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Free Practice Questions for PMA Cadet Entrance Test

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Sample PMA Cadet Entrance Test Practice Questions

Try these sample questions to review concepts for the PMA Cadet Entrance Test exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1What is the determinant of the 2×2 matrix A = [[6, 2], [4, 3]]?
A.10
B.26
C.8
D.-10
Explanation: The determinant of a 2×2 matrix [[a, b], [c, d]] is computed as ad - bc. For this matrix, det(A) = (6)(3) - (2)(4) = 18 - 8 = 10.
2For what value of k is the square matrix M = [[k, 6], [2, 3]] singular?
A.2
B.4
C.6
D.12
Explanation: A square matrix is singular if its determinant equals zero. Setting det(M) = (k)(3) - (6)(2) = 3k - 12 = 0 yields 3k = 12, so k = 4.
3Using Cramer's Rule, what is the value of x in the linear system: 2x + y = 7 and x - 3y = -7?
A.3
B.-2
C.2
D.5
Explanation: The coefficient determinant D = (2)(-3) - (1)(1) = -6 - 1 = -7. The determinant for x is Dx = (7)(-3) - (-7)(1) = -21 + 7 = -14. By Cramer's Rule, x = Dx / D = -14 / -7 = 2.
4What is the nature of the roots of the quadratic equation 3x² - 6x + 3 = 0?
A.Real, distinct, and rational
B.Complex conjugates
C.Purely imaginary
D.Real, equal, and rational
Explanation: The discriminant is Δ = b² - 4ac = (-6)² - 4(3)(3) = 36 - 36 = 0. When the discriminant is exactly zero and coefficients are rational, the roots are real, equal, and rational (both roots are x = 1).
5For the quadratic equation 2x² - 8x + 5 = 0, what is the sum of the roots?
A.4
B.-4
C.5/2
D.-5/2
Explanation: For any quadratic equation ax² + bx + c = 0, the sum of roots is given by -b / a. Here, sum = -(-8) / 2 = 8 / 2 = 4.
6Which quadratic equation has roots equal to 3 and -5?
A.x² - 2x - 15 = 0
B.x² + 2x - 15 = 0
C.x² + 2x + 15 = 0
D.x² - 8x - 15 = 0
Explanation: A quadratic equation is formed by x² - (sum)x + product = 0. The sum of roots is 3 + (-5) = -2, and the product is (3)(-5) = -15. Thus, x² - (-2)x + (-15) = x² + 2x - 15 = 0.
7In an arithmetic progression (A.P.), the first term is 5 and the common difference is 3. What is the 12th term?
A.35
B.41
C.38
D.44
Explanation: The nth term of an A.P. is Tn = a + (n - 1)d. For the 12th term, T12 = 5 + (12 - 1)(3) = 5 + (11)(3) = 5 + 33 = 38.
8What is the sum of the first 15 terms of the arithmetic series 2 + 5 + 8 + 11 + ...?
A.301
B.690
C.44
D.345
Explanation: The sum of an arithmetic series is Sn = (n / 2)[2a + (n - 1)d]. Here n = 15, a = 2, and d = 3. S15 = (15 / 2)[2(2) + (14)(3)] = (15 / 2)[4 + 42] = 7.5 × 46 = 345.
9What is the sum to infinity of the geometric progression 8, 4, 2, 1, ...?
A.16
B.12
C.24
D.32
Explanation: For an infinite geometric progression with |r| < 1, the sum is S∞ = a / (1 - r). Here a = 8 and common ratio r = 4 / 8 = 1/2. Therefore, S∞ = 8 / (1 - 0.5) = 8 / 0.5 = 16.
10What is the simplified trigonometric form of (1 - cos²θ) / (sin θ cos θ)?
A.cot θ
B.tan θ
C.sec θ
D.csc θ
Explanation: From the fundamental Pythagorean identity, 1 - cos²θ = sin²θ. Substituting gives sin²θ / (sin θ cos θ) = sin θ / cos θ = tan θ.

About the PMA Cadet Entrance Test Exam

The Pakistan Marine Academy (PMA) Cadet Entrance Test is the first stage of admission to PMA Karachi's two-year residential pre-sea training for Nautical (Deck) and Marine Engineering cadets, which leads to an Associate Degree from NED University of Engineering & Technology. Applicants need F.Sc Pre-Engineering or A Level (Physics, Chemistry, Mathematics) with at least 55% marks. This free bank offers 100 independent English-language MCQs on F.Sc Mathematics, Physics, and Chemistry, plus English and reasoning/maritime general knowledge. PMA does not publish the test's item count, format, or subject weights, so this is a study aid, not a copy of the official paper and not practice for the medical, PET, or interview stages.

Exam sponsor: Pakistan Marine Academy (PMA), Karachi, under the Ministry of Maritime Affairs; entrance test conducted by NTS. The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Stage 1: entrance test at Abbottabad, Gwadar, Karachi, Lahore, Multan, Muzaffarabad (AJK), Peshawar, Quetta, Rawalpindi/Islamabad, or Sukkur (minimum 50% to qualify). Stage 2: medical examination at a designated Army/Navy hospital. Stage 3: Physical Efficiency Test (one-mile run, 15 push-ups, 15 sit-ups, 2 chin-ups). Stage 4: final interview. Final selection is in order of merit using F.Sc marks, entry test marks, medical, PET, and interview results.

