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. C and D start a business with investments of $8000 and $12000 respectively. If they make a profit of $6000, how much will C get?

A. $2400
B. $3000
C. $2000
D. $3600

Solution

Total investment = 8000 + 12000 = 20000. C's share = (8000/20000) * 6000 = $2400.

Correct Answer: B — $3000

Q. C, D, and E start a business with investments of $12,000, $18,000, and $30,000 respectively. What is the share of D in a profit of $60,000?

A. $18,000
B. $24,000
C. $12,000
D. $30,000

Solution

D's share = (D's investment / Total investment) * Total profit = (18000 / 60000) * 60000 = $18,000.

Correct Answer: B — $24,000

Q. C, D, and E start a business with investments of $12,000, $18,000, and $30,000 respectively. What is the share of E in a profit of $60,000?

A. $20,000
B. $30,000
C. $15,000
D. $25,000

Solution

E's share = (E's investment / Total investment) * Total profit = (30000 / 60000) * 60000 = $30,000.

Correct Answer: B — $30,000

Q. C, D, and E start a business with investments of $5,000, $10,000, and $15,000 respectively. If they make a profit of $60,000, how much will C receive?

A. $10,000
B. $15,000
C. $12,000
D. $5,000

Solution

Total investment = 5000 + 10000 + 15000 = 30000. C's share = (5000 / 30000) * 60000 = $10,000.

Correct Answer: C — $12,000

Q. Calcium is important for which of the following plant processes? (2020)

A. Nutrient transport
B. Cell wall stability
C. Photosynthesis
D. Respiration

Solution

Calcium is vital for maintaining cell wall stability and structure, as well as signaling within the plant.

Correct Answer: B — Cell wall stability

Q. Calcium is important for which of the following processes in plants? (2020)

A. Nutrient transport
B. Cell division
C. Photosynthesis
D. Respiration

Solution

Calcium is vital for cell division and is a key component of cell walls, providing structural stability.

Correct Answer: B — Cell division

Q. Calcium is primarily involved in which of the following processes? (2020)

A. Photosynthesis
B. Cell wall stability
C. Nutrient transport
D. Respiration

Solution

Calcium is crucial for maintaining cell wall stability and structure in plants.

Correct Answer: B — Cell wall stability

Q. Calculate 15% of 200. (2015)

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

Solution

15% of 200 = (15/100) × 200 = 30.

Correct Answer: A — 30

Q. Calculate 18 - (3 × 4). (2015)

A. 6
B. 12
C. 10
D. 8

Solution

3 × 4 = 12, then 18 - 12 = 6.

Correct Answer: B — 12

Q. Calculate 45 ÷ 5 + 6 × 2.

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

Solution

45 ÷ 5 = 9; 6 × 2 = 12; 9 + 12 = 21.

Correct Answer: B — 18

Q. Calculate the area between the curves y = x and y = x^2 from x = 0 to x = 1.

A. 0.25
B. 0.5
C. 0.75
D. 1

Solution

The area is given by the integral from 0 to 1 of (x - x^2) dx. This evaluates to [x^2/2 - x^3/3] from 0 to 1 = (1/2 - 1/3) = 1/6 = 0.5.

Correct Answer: B — 0.5

Q. Calculate the area between the curves y = x^2 and y = 2x from x = 0 to x = 2.

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

Solution

The area is given by the integral from 0 to 2 of (2x - x^2) dx. This evaluates to [x^2 - x^3/3] from 0 to 2 = (4 - 8/3) = 4/3.

Correct Answer: A — 2

Q. Calculate the area between the curves y = x^2 and y = 4 from x = 0 to x = 2.

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

Solution

The area is given by the integral from 0 to 2 of (4 - x^2) dx. This evaluates to [4x - x^3/3] from 0 to 2 = (8 - 8/3) = 16/3.

Correct Answer: A — 4

Q. Calculate the area of a triangle with base 10 cm and height 5 cm. (2021)

A. 25 cm²
B. 50 cm²
C. 15 cm²
D. 30 cm²

Solution

Area = 1/2 * base * height = 1/2 * 10 * 5 = 25 cm².

Correct Answer: A — 25 cm²

Q. Calculate the area under the curve y = 2x + 1 from x = 1 to x = 4.

A. 15
B. 10
C. 12
D. 20

Solution

The area under the curve is given by ∫(from 1 to 4) (2x + 1) dx = [x^2 + x] from 1 to 4 = (16 + 4) - (1 + 1) = 20.

