Major Competitive Exams

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Q. If unpolarized light passes through a polarizer, what fraction of the light intensity is transmitted?

A. 0%
B. 25%
C. 50%
D. 100%

Solution

When unpolarized light passes through a polarizer, 50% of the light intensity is transmitted.

Correct Answer: C — 50%

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Q. If unpolarized light passes through a polarizer, what is the intensity of the transmitted light?

A. Zero
B. Half of the original intensity
C. Equal to the original intensity
D. Twice the original intensity

Solution

According to Malus's law, the intensity of transmitted light is half of the original intensity when unpolarized light passes through a polarizer.

Correct Answer: B — Half of the original intensity

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Q. If unpolarized light passes through a polarizer, what percentage of the light intensity will emerge?

A. 0%
B. 25%
C. 50%
D. 100%

Solution

When unpolarized light passes through a polarizer, 50% of the light intensity will emerge, according to Malus's law.

Correct Answer: C — 50%

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Q. If unpolarized light passes through two polarizers at 90 degrees to each other, what is the intensity of the transmitted light?

A. Same as incident light
B. Half of the incident light
C. Zero
D. One quarter of the incident light

Solution

When unpolarized light passes through two polarizers at 90 degrees, no light is transmitted, resulting in zero intensity.

Correct Answer: C — Zero

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Q. If unpolarized light passes through two polarizers, what is the maximum intensity of light transmitted?

A. Zero
B. Half of the original intensity
C. Equal to the original intensity
D. Dependent on the angle between the polarizers

Solution

The maximum intensity transmitted through two polarizers is given by Malus's law, which states that I = I0 * cos²(θ), where θ is the angle between the polarizers.

Correct Answer: D — Dependent on the angle between the polarizers

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Q. If V is scheduled before W and X is scheduled after W, which of the following is correct? (2020)

A. V is last
B. W is last
C. X is last
D. V is first

Solution

X is last as it is scheduled after W, which is after V.

Correct Answer: C — X is last

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Q. If V is the wife of W and X is the son of W, what is V's relationship to X? (2023)

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

Solution

V is the mother of X as she is the wife of X's father, W.

Correct Answer: A — Mother

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Q. If vector A = (1, 2, 3) and vector B = (4, 5, 6), what is A + B?

A. (5, 7, 9)
B. (4, 5, 6)
C. (1, 2, 3)
D. (0, 0, 0)

Solution

A + B = (1+4, 2+5, 3+6) = (5, 7, 9).

Correct Answer: A — (5, 7, 9)

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Q. If vector A = (1, 2, 3) and vector B = (4, 5, 6), what is the angle between them?

A. 0 degrees
B. 30 degrees
C. 60 degrees
D. 90 degrees

Solution

Cosine of angle θ = (A . B) / (|A| |B|) = (1*4 + 2*5 + 3*6) / (√14 * √77) = 0, hence θ = 90 degrees.

Correct Answer: D — 90 degrees

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Q. If vector A = (1, 2, 3) and vector B = (4, 5, 6), what is the vector A - B?

A. (-3, -3, -3)
B. (3, 3, 3)
C. (5, 7, 9)
D. (0, 0, 0)

Solution

A - B = (1-4, 2-5, 3-6) = (-3, -3, -3).

Correct Answer: A — (-3, -3, -3)

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Q. If vector A = (2, 2, 2) and vector B = (1, 1, 1), what is the scalar triple product A . (B × A)?

A. 0
B. 1
C. 2
D. 3

Solution

A . (B × A) = 0, since B × A = 0.

Correct Answer: A — 0

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Q. If vector A = (3, -2, 1) and vector B = (1, 4, -3), what is the cross product A × B?

A. (-5, -10, 14)
B. (5, 10, -14)
C. (10, 14, 5)
D. (14, -5, 10)

Solution

A × B = |i  j  k|\n|3 -2  1|\n|1  4 -3| = (-5, -10, 14).

Correct Answer: A — (-5, -10, 14)

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Q. If vector A = 2i + 3j + k and vector B = i - 2j + 4k, what is the cross product A × B?

A. -10i + 5j + 7k
B. 10i - 5j - 7k
C. 10i + 5j + 7k
D. -10i - 5j + 7k

Solution

A × B = |i  j  k|\n|2  3  1|\n|1 -2  4| = (3*4 - 1*(-2))i - (2*4 - 1*1)j + (2*(-2) - 3*1)k = 10i - 5j - 7k.

Correct Answer: A — -10i + 5j + 7k

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Q. If vector A = 2i + 3j and vector B = -i + 4j, what is the resultant vector R = A + B?

A. i + 7j
B. i + j
C. 3i + 7j
D. 3i + 4j

Solution

R = A + B = (2 - 1)i + (3 + 4)j = 1i + 7j.

Correct Answer: A — i + 7j

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Q. If vector A = 2i + 3j and vector B = 3i + 4j, what is the angle between them? (2023)

A. 0 degrees
B. 90 degrees
C. 45 degrees
D. 60 degrees

Solution

cos(θ) = (A · B) / (|A| |B|) = (2*3 + 3*4) / (√(2^2 + 3^2) * √(3^2 + 4^2)) = 0.6, θ = 53.13 degrees.

Correct Answer: D — 60 degrees

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Q. If vector A = 2i + 3j and vector B = 4i + 5j, what is the angle between A and B? (2023)

A. 0 degrees
B. 90 degrees
C. 45 degrees
D. 60 degrees

Solution

cos(θ) = (A · B) / (|A||B|) = (8 + 15) / (√(13) * √(41)). θ = 60 degrees.

