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. If set E = {x, y, z} and set F = {y, z, w}, what is the complement of set E with respect to the universal set U = {x, y, z, w, v}?
A.
{v}
B.
{w, v}
C.
{x, y, z}
D.
{y, z}
Show solution
Solution
The complement of set E with respect to the universal set U includes all elements in U that are not in E, which is {v}.
Correct Answer:
A
— {v}
Learn More →
Q. If set F contains elements {a, b, c} and set G contains elements {b, c, d}, what is the intersection of sets F and G?
A.
{a, b, c, d}
B.
{b, c}
C.
{a, d}
D.
{}
Show solution
Solution
The intersection of sets F and G includes only the elements that are present in both sets, which are {b, c}.
Correct Answer:
B
— {b, c}
Learn More →
Q. If set G = {1, 2, 3} and set H = {2, 3, 4}, what is the result of the difference G - H? (2023)
A.
{1}
B.
{2, 3}
C.
{3, 4}
D.
{}
Show solution
Solution
The difference G - H includes elements in G that are not in H, which results in {1}.
Correct Answer:
A
— {1}
Learn More →
Q. If set H contains elements {a, b, c} and set I contains elements {b, c, d}, what is the union of these two sets?
A.
{a, b, c}
B.
{b, c, d}
C.
{a, b, c, d}
D.
{a, d}
Show solution
Solution
The union of sets H and I is {a, b, c, d}, which includes all unique elements from both sets.
Correct Answer:
C
— {a, b, c, d}
Learn More →
Q. If set I = {1, 2, 3} and set J = {2, 3, 4}, what is the result of the operation I - J?
A.
{1}
B.
{2, 3}
C.
{4}
D.
{}
Show solution
Solution
The operation I - J results in the elements of set I that are not in set J, which is {1}.
Correct Answer:
A
— {1}
Learn More →
Q. If set P = {1, 2, 3, 4} and set Q = {3, 4, 5, 6}, what is the difference P - Q?
A.
{1, 2}
B.
{3, 4}
C.
{5, 6}
D.
{1, 2, 5, 6}
Show solution
Solution
The difference P - Q includes elements in P that are not in Q, which is {1, 2}.
Correct Answer:
A
— {1, 2}
Learn More →
Q. If set P = {x | x is an even number less than 10} and set Q = {x | x is a prime number less than 10}, what is the intersection of sets P and Q?
A.
{2, 4, 6, 8}
B.
{2, 3, 5, 7}
C.
{2}
D.
{4, 6, 8}
Show solution
Solution
The intersection of sets P and Q includes elements that are both even and prime. The only even prime number is 2.
Correct Answer:
C
— {2}
Learn More →
Q. If set P = {x | x is an even number less than 10} and set Q = {x | x is a prime number less than 10}, what is the union of sets P and Q?
A.
{2, 3, 4, 5, 6, 8}
B.
{2, 3, 5, 7}
C.
{2, 4, 6, 8}
D.
{2, 3, 4, 5, 7, 8}
Show solution
Solution
Set P = {2, 4, 6, 8} and set Q = {2, 3, 5, 7}. The union is {2, 3, 4, 5, 6, 7, 8}.
Correct Answer:
D
— {2, 3, 4, 5, 7, 8}
Learn More →
Q. If set P = {x | x is an even number less than 10} and set Q = {x | x is a prime number less than 10}, what is the difference P - Q?
A.
{2, 4, 6, 8}
B.
{4, 6, 8}
C.
{2, 6, 8}
D.
{2, 4, 6, 8, 3, 5, 7}
Show solution
Solution
Set P = {2, 4, 6, 8} and set Q = {2, 3, 5, 7}. The difference P - Q = {4, 6, 8}.
Correct Answer:
B
— {4, 6, 8}
Learn More →
Q. If set P = {x | x is an even number less than 10} and set Q = {x | x is a prime number less than 10}, what is P ∩ Q?
A.
{2, 4, 6, 8}
B.
{2, 3, 5, 7}
C.
{2}
D.
{4, 6, 8}
Show solution
Solution
The intersection P ∩ Q includes only the even prime number, which is {2}.
