PU PhD 2026 Question Paper Engineering Paper 1 Research Methodology

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PU PhD 2026
Question Paper ·
Engineering Paper 1
Research Methodology
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PU PhD 2026 Question Paper
SUBJECT

Engineering Paper 1 Research Methodology

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ag METHODOLOGY (COMMON)
RESEARCH

1. Which type of research is primarily concerned with discovering the "why" and "how"
of a phenomenon through in-depth understanding?
(A) Descriptive (B) Exploratory (C) Experimental (D) Quantitative
2. A "Hypothesis" is best defined as:
(A) A proven fact
(B) A tentative statement about the relationship between variables
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(C) The final conclusion of a study

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(D) A summary of the literature review
3.
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Which of the following is a prerequisite for starting research?
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(A) Having a large budget
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(B) Formulating a research problem
(C) Publishing a report
(D) Using SPSS software
4. The primary purpose of a "Review of Literature" is to:
(A) Increase the word count of the report
(B) Identify what is already known and identify gaps
(C) List the names of famous researchers
(D) Prove the researcher's hypothesis is correct
5. A "Population" in research refers to:
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(A) The total group of individuals the researcher is interested in
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(B) Only the people who answer a questionnaire

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(C) The group of researchers conducting the study
(D) A small subset of data
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6.
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Which sampling technique gives every member of the population an equal chance of
being selected?
(A) Convenience sampling (B) Purposive sampling
(C) Random sampling (D) Quota sampling
7. Which tool of data collection involves a face-to-face interaction between the researcher
and the participant?
(A) Questionnaire (B) Observation (C) Interview (D) Rating scale
8. "Tabulation" refers to:
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(A) Drawing a graph (B) Organizing data into rows and columns
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(C) Writing the final report (D) Testing a hypothesis

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9. Which of these is a measure of variability (dispersion)?

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(A) Mode (B) Standard Deviation

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(C) Mean (D) Median

a 10. In a Normal Probability Curve, the distribution is:
(A) Bi-modal (B) Highly skewed
(C) Symmetrical and bell-shaped (D) Flat-topped
11. "Kurtosis" is a measure of:
(A) The spread of data (B) The flatness or peakedness of a distribution
(C) The central point (D) The relationship between two variables
12. The process of applying findings from a sample to the entire population is called:

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(A) Tabulation (B) Interpretation (C) Generalization (D) Coding
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(1)

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PH.D. 2026 RESEARCH METHODOLOGY (COMMON)

13. Qualitative research focuses on
(A) Statistical significance
(B) Mean and Standard Deviation
(C) Meanings, experiences, and descriptions
(D) Large-scale surveys
14. In a perfectly normal distribution, which of the following is true?
(A) Mean > Median > Mode (B) Mean < Median < Mode
(C) Mean = Median = Mode (D) Mean is not equal to Median
15. A variable has a sample standard deviation of 12 and is measured for 36 independent
observations. Its standard error of the mean is:
(A) 0.33 (B) 2.00 (C) 6.00 (D) 72.00
16. A test has a population mean of 70 and standard deviation of 8. A participant obtains a
score of 76. What is the participant’s z-score?
(A) 0.50 (B) 0.75 (C) 1.25 (D) 1.50
17. Which sampling method is most appropriate when the population is geographically
dispersed, a complete list of individuals is unavailable, but a list of naturally occurring
institutions exists?
(A) Simple random sampling of individuals from a nonexistent list
(B) Cluster sampling of institutions followed by sampling within selected institutions
(C) Convenience sampling at one institution
(D) Snowball sampling of volunteers only
18. Which property of a measurement tool concerns whether it actually measures the
intended construct rather than a related but different construct?
(A) Reliability (B) Validity (C) Objectivity (D) Replicability
19. For a nominal variable with categories such as discipline, the most defensible measure
of central tendency is generally:
(A) Arithmetic mean (B) Median (C) Mode (D) Standard deviation
20. The "True Zero" property is a defining characteristic of which scale?
(A) Nominal (B) Ordinal (C) Interval (D) Ratio
21. Construct validity is primarily concerned with:
(A) Consistent results
(B) Measuring the intended theoretical concept
(C) Generalizability
(D) Sample size
22. The primary purpose of "Double-Blind" experimental design is to eliminate:
(A) Data loss (B) Researcher/Participant bias
(C) Statistical error (D) Sampling bias
23. A good research problem is feasible, significant, clear, and researchable. Which
proposed problem violates feasibility most directly?
(A) Estimating the association between sleep duration and academic performance among
500 undergraduates
(B) Exploring teachers’ experiences of implementing a new curriculum in three schools
(C) Determining the complete causal effect of every social, genetic, and environmental
factor on human intelligence
(D) Comparing two established instructional strategies using a pretest-posttest design.
(2)

