale (they are independent of origin only).
Source: Standard definition (BRAOU Sem5 Correlation, Regression & Sampling, Unit 4 Simple Linear Regression)
- Q98 Correlation & Regression
Assertion (A): If X takes values symmetric about zero and Y = X², the coefficient of correlation between X and Y is zero.
Reason (R): Karl Pearson's coefficient of correlation measures only the linear relationship between two variables.
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Answer A. Both (A) and (R) are true and (R) is the correct explanation of (A)
Y depends fully on X but not linearly; the positive and negative X values cancel in Cov(X, Y). Since r captures only linear association, r = 0, so R explains A.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q99 Correlation & Regression
If r = 0 for a data set, consider the following statements:
1. The two regression lines are perpendicular.
2. byx = bxy = 0.
3. The estimate of Y is ȳ for every value of X.
4. The standard error of estimate of Y on X is 0.
Which of the statements given above are correct?
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Answer D. 1, 2 and 3 only
With r = 0 both coefficients are 0, the lines are y = ȳ and x = x̄ (perpendicular), and ŷ = ȳ. Then Syx = σy, not 0.
Source: Standard definition (BRAOU Sem5 Correlation, Regression & Sampling, Unit 4 Simple Linear Regression)
- Q100 Correlation & Regression
Assertion (A): The coefficient of correlation between the monthly incomes of 50 families measured in rupees and their expenditures measured in thousands of rupees is the same as when both are measured in rupees.
Reason (R): Karl Pearson's coefficient of correlation is independent of change of scale.
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Answer A. Both (A) and (R) are true and (R) is the correct explanation of (A)
Dividing expenditure by 1,000 is a change of scale by a positive factor, which leaves r unchanged. So A is true because of R.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
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Start free - Q101 Correlation & Regression
Consider the following statements about Spearman's rank correlation with tied ranks:
1. Items with equal values are each given the average of the ranks they would otherwise occupy.
2. For every group of m tied items, m(m² − 1)/12 is added to Σd².
Which of the statements given above is/are correct?
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Answer C. Both 1 and 2
Tied values share the mean of their ranks (e.g. two items tying for 3rd and 4th each get 3.5), and each tie group of size m adds m(m² − 1)/12 to Σd².
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q102 Correlation & Regression
Consider the following statements:
1. 1 − r² is called the coefficient of determination.
2. The coefficient of determination always lies between 0 and 1.
Which of the statements given above is/are correct?
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Answer B. 2 only
r² is the coefficient of determination and lies between 0 and 1. 1 − r² is the coefficient of non-determination.
Source: Standard definition (BRAOU Sem5 Correlation, Regression & Sampling, Unit 4 Simple Linear Regression)
- Q103 Correlation & Regression
Which of the following is NOT a property of Karl Pearson's coefficient of correlation?
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Answer C. It changes when the scale of measurement of X is changed by a positive factor
r is bounded by ±1, symmetric in X and Y, equal to ±√(byx bxy), and independent of change of origin and scale.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q104 Correlation & Regression
Which of the following pairs is NOT correctly matched?
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Answer D. Charles Spearman : regression coefficient
Spearman is known for the rank correlation coefficient, not for regression coefficients. Galton coined 'regression', Legendre gave the least squares principle and Karl Pearson the product moment coefficient.
Source: Standard definition (BRAOU Sem5 Correlation, Regression & Sampling, Unit 4 Simple Linear Regression)
- Q105 Correlation & Regression
Consider the following statements about Karl Pearson's coefficient of correlation r:
1. r is unchanged if a constant is subtracted from every value of X.
2. r is unchanged if every value of Y is divided by a positive constant.
Which of the statements given above is/are correct?
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Answer C. Both 1 and 2
r is independent of change of origin (statement 1) and of change of scale by a positive factor (statement 2).
Source: S.P. Gupta, Statistical Methods, Correlation Analysis
- Q106 Correlation & Regression
Consider the following statements about the least squares regression line:
1. It passes through every observed point.
2. It is called the line of best fit.
Which of the statements given above is/are correct?
