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. Find the minimum value of f(x) = 4x^2 - 16x + 20. (2022)

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

Solution

The vertex gives the minimum at x = 2. f(2) = 4(2^2) - 16(2) + 20 = 4.

Correct Answer: A — 4

Q. Find the minimum value of f(x) = 4x^2 - 8x + 3. (2022)

A. 0
B. 1
C. 2
D. 3

Solution

The vertex is at x = 8/(2*4) = 1. The minimum value is f(1) = 4(1)^2 - 8(1) + 3 = -1.

Correct Answer: B — 1

Q. Find the minimum value of f(x) = x^2 + 6x + 10. (2020)

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

Solution

The minimum occurs at x = -b/(2a) = -6/(2*1) = -3. f(-3) = (-3)^2 + 6(-3) + 10 = 1.

Correct Answer: A — 2

Q. Find the minimum value of f(x) = x^2 - 4x + 6. (2021)

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

Solution

The vertex form gives the minimum at x = 2. f(2) = 2.

Correct Answer: A — 2

Q. Find the minimum value of f(x) = x^2 - 4x + 7. (2021)

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

Solution

The vertex form gives the minimum at x = 2. f(2) = 2^2 - 4*2 + 7 = 3.

Correct Answer: A — 3

Q. Find the minimum value of f(x) = x^2 - 4x + 7. (2021) 2021

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

Solution

The vertex form gives the minimum at x = 2. f(2) = 2^2 - 4*2 + 7 = 3.

Correct Answer: A — 3

Q. Find the minimum value of the function f(x) = 2x^2 - 8x + 10. (2022)

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

Solution

The minimum occurs at x = 2. f(2) = 2(2^2) - 8(2) + 10 = 6.

Correct Answer: B — 4

Q. Find the minimum value of the function f(x) = 3x^2 - 12x + 7.

A. -5
B. 1
C. 0
D. 2

Solution

The vertex occurs at x = -b/(2a) = 12/6 = 2. f(2) = 3(2^2) - 12(2) + 7 = 1.

Correct Answer: B — 1

Q. Find the minimum value of the function f(x) = 3x^2 - 12x + 9. (2022)

A. 0
B. 1
C. 3
D. 4

Solution

The minimum occurs at x = -b/(2a) = 12/(2*3) = 2. f(2) = 3(2^2) - 12(2) + 9 = 3.

Correct Answer: C — 3

Q. Find the minimum value of the function f(x) = x^2 - 4x + 5.

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

Solution

The vertex of the parabola occurs at x = 2. f(2) = 2^2 - 4(2) + 5 = 1, which is the minimum value.

Correct Answer: A — 1

Q. Find the minimum value of the function f(x) = x^4 - 8x^2 + 16.

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

Solution

f'(x) = 4x^3 - 16x. Setting f'(x) = 0 gives x = 0, ±2. f(2) = 0, which is the minimum value.

Correct Answer: A — 0

Q. Find the missing letter in the series: A, C, E, G, ?

A. H
B. I
C. J
D. K

Solution

The series consists of every second letter in the alphabet: A, C, E, G, I.

Correct Answer: A — H

Q. Find the missing number: 12, 24, 48, ?, 192

A. 96
B. 100
C. 120
D. 144

Solution

Each number is multiplied by 2. 48 * 2 = 96.

Correct Answer: A — 96

Q. Find the missing number: 5, 10, 20, ?, 80

A. 30
B. 40
C. 50
D. 60

Solution

The pattern is multiplying by 2. 20 * 2 = 40.

Correct Answer: B — 40

Q. Find the mistake: 'Either the teacher or the students was responsible for the project.'

A. No error
B. Either the teacher
C. or the students
D. was responsible

Solution

When using 'either/or', the verb should agree with the nearest subject, which is 'students' (plural), so it should be 'were'.

Correct Answer: D — was responsible

Q. Find the mistake: 'Everyone should do their best.'

A. Everyone
B. should
C. do
D. their

Solution

'Their' is often used informally, but traditionally 'his or her' is preferred. The correct sentence is 'Everyone should do his or her best.'

Correct Answer: D — their

Q. Find the mistake: 'He is more taller than his brother.'

A. He
B. is
C. more
D. taller

Solution

The correct form is 'taller' without 'more' because 'taller' is already a comparative adjective.

Correct Answer: C — more

Q. Find the mistake: 'Neither of the answers are correct.'

A. No error
B. Neither of the answers
C. are correct
D. correct

Solution

The verb should be singular to agree with 'Neither', so it should be 'is correct'.

Correct Answer: C — are correct

Q. Find the mistake: 'The committee have made their decision.'

A. The
B. committee
C. have
D. made

Solution

The correct form is 'The committee has made its decision.' 'Committee' is a collective noun and takes a singular verb.

Correct Answer: C — have

Q. Find the mistake: 'The group of students are planning a trip.'

A. No error
B. group
C. are
D. students

Solution

'Group' is a collective noun and should take a singular verb, so it should be 'is'.

Correct Answer: C — are

Q. Find the mistake: 'The information were not clear.'

A. The
B. information
C. were
D. not

Solution

'Were' should be 'was' because 'information' is an uncountable noun treated as singular.

Correct Answer: C — were

Q. Find the mistake: 'The information were not sufficient for the decision.'

A. No error
B. were
C. not
D. sufficient

Solution

'Were' should be 'was' because 'information' is an uncountable noun.

Correct Answer: B — were

Q. Find the mistake: 'The team are winning the match.'

A. The
B. team
C. are
D. winning

Solution

'are' should be 'is' because 'team' is a collective noun treated as singular.

Correct Answer: C — are

Q. Find the mode of the following set of numbers: 1, 2, 2, 3, 4, 4, 4, 5, 5.

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

Solution

The mode is 4, as it appears 3 times, which is more than any other number.

Correct Answer: C — 4

Q. Find the mode of the following set of numbers: 10, 12, 10, 15, 10, 20, 15, 15.

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

Solution

The number 10 appears 3 times and 15 appears 3 times. Since both have the highest frequency, the mode is 10 and 15 (bimodal). However, if only one mode is required, we can take the first one, which is 10.

Correct Answer: C — 15

Q. Find the mode of the following set of numbers: 10, 12, 10, 15, 10, 20, 15.

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

Solution

The mode is 10, as it appears most frequently (three times) in the data set.

Correct Answer: A — 10

Q. Find the mode of the following set of numbers: 10, 20, 20, 30, 30, 30, 40, 50.

A. 10
B. 20
C. 30
D. 40

Solution

The mode is 30, as it appears 3 times, more than any other number.

Correct Answer: C — 30

Q. Find the mode of the following set of numbers: 12, 15, 12, 18, 20, 15, 15, 22.

A. 12
B. 15
C. 18
D. 20

Solution

The mode is 15, which appears 3 times in the data set.

Correct Answer: B — 15

Q. Find the mode of the following set of numbers: 12, 15, 12, 18, 20, 15, 15.

A. 12
B. 15
C. 18
D. 20

Solution

The number 15 appears most frequently (three times), making it the mode.

Correct Answer: B — 15

Q. Find the mode of the following set of numbers: 4, 1, 2, 4, 3, 4, 5, 1.

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

Solution

The mode is 4, as it appears four times, which is more than any other number.

Correct Answer: D — 4

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