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 vector A = 3i + 4j + 5k is reflected in the plane x + y + z = 0, what is the reflected vector?

A. -3i - 4j - 5k
B. 3i + 4j + 5k
C. 0
D. None of the above

Solution

The reflection of A in the plane x + y + z = 0 is -A = -3i - 4j - 5k.

Correct Answer: A — -3i - 4j - 5k

Q. If the vector A = 5i + 12j is scaled by a factor of 2, what is the new vector?

A. 10i + 24j
B. 5i + 12j
C. 2i + 3j
D. 7i + 14j

Solution

Scaling A by 2 gives 2A = 2(5i + 12j) = 10i + 24j.

Correct Answer: A — 10i + 24j

Q. If the vectors A = (1, 2) and B = (2, 1) are given, what is the angle between them?

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

Solution

Cosine of angle θ = (A · B) / (|A| |B|) = (1*2 + 2*1) / (√5 * √5) = 4/5, θ = cos⁻¹(4/5).

Correct Answer: B — 45 degrees

Q. If the vectors A = (2, 3) and B = (4, 5) are given, what is the scalar product A · B?

A. 23
B. 22
C. 20
D. 21

Solution

A · B = 2*4 + 3*5 = 8 + 15 = 23.

Correct Answer: C — 20

Q. If the vectors A = (3, -2, 1) and B = (k, 4, -2) are orthogonal, find the value of k.

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

Solution

A · B = 3k - 8 - 2 = 0; 3k - 10 = 0; k = 10/3.

Correct Answer: A — -1

Q. If the vectors A = (x, 2, 3) and B = (4, y, 6) are orthogonal, what is the value of x + y?

A. -2
B. 0
C. 2
D. 4

Solution

A · B = x*4 + 2*y + 3*6 = 0. Thus, 4x + 2y + 18 = 0. Solving gives x + y = -9/2, which is not an option. Correcting gives x + y = 0.

Correct Answer: A — -2

Q. If the vectors A = (x, 2, 3) and B = (4, y, 6) are orthogonal, what is the value of y?

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

Solution

A · B = x*4 + 2*y + 3*6 = 0. Thus, 4x + 2y + 18 = 0. If x = 0, then y = -9. If x = 1, y = -10. The only integer solution is y = 3.

Correct Answer: B — 3

Q. If the vectors A = 1i + 2j and B = 2i + 1j, find A · B. (2023)

A. 4
B. 5
C. 6
D. 7

Solution

A · B = (1)(2) + (2)(1) = 2 + 2 = 4

Correct Answer: B — 5

Q. If the vectors A = 2i + 2j and B = 2i - 2j, find A · B.

A. 0
B. 4
C. 8
D. 2

Solution

A · B = (2)(2) + (2)(-2) = 4 - 4 = 0.

Correct Answer: B — 4

Q. If the vectors A = 2i + 3j and B = 3i + 4j are perpendicular, what is the value of A · B?

A. 0
B. 6
C. 12
D. 9

Solution

Since A and B are perpendicular, A · B = 0.

Correct Answer: A — 0

Q. If the vectors A = 3i + 4j and B = 4i + 3j, what is the scalar product A · B?

A. 25
B. 30
C. 32
D. 28

Solution

A · B = (3)(4) + (4)(3) = 12 + 12 = 24.

Correct Answer: A — 25

Q. If the vectors A = 5i + 5j and B = 5i - 5j, what is the scalar product A · B?

A. 50
B. 0
C. 25
D. 10

Solution

A · B = (5)(5) + (5)(-5) = 25 - 25 = 0.

Correct Answer: B — 0

Q. If the vectors A = 6i + 8j and B = 2i + 3j, what is A · B? (2020)

A. 42
B. 48
C. 36
D. 30

Solution

A · B = (6)(2) + (8)(3) = 12 + 24 = 36.

Correct Answer: A — 42

Q. If the vectors A = 6i + 8j and B = 3i + 4j are perpendicular, what is the value of A · B? (2021)

A. 0
B. 18
C. 30
D. 42

Solution

A · B = (6)(3) + (8)(4) = 18 + 32 = 50, but since they are perpendicular, A · B = 0.

Correct Answer: A — 0

Q. If the vectors A and B are such that A · B = |A| |B|, what is the angle between them?

A. 0°
B. 90°
C. 180°
D. None of the above

Solution

If A · B = |A| |B|, then cos(θ) = 1, which means θ = 0°.

Correct Answer: A — 0°

Q. If the velocity of a river increases, what is the expected effect on soil erosion along its banks? (2021)

A. Increases erosion
B. Decreases erosion
C. No effect
D. Depends on soil type

Solution

Increased velocity leads to higher energy, which increases soil erosion.

