UGC NET Computer Science & Applications June 2026 Question PaperPaper 1 & Paper 2 with Answer Key

50 questions with the answer key and explanations.

1. Question 1

   If the total number of applications received in Jan 2025 were double the number of applications received in Feb 2025, then the applications received under the area 'Others' in Feb 2025 were how much percent of the applications received under the same area in Jan 2025?

   A firm provides consultancy in various areas — Education, Finance, Health, Social Media, Marriage and Others — on the basis of applications received. The table gives, for each area, the percentage of that month's applications during 2025. The total number of applications received during Feb 2025 was larger than the number received in Apr 2025, and the total received during Jan 2025 was larger than the number received in Mar 2025.

   Area (% of month)	Jan	Feb	Mar	Apr
   Education	38	33	19	17
   Finance	25	30	37	45
   Health	11	18	5	18
   Social Media	5	3	10	6
   Marriage	3	7	10	11
   Others	18	9	19	3
   Total	100%	100%	100%	100%

   1. A200%
   2. B100%
   3. C50%
   4. D25%

   Answer: (D) 25%

   Explanation

   Suppose the February total is F applications; then the January total is double, namely 2F. The area 'Others' accounts for eighteen percent of applications in January, which works out to 0.18 times 2F, that is 0.36F applications. In February 'Others' accounts for nine percent, which is 0.09F applications. Expressing the February figure as a fraction of the January figure gives 0.09F divided by 0.36F, which equals one quarter, or 25 percent.

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2. Question 2

   In which area was the percentage of applications continuously increasing over time but at a continuously decreasing rate?

   A firm provides consultancy in various areas — Education, Finance, Health, Social Media, Marriage and Others — on the basis of applications received. The table gives, for each area, the percentage of that month's applications during 2025. The total number of applications received during Feb 2025 was larger than the number received in Apr 2025, and the total received during Jan 2025 was larger than the number received in Mar 2025.

   Area (% of month)	Jan	Feb	Mar	Apr
   Education	38	33	19	17
   Finance	25	30	37	45
   Health	11	18	5	18
   Social Media	5	3	10	6
   Marriage	3	7	10	11
   Others	18	9	19	3
   Total	100%	100%	100%	100%

   1. AFinance
   2. BHealth
   3. CMarriage
   4. DOthers

   Answer: (C) Marriage

   Explanation

   Marriage moves 3 → 7 → 10 → 11, so it keeps rising while the increments shrink (4, 3, 1) — increasing at a decreasing rate. Finance rises 25 → 30 → 37 → 45 but its increments grow (5, 7, 8), and Health and Others are not monotonic.

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3. Question 3

   If in the area of 'Social Media' the number of applications received in Jan 2025 was equal to the number received in Mar 2025, then the total number of applications received in Mar 2025 was ______ of the total number of applications received in Jan 2025.

   A firm provides consultancy in various areas — Education, Finance, Health, Social Media, Marriage and Others — on the basis of applications received. The table gives, for each area, the percentage of that month's applications during 2025. The total number of applications received during Feb 2025 was larger than the number received in Apr 2025, and the total received during Jan 2025 was larger than the number received in Mar 2025.

   Area (% of month)	Jan	Feb	Mar	Apr
   Education	38	33	19	17
   Finance	25	30	37	45
   Health	11	18	5	18
   Social Media	5	3	10	6
   Marriage	3	7	10	11
   Others	18	9	19	3
   Total	100%	100%	100%	100%

   1. AExact Double
   2. BExact Half
   3. CMore than Half
   4. DLess than Half

   Answer: (B) Exact Half

   Explanation

   Social Media is 5% of the Jan total (J) and 10% of the Mar total (M). Equal counts give 0.05J = 0.10M, so M = 0.5J. The Mar total is therefore exactly half the Jan total.

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4. Question 4

   In the area of Health, the number of applications received in Feb 2025 as compared to Apr 2025 was:

   A firm provides consultancy in various areas — Education, Finance, Health, Social Media, Marriage and Others — on the basis of applications received. The table gives, for each area, the percentage of that month's applications during 2025. The total number of applications received during Feb 2025 was larger than the number received in Apr 2025, and the total received during Jan 2025 was larger than the number received in Mar 2025.

   Area (% of month)	Jan	Feb	Mar	Apr
   Education	38	33	19	17
   Finance	25	30	37	45
   Health	11	18	5	18
   Social Media	5	3	10	6
   Marriage	3	7	10	11
   Others	18	9	19	3
   Total	100%	100%	100%	100%

   1. AEqual
   2. BLarger
   3. CSmaller
   4. DCannot be determined

   Answer: (B) Larger

   Explanation

   Health is 18% in both Feb and Apr, so the Health count is 0.18 × (monthly total). Since the passage states the Feb total exceeds the Apr total, 0.18 × Feb-total > 0.18 × Apr-total, so the Feb Health figure is larger.

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5. Question 5

   If the total number of applications received in Feb 2025 was less than the number received in Jan 2025 but more than that of Mar 2025, then what will be the order of the months in terms of number of applications received?

   A firm provides consultancy in various areas — Education, Finance, Health, Social Media, Marriage and Others — on the basis of applications received. The table gives, for each area, the percentage of that month's applications during 2025. The total number of applications received during Feb 2025 was larger than the number received in Apr 2025, and the total received during Jan 2025 was larger than the number received in Mar 2025.

   Area (% of month)	Jan	Feb	Mar	Apr
   Education	38	33	19	17
   Finance	25	30	37	45
   Health	11	18	5	18
   Social Media	5	3	10	6
   Marriage	3	7	10	11
   Others	18	9	19	3
   Total	100%	100%	100%	100%

   1. AApr > Mar > Feb > Jan
   2. BJan > Feb > Mar > Apr
   3. CJan > Feb > Apr > Mar
   4. DCannot be determined

   Answer: (D) Cannot be determined

   Explanation

   We are given Jan > Feb > Mar. The passage also tells us Feb > Apr, so Apr is below Feb, but nothing fixes Apr relative to Mar — Apr could be above or below Mar. Both 'Jan > Feb > Mar > Apr' and 'Jan > Feb > Apr > Mar' remain possible, so the order cannot be determined.

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6. Question 6

   The UGC has given a 10-point scale for grading. Arrange the following grades from highest to lowest performance.
   A. F
   B. P
   C. O
   D. A
   E. Ab
   Choose the correct answer from the options given below:

   1. AB, A, D, E, C
   2. BC, D, B, A, E
   3. CA, D, C, B, E
   4. DE, A, B, D, C

   Answer: (B) C, D, B, A, E

   Explanation

   On the University Grants Commission letter-grade scale the grades run, from best to worst performance, Outstanding, then Excellent, then Very Good, then Good, then Average, then Pass, then Fail, and finally Absent. Among the grades listed here that ordering places Outstanding first, then grade A, then Pass, then Fail, then Absent. Matching those grades back to the given labels produces the sequence C, D, B, A, E, so the second option is correct.

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7. Question 7

   Which of the following, taken together, make a valid syllogism?
   A. Apples are not sweets.
   B. Some apples are sweets.
   C. All sweets are tasty.
   D. Some apples are not tasty.
   E. No apple is tasty.
   Choose the correct answer from the options given below:

   1. AB, D, C only
   2. BE, A, B only
   3. CC, E, A only
   4. DC, B, E only

   Answer: (C) C, E, A only

   Explanation

   Take 'All sweets are tasty' (C) and 'No apple is tasty' (E). If any apple were a sweet it would have to be tasty, contradicting E; hence no apple is a sweet, i.e. 'Apples are not sweets' (A). So C and E validly yield A. The other groupings mix particular and negative premises that do not produce a valid conclusion.

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8. Question 8

   Arrange the following in a meaningful order, from particular to general:
   A. Family
   B. Community
   C. Member
   D. Locality
   E. Country
   Choose the correct answer from the options given below:

   1. AA, B, C, D, E
   2. BB, C, A, E, D
   3. CC, A, B, D, E
   4. DE, D, C, A, B

   Answer: (C) C, A, B, D, E

   Explanation

   Moving from the most specific unit outward: a Member belongs to a Family, families form a Community, communities occupy a Locality, and localities together make up a Country — C, A, B, D, E.

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9. Question 9

   Arrange the following computers in chronological order:
   A. The Atanasoff Berry Computer (ABC)
   B. IBM-701
   C. The Mark I Computer
   D. UNIVAC I
   E. IBM-650
   Choose the correct answer from the options given below:

   1. AC, D, A, E, B
   2. BA, C, E, B, D
   3. CA, C, E, D, B
   4. DA, C, D, B, E

   Answer: (D) A, C, D, B, E

   Explanation

   The correct history is ABC (1942) → Mark I (1944) → UNIVAC I (1951) → IBM 701 (1952) → IBM 650 (1953–54), i.e. A, C, D, B, E. The printed options 1–3 did not contain this sequence, so option D has been editorially corrected to 'A, C, D, B, E' and is the intended key.

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10. Question 10

    Which of the following are used as Social Networking Sites?
    A. Twitter
    B. Instagram
    C. LinkedIn
    D. Blackbox
    E. Snapchat
    Choose the correct answer from the options given below:

    1. AA, B only
    2. BA, B, C only
    3. CA, B, C, D only
    4. DA, B, C, E only

    Answer: (D) A, B, C, E only

    Explanation

    Twitter, Instagram, LinkedIn and Snapchat are all social-networking platforms. 'Blackbox' is not a social network (the term refers to opaque systems / flight recorders), so the correct set is A, B, C, E.

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11. Question 11

    Select the characteristics of the Learner-Centred Approach.
    A. It is centred on the needs of the learner predecided by her parents.
    B. It lays emphasis on skills.
    C. It lays emphasis on indirect strategies.
    D. It is dependent on the training the teacher has gone through.
    E. It can be used in privately managed schools only.
    Choose the correct answer from the options given below:

    1. AA and E only
    2. BB and C only
    3. CD and E only
    4. DA, B, D and E only

    Answer: (B) B and C only

    Explanation

    A learner-centred approach builds on the learner's own needs and interests, emphasises skills and competencies (B) and uses indirect, facilitative strategies (C). It is not dictated by parents (A) or limited by teacher training (D), and it is not restricted to private schools (E).

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12. Question 12

    Working of the circulatory system of the human body is shown by a teacher on a screen. Such simulations have tremendous potential for instructional purposes. This aligns best with:

    1. AComputer-aided learning
    2. BActivity-based learning
    3. CPeer-tutoring
    4. DHeuristic learning

    Answer: (A) Computer-aided learning

    Explanation

    Using a screen-based simulation to demonstrate a process is a textbook case of computer-aided learning, where the computer delivers or models the content. Activity-based and heuristic learning need the learner's own hands-on inquiry, and peer-tutoring involves students teaching each other.

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13. Question 13

    The NPE 1986 envisaged setting up residential schools with the aim of providing excellence coupled with equity and social justice. This led to the establishment of:

    1. AKendriya Vidyalayas
    2. BNavyug Schools
    3. CNavodaya Vidyalayas
    4. DEklavya Residential Schools

    Answer: (C) Navodaya Vidyalayas

    Explanation

    Jawahar Navodaya Vidyalayas were created under the National Policy on Education 1986 as pace-setting residential schools for talented rural children, combining excellence with equity. Kendriya Vidyalayas predate 1986 and serve transferable central employees; Eklavya schools are for tribal students under a later scheme.

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14. Question 14

    A term drawn from theology, concerned with the theory and method of the interpretation of human action, is known as:

    1. ATheological reasoning
    2. BPhilosophy
    3. CGrounded theory
    4. DHermeneutics

    Answer: (D) Hermeneutics

    Explanation

    Hermeneutics originated as the discipline of interpreting scripture and was extended to the interpretation of texts and human action generally; it is a key interpretive paradigm in qualitative research. Grounded theory is a method of building theory from data, not an interpretive tradition.

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15. Question 15

    Select the correct number sequences from the following:
    A. 5, 7, 13, 25, 45, 75
    B. 17, 40, 109, 224, 385
    C. 4, 11, 19, 41, 79, 169
    D. 3, 2, 0, -9, -52, -280
    E. 4, 13, 31, 67, 139, 280
    Choose the correct answer from the options given below:

    1. AB, C only
    2. BA, B only
    3. CA, C only
    4. DD, E only

    Answer: (B) A, B only

    Explanation

    Series A has first differences 2, 6, 12, 20, 30 whose second differences are a constant 2, so it follows a consistent rule. Series B has first differences 23, 69, 115, 161 with a constant second difference of 46. Series C, D and E break their own patterns, so only A and B are consistent sequences.