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Answer B. 2 only
The least squares line makes the sum of squared deviations a minimum, so it is the line of best fit. It passes through all points only when r = ±1.
Source: Standard definition (BRAOU Sem5 Correlation, Regression & Sampling, Unit 4 Simple Linear Regression)
- Q107 Time Series & Index Numbers
The quarterly trend of a firm's sales is Yc = 50 + 2X, with origin at the first quarter of 2024 and X in quarters. Under the additive model the seasonal effect of the fourth quarter is −5. The forecast for the fourth quarter of 2025 is
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Answer B. 59
From Q1 2024 (X = 0) to Q4 2025 is 7 quarters, so trend = 50 + 2 × 7 = 64. Adding the seasonal effect: 64 − 5 = 59.
Source: Standard method (degree-level analysis of time series); answer and every option computed in Python
- Q108 Time Series & Index Numbers
Base-year prices of two commodities are ₹2 and ₹5, current-year prices ₹3 and ₹6, base-year quantities 10 and 8, and current-year quantities 10 and 12. What is the Marshall-Edgeworth price index?
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Answer D. 128.57
Marshall-Edgeworth = Σp1(q0 + q1) / Σp0(q0 + q1) × 100 = (3 × 20 + 6 × 20) / (2 × 20 + 5 × 20) × 100 = 180 / 140 × 100 = 128.57.
Source: Standard method; answer and every option computed and checked in Python
- Q109 Time Series & Index Numbers
The values of a series for 2016 to 2021 are 30, 34, 38, 36, 40 and 44. Using a 4-yearly centred moving average, the trend value for 2018 is
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Answer B. 35.75
4-yearly averages: 138/4 = 34.5 (between 2017 and 2018) and 148/4 = 37 (between 2018 and 2019). Centring: (34.5 + 37)/2 = 35.75 for 2018.
Source: Standard method; answer and every option computed and checked in Python
- Q110 Time Series & Index Numbers
Two goods have base-year values (p0q0) of ₹42 and ₹58 and price relatives of 150 and 100. Paasche's price index for the same data is 100. Fisher's ideal price index is
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Answer A. 110
The weighted mean of relatives with weights p0q0 is Laspeyres' index: (63 + 58)/100 × 100 = 121. Fisher = √(121 × 100) = 110.
Source: Standard method (degree-level index numbers); answer and every option computed in Python
- Q111 Time Series & Index Numbers
Under the multiplicative model, the trend value of a quarter is 200 units, the seasonal index is 110, the cyclical relative is 95 and the irregular relative is 100. The original value of the series is
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Answer C. 209
Y = T × S × C × I = 200 × 1.10 × 0.95 × 1.00 = 209.
Source: Standard method; answer and every option computed and checked in Python
- Q112 Time Series & Index Numbers
For a group of commodities, Laspeyres' quantity index is 110 and the value index (Σp1q1/Σp0q0 × 100) is 165. Paasche's price index is
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Answer C. 150
(Σp1q1/Σp0q1) × (Σp0q1/Σp0q0) = Σp1q1/Σp0q0. So Paasche's price index = value index ÷ Laspeyres' quantity index = 165/1.10 = 150.
Source: Standard method (degree-level index numbers); answer and every option computed in Python
- Q113 Time Series & Index Numbers
Consider the following statements about the link relative method:
1. The link relative of the first season cannot be computed for the first year of the data.
2. Link relatives are obtained by dividing each figure by its centred moving average.
Which of the statements given above is/are correct?
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Answer A. 1 only
A link relative needs the previous season's figure, so the first season of the first year has none. Dividing by the moving average is the ratio-to-moving-average method.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
- Q114 Time Series & Index Numbers
Match List I (formula, × 100) with List II (index):
List I:
A. Σp1q0 / Σp0q0
B. Σq1p0 / Σq0p0
C. Σp1q1 / Σp0q0
D. Σp1q1 / Σp0q1
List II:
1. Value index
2. Laspeyres' price index
3. Paasche's price index
4. Laspeyres' quantity index
Choose the correct answer.