Time Limit

Not officially published

Passing Score

Minimum 50% marks to qualify the entrance test. Later stages are medical fitness, PET, and interview; final selection is merit-based.

Exam / Certification Fees

Rs. 4,000 non-refundable pay order or bank draft in favour of "Pakistan Marine Academy Karachi" with the application form; medical examination charges are paid separately by the candidate.

Exam sponsor website

Fees, eligibility, and exam policies can change. Confirm them with the exam sponsor before applying or paying.

Our practice resources: topics covered

We aim to reflect publicly available exam outlines and topic information in our study resources. Coverage, format, and difficulty may differ from the actual exam, and we cannot guarantee that every detail is accurate or current. Confirm exam requirements, fees, and policies with the official exam sponsor.

Not published

Mathematics

F.Sc Pre-Engineering mathematics: matrices, quadratic equations, sequences and series, trigonometry, limits, differentiation, integration, coordinate geometry, and vectors.

Not published

Physics

F.Sc Pre-Engineering physics: measurement, mechanics, fluid dynamics, oscillations and waves, optics, thermodynamics, electricity, electromagnetism, and modern physics.

Not published

Chemistry

F.Sc Pre-Engineering chemistry: mole concept, gases, atomic structure, bonding, thermochemistry, equilibrium, acids and bases, electrochemistry, and organic chemistry.

Not published

English

Grammar and usage: prepositions, subject-verb agreement, conditionals, voice, reported speech, sentence correction, synonyms, antonyms, and analogies.

Not published

General Knowledge & Reasoning

Number and letter series, odd-one-out, spatial and logical reasoning, and maritime general knowledge about Pakistani ports, shipping institutions, chokepoints, and the law of the sea.

Preparing for the PMA Cadet Entrance Test Exam

What You Need to Know

  • Passing score: Minimum 50% marks to qualify the entrance test. Later stages are medical fitness, PET, and interview; final selection is merit-based.
  • Assessment: Stage 1: entrance test at Abbottabad, Gwadar, Karachi, Lahore, Multan, Muzaffarabad (AJK), Peshawar, Quetta, Rawalpindi/Islamabad, or Sukkur (minimum 50% to qualify). Stage 2: medical examination at a designated Army/Navy hospital. Stage 3: Physical Efficiency Test (one-mile run, 15 push-ups, 15 sit-ups, 2 chin-ups). Stage 4: final interview. Final selection is in order of merit using F.Sc marks, entry test marks, medical, PET, and interview results.
  • Time limit: Not officially published
  • Exam / certification fees: Rs. 4,000 non-refundable pay order or bank draft in favour of "Pakistan Marine Academy Karachi" with the application form; medical examination charges are paid separately by the candidate. Official sources

Using Our Practice Resources

  • Work through all 100 available questions
  • Review every answer and explanation
  • Track weak areas and revisit them
  • Use our AI tutor for tough concepts

PMA Cadet Entrance Test: Suggested Study Strategy

1Revise core F.Sc Pre-Engineering formulas in Mathematics, Physics, and Chemistry, especially calculus, trigonometry, kinematics, electricity, gas laws, and stoichiometry.
2Work numerical problems by hand under a self-set time limit, because PMA does not publish the official test length or timing.
3Practise English grammar and reasoning items, and review Pakistan's ports, shipping institutions, and basic law-of-the-sea terms for general knowledge.

Frequently Asked Questions

What is the Pakistan Marine Academy cadet entrance test?

It is the first selection stage for PMA Karachi's Nautical (Deck) and Marine Engineering cadet batches. Selected cadets complete two years of residential pre-sea training and receive an Associate Degree from NED University of Engineering & Technology, plus IMO-recognised pre-sea mandatory course certificates.

What is on the PMA entrance test, and is this bank the official paper?

PMA does not publish the test's subjects, number of questions, format, or time limit; its advertisement says only that a hired testing agency (NTS for the 64th and 65th batches) conducts it. Applicants must hold F.Sc Pre-Engineering or A Level Physics, Chemistry, and Mathematics, so this bank practises those subjects plus English and reasoning. It is independent English-language MCQ practice, not an official paper or format simulation.

What score do I need to pass the PMA entrance test?

PMA requires a minimum of 50% marks to qualify the entrance test. Qualified candidates then face a medical examination, the Physical Efficiency Test, and a final interview. Final selection is in order of merit using F.Sc marks, entry test marks, medical, PET, and interview results.

What are the physical and medical standards for PMA cadets?

The 65th Batch medical proforma sets a minimum height of 157 cm (5 ft 2 in) and Mercantile Marine Department eyesight standards that differ for Deck and Engineering cadets; colour-blind candidates are unfit. The PET is a one-mile (1.6 km) run plus 15 push-ups, 15 sit-ups, and 2 chin-ups within 2 minutes each. The run time was 8 minutes in the 64th Batch advertisement and 8½ minutes in 65th Batch notices, so check the current advertisement.

How much does it cost to apply to PMA?

Applicants send a non-refundable Rs. 4,000 pay order or bank draft in favour of "Pakistan Marine Academy Karachi" with the application form. Candidates called for the medical examination also pay the hospital's examination charges and their own travel and lodging costs.