Inequalities & Simple Functions for Competitive Exams

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Inequalities & Simple Functions

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Inequalities & Simple Functions MCQ & Objective Questions

Inequalities and simple functions are crucial topics in mathematics that form the foundation for various advanced concepts. Mastering these areas is essential for students preparing for school exams and competitive tests. By practicing MCQs and objective questions, students can enhance their understanding and improve their scores in exams. Engaging with practice questions helps identify important concepts and boosts confidence in tackling exam challenges.

What You Will Practise Here

Understanding the definition and types of inequalities
Solving linear inequalities and their graphical representation
Exploring simple functions and their properties
Applying the concept of inequalities in real-life scenarios
Learning key formulas related to inequalities and functions
Identifying and interpreting function notation
Working through important inequalities & simple functions MCQ questions

Exam Relevance

The topic of inequalities and simple functions is frequently tested in various examinations, including CBSE, State Boards, NEET, and JEE. Students can expect questions that require them to solve inequalities, analyze function behavior, and apply these concepts in problem-solving scenarios. Common question patterns include multiple-choice questions that assess both theoretical knowledge and practical application, making it essential for students to be well-prepared.

Common Mistakes Students Make

Misinterpreting the signs in inequalities, leading to incorrect solutions
Confusing between different types of functions and their characteristics
Neglecting to check the domain and range of functions
Overlooking the importance of graphical representation in understanding inequalities
Failing to apply the correct formulas when solving problems

FAQs

Question: What are the key types of inequalities I should focus on?
Answer: Focus on linear inequalities, quadratic inequalities, and their graphical interpretations.

Question: How can I improve my understanding of simple functions?
Answer: Practice solving various problems and familiarize yourself with function notation and properties.

Start solving practice MCQs on inequalities and simple functions today to test your understanding and boost your exam readiness. Remember, consistent practice is the key to success!

Q. If -2 < x < 3, which of the following is true?

A. x + 1 > 0
B. x - 1 < 1
C. 2x < 5
D. x + 2 < 5

Solution

For -2 < x < 3, 2x < 6 is true, hence 2x < 5 is true.

Correct Answer: C — 2x < 5

Q. If -2x + 5 < 1, what is the value of x?

A. x < 2
B. x > 2
C. x < 3
D. x > 3

Solution

Rearranging gives -2x < -4, thus x > 2.

Correct Answer: A — x < 2

Q. If 2x + 3 < 11, what is the maximum integer value of x?

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

Solution

Solving 2x + 3 < 11 gives 2x < 8, thus x < 4. The maximum integer value is 3.

Correct Answer: B — 4

Q. If 2x + 4 > 3x - 1, what is the value of x?

A. x < 5
B. x > 5
C. x < 4
D. x > 4

Solution

Rearranging gives 4 > x, thus x < 4.

Correct Answer: A — x < 5

Q. If 2x + 4 < 3x - 1, what is the value of x?

A. x < 5
B. x > 5
C. x < 3
D. x > 3

Solution

Rearranging gives x > 5. Thus, the correct option is x < 5.

Correct Answer: A — x < 5

Q. If 3x + 2 > 5, what is the minimum integer value of x?

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

Solution

Solving gives 3x > 3, thus x > 1. The minimum integer is 2.

Correct Answer: B — 2

Q. If 3x + 2 < 5x - 6, what is the range of x?

A. x < 4
B. x > 4
C. x = 4
D. x < 3

Solution

Rearranging gives 8 < 2x, thus x > 4.

Correct Answer: B — x > 4

Q. If 3x - 2 < 4 and x is a positive integer, what is the largest possible value of x?

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

Solution

Solving gives 3x < 6, thus x < 2. The largest integer is 2.

Correct Answer: C — 3

Q. If 3x - 2 < 4x + 1, what can be concluded about x?

A. x < -3
B. x > -3
C. x < 3
D. x > 3

Solution

Rearranging gives -3 < x, thus x > -3.

Correct Answer: B — x > -3

Q. If 3x - 4 ≤ 5, what is the range of x?

A. x ≤ 3
B. x ≥ 3
C. x ≤ 2
D. x ≥ 2

Solution

Solving 3x - 4 ≤ 5 gives 3x ≤ 9, thus x ≤ 3.

Correct Answer: A — x ≤ 3

Q. If 3x - 5 < 4, what is the range of x?

A. x < 3
B. x > 3
C. x < 2
D. x > 2

Solution

Solving gives 3x < 9, thus x < 3.

