Major Competitive Exams

Cart

Major Competitive Exams

Download Q&A

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!

Civil Services Defence Exams Engineering & Architecture Admissions Government Jobs Management Admissions Undergraduate

Q. If cos(θ) = 1/2, what are the possible values of θ?

A. 30°, 150°
B. 45°, 135°
C. 60°, 120°
D. 0°, 180°

Solution

cos(θ) = 1/2 at θ = 30° and 150°.

Correct Answer: A — 30°, 150°

Q. If cos(θ) = 1/2, what is the value of sin(θ)?

A. √3/2
B. 1/2
C. 0
D. √2/2

Solution

Using the identity sin^2(θ) + cos^2(θ) = 1, we have sin^2(θ) = 1 - (1/2)^2 = 1 - 1/4 = 3/4. Thus, sin(θ) = ±√3/2.

Correct Answer: A — √3/2

Q. If cos(θ) = 1/2, what is the value of θ in degrees?

A. 30
B. 60
C. 90
D. 120

Solution

cos(30°) = 1/2, hence θ = 30°.

Correct Answer: A — 30

Q. If cos(θ) = 1/2, what is θ in degrees?

A. 30°
B. 45°
C. 60°
D. 90°

Solution

cos(60°) = 1/2, so θ = 60°

Correct Answer: C — 60°

Q. If cos^(-1)(x) = θ, then what is the value of sin(θ)?

A. x
B. √(1-x^2)
C. 1-x
D. 0

Solution

From cos^(-1)(x) = θ, we have cos(θ) = x. Therefore, sin(θ) = √(1 - cos^2(θ)) = √(1 - x^2).

Correct Answer: B — √(1-x^2)

Q. If cot A = 1, what is the value of A? (2022)

A. 45°
B. 90°
C. 60°
D. 30°

Solution

Cotangent is 1 when the angle A is 45°, as cot A = cos A/sin A = 1 when both are equal.

Correct Answer: A — 45°

Q. If cot A = 3/4, what is the value of sin A?

A. 3/5
B. 4/5
C. 5/3
D. 5/4

Solution

cot A = cos A/sin A = 3/4 implies sin A = 4/5 using the identity sin²A + cos²A = 1.

Correct Answer: A — 3/5

Q. If cot D = 3/4, what is the value of sin D?

A. 3/5
B. 4/5
C. 5/3
D. 5/4

Solution

cot D = 3/4 implies tan D = 4/3. Therefore, sin D = 4/5 (using the identity sin²D + cos²D = 1).

Correct Answer: A — 3/5

Q. If cot θ = 1, what is the value of θ?

A. 0°
B. 45°
C. 90°
D. 180°

Solution

cot θ = 1 implies tan θ = 1, which occurs at θ = 45°.

Correct Answer: B — 45°

Q. If cot θ = 3/4, what is the value of sin θ?

A. 4/5
B. 3/5
C. 5/4
D. 3/4

Solution

Using the identity cot θ = cos θ / sin θ, we find sin θ = 4/5.

Correct Answer: A — 4/5

Q. If cot θ = 5/12, what is the value of sin θ?

A. 5/13
B. 12/13
C. 13/5
D. 12/5

Solution

Using the identity cot θ = cos θ / sin θ, we can find sin θ = 12/13 using the Pythagorean theorem: sin θ = 12/√(5^2 + 12^2) = 12/13.

Correct Answer: B — 12/13

Q. If cot(x) = 5/12, what is sin(x)?

A. 12/13
B. 5/13
C. 13/12
D. 5/12

Solution

Using the identity cot(x) = cos(x)/sin(x), we can find sin(x) = 12/13 using the Pythagorean theorem.

Correct Answer: A — 12/13

Q. If D = E and E > F, which of the following is true?

A. D > F
B. F < D
C. E < D
D. D < E

Solution

Since D = E and E > F, it follows that D > F.

Correct Answer: A — D > F

Q. If D = [[2, 1], [1, 2]], what is the trace of D?

A. 1
B. 2
C. 3
D. 4

Solution

The trace of a matrix is the sum of its diagonal elements. Trace(D) = 2 + 2 = 4.

Correct Answer: C — 3

Q. If D = [[4, 2], [1, 3]], find the inverse of D. (2022)

A. [[3, -2], [-1, 4]]
B. [[3, 2], [-1, 4]]
C. [[3, -2], [1, 4]]
D. [[4, -2], [-1, 3]]

Solution

The inverse of D is given by (1/det(D)) * adj(D). Here, det(D) = (4*3) - (2*1) = 10, and adj(D) = [[3, -2], [-1, 4]]. Thus, D^(-1) = (1/10) * [[3, -2], [-1, 4]].

