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 probability of an event is 0.25, what are the odds in favor of the event?

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

Solution

Odds in favor = probability of event / (1 - probability of event) = 0.25 / 0.75 = 1:3.

Correct Answer: A — 1:3

Q. If the probability of an event is 0.7, what is the probability of its complement?

A. 0.3
B. 0.7
C. 1
D. 0.5

Solution

Probability of complement = 1 - P(event) = 1 - 0.7 = 0.3.

Correct Answer: A — 0.3

Q. If the probability of an event is 0.7, what is the probability of the event not occurring?

A. 0.3
B. 0.7
C. 0.5
D. 0.1

Solution

Probability of not occurring = 1 - P(event) = 1 - 0.7 = 0.3.

Correct Answer: A — 0.3

Q. If the probability of an event occurring is 0.3, what is the probability of it not occurring? (2023)

A. 0.3
B. 0.7
C. 0.5
D. 0.1

Solution

Probability of not occurring = 1 - P(event) = 1 - 0.3 = 0.7.

Correct Answer: B — 0.7

Q. If the probability of event A is 0.2 and the probability of event B is 0.5, what is the probability of either A or B occurring if A and B are independent?

A. 0.7
B. 0.6
C. 0.5
D. 0.4

Solution

The probability of either A or B occurring is P(A) + P(B) - P(A and B) = 0.2 + 0.5 - (0.2 * 0.5) = 0.7.

Correct Answer: A — 0.7

Q. If the probability of event A is 0.4 and event B is 0.5, what is the probability of both events occurring if they are independent?

A. 0.2
B. 0.4
C. 0.5
D. 0.6

Solution

P(A and B) = P(A) * P(B) = 0.4 * 0.5 = 0.2.

Correct Answer: A — 0.2

Q. If the probability of event A is 0.4 and the probability of event B is 0.5, what is the probability of both A and B occurring if they are independent?

A. 0.2
B. 0.4
C. 0.5
D. 0.9

Solution

For independent events, P(A and B) = P(A) * P(B) = 0.4 * 0.5 = 0.2.

Correct Answer: A — 0.2

Q. If the probability of event C is 0.2 and the probability of event D is 0.3, what is the probability of either C or D occurring if they are mutually exclusive?

A. 0.5
B. 0.6
C. 0.3
D. 0.2

Solution

For mutually exclusive events, P(C or D) = P(C) + P(D) = 0.2 + 0.3 = 0.5.

Correct Answer: B — 0.6

Q. If the probability of rain tomorrow is 0.7, what is the probability that it will not rain?

A. 0.3
B. 0.5
C. 0.7
D. 0.9

Solution

The probability that it will not rain is 1 - 0.7 = 0.3.

Correct Answer: A — 0.3

Q. If the product of two consecutive integers is 72, which of the following pairs could represent these integers?

A. 8 and 9
B. 6 and 7
C. 5 and 6
D. 9 and 10

Solution

6 and 7 are consecutive integers whose product is 42, not 72.

Correct Answer: B — 6 and 7

Q. If the product of two consecutive integers is 72, which of the following pairs could represent those integers?

A. 8 and 9
B. 6 and 7
C. 5 and 6
D. 4 and 5

Solution

The product of 6 and 7 is 42, while 8 and 9 gives 72. Therefore, the correct pair is 8 and 9.

Correct Answer: B — 6 and 7

Q. If the product of two numbers is 144 and one of the numbers is 12, what is the other number? (2023)

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

Solution

The other number can be found by dividing the product by the known number: 144 / 12 = 12.

Correct Answer: D — 6

Q. If the product of two numbers is 48 and one of the numbers is 6, what can be inferred about the other number?

A. It is 8.
B. It is 12.
C. It is 6.
D. It is 4.

Solution

If the product is 48 and one number is 6, then the other number must be 48 ÷ 6 = 8.

Correct Answer: A — It is 8.

Q. If the product of two numbers is 48, which of the following pairs could represent these numbers?

A. (2, 24)
B. (3, 16)
C. (4, 12)
D. (All of the above)

Solution

All pairs listed multiply to 48, hence they are valid pairs.

Correct Answer: D — (All of the above)

Q. If the product of two numbers is 72 and one of the numbers is 8, what is the other number?

A. 6
B. 9
C. 10
D. 12

Solution

The other number is 72 divided by 8, which equals 9.