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16. Question 16

    Select the correct statements in the context of communication models.
    A. Feedback is the transmission of the receiver's reaction back to the sender.
    B. Encoding is the task/process done at the receiver's end.
    C. Noise is anything added to the signal between transmission and reception that is not intended by the source.
    D. Decoding is the task/process done at the sender's end.
    E. Medium is the means through which the message is conveyed.
    Choose the correct answer from the options given below:

    1. AC, D & E only
    2. BB, D & E only
    3. CA, B & C only
    4. DA, C & E only

    Answer: (D) A, C & E only

    Explanation

    Feedback is the receiver's response sent back to the sender (A, true), noise is unintended interference added in the channel (C, true) and the medium carries the message (E, true). Encoding is done by the sender and decoding by the receiver, so B and D are false. The correct set A, C & E was not among the printed choices, so option D has been editorially corrected to 'A, C & E only' and is the intended key.

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17. Question 17

    The ability to access, analyze, evaluate and communicate media messages is:

    1. ANarrative Setting
    2. BPropaganda
    3. CMedia literacy
    4. DMedia hype

    Answer: (C) Media literacy

    Explanation

    Media literacy is standardly defined as the ability to access, analyse, evaluate and create/communicate messages across media. Propaganda and media hype are types of persuasive content, not a competency.

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18. Question 18

    Match List-I with List-II.
    Choose the correct answer from the options:

    List-I (Letter series)	List-II (Missing letter)
    A. Q, N, K, H, E, ? B. O, B, L, ?, I, D, F, E, C C. Z, U, Q, N, L, ? D. A, C, ?, G, I	I. C II. K III. B IV. E

    1. AA-I, B-II, C-III, D-IV
    2. BA-III, B-I, C-IV, D-II
    3. CA-I, B-II, C-IV, D-III
    4. DA-III, B-I, C-II, D-IV

    Answer: (D) A-III, B-I, C-II, D-IV

    Explanation

    A: Q, N, K, H, E step down by 3, so the missing term is B (III). C: Z, U, Q, N, L decrease by 5, 4, 3, 2, so the next is K (II). D: A, C, ?, G, I step up by 2, giving E (IV). B resolves to the missing letter C (I). Hence A-III, B-I, C-II, D-IV.

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19. Question 19

    A computer costs 50,000 rupees and a printer costs 20,000 rupees. In a sale the price of the computer is reduced by 17% and that of the printer by x%. If a person purchased both the printer and the computer for a total of 50,000 rupees, then the value of x is:

    1. A57.5
    2. B52.5
    3. C33
    4. D66

    Answer: (A) 57.5

    Explanation

    Reducing the computer price by seventeen percent leaves eighty-three percent of fifty thousand, which is forty-one thousand five hundred rupees. Since the person spends fifty thousand rupees altogether, the amount left for the printer is fifty thousand minus forty-one thousand five hundred, that is eight thousand five hundred rupees. The printer originally cost twenty thousand, so the reduction is eleven thousand five hundred rupees, and dividing that reduction by the original twenty thousand gives zero point five seven five, meaning the printer discount x equals fifty-seven point five percent.

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20. Question 20

    Arrange the following steps in the process of deduction:
    A. Theory
    B. Hypothesis
    C. Data collection
    D. Revision of theory
    E. Findings
    Choose the correct answer from the options given below:

    1. AA, B, C, E, D
    2. BB, C, D, A, E
    3. CE, B, C, A, D
    4. DA, E, B, C, D

    Answer: (A) A, B, C, E, D

    Explanation

    Deductive research starts from an existing Theory, derives a testable Hypothesis, then moves to Data collection, produces Findings, and finally leads to Revision of the theory — A, B, C, E, D.

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21. Question 21

    Select the correct statements pertaining to NEP 2020.
    A. It promotes secular and minorities education vehemently.
    B. It promotes multiple-entry–multiple-exit in higher education.
    C. It recommends that the state must spend 10 percent of GDP on education.
    D. It affirms that Sanskrit has more literature than Latin and Persian.
    E. It promotes private philanthropic education.
    Choose the correct answer from the options given below:

    1. AA, B and C
    2. BC and D
    3. CB, D and E
    4. DA and E

    Answer: (C) B, D and E

    Explanation

    NEP 2020 introduces multiple entry and exit points in higher education (B), states that Sanskrit literature is larger than that of Latin and Greek/Persian (D), and encourages private philanthropic participation in education (E). It recommends 6% of GDP (not 10%), so C is wrong, and it does not frame itself in the terms of statement A.

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22. Question 22

    Match List-I with List-II.
    Choose the correct answer from the options:

    List-I (Broken Rule)	List-II (Associated Fallacy)
    A. Middle term undistributed in the premises. B. Presence of two negative premises in an argument. C. Particular conclusion with negative premises. D. Any term distributed in the conclusion but undistributed in the premises.	I. Existential Fallacy II. Fallacy of illicit major and minor term III. Exclusive premises IV. Undistributed Middle

    1. AA-I, B-II, C-III, D-IV
    2. BA-II, B-I, C-IV, D-III
    3. CA-IV, B-II, C-III, D-I
    4. DA-IV, B-III, C-I, D-II

    Answer: (D) A-IV, B-III, C-I, D-II

    Explanation

    An undistributed middle term is the fallacy of Undistributed Middle (IV). Two negative premises is the fallacy of Exclusive Premises (III). Drawing a particular conclusion where the premise structure does not support existence is the Existential Fallacy (I). A term distributed in the conclusion but not in the premises is the fallacy of illicit major/minor term (II). Hence A-IV, B-III, C-I, D-II.

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23. Question 23

    SSD stands for:

    1. ASolid State Disk
    2. BSerial State Disk
    3. CSolid Stage Disk
    4. DSerial Stage Disk

    Answer: (A) Solid State Disk

    Explanation

    SSD stands for Solid State Disk (also called Solid State Drive) — storage built from flash memory with no moving parts, unlike a magnetic hard disk.

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24. Question 24

    Planning teaching involves making decisions. Which of the following decisions reflects this dictum?

    1. ASelection of the profession
    2. BContent selection and pedagogical methods
    3. CSelection of the course for admission
    4. DPlanning to migrate abroad

    Answer: (B) Content selection and pedagogical methods

    Explanation

    Instructional planning is about decisions internal to teaching — what content to teach and which methods and materials to use. Choosing a profession, a course, or migration are personal career decisions, not part of planning a lesson.

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25. Question 25

    Per- and Polyfluorinated alkyl substances are called 'Forever Chemicals' because they are highly persistent. They can be found in:
    A. Paper and cardboard food packaging
    B. Textiles
    C. DDT
    D. Cosmetics
    E. Nuclear industry waste
    Choose the correct answer from the options given below:

    1. AA, B, C only
    2. BA, B, D only
    3. CB, C, D only
    4. DB, C, E only

    Answer: (B) A, B, D only

    Explanation

    PFAS are used for their water- and grease-repellent properties in food packaging (A), stain-resistant textiles (B) and cosmetics (D). DDT is an organochlorine pesticide, and nuclear waste is a radiological problem — neither is a PFAS source.

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26. Question 26

    Arrange the following chronologically:
    A. University of Bombay, Calcutta and Madras
    B. University Grants Commission
    C. Panjab University, Lahore
    D. Banaras Hindu University
    E. University of Delhi
    Choose the correct answer from the options given below:

    1. AB, A, C, D, E
    2. BA, C, D, E, B
    3. CD, E, C, B, A
    4. DA, B, C, D, E

    Answer: (B) A, C, D, E, B

    Explanation

    The three presidency universities were founded in 1857, Panjab University in 1882, Banaras Hindu University in 1916, the University of Delhi in 1922, and the UGC was set up in 1953 (statutory 1956) — order A, C, D, E, B.

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27. Question 27

    Match List-I with List-II.
    Choose the correct answer from the options:

    List-I	List-II (Interval)
    A. All real x satisfying (4x + 1) < 13 and (x + 1) > 3 B. All real x satisfying 1 ≤ (x² + 1) < 5 C. All real x satisfying (x + 7) < (3x + 1) < (x + 9) D. All real x satisfying 5 < (4x − 15) < 9	I. (5, 6) II. (3, 4) III. (2, 3) IV. (−2, 2)

    1. AA-III, B-IV, C-II, D-I
    2. BA-I, B-II, C-III, D-IV
    3. CA-II, B-I, C-III, D-IV
    4. DA-IV, B-III, C-I, D-II

    Answer: (A) A-III, B-IV, C-II, D-I

    Explanation

    For item A, the first inequality gives x less than three and the second gives x greater than two, so the solution interval is from two to three, which is option three. For item B, subtracting one throughout leaves x squared between zero and four, so x lies between minus two and two, which is option four. For item C, the left comparison gives x greater than three and the right comparison gives x less than four, so the interval is from three to four, which is option two. For item D, adding fifteen and dividing by four gives x between five and six, which is option one. Hence the matching is A-III, B-IV, C-II, D-I.

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28. Question 28

    As per Maslow's hierarchy of needs, arrange the following needs from basic to self-fulfilment needs (bottom to top):
    A. Self actualization
    B. Physiological needs
    C. Belongingness and love needs
    D. Safety needs
    E. Esteem needs
    Choose the correct answer from the options given below:

    1. AB, D, C, E, A
    2. BB, C, E, A, D
    3. CA, B, D, C, E
    4. DC, A, B, D, E

    Answer: (A) B, D, C, E, A

    Explanation

    Maslow's pyramid rises Physiological → Safety → Belongingness and love → Esteem → Self-actualization, which maps to B, D, C, E, A.

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29. Question 29

    Match List-I with List-II.
    Choose the correct answer from the options:

    List-I (Actor)	List-II (Film)
    A. Tom Hanks B. Guru Dutt C. Tom Cruise D. Leonardo DiCaprio	I. Titanic II. Forrest Gump III. Pyaasa IV. Mission: Impossible

    1. AA-IV, B-III, C-I, D-II
    2. BA-I, B-III, C-II, D-IV
    3. CA-II, B-III, C-IV, D-I
    4. DA-III, B-IV, C-I, D-II

    Answer: (C) A-II, B-III, C-IV, D-I

    Explanation

    Tom Hanks starred in Forrest Gump (II), Guru Dutt in Pyaasa (III), Tom Cruise in the Mission: Impossible series (IV), and Leonardo DiCaprio in Titanic (I) — A-II, B-III, C-IV, D-I.

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30. Question 30

    Arrange the following industrial sources of noise in descending order of their noise level (in dB):
    A. Steel plate riveting
    B. High-speed drill
    C. Circular saw
    D. Farm tractor
    E. Milling machine
    Choose the correct answer from the options given below:

    1. AB, A, D, C, E
    2. BA, C, D, E, B
    3. CD, B, A, E, C
    4. DC, D, E, B, A

    Answer: (A) B, A, D, C, E

    Explanation

    By typical measured sound-pressure levels the loudest is the high-speed drill, followed by steel plate riveting, the farm tractor, the circular saw and then the milling machine — B, A, D, C, E.

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31. Question 31

    Match List-I with List-II.
    Choose the correct answer from the options:

    List-I (Institution)	List-II (Known for)
    A. Nalanda B. Ujjain C. Takshashila D. Vallabhi	I. Medicine and Arts II. Hinayana Buddhism III. Mahayana Buddhism and Secular Studies IV. Physics and Astronomy

    1. AA-II, B-I, C-III, D-IV
    2. BA-I, B-II, C-IV, D-III
    3. CA-IV, B-III, C-I, D-II
    4. DA-III, B-IV, C-I, D-II

    Answer: (D) A-III, B-IV, C-I, D-II

    Explanation

    Nalanda was renowned for Mahayana Buddhism and secular studies (III), Ujjain for physics and astronomy (IV), Takshashila for medicine and the arts (I), and Vallabhi for Hinayana Buddhism (II) — A-III, B-IV, C-I, D-II.

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32. Question 32

    Arrange the following in increasing order.
    A. True discount on a present worth of 5000 for 4 months at 9% per annum
    B. True discount on a present worth of 8000 for 3 months at 8% per annum
    C. True discount on a present worth of 6000 for 6 months at 6% per annum
    D. True discount on a present worth of 7000 for 4 months at 7% per annum
    E. True discount on a present worth of 9000 for 6 months at 5% per annum
    Choose the correct answer from the options given below:

    1. AC < A < D < B < E
    2. BA < B < D < E < C
    3. CB < A < D < C < E
    4. DA < B < D < C < E

    Answer: (D) A < B < D < C < E

    Explanation

    True discount on present worth = PW × rate × time. A = 5000 × 0.09 × 4/12 = 150; B = 8000 × 0.08 × 3/12 = 160; D = 7000 × 0.07 × 4/12 ≈ 163.3; C = 6000 × 0.06 × 6/12 = 180; E = 9000 × 0.05 × 6/12 = 225. Increasing order: A < B < D < C < E.