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24. The primary purpose of a research proposal or synopsis is to:
(A) Present only the final statistical results
(B) Demonstrate the study’s rationale, questions, methods, feasibility, and anticipated
contribution before the research is conducted
(C) Replace the need for a literature review

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(D) Guarantee that the hypothesis will be supported
25.
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A dataset contains the values 2, 3, 4, 5, 100. Which statement is most accurate?
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(A) The mean is more resistant to the extreme value than the median
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(B) The median is 4 and is less affected by the extreme value than the mean
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(C) The mode must be 100
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(D) The range is unaffected by the extreme value
26. Two tests have standard deviations of 8 and 12, with means of 40 and 100, respectively.
Which test has greater relative variability based on coefficient of variation?
(A) Test 1, because its standard deviation is smaller in absolute units
(B) Test 2, because its standard deviation is larger in absolute units
(C) Test 1, because its coefficient of variation is 20% versus 12% for Test 2
(D) Both have identical relative variability

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27. A researcher copies several sentences from a source, changes a few words, omits the

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citation, and reports only analyses supporting the hypothesis. The conduct involves:

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(A) Acceptable paraphrasing and selective emphasis

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(B) Plagiarism and selective reporting, both of which undermine research integrity
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(C) Only a formatting error in the bibliography
(D) Replication and transparent reporting
28. In a composite index, Research Design has a weight of 0.60 and Statistical Reasoning
has a weight of 0.40. A candidate scores 40 and 70, respectively, on the two components.
What is the weighted score?
(A) 48 (B) 50 (C) 52 (D) 55
29. In a goodness-of-fit test with two categories, the observed frequencies are 30 and 20,
while the expected frequencies are 25 and 25. What is the chi-square statistic?

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(A) 0.20 (B) 1.00 (C) 2.00 (D) 5.00

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30. Holding the effect size and significance level constant, which change generally increases

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the statistical power of a test?

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(A) Reducing the sample size

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(B) Increasing measurement error

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(C) Increasing the sample size
(D) Replacing a directional hypothesis with a more conservative two-sided test in every
case
31. If A is a 3×3 matrix with det(A)=4, then det(adj A) equals
(A) 4 (B) 8 (C) 16 (D) 64
32. The system 𝐱 + 𝐲 + 𝐳 = 𝟑, 𝟐𝐱 + 𝟐𝐲 + 𝟐𝐳 = 𝟔, 𝟑𝐱 + 𝟑𝐲 + 𝟑𝐳 = 𝟗 has
(A) Infinitely many solutions (B) A unique solution

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(C) No solution (D) Exactly two solutions
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(3)

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PH.D. 2026 RESEARCH METHODOLOGY (COMMON)

33. The homogeneous system AX=0 in n unknowns has a non-trivial solution if and only if
(A) Rank(A) = n (B) Rank(A) < 𝑛 (C) Det(A) ≠ 0 (D) A is symmetric
𝟑)
34. A 3×3 matrix 𝐀 has eigenvalues 𝟏, 𝟐 and 𝟑. The value of 𝐝𝐞𝐭(𝐀 is
(A) 6 (B) 18 (C) 36 (D) 216
35. At 𝐱 = 𝟎, the function 𝐟(𝐱) = | 𝐱 | is
(A) Discontinuous (B) Continuous but not differentiable
(C) Differentiable (D) Neither continuous nor differentiable
𝝏(𝒙,𝒚)
36. For the transformation 𝐱 = 𝐫 𝐜𝐨𝐬𝛉, 𝐲 = 𝐫 𝐬𝐢𝐧𝛉, the Jacobian equals
𝝏(𝒓,𝜽)

