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 3rd term of a geometric sequence is 12 and the common ratio is 2, what is the first term? (2023)

A. 3
B. 6
C. 4
D. 8

Solution

The 3rd term is given by ar^2. So, 12 = a(2^2) => a = 12/4 = 3.

Correct Answer: B — 6

Q. If the 3rd term of a GP is 27 and the common ratio is 3, what is the first term?

A. 3
B. 9
C. 1
D. 27

Solution

Let the first term be a. Then, the 3rd term is ar^2 = 27. Thus, a * 3^2 = 27, giving a = 3.

Correct Answer: B — 9

Q. If the 3rd term of an arithmetic progression is 12 and the 7th term is 24, what is the common difference?

A. 3
B. 4
C. 6
D. 5

Solution

Let the first term be a and the common difference be d. We have a + 2d = 12 and a + 6d = 24. Subtracting these gives 4d = 12, so d = 3.

Correct Answer: B — 4

Q. If the 3rd term of an arithmetic progression is 15 and the 6th term is 24, what is the common difference?

A. 3
B. 4
C. 5
D. 6

Solution

Let the first term be a and the common difference be d. From the equations a + 2d = 15 and a + 5d = 24, solving gives d = 3.

Correct Answer: B — 4

Q. If the 3rd term of an arithmetic progression is 15 and the 7th term is 27, what is the common difference?

A. 3
B. 4
C. 5
D. 6

Solution

Let the first term be a and the common difference be d. From the equations a + 2d = 15 and a + 6d = 27, solving gives d = 3.

Correct Answer: B — 4

Q. If the 3rd term of an arithmetic sequence is 12 and the 7th term is 24, what is the common difference? (2023)

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

Solution

Let the first term be a and the common difference be d. Then, a + 2d = 12 and a + 6d = 24. Solving these gives d = 3.

Correct Answer: B — 3

Q. If the 5th term of an arithmetic progression is 15 and the 10th term is 30, what is the common difference?

A. 3
B. 4
C. 5
D. 6

Solution

Let the first term be a and the common difference be d. From the equations a + 4d = 15 and a + 9d = 30, we can find d = 3.

Correct Answer: A — 3

Q. If the 5th term of an arithmetic progression is 20 and the 10th term is 35, what is the first term?

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

Solution

Let the first term be a and the common difference be d. From the equations a + 4d = 20 and a + 9d = 35, we can solve for a to find it is 10.

Correct Answer: B — 10

Q. If the 6th term of an arithmetic progression is 30 and the 9th term is 45, what is the common difference?

A. 5
B. 6
C. 7
D. 8

Solution

Let the first term be a and the common difference be d. From the equations a + 5d = 30 and a + 8d = 45, we can find d = 5.

Correct Answer: A — 5

Q. If the 7th term of an arithmetic progression is 25 and the common difference is 3, what is the 1st term?

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

Solution

Using the formula for the nth term, a + 6d = 25. Substituting d = 3 gives a + 18 = 25, thus a = 7.

Correct Answer: A — 10

Q. If the 7th term of an arithmetic progression is 50 and the common difference is 5, what is the first term?

A. 25
B. 30
C. 35
D. 40

Solution

Using the formula for the nth term, a + 6d = 50. Substituting d = 5 gives a + 30 = 50, hence a = 20.

Correct Answer: B — 30

Q. If the activation energy of a reaction is increased, what happens to the rate constant k?

A. Increases
B. Decreases
C. Remains the same
D. Becomes zero

Solution

According to the Arrhenius equation, an increase in activation energy results in a decrease in the rate constant k.

Correct Answer: B — Decreases

Q. If the amount after 2 years at compound interest is Rs. 1210 and the principal is Rs. 1000, what is the rate of interest?

A. 10%
B. 5%
C. 12%
D. 15%

Solution

Using the formula A = P(1 + r)^t, we have 1210 = 1000(1 + r)^2. Solving gives r = 0.1 or 10%.

Correct Answer: A — 10%

Q. If the amplitude of a damped oscillator decreases to half its value in 5 seconds, what is the damping ratio?

A. 0.1
B. 0.2
C. 0.3
D. 0.4

Solution

Using the formula A(t) = A_0 e^(-ζω_nt), we find ζ = 0.2.

Correct Answer: B — 0.2

Q. If the amplitude of a simple harmonic motion is doubled, how does the maximum velocity change?

A. It doubles
B. It quadruples
C. It remains the same
D. It halves

Solution

Maximum velocity V_max = Aω. If A is doubled, V_max also doubles.

Correct Answer: A — It doubles

Q. If the amplitude of a simple harmonic motion is doubled, how does the total energy change?

A. Remains the same
B. Doubles
C. Quadruples
D. Halves

Solution

The total energy E in SHM is given by E = (1/2)kA². If A is doubled, E becomes (1/2)k(2A)² = 4(1/2)kA², which is quadrupled.

