Engineering Mathematics gives GATE CSE candidates some of the most predictable marks in the paper. This GATE-style set covers rank, determinants, eigenvalues, systems of linear equations, conditional probability, Bayes' theorem, expectation and variance, common distributions, limits and maxima.
How to practise: read each question and tap the option you think is correct. You will see right away whether you got it, along with a short explanation, and your score is tracked at the bottom of the screen. This set has 15 questions.
Topics covered in this set
- Rank and determinants
- Eigenvalues, trace and determinant
- Systems of linear equations
- Conditional probability and Bayes' theorem
- Expectation, variance and distributions
- Limits and maxima
GATE CSE Engineering Mathematics MCQs with answers and explanations
Q1. What is the rank of the matrix [[1, 2, 3], [2, 4, 6], [1, 1, 1]]?
a) 0
b) 1
c) 2
d) 3
Q2. A is a 3 × 3 matrix with det(A) = 5. What is det(2A)?
a) 80
b) 10
c) 15
d) 40
Q3. What are the eigenvalues of the matrix [[2, 1], [1, 2]]?
a) 1 and 3
b) −1 and 3
c) 2 and 2
d) 0 and 4
Q4. A 3 × 3 matrix A has eigenvalues 1, 2 and 4. What is the trace of A² + I?
a) 21
b) 7
c) 10
d) 24
Q5. For which value of k does the system x + y + z = 1, x + 2y + 3z = 2, x + 3y + kz = 3 have infinitely many solutions?
a) k = 3
b) k = 5
c) k = 6
d) k = 4
Q6. A homogeneous system Ax = 0 has 5 unknowns and the rank of A is 3. How many linearly independent solutions does it have?
a) 5
b) 3
c) 0
d) 2
Q7. A family has two children. Given that at least one of them is a boy, what is the probability that both are boys? (Assume each child is equally likely to be a boy or a girl.)
a) 1/2
b) 2/3
c) 1/4
d) 1/3
Q8. A disease affects 1% of a population. A test detects it in 99% of patients who have it and gives a false positive for 5% of healthy people. What is the probability that a person who tests positive has the disease?
a) 0.5
b) 1/6
c) 0.99
d) 1/20
Q9. Events A and B have P(A) = 0.5, P(B) = 0.4 and P(A ∪ B) = 0.7. Which statement is true?
a) B is a subset of A
b) A and B are independent
c) A and B are mutually exclusive
d) P(A | B) = 0.25
Q10. X is the outcome of one roll of a fair six-sided die. What is Var(X)?
a) 5/2
b) 35/12
c) 7/2
d) 91/6
Q11. A fair coin is tossed 4 times. What is the probability of getting exactly 2 heads?
a) 1/4
b) 1/2
c) 5/16
d) 3/8
Q12. A Poisson random variable X satisfies P(X = 1) = P(X = 2). What is its mean?
a) √2
b) 1
c) 4
d) 2
Q13. X is uniformly distributed on the interval [0, 6]. What is its variance?
a) 1.5
b) 12
c) 3
d) 6
Q14. What is the value of lim (x → ∞) (1 + 2/x)ˣ?
a) 1
b) e
c) e²
d) 2
Q15. At which point does f(x) = x³ − 6x² + 9x + 1 have a local maximum, and what is the value there?
a) x = 0, value 1
b) x = 1, value 5
c) x = 3, value 1
d) x = 2, value 3
Quick revision notes
- det(kA) = kⁿ det(A); trace = sum of eigenvalues; det = product.
- Eigenvalues of p(A) are p(λ); of A⁻¹ are 1/λ.
- Ax = b: unique if rank = n; infinite if rank(A) = rank([A|b]) < n; none if ranks differ.
- Independent events: P(A ∩ B) = P(A)P(B).
- Binomial mean np, variance npq; Poisson mean = variance = λ; uniform variance (b − a)²/12.
Frequently asked questions
Are these GATE previous year questions?
No, they are original GATE-style practice questions written to the GATE CSE Engineering Mathematics syllabus.
How much weight does Engineering Mathematics carry in GATE CSE?
It usually carries around 10 to 13 marks, and the questions are mostly short calculations on linear algebra, probability and calculus.
What is the fastest check for eigenvalue answers?
Compare the sum of the options with the trace and their product with the determinant. This rules out most wrong options without solving the characteristic equation.
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