Q. If \( B = \begin{pmatrix} 1 & 2 & 1 \\ 0 & 1 & 0 \\ 2 & 3 & 1 \end{pmatrix} \), what is \( |B| \)?
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Solution
The determinant is calculated as 1(1*1 - 0*3) - 2(0*1 - 1*2) + 1(0*3 - 1*2) = 1 - 4 - 2 = -5.
Correct Answer:
B
— 2
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Q. If \( B = \begin{pmatrix} 1 & 2 & 3 \\ 0 & 1 & 4 \\ 5 & 6 & 0 \end{pmatrix} \), what is \( \det(B) \)?
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Solution
Using the determinant formula, we find \( \det(B) = 1(1*0 - 4*6) - 2(0 - 4*5) + 3(0 - 1*5) = -24 \).
Correct Answer:
A
— -24
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Q. If \( B = \begin{pmatrix} 1 & 2 \\ 2 & 4 \end{pmatrix} \), what is \( |B| \)?
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Solution
The determinant is 0 because the rows are linearly dependent.
Correct Answer:
A
— 0
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Q. If \( B = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \), what is \( |B| \)?
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Solution
The determinant is \( 1*4 - 2*3 = 4 - 6 = -2 \).
Correct Answer:
A
— -2
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Q. If \( B = \begin{pmatrix} 1 & 2 \\ 3 & 5 \end{pmatrix} \), what is \( |B| \)?
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Solution
The determinant is \( 1*5 - 2*3 = 5 - 6 = -1 \).
Correct Answer:
B
— 1
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Q. If \( B = \begin{pmatrix} 2 & 3 \\ 1 & 4 \end{pmatrix} \), find \( |B| \).
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Solution
The determinant is \( 2*4 - 3*1 = 8 - 3 = 5 \).
Correct Answer:
A
— 5
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Q. If \( C = \begin{pmatrix} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 3 & 6 \end{pmatrix} \), find \( |C| \).
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Solution
The determinant is 0 because the first column is a linear combination of the others.
Correct Answer:
A
— 0
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Q. If \( C = \begin{pmatrix} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 3 & 6 \end{pmatrix} \), find \( \det(C) \).
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Solution
The determinant is 0 because the first column is a linear combination of the other columns.
Correct Answer:
A
— 0
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Q. If \( C = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \), what is the determinant of C?
A.
ad - bc
B.
bc - ad
C.
a + d
D.
b + c
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Solution
The determinant of C is given by the formula \( ad - bc \).
Correct Answer:
A
— ad - bc
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Q. If \( D = \begin{vmatrix} 2 & 3 & 1 \\ 1 & 0 & 2 \\ 4 & 1 & 0 \end{vmatrix} \), find \( D \).
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Solution
Calculating gives \( 2(0*0 - 2*1) - 3(1*0 - 2*4) + 1(1*1 - 0*4) = -4 + 24 + 1 = 21 \).
Correct Answer:
A
— -10
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Q. If \( F = \begin{pmatrix} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 3 & 6 \end{pmatrix} \), what is the value of the determinant?
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Solution
The determinant is 0 because the first column is a linear combination of the other columns.
Correct Answer:
A
— 0
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Q. If \( J = \begin{pmatrix} 1 & 2 & 1 \\ 0 & 1 & 0 \\ 2 & 1 & 3 \end{pmatrix} \), what is the value of the determinant?
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Solution
The determinant is calculated as \( 1(1*3 - 0*1) - 2(0*3 - 1*2) + 1(0*1 - 1*2) = 3 + 4 - 2 = 5 \).
Correct Answer:
A
— 0
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Q. What is the determinant of the matrix \( E = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \)?
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Solution
The determinant is calculated as \( 1*4 - 2*3 = 4 - 6 = -2 \).
Correct Answer:
A
— -2
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Q. What is the determinant of the matrix \( H = \begin{pmatrix} 1 & 2 \\ 2 & 4 \end{pmatrix} \)?
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Solution
The determinant is 0 because the rows are linearly dependent.