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Answer D. A-2, B-4, C-1, D-3
A is Laspeyres' price index, B is Laspeyres' quantity index, C is the value index and D is Paasche's price index.
Source: Standard definition (degree-level index numbers, as in Telangana B.A./B.Com statistics texts)
- Q115 Time Series & Index Numbers
Consider the following statements:
1. The additive model Y = T + S + C + I assumes that the four components are independent of one another.
2. In the multiplicative model Y = T × S × C × I, the trend is in original units while S, C and I are expressed as relatives (ratios or indices).
Which of the statements given above is/are correct?
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Answer C. Both 1 and 2
The additive model treats components as independent and all in original units. The multiplicative model treats them as interdependent: T is in original units and S, C, I are ratios/percentages of the trend.
Source: S.P. Gupta, Statistical Methods: Analysis of Time Series (standard B.Com/B.A. text)
- Q116 Time Series & Index Numbers
Consider the following statements about India's official price indices (as of 2026):
1. The all-India Consumer Price Index (Rural, Urban and Combined) is compiled by the National Statistics Office (NSO), MoSPI, and its current series has base year 2024 = 100.
2. The Wholesale Price Index is compiled by the Office of the Economic Adviser, DPIIT, and its current series has base year 2022-23.
3. The Consumer Price Index for Industrial Workers (CPI-IW) is compiled by the NSO with base year 2024 = 100.
Which of the statements given above are correct?
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Answer C. 1 and 2 only
CPI (Rural/Urban/Combined): NSO, MoSPI; base revised from 2012 to 2024 = 100 with the January 2026 index. WPI: Office of the Economic Adviser, DPIIT; base revised from 2011-12 to 2022-23 in June 2026. CPI-IW: Labour Bureau (Ministry of Labour and Employment), base 2016 = 100.
Source: Medha AI; base years from the MoSPI/NSO (CPI 2024 = 100, Feb 2026; IIP 2022-23, 2026), Office of the Economic Adviser, DPIIT (WPI 2022-23, Jun 2026) and Labour Bureau (CPI-IW 2016 = 100) releases, checked Oct 2026
- Q117 Time Series & Index Numbers
Match List I (trend) with List II (property of the trend values):
List I:
A. Straight-line trend
B. Second-degree parabola
C. Exponential trend
D. Moving average trend
List II:
1. Second differences are constant
2. No mathematical equation is obtained
3. First differences are constant
4. The ratio of successive values is constant
Choose the correct answer.
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Answer D. A-3, B-1, C-4, D-2
A straight line rises by a constant amount (constant first differences). A parabola has constant second differences. An exponential curve rises at a constant rate (constant ratio). A moving average gives values but no equation.
Source: Standard definition (degree-level analysis of time series, as in Telangana B.A./B.Com statistics texts)
- Q118 Time Series & Index Numbers
Assertion (A): A chain base index is preferable when the main interest is in comparing a year's prices with those of the immediately preceding year.
Reason (R): Each link relative compares a year with the year just before it.
Choose the correct answer.
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Answer A. Both A and R are true, and R is the correct explanation of A
Link relatives measure year-to-year change directly, which is why a chain base suits comparisons with the preceding year.
Source: Standard definition (degree-level index numbers, as in Telangana B.A./B.Com statistics texts)
- Q119 Time Series & Index Numbers
Match List I (example) with List II (component of time series):
List I:
A. Steady rise in India's population over decades
B. Higher sale of umbrellas every monsoon
C. Alternating boom and slump in business every few years
D. Fall in factory output due to a sudden strike
List II:
1. Irregular variation
2. Cyclical variation
3. Seasonal variation
4. Secular trend
Select the correct answer using the code given below.
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Answer D. A-4, B-3, C-2, D-1
Long-term population growth is secular trend; monsoon umbrella sales are seasonal; boom-slump over years is cyclical; a sudden strike causes irregular variation.
