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 HCF of three numbers is 1, which of the following can be true?

A. All three numbers are prime
B. All three numbers are even
C. All three numbers are odd
D. Two numbers are even and one is odd

Solution

If the HCF is 1, it is possible that all three numbers are prime, as they would not share any common factors.

Correct Answer: A — All three numbers are prime

Q. If the HCF of three numbers is 5 and their LCM is 300, what can be said about the numbers?

A. They are all multiples of 5
B. They are all prime
C. They are all even
D. They are all odd

Solution

Since the HCF is 5, all three numbers must be multiples of 5.

Correct Answer: A — They are all multiples of 5

Q. If the HCF of three numbers is 5 and their LCM is 300, what is the product of the three numbers? (2023)

A. 1500
B. 3000
C. 6000
D. 7500

Solution

The product of the three numbers is equal to HCF * LCM = 5 * 300 = 1500.

Correct Answer: B — 3000

Q. If the HCF of three numbers is 7 and their LCM is 420, what is the maximum possible value of the product of these three numbers? (2023)

A. 2940
B. 840
C. 1260
D. 2100

Solution

The product of the three numbers is equal to HCF * LCM. Thus, 7 * 420 = 2940.

Correct Answer: C — 1260

Q. If the HCF of three numbers is 7 and their LCM is 420, what is the product of the three numbers? (2023)

A. 2940
B. 840
C. 2100
D. 1470

Solution

The product of the three numbers = HCF * LCM = 7 * 420 = 2940.

Correct Answer: A — 2940

Q. If the HCF of two numbers is 1, what can be inferred about the two numbers? (2023)

A. They are both prime.
B. They are coprime.
C. They are multiples of each other.
D. They are both even.

Solution

If the HCF is 1, it means the two numbers are coprime, meaning they have no common factors other than 1.

Correct Answer: B — They are coprime.

Q. If the HCF of two numbers is 1, what can be said about the two numbers? (2023)

A. They are prime
B. They are coprime
C. They are even
D. They are odd

Solution

If the HCF is 1, the two numbers are coprime, meaning they have no common factors other than 1.

Correct Answer: B — They are coprime

Q. If the HCF of two numbers is 12 and their LCM is 120, what is the product of the two numbers?

A. 144
B. 1200
C. 240
D. 100

Solution

The product of two numbers is equal to the product of their HCF and LCM. Therefore, the product = 12 * 120 = 1440.

Correct Answer: B — 1200

Q. If the HCF of two numbers is 12 and their LCM is 144, what is the product of the two numbers? (2023)

A. 1728
B. 864
C. 144
D. 288

Solution

The product of two numbers is equal to the product of their HCF and LCM. Therefore, 12 * 144 = 1728.

Correct Answer: A — 1728

Q. If the HCF of two numbers is 15 and their product is 450, what is their LCM?

A. 30
B. 45
C. 60
D. 75

Solution

The LCM can be found using the formula: LCM = (Product of the numbers) / HCF. Thus, LCM = 450 / 15 = 30.

Correct Answer: B — 45

Q. If the HCF of two numbers is 5 and their LCM is 100, what is the sum of the two numbers? (2023)

A. 30
B. 25
C. 50
D. 45

Solution

Let the two numbers be 5x and 5y. Then, HCF(5x, 5y) = 5 and LCM(5x, 5y) = 100. This gives xy = 20. The pairs (x, y) that satisfy this are (4, 5) or (5, 4), leading to the sum 5(4 + 5) = 45.

Correct Answer: A — 30

Q. If the HCF of two numbers is 5 and their LCM is 100, what is the sum of the two numbers if one of them is 25?

A. 50
B. 75
C. 100
D. 125

Solution

Let the other number be x. Then, HCF(25, x) = 5 and LCM(25, x) = 100. Therefore, 25 * x = 5 * 100, which gives x = 20. The sum is 25 + 20 = 45.

Correct Answer: A — 50

Q. If the HCF of two numbers is 5 and their product is 100, what could be the two numbers? (2023)

A. 5 and 20
B. 10 and 10
C. 15 and 5
D. 25 and 4

Solution

If HCF is 5, the two numbers can be expressed as 5a and 5b. Thus, 5a * 5b = 100 implies ab = 4. The pair (1, 4) gives us 5 and 20.

Correct Answer: A — 5 and 20

Q. If the HCF of two numbers is 5 and their product is 100, what is their LCM?

A. 20
B. 25
C. 15
D. 10

Solution

Using the relationship between HCF, LCM, and product: HCF * LCM = Product. Thus, LCM = 100 / 5 = 20.

Correct Answer: B — 25

Q. If the HCF of two numbers is 5 and their product is 1000, what is their LCM? (2023)

A. 200
B. 100
C. 250
D. 150

Solution

Using the relation HCF * LCM = Product of the numbers, we have LCM = 1000 / 5 = 200.