Correct Answer: A — 6

Q. If the product of two numbers is a multiple of 15, which of the following must be true?

A. At least one of the numbers is a multiple of 3.
B. At least one of the numbers is a multiple of 5.
C. Both numbers are even.
D. Both numbers are odd.

Solution

For the product to be a multiple of 15, at least one of the numbers must be a multiple of 5.

Correct Answer: B — At least one of the numbers is a multiple of 5.

Q. If the quadratic equation ax^2 + bx + c = 0 has roots 3 and -2, what is the value of a?

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

Solution

Using the fact that the product of the roots is c/a and the sum is -b/a, we can set a = 1, b = -1, c = -6.

Correct Answer: A — 1

Q. If the quadratic equation ax^2 + bx + c = 0 has roots p and q, what is the value of p + q? (2020)

A. -b/a
B. b/a
C. c/a
D. -c/a

Solution

By Vieta's formulas, the sum of the roots p + q = -b/a.

Correct Answer: A — -b/a

Q. If the quadratic equation ax^2 + bx + c = 0 has roots p and q, which of the following is correct?

A. p + q = -b/a and pq = c/a
B. p + q = b/a and pq = -c/a
C. p + q = c/a and pq = -b/a
D. p + q = -c/a and pq = b/a

Solution

According to Vieta's formulas, the sum of the roots p and q is -b/a and the product is c/a.

Correct Answer: A — p + q = -b/a and pq = c/a

Q. If the quadratic equation x^2 + 2px + p^2 - 4 = 0 has real roots, what is the condition on p?

A. p > 2
B. p < 2
C. p = 2
D. p >= 2

Solution

The discriminant must be non-negative: (2p)^2 - 4(1)(p^2 - 4) >= 0 => 4p^2 - 4p^2 + 16 >= 0, which is always true. Thus, p can be any real number.

Correct Answer: D — p >= 2

Q. If the quadratic equation x^2 + 2px + p^2 - 4 = 0 has roots that are equal, what is the value of p?

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

Solution

Setting the discriminant to zero: (2p)^2 - 4(1)(p^2 - 4) = 0 leads to p = ±2.

Correct Answer: C — -2

Q. If the quadratic equation x^2 + 2x + 1 = 0 is solved, what are the roots? (2022)

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

Solution

The equation can be factored as (x + 1)(x + 1) = 0, giving the root -1 with multiplicity 2.

Correct Answer: A — -1

Q. If the quadratic equation x^2 + 2x + 1 = 0 is solved, what is the nature of its roots? (2019)

A. Real and distinct
B. Real and equal
C. Complex
D. None of the above

Solution

The discriminant is 2^2 - 4*1*1 = 0, indicating that the roots are real and equal.

Correct Answer: B — Real and equal

Q. If the quadratic equation x^2 + 2x + 1 = 0 is solved, what is the nature of the roots? (2022)

A. Real and distinct
B. Real and equal
C. Complex
D. None of the above

Solution

The discriminant is 0, indicating that the roots are real and equal.

Correct Answer: B — Real and equal

Q. If the quadratic equation x^2 + 2x + 1 = 0 is solved, what is the value of x? (2023)

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

Solution

The equation can be factored as (x + 1)^2 = 0, giving the root x = -1.

Correct Answer: A — -1

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

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

Solution

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

Correct Answer: C — -1

Q. If the quadratic equation x^2 + 2x + k = 0 has no real roots, what is the condition on k?

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

Solution

For no real roots, the discriminant must be less than zero: 2^2 - 4*1*k < 0, hence k > 1.

Correct Answer: A — k < 0

Q. If the quadratic equation x^2 + 2x + k = 0 has no real roots, what is the condition for k?

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

Solution

For no real roots, the discriminant must be less than zero: 2^2 - 4*1*k < 0 => 4 - 4k < 0 => k > 1.

Correct Answer: A — k < 0

Q. If the quadratic equation x^2 + 2x + k = 0 has no real roots, what must be true about k?

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

Solution

For no real roots, the discriminant must be less than zero: 2^2 - 4*1*k < 0, thus k > 1.

Correct Answer: B — k < 0

Q. If the quadratic equation x^2 + 2x + k = 0 has one root equal to -1, what is the value of k? (2022)

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

Solution

Substituting x = -1 into the equation gives (-1)^2 + 2(-1) + k = 0, leading to 1 - 2 + k = 0, thus k = 1.

Correct Answer: B — 1

Showing 11701 to 11730 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