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33. Question 33

    'A break in the chronology of a narrative in which events from the past are disclosed to the reader, listener or viewer and which have a bearing on the present situation' can be easily noticed in cinema. What is this style called?

    1. AFlash forward
    2. BFlash folk
    3. CFlashback
    4. DFlak

    Answer: (C) Flashback

    Explanation

    Interrupting the present narrative to show earlier events that bear on the current situation is a flashback. A flash-forward does the opposite — it jumps ahead to future events.

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34. Question 34

    Match List-I with List-II.
    Choose the correct answer from the options:

    List-I (Fuel Alcohol)	List-II (Characteristic)
    A. Methanol B. Ethanol C. Gasohol D. Butanol	I. Mixture of ethanol and gasoline II. High energy content III. Produced by bacterial anaerobic digestion IV. Can be derived from potato waste

    1. AA-I, B-II, C-IV, D-III
    2. BA-II, B-IV, C-I, D-III
    3. CA-II, B-III, C-IV, D-I
    4. DA-III, B-IV, C-I, D-II

    Answer: (B) A-II, B-IV, C-I, D-III

    Explanation

    Methanol has a high energy content relative to other fuel alcohols (II), ethanol can be produced from potato waste and other biomass (IV), gasohol is a blend of ethanol and gasoline (I), and butanol can be obtained by bacterial anaerobic digestion (III) — A-II, B-IV, C-I, D-III.

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35. Question 35

    Match List-I with List-II.
    Choose the correct answer from the options:

    List-I (Scheme / Institution)	List-II (Function)
    A. Rashtriya Avishkar Abhiyan B. e-Pathshala C. NAS D. NTSE	I. Identification of talented students II. Assessment of learning outcomes III. To promote scientific temper and innovation IV. Digital access to textbooks and resources

    1. AA-III, B-IV, C-II, D-I
    2. BA-IV, B-III, C-I, D-II
    3. CA-II, B-I, C-IV, D-III
    4. DA-I, B-II, C-III, D-IV

    Answer: (A) A-III, B-IV, C-II, D-I

    Explanation

    Rashtriya Avishkar Abhiyan promotes scientific temper and innovation (III), e-Pathshala provides digital access to textbooks and resources (IV), the National Achievement Survey assesses learning outcomes (II), and the NTSE identifies talented students (I) — A-III, B-IV, C-II, D-I.

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36. Question 36

    Match List-I with List-II.
    Choose the correct answer from the options:

    List-I (Approach of Scale Construction)	List-II (Process Followed)
    A. Arbitrary approach B. Factor Scales C. Consensus approach D. Cumulative Scales	I. A panel evaluates the items chosen for inclusion in the instrument according to their relevance II. Scale is developed on an ad hoc basis III. Intercorrelation of items which indicates that a common factor accounts for the relationship between items IV. Chosen on the basis of their conforming to some ranking of items with ascending or descending discriminating power

    1. AA-III, B-II, C-I, D-IV
    2. BA-II, B-III, C-I, D-IV
    3. CA-II, B-III, C-IV, D-I
    4. DA-III, B-II, C-IV, D-I

    Answer: (B) A-II, B-III, C-I, D-IV

    Explanation

    In the arbitrary approach the scale is built on an ad hoc basis (II). Factor scales are derived from the intercorrelation of items reflecting a common factor (III). In the consensus approach a panel judges the relevance of items for inclusion (I). Cumulative (Guttman-type) scales order items by ascending or descending discriminating power (IV) — A-II, B-III, C-I, D-IV.

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37. Question 37

    E-learning strategies are supported by:
    A. Virtual Classroom
    B. TCP/IP
    C. Instant messaging
    D. Satellite classroom
    E. Web casting
    Choose the correct answer from the options given below:

    1. AA, B, C only
    2. BC, D, E only
    3. CA, C, E only
    4. DA, D, C only

    Answer: (C) A, C, E only

    Explanation

    Virtual classrooms, instant messaging and web casting are instructional strategies for delivering e-learning. TCP/IP is the underlying network protocol (infrastructure, not a strategy) and a satellite classroom is a transmission arrangement rather than an e-learning strategy, so the answer is A, C, E only.

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38. Question 38

    Arrange the following United Nations conferences/conventions according to the year they were held:
    A. The Stockholm Conference
    B. The Kyoto Protocol
    C. The Montreal Protocol
    D. The Vienna Convention for the Protection of the Ozone Layer
    E. The Convention on Biological Diversity
    Choose the correct answer from the options given below:

    1. AA, B, C, D, E
    2. BA, C, E, D, B
    3. CA, D, C, E, B
    4. DA, E, B, C, D

    Answer: (C) A, D, C, E, B

    Explanation

    Chronology: Stockholm Conference (1972), Vienna Convention (1985), Montreal Protocol (1987), Convention on Biological Diversity (1992) and Kyoto Protocol (1997) — A, D, C, E, B.

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39. Question 39

    Arrange the steps of research sequentially:
    A. Writing report
    B. Data analysis
    C. Review of literature
    D. Choice of research design
    E. Sampling and data collection
    Choose the correct answer from the options given below:

    1. AE, D, A, C, B
    2. BB, A, D, C, E
    3. CE, B, D, C, A
    4. DC, D, E, B, A

    Answer: (D) C, D, E, B, A

    Explanation

    A research study proceeds Review of literature → Choice of research design → Sampling and data collection → Data analysis → Writing report — C, D, E, B, A.

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40. Question 40

    The difference in sea-surface temperature between one location in the Western Indian Ocean and one location in the Eastern Indian Ocean is called:

    1. AIndian Ocean Dipole
    2. BIndian Ocean Oscillation
    3. CEl Nino Southern Oscillation
    4. DMadden-Julian Oscillation

    Answer: (A) Indian Ocean Dipole

    Explanation

    The Indian Ocean Dipole (IOD) is defined by the gradient in sea-surface temperature between the western and eastern tropical Indian Ocean. ENSO is a Pacific phenomenon and the Madden-Julian Oscillation is an eastward-moving tropical convection pulse.

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41. Question 41

    Which of the following Pramanas (valid means of knowledge) are accepted by the Nyaya school of philosophy?

    1. APratyaksha and Anumana only
    2. BAnumana and Verbal Testimony (Shabda) only
    3. CPratyaksha and Upamana only
    4. DPratyaksha, Anumana, Verbal Testimony (Shabda) and Upamana

    Answer: (D) Pratyaksha, Anumana, Verbal Testimony (Shabda) and Upamana

    Explanation

    Nyaya accepts four pramanas: Pratyaksha (perception), Anumana (inference), Upamana (comparison) and Shabda (verbal testimony). Schools such as Charvaka accept only perception; the fuller list of six belongs to Advaita Vedanta.

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42. Question 42

    In the first figure, which are the valid moods?
    A. AAA
    B. AEE
    C. EAE
    D. AOO
    E. EIO
    Choose the correct answer from the options given below:

    1. AA, C, E only
    2. BB, A, C only
    3. CD, B, A only
    4. DE, A, B only

    Answer: (A) A, C, E only

    Explanation

    The valid moods of the first figure are AAA (Barbara), EAE (Celarent), AII (Darii) and EIO (Ferio). From the given list that is A, C and E. AEE and AOO are not valid in the first figure.

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43. Question 43

    Match List-I with List-II.
    Choose the correct answer from the options:

    List-I (Teaching Model)	List-II (Feature)
    A. Personal Basis Model B. Social Interaction Model C. Behaviour Altering Model D. Information Development Model	I. Working in a group II. Teacher as the main figure in class III. Memorization, practice and transfer of learning IV. Instruction based on human relations

    1. AA-I, B-IV, C-II, D-III
    2. BA-IV, B-I, C-II, D-III
    3. CA-IV, B-III, C-I, D-II
    4. DA-I, B-III, C-II, D-IV

    Answer: (B) A-IV, B-I, C-II, D-III

    Explanation

    The Personal Basis (personal source) model is built on human relations and the learner's self (IV). The Social Interaction model centres on working in a group (I). Behaviour-altering models place the teacher/environment as the controlling figure that shapes responses (II). Information-development (information-processing) models stress memorization, practice and transfer of learning (III) — A-IV, B-I, C-II, D-III.

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44. Question 44

    Which of the following are methods of control of intervening variables?
    A. Deductive manipulation
    B. Inferential manipulation
    C. Statistical manipulation
    D. Physical manipulation
    E. Selective manipulation
    Choose the correct answer from the options given below:

    1. AA, B, C only
    2. BB, C, D only
    3. CC, D, E only
    4. DE, A, B only

    Answer: (C) C, D, E only

    Explanation

    Extraneous or intervening variables are controlled by physical manipulation (holding conditions constant / randomisation), selective manipulation (choosing or matching cases) and statistical manipulation (partialling out effects through analysis). 'Deductive' and 'inferential' manipulation are not recognised control techniques, so the answer is C, D, E only.

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45. Question 45

    Match List-I with List-II.
    Choose the correct answer from the options:

    List-I (Concept)	List-II (Feature)
    A. Algorithm B. Modem C. Bandwidth D. Flowchart	I. Range of frequencies over which signals are transmitted II. Converts digital signals to sine waves and vice-versa III. Pictorial representation of a computational procedure IV. Finite sequence to solve a problem

    1. AA-IV, B-I, C-II, D-III
    2. BA-IV, B-II, C-I, D-III
    3. CA-II, B-IV, C-III, D-I
    4. DA-II, B-III, C-IV, D-I

    Answer: (B) A-IV, B-II, C-I, D-III

    Explanation

    An algorithm is a finite sequence of steps to solve a problem (IV). A modem converts digital signals to analog (sine) waves and back (II). Bandwidth is the range of frequencies over which signals are transmitted (I). A flowchart is a pictorial representation of a computational procedure (III) — A-IV, B-II, C-I, D-III.

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46. Question 46

    As per the passage, disability can be done away with by:

    Perhaps the best known of these sociologists is Oliver (1990), who argues that the biomedical model of disability leads to what he calls an ideology of personal tragedy which stresses the need for the individual disabled person to come to terms with 'their' problem, by struggling to cope as best they can.

    Oliver calls this the personal tragedy model because it tends to describe disability as some terrible personal problem, which has ruined that person's life. He suggests that this model has now become taken for granted, achieving 'ideological hegemony' in the way that disabled people are viewed.

    In place of the individualistic or personal tragedy model, Oliver argues that disability should be seen as a social problem and that it can only be understood within a wider social and economic framework, that is, within a social model.

    Oliver argues that a clear distinction can be made between impairment and disability. A person may have a physical impairment of some kind, but it only becomes a disability when society organises social and economic features in such a way as to translate the impairment into a disability. For example, if the only means to enter a cinema is by using steps, then a person who has an impairment which leads them to use a wheelchair becomes disabled. However, if a ramp is provided and the ticket booth is at a lower height, and adequate spaces are provided for wheelchair users, then the person is no longer disabled. So, disability derives from organising society in such a way as to change impairment into disability.

    1. AGiving adequate medical treatment to everyone.
    2. BReorganizing society to facilitate access of all social space to the impaired.
    3. CRe-orienting disabled persons.
    4. DRe-orienting parents to prevent the birth of disabled children.

    Answer: (B) Reorganizing society to facilitate access of all social space to the impaired.

    Explanation

    Oliver's social model holds that disability is produced when society is organised so that impaired people cannot use social spaces; therefore removing those barriers — ramps, lower counters, adequate space — removes the disability. Medical treatment (A) and 're-orienting' disabled persons or parents (C, D) target the individual, which is exactly the personal-tragedy view Oliver rejects.

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47. Question 47

    According to the passage, Oliver rebuts the personal tragedy model because:

    Perhaps the best known of these sociologists is Oliver (1990), who argues that the biomedical model of disability leads to what he calls an ideology of personal tragedy which stresses the need for the individual disabled person to come to terms with 'their' problem, by struggling to cope as best they can.

    Oliver calls this the personal tragedy model because it tends to describe disability as some terrible personal problem, which has ruined that person's life. He suggests that this model has now become taken for granted, achieving 'ideological hegemony' in the way that disabled people are viewed.

    In place of the individualistic or personal tragedy model, Oliver argues that disability should be seen as a social problem and that it can only be understood within a wider social and economic framework, that is, within a social model.

    Oliver argues that a clear distinction can be made between impairment and disability. A person may have a physical impairment of some kind, but it only becomes a disability when society organises social and economic features in such a way as to translate the impairment into a disability. For example, if the only means to enter a cinema is by using steps, then a person who has an impairment which leads them to use a wheelchair becomes disabled. However, if a ramp is provided and the ticket booth is at a lower height, and adequate spaces are provided for wheelchair users, then the person is no longer disabled. So, disability derives from organising society in such a way as to change impairment into disability.

