Major Competitive Exams

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Major Competitive Exams

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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!

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Q. If the amplitude of a wave is tripled, how does the energy of the wave change?

A. Increases by a factor of 3
B. Increases by a factor of 6
C. Increases by a factor of 9
D. Remains the same

Solution

Energy is proportional to the square of the amplitude, so if amplitude is tripled, energy increases by a factor of 3^2 = 9.

Correct Answer: C — Increases by a factor of 9

Q. If the amplitude of a wave is tripled, what happens to its energy?

A. Increases by a factor of 3
B. Increases by a factor of 6
C. Increases by a factor of 9
D. Remains the same

Solution

The energy of a wave is proportional to the square of its amplitude, so if amplitude is tripled, energy increases by a factor of 3^2 = 9.

Correct Answer: C — Increases by a factor of 9

Q. If the amplitude of a wave is tripled, what happens to the energy carried by the wave? (2019)

A. It remains the same
B. It doubles
C. It triples
D. It increases by a factor of nine

Solution

The energy carried by a wave is proportional to the square of the amplitude. Therefore, if the amplitude is tripled, the energy increases by a factor of 3^2 = 9.

Correct Answer: D — It increases by a factor of nine

Q. If the angle between the current element and the line joining the current element to the point of interest is 90 degrees, what is the contribution of that current element to the magnetic field?

A. Maximum
B. Minimum
C. Zero
D. Undefined

Solution

If the angle is 90 degrees, the sine of the angle is zero, resulting in zero contribution to the magnetic field from that current element.

Correct Answer: C — Zero

Q. If the angle between the force and the lever arm is 90 degrees, how does it affect the torque?

A. Torque is zero
B. Torque is maximum
C. Torque is half
D. Torque is minimum

Solution

Torque is maximum when the angle is 90 degrees because τ = F × r × sin(θ) and sin(90°) = 1.

Correct Answer: B — Torque is maximum

Q. If the angle between the force and the lever arm is 90 degrees, what is the torque produced by a 15 N force applied at a distance of 2 m?

A. 0 Nm
B. 15 Nm
C. 30 Nm
D. 45 Nm

Solution

Torque (τ) = F × d × sin(θ) = 15 N × 2 m × sin(90°) = 30 Nm.

Correct Answer: C — 30 Nm

Q. If the angle between the transmission axis of two polarizers is 90 degrees, what is the intensity of light passing through them?

A. Maximum intensity
B. Half of the original intensity
C. Zero intensity
D. Equal to the intensity of the first polarizer

Solution

When the angle between the transmission axes of two polarizers is 90 degrees, no light passes through, resulting in zero intensity.

Correct Answer: C — Zero intensity

Q. If the angle between the transmission axis of two polarizers is 90 degrees, what is the transmitted intensity of light?

A. Maximum intensity
B. Half of the original intensity
C. Zero intensity
D. One-fourth of the original intensity

Solution

When the angle between the transmission axes of two polarizers is 90 degrees, no light is transmitted, resulting in zero intensity.

Correct Answer: C — Zero intensity

Q. If the angle between two vectors A and B is 60 degrees and |A| = 5, |B| = 10, what is the scalar product A · B? (2020)

A. 25
B. 30
C. 35
D. 50

Solution

A · B = |A||B|cos(60°) = 5 * 10 * 0.5 = 25

Correct Answer: B — 30

Q. If the angle between two vectors A and B is 60 degrees and |A| = 5, |B| = 10, what is A · B?

A. 25
B. 30
C. 35
D. 20

Solution

A · B = |A||B|cos(60°) = 5 * 10 * 0.5 = 25.

Correct Answer: B — 30

Q. If the angle between two vectors A and B is 90 degrees, what is A · B?

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

Solution

A · B = |A||B|cos(90°) = |A||B| * 0 = 0.

Correct Answer: A — 0

Q. If the angle between two vectors A and B is 90 degrees, what is the value of A · B?

A. 1
B. 0
C. undefined
D. 1/2

Solution

If the angle is 90 degrees, A · B = |A||B|cos(90) = 0.

Correct Answer: B — 0

Q. If the angle between vectors A = 2i + 3j and B = 4i + 5j is 60 degrees, find A · B.

A. 20
B. 25
C. 30
D. 35

Solution

A · B = |A||B|cos(60°) = √(2^2 + 3^2) * √(4^2 + 5^2) * 1/2 = √13 * √41 * 1/2 = 20.

Correct Answer: B — 25

Q. If the angle of elevation from a point 30 meters away from the base of a hill is 60 degrees, what is the height of the hill?

A. 15√3 meters
B. 30 meters
C. 20 meters
D. 10√3 meters

Solution

Using the tangent function, tan(60) = height / 30. Therefore, height = 30 * tan(60) = 30 * √3 = 30√3 meters.

Correct Answer: A — 15√3 meters

Q. If the angle of elevation from a point 50 meters away from a tower is 60 degrees, what is the height of the tower?

A. 25√3 meters
B. 50 meters
C. 43.3 meters
D. 30 meters

Solution

Using the tangent function, tan(60) = height / 50. Therefore, height = 50 * tan(60) = 50 * √3 ≈ 86.6 meters.

Correct Answer: A — 25√3 meters

Q. If the angle of elevation from a point 50 meters away from the base of a hill is 30 degrees, what is the height of the hill?

A. 25 meters
B. 50 meters
C. 15 meters
D. 20 meters

Solution

Using tan(30) = height/50, height = 50 * (1/√3) = 50/√3 = 25 meters.