Correct Answer: A — [[3, -2], [-1, 4]]

Q. If D = [[4, 2], [1, 3]], what is the inverse of D?

A. [[3, -2], [-1, 4]]
B. [[3, 2], [-1, 4]]
C. [[4, -2], [-1, 3]]
D. [[3, -4], [1, 2]]

Solution

The inverse of D is given by (1/det(D)) * adj(D). Here, det(D) = (4*3) - (2*1) = 10. The adjugate is [[3, -2], [-1, 4]]. Thus, D^(-1) = (1/10) * [[3, -2], [-1, 4]].

Correct Answer: A — [[3, -2], [-1, 4]]

Q. If D = {1, 2, 3, 4, 5, 6}, how many subsets contain exactly 3 elements?

A. 20
B. 30
C. 40
D. 50

Solution

The number of ways to choose 3 elements from a set of 6 is given by the combination formula C(n, r) = n! / (r!(n-r)!). Here, C(6, 3) = 20.

Correct Answer: A — 20

Q. If D = {1, 2, 3, 4}, how many proper subsets does D have?

A. 4
B. 8
C. 15
D. 16

Solution

The total number of subsets of D is 2^4 = 16. Proper subsets are all subsets except the set itself, so there are 16 - 1 = 15 proper subsets.

Correct Answer: B — 8

Q. If D = {1, 2, 3, 4}, what is the number of proper subsets of D?

A. 15
B. 16
C. 14
D. 12

Solution

The total number of subsets is 2^4 = 16. Proper subsets exclude the set itself, so 16 - 1 = 15.

Correct Answer: A — 15

Q. If D = {1, 2, 3}, which of the following is not a subset of D?

A. {1, 2}
B. {2, 3}
C. {1, 2, 3}
D. {4}

Solution

A subset must contain elements from the original set. {4} is not a subset of D.

Correct Answer: D — {4}

Q. If D = {1, 2}, what is the number of proper subsets of D?

A. 1
B. 2
C. 3
D. 4

Solution

The proper subsets of D = {1, 2} are {∅}, {1}, and {2}. So, there are 3 subsets, but excluding D itself gives us 2 proper subsets.

Correct Answer: C — 3

Q. If D = {1, 2}, what is the power set of D?

A. {∅, {1}, {2}, {1, 2}}
B. {∅, {1}, {2}}
C. {1, 2}
D. {1, 2, ∅}

Solution

The power set of D = {1, 2} is {∅, {1}, {2}, {1, 2}} which contains 4 subsets.

Correct Answer: A — {∅, {1}, {2}, {1, 2}}

Q. If D = {1, 2}, which of the following is NOT a subset of D?

A. {1}
B. {2}
C. {1, 2}
D. {3}

Solution

A subset can only contain elements from the original set. {3} is not a subset of D.

Correct Answer: D — {3}

Q. If D = {2, 4, 6}, which of the following is not a subset of D?

A. {2}
B. {4, 6}
C. {1}
D. {2, 4, 6}

Solution

A subset can only contain elements from the original set. {1} is not a subset of D.

Correct Answer: C — {1}

Q. If D = {a, b}, how many subsets does D have?

A. 2
B. 3
C. 4
D. 5

Solution

The number of subsets of a set with n elements is 2^n. Here, n = 2, so 2^2 = 4.

Correct Answer: C — 4

Q. If D = {a, b}, how many subsets of D contain the element 'a'?

A. 1
B. 2
C. 3
D. 4

Solution

The subsets containing 'a' are {a}, {a, b}, so there are 2 subsets.

Correct Answer: C — 3

Q. If D is sitting opposite to E in a circular table and F is sitting to the left of D, who is sitting to the right of E?

A. D
B. F
C. E
D. None of the above

Solution

Since D is opposite E, F sitting to the left of D means F is also opposite to E. Therefore, the person sitting to the right of E is F.

Correct Answer: B — F

Q. If D is sitting to the immediate right of E and F is sitting opposite D, who is sitting to the left of E?

A. D
B. C
C. B
D. A

Solution

The arrangement can be visualized as A-B-C-E-D-F. Therefore, A is sitting to the left of E.

Correct Answer: D — A

Q. If D is the daughter of E and F, and F is the son of G, what is the relationship of G to D? (2021)

A. Grandfather
B. Father
C. Uncle
D. Brother

Solution

F is the son of G, making G the grandfather of D.

Correct Answer: A — Grandfather

Q. If D is the mother of E and E is the sister of F, how is D related to F?

A. Aunt
B. Mother
C. Sister
D. Cousin

Solution

D is the mother of E, and since E is the sister of F, D is also the mother of F.

Correct Answer: B — Mother

Showing 9841 to 9870 of 31669 (1056 Pages)

Soulshift Feedback ×

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?

Not likely Very likely