Source: S.P. Gupta, Statistical Methods: Analysis of Time Series (standard B.Com/B.A. text)
- Q120 Time Series & Index Numbers
Consider the following reasons:
1. The old base year is too distant to be relevant.
2. Two index series with different base years have to be compared.
3. Money values have to be converted into real values.
Which of the above are valid reasons for shifting the base of an index series?
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Answer A. 1 and 2 only
The base is shifted when the old base is too old or abnormal, or to compare series with different bases. Converting money values to real values is deflating.
Source: Standard definition (degree-level index numbers, as in Telangana B.A./B.Com statistics texts)
- Q121 Time Series & Index Numbers
Consider the following statements:
1. Seasonal variations have a fixed period, so they can be predicted fairly accurately.
2. Cyclical variations have a fixed period of 12 months.
Which of the statements given above is/are correct?
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Answer A. 1 only
Seasonal variations repeat regularly within a year and are predictable. Cyclical variations last more than a year and vary in length, so statement 2 is false.
Source: Standard definition (degree-level analysis of time series, as in Telangana B.A./B.Com statistics texts)
- Q122 Time Series & Index Numbers
Consider the following possible uses of a consumer price index:
1. Fixing dearness allowance
2. Deflating money wages to find real wages
3. Measuring the purchasing power of money
4. Measuring the correlation between two variables
Which of the above are uses of a consumer price index?
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Answer B. 1, 2 and 3 only
A consumer price index is used to fix dearness allowance, to deflate money wages and to measure the purchasing power of money. It does not measure correlation.
Source: Standard definition (degree-level index numbers, as in Telangana B.A./B.Com statistics texts)
- Q123 Time Series & Index Numbers
Which of the following is NOT generally regarded as a use of time series analysis?
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Answer B. Measuring the degree of association between two different variables at one point of time
Time series analysis studies one variable over time: its past behaviour, forecasting and evaluation of performance. Association between two variables at a point of time is the subject of correlation.
Source: S.P. Gupta, Statistical Methods: Analysis of Time Series (standard B.Com/B.A. text)
- Q124 Time Series & Index Numbers
Which of the following pairs of index and formula (× 100) is NOT correctly matched?
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Answer D. Dorbish–Bowley – √(Laspeyres × Paasche)
Dorbish–Bowley's index is the arithmetic mean of Laspeyres' and Paasche's indices. The geometric mean of the two is Fisher's ideal index.
Source: Standard definition (degree-level index numbers, as in Telangana B.A./B.Com statistics texts)
- Q125 Sampling Techniques
No estimate of σ is available, but the values of a variable are known to range over about 120 units. Taking σ ≈ range/6, z = 2 and a margin of error of ±4, what sample size is needed?
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Answer B. 100
σ ≈ 120/6 = 20. n = (zσ/d)² = (2 × 20/4)² = 10² = 100.
Source: Standard sample-size result; answer and every option computed in Python
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Start free - Q126 Sampling Techniques
Which of the following hold for SRSWOR of size n (n > 1) from N units?
1. Every unit has probability n/N of being included.
2. The sample mean is unbiased for the population mean.
3. Var(ȳ) is smaller than under SRSWR of the same size.
4. The sample variance s² (divisor n − 1) is unbiased for σ² (divisor N).
Select the correct answer using the code given below.
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Answer D. 1, 2 and 3 only
1, 2 and 3 only. In SRSWOR, E(s²) = S² (divisor N − 1), not σ².
Source: Standard result (BRAOU Sem5 Unit 10; note: SRSWOR is the more precise design, Var(WOR) = (N − n)S²/(Nn) < Var(WR) = (N − 1)S²/(Nn))
- Q127 Sampling Techniques
About 20% of the students in a district are believed to be anaemic. Using z = 2, how many students must be sampled to estimate this proportion within ±4 percentage points?
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Answer B. 400
n = z²pq/d² = 4 × 0.2 × 0.8/(0.04)² = 0.64/0.0016 = 400.