Correct Answer:
C
— {2}
Learn More →
Q. If set R = {1, 2, 3, 4, 5} and set S = {4, 5, 6, 7}, what is the symmetric difference of sets R and S?
A.
{1, 2, 3, 6, 7}
B.
{4, 5}
C.
{1, 2, 3, 4, 5, 6, 7}
D.
{6, 7}
Show solution
Solution
The symmetric difference of sets R and S includes elements that are in either set but not in both. Thus, it is {1, 2, 3, 6, 7}.
Correct Answer:
A
— {1, 2, 3, 6, 7}
Learn More →
Q. If set R = {1, 2, 3, 4} and set S = {3, 4, 5, 6}, what is the difference R - S?
A.
{1, 2}
B.
{3, 4}
C.
{5, 6}
D.
{}
Show solution
Solution
The difference R - S includes elements in R that are not in S, which is {1, 2}.
Correct Answer:
A
— {1, 2}
Learn More →
Q. If set R = {1, 2, 3, 4} and set S = {3, 4, 5, 6}, what is the symmetric difference of sets R and S?
A.
{1, 2, 5, 6}
B.
{3, 4}
C.
{1, 2, 3, 4, 5, 6}
D.
{3, 4, 5}
Show solution
Solution
The symmetric difference is the set of elements in either set R or set S but not in both, which is {1, 2, 5, 6}.
Correct Answer:
A
— {1, 2, 5, 6}
Learn More →
Q. If set T = {1, 2, 3} and set U = {2, 3, 4}, what is the difference T - U?
A.
{1}
B.
{2, 3}
C.
{4}
D.
{}
Show solution
Solution
The difference T - U includes elements that are in set T but not in set U, which is {1}.
Correct Answer:
A
— {1}
Learn More →
Q. If set T = {1, 2, 3} and set U = {2, 3, 4}, what is the hybrid set formed by the symmetric difference of T and U?
A.
{1, 4}
B.
{1, 2, 3, 4}
C.
{2, 3}
D.
{1, 2, 4}
Show solution
Solution
The symmetric difference of sets T and U is {1, 4}, which includes elements that are in either set but not in both.
Correct Answer:
A
— {1, 4}
Learn More →
Q. If set T = {1, 2, 3} and set U = {2, 3, 4}, what is the hybrid set formed by the intersection of T and U?
A.
{1, 2, 3, 4}
B.
{2, 3}
C.
{1, 4}
D.
{}
Show solution
Solution
The hybrid set formed by the intersection of set T and set U includes only the elements that are common to both sets, which are {2, 3}.
Correct Answer:
B
— {2, 3}
Learn More →
Q. If set X = {1, 2, 3} and set Y = {3, 4, 5}, what is the hybrid set formed by X and Y? (2023)
A.
{1, 2, 3, 4, 5}
B.
{3}
C.
{1, 2, 4, 5}
D.
{1, 2, 3, 4, 5, 6}
Show solution
Solution
The hybrid set formed by combining sets X and Y includes all unique elements from both sets, resulting in {1, 2, 3, 4, 5}.
Correct Answer:
A
— {1, 2, 3, 4, 5}
Learn More →
Q. If set X = {a, b, c} and set Y = {b, c, d}, what is the union of sets X and Y?
A.
{a, b, c, d}
B.
{b, c}
C.
{a, b}
D.
{c, d}
Show solution
Solution
The union of sets X and Y includes all unique elements from both sets. Thus, the union is {a, b, c, d}.
Correct Answer:
A
— {a, b, c, d}
Learn More →
Q. If set X contains elements {1, 2, 3} and set Y contains elements {3, 4, 5}, what is the hybrid set formed by the union of X and Y?
A.
{1, 2, 3, 4, 5}
B.
{1, 2, 3}
C.
{3, 4, 5}
D.
{1, 2, 4, 5}
Show solution
Solution
The hybrid set formed by the union of sets X and Y includes all unique elements from both sets, which are {1, 2, 3, 4, 5}.
Correct Answer:
A
— {1, 2, 3, 4, 5}
Learn More →
Q. If set X contains {1, 2, 3} and set Y contains {3, 4, 5}, what is the hybrid set formed by the union of X and Y?
A.
