Major Competitive Exams

My Learning Cart

?

Welcome to

Soulshift

Categories

Account

Major Competitive Exams

Download Q&A

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!

Civil Services Defence Exams Engineering & Architecture Admissions Government Jobs Management Admissions Undergraduate

Q. If the roots of the equation x^2 + 6x + 9 = 0 are equal, what is the value of the root? (2023)

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

Solution

The equation can be factored as (x+3)(x+3)=0, hence the root is -3.

Correct Answer: A — -3

Q. If the roots of the equation x^2 + 6x + k = 0 are -2 and -4, what is the value of k?

A. 4
B. 8
C. 10
D. 12

Solution

Using the sum and product of roots: -2 + -4 = -6 and -2*-4 = k => k = 8.

Correct Answer: C — 10

Q. If the roots of the equation x^2 + 6x + k = 0 are real and distinct, what must be the condition on k? (2023)

A. k < 9
B. k > 9
C. k = 9
D. k ≤ 9

Solution

For real and distinct roots, the discriminant must be greater than zero: 6^2 - 4*1*k > 0 leads to k < 9.

Correct Answer: A — k < 9

Q. If the roots of the equation x^2 + mx + n = 0 are -2 and -3, what is the value of m + n?

A. -5
B. -6
C. -7
D. -8

Solution

The sum of the roots is -(-2 - 3) = 5, so m = 5. The product of the roots is (-2)(-3) = 6, so n = 6. Thus, m + n = 5 + 6 = 11.

Correct Answer: C — -7

Q. If the roots of the equation x^2 + mx + n = 0 are 3 and 4, what is the value of n? (2022)

A. 12
B. 7
C. 10
D. 15

Solution

Using Vieta's formulas, n = 3 * 4 = 12.

Correct Answer: A — 12

Q. If the roots of the equation x^2 + px + q = 0 are -2 and -3, what is the value of p?

A. 5
B. 6
C. 7
D. 8

Solution

Using Vieta's formulas, p = -(-2 - 3) = 5.

Correct Answer: A — 5

Q. If the roots of the equation x^2 + px + q = 0 are -2 and -3, what is the value of p + q?

A. -5
B. -6
C. -7
D. -8

Solution

Using Vieta's formulas, p = -(-2 - 3) = 5 and q = (-2)(-3) = 6. Therefore, p + q = 5 + 6 = 11.

Correct Answer: C — -7

Q. If the roots of the equation x^2 + px + q = 0 are 1 and -1, what is the value of p?

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

Solution

The sum of the roots is 0, hence p = -sum = 0.

Correct Answer: A — 0

Q. If the roots of the equation x^2 + px + q = 0 are 4 and -1, what is the value of p?

A. 3
B. 5
C. 4
D. 7

Solution

Using the sum of roots formula, p = -(4 + (-1)) = -3.

Correct Answer: B — 5

Q. If the roots of the equation x^2 + px + q = 0 are 4 and -2, what is the value of p?

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

Solution

Using the sum of roots formula, p = -(4 + (-2)) = -2.

Correct Answer: A — 2

Q. If the roots of the equation x^2 + px + q = 0 are equal, what is the relationship between p and q?

A. p^2 = 4q
B. p^2 > 4q
C. p^2 < 4q
D. p + q = 0

Solution

For equal roots, the discriminant must be zero: p^2 - 4q = 0, hence p^2 = 4q.

Correct Answer: A — p^2 = 4q

Q. If the roots of the equation x^2 - 10x + k = 0 are 5 and 5, what is the value of k?

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

Solution

The product of the roots is 5*5 = 25, hence k = 25.

Correct Answer: A — 25

Q. If the roots of the equation x^2 - 2x + k = 0 are real and distinct, what is the condition for k?

A. k > 1
B. k < 1
C. k = 1
D. k ≥ 1

Solution

The discriminant must be positive for real and distinct roots: (-2)^2 - 4*1*k > 0, which simplifies to 4 - 4k > 0, or k < 1.

Correct Answer: A — k > 1

Q. If the roots of the equation x^2 - 4x + k = 0 are real and distinct, what is the condition for k? (2023)

A. k > 4
B. k < 4
C. k = 4
D. k ≤ 4

Solution

The discriminant must be greater than zero for real and distinct roots: (-4)^2 - 4*1*k > 0, which simplifies to 16 - 4k > 0, or k < 4.

Correct Answer: A — k > 4

Q. If the roots of the equation x^2 - 5x + 6 = 0 are p and q, what is the value of p + q?

A. 5
B. 6
C. 3
D. 0

Solution

According to Vieta's formulas, the sum of the roots p + q is equal to -(-5) = 5.

