UGC NET Questions (Paper – 1)

Quantitative research emphasises numerical measurement of variables and uses statistical methods to summarise and analyse data. It often relies on structured instruments, large samples and objective procedures to test hypotheses or estimate population parameters. This approach is typically associated with the positivist paradigm and seeks to produce generalisable findings. Therefore, research that focuses on numerical data and statistical analysis is correctly called quantitative research.

Option A:
Qualitative research explores meanings, experiences and processes through non-numerical data such as interviews and observations. It does not primarily rely on numerical measurement and statistical analysis, so it does not match the stem.

Option B:
Option B, quantitative research, is designed to quantify relationships, differences or trends, often using descriptive and inferential statistics. Variables are operationalised in measurable units, and results are expressed in numbers like percentages or means. This aligns closely with the description, making this option correct.

Option C:
Narrative research focuses on collecting and analysing stories or life histories and is usually qualitative in nature. Its main concern is understanding narrative structure and meaning, not numerical data.

Option D:
Ethnographic research is a qualitative strategy involving immersion in a cultural setting to understand shared practices and meanings. Although it may generate some counts, it is not primarily numerical and statistical in orientation, so it is not the right answer.

The normal distribution is a theoretical, continuous probability distribution that is symmetric around its mean and has a characteristic bell shape. Many natural and measurement-related variables approximate this form under suitable conditions. In a normal distribution, fixed proportions of scores fall within one, two or three standard deviations of the mean. Therefore, the symmetric bell-shaped distribution described in the stem is correctly called the normal distribution.

Option A:
The binomial distribution deals with discrete outcomes of a fixed number of trials with two possible results, such as success and failure, and is not continuous or bell-shaped in the same way.

Option B:
The normal distribution underlies many parametric statistical tests and allows use of z-scores and confidence intervals. Its shape is fully determined by its mean and standard deviation, matching the stem exactly and making this option correct.

Option C:
The Poisson distribution models counts of rare events over space or time and is typically skewed, especially at low expected counts, not symmetric and bell-shaped like the normal.

Option D:
A skewed distribution is any distribution lacking symmetry, often with one tail longer than the other, which contradicts the symmetric property stated in the question.

This option is correct because standard deviation measures the spread of data around the mean and is defined using squared deviations. Squaring removes negative signs before averaging and taking the square root. The square root of a non-negative number is also non-negative. Therefore, standard deviation cannot be negative and is always non negative.

Option A:
Standard deviation can be zero only in the special case where all observations are equal to the mean. In most real data sets, values vary, giving a positive spread. Hence, "always zero" is incorrect.

Option B:
Although different data sets can have different standard deviations, the value is never negative. It can be zero or positive depending on the variation in the data. This means the correct description is that standard deviation is always non negative.

Option C:
"Always one" would suggest that every data set has the same fixed amount of spread, which is not true. Different data sets can have very large or very small variability. Therefore, this option is wrong.

Option D:
Saying standard deviation may be negative contradicts the mathematical definition involving squared deviations and square roots. Since squares are non negative, their average and square root cannot be negative either. Thus, this option is mathematically impossible.

A ratio scale possesses all the properties of an interval scale—equal units and meaningful differences—plus a true zero point that indicates the complete absence of the quantity being measured. Because of the true zero, statements such as one value being twice another are meaningful. Examples include height, weight and Kelvin temperature. Thus, a scale with equal units and a true zero that allows ratio comparisons is correctly called a ratio scale.

Option A:
Nominal scales classify objects into categories without any inherent order, such as gender or blood group. They do not have equal units or a zero point with quantitative meaning, so they do not match the stem.

Option B:
Ordinal scales rank order items but do not guarantee equal intervals between ranks; they allow comparison of “greater than” or “less than” but not meaningful differences or ratios. Hence, ordinal is not the right answer.

Option C:
Interval scales have equal units and allow meaningful differences to be calculated, but they lack a true zero, so ratios can be misleading. Celsius temperature is a classic example. Therefore, interval does not fulfil the true-zero condition in the stem.

Option D:
Option D, ratio scale, uniquely combines equal intervals with an absolute zero, enabling multiplication and division operations that are not valid on other scales. This matches the description in the question precisely.

Variance is defined as the square of the standard deviation. Since standard deviation is the square root of variance, squaring the standard deviation gives the variance (a measure of dispersion).

Option A:
Variance is correct because it equals (standard deviation)² and measures how spread out data are around the mean using squared deviations.

Option B:
Mean is a measure of central tendency (average), not the square of standard deviation, so it does not match the definition.

Option C:
Range is max − min, another dispersion measure, but it is not equal to (standard deviation)².

Option D:
Median is the middle value of ordered data and is unrelated to squaring the standard deviation.

This option is correct because the probability of an event and its complement must sum to 1. If P(A) = p, then P(A') = 1 − p. This follows directly from the rule that A and A' are mutually exclusive and exhaustive. Therefore, the complement has probability 1 − p.

Option A:
If we use p as the probability of A', then P(A) + P(A') would be p + p = 2p, which equals 1 only when p = 1/2. This does not hold in general and contradicts probability axioms. Hence, this option is incorrect.

Option B:
The expression 1/p would usually exceed 1 for p less than 1 and is not bounded between 0 and 1. Probabilities cannot exceed 1, so this form cannot represent the complement probability.

Option C:
The expression p² is smaller than p for values between 0 and 1 and does not generally satisfy P(A) + P(A') = 1. It is just another function of p, not the complement. Thus, this option is not correct.

Option D:
The value 1 − p ensures that P(A) + P(A') equals 1, satisfying the basic complement rule. It also remains between 0 and 1 whenever p is between 0 and 1. Therefore, this formula correctly represents P(A').