    1. AIt is an accident that makes one impaired, not a wilful choice.
    2. BIn society, disability is a taboo.
    3. CIt sees disability as an individualistic problem that disrupts one's life.
    4. DIt is not the willingness of God to make someone disabled.

    Answer: (C) It sees disability as an individualistic problem that disrupts one's life.

    Explanation

    The passage says the personal tragedy model 'tends to describe disability as some terrible personal problem, which has ruined that person's life' and stresses that the individual must cope alone. Oliver objects precisely to this individualistic framing; the other options are not the reason given in the text.

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48. Question 48

    According to the passage, society organizes social and economic features in such a way that:

    Perhaps the best known of these sociologists is Oliver (1990), who argues that the biomedical model of disability leads to what he calls an ideology of personal tragedy which stresses the need for the individual disabled person to come to terms with 'their' problem, by struggling to cope as best they can.

    Oliver calls this the personal tragedy model because it tends to describe disability as some terrible personal problem, which has ruined that person's life. He suggests that this model has now become taken for granted, achieving 'ideological hegemony' in the way that disabled people are viewed.

    In place of the individualistic or personal tragedy model, Oliver argues that disability should be seen as a social problem and that it can only be understood within a wider social and economic framework, that is, within a social model.

    Oliver argues that a clear distinction can be made between impairment and disability. A person may have a physical impairment of some kind, but it only becomes a disability when society organises social and economic features in such a way as to translate the impairment into a disability. For example, if the only means to enter a cinema is by using steps, then a person who has an impairment which leads them to use a wheelchair becomes disabled. However, if a ramp is provided and the ticket booth is at a lower height, and adequate spaces are provided for wheelchair users, then the person is no longer disabled. So, disability derives from organising society in such a way as to change impairment into disability.

    1. AEnabled-bodied are more intelligent citizens.
    2. BImpairment translates into quality of social adjustment of everyone.
    3. CAccessing social space becomes a challenge for the impaired.
    4. DImpaired people must be provided everything within their residence.

    Answer: (C) Accessing social space becomes a challenge for the impaired.

    Explanation

    The cinema example shows that when the only entrance is by steps, a person using a wheelchair is excluded — society's arrangement of space turns the impairment into a barrier to accessing social space. The passage does not claim anything about intelligence or confining impaired people to their homes.

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49. Question 49

    According to the passage, the clear distinction between impairment and disability is:

    Perhaps the best known of these sociologists is Oliver (1990), who argues that the biomedical model of disability leads to what he calls an ideology of personal tragedy which stresses the need for the individual disabled person to come to terms with 'their' problem, by struggling to cope as best they can.

    Oliver calls this the personal tragedy model because it tends to describe disability as some terrible personal problem, which has ruined that person's life. He suggests that this model has now become taken for granted, achieving 'ideological hegemony' in the way that disabled people are viewed.

    In place of the individualistic or personal tragedy model, Oliver argues that disability should be seen as a social problem and that it can only be understood within a wider social and economic framework, that is, within a social model.

    Oliver argues that a clear distinction can be made between impairment and disability. A person may have a physical impairment of some kind, but it only becomes a disability when society organises social and economic features in such a way as to translate the impairment into a disability. For example, if the only means to enter a cinema is by using steps, then a person who has an impairment which leads them to use a wheelchair becomes disabled. However, if a ramp is provided and the ticket booth is at a lower height, and adequate spaces are provided for wheelchair users, then the person is no longer disabled. So, disability derives from organising society in such a way as to change impairment into disability.

    1. AImpairment is physical whereas disability is a mental problem.
    2. BImpairment is personal whereas disability is social.
    3. CImpairment can be treated medically and disability cannot be cured.
    4. DImpairment is inaccessibility to social spaces whereas disability is fair access to every social space.

    Answer: (B) Impairment is personal whereas disability is social.

    Explanation

    Oliver draws the line between a bodily impairment a person has and the disability that society creates when it organises social and economic life so as to translate that impairment into exclusion. So impairment is personal/bodily while disability is socially produced.

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50. Question 50

    According to the passage, Oliver argues that disability is a social problem because:

    Perhaps the best known of these sociologists is Oliver (1990), who argues that the biomedical model of disability leads to what he calls an ideology of personal tragedy which stresses the need for the individual disabled person to come to terms with 'their' problem, by struggling to cope as best they can.

    Oliver calls this the personal tragedy model because it tends to describe disability as some terrible personal problem, which has ruined that person's life. He suggests that this model has now become taken for granted, achieving 'ideological hegemony' in the way that disabled people are viewed.

    In place of the individualistic or personal tragedy model, Oliver argues that disability should be seen as a social problem and that it can only be understood within a wider social and economic framework, that is, within a social model.

    Oliver argues that a clear distinction can be made between impairment and disability. A person may have a physical impairment of some kind, but it only becomes a disability when society organises social and economic features in such a way as to translate the impairment into a disability. For example, if the only means to enter a cinema is by using steps, then a person who has an impairment which leads them to use a wheelchair becomes disabled. However, if a ramp is provided and the ticket booth is at a lower height, and adequate spaces are provided for wheelchair users, then the person is no longer disabled. So, disability derives from organising society in such a way as to change impairment into disability.

    1. AIt is a divine curse to be suffered by the society.
    2. BPhysical impairment translates into disability due to social and economic structures.
    3. CIndividual as a part of society has gone through personal tragedy.
    4. DImpairment and disability are one and the same.

    Answer: (B) Physical impairment translates into disability due to social and economic structures.

    Explanation

    Oliver insists disability 'can only be understood within a wider social and economic framework' — it is the way society organises social and economic features that converts an impairment into a disability. Option C restates the personal-tragedy view he rejects, and option D denies the impairment/disability distinction he insists on.

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100 questions with the answer key and explanations.

1. Question 1

   Match List-I with List-II.

   List-I	List-II
   A. Pivot point B. Fixed point C. Mirror image D. Distortion	I. Reflection II. Shear III. Rotation IV. Scaling

   1. AA-III, B-IV, C-I, D-II
   2. BA-III, B-IV, C-II, D-I
   3. CA-IV, B-III, C-II, D-I
   4. DA-I, B-II, C-III, D-IV

   Answer: (A) A-III, B-IV, C-I, D-II

   Explanation

   A pivot point remains fixed during rotation, a fixed point is associated with scaling, a mirror image is produced by reflection, and shear produces distortion. Therefore the matching is A-III, B-IV, C-I, D-II.

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2. Question 2

   How many edges are there in a graph with 10 vertices, each of degree six?

   1. A60
   2. B45
   3. C20
   4. D30

   Answer: (D) 30

   Explanation

   By the handshaking lemma, the sum of degrees equals twice the number of edges. The degree sum is 10 × 6 = 60, so the graph has 60/2 = 30 edges. Taking 60 itself would confuse the degree sum with the edge count.

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3. Question 3

   Which of the following have true value when the universe of discourse is all integers?

   A. ∃n (2n = 3n)
   B. ∃n (n² > n)
   C. ∀n (2n > n)
   D. ∃n (n² = 2)
   E. ∀x∀y ∃z (xy = z)

   1. AB, C and E only
   2. BA, B and E only
   3. CA, B, C and D only
   4. DB, C, D and E only

   Answer: (B) A, B and E only

   Explanation

   A is true at n = 0, and B is true, for example at n = 2. C fails at negative integers, D is false because √2 is not an integer, and E is true because the product of any two integers is an integer. Hence A, B and E are true.

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4. Question 4

   Arrange the following in the correct order in the context of the OSI model, from bottom to top.

   A. Network layer
   B. Physical layer
   C. Presentation layer
   D. Data link layer
   E. Application layer

   1. AD, A, C, B, E
   2. BA, C, E, B, D
   3. CB, D, A, C, E
   4. DC, A, B, E, D

   Answer: (C) B, D, A, C, E

   Explanation

   The OSI stack rises from Physical to Data Link to Network to Presentation to Application. Replacing these with the supplied letters gives B, D, A, C, E.

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5. Question 5

   Which topology requires a central controller or a hub?

   1. ABus
   2. BStar
   3. CMesh
   4. DRing

   Answer: (B) Star

   Explanation

   A star topology connects every device to a central hub or switch. Bus and ring topologies use a shared backbone or loop, while a mesh uses multiple direct links.

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6. Question 6

   Match List-I with List-II.

   List-I	List-II
   A. Wait-for graph B. Precedence graph C. Rigorous 2PL D. Strict 2PL	I. Holds all locks until it commits II. Holds write-locks until it commits III. Used to check deadlocks IV. Used to check serializability

   1. AA-III, B-IV, C-I, D-II
   2. BA-III, B-IV, C-II, D-I
   3. CA-IV, B-I, C-II, D-III
   4. DA-IV, B-III, C-II, D-I

   Answer: (B) A-III, B-IV, C-II, D-I

   Explanation

   A wait-for graph is used to detect deadlocks, and a precedence graph is used to test serializability. Rigorous 2PL retains all locks until commit, whereas strict 2PL retains write locks until commit.

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7. Question 7

   Match List-I with List-II.

   List-I: SMTP response code	List-II: Description
   A. 214 B. 421 C. 220 D. 554	I. Service ready II. Transaction failed III. Help message IV. Service not available

   1. AA-III, B-IV, C-I, D-II
   2. BA-IV, B-III, C-I, D-II
   3. CA-IV, B-I, C-III, D-II
   4. DA-II, B-I, C-IV, D-III

   Answer: (A) A-III, B-IV, C-I, D-II

   Explanation

   SMTP code 214 is a help message, 421 means service not available, 220 means service ready, and 554 indicates a transaction failed. These pairings produce A-III, B-IV, C-I, D-II.

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8. Question 8

   Identify the incorrect statements about protocols used in the TCP/IP protocol suite.

   A. IP is a reliable connectionless protocol.
   B. ARP finds a node's physical address from its logical address.
   C. ICMP sends notification of datagram problems to the recipient of the message.
   D. IGMP facilitates simultaneous transmission of a message to a group of recipients.

   1. AB and D only
   2. BD only
   3. CA and C only
   4. DA, C and D only

   Answer: (C) A and C only

   Explanation

   IP is connectionless but does not provide reliable delivery, so A is incorrect. ICMP reports errors to the sender/source, not the recipient, so C is incorrect. ARP and IGMP are correctly described.

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9. Question 9

   Which technology enables the creation of virtual servers in a cloud-computing environment?

   1. ADNS server
   2. BHypervisor
   3. CFirewall
   4. DLoad balancer

   Answer: (B) Hypervisor

   Explanation

   A hypervisor abstracts physical hardware so that several isolated virtual machines can run on a host. DNS, firewalls, and load balancers serve different network or traffic-management roles.

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10. Question 10

    Which document outlines the functional and non-functional requirements of a software system?

    1. ASRS document
    2. BDesign document
    3. CTest plan
    4. DUser manual

    Answer: (A) SRS document

    Explanation

    A Software Requirements Specification defines what the system must do and the quality constraints it must meet. Design documents describe implementation choices, while test plans and manuals serve later purposes.

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11. Question 11

    What does Amdahl's Law describe in the context of parallel processing?

    1. AMaximum speedup achievable, considering serial and parallel portions of a program
    2. BEfficiency of message passing in a distributed-memory system
    3. CComputational efficiency of a parallel algorithm
    4. DReliability of a fault-tolerant system

    Answer: (A) Maximum speedup achievable, considering serial and parallel portions of a program

    Explanation

    Amdahl's Law bounds the speedup obtainable by parallelisation using the fraction that remains serial. Even infinitely fast parallel work cannot remove the serial bottleneck.

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12. Question 12

    Arrange the following in terms of capacity from smallest to largest.

    A. L3 cache
    B. L1 cache
    C. CPU register
    D. L2 cache

    1. AC, D, B, A
    2. BC, A, B, D
    3. CC, B, D, A
    4. DA, C, D, B

    Answer: (C) C, B, D, A

    Explanation

    Registers are the smallest storage locations, followed by L1 cache, then L2 cache, and then the larger L3 cache. Thus the increasing-capacity sequence is C, B, D, A.

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13. Question 13

    Let ⟨H₁, *⟩ and ⟨H₂, *⟩ be subgroups of the group ⟨G, *⟩. Which statement is false?

    1. AH₁H₂ = {h₁ * h₂ : h₁ ∈ H₁ and h₂ ∈ H₂} is a subgroup.
    2. BH₁H₂ is a normal subgroup when H₁ and H₂ are normal subgroups.
    3. C⟨H₁ ∩ H₂, *⟩ is a subgroup.
    4. DThe set difference H₁ − H₂ is a subgroup.

    Answer: (A) H₁H₂ = {h₁ * h₂ : h₁ ∈ H₁ and h₂ ∈ H₂} is a subgroup.

