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 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 diameter of a circle if its area is 50π square units? (2017)
A.
10 units
B.
5 units
C.
20 units
D.
15 units
Show solution
Solution
Area = πr²; 50π = πr²; r² = 50; r = √50; Diameter = 2√50 ≈ 10 units.
Correct Answer:
A
— 10 units
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Q. What is the diameter of a circle if its area is 78.5 cm²? (2020)
A.
10 cm
B.
8 cm
C.
6 cm
D.
12 cm
Show solution
Solution
Area = πr²; 78.5 = π * r²; r² = 78.5/π; d = 2√(78.5/π) = 10 cm.
Correct Answer:
A
— 10 cm
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Q. What is the diameter of a circle with a radius of 9 cm? (2022)
A.
9 cm
B.
18 cm
C.
27 cm
D.
36 cm
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Solution
Diameter = 2 * radius = 2 * 9 cm = 18 cm.
Correct Answer:
B
— 18 cm
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Q. What is the diameter of a circle with an area of 50.24 cm²? (2019)
A.
8 cm
B.
10 cm
C.
12 cm
D.
14 cm
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Solution
Area = πr²; 50.24 = πr²; r² = 50.24/π; r ≈ 4 cm; Diameter = 2r = 8 cm.
Correct Answer:
B
— 10 cm
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Q. What is the diameter of a circle with an area of 50π square units? (2017)
A.
10 units
B.
5 units
C.
20 units
D.
15 units
Show solution
Solution
Area = πr²; 50π = πr²; r² = 50; r = √50; Diameter = 2√50 ≈ 10 units.
Correct Answer:
A
— 10 units
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Q. What is the diameter of a circle with an area of 78.5 cm²? (2018)
A.
10 cm
B.
8 cm
C.
6 cm
D.
12 cm
Show solution
Solution
Area = πr²; 78.5 = πr²; r² = 78.5/π; d = 2√(78.5/π) ≈ 10 cm.
Correct Answer:
A
— 10 cm
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Q. What is the dielectric constant of a vacuum? (2023)
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Solution
The dielectric constant (κ) of a vacuum is defined as 1, which serves as the reference for other materials.
Correct Answer:
A
— 1
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Q. What is the difference between the amounts obtained by investing $1000 at 8% per annum for 2 years in simple interest and compound interest?
A.
$16
B.
$24
C.
$32
D.
$40
Show solution
Solution
SI = 1000 * 8/100 * 2 = $160. CI = 1000(1 + 0.08)^2 = $1166.4. Difference = $1166.4 - $160 = $24.
Correct Answer:
B
— $24
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Q. What is the difference between the compound interest and simple interest on a principal of $1000 at 8% per annum after 2 years?
A.
$16
B.
$32
C.
$24
D.
$20
Show solution
Solution
SI = 1000 × 0.08 × 2 = $160. CI = 1000(1 + 0.08)^2 - 1000 = 1000(1.1664) - 1000 = $166.40. Difference = $166.40 - $160 = $6.40.
Correct Answer:
B
— $32
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Q. What is the difference between the compound interest and simple interest on a sum of $1000 at 5% per annum after 2 years? (2023)
A.
$10
B.
$20
C.
$30
D.
$40
Show solution
Solution
SI = 1000 * 5 * 2 / 100 = $100. CI = 1000[(1 + 0.05)^2 - 1] = $102.5. The difference is $2.5.
Correct Answer:
B
— $20
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Q. What is the difference in sales between Product A and Product B in Q2?
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Solution
Sales for Product A in Q2 = 120, Product B = 100. Difference = 120 - 100 = 20.
Correct Answer:
B
— 20
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Q. What is the difference in sales between Product A and Product C in Q2?
A.
$500
B.
$1000
C.
$1500
D.
$2000
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Solution
Product A sold $2000 and Product C sold $3000 in Q2. The difference is $3000 - $2000 = $1000.
Correct Answer:
B
— $1000
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Q. What is the dimension of electric charge?
A.
[M^1 L^2 T^-3 I^1]
B.
[M^0 L^0 T^0 I^1]
C.
[M^1 L^1 T^-2 I^1]
D.
[M^0 L^1 T^-1 I^1]
Show solution
Solution
The dimension of electric charge is [M^1 L^2 T^-3 I^1].
Correct Answer:
A
— [M^1 L^2 T^-3 I^1]
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Q. What is the dimension of energy? (2020)
A.
M^1L^2T^-2
B.
M^1L^1T^-1
C.
M^0L^2T^-2
D.
M^1L^0T^-1
Show solution
Solution
The dimension of energy is M^1L^2T^-2.
Correct Answer:
A
— M^1L^2T^-2
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Q. What is the dimension of force? (2019)
A.
M^1L^1T^-2
B.
M^1L^2T^-2
C.
M^1L^0T^-2
D.
M^0L^1T^-1
Show solution
Solution
The dimension of force is M^1L^1T^-2.