Source: Standard sample-size result; answer and every option computed in Python
- Q128 Sampling Techniques
Consider the following:
Assertion (A): SRSWOR gives a more precise estimate of the population mean than SRSWR of the same size.
Reason (R): In SRSWOR no unit is repeated, so the sample contains more distinct units and more information.
Select the correct answer using the code given below.
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Answer A. Both A and R are true, and R is the correct explanation of A
Both are true and R explains A. Var(ȳ) WOR is smaller by the factor (N − n)/(N − 1).
Source: Standard result (BRAOU Sem5 Unit 10; note: SRSWOR is the more precise design, Var(WOR) = (N − n)S²/(Nn) < Var(WR) = (N − 1)S²/(Nn))
- Q129 Sampling Techniques
Match List I (design) with List II (key requirement or feature):
List I:
A. Stratified random sampling
B. Systematic sampling
C. Cluster sampling
D. Simple random sampling without replacement
List II:
1. An ordered list, a random start and a fixed interval
2. Stratum sizes known and a separate random sample from every stratum
3. Every possible sample of size n equally likely
4. Only a list of groups is needed; all units in the selected groups are studied
Select the correct answer using the code given below.
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Answer A. A-2, B-1, C-4, D-3
A-2, B-1, C-4, D-3. Cluster sampling enumerates whole selected groups; stratified sampling samples every stratum.
Source: Standard definition (BRAOU Sem5 Correlation, Regression & Sampling, Units 11 Stratified and 12 Systematic Sampling)
- Q130 Sampling Techniques
An opinion poll uses a simple random sample of 625 voters. Taking p = 0.5 and z = 2, what is the margin of error of the sample proportion?
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Answer C. ±4 percentage points
SE = √(pq/n) = √(0.25/625) = 0.02. Margin = z × SE = 2 × 0.02 = 0.04, i.e. ±4 percentage points.
Source: Standard sample-size result; answer and every option computed in Python
- Q131 Sampling Techniques
Consider the following statements about sampling units:
1. Sampling units must not overlap, so that no unit of the population belongs to two of them.
2. Taken together, the sampling units must cover the whole population.
Which of the statements given above is/are correct?
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Answer C. Both 1 and 2
Both are correct. Sampling units must be clearly defined, non-overlapping and must together cover the whole population.
Source: Standard definition (BRAOU Sem5 Correlation, Regression & Sampling, sampling units; S.P. Gupta, Sampling)
- Q132 Sampling Techniques
Consider the following statements about the sample mean ȳ of a simple random sample:
1. ȳ is an unbiased estimator of the population mean under SRSWR.
2. ȳ is an unbiased estimator of the population mean under SRSWOR.
Which of the statements given above is/are correct?
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Answer C. Both 1 and 2
Both are correct. Under both SRSWR and SRSWOR, E(ȳ) = Ȳ.
Source: Standard definition (BRAOU Sem5 Correlation, Regression & Sampling, Unit 10 Simple Random Sampling)
- Q133 Sampling Techniques
Consider the following statements:
1. Equal allocation is reasonable when the strata are of about the same size and variability.
2. Equal allocation always gives the smallest variance of ȳst.
Which of the statements given above is/are correct?
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Answer A. 1 only
Only 1. Equal allocation is close to optimum only when strata are alike in size and variability.
Source: Standard definition (BRAOU Sem5 Correlation, Regression & Sampling, Units 11 Stratified and 12 Systematic Sampling)
- Q134 Sampling Techniques
Consider the following statements:
1. A parameter, such as the population mean μ, is a fixed constant for a given population.
2. A statistic, such as the sample mean x̄, varies from one sample to another.
Which of the statements given above is/are correct?
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Answer C. Both 1 and 2
Both are correct. A parameter is a fixed population constant; a statistic is computed from a sample and varies from sample to sample.
Source: Standard definition (BRAOU Sem5 Correlation, Regression & Sampling, sampling units; S.P. Gupta, Sampling)
- Q135 Basics of Computers
What is the octal equivalent of the hexadecimal number (3A7)₁₆?
