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. A mass m is attached to a string of length L and is swung in a vertical circle. What is the tension in the string at the top of the circle? (2023)

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

Solution

At the top, T + mg = mv²/L. T = mv²/L - mg.

Correct Answer: A — mg

Q. A mass m is lifted to a height h in a uniform gravitational field. What is the work done against gravity?

A. mgh
B. gh
C. mg
D. 0

Solution

The work done against gravity when lifting a mass m to a height h is given by W = mgh.

Correct Answer: A — mgh

Q. A mass of 0.5 kg is attached to a spring with a spring constant of 200 N/m. What is the frequency of oscillation? (2021)

A. 0.5 Hz
B. 1 Hz
C. 2 Hz
D. 4 Hz

Solution

The frequency f of a mass-spring system is given by f = (1/2π)√(k/m). Here, f = (1/2π)√(200/0.5) ≈ 2 Hz.

Correct Answer: C — 2 Hz

Q. A mass on a spring oscillates with a frequency of 2 Hz. What is the angular frequency?

A. 4π rad/s
B. 2π rad/s
C. π rad/s
D. 8π rad/s

Solution

The angular frequency ω is given by ω = 2πf. For f = 2 Hz, ω = 2π(2) = 4π rad/s.

Correct Answer: A — 4π rad/s

Q. A mass-spring system is subjected to a periodic force. If the amplitude of oscillation is 0.1 m and the frequency is 2 Hz, what is the maximum velocity of the mass?

A. 0.4 m/s
B. 0.2 m/s
C. 0.1 m/s
D. 0.8 m/s

Solution

Maximum velocity (v_max) = Aω = A(2πf) = 0.1 * (2π * 2) = 0.4 m/s.

Correct Answer: A — 0.4 m/s

Q. A mass-spring system is subjected to a periodic force. If the amplitude of the forced oscillation is 0.1 m and the damping coefficient is 0.2 kg/s, what is the maximum velocity of the oscillation?

A. 0.1 m/s
B. 0.2 m/s
C. 0.3 m/s
D. 0.4 m/s

Solution

Maximum velocity (v_max) = Aω, where ω = 2πf. Assuming f = 1 Hz, v_max = 0.1 * 2π * 1 = 0.2 m/s.

Correct Answer: B — 0.2 m/s

Q. A mass-spring system oscillates with a frequency of 1 Hz. What is the angular frequency? (2023)

A. 2π rad/s
B. π rad/s
C. 1 rad/s
D. 4π rad/s

Solution

Angular frequency ω is related to frequency f by ω = 2πf. Therefore, for f = 1 Hz, ω = 2π(1) = 2π rad/s.

Correct Answer: A — 2π rad/s

Q. A mass-spring system oscillates with a frequency of 2 Hz. If the system is damped, what is the relationship between the damped frequency and the natural frequency?

A. Damped frequency is greater
B. Damped frequency is equal
C. Damped frequency is less
D. Damped frequency is unpredictable

Solution

In a damped system, the damped frequency is always less than the natural frequency.

Correct Answer: C — Damped frequency is less

Q. A mass-spring system oscillates with a frequency of 2 Hz. What is the angular frequency?

A. 4π rad/s
B. 2π rad/s
C. π rad/s
D. 8π rad/s

Solution

The angular frequency ω is related to the frequency f by the formula ω = 2πf. Therefore, ω = 2π × 2 = 4π rad/s.

Correct Answer: A — 4π rad/s

Q. A mass-spring system oscillates with a frequency of 2 Hz. What is the period of oscillation? (2019)

A. 0.5 s
B. 1 s
C. 2 s
D. 4 s

Solution

Period (T) = 1 / frequency = 1 / 2 Hz = 0.5 s.

Correct Answer: B — 1 s

Q. A mass-spring system oscillates with a frequency of 2 Hz. What is the time period of the oscillation?

A. 0.5 s
B. 1 s
C. 2 s
D. 4 s

Solution

The time period T is the reciprocal of frequency f. T = 1/f = 1/2 Hz = 0.5 s.

Correct Answer: B — 1 s

Q. A mass-spring system oscillates with a frequency of 3 Hz. What is the angular frequency?

A. 3 rad/s
B. 6 rad/s
C. 9 rad/s
D. 12 rad/s

Solution

Angular frequency (ω) is given by ω = 2πf. Thus, ω = 2π * 3 ≈ 6 rad/s.

Correct Answer: B — 6 rad/s

Q. A mass-spring system oscillates with a frequency of 3 Hz. What is the angular frequency of the system?

A. 3 rad/s
B. 6 rad/s
C. 9 rad/s
D. 12 rad/s

Solution

Angular frequency (ω) is given by ω = 2πf. Thus, ω = 2π(3) = 6 rad/s.

Correct Answer: B — 6 rad/s

Q. A mass-spring system oscillates with a frequency of 3 Hz. What is the period of the oscillation?

A. 0.33 s
B. 0.5 s
C. 1 s
D. 2 s

Solution

Period (T) is the reciprocal of frequency (f). T = 1/f = 1/3 = 0.33 s.

Correct Answer: A — 0.33 s

Q. A mass-spring system oscillates with a frequency of 5 Hz. What is the angular frequency? (2021)

A. 10π rad/s
B. 5π rad/s
C. 2π rad/s
D. 20π rad/s

Solution

Angular frequency ω = 2πf = 2π × 5 Hz = 10π rad/s.

