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 ratio of boys to girls in a class is 3:2 and there are 15 boys, how many girls are there?

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

Solution

Let the number of girls be 2x. Then, 3x = 15; x = 5. Number of girls = 2x = 10.

Correct Answer: B — 10

Q. If the ratio of boys to girls in a class is 3:2 and there are 30 students in total, how many girls are there? (2019)

A. 12
B. 18
C. 15
D. 10

Solution

Let boys = 3x and girls = 2x. Then, 3x + 2x = 30 => 5x = 30 => x = 6. Girls = 2x = 12.

Correct Answer: A — 12

Q. If the ratio of consecutive terms in a geometric series is constant, what can be inferred about the series? (2023)

A. It is increasing.
B. It is decreasing.
C. It is exponential.
D. It is linear.

Solution

A constant ratio of consecutive terms indicates that the series is exponential.

Correct Answer: C — It is exponential.

Q. If the ratio of consecutive terms in a geometric series is constant, what is this constant called? (2023)

A. Common difference
B. Common ratio
C. Term factor
D. Sequence multiplier

Solution

The constant ratio of consecutive terms in a geometric series is called the common ratio.

Correct Answer: B — Common ratio

Q. If the ratio of consecutive terms in a geometric series is constant, what is this ratio called? (2023)

A. Common difference
B. Common ratio
C. Term ratio
D. Sequence ratio

Solution

The constant ratio of consecutive terms in a geometric series is called the common ratio.

Correct Answer: B — Common ratio

Q. If the ratio of the ages of A and B is 3:4 and the sum of their ages is 28 years, what is A's age? (2021)

A. 12
B. 14
C. 16
D. 18

Solution

Let A's age be 3x and B's age be 4x. Then, 3x + 4x = 28, giving 7x = 28, so x = 4. Thus, A's age = 3x = 12.

Correct Answer: B — 14

Q. If the ratio of the ages of A and B is 3:4 and the sum of their ages is 28, what is A's age? (2022)

A. 12
B. 14
C. 16
D. 18

Solution

Let A's age be 3x and B's age be 4x. Then, 3x + 4x = 28, so 7x = 28, giving x = 4. Thus, A's age = 3x = 12.

Correct Answer: A — 12

Q. If the ratio of the ages of A and B is 3:4 and the sum of their ages is 56 years, what is A's age?

A. 24
B. 21
C. 28
D. 30

Solution

Let A's age be 3x and B's age be 4x. Then, 3x + 4x = 56, giving 7x = 56, so x = 8. Thus, A's age = 3x = 24.

Correct Answer: A — 24

Q. If the ratio of the ages of A and B is 3:4 and the sum of their ages is 56, what is A's age?

A. 24
B. 28
C. 32
D. 36

Solution

Let A's age be 3x and B's age be 4x. Then, 3x + 4x = 56, 7x = 56, x = 8. A's age = 3x = 24.

Correct Answer: B — 28

Q. If the ratio of the ages of A and B is 3:4 and the sum of their ages is 70, what is A's age? (2022)

A. 30
B. 35
C. 40
D. 45

Solution

Let A's age be 3x and B's age be 4x. Then, 3x + 4x = 70, giving 7x = 70, so x = 10. Thus, A's age = 3x = 30.

Correct Answer: B — 35

Q. If the ratio of the ages of A and B is 5:3 and the sum of their ages is 64 years, what is A's age?

A. 40
B. 32
C. 30
D. 28

Solution

Let A's age be 5x and B's age be 3x. Then, 5x + 3x = 64, which gives 8x = 64. Therefore, x = 8, and A's age is 5x = 40 years.

Correct Answer: A — 40

Q. If the ratio of the lengths of two rectangles is 5:7 and the length of the first rectangle is 25 cm, what is the length of the second rectangle?

A. 30
B. 35
C. 40
D. 45

Solution

Let the length of the first rectangle = 5x and the second = 7x. Given 5x = 25, x = 5. Therefore, length of the second rectangle = 7x = 7*5 = 35.

Correct Answer: A — 30

Q. If the ratio of the lengths of two rectangles is 7:4 and the length of the first rectangle is 28 cm, what is the length of the second rectangle?

A. 16
B. 12
C. 14
D. 10

Solution

Let the lengths be 7x and 4x. Given 7x = 28, x = 4. Therefore, the length of the second rectangle = 4x = 4*4 = 16.

Correct Answer: A — 16

Q. If the ratio of the lengths of two ropes is 5:7 and the total length of the ropes is 72 meters, what is the length of the shorter rope?

A. 30
B. 25
C. 20
D. 28

Solution

Let the lengths be 5x and 7x. Given 5x + 7x = 72, 12x = 72, x = 6. Therefore, shorter rope = 5x = 5*6 = 30.

Correct Answer: B — 25

Q. If the ratio of the lengths of two sides of a triangle is 3:4 and the length of the shorter side is 9 cm, what is the length of the longer side? (2022)

A. 12 cm
B. 15 cm
C. 18 cm
D. 21 cm

Solution

If the shorter side is 9 cm and the ratio is 3:4, then the longer side is (4/3) × 9 cm = 12 cm.

Correct Answer: A — 12 cm

Q. If the ratio of the lengths of two sides of a triangle is 3:5 and the perimeter is 64 cm, what is the length of the longer side?

