UGC NET Questions (Paper – 1)

Statement A is correct because correlation quantifies both direction and strength of linear association. Statement C is true as a value near zero indicates weak or no linear correlation. Statement D is also correct because correlation alone cannot establish cause and effect. Statement E accurately states that in negative correlation, higher values of one variable are associated with lower values of the other. Statement B is false since +1 represents perfect positive, not negative, linear relationship. Therefore, A, C, D and E only are correct.

Option A:
Option A is incomplete since it omits D (correlation is not causation).

Option B:
Option B is incomplete because it omits C and does not include the full correct set.

Option C:
Option C is incorrect because it excludes A (definition) and omits D (causation warning).

Option D:
Option D is correct as it joins all four accurate statements and excludes only B, which misstates the meaning of +1.

Statements A, B, C and D together summarise the standard relationships between mutually exclusive and independent events. A correctly defines mutual exclusivity as events that cannot happen simultaneously. B properly describes independence in terms of unchanged probabilities. C follows because if two non-trivial events are mutually exclusive, their joint probability is zero and cannot equal the product of positive probabilities, so they are not independent. D restates the formal definition of independence using the product rule. E is false since mutual exclusivity and independence are distinct concepts, so the correct set is A, B, C and D only.

Option A:
Option A is incomplete because it omits D and thus fails to express the formal product definition of independence, even though A, B and C are true. The absence of D makes the description of independence less precise.

Option B:
Option B is correct as it combines the basic definitions and implications about mutual exclusivity and independence and excludes E, which wrongly equates the two. It matches the conceptual treatment of events found in NET-level probability questions.

Option C:
Option C is incorrect because it includes E, the false claim that mutual exclusivity and independence mean the same thing, and leaves out B, which is a core statement about independence. This mixture of error and omission invalidates the option.

Option D:
Option D is wrong as it drops A and includes only B, C and D, leaving out the explicit definition of mutual exclusivity while still not rejecting E. It therefore does not provide the complete and correct set of statements.

Statements C and E are the wrong statements here. A is correct because probabilities range from 0 to 1. B is true since probabilities of all mutually exclusive and exhaustive outcomes sum to 1. D correctly states that a certain event has probability 1. C is false because 0.7 indicates a more likely event than 0.4. E is false because P(A ∪ B) equals P(A) + P(B) only when A and B are mutually exclusive; otherwise the intersection must be subtracted. Therefore, the wrong statements are C and E only.

Option A:
Option A is incomplete because it selects only C as wrong and ignores E, which misapplies the addition rule for probabilities of unions.

Option B:
Option B is correct as it identifies both C and E as incorrect, thereby recognising that both comparative likelihood and union probabilities are mishandled in those statements.

Option C:
Option C is wrong since it mislabels A as wrong, even though A accurately describes the probability range, and still keeps C and E, mixing correct and incorrect judgments.

Option D:
Option D is incorrect because it classifies B and D as wrong despite them stating fundamental probability principles, and it omits E, which actually contains an error about unions.

Statements A, B, C and E describe core properties of means. A gives the definition of arithmetic mean. B is true because the overall mean of two groups must fall between their group means, weighted by group sizes. C is correct in explaining that weighted averages give more influence to values with higher weights. E holds since adding a constant to all values shifts the mean by that constant. D is false because the mean need not be one of the data values, especially for continuous data. Hence A, B, C and E only are correct.

Option A:
Option A is incomplete because it leaves out E and therefore ignores the important transformation property showing how means shift under addition of a constant. It does not include all correct statements.

Option B:
Option B is wrong since it excludes C and includes only A, B and E, failing to mention the key feature of weighted averages, which are frequently tested in aptitude problems.

Option C:
Option C is correct because it collects all four true statements while excluding D, which wrongly asserts that the mean must be a data point. This combination matches the conceptual understanding required in NET statistics questions.

Option D:
Option D is incorrect as it omits A and does not include all four true statements together, so it cannot be the correct combination.