Correct Answer: A — 5

Q. If the roots of the equation x^2 - 5x + k = 0 are equal, what is the value of k?

A. 0
B. 5
C. 6
D. 25

Solution

For the roots to be equal, the discriminant must be zero. Thus, b^2 - 4ac = 0 => 25 - 4k = 0 => k = 25.

Correct Answer: C — 6

Q. If the roots of the equation x^2 - 5x + k = 0 are real and equal, what is the minimum value of k?

A. 0
B. 5
C. 6
D. 10

Solution

The minimum value of k is 6, as the discriminant must be zero.

Correct Answer: C — 6

Q. If the roots of the equation x^2 - 5x + k = 0 are real and equal, what is the value of k?

A. 0
B. 5
C. 6
D. 25

Solution

For real and equal roots, the discriminant must be zero: 25 - 4k = 0, thus k = 6.

Correct Answer: C — 6

Q. If the roots of the equation x^2 - 6x + k = 0 are 2 and 4, find the value of k.

A. 8
B. 10
C. 12
D. 14

Solution

Using Vieta's formulas, k = 2 * 4 = 8.

Correct Answer: B — 10

Q. If the roots of the equation x^2 - 6x + k = 0 are 3 and 3, what is the value of k? (2020)

A. 6
B. 9
C. 12
D. 15

Solution

The equation can be expressed as (x - 3)^2 = 0, which expands to x^2 - 6x + 9 = 0. Thus, k = 9.

Correct Answer: B — 9

Q. If the roots of the equation x^2 - 6x + k = 0 are real and distinct, what is the range of k? (2020)

A. k < 9
B. k > 9
C. k = 9
D. k ≤ 9

Solution

For real and distinct roots, the discriminant must be greater than zero: (-6)^2 - 4*1*k > 0, leading to k < 9.

Correct Answer: A — k < 9

Q. If the roots of the equation x^2 - 7x + 10 = 0 are a and b, what is the value of ab? (2021)

A. 10
B. 7
C. 5
D. 3

Solution

By Vieta's formulas, ab = 10, which is the constant term of the polynomial.

Correct Answer: A — 10

Q. If the roots of the equation x^2 - 7x + p = 0 are 3 and 4, what is the value of p?

A. 12
B. 15
C. 16
D. 20

Solution

Using Vieta's formulas, the sum of the roots is 7 and the product is p. Thus, 3 * 4 = p, so p = 12.

Correct Answer: C — 16

Q. If the roots of the equation x^2 - 7x + p = 0 are in the ratio 3:4, what is the value of p?

A. 12
B. 16
C. 20
D. 24

Solution

Let the roots be 3k and 4k. Then, 3k + 4k = 7 => 7k = 7 => k = 1. The product of the roots is 3k * 4k = 12k^2 = p => p = 12.

Correct Answer: C — 20

Q. If the roots of the equation x^2 - kx + 8 = 0 are equal, what is the value of k?

A. 4
B. 8
C. 16
D. 0

Solution

For equal roots, the discriminant must be zero: k^2 - 4*1*8 = 0, solving gives k = 4.

Correct Answer: A — 4

Q. If the roots of the equation x² + 2x + k = 0 are 1 and -3, what is the value of k? (2020)

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

Solution

Using the sum and product of roots: 1 + (-3) = -2 and 1 * (-3) = -3, thus k = 3.

Correct Answer: C — 3

Q. If the roots of the equation x² + 2x + k = 0 are real and distinct, what is the condition for k? (2020)

A. k > 1
B. k < 1
C. k > 4
D. k < 4

Solution

The discriminant must be greater than zero: 2² - 4*1*k > 0, which simplifies to k < 1.

Correct Answer: C — k > 4

Q. If the roots of the equation x² + 5x + 6 = 0 are a and b, what is the value of a + b? (2019)

A. 5
B. 6
C. 10
D. 4

Solution

The sum of the roots is given by -b/a = -5/1 = -5.

Correct Answer: A — 5

Q. If the roots of the equation x² + 5x + k = 0 are -2 and -3, find k. (2020)

A. 6
B. 5
C. 7
D. 8

Solution

Using the product of roots: k = (-2)(-3) = 6.

Correct Answer: A — 6

Q. If the roots of the equation x² + 5x + k = 0 are 1 and 4, find k. (2020)

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

Solution

Using the sum and product of roots: k = 1*4 = 4, and sum = 1 + 4 = 5, thus k = 7.

Correct Answer: D — 7

Showing 12001 to 12030 of 31669 (1056 Pages)

Soulshift Feedback ×

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?

Not likely Very likely