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Answer D. 1647
Convert through binary: (3A7)₁₆ = 0011 1010 0111. Regroup in threes from the right: 001 110 100 111 → 1 6 4 7. So (3A7)₁₆ = (1647)₈ (both equal 935 in decimal).
Source: Standard method; answer and every option computed and checked in Python
- Q136 Basics of Computers
The Gray code 1101 is converted to binary. What is the result?
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Answer B. 1001
Copy the MSB, then each binary bit = previous binary bit ⊕ current Gray bit: 1, 1⊕1 = 0, 0⊕0 = 0, 0⊕1 = 1, so binary = 1001 (decimal 9). Check: 1001 → Gray 1101.
Source: Standard method; answer and every option computed and checked in Python
- Q137 Basics of Computers
Using 8-bit 2's complement arithmetic, 00111100 (60) is subtracted from 00101101 (45) by adding the 2's complement of 60. What is the 8-bit result?
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Answer D. 11110001
2's complement of 00111100 is 11000100; 00101101 + 11000100 = 11110001, which is −15.
Source: Standard computer fundamentals; answer and every option computed in Python
- Q138 Basics of Computers
Match List I (number) with List II (decimal value):
List I:
A. (1110)₂
B. (21)₈
C. (1C)₁₆
D. (101011)₂
List II:
1. 17
2. 43
3. 14
4. 28
Select the correct answer using the code given below.
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Answer D. A-3, B-1, C-4, D-2
(1110)₂ = 8 + 4 + 2 = 14; (21)₈ = 16 + 1 = 17; (1C)₁₆ = 16 + 12 = 28; (101011)₂ = 32 + 8 + 2 + 1 = 43.
Source: Standard method; answer and every option computed and checked in Python
- Q139 Basics of Computers
Consider the following statements about Unicode:
1. The first 128 Unicode code points are the same as the ASCII characters.
2. UTF-8 always uses exactly 2 bytes for every character.
Which of the statements given above is/are correct?
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Answer A. 1 only
Unicode code points U+0000 to U+007F are identical to ASCII. UTF-8 is a variable-length encoding using 1 to 4 bytes per character (ASCII characters take 1 byte).
Source: The Unicode Standard (unicode.org), Encoding forms
- Q140 Basics of Computers
Consider the following statements:
1. In a rotate operation no bit is lost; the bit moved out at one end comes back at the other end.
2. Shifting an unsigned number left by one place doubles it, provided no 1 bit is moved out of the leftmost position.
Which of the statements given above is/are correct?
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Answer C. Both 1 and 2
Both are correct: a rotation is circular, and a left shift multiplies by 2 as long as the result still fits in the register.
Source: Standard computer fundamentals
- Q141 Basics of Computers
Columns in a worksheet are labelled A, B, …, Z, AA, AB, …. What is the column number of column AB?
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Answer B. 28
Column letters act as a base-26 code with A = 1 … Z = 26. AB = 1 × 26 + 2 = 28.
Source: Standard spreadsheet method; answer and every option computed and checked in Python
- Q142 Basics of Computers
Consider the following statements:
1. In a four-digit hexadecimal integer, the place value of the leftmost position is 16³.
2. The hexadecimal letters A to F stand for the decimal values 10 to 15.
3. 8 is a valid digit in the octal system.
4. The binary system uses only two symbols, 0 and 1.
Which of the statements given above are correct?
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Answer C. 1, 2 and 4 only
Place values of a four-digit hex integer are 16³, 16², 16¹, 16⁰, so 1 is correct; A–F = 10–15, so 2 is correct; octal digits are 0–7, so 3 is wrong; binary uses 0 and 1, so 4 is correct.
Source: Standard B.Com/B.Sc. Computer Fundamentals textbook (Telugu Akademi), Number Systems
- Q143 Basics of Computers
Consider the following statements:
1. The 4-bit groups 1010 to 1111 are invalid in BCD (8421) code.
2. BCD usually needs more bits than pure binary to represent the same number.
3. Gray code is a weighted code.
Which of the statements given above are correct?