A. 30
B. 25
C. 20
D. 15

Solution

Let the sides be 3x and 5x. Then, 3x + 5x = 64, 8x = 64, x = 8. Therefore, the longer side = 5x = 5*8 = 40.

Correct Answer: B — 25

Q. If the ratio of the lengths of two sides of a triangle is 7:5 and the perimeter is 48 cm, what is the length of the longer side?

A. 28 cm
B. 20 cm
C. 24 cm
D. 16 cm

Solution

Let the lengths of the sides be 7x and 5x. Then, 7x + 5x = 48, which gives 12x = 48. Thus, x = 4, and the longer side is 7x = 28 cm.

Correct Answer: A — 28 cm

Q. If the ratio of the lengths of two sides of a triangle is 7:9 and the longer side is 36 cm, what is the length of the shorter side?

A. 28
B. 30
C. 32
D. 24

Solution

Let the shorter side be 7x and the longer side be 9x. Given 9x = 36, x = 4. Therefore, shorter side = 7x = 7*4 = 28.

Correct Answer: A — 28

Q. If the ratio of the number of apples to oranges is 7:3 and there are 42 apples, how many oranges are there?

A. 18
B. 12
C. 15
D. 21

Solution

Let apples = 7x and oranges = 3x. Given 7x = 42, x = 6. Therefore, oranges = 3x = 3*6 = 18.

Correct Answer: A — 18

Q. If the ratio of the number of cats to dogs in a shelter is 2:3 and there are 30 dogs, how many cats are there?

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

Solution

The ratio of cats to dogs is 2:3. If there are 30 dogs, the number of cats can be calculated as (2/3) * 30 = 20 cats.

Correct Answer: A — 20

Q. If the ratio of the sides of a triangle is 3:4:5, what is the length of the longest side if the perimeter is 36 cm? (2021)

A. 15 cm
B. 12 cm
C. 9 cm
D. 18 cm

Solution

Let the sides be 3x, 4x, and 5x. Then, 3x + 4x + 5x = 36. Thus, 12x = 36, giving x = 3. The longest side is 5x = 15 cm.

Correct Answer: A — 15 cm

Q. If the ratio of the sides of a triangle is 3:4:5, what is the perimeter if the shortest side is 6 cm? (2021)

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

Solution

If the shortest side is 6 cm, the sides are 6, 8, and 10 cm. Perimeter = 6 + 8 + 10 = 24 cm.

Correct Answer: B — 36 cm

Q. If the ratio of the sides of a triangle is 3:4:5, what type of triangle is it? (2019)

A. Equilateral
B. Isosceles
C. Scalene
D. Right-angled

Solution

A triangle with sides in the ratio 3:4:5 is a right-angled triangle.

Correct Answer: D — Right-angled

Q. If the ratio of the speeds of two cars is 5:7 and the faster car travels 140 km in an hour, how far does the slower car travel in the same time?

A. 100
B. 120
C. 140
D. 160

Solution

Let speeds be 5x and 7x. Given 7x = 140, x = 20. Slower car's speed = 5x = 5*20 = 100 km.

Correct Answer: A — 100

Q. If the ratio of two numbers is 7:9 and their sum is 128, what are the two numbers?

A. 56, 72
B. 49, 81
C. 63, 72
D. 70, 58

Solution

Let the numbers be 7x and 9x. Then, 7x + 9x = 128, 16x = 128, x = 8. Therefore, the numbers are 7*8 = 56 and 9*8 = 72.

Correct Answer: A — 56, 72

Q. If the ratio of two numbers is 7:9 and their sum is 128, what is the larger number?

A. 72
B. 56
C. 64
D. 80

Solution

Let the numbers be 7x and 9x. Then, 7x + 9x = 128, 16x = 128, x = 8. Larger number = 9x = 9*8 = 72.

Correct Answer: A — 72

Q. If the refractive index of a medium is 1.33, what is the critical angle for total internal reflection?

A. 48.6°
B. 60.0°
C. 30.0°
D. 45.0°

Solution

Critical angle θc = sin⁻¹(1/1.33) ≈ 48.6°.

Correct Answer: A — 48.6°

Q. If the refractive index of a medium is 1.33, what is the maximum angle of incidence for total internal reflection when light travels to air?

A. 41.8°
B. 48.6°
C. 53.1°
D. 60.0°

Solution

The critical angle θc can be calculated as θc = sin^(-1)(n2/n1) = sin^(-1)(1.00/1.33) ≈ 48.6°.

Correct Answer: A — 41.8°

Q. If the refractive index of a medium is 1.33, what is the speed of light in that medium if the speed of light in vacuum is 3 x 10^8 m/s?

A. 2.25 x 10^8 m/s
B. 2.5 x 10^8 m/s
C. 2.75 x 10^8 m/s
D. 3 x 10^8 m/s

Solution

Speed of light in medium = c/n = (3 x 10^8 m/s) / 1.33 ≈ 2.25 x 10^8 m/s.

Correct Answer: A — 2.25 x 10^8 m/s

Q. If the refractive index of a medium is 1.5, what is the maximum angle of incidence for total internal reflection when light travels to air?

A. 41.8°
B. 48.6°
C. 60.0°
D. 90.0°

Solution

The critical angle θc is given by sin(θc) = n2/n1 = 1/1.5, which gives θc ≈ 41.8°.

Correct Answer: A — 41.8°

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