Statement A correctly describes qualitative data as categorical. Statement B is true for quantitative data, which involve numerical magnitudes. Statement D is also correct, since continuous data can, in principle, assume any value in an interval with arbitrary precision. Statement C is false because discrete data take countable values with gaps, while continuous data take any value in an interval. Statement E is false as understanding data type helps in choosing appropriate measures and graphs. Hence, A, B and D only are correct.

Option A:
Option A is incomplete because it omits D (continuous data).

Option B:
Option B is correct since it includes all true statements and excludes C and E.

Option C:
Option C is wrong because it includes C (false).

Option D:
Option D is incorrect because it includes C (false) and omits B.

Statement A is correct because range is maximum minus minimum. Statement B accurately defines the IQR as Q3 − Q1. Statement D is also true since IQR is less sensitive to outliers than the range. Statement C is false because a single extreme value can change the range a lot, and E is false because range and IQR are generally different. Therefore, A, B and D only are correct.

Option A:
Option A is incomplete because it omits D (robustness of IQR).

Option B:
Option B is incorrect as it includes C (false).

Option C:
Option C is wrong because it includes E (false) and omits A.

Option D:
Option D is correct since it includes all correct statements and excludes C and E.

Statements A, B and C give the standard description and formula for arithmetic and weighted means. A is correct because the simple mean assigns equal weight to each observation. B and C correctly explain that weighted means use different weights and are computed as the weighted sum divided by the total weight. Statement E is true because if all weights are equal, the weighted mean collapses to the ordinary mean. Statement D is false since a weighted mean, like the arithmetic mean, can lie between observed values and need not coincide with any one observation, so the correct set is A, B, C and E only.

Option A:
Option A is incomplete because it omits C and E and so does not show how weighted means are actually computed or how they relate back to the arithmetic mean when weights are equal. It therefore does not represent all correct statements.

Option B:
Option B is also incomplete as it does not include E, ignoring the simplifying case in which weights are equal, even though it correctly includes A, B and C. The missing link to the arithmetic mean makes it insufficient.

Option C:
Option C is wrong because, although it includes B, C and E, it omits A, which states the key contrast between arithmetic and weighted means, and still does not highlight the equal-weight case as a special instance in context.

Option D:
Option D is correct because it brings together the accurate description of both kinds of means and the proper computation rule, while explicitly excluding D, which incorrectly insists that the mean must be one of the data points. This aligns with the conceptual treatment of averages in NET questions.

Statement A correctly defines variance as the mean of squared deviations from the mean (in the population sense). Statement B is true because standard deviation is the positive square root of variance. Statement D is also correct since a larger standard deviation reflects more spread in the data. Statement C is false because if all observations are equal, both variance and standard deviation are zero. Statement E is false for the same reason. Therefore, A, B and D only are correct.

Option A:
Option A is incomplete; while A and B are true, it omits D and thus fails to connect standard deviation to dispersion.

Option B:
Option B is correct because it includes all three accurate statements and excludes C and E, both of which incorrectly deny the possibility of zero spread.

Option C:
Option C is wrong because it includes C (false), even though B and D are true.

Option D:
Option D is wrong because it includes E (false) and omits B (definition link), so it cannot be correct.

B is the definition of independence: P(A ∩ B) = P(A)P(B). C is correct because mutually exclusive events with positive probabilities have P(A ∩ B)=0 but P(A)P(B)>0, so they cannot be independent. D is true because independence carries over to complements. A is false (addition relates to mutually exclusive unions, not independence). E is false because for independent events P(A|B) = P(A), not 0. Therefore B, C and D only are correct.

Option A:
Option A is incomplete because it includes only B and leaves out C and D, which are also correct statements.

Option B:
Option B is correct as it includes exactly the true statements and excludes A and E, which confuse addition/conditional probability with independence.

Option C:
Option C is wrong because it includes E, which misstates conditional probability under independence.

Option D:
Option D is incorrect because it includes A, which is not the criterion for independence.