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Answer B. 1 and 2 only
BCD uses only 10 of the 16 four-bit groups (1010–1111 are invalid), so it is less compact than binary (e.g. 99 needs 8 bits in BCD but 7 in binary). Gray code is unweighted.
Source: Standard digital logic texts (M. Morris Mano, Digital Logic and Computer Design), Binary codes
- Q144 Basics of Computers
Consider the following statements about the XNOR gate:
1. Its output is 1 when both inputs are equal.
2. It is the complement of the XOR gate.
3. For inputs A and B its output is A·B + A'·B'.
Which of the statements given above are correct?
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Answer D. 1, 2 and 3
XNOR (equivalence gate) gives 1 for inputs 00 and 11; it is NOT of XOR, and its expression is A·B + A'·B'.
Source: Standard computer fundamentals textbook (e.g., P. K. Sinha, Computer Fundamentals), Logic Gates
- Q145 Basics of Computers
Consider the following statements:
1. Each octal digit can be written as a group of exactly three binary digits.
2. Each hexadecimal digit can be written as a group of exactly four binary digits.
Which of the statements given above is/are correct?
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Answer C. Both 1 and 2
Because 8 = 2³, each octal digit 0–7 matches a 3-bit group 000–111; because 16 = 2⁴, each hexadecimal digit 0–F matches a 4-bit group 0000–1111.
Source: Standard B.Com/B.Sc. Computer Fundamentals textbook (Telugu Akademi), Number Systems
- Q146 Basics of Computers
Consider the following statements:
1. BCD (8421) is a weighted code.
2. Excess-3 is a weighted code.
Which of the statements given above is/are correct?
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Answer A. 1 only
In 8421 BCD each bit position carries a weight (8, 4, 2, 1). Excess-3 is BCD + 3, so its bits do not carry fixed weights; it is an unweighted code, like Gray code.
Source: Standard digital logic texts (M. Morris Mano), Binary codes
- Q147 Basics of Computers
Which of the following pairs of flowchart symbol and its use is NOT correctly matched?
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Answer C. Small circle : start or stop of the flowchart
Start and Stop use the oval (terminal) symbol; the small circle is a connector.
Source: Standard computer fundamentals
- Q148 Basics of Computers
Match List I (chart type) with List II (best use):
List I:
A. Pie chart
B. Line chart
C. Column chart
D. Scatter (XY) chart
List II:
1. Trend of a value over time
2. Relationship between two numeric variables
3. Share of each part in a whole
4. Comparison of values across categories
Select the correct answer using the code given below.
Show answerHide answer
Answer B. A-3, B-1, C-4, D-2
Pie shows parts of a whole; line shows change over time; column compares categories; scatter plots paired numeric values to show a relationship.
Source: MS Excel / LibreOffice Calc documentation; Telugu Akademi B.Com Computer Applications, spreadsheets
- Q149 Basics of Computers
Match List I (number system) with List II (base):
List I:
A. Binary
B. Octal
C. Decimal
D. Hexadecimal
List II:
1. 16
2. 2
3. 10
4. 8
Select the correct answer using the code given below.
Show answerHide answer
Answer A. A-2, B-4, C-3, D-1
Binary = base 2, octal = base 8, decimal = base 10, hexadecimal = base 16.
Source: Standard B.Com/B.Sc. Computer Fundamentals textbook (Telugu Akademi), Number Systems
- Q150 Basics of Computers
Using the binary convention (1 KB = 1024 bytes), which of the following pairs is NOT correctly matched?
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Answer C. 1 MB : 1024 bytes
1 nibble = 4 bits, 1 byte = 8 bits, 1 KB = 1024 bytes, 1 MB = 1024 KB = 2^20 bytes and 1 GB = 1024 MB. 1024 bytes is 1 KB, not 1 MB.
Source: Standard computer fundamentals texts (P.K. Sinha, Computer Fundamentals), Units of storage
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