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Test Level 2: Inequalities - 1 - CAT MCQ


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10 Questions MCQ Test Level-wise Tests for CAT - Test Level 2: Inequalities - 1

Test Level 2: Inequalities - 1 for CAT 2024 is part of Level-wise Tests for CAT preparation. The Test Level 2: Inequalities - 1 questions and answers have been prepared according to the CAT exam syllabus.The Test Level 2: Inequalities - 1 MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test Level 2: Inequalities - 1 below.
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Test Level 2: Inequalities - 1 - Question 1

What values of 'x' satisfy the inequality x2/3 + x1/3 - 2 ≤ 0?

Detailed Solution for Test Level 2: Inequalities - 1 - 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

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 for Test Level 2: Inequalities - 1 - 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

a2 + b2 is always

Detailed Solution for Test Level 2: Inequalities - 1 - 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

If xyz = 8, then what is the minimum value of 2x + 2y + 2z?  

Detailed Solution for Test Level 2: Inequalities - 1 - 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

How many pairs of natural numbers at (x, y) satisfy the inequality 3x + 5y < 20?  

Detailed Solution for Test Level 2: Inequalities - 1 - 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

|x| ≤ 2 and |y + 3| ≤ 5. What is the minimum possible value of x + y?

Detailed Solution for Test Level 2: Inequalities - 1 - 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

Which of the following inequalities best describes a real number x, satisfying  for every positive integer n?

Detailed Solution for Test Level 2: Inequalities - 1 - 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

What values of x satisfy > 1, x ≠ 4?

Detailed Solution for Test Level 2: Inequalities - 1 - Question 8



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

Test Level 2: Inequalities - 1 - Question 9

How many whole number pairs satisfy both the inequalities 2x + 3y ≤ 12 and 9x + 4y ≤ 72?  

Detailed Solution for Test Level 2: Inequalities - 1 - Question 9


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

Total = 19

Test Level 2: Inequalities - 1 - Question 10

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 for Test Level 2: Inequalities - 1 - Question 10



So, we can't find the value of N 

So, the answer can't be determined.

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