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Determinants

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Q. Evaluate \( \begin{vmatrix} x & 1 \\ 1 & y \end{vmatrix} \) when \( x = 2 \) and \( y = 3 \).
  • A. 5
  • B. 6
  • C. 7
  • D. 8
Q. Find the determinant of the matrix \( D = \begin{pmatrix} 1 & 0 & 2 \\ 0 & 1 & 3 \\ 0 & 0 & 1 \end{pmatrix} \).
  • A. 0
  • B. 1
  • C. 2
  • D. 3
Q. Find the determinant of the matrix \( I = \begin{pmatrix} 3 & 2 \\ 1 & 4 \end{pmatrix} \).
  • A. 10
  • B. 11
  • C. 12
  • D. 13
Q. Find the determinant of the matrix \( \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix} \).
  • A. 0
  • B. 1
  • C. 2
  • D. 3
Q. Find the determinant of the matrix \( \begin{pmatrix} 2 & 1 \\ 3 & 4 \end{pmatrix} \).
  • A. 5
  • B. 10
  • C. 7
  • D. 6
Q. Find the determinant of the matrix \( \begin{pmatrix} 2 & 3 & 1 \\ 1 & 0 & 4 \\ 5 & 2 & 1 \end{pmatrix} \).
  • A. -1
  • B. 0
  • C. 1
  • D. 2
Q. Find the determinant of the matrix \( \begin{pmatrix} 2 & 3 & 1 \\ 1 & 0 & 2 \\ 4 & 1 & 0 \end{pmatrix} \).
  • A. -10
  • B. 10
  • C. 0
  • D. 5
Q. Find the determinant of the matrix \( \begin{pmatrix} 2 & 3 \\ 1 & 4 \end{pmatrix} \).
  • A. 5
  • B. 6
  • C. 7
  • D. 8
Q. Find the determinant of the matrix \( \begin{pmatrix} a & b \\ c & d \end{pmatrix} \).
  • A. ad - bc
  • B. bc - ad
  • C. a + b + c + d
  • D. a^2 + b^2
Q. Find the determinant of the matrix | 1 0 0 | | 0 1 0 | | 0 0 1 |.
  • A. 0
  • B. 1
  • C. 2
  • D. 3
Q. Find the determinant of the matrix | 1 2 3 | | 0 1 4 | | 5 6 0 |.
  • A. -12
  • B. 0
  • C. 12
  • D. 24
Q. Find the determinant of the matrix: | 1 2 | | 3 5 |.
  • A. -1
  • B. 1
  • C. 2
  • D. 3
Q. Find the value of the determinant \( \begin{pmatrix} a & b \\ c & d \end{pmatrix} \) when \( a=1, b=2, c=3, d=4 \).
  • A. -2
  • B. 2
  • C. 0
  • D. 1
Q. Find the value of the determinant \( |D| \) where \( D = \begin{pmatrix} 1 & 2 & 3 \\ 0 & 1 & 4 \\ 5 & 6 & 0 \end{pmatrix} \).
  • A. -12
  • B. -10
  • C. -8
  • D. -6
Q. Find the value of the determinant: | 2 3 1 | | 1 0 4 | | 0 5 2 |
  • A. -1
  • B. 1
  • C. 2
  • D. 3
Q. Find the value of the determinant: | 2 3 1 | | 1 0 4 | | 5 6 2 |
  • A. -20
  • B. -10
  • C. 10
  • D. 20
Q. Find the value of the determinant: | 2 3 1 | | 1 0 4 | | 5 6 7 |
  • A. -30
  • B. -20
  • C. 20
  • D. 30
Q. Find the value of the determinant: | x 1 2 | | 3 x 4 | | 5 6 x | when x = 1.
  • A. -6
  • B. 0
  • C. 6
  • D. 12
Q. Find the value of \( k \) for which the determinant \( \begin{vmatrix} 1 & 2 & 3 \\ 4 & k & 6 \\ 7 & 8 & 9 \end{vmatrix} = 0 \)
  • A. 5
  • B. 6
  • C. 7
  • D. 8
Q. Find the value of \( \det \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix} \).
  • A. 0
  • B. 1
  • C. 2
  • D. 3
Q. For the matrix \( B = \begin{pmatrix} 1 & 2 \\ 2 & 4 \end{pmatrix} \), what is the determinant \( |B| \)?
  • A. 0
  • B. 1
  • C. 2
  • D. 4
Q. If A = | 1 2 | | 3 4 |, find det(A).
  • A. -2
  • B. 2
  • C. 0
  • D. 4
Q. If A = | 1 2 | | 3 4 |, what is det(A)?
  • A. -2
  • B. 2
  • C. 0
  • D. 4
Q. If A = | 1 2 | | 3 5 |, what is det(2A)?
  • A. -10
  • B. 10
  • C. 20
  • D. 40
Q. If B = | 2 3 | | 1 4 |, find det(B).
  • A. -5
  • B. 5
  • C. 6
  • D. 7
Q. If the determinant | x 2 | | 3 4 | = 0, find x.
  • A. 1
  • B. 2
  • C. 3
  • D. 4
Q. If \( A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \), find \( |A| \).
  • A. -2
  • B. 2
  • C. 0
  • D. 1
Q. If \( A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \), what is \( |2A| \)?
  • A. -8
  • B. 8
  • C. 4
  • D. 16
Q. If \( A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \), what is \( |A| \)?
  • A. -2
  • B. 2
  • C. 0
  • D. 4
Q. If \( A = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \), what is the determinant of A?
  • A. ad - bc
  • B. bc - ad
  • C. a + d
  • D. b + c
Showing 31 to 60 of 90 (3 Pages)

Determinants MCQ & Objective Questions

Understanding determinants is crucial for students preparing for various exams in India. This mathematical concept not only forms the backbone of linear algebra but also plays a significant role in solving problems related to matrices. Practicing MCQs and objective questions on determinants enhances your problem-solving skills and boosts your confidence, ensuring you score better in exams.

What You Will Practise Here

  • Definition and properties of determinants
  • Calculation of determinants for 2x2 and 3x3 matrices
  • Applications of determinants in solving linear equations
  • Expansion of determinants using minors and cofactors
  • Understanding the geometric interpretation of determinants
  • Common theorems related to determinants
  • Practice questions on determinants with detailed solutions

Exam Relevance

Determinants are a vital topic in the curriculum for CBSE, State Boards, NEET, and JEE exams. You can expect questions that require you to compute determinants, apply properties, or solve real-world problems using determinants. Common question patterns include direct computation, application in systems of equations, and theoretical questions that test your understanding of the concept.

Common Mistakes Students Make

  • Confusing the properties of determinants, especially when dealing with larger matrices.
  • Making arithmetic errors while calculating determinants, particularly in 3x3 matrices.
  • Overlooking the importance of signs when using minors and cofactors.
  • Failing to recognize when a determinant equals zero and its implications.

FAQs

Question: What is a determinant?
Answer: A determinant is a scalar value that can be computed from the elements of a square matrix, providing important information about the matrix, such as whether it is invertible.

Question: How do I calculate the determinant of a 3x3 matrix?
Answer: To calculate the determinant of a 3x3 matrix, you can use the rule of Sarrus or the method of minors and cofactors.

Ready to master determinants? Start solving practice MCQs today to test your understanding and improve your exam readiness!

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