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. For which value of k does the equation x^2 + kx + 4 = 0 have one root equal to 2?

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

Solution

Substituting x = 2 into the equation gives 2^2 + 2k + 4 = 0, leading to k = -4.

Correct Answer: B — -2

Q. For which value of k does the equation x^2 - 4x + k = 0 have roots that differ by 2?

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

Solution

Let the roots be r and r+2. Then, r + (r+2) = 4 and r(r+2) = k leads to k = 4.

Correct Answer: C — 4

Q. For which value of k does the equation x^2 - kx + 9 = 0 have roots that are both positive?

A. k < 6
B. k > 6
C. k = 6
D. k = 0

Solution

For both roots to be positive, k must be greater than 6, as the sum of the roots must be positive.

Correct Answer: B — k > 6

Q. For which value of k does the equation x² - kx + 9 = 0 have no real roots? (2021)

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

Solution

The discriminant must be less than zero: k² - 4*1*9 < 0, thus k² < 36, so k > 6 or k < -6.

Correct Answer: A — 6

Q. For which value of k does the equation x² - kx + 9 = 0 have roots that are both positive? (2023)

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

Solution

For both roots to be positive, k must be greater than 0 and k² > 4*9 = 36, thus k > 6.

Correct Answer: B — 8

Q. For which value of k does the quadratic equation x^2 - kx + 4 = 0 have no real roots?

A. k < 4
B. k = 4
C. k > 4
D. k ≤ 4

Solution

The discriminant must be negative: k^2 - 16 < 0, hence k > 4.

Correct Answer: C — k > 4

Q. For which value of k is the function f(x) = kx + 2 continuous at x = 3? (2023)

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

Solution

The function f(x) = kx + 2 is a linear function and is continuous for all k at x = 3.

Correct Answer: B — k = 1

Q. For which value of k is the function f(x) = kx^2 + 2x + 1 differentiable at x = -1?

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

Solution

f'(x) = 2kx + 2; f'(-1) = -2k + 2 must exist for any k.

Correct Answer: A — 0

Q. For which value of k is the function f(x) = { kx + 1, x < 2; 3, x >= 2 } continuous at x = 2?

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

Solution

To be continuous at x = 2, k(2) + 1 must equal 3. Thus, 2k + 1 = 3, leading to k = 1.

Correct Answer: B — 2

Q. For which value of k is the function f(x) = { kx + 1, x < 2; 3, x = 2; 2x - 1, x > 2 } continuous at x = 2?

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

Solution

To ensure continuity at x = 2, k(2) + 1 must equal 3. Thus, k = 1.

Correct Answer: B — 2

Q. For which value of k is the function f(x) = { kx + 1, x < 2; 3, x ≥ 2 } continuous at x = 2? (2019)

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

Solution

To be continuous at x = 2, k(2) + 1 must equal 3. Thus, 2k + 1 = 3, giving k = 1.

Correct Answer: B — 2

Q. For which value of m does the equation x² + mx + 9 = 0 have roots that are both negative? (2021)

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

Solution

For both roots to be negative, m must be greater than 0 and m² < 36. Thus, m must be in the range (-6, 0). The suitable value is -4.

Correct Answer: B — -4

Q. For which value of m does the equation x² - mx + 9 = 0 have roots 3 and 3? (2023)

A. 6
B. 9
C. 3
D. 0

Solution

The sum of the roots is 3 + 3 = 6, hence m = 6.

Correct Answer: A — 6

Q. For which value of m is the function f(x) = { 3x + m, x < 1; 2, x = 1; mx + 1, x > 1 continuous at x = 1?

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

Solution

Setting 3 + m = 2 and 2 = m + 1 gives m = 1 for continuity.

Correct Answer: B — 0

Q. For which value of p does the equation x² + px + 4 = 0 have roots 2 and -2? (2022)

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

Solution

Using the sum of roots: 2 + (-2) = -p, hence p = 0.

Correct Answer: C — -4

Q. For which value of p does the equation x² + px + 4 = 0 have roots that are both negative? (2022)

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

Solution

For both roots to be negative, p must be greater than 0 and p² > 16. Thus, p < -4.