{1, 2, 3, 4, 5}
B.
{3}
C.
{1, 2}
D.
{4, 5}
Show solution
Solution
The union of set X and set Y includes all unique elements from both sets, resulting in {1, 2, 3, 4, 5}.
Correct Answer:
A
— {1, 2, 3, 4, 5}
Learn More →
Q. If set X contains {1, 2, 3} and set Y contains {3, 4, 5}, what is the hybrid set formed by the union of set X and set Y?
A.
{1, 2, 3, 4, 5}
B.
{1, 2, 3}
C.
{3, 4}
D.
{1, 2, 4, 5}
Show solution
Solution
The hybrid set formed by the union of set X and set Y includes all unique elements from both sets, which are {1, 2, 3, 4, 5}.
Correct Answer:
A
— {1, 2, 3, 4, 5}
Learn More →
Q. If set X contains {1, 2, 3} and set Y contains {3, 4, 5}, what is the intersection of set X and set Y?
A.
{1, 2, 3, 4, 5}
B.
{3}
C.
{1, 2}
D.
{}
Show solution
Solution
The intersection of set X and set Y is {3}, as it is the only element common to both sets.
Correct Answer:
B
— {3}
Learn More →
Q. If sin 2A = 2 sin A cos A, what is the double angle formula for cosine?
A.
cos 2A = cos²A - sin²A
B.
cos 2A = 2 sin A cos A
C.
cos 2A = sin²A - cos²A
D.
cos 2A = 1 - 2 sin²A
Show solution
Solution
The double angle formula for cosine is cos 2A = cos²A - sin²A.
Correct Answer:
A
— cos 2A = cos²A - sin²A
Learn More →
Q. If sin 2A = 2 sin A cos A, what is the value of sin 2A when sin A = 1/2?
Show solution
Solution
Using the double angle formula, sin 2A = 2(1/2)(√(1 - (1/2)²)) = 2(1/2)(√(3/4)) = 1.
Correct Answer:
B
— 1
Learn More →
Q. If sin 2θ = 2 sin θ cos θ, what is the value of sin 2(30°)?
Show solution
Solution
sin 2(30°) = sin 60° = √3/2.
Correct Answer:
C
— √3/2
Learn More →
Q. If sin A = 0, what is the value of A? (2019)
A.
0°
B.
90°
C.
180°
D.
360°
Show solution
Solution
Sin A = 0 at A = 0°, 180°, and 360°. The principal value is 0°.
Correct Answer:
A
— 0°
Learn More →
Q. If sin A = 0.6, what is cos A?
A.
0.8
B.
0.6
C.
0.4
D.
0.2
Show solution
Solution
Using the identity sin^2 A + cos^2 A = 1, we have cos A = sqrt(1 - (0.6)^2) = sqrt(1 - 0.36) = sqrt(0.64) = 0.8.
Correct Answer:
A
— 0.8
Learn More →
Q. If sin A = 0.6, what is the value of cos A to two decimal places?
A.
0.8
B.
0.6
C.
0.4
D.
0.2
Show solution
Solution
Using the Pythagorean identity, cos A = √(1 - sin²A) = √(1 - 0.36) = √(0.64) = 0.8.
Correct Answer:
A
— 0.8
Learn More →
Q. If sin A = 0.6, what is the value of cos A?
A.
0.8
B.
0.6
C.
0.4
D.
0.2
Show solution
Solution
Using the identity sin^2 A + cos^2 A = 1, we have cos A = sqrt(1 - (0.6)^2) = sqrt(1 - 0.36) = sqrt(0.64) = 0.8.
Correct Answer:
A
— 0.8
Learn More →
Q. If sin A = 0.6, what is the value of tan A?
A.
0.8
B.
1.2
C.
0.75
D.
1.5
Show solution
Solution
Using the identity tan A = sin A / cos A, we find cos A = sqrt(1 - (0.6)^2) = 0.8, thus tan A = 0.6 / 0.8 = 0.75.
Correct Answer:
B
— 1.2
Learn More →
Showing 10411 to 10440 of 31669 (1056 Pages)