Correct Answer: C — Quadruples

Q. If the amplitude of a simple harmonic motion is doubled, what happens to the total energy of the system? (2022)

A. It remains the same
B. It doubles
C. It quadruples
D. It halves

Solution

Total energy (E) in SHM is proportional to the square of the amplitude (A). If A is doubled, E becomes 4A^2, hence it quadruples.

Correct Answer: C — It quadruples

Q. If the amplitude of a simple harmonic motion is halved, how does the maximum velocity change?

A. Halved
B. Doubled
C. Remains the same
D. Quadrupled

Solution

Maximum velocity V_max = ωA. If A is halved, V_max is also halved.

Correct Answer: A — Halved

Q. If the amplitude of a simple harmonic oscillator is doubled, how does the total energy change?

A. Remains the same
B. Doubles
C. Quadruples
D. Halves

Solution

The total energy in simple harmonic motion is proportional to the square of the amplitude. If amplitude is doubled, energy increases by a factor of 2^2 = 4.

Correct Answer: C — Quadruples

Q. If the amplitude of a simple harmonic oscillator is doubled, what happens to its total energy?

A. It remains the same
B. It doubles
C. It quadruples
D. It halves

Solution

The total energy of a simple harmonic oscillator is proportional to the square of the amplitude. If the amplitude is doubled, the energy increases by a factor of 2^2 = 4.

Correct Answer: C — It quadruples

Q. If the amplitude of a simple harmonic oscillator is halved, how does the total energy change?

A. Remains the same
B. Halved
C. Doubled
D. Quadrupled

Solution

The total energy in SHM is proportional to the square of the amplitude. If amplitude is halved, energy is reduced to (1/2)^2 = 1/4, which is halved.

Correct Answer: B — Halved

Q. If the amplitude of a simple harmonic oscillator is increased, what happens to its total energy? (2021)

A. Increases
B. Decreases
C. Remains the same
D. Becomes zero

Solution

The total energy (E) in a simple harmonic oscillator is given by E = (1/2)kA². If amplitude (A) increases, energy increases.

Correct Answer: A — Increases

Q. If the amplitude of a simple harmonic oscillator is tripled, how does the total energy change? (2020)

A. Increases by 3 times
B. Increases by 6 times
C. Increases by 9 times
D. Remains the same

Solution

Total energy in SHM is proportional to the square of the amplitude. If amplitude is tripled, energy increases by 3^2 = 9 times.

Correct Answer: C — Increases by 9 times

Q. If the amplitude of a wave is doubled, how does it affect the energy of the wave? (2020)

A. Remains the same
B. Doubles
C. Increases by four times
D. Halves

Solution

Energy of a wave is proportional to the square of the amplitude. If amplitude is doubled, energy increases by (2^2) = 4 times.

Correct Answer: C — Increases by four times

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

A. Remains the same
B. Doubles
C. Increases by a factor of four
D. Increases by a factor of eight

Solution

The energy of a wave is proportional to the square of the amplitude. If the amplitude is doubled, the energy increases by a factor of 2^2 = 4.

Correct Answer: C — Increases by a factor of four

Q. If the amplitude of a wave is doubled, how does this affect the energy carried by the wave? (2021)

A. Energy is halved
B. Energy remains the same
C. Energy is doubled
D. Energy is quadrupled

Solution

The energy carried by a wave is proportional to the square of the amplitude. Therefore, if the amplitude is doubled, the energy increases by a factor of four.

Correct Answer: D — Energy is quadrupled

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

A. Remains the same
B. Doubles
C. Increases by a factor of four
D. Increases by a factor of eight

Solution

The energy of a wave is proportional to the square of its amplitude. Therefore, if the amplitude is doubled, the energy increases by a factor of four.

Correct Answer: C — Increases by a factor of four

Q. If the amplitude of a wave is increased, what effect does it have on the energy carried by the wave? (2019)

A. Energy decreases
B. Energy remains the same
C. Energy increases
D. Energy becomes zero

Solution

The energy carried by a wave is proportional to the square of its amplitude. Therefore, if the amplitude increases, the energy also increases.

Correct Answer: C — Energy increases

Q. If the amplitude of a wave is increased, what effect does it have on the energy of the wave? (2022)

A. Energy decreases
B. Energy remains the same
C. Energy increases
D. Energy becomes zero

Solution

The energy of a wave is proportional to the square of its amplitude. Therefore, if the amplitude increases, the energy also increases.

Correct Answer: C — Energy increases

Q. If the amplitude of a wave is increased, what happens to its energy? (2019)

A. Decreases
B. Increases
C. Remains the same
D. Becomes zero

Solution

The energy of a wave is proportional to the square of its amplitude. Therefore, if the amplitude increases, the energy also increases.

Correct Answer: B — Increases

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