Correct Answer: A — 15

Q. Calculate the area under the curve y = cos(x) from x = 0 to x = π/2.

A. 1
B. 0
C. π/2
D. 2

Solution

The area under the curve y = cos(x) from x = 0 to x = π/2 is given by ∫(from 0 to π/2) cos(x) dx = [sin(x)] from 0 to π/2 = 1 - 0 = 1.

Correct Answer: A — 1

Q. Calculate the area under the curve y = x^2 + 2x from x = 0 to x = 2.

A. 4
B. 6
C. 8
D. 10

Solution

The area under the curve is given by ∫(from 0 to 2) (x^2 + 2x) dx = [x^3/3 + x^2] from 0 to 2 = (8/3 + 4) = 20/3.

Correct Answer: B — 6

Q. Calculate the area under the curve y = x^3 from x = 0 to x = 2.

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

Solution

The area under the curve is given by ∫(from 0 to 2) x^3 dx = [x^4/4] from 0 to 2 = (16/4) - (0) = 4.

Correct Answer: B — 8

Q. Calculate the area under the curve y = x^4 from x = 0 to x = 2.

A. 4
B. 8
C. 16
D. 32

Solution

The area under the curve y = x^4 from x = 0 to x = 2 is given by ∫(from 0 to 2) x^4 dx = [x^5/5] from 0 to 2 = (32/5) - 0 = 32/5.

Correct Answer: B — 8

Q. Calculate the coefficient of x^2 in the expansion of (2x + 3)^4.

A. 36
B. 48
C. 54
D. 64

Solution

The coefficient of x^2 is C(4,2) * (2)^2 * (3)^2 = 6 * 4 * 9 = 216.

Correct Answer: B — 48

Q. Calculate the coefficient of x^2 in the expansion of (x + 1/2)^6.

A. 15/4
B. 45/8
C. 15/8
D. 5/4

Solution

The coefficient of x^2 is C(6,2) * (1/2)^2 = 15 * 1/4 = 15/4.

Correct Answer: B — 45/8

Q. Calculate the coefficient of x^2 in the expansion of (x + 1/2)^8. (2021)

A. 28
B. 56
C. 70
D. 84

Solution

The coefficient of x^2 is C(8,2) * (1/2)^6 = 28 * 1/64 = 28/64 = 7/16.

Correct Answer: C — 70

Q. Calculate the coefficient of x^2 in the expansion of (x + 1/x)^6. (2019)

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

Solution

The coefficient of x^2 is given by 6C2 * (1)^4 = 15.

Correct Answer: A — 15

Q. Calculate the coefficient of x^2 in the expansion of (x + 4)^6.

A. 96
B. 144
C. 192
D. 256

Solution

The coefficient of x^2 is given by C(6,2) * 4^4 = 15 * 256 = 3840.

Correct Answer: A — 96

Q. Calculate the coefficient of x^3 in the expansion of (x + 1/2)^6.

A. 20
B. 30
C. 40
D. 50

Solution

The coefficient of x^3 is given by C(6,3) * (1/2)^3 = 20 * 1/8 = 2.5.

Correct Answer: A — 20

Q. Calculate the coefficient of x^3 in the expansion of (x - 1)^5.

A. -5
B. 10
C. -10
D. 5

Solution

The coefficient of x^3 is C(5,3) * (-1)^2 = 10.

Correct Answer: B — 10

Q. Calculate the coefficient of x^4 in the expansion of (3x - 2)^6.

A. 540
B. 720
C. 810
D. 960

Solution

The coefficient of x^4 is C(6,4) * (3)^4 * (-2)^2 = 15 * 81 * 4 = 4860.

Correct Answer: A — 540

Q. Calculate the coefficient of x^4 in the expansion of (x + 1/2)^6. (2021)

A. 15/8
B. 45/8
C. 5/8
D. 1/8

Solution

The coefficient of x^4 is C(6,4)(1/2)^2 = 15 * 1/4 = 15/4.

Correct Answer: B — 45/8

Q. Calculate the coefficient of x^4 in the expansion of (x + 2)^6.

A. 15
B. 60
C. 90
D. 120

Solution

The coefficient of x^4 is C(6,4) * 2^2 = 15 * 4 = 60.

Correct Answer: C — 90

Q. Calculate the coefficient of x^4 in the expansion of (x + 3)^6. (2021)

A. 54
B. 81
C. 108
D. 729

Solution

The coefficient of x^4 is C(6,4)(3)^2 = 15 * 9 = 135.

Correct Answer: C — 108

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