    Explanation

    The supplied source confirms option A as the false statement. The product set H₁H₂ need not be a subgroup unless additional conditions, such as normality of one factor, hold. Intersections of subgroups are always subgroups.

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14. Question 14

    Which field deals with interaction between computers and humans using natural language?

    1. APROLOG
    2. BELIZA
    3. CNLP
    4. DLISP

    Answer: (C) NLP

    Explanation

    Natural Language Processing (NLP) is the AI field concerned with computer processing and generation of human language. PROLOG and LISP are programming languages, while ELIZA is an early NLP-style program rather than the name of the field.

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15. Question 15

    In rate-monotonic scheduling, a task has a period of 80 ms and an execution time of 55 ms. What are its processor utilisation and task rate?

    1. A0.69, 12.5 Hz
    2. B0.58, 12.3 Hz
    3. C0.48, 11.4 Hz
    4. D0.38, 10.5 Hz

    Answer: (A) 0.69, 12.5 Hz

    Explanation

    Utilisation is execution time divided by period: 55/80 = 0.6875, approximately 0.69. The task rate is 1/0.08 seconds = 12.5 Hz. The other rates do not correspond to an 80 ms period.

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16. Question 16

    What is the correct sequence of the database-design process?

    A. Create conceptual schema
    B. Data model mapping
    C. Requirements collection and analysis
    D. Physical design

    1. AC, A, B, D
    2. BC, B, A, D
    3. CA, B, C, D
    4. DA, C, B, D

    Answer: (A) C, A, B, D

    Explanation

    Database design starts by collecting and analysing requirements. It then develops a conceptual schema, maps that conceptual model to the selected data model, and finally performs physical design. Therefore the order is C, A, B, D.

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17. Question 17

    Choose the correct bottom-to-top order in the OSI model.

    A. Transforming datagrams into frames for transmission
    B. Transmission of bits over a communication channel
    C. Handling the user interface
    D. Control and monitoring of the subnet
    E. Transmission using a connection-oriented or connectionless protocol

    1. AA, B, C, D, E
    2. BB, C, D, E, A
    3. CB, A, D, E, C
    4. DA, B, D, E, C

    Answer: (C) B, A, D, E, C

    Explanation

    Physical-layer work is B, data-link framing is A, network-layer subnet control is D, transport-layer service is E, and user-facing handling is C. This gives B, A, D, E, C.

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18. Question 18

    Given Pred(x) = x − 1 and T(x, y + 1) = Pred(T(x, y)), with T(x, 0) = x, which operation is a candidate for T?

    1. ASubtraction operation
    2. BAddition operation
    3. CMultiplication operation
    4. DDivision operation

    Answer: (A) Subtraction operation

    Explanation

    The recurrence applies the predecessor operation once for every increment of y. Thus T(x, y) = x − y, which is subtraction; addition would instead require a successor operation.

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19. Question 19

    For relation schema r(M, Y, P, MP, C), the functional dependencies are M → MP, {M, Y} → P, and MP → C. Which is a key?

    1. AM
    2. B{M, Y}
    3. C{M, C}
    4. DMP

    Answer: (B) {M, Y}

    Explanation

    From M, we obtain MP and then C, but not Y or P. Adding Y allows {M, Y} → P, so the closure of {M, Y} contains every attribute. Neither M nor MP supplies Y and P, making {M, Y} the key.

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20. Question 20

    Which item is a problem in piggybacking acknowledgement frames?

    A. There is no need to send separate acknowledgement frames.
    B. It requires more bandwidth.
    C. The data-link layer must decide how long to wait for a packet to which the acknowledgement can be attached.
    D. The number of acknowledgement frames decreases.

    1. AA and D only
    2. BB only
    3. CB and C only
    4. DC only

    Answer: (D) C only

    Explanation

    Piggybacking reduces separate acknowledgement frames and saves bandwidth, so A and D are benefits and B is false. Its drawback is deciding how long to delay an acknowledgement while waiting for outgoing data; that is C only.

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21. Question 21

    What is the maximum number of nodes that can be inserted in the AVL tree without changing its height?

    

    AVL tree with nodes 60, 50, 70, and 80.

    1. A2
    2. B4
    3. C3
    4. D5

    Answer: (C) 3

    Explanation

    The displayed tree has height 2 and currently contains 4 nodes. A binary tree of height 2 can contain at most 2³ − 1 = 7 nodes, so 7 − 4 = 3 additional nodes can be inserted without increasing its height.

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22. Question 22

    Each relation is defined on {1, 2, 3, 4}. Match List-I with List-II.

    List-I: Relation	List-II: Relation type
    A. {(2,2), (2,3), (2,4), (3,2), (3,3), (3,4)} B. {(2,4), (4,2)} C. {(1,2), (2,3), (3,4)} D. {(1,3), (1,4), (2,3), (2,4), (3,1), (3,4)}	I. Antisymmetric II. Only transitive III. Only symmetric IV. Neither symmetric nor transitive

    1. AA-II, B-III, C-I, D-IV
    2. BA-II, B-III, C-IV, D-I
    3. CA-IV, B-III, C-I, D-II
    4. DA-I, B-III, C-IV, D-II

    Answer: (A) A-II, B-III, C-I, D-IV

    Explanation

    A is transitive: its chained pairs such as (2,3) and (3,4) require (2,4), which is present, but it is not symmetric. B contains both (2,4) and (4,2), making it only symmetric. C has no reversed distinct pair, so it is antisymmetric, while D has neither property. Hence A-II, B-III, C-I, D-IV is the required match.

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23. Question 23

    Match List-I with List-II.

    List-I	List-II
    A. Macros B. Assembler C. Loader D. Compiler	I. Converts high-level code to object (machine) code II. Used for code expansion III. Used to translate assembly-language code to object code IV. Used to allocate memory and relocate a program in memory

    1. AA-IV, B-III, C-I, D-II
    2. BA-II, B-III, C-I, D-IV
    3. CA-II, B-III, C-IV, D-I
    4. DA-IV, B-I, C-III, D-II

    Answer: (C) A-II, B-III, C-IV, D-I

    Explanation

    A macro is used for code expansion, an assembler translates assembly language to object code, a loader allocates memory and relocates a program, and a compiler translates high-level code. Therefore A-II, B-III, C-IV, D-I is correct.

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24. Question 24

    How many solutions does x + y + z = 11 have, where x, y, and z are non-negative integers?

    1. A33
    2. B66
    3. C68
    4. D78

    Answer: (D) 78

    Explanation

    By stars and bars, the number of non-negative solutions to x + y + z = 11 is C(11 + 3 − 1, 3 − 1) = C(13, 2) = 78. This counts every allocation of 11 identical units among the three variables.

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25. Question 25

    Out of 32 people, 30 save paper and 14 save plastic bottles. If every person saves paper, plastic bottles, or both, how many save both?

    1. A12
    2. B14
    3. C16
    4. D18

    Answer: (A) 12

    Explanation

    Use inclusion–exclusion: |paper ∩ plastic| = |paper| + |plastic| − |paper ∪ plastic| = 30 + 14 − 32 = 12. Adding the two group totals without subtracting the overlap would double-count those 12 people.

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26. Question 26

    Arrange these language families from specialization to generalization.

    A. All regular languages
    B. All Turing-acceptable languages
    C. All Turing-decidable languages
    D. All context-free languages

    1. AA, B, C, D
    2. BA, C, B, D
    3. CA, D, C, B
    4. DA, D, B, C

    Answer: (C) A, D, C, B

    Explanation

    Every regular language is context-free; every context-free language is decidable; and every decidable language is Turing-acceptable (recursively enumerable). The inclusions therefore grow as A, D, C, B.

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27. Question 27

    What is the maximum Hamming distance among all pairs of the following binary codes?

    Code	Binary value
    C₁	00000
    C₂	01011
    C₃	10101

    1. A2
    2. B3
    3. C4
    4. D5

    Answer: (C) 4

    Explanation

    C₁ and C₂ differ in three positions, C₁ and C₃ differ in three positions, while C₂ = 01011 and C₃ = 10101 differ in four positions. Thus the maximum pairwise Hamming distance is 4.

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28. Question 28

    Which is not a concern during the management of a software project?

    1. AProject/product information
    2. BProduct quality
    3. CTime
    4. DMoney

    Answer: (B) Product quality

    Explanation

    The project-management concerns in this classification are information, time, and money. Product quality is an outcome/quality attribute managed through engineering and quality assurance, rather than one of those named management concerns.

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29. Question 29

    Which relational-algebra expression is equivalent to the SQL query SELECT X FROM B WHERE Y?

    1. Aσᵧ(πₓ(B))
    2. Bπᵧ(σₓ(B))
    3. Cσₓ(πₓ(B))
    4. Dπₓ(σᵧ(B))

    Answer: (D) πₓ(σᵧ(B))

    Explanation

    The WHERE predicate is applied first, so σᵧ selects from relation B. The SELECT list is then applied, so πₓ projects attribute X. Reversing that order can discard the attribute needed by the selection.

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30. Question 30

    Which of the following are true?

    A. A database may have only one primary key.
    B. Every key is a candidate key.
    C. There can be multiple candidate keys.
    D. There can be more than one superkey.
    E. Every candidate key is a primary key.

    1. AA, C, D only
    2. BA, D, E only
    3. CB, C, D only
    4. DB, D, E only

    Answer: (A) A, C, D only

    Explanation

    A relation design chooses one candidate key as its primary key, but may have several candidate keys and many superkeys. A superkey need not be minimal, so B is false; only the selected candidate key is primary, so E is false.

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31. Question 31

    Match List-I with List-II.

    List-I	List-II
    A. Commutative law B. Distributive law C. De Morgan law D. Absorption law	I. P ∧ (Q ∨ R) ≡ (P ∧ Q) ∨ (P ∧ R) II. P ∧ (P ∨ Q) ≡ P III. P ∧ Q ≡ Q ∧ P IV. ¬(P ∨ Q) ≡ ¬P ∧ ¬Q

    1. AA-III, B-IV, C-II, D-I
    2. BA-II, B-I, C-IV, D-III
    3. CA-III, B-I, C-IV, D-II
    4. DA-IV, B-II, C-III, D-I

    Answer: (C) A-III, B-I, C-IV, D-II

    Explanation

    Commutativity is P ∧ Q ≡ Q ∧ P (III). Distribution is P ∧ (Q ∨ R) ≡ (P ∧ Q) ∨ (P ∧ R) (I), De Morgan's law is ¬(P ∨ Q) ≡ ¬P ∧ ¬Q (IV), and absorption is P ∧ (P ∨ Q) ≡ P (II). Thus the apparently similar formulas in I and II must not be swapped: I expands a conjunction while II removes a redundant disjunction.

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32. Question 32

    Match List-I with List-II.

    List-I	List-II
    A. Merge sort B. Binary search C. Quick sort D. Search in an unsorted array	I. n² II. n log n III. n IV. log n

    1. AA-I, B-IV, C-II, D-III
    2. BA-I, B-II, C-III, D-IV
    3. CA-II, B-I, C-III, D-IV
    4. DA-II, B-IV, C-I, D-III

    Answer: (D) A-II, B-IV, C-I, D-III

    Explanation

    Merge sort has O(n log n) complexity, binary search has O(log n), quicksort has O(n²) in the worst case, and searching an unsorted array has O(n). This produces A-II, B-IV, C-I, D-III.

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33. Question 33

    Which of the following statements is incorrect?

    1. AFor a context-free grammar G and string x, membership x ∈ L(G) can be decided in polynomial time.
    2. BIf L is context-free, then its complement is also context-free.
    3. CThe language {aⁿbᵐcᵖ : m, n, p ≥ 0, m ≠ n or m ≠ p} is not deterministic context-free.
    4. DThe class of deterministic context-free languages is closed under intersection.

    Answer: (B) If L is context-free, then its complement is also context-free.

    Explanation

    The supplied source confirms option B as the intended incorrect statement: context-free languages are not closed under complement. The paper designates B as the single answer for this MCQ.

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34. Question 34

    For sending input I₆ to the output line of an 8×1 multiplexer, which selection-line combination is required?

    1. A001
    2. B100
    3. C110
    4. D111

    Answer: (C) 110

    Explanation

    An 8-to-1 multiplexer uses three select bits to encode the input index in binary. Since 6 in binary is 110, the select lines S₂S₁S₀ must be 110; 111 would instead select I₇.

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35. Question 35

    Arrange these C++ data types in non-decreasing order of representation length.

    A. char
    B. int
    C. float
    D. double

    1. AB, A, C, D
    2. BA, B, D, C
    3. CD, C, B, A
    4. DA, B, C, D

    Answer: (D) A, B, C, D

    Explanation

    A char uses the least storage, followed by int; float is normally smaller than double. Hence the non-decreasing order is char, int, float, double: A, B, C, D.

