COMEDK UGET 2025 Matrices and Determinants Practice Questions with Solutions

COMEDK UGET 2025 Matrices and Determinants Practice Questions with Solutions: COMEDK practice questions guide you by helping you assess your exam preparation, strengths and shortcomings, and focusing on key ares that need improvement. By solving sample questions from Matrices and Determinants for COMEDK exam 2025, you can gain better understanding of the topics, format of the questions, and difficulty level of the section. In this article, we have provided some of the most important and expected COMEDK UGET 2025 Matrices and Determinants practice questions with solutions based on the past years' paper analysis. COMEDK UGET 2025 Mathematics syllabus provides a significant weightage for Matrices and Determinants. This chapter covers around 6-8% of weightage; you can expect around 4-5 questions from this topic. It is recommended that you study this chapter diligently and solve the sample questions, focusing on important topics to score best marks in COMEDK UGET 2025 exam .

Also Check - COMEDK Chapter Wise PYQ for Mathematics

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COMEDK UGET 2025 Matrices and Determinants Important Topics

While the Algebra section is one of the most scoring sections in the Mathematics paper, it is recommended that you prepare the Matrices and Determinants important topics to ensure you are able to solve all the questions with accuracy on the day of the exam. In the following table, we have provided the detailed Matrices and Determinants from the COMEDK 2025 syllabus:

Also Check - Do or Die Chapters for COMEDK UGET 2025 Mathematics

COMEDK UGET 2025 Matrices and Determinants Expected Weightage

COMEDK Matrices and Determinants weightage will help you understand how many marks will be covered from this chapter. As per recent trends, we can assume that Matrices weightage will be around 6-8%. Therefore, you can expect around 4-5 questions. In the following table, we have detailed the Matrices and Determinants weightage in COMEDK Mathematics exam:

COMEDK UGET 2025 Matrices and Determinants Practice Questions with Solutions

In this section, we have shared a few COMEDK UGET 2025 Matrices and Determinants practice questions with solutions. By attempting these mock questions, analyze your performance and track your progress. This will also help you to improve your speed and accuracy, and boost confidence before taking the actual exam.

Q1. If A (adj A) = 5I, where I is the identity matrix of order 3, then |adj A| =

a. 125

b. 25

c. 5

d. 10

Ans. b. 25

Solution: We start with the well-known property of matrices:

A.(adjA) = |A|.I

Where |A| denotes the determinant of A and I is the identity matrix.

In this problem, we are given:

A.(adjA) = 5I

Comparing the two equations, it follows directly that:

|A|I = 5I = 5

Next, recall another important property for any n x n matrix:

|adj A| = |A| ^n-1

Since A is of order 3 (n = 3), we have:

|adj A| = |A| ² = 25

Q2. A square matrix P satisfies P2 = I - P where I is the identity matrix. If Pn= 5I - 8P, then n is equal to?

a. 6

b. 4

c. 8

d. 10

Ans. a. 6

Solution: We start with the given relation for the square matrix P:

P ² = I - P

Since any power of P can be expressed in the form αI + βP, we write

P ⁿ = 5I - 8P

Let’s determine the coefficients step by step:

For n = 0

We have P ⁰ = I, so,

a ₀ = 1, b ₁ = 0,

For n = 1,

We have P ¹ = P

a ₁ = 0, and b ₁ = 1

For n = 2

a ₂ = 1, b ₂ = -1

For n =3, multiplying P ² .P

P ³ = 2P - I

a ₃ = -1, b ₃ = 2.

For n = 4, multiplying P ³ .P

P ⁴ = 2I - 3P

a ₄ = 2, b ₄ = -3

For n = 5, multiplying P ⁴ .P

P ⁵ = - 3I + 5P

a ₅ = -3, b ₅ = 5

For n = 6, multiplying P ⁵ .P

P ⁶ = 5I - 8P

a ₆ = 5, b ₆ = -8

Thus the correct answer is 6.

Q3. If A is a matrix of order 4 such that A(adj.A) = 10I, then |adj A| is equal to:

a. 10

b. 100

c. 1000

d. 10000

Ans. c. 1000

Solution: Given, A(adj A) = 10I

We know that A(adj.A) = |A|I

10I = |A|I

|A| = 10

We know that |adj A| = |A| ^n-1 , where n is order of A

10 ³ = 1000.

Q4. A and B are invertible matrices of the same order such that |(AB)-1| = 8 if |A| = 2 then |B| is:

a. 6

b. 16

c. 1\16

d. 4

Ans. c. 1/16

Solution: To solve this problem, we'll use the properties of determinants specifically relating to the multiplication of matrices and the determinant of an inverse matrix.

If A and B are invertible matrices of the same order, then

The determinant of the product of two matrices is the product of their determinants, i.e., |AB| = |A||B|

The determinant of the inverse of a matrix is the inverse of the determinant of the matrix, i.e., |(AB} ^-1 |  = 1/|AB|

GIven, |(AB} ^-1 | = |AB| = 1/8

|AB| = |A||B|

|B| = 1/8 ∻ 2 = 1/16

Q5. Solution of x - y + z; x -2y +2z = 9 and 2x + y + 3z = 1 is:

a. x =3; y = 6; z = 9

b. x =-4; y = -3; z = 2

c. x = -1; y = -3; z = 2

d. x = 2; y = 4; z = 6

Ans. c. x = -1; y = -3; z = 2

Solution: To find the solution of the given system of linear equations:

x - y + z = 4 …1

x - 2y + 2z = 9 …2

2x + y +3z = 1 …3

Let's try to eliminate variables to solve for each variable and see which option fits:

First, subtract equation (1) from equation (2) to eliminate the variable x

(x - 2y + 2z) - (x - y + z) = 9 - 4 = 5

- y + z = 5 …(4)

Now, we can use equations (4) and (1) to eliminate z

Multiply equation (4) by -1 and add to equation (1):

z - y = -5

x - y + z = 4

x = -5 …(5)

From equation (4)

- y + z = 5

From equation 3

y = -3 …(6)

Simplifying,

z = 2 …(7)

x = -1; y = -3; z = 2

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