In Mathematics, inequalities define some values that represent some statement of an order. In CAT 2021, candidates can expect around 2-3 questions from inequalities. The basic concepts of this topic could also be used while framing the questions from other topics like Range of Inequalities, Modulus functions, Possible solutions etc. The section CAT Inequalities comprises various topics such as linear and quadratic equations, finding roots, polynomials, functions, etc. Download CAT Question Paper

Read the article to know more about the basic concepts, types of inequalities, rules and solved sample questions to get an idea about the type of questions that can be framed from this topic in CAT 2021.  

What are Inequalities?

There are some inequality symbols in maths mentioned below:  

• less than (<)
• greater than (>)
• less than or equal (≤)
• greater than or equal (≥)
• not equal symbol (≠).

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Rules for Inequalities

Rule No. 1 

You can jump over the middle inequality in the following case

• If, a < b and b < c, then a < c
• If, a > b and b > c, then a > c

Rule No. 2

Swapping of numbers as mentioned in the following case:

• If, a > b, then b < a
• If, a < b, then b < a

Rule No. 3

Only one of the following can be true. All the statements cannot hold true at one position

• a > b
• a = b
• b > a

Rule No. 4

Adding the same number to the inequality number will not change the inequality. Here we are adding c to all the following inequalities.

• If a < b, then a − c < b − c
• If a > b, then a + c > b + c, and
• If a > b, then a − c > b − c

Rule No. 5

Similarly, if we multiply the inequality by the same isite number then there will be no effect on the inequalities.

• If a < b, and c is positive, then ac < bc
• If a < b, and c is negative, then ac > bc (inequality swaps by adding negative number)

Rule No. 6

Placing negative signs in front of inequalities will change the direction of the inequality.

• If a < b then −a > −b
• If a > b, then −a < −b

How to Solve Inequalities?

Some specific rules to solve Inequalities are mentioned below.

• If there is a common term in a statement then the relation is defined. For example, if A > B and B < C, the outcome of it will be A > C.
• If no common trend can be found in a statement then the relation can be said undefined. For example, if A > B and C > D, the relation between A and D is undefined.
• If there are complementary pairs in a statement, then only the complementary relation can be defined. For example, if A ≥ B and B ≥ C, the relation between A and C can only be A ≥ C and not A > C.

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CAT Inequalities Solved Questions

In the below section, some solved questions regarding CAT Inequalities are given. 

Ques. x3 – 5x2 + 8x – 4 > 0?

1. (2, ∞)
2. (1, 2) ∪ (2, ∞)
3. (-∞, 1) ∪ (2, ∞)
4. (-∞, 1)

Correct Answer: ( 2)

Ques. Find out the maximum value a × b × c can take where a + b + c = 31 when a, b, c are distinct positive integers.

1. 1080
2. 1200
3. 1024
4. 1056

Correct Answer: ( 1)

Ques. The distinct natural numbers i.e a, b, c are less than 25. Calculate the maximum possible value of |a – b| + |b – c| – |c – a|?

1. 44
2. 46
3. 23
4. 21

Correct Answer: ( 1)

Ques. Considering the integers p, q such that – 3 < p < 4, – 8 < q < 7, Find out the highest possible value of p2 + pq + q2?

1. 60
2. 67
3. 93
4. 84

Correct Answer: ( 2)

Ques. What are the number of integer values that are the reason for the good of the following inequality h? (x + 2) (x + 4) (x + 6)........(x + 100) < 0?

1. 25
2. 50
3. 49
4. 47

Correct Answer: ( 1)

Ques. In a situation where a, b, c are integers such that – 50 < a, b, c < 50 and a + b + c = 30, Calculate the highest possible value of abc.

1. 1000
2. 5000
3. 4410
4. 4560

Correct Answer: ( 3)

Ques. Calculate x2 - |x + 3| + x > 0?

1. x ∊ (-∞,-1] ∪ [√3, 3)
2. x ∊ (-∞,-√3) ∪ (√3, ∞)
3. x ∊ (-4,-3) ∪ (4, ∞)
4. x ∊ (-8,-3] ∪ [2, ∞)

Correct Answer: ( 2)

Ques. What is the range of f(x) = x2 – 6x + 14?

1. (-∞, 8)
2. (-∞, 100)
3. (-∞, 45)
4. (5, ∞)

Correct Answer: ( 4)

Ques. What is the possible outcome of (x–4)(x+3)(x+4)(x+5) > 0?

1. x ∊ (-∞,-5) ∪ (-4 , -3) ∪ (4, ∞)
2. x ∊ (-∞,-5) ∪ (4, ∞)
3. x ∊ (-4,-3) ∪ (4, ∞)
4. x ∊ (-5,-3] ∪ [4, ∞)

Correct Answer: ( 1)

Ques. Find out the less possible value of f(x) = x2 – 5x + 41. 

1. 1394
2. 1494
3. 1294
4. 1429

Correct Answer: ( 1)

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CAT Inequalities Preparation Tips

Before appearing in CAT 2021, candidates must know some preparation tips to excel in the exam. Here, some simple tips for the preparation of CAT Inequalities are given. 

• Know the primary concept of the topic
• Familiar with all the terms related to the topic
• Before conclusion, read the statement carefully
• Do analyse the statement with the correct form
• Practice all the previous years question and give mock test daily