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36. Question 36

    The number of leaf nodes in a full 4-ary rooted tree with n nodes is:

    1. An/2
    2. B(2n − 1)/4
    3. C(n + 1)/4
    4. D(3n + 1)/4

    Answer: (D) (3n + 1)/4

    Explanation

    If I is the number of internal nodes, a full 4-ary tree has n = 4I + 1. Its leaves are L = n − I = 3I + 1 = (3n + 1)/4. The other formulas do not satisfy this relation for a full 4-ary tree.

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37. Question 37

    Match List-I with List-II.

    List-I: Process model	List-II: Characteristic
    A. Classical waterfall model B. Prototype model C. Evolutionary model D. Spiral model	I. Risk analysis II. Large problem with incremental delivery III. Clear requirements IV. Requirements are not well understood

    1. AA-I, B-III, C-II, D-IV
    2. BA-III, B-IV, C-II, D-I
    3. CA-II, B-III, C-IV, D-I
    4. DA-IV, B-I, C-III, D-II

    Answer: (B) A-III, B-IV, C-II, D-I

    Explanation

    The classical waterfall model assumes clear requirements. A prototype is suited to poorly understood requirements, an evolutionary model supports incremental delivery, and the spiral model centres on risk analysis. Thus the matching is A-III, B-IV, C-II, D-I.

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38. Question 38

    Match List-I with List-II.

    List-I	List-II
    A. Latency B. Delay C. Throughput D. Interrupt	I. Number of tasks completed in a given time period II. Causes the current activity to be deferred III. Time elapsed before next activity starts IV. Time to complete a single task

    1. AA-I, B-III, C-II, D-IV
    2. BA-III, B-IV, C-I, D-II
    3. CA-IV, B-II, C-III, D-I
    4. DA-IV, B-III, C-I, D-II

    Answer: (D) A-IV, B-III, C-I, D-II

    Explanation

    Latency is the time to complete one task, delay is the time before the next activity starts, throughput is the number of tasks completed per time period, and an interrupt defers the current activity. This gives A-IV, B-III, C-I, D-II.

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39. Question 39

    Match List-I with List-II.

    List-I	List-II
    A. long signed int B. double C. long double D. unsigned character	I. %lf II. %Lf III. %c IV. %ld

    1. AA-II, B-I, C-IV, D-III
    2. BA-IV, B-I, C-II, D-III
    3. CA-III, B-I, C-II, D-IV
    4. DA-I, B-II, C-IV, D-III

    Answer: (B) A-IV, B-I, C-II, D-III

    Explanation

    A long signed int uses %ld, double uses %lf, long double uses %Lf, and an unsigned character is read or printed with %c. Hence the matching is A-IV, B-I, C-II, D-III.

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40. Question 40

    Match List-I with List-II.

    List-I: Language	List-II: Type
    A. L₁ = {aⁿbᵐ | n, m ≥ 0} B. L₂ = {aⁿbᵐ | n = m ≥ 0} C. L₃ = {aⁿbⁿcⁿdⁿeⁿ | n ≥ 1} D. L₄ = {aⁿbᵐcᵐdⁿe² | n, m ≥ 0}	I. Unrestricted II. Context sensitive III. Regular IV. Context free

    1. AA-III, B-I, C-II, D-IV
    2. BA-III, B-IV, C-I, D-II
    3. CA-III, B-II, C-IV, D-I
    4. DA-II, B-III, C-IV, D-I

    Answer: (B) A-III, B-IV, C-I, D-II

    Explanation

    The supplied source annotation designates option B, A-III, B-IV, C-I, D-II, as the intended key. The language definitions are retained exactly as printed so learners can compare the paper's classification convention with the formal language hierarchy.

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41. Question 41

    The term "double buffered" is used in which of the following?

    1. ASynchronous communication interface
    2. BAsynchronous communication interface
    3. CAddressing mode
    4. DSerial communication

    Answer: (B) Asynchronous communication interface

    Explanation

    Double buffering permits one buffer to be filled while another is consumed, helping asynchronous producer and consumer rates operate smoothly. It is not an addressing mode, and serial communication by itself does not define double buffering.

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42. Question 42

    To define the relationship between two entity sets, which operation can be used?

    1. AConcatenation
    2. BAddition
    3. CCartesian product
    4. DUnion

    Answer: (C) Cartesian product

    Explanation

    A relationship set is formally a subset of the Cartesian product of participating entity sets. Concatenation, addition, and union do not construct tuples across the two sets in this way.

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43. Question 43

    What is the output of this C program?

    #include <stdio.h>
    int main() {
    int i;
    for (i = 0; i++ < 10;)
    printf("%d", i++);
    return 0;
    }

    1. A0123456789
    2. B12345678
    3. C13579
    4. D2468

    Answer: (C) 13579

    Explanation

    Each loop test increments i once, and printf prints i before incrementing it again. The printed values are therefore 1, 3, 5, 7, and 9; the next condition sees 10 and terminates the loop.

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44. Question 44

    For disk tracks numbered 0–49, the head starts at 15 and requests arrive for 4, 40, 11, 35, 7, and 14. Order these algorithms by total head movement in ascending order, assuming initial movement toward higher-numbered tracks when required.

    A. FCFS
    B. LOOK
    C. SSTF
    D. SCAN

    1. AC, B, D, A
    2. BB, A, C, D
    3. CC, D, B, A
    4. DD, B, C, A

    Answer: (A) C, B, D, A

    Explanation

    SSTF travels 47 tracks, LOOK travels 61, SCAN travels 79, and FCFS travels 135. Thus the ascending order is SSTF, LOOK, SCAN, FCFS: C, B, D, A.

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45. Question 45

    For the primal program max cᵀx subject to Ax ≤ b, which stated dual program is true?

    1. Amin bᵀy subject to Aᵀy ≤ c, y ≥ 0
    2. Bmin bᵀy subject to Aᵀy ≥ c, y ≥ 0
    3. Cmin bᵀy subject to Aᵀy = c, y ≥ 0
    4. Dmax bᵀy subject to Aᵀy = c

    Answer: (C) min bᵀy subject to Aᵀy = c, y ≥ 0

    Explanation

    The paper uses the equality-form dual: minimise bᵀy subject to Aᵀy = c and y ≥ 0. Under that convention, option C is the stated dual program.

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46. Question 46

    Choose the right sequence of stages for data transmission using CSMA/CD.

    A. If the channel is clear, the sender sends data.
    B. The sender senses the channel for activity.
    C. The sender waits for a random back-off time before retransmitting.
    D. Collision detection occurs if two devices transmit at the same time.

    1. AA, B, D, C
    2. BB, A, D, C
    3. CB, A, C, D
    4. DC, B, A, D

    Answer: (B) B, A, D, C

    Explanation

    CSMA/CD first senses the medium, then transmits if it is idle. A collision may be detected during transmission, after which a random back-off precedes retransmission. This is B, A, D, C.

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47. Question 47

    Arrange these numbers in ascending order by the number of distinct prime factors.

    A. 729
    B. 1001
    C. 1111
    D. 420

    1. AA, C, B, D
    2. BD, A, B, C
    3. CA, B, C, D
    4. DD, A, C, B

    Answer: (A) A, C, B, D

    Explanation

    Factor each number and count unique primes, not repeated powers: 729 = 3⁶ has 1; 1111 = 11 × 101 has 2; 1001 = 7 × 11 × 13 has 3; and 420 = 2² × 3 × 5 × 7 has 4. Sorting those counts from 1 to 4 gives A, C, B, D.

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48. Question 48

    A problem of size n requires n² bit operations. What is the largest instance that can be solved in one second if each bit operation takes 10⁻⁹ second?

    1. A10⁹
    2. B3.16 × 10⁴
    3. C3.96 × 10⁷
    4. D2 × 10⁹

    Answer: (B) 3.16 × 10⁴

    Explanation

    One second permits 10⁹ operations. Solving n² = 10⁹ gives n = √10⁹ ≈ 3.16 × 10⁴. The larger choices confuse the operation budget with the square root of that budget.

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49. Question 49

    Match List-I with List-II.

    List-I	List-II
    A. Disk scheduling B. Batch processing C. Time sharing D. Interrupt processing	I. Round robin II. SCAN III. LIFO IV. FIFO

    1. AA-III, B-IV, C-II, D-I
    2. BA-IV, B-III, C-II, D-I
    3. CA-II, B-IV, C-I, D-III
    4. DA-II, B-I, C-IV, D-III

    Answer: (C) A-II, B-IV, C-I, D-III

    Explanation

    Disk scheduling uses SCAN, batch processing is handled in FIFO order, time sharing uses round robin, and interrupt processing uses LIFO nesting. Therefore the match is A-II, B-IV, C-I, D-III.

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50. Question 50

    Classifying email as spam, labeling web pages by context, and voice recognition are examples of which approach?

    1. AReinforcement learning
    2. BShortest-path algorithm
    3. CSupervised learning
    4. DUnsupervised learning

    Answer: (C) Supervised learning

    Explanation

    These tasks learn from examples with known labels, such as spam/not spam or a known spoken word. That is supervised learning; unsupervised learning has no target labels, while reinforcement learning optimises rewards through interaction.

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51. Question 51

    Match List-I with List-II.

    A. Stack
    B. Queue
    C. Linked list
    D. Binary search tree

    List-I	List-II
    A. Stack B. Queue C. Linked list D. Binary search tree	I. FIFO II. LIFO III. Ordered children IV. Sequentially linked dynamic nodes

    1. AA-IV, B-I, C-II, D-III
    2. BA-II, B-I, C-IV, D-III
    3. CA-III, B-IV, C-I, D-II
    4. DA-II, B-I, C-III, D-IV

    Answer: (B) A-II, B-I, C-IV, D-III

    Explanation

    A stack follows LIFO (II), a queue follows FIFO (I), a linked list has dynamically sized sequentially linked nodes (IV), and a binary search tree has ordered child nodes (III). Hence A-II, B-I, C-IV, D-III.

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52. Question 52

    The combination of selection lines for sending input I₁₄ to the output in the shown 64 × 1 multiplexer is:

    

    64 × 1 multiplexer selection-line diagram.

    1. A001111
    2. B110000
    3. C111100
    4. D001110

    Answer: (D) 001110

    Explanation

    A 64-to-1 multiplexer needs six selection bits. The binary representation of input index 14 is 001110, so S₅…S₀ must be 001110; the other choices represent input indices 15, 48, and 60.

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53. Question 53

    Match List-I with List-II.

    List-I	List-II
    A. SMTP	I. Network layer
    B. UDP	II. Transport layer
    C. Ethernet	III. Application layer
    D. IP	IV. Data-link layer

    1. AA-I, B-II, C-III, D-IV
    2. BA-III, B-II, C-IV, D-I
    3. CA-II, B-II, C-IV, D-I
    4. DA-I, B-III, C-IV, D-II

    Answer: (B) A-III, B-II, C-IV, D-I

    Explanation

    SMTP is an application-layer protocol, UDP is transport-layer, Ethernet is data-link-layer, and IP is network-layer. Thus the match is A-III, B-II, C-IV, D-I.

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54. Question 54

    For the shown neural network, what are the net input yᵢₙ and final threshold output y?

    

    Neural-network inputs, weights, bias, and threshold function.

    1. Ayᵢₙ = 2.03, y = 1
    2. Byᵢₙ = 1.53, y = 1
    3. Cyᵢₙ = 1.07, y = 1
    4. Dyᵢₙ = 0.57, y = 0

    Answer: (C) yᵢₙ = 1.07, y = 1

    Explanation

    Using the diagram values, yᵢₙ = (0.5×0.5) + (0.6×−0.8) + (0.8×1) + 0.5 = 1.07. Since the threshold function returns 1 for an input at least 1, y = 1; the alternatives use an incorrect sign, omit a term, or put the total below the threshold.

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55. Question 55

    Match List-I with List-II.

    A. FDM
    B. Digital circuits
    C. A two-variable function
    D. J-K flip-flop

    List-I	List-II
    A. FDM B. Digital circuits C. Two-variable function D. J-K flip-flop	I. Four minterms II. Frequency Division Multiplexing III. Universal flip-flop IV. Combinational or sequential

    1. AA-II, B-I, C-IV, D-III
    2. BA-II, B-IV, C-I, D-III
    3. CA-II, B-III, C-I, D-IV
    4. DA-II, B-I, C-III, D-IV

    Answer: (B) A-II, B-IV, C-I, D-III

    Explanation

    FDM means frequency-division multiplexing (II). Digital circuits may be combinational or sequential (IV), a two-variable Boolean function has four minterms (I), and the J-K flip-flop is universal (III).

