Matrices and Determinants form a significant and often scoring topic in the NDA 2 2025 Mathematics paper. Regular practice with a variety of questions is key to mastering the concepts and improving your problem-solving speed and accuracy. This article presents some practice questions on matrices and determinants relevant to the NDA 2 2025 syllabus, along with hints to guide your approach.
Practice Questions:
Question 1:
If A=(1324), then find A−1.
(Hint: For a 2×2 matrix A=(acbd), A−1=ad−bc1(d−c−ba), provided ad−bc=0.)**
Question 2:
What is the value of the determinant 111abcb+cc+aa+b
?
(Hint: Apply properties of determinants, such as C3→C3+C2.)**
Question 3:
If A=(23−14) and B=(572−3), find 2A−3B.
(Hint: Perform scalar multiplication on each matrix and then subtract the corresponding elements.)**
Question 4:
For what value of k is the matrix (k326) singular?
(Hint: A matrix is singular if its determinant is equal to zero.)**
Question 5:
If A=100020003
, find A2.
(Hint: Multiply matrix A by itself.)**
Question 6:
Consider the system of linear equations: x+y+z=3 x−y+z=1 2x+y−z=2
Determine if this system has a unique solution, no solution, or infinitely many solutions using determinants.
(Hint: Calculate the determinant of the coefficient matrix. If it’s non-zero, there’s a unique solution.)**
Question 7:
If A is a square matrix of order 3 and ∣A∣=5, what is the value of ∣3A∣?
(Hint: For a square matrix A of order n, ∣kA∣=kn∣A∣.)**
Question 8:
Find the adjoint of the matrix B=(1324).
(Hint: The adjoint of a 2×2 matrix B=(acbd) is adj(B)=(d−c−ba).)**
Question 9:
If A=(cosθsinθ−sinθcosθ), find ATA.
(Hint: First find the transpose of matrix A (AT), then multiply AT by A.)**
Question 10:
What is the rank of the matrix C=(122436)?
(Hint: The rank of a matrix is the maximum number of linearly independent rows or columns.)**
Practice Tips:
- Understand the Properties: Ensure you have a strong grasp of the properties of matrices and determinants.
- Apply Formulas Correctly: Pay close attention to the formulas and their conditions of applicability.
- Practice Different Types: Solve a variety of problems, including finding inverses, determinants, adjoints, and solving systems of linear equations.
- Time Yourself: Practice solving these questions within a time limit to improve your speed.
Regular practice with these types of questions will solidify your understanding of matrices and determinants and prepare you well for the NDA 2 2025 Mathematics paper. Remember to review the underlying concepts if you find any of these questions challenging.
#NDA2025 #NDAMaths #Matrices #Determinants #MathPractice #DefenceExams #Algebra
