Major Competitive Exams MCQ & Objective Questions
Major Competitive Exams play a crucial role in shaping the academic and professional futures of students in India. These exams not only assess knowledge but also test problem-solving skills and time management. Practicing MCQs and objective questions is essential for scoring better, as they help in familiarizing students with the exam format and identifying important questions that frequently appear in tests.
What You Will Practise Here
Key concepts and theories related to major subjects
Important formulas and their applications
Definitions of critical terms and terminologies
Diagrams and illustrations to enhance understanding
Practice questions that mirror actual exam patterns
Strategies for solving objective questions efficiently
Time management techniques for competitive exams
Exam Relevance
The topics covered under Major Competitive Exams are integral to various examinations such as CBSE, State Boards, NEET, and JEE. Students can expect to encounter a mix of conceptual and application-based questions that require a solid understanding of the subjects. Common question patterns include multiple-choice questions that test both knowledge and analytical skills, making it essential to be well-prepared with practice MCQs.
Common Mistakes Students Make
Rushing through questions without reading them carefully
Overlooking the negative marking scheme in MCQs
Confusing similar concepts or terms
Neglecting to review previous years’ question papers
Failing to manage time effectively during the exam
FAQs
Question: How can I improve my performance in Major Competitive Exams?Answer: Regular practice of MCQs and understanding key concepts will significantly enhance your performance.
Question: What types of questions should I focus on for these exams?Answer: Concentrate on important Major Competitive Exams questions that frequently appear in past papers and mock tests.
Question: Are there specific strategies for tackling objective questions?Answer: Yes, practicing under timed conditions and reviewing mistakes can help develop effective strategies.
Start your journey towards success by solving practice MCQs today! Test your understanding and build confidence for your upcoming exams. Remember, consistent practice is the key to mastering Major Competitive Exams!
Q. What is the determinant of J = [[5, 4], [2, 3]]? (2022)
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Solution
The determinant of J is (5*3) - (4*2) = 15 - 8 = 7.
Correct Answer:
A
— 7
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Q. What is the determinant of the identity matrix I = [[1, 0], [0, 1]]? (2021)
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Solution
Det(I) = (1*1) - (0*0) = 1 - 0 = 1.
Correct Answer:
B
— 1
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Q. What is the determinant of the matrix E = [[1, 2, 3], [0, 1, 4], [5, 6, 0]]? (2021)
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Solution
The determinant of E is calculated using the rule of Sarrus or cofactor expansion, resulting in -14.
Correct Answer:
A
— -14
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Q. What is the determinant of the matrix E = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]?
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Solution
The determinant of E is 0 because the rows are linearly dependent.
Correct Answer:
A
— 0
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Q. What is the determinant of the matrix G = [[2, 4], [1, 3]]? (2021)
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Solution
The determinant of G is (2*3) - (4*1) = 6 - 4 = 2.
Correct Answer:
A
— 2
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Q. What is the determinant of the matrix H = [[1, 1, 1], [1, 2, 3], [1, 3, 6]]?
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Solution
The determinant can be calculated using the formula for 3x3 matrices. Here, the first column is the same, leading to a determinant of 0.
Correct Answer:
A
— 0
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Q. What is the determinant of the matrix J = [[2, 3], [4, 5]]? (2023)
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Solution
The determinant of J is (2*5) - (3*4) = 10 - 12 = -2.
Correct Answer:
A
— -2
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Q. What is the determinant of the matrix J = [[5, 6], [7, 8]]? (2019)
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Solution
The determinant of J is (5*8) - (6*7) = 40 - 42 = -2.
Correct Answer:
A
— -2
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Q. What is the determinant of the matrix [[0, 1], [1, 0]]?
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Solution
The determinant is calculated as (0*0) - (1*1) = 0 - 1 = -1.
Correct Answer:
C
— -1
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Q. What is the determinant of the matrix \( A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \)? (2021)
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Solution
The determinant of a 2x2 matrix \( A = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \) is given by \( ad - bc \). Here, \( 1*4 - 2*3 = 4 - 6 = -2 \).
Correct Answer:
A
— -2
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Q. What is the determinant of the matrix \( C = \begin{pmatrix} 5 & 0 \\ 0 & 7 \end{pmatrix} \)? (2020)
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Solution
The determinant of a diagonal matrix is the product of its diagonal elements: \( 5*7 = 35 \).
Correct Answer:
A
— 35
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Q. What is the determinant of the matrix \( C = \begin{pmatrix} 5 & 6 \\ 7 & 8 \end{pmatrix} \)? (2020)
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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 \( E = \begin{pmatrix} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 3 & 6 \end{pmatrix} \)? (2023)
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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. 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 \( F = \begin{pmatrix} 1 & 0 & 2 \\ 0 & 1 & 3 \\ 0 & 0 & 1 \end{pmatrix} \)? (2022)
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Solution
The determinant of an upper triangular matrix is the product of its diagonal elements: \( 1*1*1 = 1 \).
Correct Answer:
A
— 1
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Q. What is the determinant of the matrix \( F = \begin{pmatrix} 1 & 2 & 3 \\ 0 & 1 & 4 \\ 5 & 6 & 0 \end{pmatrix} \)? (2022)
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Solution
Using the determinant formula for 3x3 matrices, we find \( 1(1*0 - 4*6) - 2(0*0 - 4*5) + 3(0*6 - 1*5) = 1(0 - 24) - 2(0 - 20) + 3(0 - 5) = -24 + 40 - 15 = 1 \).
Correct Answer:
A
— -14
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Q. What is the determinant of the matrix \( F = \begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{pmatrix} \)? (2020)
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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 \( F = \begin{pmatrix} 2 & 5 \\ 3 & 7 \end{pmatrix} \)? (2023)
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Solution
The determinant is calculated as \( 2*7 - 5*3 = 14 - 15 = -1 \).
Correct Answer:
A
— -1
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Q. What is the determinant of the matrix \( G = \begin{pmatrix} 2 & 3 \\ 5 & 7 \end{pmatrix} \)? (2023)
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Solution
The determinant is \( 2*7 - 3*5 = 14 - 15 = -1 \).
Correct Answer:
A
— 1
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Q. What is the determinant of the matrix \( H = \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix} \)? (2022)
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Solution
The determinant of the identity matrix is always 1.
Correct Answer:
B
— 1
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Q. What is the determinant of the matrix \( H = \begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{pmatrix} \)? (2023)
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Solution
The determinant of this matrix is 0 because the rows are linearly dependent.
Correct Answer:
A
— 0
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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 \( I = \begin{pmatrix} 4 & 2 \\ 1 & 3 \end{pmatrix} \)? (2021)
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Solution
The determinant is \( 4*3 - 2*1 = 12 - 2 = 10 \).
Correct Answer:
A
— 10
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Q. What is the determinant of the matrix \( J = \begin{pmatrix} 5 & 6 \\ 7 & 8 \end{pmatrix} \)? (2021)
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Solution
Det(J) = (5*8) - (6*7) = 40 - 42 = -2.
Correct Answer:
A
— -2
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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 \( \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \)?
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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 \( \begin{pmatrix} 1 & 2 \\ 3 & 5 \end{pmatrix} \)?
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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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