Correct Answer: A — x < 3

Q. If 4x + 1 > 2x + 5, what is the minimum integer value of x?

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

Solution

Solving gives 2x > 4, thus x > 2. The minimum integer is 3.

Correct Answer: B — 3

Q. If 4x + 1 > 9, what is the minimum integer value of x?

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

Solution

Solving 4x + 1 > 9 gives 4x > 8, thus x > 2. The minimum integer value is 3.

Correct Answer: B — 3

Q. If 4x + 1 > 9, what is the smallest integer value of x?

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

Solution

Solving gives 4x > 8, thus x > 2. The smallest integer is 3.

Correct Answer: A — 2

Q. If 4x + 1 ≤ 13, what is the range of x?

A. x ≤ 3
B. x < 3
C. x ≥ 3
D. x > 3

Solution

Solving 4x + 1 ≤ 13 gives 4x ≤ 12, thus x ≤ 3.

Correct Answer: A — x ≤ 3

Q. If 5 - 2x > 1, what is the minimum integer value of x?

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

Solution

Solving the inequality: -2x > -4, thus x < 2. The minimum integer value of x is 1.

Correct Answer: B — 2

Q. If 5 - x > 2, what is the maximum integer value of x?

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

Solution

5 - x > 2 => x < 3. The maximum integer value of x is 2.

Correct Answer: B — 3

Q. If 7 - 2x < 1, what is the value of x?

A. x < 3
B. x > 3
C. x = 3
D. x = 4

Solution

Rearranging gives 6 < 2x, thus x > 3.

Correct Answer: B — x > 3

Q. If A > B and B > C, which of the following is true?

A. A > C
B. C > A
C. B < A
D. C < B

Solution

If A > B and B > C, then by transitive property, A > C is true.

Correct Answer: A — A > C

Q. If a < 5 and b > 2, which of the following must be true?

A. a + b < 7
B. a - b < 3
C. a * b < 10
D. a / b < 3

Solution

Since a < 5 and b > 2, a / b can be less than 3 if a is close to 5 and b is just above 2. The other options do not hold true in all cases.

Correct Answer: D — a / b < 3

Q. If A < B and B ≤ C, which of the following is true?

A. A < C
B. C < A
C. B < A
D. C = B

Solution

Since A < B and B ≤ C, it follows that A < C.

Correct Answer: A — A < C

Q. If A ≤ B and B < C, which of the following is true?

A. A < C
B. C < A
C. B = A
D. C < B

Solution

From A ≤ B and B < C, we can conclude A < C.

Correct Answer: A — A < C

Q. If D = E and E > F, which of the following is true?

A. D > F
B. F < D
C. E < D
D. D < E

Solution

Since D = E and E > F, it follows that D > F.

Correct Answer: A — D > F

Q. If M ≥ N and N > O, which of the following is true?

A. M > O
B. M < O
C. N < M
D. O = N

Solution

From M ≥ N and N > O, we can conclude M > O.

Correct Answer: A — M > O

Q. If P > Q and Q = R, which of the following is true?

A. P > R
B. R < P
C. Q < P
D. P = Q

Solution

Since Q = R and P > Q, it follows that P > R.

Correct Answer: A — P > R

Q. If P ≤ Q and Q < R, which of the following is true?

A. P < R
B. P = R
C. Q = P
D. R < P

Solution

Since P ≤ Q and Q < R, it follows that P < R.

Correct Answer: A — P < R

Q. If x > 3 and x < 7, which of the following is true?

A. x + 2 > 9
B. x - 1 < 5
C. 2x < 10
D. x / 2 > 4

Solution

Since x is between 3 and 7, x - 1 will be between 2 and 6, thus x - 1 < 5 is true.

Correct Answer: B — x - 1 < 5

Q. If X > Y and Y = Z, which of the following is true?

A. X > Z
B. Z > X
C. Y < Z
D. X = Y

Solution

Since Y = Z and X > Y, it follows that X > Z.

Correct Answer: A — X > Z

Q. If X < Y and Y = Z, which of the following is true?

A. X < Z
B. Z < X
C. Y < X
D. X = Y

Solution

Since Y = Z, and X < Y, it follows that X < Z.

Correct Answer: A — X < Z

Q. If x + 3 > 2x - 1, what is the value of x?

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

Solution

Rearranging gives 3 + 1 > 2x - x, thus 4 > x, so x < 4.

Correct Answer: A — 1

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