Free Practice Questions for CUSAT CAT B.Tech

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Key Facts: CUSAT CAT B.Tech Exam

225 MCQs

Total questions in the official exam

CUSAT Admission prospectus

180 Mins

Total exam duration allowed

CUSAT CAT Guidelines

₹1,500 / ₹700

Application fee for General / Kerala SC-ST (max two test codes)

CUSAT Prospectus 2026

+4 / -1

Marking scheme (Correct/Incorrect)

CUSAT Marking Rules

The CUSAT CAT B.Tech exam (Test Code 101) features 225 MCQs in 180 minutes: Mathematics 90, Physics 75, Chemistry 60. Marking is +4 correct and -1 incorrect. Application fee is ₹1,500 general / ₹700 Kerala SC/ST (max two test codes).

Sample CUSAT CAT B.Tech Practice Questions

Try these sample questions to review concepts for the CUSAT CAT B.Tech exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1For what value of k is the matrix A = [[2, k], [3, 6]] singular?

A.4

B.3

C.6

D.2

Explanation: A matrix is singular if its determinant is zero. For matrix A, the determinant is (2 * 6) - (3 * k) = 12 - 3k. Setting this equal to zero gives 12 - 3k = 0, which yields k = 4.

2If sin(x) + cos(x) = sqrt(2) * cos(x), what is the value of cos(x) - sin(x)?

A.-sqrt(2) * sin(x)

B.sqrt(2) * sin(x)

C.sqrt(2) * cos(x)

D.-sqrt(2) * cos(x)

Explanation: Squaring both sides of the given equation sin(x) + cos(x) = sqrt(2)*cos(x) yields 1 + 2*sin(x)*cos(x) = 2*cos^2(x). This simplifies to 2*sin(x)*cos(x) = cos^2(x) - sin^2(x). Let P = cos(x) - sin(x). Squaring P gives P^2 = 1 - 2*sin(x)*cos(x) = 1 - (cos^2(x) - sin^2(x)) = 2*sin^2(x). Hence, P = sqrt(2) * sin(x).

3What is the value of the limit as x approaches 0 of tan(3x) / sin(2x)?

A.2/3

B.1

C.3/2

D.0

Explanation: We can rewrite the expression as [tan(3x)/(3x)] * [(2x)/sin(2x)] * (3/2). Taking the limit as x approaches 0, the standard limits tan(u)/u and v/sin(v) both equal 1. Thus, the limit is 1 * 1 * (3/2) = 3/2.

4Find the modulus of the complex number z = (3 + 4i) / (1 - 2i).

A.5

B.sqrt(3)

C.1

D.sqrt(5)

Explanation: The modulus of a quotient of complex numbers is the quotient of their moduli: |z| = |3 + 4i| / |1 - 2i|. Since |3 + 4i| = sqrt(3^2 + 4^2) = 5, and |1 - 2i| = sqrt(1^2 + (-2)^2) = sqrt(5), we get |z| = 5 / sqrt(5) = sqrt(5).

5If the vectors a = 2i + 3j - k and b = i - j + kk are perpendicular to each other, what is the value of the scalar coefficient k?

A.-1

B.1

C.5

D.-5

Explanation: Two vectors are perpendicular if and only if their dot product is zero: a · b = 0. Here a = 2i + 3j - k and b = i - j + kk, so (2)(1) + (3)(-1) + (-1)(k) = 0, which simplifies to 2 - 3 - k = 0, or -1 - k = 0, yielding k = -1.

6The mean of 5 observations is 6. If three of the observations are 4, 6, and 8, and the other two are in the ratio 1:3, find the larger of the two remaining observations.

A.3

B.9

C.12

D.6

Explanation: The sum of the 5 observations is 5 * 6 = 30. The sum of the three given observations is 4 + 6 + 8 = 18. Thus, the sum of the remaining two is 30 - 18 = 12. Let them be x and 3x. Then x + 3x = 12, which gives 4x = 12, so x = 3. The larger of the two is 3x = 9.

7The 5th term of an Arithmetic Progression (AP) is 15 and the 9th term is 27. Find the first term of the AP.

A.4

B.5

C.3

D.6

Explanation: Let a be the first term and d be the common difference. Then a + 4d = 15 and a + 8d = 27. Subtracting the two equations gives 4d = 12, so d = 3. Substituting d = 3 into the first equation: a + 4(3) = 15 yields a = 3.

8Two fair six-sided dice are rolled. What is the probability that the sum of the numbers showing on the two dice is a prime number?