Correct Answer: A — 200

Q. If the HCF of two numbers is 8 and their LCM is 48, what could be one of the possible pairs of numbers? (2023)

A. 16 and 24
B. 8 and 32
C. 4 and 12
D. 20 and 16

Solution

The numbers can be 16 and 24, as their HCF is 8 and LCM is 48.

Correct Answer: A — 16 and 24

Q. If the HCF of two numbers is 8 and their product is 288, what is their LCM? (2023)

A. 36
B. 24
C. 32
D. 48

Solution

Using the relationship between HCF, LCM, and the product of two numbers: LCM = Product / HCF = 288 / 8 = 36.

Correct Answer: A — 36

Q. If the height of a cylinder is doubled while keeping the radius constant, how does the volume change?

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

Solution

Volume of a cylinder = πr²h. If height is doubled, volume becomes 2πr²h, which is double the original volume.

Correct Answer: B — It doubles

Q. If the height of an isosceles triangle is 12 cm and the base is 10 cm, what is the area of the triangle?

A. 60 cm²
B. 70 cm²
C. 80 cm²
D. 90 cm²

Solution

The area of a triangle is given by (1/2) * base * height = (1/2) * 10 * 12 = 60 cm².

Correct Answer: A — 60 cm²

Q. If the hexadecimal number A3 is converted to decimal, what is its value? (2023)

A. 163
B. 1630
C. 103
D. 83

Solution

A3 in hexadecimal is calculated as 10*16^1 + 3*16^0 = 160 + 3 = 163.

Correct Answer: A — 163

Q. If the image distance is equal to the object distance for a lens, what is the magnification?

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

Solution

Magnification (m) = v/u = 1 when image distance equals object distance.

Correct Answer: B — 1

Q. If the image distance of a convex lens is 40 cm and the object distance is 30 cm, what is the focal length of the lens?

A. 10 cm
B. 20 cm
C. 30 cm
D. 15 cm

Solution

Using the lens formula 1/f = 1/v - 1/u, we have 1/f = 1/40 - 1/(-30) = 1/40 + 1/30. Solving gives f = 20 cm.

Correct Answer: B — 20 cm

Q. If the incidence rate of a disease is 3 cases per 1000 people per year, how many new cases would you expect in a population of 50,000? (2022)

A. 150
B. 200
C. 300
D. 500

Solution

Expected new cases = (Incidence rate × Population) / 1000 = (3 × 50000) / 1000 = 150.

Correct Answer: C — 300

Q. If the income of the poorest 20% of the population increases by 15% and the richest 20% by 5%, what is the average increase in income for both groups?

A. 10%
B. 12%
C. 13%
D. 14%

Solution

Average increase = (15% + 5%) / 2 = 10%. However, considering the weight of the groups, the effective average increase is closer to 13%.

Correct Answer: C — 13%

Q. If the inductance of a coil is 0.5H and the frequency is 60Hz, what is the inductive reactance? (2023)

A. 31.42 ohms
B. 18.85 ohms
C. 37.70 ohms
D. 25.13 ohms

Solution

Xl = 2πfL = 2π × 60 × 0.5 = 31.42 ohms.

Correct Answer: A — 31.42 ohms

Q. If the inductance of a coil is 2 H and the frequency is 50 Hz, what is the inductive reactance?

A. 100 π
B. 100
C. 314
D. 628

Solution

Inductive reactance X_L = 2πfL = 2π(50)(2) = 628 Ω.

Correct Answer: C — 314

Q. If the inductance of a coil is doubled, what happens to its inductive reactance at a constant frequency? (2022)

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

Solution

Inductive reactance (X_L) is given by X_L = 2πfL. If the inductance (L) is doubled, X_L will also double.

Correct Answer: A — It doubles

Q. If the inductive reactance of a coil is 30Ω and the resistance is 10Ω, what is the total impedance? (2018)

A. 10Ω
B. 30Ω
C. 33.33Ω
D. 40Ω

Solution

Total impedance Z = √(R² + (XL)²) = √(10² + 30²) = √(100 + 900) = √1000 = 31.62Ω.

Correct Answer: C — 33.33Ω

Q. If the inflation rate increases from 2% to 4%, how much more will a $100 item cost after one year?

A. $2
B. $4
C. $6
D. $8

Solution

Cost after 2% inflation = 100 * 1.02 = $102; Cost after 4% inflation = 100 * 1.04 = $104; Difference = $104 - $102 = $2.

Correct Answer: B — $4

Q. If the inflation rate is 3% and a product costs $100 today, what will be its cost in one year?

A. $102
B. $103
C. $104
D. $105

Solution

Future cost = Current cost * (1 + inflation rate) = 100 * (1 + 0.03) = $103

Correct Answer: B — $103

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