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56. Question 56

    The number of pixel columns divided by the number of scan lines displayed by a system is called:

    1. APixmap
    2. BBitmap
    3. CAspect ratio
    4. DDepth

    Answer: (C) Aspect ratio

    Explanation

    Aspect ratio is the ratio of horizontal pixels (or columns) to vertical scan lines. A bitmap/pixmap is an image representation, while depth refers to bits per pixel.

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57. Question 57

    Which is not part of the general activation record of a procedure?

    1. ALocal data
    2. BGlobal data
    3. CAccess link
    4. DTemporaries

    Answer: (B) Global data

    Explanation

    An activation record stores data associated with one invocation: local variables, temporary values, and links for non-local access. Global data has program-wide lifetime and is not stored in each procedure activation record.

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58. Question 58

    The number of vertices of odd degree in any graph is:

    1. AOdd
    2. BEven
    3. Cn − e
    4. DPrime

    Answer: (B) Even

    Explanation

    By the handshaking lemma, the sum of all vertex degrees equals 2e and is even. An even sum can contain only an even number of odd summands, so odd-degree vertices occur in pairs.

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59. Question 59

    Match List-I with List-II.

    A. Waterfall model
    B. Agile methodology
    C. Test-driven development
    D. Continuous integration

    List-I	List-II
    A. Waterfall B. Agile C. TDD D. CI	I. Collaboration/release feedback II. Automated integration III. Fixed sequential steps IV. Tests before code

    1. AA-III, B-I, C-II, D-IV
    2. BA-II, B-I, C-IV, D-II
    3. CA-I, B-III, C-II, D-IV
    4. DA-III, B-I, C-IV, D-II

    Answer: (D) A-III, B-I, C-IV, D-II

    Explanation

    Waterfall is sequential fixed stages (III), Agile uses iterative collaboration and feedback (I), TDD writes tests before implementation (IV), and continuous integration uses frequent integration and automated testing (II).

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60. Question 60

    In the worst case, the smallest number of comparisons required by a comparison-based sorting algorithm is:

    1. A⌈log n⌉
    2. B⌈log₂(n!)⌉
    3. C⌈log n(n − 1)⌉
    4. Dn

    Answer: (B) ⌈log₂(n!)⌉

    Explanation

    A comparison sort must distinguish among n! possible input orders. Its decision tree therefore needs at least n! leaves, so its worst-case height is at least ⌈log₂(n!)⌉ comparisons.

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61. Question 61

    A single bit travels at 3 × 10⁸ m/s through a 12,000 km fibre-optic cable. What is its one-way propagation delay?

    1. A20 ms
    2. B5 ms
    3. C50 ms
    4. D40 ms

    Answer: (D) 40 ms

    Explanation

    Convert 12,000 km to 1.2 × 10⁷ m. Divide distance by the stated speed: (1.2 × 10⁷)/(3 × 10⁸) = 0.04 seconds. Multiplying by 1,000 converts this to 40 ms, so option D is correct; 20 ms and 5 ms result from incorrect unit conversion or arithmetic.

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62. Question 62

    Which statements about UDP are true?

    A. It is called Uniform Data Protocol.
    B. It is called User Datagram Protocol.
    C. It belongs to the Transport layer.
    D. It belongs to the Network layer.

    1. AA and C only
    2. BB and C only
    3. CA and D only
    4. DB and D only

    Answer: (B) B and C only

    Explanation

    UDP expands to User Datagram Protocol and operates at the transport layer. IP is a network-layer protocol; “Uniform Data Protocol” is not UDP’s expansion.

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63. Question 63

    Match the equivalent propositions in List-I and List-II.

    List-I	List-II
    A. P → (Q → P) B. P → (Q ∨ R) C. (P → Q) ∧ (R → Q) D. ¬(P ⇔ Q)	I. (P ∨ Q) ∧ ¬(P ∧ Q) II. (P ∨ R) → Q III. (P → Q) ∨ (P → R) IV. ¬P → (P → Q)

    1. AA-IV, B-II, C-III, D-I
    2. BA-IV, B-III, C-II, D-I
    3. CA-I, B-II, C-III, D-IV
    4. DA-I, B-III, C-II, D-IV

    Answer: (B) A-IV, B-III, C-II, D-I

    Explanation

    For A, Q → P is ¬Q ∨ P, so P → (Q → P) is ¬P ∨ ¬Q ∨ P, a tautology; IV is also a tautology. For B, P → (Q ∨ R) becomes ¬P ∨ Q ∨ R, exactly III. Applying (X→Q) = ¬X∨Q to C gives (¬P∨Q)∧(¬R∨Q) = ¬(P∨R)∨Q, which is II. Finally ¬(P⇔Q) is true exactly when one, but not both, of P and Q is true, which is I.

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64. Question 64

    Which is not a characteristic of linked-list file allocation?

    1. ANo space is lost to external disk fragmentation, apart from possible internal fragmentation in the final block
    2. BReading files or random access is very fast
    3. CThe data portion of a block is reduced because a pointer occupies some bytes
    4. DThe disadvantages can be mitigated with a main-memory File Allocation Table (FAT)

    Answer: (B) Reading files or random access is very fast

    Explanation

    Linked allocation follows pointers one block at a time, so direct/random access is slow. It avoids external fragmentation, reserves pointer space in each block, and FAT can retain the links in memory to improve traversal.

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65. Question 65

    A safe expression in relational calculus is guaranteed to yield:

    1. AA finite number of tuples
    2. BA finite number of attributes
    3. CA finite number of null values
    4. DA finite number of indices

    Answer: (A) A finite number of tuples

    Explanation

    Safety (range restriction) ensures that query variables range over values drawn from the finite database domain. This prevents an expression from describing infinitely many result tuples.

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66. Question 66

    A doctor knows P(s | m) = 0.70, P(m) = 1/50,000, and P(s) = 0.01, where s is a stiff neck and m is meningitis. Compute P(m | s).

    1. A0.014
    2. B0.0014
    3. C0.14
    4. D0.00014

    Answer: (B) 0.0014

    Explanation

    Bayes’ rule gives P(m | s) = P(s | m)P(m)/P(s) = 0.70 × (1/50,000) / 0.01 = 0.0014. The disease remains unlikely even after observing the symptom because its prior probability is very small.

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67. Question 67

    Let P denote power set and ∅ the empty set. Arrange in non-decreasing cardinality:

    A. P({a,b,{a,b}})
    B. P({∅,a,{a},{{a}}})
    C. P(P(∅))
    D. P(P({a}))
    E. P({{a,b},c})

    1. AC, D, A, B, E
    2. BD, C, E, A, B
    3. CC, D, E, A, B
    4. DD, C, B, A, E

    Answer: (C) C, D, E, A, B

    Explanation

    P(∅) has one member, so C = P(P(∅)) has 2 members. P({a}) has 2 members, so D has 4; E also has two underlying elements and has 4. A has three underlying elements and therefore 8 members, while B has four and therefore 16. Thus C, D, E, A, B is the listed non-decreasing order.

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68. Question 68

    What is the height of the binary search tree formed by inserting 40, 60, 50, 37, 52, 15, 8, 22 in that order?

    1. A4
    2. B3
    3. C2
    4. D1

    Answer: (B) 3

    Explanation

    The longest root-to-leaf path is 40 → 37 → 15 → 8 (or 40 → 60 → 50 → 52). It has three edges, so under the usual edge-height definition the tree height is 3.

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69. Question 69

    Let R = {(1,2),(3,4),(2,2)} and S = {(4,2),(2,5),(3,1),(1,3)}. What is R ∘ S?

    1. A{(4,2),(3,2),(2,5)}
    2. B{(1,5),(3,2),(2,5)}
    3. C{(3,1),(2,5)}
    4. D{(2,5),(3,1),(2,3),(3,3)}

    Answer: (B) {(1,5),(3,2),(2,5)}

    Explanation

    Using the paper's stated composition convention, the resulting relation is {(1,5),(3,2),(2,5)}, which is option B. This convention fixes the order in which the two relation mappings are composed for this question.

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70. Question 70

    Which option is the minimized DFA equivalent to the DFA shown?

    

    Original DFA and the four proposed minimized automata.

    1. AOption 1
    2. BOption 2
    3. COption 3
    4. DOption 4

    Answer: (A) Option 1

    Explanation

    The accepting state q4 is distinct. The remaining non-accepting states partition into two equivalent behaviours, producing the three-state DFA shown in option 1: an initial state A, state B with a 0 loop, and accepting state C reached on 1.

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71. Question 71

    For the reference string 7,0,1,2,0,3,0,4,2,3,0,3,2,1,2,0,1,7,0,1 with three frames, what is the hit ratio under optimal page replacement?

    1. A11/20
    2. B10/20
    3. C9/20
    4. D12/20

    Answer: (A) 11/20

    Explanation

    Simulating OPT gives 11 hits in the 20 references. On each miss with full frames, OPT replaces the resident page whose next use is farthest in the future (or never occurs again), so the hit ratio is 11/20.

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72. Question 72

    Average main-memory access time is 130 ns, cache access time is 100 ns, and the cache hit ratio is 75%. What is the average time to access a word?

    1. A130 ns
    2. B150 ns
    3. C132.5 ns
    4. D107.5 ns

    Answer: (D) 107.5 ns

    Explanation

    Separate the accesses into 75 cache hits and 25 misses per 100 references. Those contribute 75 × 100 ns and 25 × 130 ns respectively, totalling 10,750 ns; dividing by 100 gives 107.5 ns. The other answers omit the hit ratio or reverse the two access times.

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73. Question 73

    Which IC family has the lowest power consumption?

    1. AECL
    2. BMOS
    3. CTTL
    4. DCMOS

    Answer: (D) CMOS

    Explanation

    CMOS has very low static power consumption because its complementary transistor pair ideally draws significant current only while switching. ECL and TTL consume substantially more steady power.

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74. Question 74

    How will the shown min-heap appear after inserting key 32?

    

    Original min-heap and the four candidate heaps after insertion.

    1. AOption 1
    2. BOption 2
    3. COption 3
    4. DOption 4

    Answer: (C) Option 3

    Explanation

    The new key is first placed at the next open leaf, as the left child of 40. Since 32 < 40, it swaps once with 40; it then stops because 32 > its new parent 10. This is exactly the heap shown in option 3.

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75. Question 75

    What is the maximum bit rate of a noiseless channel with bandwidth 2 kHz transmitting a signal with 8 levels?

    1. A12000 bps
    2. B16000 bps
    3. C4000 bps
    4. D32000 bps

    Answer: (A) 12000 bps

    Explanation

    By the Nyquist formula, maximum bit rate = 2B log₂L = 2 × 2000 × log₂8 = 4000 × 3 = 12,000 bps. Using 8 directly rather than log₂8 produces the larger distractors.

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76. Question 76

    Which of the following is not an interprocess communication mechanism in UNIX?

    1. APipes
    2. BMessages
    3. CShared memory
    4. DSemaphore

    Answer: (D) Semaphore

    Explanation

    Pipes, message queues, and shared memory transfer information between processes. A semaphore is principally a synchronization primitive: it coordinates access rather than carrying a message payload.

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77. Question 77

    Which statements about C++ constructors are correct?

    A. They have the same name as the class.
    B. They can return values.
    C. They are called automatically when an object is created.
    D. They can be overloaded.
    E. They can be inherited.

    1. AA, B, C and D only
    2. BA, C and D only
    3. CB, C and D only
    4. DC, D and E only

    Answer: (B) A, C and D only

    Explanation

    A constructor is named for its class, is invoked on object creation, and may be overloaded. It has no return type or return value, and constructors are not inherited, so A, C, and D are the correct statements.

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78. Question 78

    A tree is:

    A. a circuitless connected graph
    B. a connected graph of n vertices with (n − 1) edges
    C. a circuitless graph of n vertices with (n − 1) edges
    D. a minimally connected graph

    1. AA, B and C only
    2. BB, C and D only
    3. CA, B, C and D
    4. DA and B only

    Answer: (C) A, B, C and D

    Explanation

    These are equivalent characterisations of a finite tree. A connected acyclic graph has n − 1 edges; an acyclic graph with n − 1 edges is connected; and every edge is necessary for connectivity, which is minimal connectedness.

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79. Question 79

    If f(n) = θ(g(n)) and g(n) = O(h(n)), which statement is true?

    1. Af(n) = O(h(n))
    2. Bf(n) = θ(h(n))
    3. Ch(n) = O(f(n))
    4. Dh(n) = θ(f(n))

    Answer: (A) f(n) = O(h(n))

    Explanation

    f(n) = θ(g(n)) implies f(n) = O(g(n)). Combining this with g(n) = O(h(n)) and transitivity of big-O gives f(n) = O(h(n)). The information does not establish a reverse bound, so the theta claims need not hold.

