The CAT QA section requires speed and accuracy, along with a thorough understanding of the Inequalities. This article provides a set of MCQs on Inequalities to help you understand the topic and improve your problem-solving skills with the help of detailed solutions by ensuring conceptual clarity, which will help you in the CAT 2025 exam preparation

Whether you're revising the basics or testing your knowledge, these MCQs will serve as a valuable practice resource.

The CAT 2025 exam is expected to follow a similar trend to the CAT 2024, with 22 questions from the QA section out of a total of 68 questions.

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CAT MCQs on Inequalities

1. Mohan’s fixed commission is ₹560 per assignment. Cost = ₹\(2n^2\), where \(n\) = number of chairs made. If average cost per chair ≤ ₹68, then minimum and maximum values of \(n\) are:
A
13 and 19
B
13 and 20
C
14 and 19
D
14 and 20

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2. If \( a, b, c \) are three real numbers, then which of the following is not true?
A
\( |a + b| \leq |a| + |b| \)
B
\( |a - b| \leq |a| + |b| \)
C
\( |a - b| \leq |a| - |b| \)
D
\( |a - c| \leq |a - b| + |b - c| \)

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3. The shaded portion of the figure shows the graph of which of the following?
A
\( x (y - 2x) \geq 0 \)
B
\( x (y - 2x) \leq 0 \)
C
\( x \left( y + \frac{x}{2} \right) \geq 0 \)
D
\( x \left( y - \frac{x}{2} \right) \leq 0 \)

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4. If \(x \geq y>1\), the value of \(\log_x\left(\frac{x}{y}\right) + \log_y\left(\frac{y}{x}\right)\) can never be:
A
-1
B
-0.5
C
0
D
1

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5. If \(x>5\) and \(y<-1\), then which of the following statements is true?
A
(x + 4y)>1
B
x>-4y
C
-4x<5y
D
None of these

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6. m is the smallest positive integer such that for any integer \(n \ge m\), the quantity \(n^3 - 7n^2 + 11n - 5\) is positive. What is the value of m?
A
4
B
5
C
8
D
None of these

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7. If a, b, c, d are four positive real numbers such that $abcd = 1$, what is the minimum value of \((1+a)(1+b)(1+c)(1+d)\)?
A
4
B
1
C
16
D
18

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8. Let x and y be positive numbers such that x+y = 1. Find the minimum value of \(\left(x + \frac{1}{x}\right)^2 + \left(y + \frac{1}{y}\right)^2\).
A
12
B
20
C
12.5
D
13.3

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9. Given: \( x<0 \), \( 01 \). Which of the following may be false?
A
\( x^2 - z^2 \) is positive
B
\( yz<1 \)
C
\( xy \neq 0 \)
D
\( y^2 - z^2 \) is always negative

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10. Out of two-thirds of the total number of basketball matches, a team has won 17 matches and lost 3 of them. What is the maximum number of matches that the team can lose and still win more than three-fourths of the total number of matches, if it is true that no match can end in a tie?
A
4
B
6
C
5
D
3

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