Correct Answer:
A
— 0
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Q. What is the determinant of the matrix \( \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix} \)?
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Solution
The determinant of the identity matrix is 1.
Correct Answer:
B
— 1
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Q. What is the determinant of the matrix \( \begin{pmatrix} 1 & 1 \\ 1 & 1 \end{pmatrix} \)?
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Solution
The determinant is calculated as (1*1) - (1*1) = 1 - 1 = 0.
Correct Answer:
A
— 0
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Q. What is the determinant of the matrix \( \begin{pmatrix} 1 & 2 & 1 \\ 0 & 1 & 0 \\ 2 & 3 & 1 \end{pmatrix} \)?
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Solution
The determinant is calculated as \( 1(1*1 - 0*3) - 2(0*1 - 0*2) + 1(0*3 - 1*2) = 1 - 0 - 2 = -1 \).
Correct Answer:
B
— 1
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Q. What is the determinant of the matrix \( \begin{pmatrix} 1 & 2 \\ 2 & 4 \end{pmatrix} \)?
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Solution
The determinant is 0 because the rows are linearly dependent.
Correct Answer:
A
— 0
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Q. What is the determinant of the matrix \( \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \)?
Show solution
Solution
The determinant is calculated as \( 1*4 - 2*3 = 4 - 6 = -2 \).
Correct Answer:
A
— -2
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Q. What is the determinant of the matrix \( \begin{pmatrix} 1 & 2 \\ 3 & 5 \end{pmatrix} \)?
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Solution
The determinant is calculated as \( 1*5 - 2*3 = 5 - 6 = -1 \).
Correct Answer:
B
— 1
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Q. What is the determinant of the matrix \( \begin{pmatrix} 3 & 2 \\ 1 & 4 \end{pmatrix} \)?
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Solution
The determinant is calculated as (3*4) - (2*1) = 12 - 2 = 10.
Correct Answer:
A
— 10
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Q. What is the determinant of the matrix \( \begin{pmatrix} 5 & 6 \\ 7 & 8 \end{pmatrix} \)?
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Solution
The determinant is calculated as \( 5*8 - 6*7 = 40 - 42 = -2 \).
Correct Answer:
A
— -2
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Q. What is the determinant of the matrix: | 1 2 3 | | 4 5 6 | | 7 8 10 |?
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Solution
Calculating gives a determinant of -3.
Correct Answer:
A
— -3
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Q. What is the value of the determinant of the matrix \( A = \begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{pmatrix} \)?
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Solution
The determinant of matrix A is 0 because the rows are linearly dependent.
Correct Answer:
A
— 0
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Q. What is the value of the determinant of the matrix \( \begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{pmatrix} \)?
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Solution
The determinant of the matrix is 0 because the rows are linearly dependent.
Correct Answer:
A
— 0
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Q. What is the value of the determinant \( \begin{vmatrix} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 3 & 6 \end{vmatrix} \)?
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Solution
The determinant is 0 because the first column is repeated.
Correct Answer:
A
— 0
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Q. What is the value of the determinant \( \begin{vmatrix} a & b \\ c & d \end{vmatrix} \) when \( a = 1, b = 2, c = 3, d = 4 \)?
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Solution
The determinant is \( 1*4 - 2*3 = 4 - 6 = -2 \).
Correct Answer:
A
— -2
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Q. What is the value of the determinant | 1 2 3 | | 0 1 4 | | 5 6 0 |?
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Solution
Calculating the determinant gives -12.
Correct Answer:
A
— -12
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Q. What is the value of the determinant | a b | | c d | when a = 2, b = 3, c = 4, d = 5?
Show solution
Solution
det = (2)(5) - (3)(4) = 10 - 12 = -2.
Correct Answer:
C
— 2
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Q. What is the value of \( \begin{vmatrix} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 3 & 6 \end{vmatrix} \)?
Show solution
Solution
The determinant is 0 because the first column is repeated.
Correct Answer:
A
— 0
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Showing 61 to 90 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!