Correct Answer: A — 25 meters

Q. If the angle of elevation from a point 50 meters away from the base of a tower is 30 degrees, what is the height of the tower?

A. 25 meters
B. 50 meters
C. 10√3 meters
D. 15 meters

Solution

Let h be the height of the tower. tan(30°) = h/50. Therefore, h = 50 * tan(30°) = 50 * (1/√3) = 50/√3 = 25√3/3 meters.

Correct Answer: A — 25 meters

Q. If the angle of elevation of a hill from a point on the ground is 30 degrees and the distance from the point to the base of the hill is 100 m, what is the height of the hill? (2021)

A. 50 m
B. 30 m
C. 20 m
D. 10 m

Solution

Height = distance * tan(30) = 100 * (1/√3) ≈ 57.74 m, which rounds to 50 m.

Correct Answer: A — 50 m

Q. If the angle of elevation of the sun is 30 degrees, how tall is a 10 m pole casting a shadow? (2023)

A. 5 m
B. 10 m
C. 15 m
D. 20 m

Solution

Height = shadow * tan(angle) = 10 * tan(30) = 10 * (1/√3) ≈ 10 m.

Correct Answer: B — 10 m

Q. If the angle of elevation of the sun is 30 degrees, how tall is a 10 meter pole casting a shadow?

A. 5√3 m
B. 10 m
C. 10√3 m
D. 5 m

Solution

Height = shadow * tan(angle) = 10 * √3 = 5√3 m.

Correct Answer: A — 5√3 m

Q. If the angle of elevation of the sun is 30 degrees, how tall is a 10-meter pole casting a shadow of 10√3 meters? (2023)

A. 5 m
B. 10 m
C. 15 m
D. 20 m

Solution

Height = Shadow * tan(30) = 10√3 * (1/√3) = 10 m.

Correct Answer: B — 10 m

Q. If the angle of incidence in a medium is 45° and the refractive index of the medium is 1.5, what is the angle of refraction in air?

A. 30°
B. 45°
C. 60°
D. 90°

Solution

Using Snell's law: n1 * sin(θ1) = n2 * sin(θ2), 1.5 * sin(45°) = 1 * sin(θ2) => sin(θ2) = 1.5 * 0.7071 = 1.0607, which is not possible, hence total internal reflection occurs.

Correct Answer: C — 60°

Q. If the angle of incidence in a medium is 70° and the refractive index of the medium is 1.5, will total internal reflection occur?

A. Yes
B. No
C. Only at certain angles
D. Not applicable

Solution

Since 70° > θc = sin⁻¹(1/1.5) ≈ 41.8°, total internal reflection will occur.

Correct Answer: A — Yes

Q. If the angle of incidence in glass (n=1.5) is 60°, will total internal reflection occur when light travels to air?

A. Yes
B. No
C. Depends on the angle
D. Not enough information

Solution

Since the critical angle for glass to air is sin⁻¹(1.00/1.5) ≈ 41.8°, and 60° > 41.8°, total internal reflection occurs.

Correct Answer: A — Yes

Q. If the angle of incidence is 30° in a medium with a refractive index of 1.5, what is the angle of refraction in air?

A. 19.5°
B. 20.0°
C. 22.5°
D. 25.0°

Solution

Using Snell's law: n1 * sin(θ1) = n2 * sin(θ2). Here, n1 = 1.5, n2 = 1.0, and θ1 = 30°. Thus, sin(θ2) = (1.5 * sin(30°))/1.0 = 0.75, leading to θ2 ≈ 48.6°.

Correct Answer: A — 19.5°

Q. If the angle of incidence is 70° in a medium with a refractive index of 1.5, what is the angle of refraction in air?

A. 30°
B. 20°
C. 10°
D. Total internal reflection occurs

Solution

Since the angle of incidence (70°) is greater than the critical angle (approximately 41.8° for glass to air), total internal reflection occurs.

Correct Answer: D — Total internal reflection occurs

Q. If the angle of incidence is 70° in a medium with a refractive index of 1.6, will total internal reflection occur when it hits air?

A. Yes
B. No
C. Only if the angle is less than 90°
D. Not enough information

Solution

Critical angle θc = sin⁻¹(1/1.6) ≈ 38.7°. Since 70° > 38.7°, total internal reflection occurs.

Correct Answer: A — Yes

Q. If the angle of incidence is 70° in glass (n=1.5), will total internal reflection occur when light travels to air?

A. Yes
B. No
C. Only if the angle of refraction is 30°
D. Only if the angle of refraction is 45°

Solution

The critical angle for glass to air is sin⁻¹(1/1.5) ≈ 41.8°. Since 70° > 41.8°, total internal reflection will occur.

Correct Answer: A — Yes

Q. If the angle of incidence is equal to the angle of refraction, what can be said about the two media?

A. They are the same medium.
B. They have the same refractive index.
C. The light is traveling in a vacuum.
D. The light is not refracted.

Solution

When the angle of incidence equals the angle of refraction, it indicates that the light is passing from one medium to another of the same optical density, hence they are the same medium.

Correct Answer: A — They are the same medium.

Q. If the angle of incidence is equal to the angle of refraction, what is the medium?

A. Vacuum
B. Air
C. Glass
D. Optically denser medium

Solution

According to Snell's law, if the angle of incidence equals the angle of refraction, the light is traveling in the same medium, which can be vacuum or air.

Correct Answer: A — Vacuum

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