A.7/18

B.1/2

C.11/36

D.5/12

Explanation: The total number of outcomes is 36. Prime sums can be 2, 3, 5, 7, or 11. The outcomes for these sums are: 2: (1,1) [1]; 3: (1,2), (2,1) [2]; 5: (1,4), (2,3), (3,2), (4,1) [4]; 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) [6]; 11: (5,6), (6,5) [2]. Total favorable outcomes = 1 + 2 + 4 + 6 + 2 = 15. Probability = 15/36 = 5/12.

9In a class of 50 students, 30 play cricket, 25 play football, and 10 play both sports. How many students play neither cricket nor football?

A.5

B.10

C.15

D.20

Explanation: Let C be the students who play cricket and F be the students who play football. Using the principle of inclusion-exclusion, the number of students who play at least one sport is n(C u F) = n(C) + n(F) - n(C n F) = 30 + 25 - 10 = 45. The number of students who play neither is 50 - 45 = 5.

10Find the slope of a straight line perpendicular to the line passing through the points (2, 5) and (4, -1).

A.-3

B.1/3

C.3

D.-1/3

Explanation: The slope of the line passing through the points is m1 = (-1 - 5) / (4 - 2) = -6 / 2 = -3. Two perpendicular lines have slopes that satisfy m1 * m2 = -1. Therefore, -3 * m2 = -1, which yields m2 = 1/3.

About the CUSAT CAT B.Tech Exam

The CUSAT CAT B.Tech exam is a state-level entrance exam conducted for admissions into undergraduate engineering courses at Cochin University of Science and Technology's constituent colleges. This practice test contains exactly 100 questions representing the syllabus proportions: 40 questions of Mathematics, 35 questions of Physics, and 25 questions of Chemistry. All calculations are fully detailed with step-by-step solutions.

Exam sponsor: Cochin University of Science and Technology. The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Questions

225 questions

Time Limit

180 minutes

Passing Score

Min. normalised score 10 (PCM combined; SC/ST exempt)

Exam / Certification Fees

₹1,500 for General / ₹700 for Kerala SC/ST

Exam sponsor website

Reported exam pass rate: Competitive. Admissions to premier B.Tech courses are highly competitive and rank-dependent. Exam sponsor website

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

Official sources

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.

40%

Mathematics

Calculus, Linear Algebra, Coordinate Geometry, Vectors, Trigonometry, Complex Numbers, Sequences and Series, Probability, and Statistics (90 questions).

33.3%

Physics

Mechanics, Heat and Thermodynamics, Electrostatics, Magnetism, Optics, Modern Physics, and Waves (75 questions).

26.7%

Chemistry

Physical Chemistry (atomic structure, chemical kinetics, electrochemistry, thermodynamics), Organic Chemistry (reaction mechanisms, functional groups, hydrocarbons), and Inorganic Chemistry (s/p/d/f blocks, coordination compounds) (60 questions).

Preparing for the CUSAT CAT B.Tech Exam

What You Need to Know

Passing score: Min. normalised score 10 (PCM combined; SC/ST exempt)
Exam length: 225 questions
Time limit: 180 minutes
Exam / certification fees: ₹1,500 for General / ₹700 for Kerala SC/ST 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

CUSAT CAT B.Tech: Suggested Study Strategy

1Dedicate maximum revision time to Mathematics, as it represents 40% of the questions and is critical for qualifying criteria.

2Practice speed calculations regularly. Managing 225 questions in 180 minutes requires solving each question in under 48 seconds on average.

3Understand the marking scheme. Avoid blind guessing because the -1 mark penalty can significantly lower your percentile rank.

4Solve standard formula-based questions from Class 11 and 12 PCM textbooks, focusing on mechanics, electrostatics, integrations, and chemical kinetics.

5Keep concise formula notebooks for quick review of physics equations, chemistry conversion charts, and mathematical derivatives.

Frequently Asked Questions

Is there negative marking in the CUSAT CAT B.Tech exam?

Yes, CUSAT CAT has negative marking. Candidates receive +4 marks for each correct response, and -1 mark is deducted for each incorrect answer.

What is the minimum eligibility criteria for B.Tech admission at CUSAT?

Candidates must have passed Class 12 or equivalent with Physics, Chemistry, and Mathematics (PCM). They must secure a minimum of 50% marks in Mathematics and 50% aggregate marks in PCM subjects combined.

What is the official section-wise question breakdown?

The official exam features 225 questions in total: 90 questions in Mathematics, 75 questions in Physics, and 60 questions in Chemistry.

What is the application fee for the B.Tech exam?

The application fee is ₹1,500 for General category candidates and ₹700 for Kerala SC/ST candidates for a maximum of two test codes (Prospectus 2026).

How is the rank list prepared?

The CAT score is S = 4R − 1W. For Test Code 101, general candidates need a minimum normalised score of 10 for Mathematics, Physics, and Chemistry put together; Kerala SC/ST candidates are exempt from that minimum. Candidates who answer no questions are disqualified.