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80. Question 80

    What is z after this C code executes?

    x = 16;
    y = 4;
    z = x >> y;

    1. A5
    2. B4
    3. C2
    4. D1

    Answer: (D) 1

    Explanation

    Right shifting a positive integer by four places divides it by 2⁴. Thus 16 >> 4 equals 16 / 16 = 1; the other answers correspond to fewer shifts or a different operation.

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81. Question 81

    Simplify F(A,B,C,D) = Σm(3,6,7,11,12,13,14,15) using a four-variable Karnaugh map.

    1. AĀB + B̄C + C̄D
    2. BĀB + C̄D + AB̄
    3. CAB + BC + CD
    4. DCD + AC̄ + BD

    Answer: (C) AB + BC + CD

    Explanation

    The four adjacent cells m12, m13, m14, and m15 form the product AB. The cells m6, m7, m14, and m15 form BC. The cells m3, m7, m11, and m15 form CD. Evaluating AB + BC + CD therefore yields true precisely for 3, 6, 7, 11, 12, 13, 14, and 15. For example, m3 is covered by CD, m6 by BC, and m12 by AB; no product term turns on a minterm outside the stated set. Hence option C is the minimal correct form.

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82. Question 82

    Which additional property must a group (G, *) satisfy to be an abelian group?

    1. ACommutative
    2. BIdentity
    3. CInverse
    4. DAssociativity

    Answer: (A) Commutative

    Explanation

    A group already has an associative operation, an identity, and inverses. It is called abelian precisely when its operation is also commutative: a * b = b * a for every pair of group elements.

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83. Question 83

    The shown transformation is a reflection about which axis?

    

    Original and reflected triangle positions about the vertical axis.

    1. AA and D only
    2. BA and C only
    3. CB and C only
    4. DB and D only

    Answer: (C) B and C only

    Explanation

    The object moves from the left side of the vertical axis to the right side while retaining its vertical coordinates and reversing left/right orientation. Thus it is a reflection about the y-axis, equivalently the line x = 0. Statements B and C describe the same reflection.

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84. Question 84

    What is memory interleaving?

    1. ALayering memory stacks one above another
    2. BA hierarchy of different memory types
    3. CDividing memory into modules so the CPU can access multiple modules simultaneously
    4. DCombining different memory types

    Answer: (C) Dividing memory into modules so the CPU can access multiple modules simultaneously

    Explanation

    Interleaved memory distributes consecutive addresses across independent memory modules. While one module completes an access, another can begin the next, improving throughput through overlapping accesses.

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85. Question 85

    Match List-I with List-II.

    A. Planar graph
    B. Bipartite graph
    C. PERT
    D. CPM

    List-I	List-II
    A. Planar graph B. Bipartite graph C. PERT D. CPM	I. Probabilistic model II. Deterministic model III. 4-colourable IV. 2-colourable

    1. AA-II, B-IV, C-I, D-III
    2. BA-III, B-IV, C-I, D-II
    3. CA-II, B-IV, C-I, D-III
    4. DA-III, B-IV, C-II, D-I

    Answer: (B) A-III, B-IV, C-I, D-II

    Explanation

    A planar graph is four-colourable (III), a bipartite graph is two-colourable (IV), PERT is probabilistic (I), and CPM is deterministic (II). This gives A-III, B-IV, C-I, D-II.

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86. Question 86

    Match List-I with List-II.

    A. Data-link layer
    B. Network layer
    C. Transport layer
    D. Presentation layer

    List-I	List-II
    A. Data-link B. Network C. Transport D. Presentation	I. Encryption II. Connection control III. Routing IV. Framing

    1. AA-IV, B-III, C-I, D-II
    2. BA-III, B-IV, C-II, D-I
    3. CA-IV, B-II, C-III, D-I
    4. DA-IV, B-III, C-II, D-I

    Answer: (D) A-IV, B-III, C-II, D-I

    Explanation

    The data-link layer performs framing (IV), the network layer performs routing (III), the transport layer provides connection control (II), and the presentation layer handles encryption/representation (I).

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87. Question 87

    A BST is formed by inserting Mathematics, Physics, Geography, Zoology, Metrology, Geology, Psychology, and Chemistry in dictionary order. Arrange these words in increasing order of their tree level:

    A. Mathematics
    B. Zoology
    C. Psychology
    D. Physics

    1. AA, D, C, B
    2. BA, C, D, B
    3. CA, D, B, C
    4. DC, B, D, A

    Answer: (C) A, D, B, C

    Explanation

    Mathematics is the root (level 0). Physics is its right child (level 1). Zoology is to the right of Physics (level 2), while Psychology lies to the left of Zoology (level 3). Thus the required increasing-level order is A, D, B, C.

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88. Question 88

    In open addressing, how are collisions typically resolved?

    1. ABy probing to find the next available table slot
    2. BBy creating a linked list at the collision point
    3. CBy rehashing the entire table
    4. DBy storing colliding elements in a separate array

    Answer: (A) By probing to find the next available table slot

    Explanation

    Open addressing stores every key in the hash table itself. On a collision it probes alternative positions, for example by linear probing, quadratic probing, or double hashing, until an unused slot is found.

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89. Question 89

    If L₁ is a regular language and L₂ is a context-free language, which statement is correct?

    1. AAny subset of L₁ ∪ L₂ is context-free
    2. BL₁ ∩ L₂ is context-free
    3. CL₁ / L₂ is regular
    4. DL₁ ∩ L₂ is accepted by a deterministic pushdown automaton

    Answer: (B) L₁ ∩ L₂ is context-free

    Explanation

    Context-free languages are closed under intersection with regular languages. Construct a product of a pushdown automaton for L₂ and a finite automaton for L₁ to recognise L₁ ∩ L₂. CFLs are not closed under arbitrary subsets or intersection with another CFL, and the resulting CFL need not be deterministic.

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90. Question 90

    Which statement may be false for a decision problem X ∈ NP?

    1. AX can be solved in nondeterministic polynomial time
    2. BX can be solved in exponential time
    3. CX can be solved in polynomial space
    4. DX can be solved in deterministic polynomial time

    Answer: (D) X can be solved in deterministic polynomial time

    Explanation

    Membership in NP guarantees a nondeterministic polynomial-time algorithm. Such a computation can be simulated deterministically in exponential time and therefore uses at most polynomial space for a bounded path, but whether every NP problem has a deterministic polynomial-time algorithm is exactly the unresolved P versus NP question.

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91. Question 91

    A program takes 100 man-days to write in FORTRAN. Rewriting the 1% hot code in assembly takes four times the original FORTRAN effort for that portion. If the team finishes the entire FORTRAN program plus this rewrite in 13 days, how many programmers are on the team?

    1. A13 programmers
    2. B10 programmers
    3. C8 programmers
    4. D100/13 programmers

    Answer: (C) 8 programmers

    Explanation

    Writing the full FORTRAN program costs 100 man-days. Rewriting 1% costs 4 × 1 = 4 further man-days, for a total of 104 man-days. Dividing 104 by 13 calendar days gives 8 programmers.

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92. Question 92

    In the given program, 1% of the code accounts for 50% of execution time. What percentage decrease in execution time results from rewriting that 1% in assembly language, which runs five times faster?

    1. A20%
    2. B32%
    3. C40%
    4. D60%

    Answer: (C) 40%

    Explanation

    Treat the original runtime as 100 units. The unchanged 99% of code takes 50 units; the hot 1% originally takes 50 but after a 5× speedup takes 10. The new total is 60, so the reduction is 100 − 60 = 40%.

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93. Question 93

    If 99% of the program is written in FORTRAN and 1% directly in assembly, what is the percentage increase in programming time compared with writing all FORTRAN first and then rewriting the 1% in assembly?

    1. A10%
    2. B5%
    3. C13%
    4. D8%

    Answer: (B) 5%

    Explanation

    Writing 99% in FORTRAN costs 99 man-days and writing 1% directly in assembly costs 10 man-days, totalling 109. The alternative costs 100 + 4 = 104 man-days. The increase is (109 − 104)/104 × 100 ≈ 4.81%, which rounds to 5%.

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94. Question 94

    How many days will two programmers take to write the whole program in FORTRAN and then rewrite the 1% hot code in assembly language?

    1. A52
    2. B53
    3. C54
    4. D55

    Answer: (A) 52

    Explanation

    The complete FORTRAN version costs 100 man-days. Converting the 1% part costs four times 1 man-day, adding 4, so the total is 104 man-days. Two programmers complete 104/2 = 52 days of work.

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95. Question 95

    If 99% of the program is written in FORTRAN and 1% in assembly, what is the percentage increase in execution time compared with writing the whole program in FORTRAN and then rewriting the 1% in assembly?

    1. A0.9%
    2. B1%
    3. C0.1%
    4. D0%

    Answer: (D) 0%

    Explanation

    Both alternatives execute the same final language mix: 99% FORTRAN and the same 1% hot code in assembly. The hot portion is five times faster in either case, so the resulting execution time is identical. Therefore the increase is 0%.

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96. Question 96

    For the grammar S → AB; B → +AB | ε; A → CD; D → *CD | ε; C → [S] | x, find FOLLOW(A) and FOLLOW(C).

    1. AFOLLOW(A) = {], $}; FOLLOW(C) = {+, ], $}
    2. BFOLLOW(A) = {+, ], $}; FOLLOW(C) = {*, +, ], $}
    3. CFOLLOW(A) = {, $, [}; FOLLOW(C) = {, [, $}
    4. DFOLLOW(A) = {*, ], $}; FOLLOW(C) = {+, ], $}

    Answer: (B) FOLLOW(A) = {+, ], $}; FOLLOW(C) = {*, +, ], $}

    Explanation

    In S → AB, FIRST(B) contributes + to FOLLOW(A), and because B can derive ε, FOLLOW(S) = {], $} also contributes. In A → CD, FIRST(D) contributes * to FOLLOW(C); D can derive ε, so FOLLOW(A) also contributes +, ], and $. Therefore FOLLOW(A) = {+, ], $} and FOLLOW(C) = {*, +, ], $}.

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97. Question 97

    For the grammar S → AB; B → +AB | ε; A → CD; D → *CD | ε; C → [S] | x, identify the correct statement.

    1. AThe grammar is left recursive
    2. BThe grammar needs left factorization
    3. C[[x*x]+x] is a valid sentence of the grammar
    4. DThe grammar has an SLR(0) parser

    Answer: (C) [[x*x]+x] is a valid sentence of the grammar

    Explanation

    The grammar generates expressions made from x and bracketed S expressions, with D adding repeated multiplication and B adding repeated addition. Thus [[x*x]+x] derives through C → [S], S → AB, and the recursive B/D productions. It is neither left recursive nor left-factored, and “SLR(0)” is not a parser class.

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98. Question 98

    For the grammar S → AB; B → +AB | ε; A → CD; D → *CD | ε; C → [S] | x, how many non-blank LL(1) table entries occur in the B and D rows?

    1. AB = 3; D = 4
    2. BB = 6; D = 5
    3. CB = 2; D = 3
    4. DB = 1; D = 2

    Answer: (A) B = 3; D = 4

    Explanation

    For B → +AB, FIRST is {+}, so M[B,+] is one non-blank entry. Because B → ε, put that production under every symbol in FOLLOW(B) = {], $}, yielding two more entries and B = 3. Likewise D → CD gives M[D,], while D → ε is entered for FOLLOW(D) = {+, ], $}; that is one plus three, so D = 4.

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99. Question 99

    For the grammar S → AB; B → +AB | ε; A → CD; D → *CD | ε; C → [S] | x, find FIRST(S) and FIRST(D).

    1. AFIRST(S) = {+, [, x}; FIRST(D) = {+, *}
    2. BFIRST(S) = {[, ], x}; FIRST(D) = {+, ε}
    3. CFIRST(S) = {[, x}; FIRST(D) = {*, ε}
    4. DFIRST(S) = {[, x, ε}; FIRST(D) = {*, ε}

    Answer: (C) FIRST(S) = {[, x}; FIRST(D) = {*, ε}

    Explanation

    S begins with A, A begins with C, and C begins only with [ or x, so FIRST(S) = {[, x}. D directly derives CD or ε, hence FIRST(D) = {, ε}.

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100. Question 100

     For the augmented grammar S′ → S; S → AB; B → +AB | ε; A → CD; D → *CD | ε; C → [S] | x, how many productions are in the I₁ state of the canonical LR(0) set?

     1. A1
     2. B2
     3. C4
     4. D6

     Answer: (A) 1

     Explanation

     I₀ contains S′ → ·S together with the closure productions for S, A, and C. Taking GOTO(I₀, S) produces I₁ = {S′ → S·}; the dot is at the end, so no closure expansion is added. Thus I₁ has exactly one item/production.

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