100+ Free KEAM Practice Questions

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The integral ∫₀^(π/2) sin x dx equals:

−1

π/2

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2026 Statistics

Key Facts: KEAM Exam

150 MCQs

Single CBT paper in KEAM 2026 (Math 75 + Phy 45 + Chem 30)

cee.kerala.gov.in KEAM 2026 notification

180 minutes

Total exam duration

KEAM 2026 Prospectus

+4 / −1

Marking scheme per MCQ

Commissioner of Entrance Examinations, Kerala

INR 875

General-category application fee for KEAM 2026

CEE Kerala notification

100

Free practice questions on this page

OpenExamPrep

KEAM 2026 is a single 180-minute CBT of 150 MCQs (Math 75 + Physics 45 + Chemistry 30) with +4/−1 marking and 5 options per question. It admits candidates to Kerala B.Tech and B.Pharm programmes; rank uses Paper score and Plus Two marks combined.

Sample KEAM Practice Questions

Try these sample questions to test your KEAM exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, what is A ∩ B?

A.{1, 2}

B.{3, 4}

C.{1, 2, 5, 6}

D.{1, 2, 3, 4, 5, 6}

Explanation: The intersection A ∩ B consists of elements present in BOTH sets. Elements 3 and 4 appear in both A and B, so A ∩ B = {3, 4}.

2What is the value of sin(75°) using the angle-addition identity sin(45° + 30°)?

A.(√6 − √2) / 4

B.(√6 + √2) / 4

C.(√3 − √2) / 4

D.(√6 + √3) / 4

Explanation: sin(75°) = sin(45° + 30°) = sin45°·cos30° + cos45°·sin30° = (√2/2)(√3/2) + (√2/2)(1/2) = (√6 + √2)/4. This is a standard exact value from compound-angle identities.

3If the roots of the quadratic equation x² − 5x + 6 = 0 are α and β, what is α² + β²?

A.11

B.13

C.25

D.37

Explanation: By Vieta's formulas, α + β = 5 and αβ = 6. Then α² + β² = (α + β)² − 2αβ = 25 − 12 = 13.

4What is the derivative of f(x) = x³ sin(x) with respect to x?

A.3x² cos(x)

B.x³ cos(x) + 3x² sin(x)

C.3x² sin(x) − x³ cos(x)

D.x² (3 sin(x) − x cos(x))

Explanation: Apply the product rule: (uv)' = u'v + uv'. With u = x³ and v = sin(x), f'(x) = 3x²·sin(x) + x³·cos(x) = x³cos(x) + 3x²sin(x).

5What is the integral ∫(2x + 3) dx?

A.x² + 3x + C

B.2x² + 3x + C

C.x² + 3 + C

D.2 + C

Explanation: Integrate term by term: ∫2x dx = x² and ∫3 dx = 3x. Adding the constant of integration gives x² + 3x + C.

6If matrix A = [[1, 2], [3, 4]], what is the determinant of A?

A.−2

B.2

C.10

D.−10

Explanation: For a 2×2 matrix [[a, b], [c, d]], det(A) = ad − bc. Here det(A) = (1)(4) − (2)(3) = 4 − 6 = −2.

7What is the modulus of the complex number z = 3 + 4i?

A.5

B.7

C.25

D.1

Explanation: The modulus of a complex number z = a + bi is |z| = √(a² + b²). Here |z| = √(9 + 16) = √25 = 5.

8In how many ways can the letters of the word KERALA be arranged?

A.120

B.360

C.720

D.240

Explanation: KERALA has 6 letters with A repeated twice. The number of distinct arrangements is 6!/2! = 720/2 = 360.

9What is the value of C(10, 2) — the number of ways to choose 2 items from 10?

A.20

B.45

C.90

D.100

Explanation: C(n, r) = n!/(r!(n−r)!). C(10, 2) = 10!/(2!·8!) = (10·9)/(2·1) = 45.

10What is the sum of the first 20 terms of the arithmetic progression 3, 7, 11, 15, ...?

A.780

B.820

C.860

D.900

Explanation: AP has first term a = 3 and common difference d = 4. Sum Sₙ = n/2 · (2a + (n−1)d) = (20/2) · (2·3 + 19·4) = 10 · (6 + 76) = 10 · 82 = 820.

About the KEAM Exam

KEAM (Kerala Engineering Architecture Medical) is the state-level entrance examination conducted by the Office of the Commissioner for Entrance Examinations, Kerala, for admission to professional undergraduate courses in Kerala — primarily B.Tech engineering and B.Pharm pharmacy programmes. The examination is governed by the Kerala Professional Colleges/Institutions (Prohibition of Capitation Fee, Regulation of Admission, Fixation of Non-Exploitative Fee and Other Measures to Ensure Equity and Excellence in Professional Education) Act 2006. From 2026, KEAM moves to a single Computer-Based Test of 150 MCQs (Mathematics 75 + Physics 45 + Chemistry 30) in 180 minutes, replacing the earlier two-paper offline format. Despite the historical name including 'Medical' and 'Architecture', the 2026 KEAM is used only for engineering and pharmacy admissions; medical aspirants take NEET-UG, and architecture aspirants take NATA. The exam is based on the Kerala State Plus Two (Class 11 and 12) syllabus, broadly aligned with NCERT.

