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CAT Exam  >  CAT Test  >  Level-wise Tests  >  Test Level 2: Inequalities - 1 - CAT MCQ

Test Level 2: Inequalities - 1 CAT MCQs & solutions - Free


MCQ Practice Test & Solutions: Test Level 2: Inequalities - 1 (10 Questions)

You can prepare effectively for CAT Level-wise Tests for CAT with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Test Level 2: Inequalities - 1". These 10 questions have been designed by the experts with the latest curriculum of CAT 2026, to help you master the concept.

Test Highlights:

  • - Format: Multiple Choice Questions (MCQ)
  • - Duration: 10 minutes
  • - Number of Questions: 10

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Test Level 2: Inequalities - 1 - Question 1
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What values of 'x' satisfy the inequality x2/3 + x1/3 - 2 ≤ 0?

Detailed Solution: Question 1

x2/3 + x1/3 - 2 ≤ 0
Or (x1/3 - 1)(x1/3 + 2) ≤ 0
Or -8 ≤ x ≤ 1

Test Level 2: Inequalities - 1 - Question 2
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If f(x) = x3 - 4x + p and f(0) and f(1) have opposite signs, then which of the following is necessarily true?

Detailed Solution: Question 2

f(0) = p and f(1) = p - 3
Since f(0) and f(1) have opposite signs, so if p < 0, then p - 3 > 0, i.e. p > 3, which is not possible.
Or, p > 0 and p - 3 < 0
⇒ p < 3
⇒ 0 < p < 3
Hence, answer option 2 is correct.

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Test Level 2: Inequalities - 1 - Question 3
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a2 + b2 is always

Detailed Solution: Question 3

As (a - b)2 is never negative.
a2 + b2 - 2ab is greater than or equal to zero.
Therefore, we can say that a2 + b2 ≥ 2ab.

Test Level 2: Inequalities - 1 - Question 4
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If xyz = 8, then what is the minimum value of 2x + 2y + 2z?  

Detailed Solution: Question 4

Since AM ≥ GM,

x + y + z ≥ 6
To get minimum value, take x + y + z = 6.

⇒ 2x + 2y + 2z ≥ 12
Minimum value = 12

Test Level 2: Inequalities - 1 - Question 5
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How many pairs of natural numbers at (x, y) satisfy the inequality 3x + 5y < 20?  

Detailed Solution: Question 5

(x, y) pairs satisfying the condition are (1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (3, 1), (3, 2) and (4, 1).
So, total 8 pairs are there.

Test Level 2: Inequalities - 1 - Question 6
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|x| ≤ 2 and |y + 3| ≤ 5. What is the minimum possible value of x + y?

Detailed Solution: Question 6

|x| ≤ 2 ⇒ minimum value of x = - 2.
|y + 3| ≤ 5 ⇒ minimum value of y = - 8.
So, x + y = - 2 - 8 = - 10.

Test Level 2: Inequalities - 1 - Question 7
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Which of the following inequalities best describes a real number x, satisfying  for every positive integer n?

Detailed Solution: Question 7

Given that

For any positive n,

Again, from inequality (ii), 

So, from inequalities (i) , (iii) and (iv), we get 0 < x ≤ 4

Test Level 2: Inequalities - 1 - Question 8
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What values of x satisfy > 1, x ≠ 4?

Detailed Solution: Question 8



|x - 4| < 2
-2 < x - 4 < 2
2 < x < 6
x = (2, 4)  (4, 6)

Test Level 2: Inequalities - 1 - Question 9
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How many whole number pairs satisfy both the inequalities 2x + 3y ≤ 12 and 9x + 4y ≤ 72?  

Detailed Solution: Question 9


The common part is x ≥ 0, y ≥ 0, 2x + 3y ≤ 12.

Total = 19

Test Level 2: Inequalities - 1 - Question 10
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If x > y > z > w, M (a, b) = maximum of a and b, and N (a, b) = minimum of a and b, then what is the value of M

Detailed Solution: Question 10



So, we can't find the value of N 

So, the answer can't be determined.

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About this CAT Practice Test

This test contains 10 MCQs on Test Level 2: Inequalities - 1 with detailed solutions for each question. It is part of the Level-wise Tests for CAT course on EduRev, designed to align with the current CAT syllabus. Each solution explains not just the correct answer but also gives you an understanding of the topic — not just to attempt the question but also help you prepare for the exam with practice.

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