Correct Answer: D — 60 degrees

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Q. If vector A = 2i + 3j and vector B = 4i + 5j, what is the angle between them?

A. 0 degrees
B. 90 degrees
C. 45 degrees
D. 60 degrees

Solution

cos(θ) = (A · B) / (|A||B|) = (2*4 + 3*5) / (√(2^2 + 3^2) * √(4^2 + 5^2)) = 0.5, θ = 60 degrees.

Correct Answer: D — 60 degrees

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Q. If vector A = 2i + 3j and vector B = 4i + 6j, are the vectors A and B parallel?

A. Yes
B. No
C. Cannot be determined
D. Only if scaled

Solution

Vectors A and B are parallel because B = 2A.

Correct Answer: A — Yes

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Q. If vector A = 2i + 3j and vector B = 4i + k, what is the angle between A and B?

A. 90 degrees
B. 60 degrees
C. 45 degrees
D. 30 degrees

Solution

cos(θ) = (A · B) / (|A| |B|). A · B = 8 + 0 + 3(0) = 8; |A| = √(2^2 + 3^2) = √13; |B| = √(4^2 + 1^2) = √17. θ = cos^(-1)(8/(√13 * √17)).

Correct Answer: B — 60 degrees

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Q. If vector A = 3i + 4j and vector B = 2i - j, what is the dot product A · B?

A. 10
B. 5
C. 7
D. 8

Solution

A · B = (3)(2) + (4)(-1) = 6 - 4 = 2.

Correct Answer: A — 10

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Q. If vector A = 3i + 4j and vector B = 4i + 3j, what is the cross product A × B?

A. -1k
B. 1k
C. 0
D. 7k

Solution

A × B = |i  j  k| |3  4  0| |4  3  0| = (0 - 0)i - (0 - 0)j + (9 - 12)k = -3k.

Correct Answer: B — 1k

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Q. If vector A = 4i + 3j and vector B = -3i + 4j, what is the angle between them?

A. 90 degrees
B. 45 degrees
C. 60 degrees
D. 30 degrees

Solution

cos(θ) = (A · B) / (|A||B|) = (4*-3 + 3*4) / (5*5) = 0, θ = 90 degrees.

Correct Answer: A — 90 degrees

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Q. If vector A = 4i + 3j and vector B = -i + 2j, what is the resultant vector A + B? (2019)

A. 3i + 5j
B. 5i + j
C. 3i + j
D. 5i + 5j

Solution

A + B = (4 - 1)i + (3 + 2)j = 3i + 5j.

Correct Answer: A — 3i + 5j

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Q. If vector A = 4i + 3j and vector B = -i + 2j, what is the resultant vector R = A + B? (2019)

A. 3i + 5j
B. 5i + j
C. 3i + j
D. 5i + 5j

Solution

R = A + B = (4 - 1)i + (3 + 2)j = 3i + 5j.

Correct Answer: A — 3i + 5j

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Q. If vector A = 4i + 3j and vector B = 3i + 4j, what is the angle between A and B?

A. 45 degrees
B. 60 degrees
C. 90 degrees
D. 135 degrees

Solution

cos(θ) = (A · B) / (|A||B|) = (12 + 12) / (5 * 5) = 24/25, θ = cos^(-1)(24/25) ≈ 60 degrees.

Correct Answer: B — 60 degrees

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Q. If vector A = 4i + 3j and vector B = 4i - 3j, what is the angle between A and B? (2019)

A. 0 degrees
B. 90 degrees
C. 180 degrees
D. 45 degrees

Solution

A · B = 16 - 9 = 7. |A| = 5, |B| = 5. cos(θ) = 7/(5*5) = 0.28, θ = 180 degrees.

Correct Answer: C — 180 degrees

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Q. If vector A = 5i + 12j and vector B = -5i + 12j, what is the angle between them?

A. 0 degrees
B. 90 degrees
C. 180 degrees
D. 45 degrees

Solution

A · B = (5)(-5) + (12)(12) = -25 + 144 = 119. Since A and B are in opposite directions, the angle is 180 degrees.

Correct Answer: C — 180 degrees

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Q. If vector A = 5i + 12j and vector B = -5i + 12j, what is the resultant vector A + B? (2021)

A. 0i + 24j
B. 10i + 0j
C. 0i + 12j
D. 5i + 12j

Solution

A + B = (5 - 5)i + (12 + 12)j = 0i + 24j.

Correct Answer: A — 0i + 24j

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Q. If vector A = 5i + 12j and vector B = 12i - 5j, what is the angle between A and B?

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

Solution

cos(θ) = (A · B) / (|A||B|) = (5*12 + 12*(-5)) / (√(169) * √(169)) = 0, θ = 90 degrees.

Correct Answer: C — 90 degrees

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Q. If vector A = 5i + 12j and vector B = 12i - 5j, what is the value of A × B?

A. -85
B. 85
C. 0
D. 60

Solution

A × B = |i  j  k| |5  12  0| |12 -5  0| = (0 - 0)i - (0 - 0)j + (5*-5 - 12*12)k = -85k.

Correct Answer: A — -85

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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!

Major Competitive Exams

Major Competitive Exams MCQ & Objective Questions

What You Will Practise Here

Exam Relevance

Common Mistakes Students Make

FAQs

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