Statements A, B and C provide standard definitions of mean, median and mode. Statement E is also correct because in skewed distributions extreme values can distort the mean, making the median more representative. Statement D is false since equality of mean, median and mode holds only for certain symmetric distributions and not for every data set. Therefore, the combination A, B, C and E only is correct.

Option A:
Option A is correct as it collects all the accurate statements while leaving out D, which overgeneralises the equality of the three measures.

Option B:
Option B is incomplete because it omits E and therefore ignores the practical guidance on skewed data.

Option C:
Option C is wrong since it includes D, the false assertion about universal equality.

Option D:
Option D is wrong because it includes D and omits A, losing a core definition while keeping a false rule.

Statements A, B and E state standard facts about central tendency. A is correct because mean can lie left or right of the median in skewed distributions or coincide in symmetric cases. B is correct for perfectly symmetric unimodal distributions such as the normal distribution. E is correct since the median position splits an ordered data set into two halves with equal counts. C is false because mean and median need not always be equal, and D is false because mode may be non-unique or even absent, so A, B and E only is the correct combination.

Option A:
Option A is correct since it includes all and only the true statements: A about relative positions of mean and median, B about equality in symmetric unimodal distributions and E about the median’s partition property. It excludes C and D, both of which overstate what must always happen.

Option B:
Option B is incorrect because it adds C, which wrongly claims that median always equals mean for any data set. Including C introduces a false universal statement about equality of mean and median.

Option C:
Option C is wrong as it includes C again, making the set A, B, C, E contain one false member. A correct combination must consist entirely of true statements, so this option cannot be chosen.

Option D:
Option D is incorrect because it includes D, which asserts that the mode must always be unique. In reality, a distribution may be bimodal, multimodal or have no mode, so adding D makes this option incorrect.

A defines conditional probability, and B states the law of total probability for a partition. C is true because independence means conditioning on B does not change the probability of A. D is true because Bayes’ theorem updates a prior probability using likelihood/evidence. E is false: P(A∣B) + P(A∣B′) is not generally 1 (they are conditional probabilities on different conditions; their sum can be greater than 1 or less than 1). Therefore A, B, C and D only are correct.

Option A:
Option A is incorrect because it omits D, and Bayes’ theorem is a correct statement commonly paired with conditional probability concepts.

Option B:
Option B is incorrect because it omits A, which is the defining formula for conditional probability.

Option C:
Option C is correct because it includes all and only the true statements (A, B, C and D) and excludes E, which is not a valid identity in general.

Option D:
Option D is incorrect because it omits B, the law of total probability, which is true.

Statements A and B correctly describe simple random and stratified sampling. Statement C is also true as cluster sampling initially chooses whole clusters for inclusion. Statement E is correct because systematic sampling indeed selects every nth unit after a random start. Statement D is false since convenience sampling is non-probability based and can easily introduce bias. Thus, A, B, C and E only are correct.

Option A:
Option A is incomplete as it omits E (systematic sampling).

Option B:
Option B is wrong because it includes D (false).

Option C:
Option C is correct because it unites all of the true descriptions and excludes D.

Option D:
Option D is incorrect since it retains D (false) and omits A.

Statement A is correct because regression distinguishes a response (dependent) variable from an explanatory (independent) variable. Statement C is true as the least squares criterion minimises the sum of squared vertical residuals. Statement D is also correct since regression is widely used to predict and to analyse how variables relate. Statement B is false because the regression of Y on X is primarily used to predict Y for given X, not the other way around. Statement E is false because a horizontal line means Y is constant and does not change with X. Consequently, A, C and D only are correct.

Option A:
Option A is correct as it collects the essential properties of simple linear regression and excludes B and E.

Option B:
Option B is incorrect because it includes B (wrong predictive direction).

Option C:
Option C is wrong as it includes E (false).

Option D:
Option D is incorrect because it retains B (false) and omits A (dependent/independent distinction).