Correct Answer: A — Increases erosion

Q. If the velocity of a river is 3 m/s and the width of the river is 20 m, what is the discharge of the river?

A. 60 m³/s
B. 30 m³/s
C. 20 m³/s
D. 15 m³/s

Solution

Discharge = Velocity × Area. Area = Width × Depth. Assuming depth = 1 m, Area = 20 m × 1 m = 20 m². Discharge = 3 m/s × 20 m² = 60 m³/s.

Correct Answer: A — 60 m³/s

Q. If the velocity of an object doubles, what happens to its kinetic energy?

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

Solution

Kinetic energy (KE) is given by KE = 1/2 mv². If velocity (v) doubles, KE increases by a factor of 2² = 4, hence it quadruples.

Correct Answer: C — It quadruples

Q. If the vertex of the parabola y = ax^2 + bx + c is at (1, -2), what is the value of a if b = 4 and c = -6?

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

Solution

The vertex form of a parabola is given by x = -b/(2a). Here, 1 = -4/(2a) => 2a = -4 => a = -2.

Correct Answer: A — 1

Q. If the viscosity of a fluid is doubled, what happens to the flow rate through a pipe, assuming all other factors remain constant?

A. Doubles
B. Halves
C. Remains the same
D. Increases fourfold

Solution

If viscosity is doubled, the flow rate through a pipe will halve, as flow rate is inversely proportional to viscosity.

Correct Answer: B — Halves

Q. If the viscosity of a fluid is doubled, what happens to the flow rate through a constant diameter pipe?

A. Doubles
B. Halves
C. Remains the same
D. Increases fourfold

Solution

If viscosity is doubled, the flow rate through a constant diameter pipe is halved.

Correct Answer: B — Halves

Q. If the viscosity of a fluid is high, what does it imply about the fluid's flow?

A. It flows easily
B. It flows slowly
C. It is incompressible
D. It is a gas

Solution

A high viscosity indicates that the fluid flows slowly.

Correct Answer: B — It flows slowly

Q. If the viscosity of a liquid is doubled, how does it affect the flow rate through a pipe?

A. Flow rate doubles
B. Flow rate halves
C. Flow rate remains the same
D. Flow rate quadruples

Solution

According to Poiseuille's law, if viscosity is doubled, the flow rate is halved, assuming all other factors remain constant.

Correct Answer: B — Flow rate halves

Q. If the viscosity of a liquid is doubled, what happens to the flow rate through a pipe, assuming all other factors remain constant?

A. Flow rate doubles
B. Flow rate halves
C. Flow rate remains the same
D. Flow rate quadruples

Solution

According to Poiseuille's law, if viscosity is doubled, the flow rate will be halved, assuming other factors remain constant.

Correct Answer: B — Flow rate halves

Q. If the voltage across a capacitor in an AC circuit is 100 V and the capacitive reactance is 50 Ω, what is the current through the capacitor? (2021)

A. 2 A
B. 0.5 A
C. 5 A
D. 10 A

Solution

Using Ohm's law, I = V/Xc = 100 V / 50 Ω = 2 A.

Correct Answer: B — 0.5 A

Q. If the voltage across a capacitor in an AC circuit is 100 V and the capacitive reactance is 50 ohms, what is the current? (2020)

A. 2 A
B. 0.5 A
C. 5 A
D. 10 A

Solution

Using Ohm's law, I = V/Xc = 100 V / 50 ohms = 2 A.

Correct Answer: B — 0.5 A

Q. If the voltage across a capacitor in an AC circuit is 100 V and the capacitive reactance is 50 ohms, what is the current through the capacitor? (2021)

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

Solution

Current I = V/Xc = 100 V / 50 ohms = 2 A.

Correct Answer: B — 1 A

Q. If the voltage across a capacitor in an AC circuit is 100 V RMS, what is the peak voltage? (2022)

A. 100 V
B. 141.42 V
C. 200 V
D. 70.71 V

Solution

The peak voltage (V_peak) is calculated as V_peak = V_rms × √2 = 100 V × √2 ≈ 141.42 V.

Correct Answer: B — 141.42 V

Q. If the voltage across a capacitor in an AC circuit is 100V and the capacitive reactance is 50 ohms, what is the current? (2023)

A. 2A
B. 0.5A
C. 5A
D. 10A

Solution

Using Ohm's law, I = V/Xc = 100V/50Ω = 2A.

Correct Answer: A — 2A

Q. If the voltage across a capacitor in an AC circuit is 100V and the capacitive reactance is 50Ω, what is the current? (2021)

A. 2A
B. 0.5A
C. 5A
D. 100A

Solution

Using Ohm's law, I = V/Xc = 100V/50Ω = 2A.

Correct Answer: B — 0.5A

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