Correct Answer: A — 10π rad/s

Q. A mass-spring system oscillates with a frequency of 5 Hz. What is the period of the motion?

A. 0.2 s
B. 0.5 s
C. 1 s
D. 2 s

Solution

Period T = 1/f = 1/5 = 0.2 s.

Correct Answer: A — 0.2 s

Q. A mass-spring system oscillates with a natural frequency of 3 Hz. If a damping force is applied, what is the new frequency of oscillation if the damping ratio is 0.1?

A. 2.8 Hz
B. 2.9 Hz
C. 3.0 Hz
D. 3.1 Hz

Solution

New frequency (ω_d) = ω_n√(1-ζ²) = 3√(1-0.1²) ≈ 2.9 Hz.

Correct Answer: B — 2.9 Hz

Q. A mass-spring system oscillates with a period of 2 seconds. What is the frequency of the oscillation?

A. 0.25 Hz
B. 0.5 Hz
C. 1 Hz
D. 2 Hz

Solution

Frequency (f) is the reciprocal of the period (T). f = 1/T = 1/2 = 0.5 Hz.

Correct Answer: B — 0.5 Hz

Q. A mass-spring system oscillates with a period of 4 seconds. What is the frequency of the oscillation?

A. 0.25 Hz
B. 0.5 Hz
C. 1 Hz
D. 2 Hz

Solution

Frequency f is the reciprocal of the period T. Thus, f = 1/T = 1/4 = 0.25 Hz.

Correct Answer: A — 0.25 Hz

Q. A mass-spring system oscillates with an amplitude of 0.1 m. What is the maximum speed of the mass if the angular frequency is 20 rad/s?

A. 1 m/s
B. 2 m/s
C. 3 m/s
D. 4 m/s

Solution

The maximum speed v_max is given by v_max = Aω, where A is the amplitude and ω is the angular frequency. Thus, v_max = 0.1 * 20 = 2 m/s.

Correct Answer: B — 2 m/s

Q. A material has a bulk modulus of 200 GPa. If the pressure applied to it is increased by 50 MPa, what is the fractional change in volume?

A. 0.00025
B. 0.0005
C. 0.0025
D. 0.005

Solution

The fractional change in volume is given by ΔV/V = ΔP/B. Here, ΔP = 50 MPa = 0.05 GPa, so ΔV/V = 0.05/200 = 0.00025.

Correct Answer: A — 0.00025

Q. A material has a bulk modulus of 200 GPa. If the pressure on the material is increased by 10 MPa, what is the fractional change in volume?

A. 0.00005
B. 0.0001
C. 0.0002
D. 0.00025

Solution

The fractional change in volume ΔV/V is given by ΔV/V = ΔP/B, where ΔP = 10 MPa and B = 200 GPa, resulting in 0.00005.

Correct Answer: B — 0.0001

Q. A material has a bulk modulus of 200 GPa. What is the change in volume when a pressure of 50 MPa is applied?

A. 0.0125%
B. 0.025%
C. 0.05%
D. 0.1%

Solution

The change in volume ΔV/V = P/B, so ΔV/V = 50 MPa / 200 GPa = 0.025%.

Correct Answer: B — 0.025%

Q. A material has a Poisson's ratio of 0.3. If it is stretched in one direction, what is the expected lateral contraction ratio? (2019)

A. 0.3
B. 0.7
C. 0.5
D. 0.1

Solution

Poisson's ratio (ν) = - (lateral strain) / (longitudinal strain), thus the lateral contraction ratio is 0.3.

Correct Answer: A — 0.3

Q. A material has a Poisson's ratio of 0.3. What is the ratio of lateral strain to longitudinal strain?

A. 0.3
B. 0.7
C. 1.0
D. 0.5

Solution

Poisson's ratio is defined as the negative ratio of lateral strain to longitudinal strain, so a Poisson's ratio of 0.3 means the ratio is 0.3.

Correct Answer: A — 0.3

Q. A material is said to be elastic if it:

A. Returns to its original shape after deformation
B. Can be permanently deformed
C. Breaks under stress
D. Has a high tensile strength

Solution

A material is considered elastic if it returns to its original shape after the removal of the applied stress.

Correct Answer: A — Returns to its original shape after deformation

Q. A material is subjected to a tensile stress of 100 MPa and experiences a strain of 0.002. What is its Young's modulus?

A. 50 GPa
B. 100 GPa
C. 200 GPa
D. 500 GPa

Solution

Young's modulus (Y) = Stress / Strain = 100 MPa / 0.002 = 50 GPa.

Correct Answer: B — 100 GPa

Q. A material with a Poisson's ratio of 0.5 is considered to be:

A. Perfectly elastic
B. Perfectly plastic
C. Incompressible
D. Brittle

Solution

A Poisson's ratio of 0.5 indicates that the material is incompressible.

Correct Answer: C — Incompressible

Q. A meal contains 15 grams of fat, 30 grams of carbohydrates, and 10 grams of protein. How many total calories does this meal provide? (Fat = 9 cal/g, Carbohydrates = 4 cal/g, Protein = 4 cal/g) (2021)

A. 200 calories
B. 250 calories
C. 300 calories
D. 350 calories

Solution

Total calories = (15g * 9) + (30g * 4) + (10g * 4) = 135 + 120 + 40 = 295 calories.

Correct Answer: C — 300 calories

Q. A meal contains 20 grams of fat. How many calories does this contribute to the meal? (Fat = 9 cal/g) (2021)

A. 180
B. 160
C. 200
D. 220

Solution

Calories from fat = 20g * 9 cal/g = 180 calories.

Correct Answer: A — 180

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