Correct Answer: C — -4

Q. For which value of p does the equation x² + px + 9 = 0 have roots that are both negative? (2021)

A. -6
B. -4
C. -3
D. -2

Solution

For both roots to be negative, p must be positive and p² > 4*9. Thus, p > 6, so p = -4 is valid.

Correct Answer: B — -4

Q. For which value of p does the equation x² - px + 9 = 0 have roots 3 and 3? (2021)

A. 6
B. 3
C. 9
D. 0

Solution

The sum of the roots is 3 + 3 = 6, hence p = 6.

Correct Answer: A — 6

Q. For which value of p is the function f(x) = { x^2 + p, x < 0; 3x - 1, x >= 0 } continuous at x = 0?

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

Solution

Setting the two pieces equal at x = 0 gives us p = -1.

Correct Answer: B — 0

Q. From a deck of 52 cards, how many ways can you choose 5 cards?

A. 2598960
B. 1001
C. 3125
D. 1024

Solution

The number of ways to choose 5 cards from 52 is 52C5 = 2598960.

Correct Answer: A — 2598960

Q. From a group of 10 people, how many ways can a committee of 4 be formed?

A. 210
B. 120
C. 150
D. 180

Solution

The number of ways to choose 4 people from 10 is given by 10C4 = 210.

Correct Answer: A — 210

Q. From a group of 8 people, how many ways can a team of 3 be selected? (2022)

A. 56
B. 24
C. 36
D. 48

Solution

The number of ways to choose 3 people from 8 is given by 8C3 = 56.

Correct Answer: A — 56

Q. From a group of 8 people, how many ways can a team of 4 be selected?

A. 70
B. 56
C. 80
D. 90

Solution

The number of ways to choose 4 people from 8 is given by 8C4 = 70.

Correct Answer: B — 56

Q. From a point A, the angle of elevation of the top of a building is 45 degrees. If the height of the building is 20 meters, how far is point A from the base of the building?

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

Solution

Using tan(45°) = height/distance, we have 1 = 20/distance. Therefore, distance = 20 m.

Correct Answer: B — 20 m

Q. From a point on the ground, the angle of elevation of the top of a hill is 30 degrees. If the distance from the point to the base of the hill is 100 meters, what is the height of the hill?

A. 50 m
B. 60 m
C. 70 m
D. 80 m

Solution

Using tan(30°) = height/100, we have 1/√3 = height/100. Therefore, height = 100/√3 ≈ 57.74 m.

Correct Answer: A — 50 m

Q. From a point on the ground, the angle of elevation of the top of a hill is 30 degrees. If the height of the hill is 50 meters, how far is the point from the base of the hill?

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

Solution

Using tan(30°) = height/distance, we have 1/√3 = 50/distance. Therefore, distance = 50√3 ≈ 86.6 m.

Correct Answer: C — 100 m

Q. From a point on the ground, the angle of elevation to the top of a 40 m high building is 45 degrees. How far is the point from the base of the building?

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

Solution

Using tan(45°) = height/distance, we have distance = height/tan(45°) = 40/1 = 40 m.

Correct Answer: A — 40 m

Q. From a point on the ground, the angle of elevation to the top of a 75 m high building is 45 degrees. How far is the point from the building?

A. 75 m
B. 50 m
C. 100 m
D. 25 m

Solution

Using tan(45°) = height/distance, we have distance = height/tan(45°) = 75/1 = 75 m.

Correct Answer: A — 75 m

Q. From a point on the ground, the angle of elevation to the top of a building is 45 degrees. If the building is 50 meters tall, how far is the point from the base of the building?

A. 50 m
B. 25 m
C. 100 m
D. 75 m

Solution

Distance = height / tan(angle) = 50 / 1 = 50 m.

Correct Answer: A — 50 m

Q. From a point on the ground, the angle of elevation to the top of a building is 45 degrees. If the point is 10 meters away from the building, what is the height of the building?

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

Solution

Using the tangent function, tan(45) = height / 10. Therefore, height = 10 * tan(45) = 10 meters.

Correct Answer: A — 10 meters

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