(A) 1 (B) r (C) 𝑟 (D)
37. For 𝐟(𝐱, 𝐲), a stationary point is a saddle point when 𝐫𝐭 − 𝐬𝟐 is
(A) > 0 𝑤𝑖𝑡ℎ 𝑟 > 0 (B) > 0 𝑤𝑖𝑡ℎ 𝑟 < 0 (C ) <0 (D) = 0
𝟏
38. The sequence 𝒂𝒏 = , 𝒏 ∈ ℕ is
𝒏
(A) Increasing and bounded (B) Decreasing and bounded
(C) Increasing and unbounded (D) Neither increasing nor decreasing
𝟏
39. The series ∑𝒏 𝟏 converges if and only if
𝒏𝒑
(A) p ≤ 1 (B) p > 1 (C) p < 1 (D) p = 1
𝒙𝒏
40. The radius of convergence of the power series ∑𝒏 𝟎 is
𝒏!
(A) 0 (B) 1 (C) e (D) ∞
41. The equation 𝐌 𝐝𝐱 + 𝐍 𝐝𝐲 = 𝟎 is exact if
(A) = (B) = (C) =− (D) M = N
42. The particular integral of (𝑫𝟐 − 𝟒)𝒚 = 𝒆𝟐 𝒙 is
(A) 𝑒 (B) 𝑒 (C) 𝑒 (D) − 𝑒
𝒅𝟐 𝒚 𝒅𝒚
43. The Cauchy-Euler equation 𝒙𝟐 +𝒙 − 𝒚 = 𝟎 is reduced to a linear equation with
𝒅𝒙𝟐 𝒅𝒙
constant coefficients by the substitution
(A) y = e (B) x = z (C) y = v x (D) x = e
𝐧 ),
44. The Laplace transform 𝐋(𝐭 where 𝐧 is a positive integer equals
! ! ( )!
(A) (B) (C) (D)
𝟏
45. 𝑳 𝟏 equals
𝒔𝟐 𝟒

(A) sin 2t (B) cos 2t (C) 𝑐𝑜𝑠 2𝑡 (D) 𝑠𝑖𝑛 2𝑡
46. The sufficient conditions for a function to possess a Fourier series of 𝐟(𝐱) are known as
(A) Cauchy’s condition (B) Dirichlet’s conditions
(C) Lipschitz conditions (D) Euler’s conditions
𝟏
47. From the Fourier series of 𝐟(𝐱) = 𝐱 𝟐 on (−𝝅, 𝝅), the sum ∑𝒏 𝟏 𝟐 equals
𝒏

(A) (B) (C) (D)
(4)

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RESEARCH

48. The PDE obtained by eliminated the arbitrary constants 𝐚 and 𝐛 from
z = ax + by + ab is
(A) z = px + qy (B) z = px + qy + pq
(C) pq = z (D) z = px + qy +
49. The PDE obtained by eliminating the arbitrary function 𝐟 from 𝐳 = 𝐟(𝐱 𝟐 + 𝐲 𝟐 ) is

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(A) xp + yq = 0 (B) xp − yq = 0 (C) p + q = 0 (D) yp − x q = 0

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𝟐 𝟐

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50. A complete integral of 𝒑 + 𝒒 = 𝟏 is

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(A) z = ax + by + c (B) z = a(x + y) + c

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(C) z = x + y + (D) z = ax + √1 − a y + c
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a (ROUGH WORK)

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(5)

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PH.D. 2026 RESEARCH METHODOLOGY (COMMON)

(ROUGH WORK)

(6)

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