Matrices, determinants and probability are reliable scoring areas in JEE Main. This set covers determinant properties, powers, adjoint and inverse, consistency of linear equations, conditional probability, Bayes theorem and the binomial distribution, with the working for each answer.
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
- Determinants and their properties
- Powers, transpose and inverse of a matrix
- Adjoint and |kA|
- Consistency of a system of linear equations
- Classical and conditional probability
- Bayes theorem and binomial distribution
JEE Mathematics MCQs with answers and explanations
Q1. What is the determinant of the matrix [[1, 2], [3, 4]]?
a) −2
b) 2
c) 10
d) −10
Q2. A is a 3 × 3 matrix with |A| = 4. What is |2A|?
a) 16
b) 8
c) 64
d) 32
Q3. If A = [[1, 1], [0, 1]], what is A⁵?
a) [[1, 1], [0, 1]]
b) [[1, 5], [0, 1]]
c) [[1, 25], [0, 1]]
d) [[5, 5], [0, 5]]
Q4. What is the inverse of [[2, 1], [5, 3]]?
a) [[3, −1], [−5, 2]]
b) [[−3, 1], [5, −2]]
c) [[3, 1], [5, 2]]
d) [[2, −1], [−5, 3]]
Q5. A is a 3 × 3 matrix with |A| = 5. What is |adj A|?
a) 25
b) 125
c) 5
d) 15
Q6. What is the determinant of [[1, 2, 3], [4, 5, 6], [7, 8, 9]]?
a) 0
b) −3
c) 6
d) 3
Q7. For what value of k does the system x + 2y = 3, 2x + ky = 5 have no solution?
a) 2
b) −4
c) 1
d) 4
Q8. If A is a skew-symmetric matrix of order 3, what is |A|?
a) It depends on the entries
b) 0
c) 1
d) −1
Q9. For matrices A and B for which AB is defined, what is (AB)ᵀ?
a) AB
b) AᵀBᵀ
c) BA
d) BᵀAᵀ
Q10. Two fair dice are thrown. What is the probability that the sum is 7?
a) 1/12
b) 1/6
c) 5/36
d) 7/36
Q11. A fair coin is tossed 3 times. What is the probability of getting at least one head?
a) 7/8
b) 1/2
c) 3/4
d) 3/8
Q12. If P(A) = 0.5, P(B) = 0.4 and P(A ∩ B) = 0.2, what is P(A | B)?
a) 0.8
b) 0.5
c) 0.2
d) 0.4
Q13. Bag I has 3 red and 2 black balls, and Bag II has 2 red and 3 black balls. A bag is chosen at random and a ball drawn from it is red. What is the probability that it came from Bag I?
a) 2/5
b) 1/2
c) 3/10
d) 3/5
Q14. A fair coin is tossed 4 times. What is the probability of exactly 2 heads?
a) 3/8
b) 5/16
c) 1/2
d) 1/4
Q15. For a binomial distribution with n = 10 and p = 0.3, what is the variance?
a) 0.21
b) 3
c) 2.1
d) 7
Quick revision notes
- |kA| = kⁿ|A|; |adj A| = |A|ⁿ⁻¹; A⁻¹ = adj A / |A|.
- (AB)ᵀ = BᵀAᵀ and (AB)⁻¹ = B⁻¹A⁻¹.
- Skew-symmetric of odd order ⇒ determinant 0.
- |A| = 0 with inconsistent equations ⇒ no solution; with dependent equations ⇒ infinitely many.
- P(A | B) = P(A ∩ B)/P(B); binomial mean np, variance npq.
Frequently asked questions
Are these JEE previous year questions?
No. They are original practice questions at the JEE Main level.
How do I decide if a linear system has no solution or infinitely many?
If the determinant is non-zero there is a unique solution. If it is zero, check whether the equations contradict each other (no solution) or are multiples of each other (infinitely many).
When should I use Bayes theorem?
Use it when you know the result of an experiment and need the probability of the cause, such as which bag a ball came from.
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