Questions

100 scored questions

Time Limit

180 minutes (single CBT)

Passing Score

No pass mark; rank used for Kerala B.Tech/Pharmacy seat allotment

Exam Fee

INR 875 (General); INR 425 (SC/ST) for KEAM 2026 within Kerala (Commissioner of Entrance Examinations (CEE), Government of Kerala)

KEAM Exam Content Outline

50%

Mathematics (75 MCQs)

Sets, relations, functions, complex numbers, matrices, determinants, sequences and series, permutations and combinations, binomial theorem, trigonometry, vectors, 3D geometry, conic sections (parabola, ellipse, hyperbola), straight lines and circles, calculus (limits, continuity, differentiation, integration, applications), probability, statistics, linear inequalities, mathematical reasoning

30%

Physics (45 MCQs)

Units and measurements, kinematics, laws of motion, work-energy-power, rotational motion, gravitation, properties of solids and fluids, thermodynamics, kinetic theory of gases, oscillations, waves, electrostatics, current electricity, magnetic effects, electromagnetic induction, AC, electromagnetic waves, ray and wave optics, dual nature of matter and radiation, atoms and nuclei, semiconductor electronics

20%

Chemistry (30 MCQs)

Atomic structure, chemical bonding, states of matter, chemical thermodynamics, equilibrium, redox, hydrogen, s-block, p-block, d-and-f-block elements, coordination compounds, hydrocarbons, haloalkanes and haloarenes, alcohols, phenols and ethers, aldehydes, ketones and carboxylic acids, amines, biomolecules, polymers, chemistry in everyday life, environmental chemistry

How to Pass the KEAM Exam

What You Need to Know

Passing score: No pass mark; rank used for Kerala B.Tech/Pharmacy seat allotment
Exam length: 100 questions
Time limit: 180 minutes (single CBT)
Exam fee: INR 875 (General); INR 425 (SC/ST) for KEAM 2026 within Kerala

Keys to Passing

Complete 500+ practice questions
Score 80%+ consistently before scheduling
Focus on highest-weighted sections
Use our AI tutor for tough concepts

KEAM Study Tips from Top Performers

1Finish NCERT Mathematics, Physics, and Chemistry for Class 11 and Class 12 before any coaching module — KEAM tests the Kerala State Plus Two syllabus, which closely mirrors NCERT

2Practise 5-option MCQs deliberately — process-of-elimination is sharper when there are 5 choices, so train yourself to eliminate two clearly-wrong options first

3Take at least 10-15 full-length KEAM mock tests of 150 MCQs in 180 minutes to build pacing — Mathematics with 75 questions is the throughput bottleneck

4Track accuracy by section: with −1 negative marking, blindly guessing on more than ~10 doubtful questions usually hurts more than helps; mark-for-review and return to them

5For Mathematics, prioritise calculus, vectors, 3D geometry, conic sections, and probability — these recur heavily and reward formula fluency

6For Physics and Chemistry, master the NCERT diagrams and standard reactions/equations rather than memorising long derivations — KEAM rewards concept recall and standard problem patterns

Frequently Asked Questions

What is the KEAM 2026 exam pattern?

KEAM 2026 is a single Computer-Based Test of 150 multiple-choice questions in 180 minutes. It covers Mathematics (75 questions), Physics (45 questions), and Chemistry (30 questions) in a 5:3:2 marks weightage. Each MCQ has 5 options with one correct answer, and marking is +4 for correct, −1 for incorrect, and 0 for unattempted. This single-paper CBT format replaces the earlier two-paper offline structure used until 2025.

Does KEAM 2026 still admit medical and architecture candidates?

No. From 2026, KEAM is used only for B.Tech engineering and B.Pharm pharmacy admissions in Kerala. Medical aspirants must qualify NEET-UG conducted by NTA, and architecture aspirants must qualify NATA conducted by the Council of Architecture. The historical name 'KEAM' is retained even though the medical and architecture components are no longer administered through this entrance.

How is the KEAM rank calculated?

The KEAM rank for B.Tech allotment is computed from a 50:50 weightage of the standardised KEAM Paper score and the standardised Plus Two (Class 12) marks in Mathematics, Physics, and Chemistry. The Office of the Commissioner for Entrance Examinations publishes the exact normalisation formula each year in the KEAM Prospectus, and the same rank list is used for centralised seat allotment in Kerala engineering colleges.

Who conducts KEAM and where do I apply?

KEAM is conducted by the Office of the Commissioner for Entrance Examinations (CEE), Government of Kerala. Applications are filed online on the official portal cee.kerala.gov.in, typically opening in early February and closing in March. Admit cards are released about two weeks before the exam, which usually takes place in late April or May.

What is the syllabus for KEAM 2026?

The KEAM 2026 syllabus is based on the Kerala State Plus Two (Higher Secondary) curriculum for Class 11 and Class 12 in Mathematics, Physics, and Chemistry. The Kerala State Higher Secondary syllabus is broadly aligned with NCERT, so NCERT textbooks are widely used for preparation. The detailed topic-wise syllabus is published in the official KEAM Prospectus on cee.kerala.gov.in.

What is the eligibility for KEAM 2026?

Candidates must have passed Class 12 (or equivalent) with Mathematics, Physics, and Chemistry as core subjects, securing the minimum aggregate marks specified in the Prospectus (typically 45 percent for general category in PCM, 40 percent for SEBC, and a relaxation for SC/ST). The candidate must be an Indian citizen and meet domicile requirements as defined in the KEAM Prospectus to claim Kerala State quota seats.

How should I prepare for KEAM 2026 given the new CBT format?

Build deep mastery of NCERT and the Kerala State Plus Two textbooks for the syllabus, then practise solving in the CBT environment to get comfortable with on-screen navigation, marking for review, and the timer. Take full-length mock tests of 150 questions in 180 minutes regularly to develop pace — Mathematics carries 75 questions so allocating roughly 90 minutes for Maths and 90 minutes for Physics and Chemistry combined is a common strategy.

100+ Free KEAM Practice Questions

KEAM