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Inequalities

Inequalities

MODULES

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Basics of Inequalities
Quadratic Inequalities
Basics of Modulus
Multiple Modulus Functions
Sum or Product is Constant
Max & Min for Range & Substitution
Past Questions

CONCEPTS & CHEATSHEET

Concept Revision Video

SPEED CONCEPTS

Inequalities 1
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Inequalities 2
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PRACTICE

Inequalities : Level 1
Inequalities : Level 2
Inequalities : Level 3
ALL MODULES

CAT 2025 Lesson : Inequalities - Past Questions

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7. Past Questions

Question 1

If x2x^2 x2+ y2y^2y2 = 0.1 and |xxx– yyy| = 0.2, then |xxx | + |yyy | is equal to
[CAT 2000]

0.30.30.3
0.40.40.4
0.20.20.2
0.60.60.6

Answer: (2) 0.40.40.4

Question 2

If three positive real numbers x,y,zx, y, zx,y,z satisfy yyy– xxx = zzz – yyy and xyzxyzxyz = 4, then what is the minimum possible value of yyy?
[CAT 2003R]

21/32^{1/3}21/3
22/32^{2/3}22/3
21/42^{1/4}21/4
23/42^{3/4}23/4

Answer: (2) 22/32^{2/3}22/3

Question 3

If x satisfies the inequality |xxx – 1| + |xxx – 2| + |xxx – 3| ≥ 6, then:
[IIFT 2011]

0≤x≤40 ≤ x ≤ 4 0≤x≤4
x≤0x ≤ 0x≤0 or x≥4x ≥ 4x≥4
x≤−2x ≤ -2x≤−2 or x≥3x ≥ 3 x≥3
None of the above

Answer: (2)x≤0x ≤ 0x≤0 or x≥4x ≥ 4x≥4

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