Correct Answer:
A
— M^1L^1T^-2
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Q. What is the dimension of frequency?
A.
M^0L^0T^-1
B.
M^1L^0T^-1
C.
M^0L^1T^-1
D.
M^0L^0T^0
Show solution
Solution
Frequency is defined as the number of cycles per unit time, thus its dimension is [M^0L^0T^-1].
Correct Answer:
A
— M^0L^0T^-1
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Q. What is the dimension of the gravitational constant G?
A.
M^-1L^3T^-2
B.
M^1L^3T^-2
C.
M^1L^2T^-2
D.
M^0L^0T^0
Show solution
Solution
The gravitational constant G has dimensions of [M^-1L^3T^-2] as it relates mass, distance, and time in the law of gravitation.
Correct Answer:
A
— M^-1L^3T^-2
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Q. What is the dimension of velocity? (2022)
A.
M^1L^1T^-1
B.
M^0L^1T^-1
C.
M^1L^0T^-1
D.
M^1L^1T^0
Show solution
Solution
Velocity is defined as displacement per unit time, hence its dimension is M^0L^1T^-1.
Correct Answer:
B
— M^0L^1T^-1
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Q. What is the dimension of work? (2022)
A.
M^1L^2T^-2
B.
M^1L^1T^-2
C.
M^0L^2T^-2
D.
M^1L^0T^-1
Show solution
Solution
The dimension of work is M^1L^2T^-2.
Correct Answer:
A
— M^1L^2T^-2
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Q. What is the dimensional formula for acceleration?
A.
[M^0 L^1 T^-2]
B.
[M^0 L^0 T^-2]
C.
[M^1 L^1 T^-2]
D.
[M^1 L^0 T^-2]
Show solution
Solution
The dimensional formula for acceleration is [M^0 L^1 T^-2], as it is defined as the change in velocity per unit time.
Correct Answer:
A
— [M^0 L^1 T^-2]
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Q. What is the dimensional formula for electric charge?
A.
[M^1 L^2 T^-3 I^-1]
B.
[M^0 L^0 T^1 I^1]
C.
[M^0 L^1 T^-2 I^1]
D.
[M^1 L^1 T^-2 I^-1]
Show solution
Solution
The dimensional formula for electric charge is [M^1 L^2 T^-3 I^-1], derived from the definition of current (I = Q/t).
Correct Answer:
A
— [M^1 L^2 T^-3 I^-1]
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Q. What is the dimensional formula for energy?
A.
[M^1 L^2 T^-2]
B.
[M^1 L^1 T^-2]
C.
[M^1 L^2 T^0]
D.
[M^0 L^1 T^-2]
Show solution
Solution
Energy has the dimensional formula [M^1 L^2 T^-2], as it is measured in Joules (1 J = 1 kg·m²/s²).
Correct Answer:
A
— [M^1 L^2 T^-2]
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Q. What is the dimensional formula for force? (2022)
A.
[M^1 L^1 T^-2]
B.
[M^1 L^0 T^-2]
C.
[M^0 L^1 T^-1]
D.
[M^1 L^2 T^0]
Show solution
Solution
Force has the dimensional formula [M^1 L^1 T^-2].
Correct Answer:
A
— [M^1 L^1 T^-2]
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Q. What is the dimensional formula for frequency?
A.
[M^0 L^0 T^-1]
B.
[M^1 L^0 T^-1]
C.
[M^0 L^1 T^0]
D.
[M^0 L^0 T^1]
Show solution
Solution
The dimensional formula for frequency is [M^0 L^0 T^-1], as it is defined as the number of cycles per unit time.
Correct Answer:
A
— [M^0 L^0 T^-1]
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Q. What is the dimensional formula for pressure?
A.
M¹L⁻¹T⁻²
B.
M¹L²T⁻²
C.
M⁰L⁰T⁰
D.
M¹L⁰T⁻²
Show solution
Solution
Pressure is defined as force per unit area. The dimensional formula for force is M¹L¹T⁻², and for area is L², thus pressure = M¹L¹T⁻² / L² = M¹L⁻¹T⁻².
Correct Answer:
A
— M¹L⁻¹T⁻²
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Q. What is the dimensional formula for velocity?
A.
MLT⁻¹
B.
ML²T⁻²
C.
M⁰L⁰T⁻¹
D.
M⁰L¹T⁻²
Show solution
Solution
Velocity is defined as displacement per unit time, which gives the dimensional formula of [MLT⁻¹].
Correct Answer:
A
— MLT⁻¹
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Q. What is the dimensional formula for work?
A.
[M^1 L^2 T^-2]
B.
[M^1 L^1 T^-1]
C.
[M^0 L^2 T^-2]
D.
[M^1 L^0 T^-2]
Show solution
Solution
Work has the dimensional formula [M^1 L^2 T^-2].
Correct Answer:
A
— [M^1 L^2 T^-2]
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