30+ CAT Algebra Questions with Answers + Free PDF Download (CAT 2026)

Looking for CAT Algebra Questions to practice for CAT 2026? Here are 30+ CAT algebra questions across easy, moderate, and advanced levels - plus topic-wise PDF downloads (linear, quadratic, inequalities, logarithms) and quick solving tips.

Around 10-12 questions are asked from this section in the main CAT exam. So, to make it easy for you all, we have provided Practice 30+ CAT Algebra questions (Easy, Moderate & Advanced) with answers + downloadable PDF

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Please continue reading to know the types of CAT 2026 Algebra Questions that are commonly found on the CAT exam, essential strategies for answering them, and practice tips that will help you succeed will all be covered in this article.  Let's explore CAT algebra and the previous year CAT questions PDF together and give you the resources you need to succeed.

What are the CAT Algebra Questions 2026?

CAT Algebra questions are a part of the Quantitative Ability section in the CAT exam pattern and assess a candidate’s understanding of fundamental algebraic concepts. These include topics such as linear and quadratic equations, inequalities, functions, and expressions. Mastery of these algebra CAT questions is essential for improving overall quant scores and enhancing problem-solving speed.

Download Section-wise CAT 2026 Algebra Questions PDF below

CAT Linear Questions PDF	Download Now
CAT Quadratic Questions PDF	Download Now
CAT Inequalities Questions PDF	Download Now
CAT Logarithm Questions PDF	Download Now

Easy Level Important CAT Algebra Questions 2026

1. If the sum of a number and its reciprocal is 5, i.e., x+1x=5x + \frac{1}{x} = 5x+x1=5, what is the value of x2+1x2x^2 + \frac{1}{x^2}x2+x21?
a) 21
b) 23
c) 25
d) 19
Answer: a) 21

2. The product of two numbers is 12 and their sum is 7. What is the value of the sum of their squares?
a) 37
b) 49
c) 25
d) 61
Answer: a) 37

3. If x2−6x+8=0x^2 - 6x + 8 = 0x2−6x+8=0, find the sum of the roots of the equation.
a) -6
b) 6
c) 8
d) -8
Answer: b) 6

4. The roots of the quadratic equation x2+px+q=0x^2 + px + q = 0x2+px+q=0 are 3 and 4. What is the value of p?
a) -7
b) 7
c) -12
d) 12
Answer: a) -7

5. If x+1x=2x + \frac{1}{x} = 2x+x1=2, find x3+1x3x^3 + \frac{1}{x^3}x3+x31.
a) 0
b) 2
c) 6
d) 8
Answer: a) 0

6. If one root of the quadratic equation x2+7x+10=0x^2 + 7x + 10 = 0x2+7x+10=0 is -2, what is the other root?
a) -5
b) 5
c) 2
d) -3
Answer: a) -5

7. The sum of the roots of a quadratic equation is 9 and the product is 20. What is the equation?
a) x2+9x+20=0x^2 + 9x + 20 = 0x2+9x+20=0
b) x2−9x+20=0x^2 - 9x + 20 = 0x2−9x+20=0
c) x2−9x+20=0x^2 - 9x + 20 = 0x2−9x+20=0
d) x2−9x−20=0x^2 - 9x - 20 = 0x2−9x−20=0
Answer: c) x2−9x+20=0x^2 - 9x + 20 = 0x2−9x+20=0

8. If x=2+3x = 2 + \sqrt{3}x=2+3, then find the value of 1x\frac{1}{x}x1.
a) 2−32 - \sqrt{3}2−3
b) 2+37\frac{2 + \sqrt{3}}{7}72+3
c) 12−3\frac{1}{2 - \sqrt{3}}2−31
d) 2−31\frac{2 - \sqrt{3}}{1}12−3
Answer: a) 2−32 - \sqrt{3}2−3

9. If a+b=10a + b = 10a+b=10 and ab=24ab = 24ab=24, find the value of a2+b2a^2 + b^2a2+b2.
a) 100
b) 76
c) 52
d) 50
Answer: c) 52

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Moderate Level CAT Algebra Questions 2026

11. If a−b=3a - b = 3a−b=3 and ab=10ab = 10ab=10, find the value of a2+b2a^2 + b^2a2+b2.
a) 19
b) 29
c) 39
d) 49
Answer: b) 29

12. Find the value of xxx if x2−9x+20=0x^2 - 9x + 20 = 0x2−9x+20=0.
a) 4, 5
b) 2, 10
c) 3, 6
d) 1, 20
Answer: a) 4, 5

13. If x+1x=4x + \frac{1}{x} = 4x+x1=4, then find x3+1x3x^3 + \frac{1}{x^3}x3+x31.
a) 64
b) 52
c) 58
d) 60
Answer: b) 52

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14. If x2+y2=34x^2 + y^2 = 34x2+y2=34 and xy=12xy = 12xy=12, find (x+y)2(x + y)^2(x+y)2.
a) 49
b) 34
c) 58
d) 64
Answer: a) 49

15. If f(x)=x2−4x+7f(x) = x^2 - 4x + 7f(x)=x2−4x+7, what is the minimum value of f(x)f(x)f(x)?
a) 3
b) 4
c) 2
d) 5
Answer: a) 3

16. Find the number of integer solutions for the equation x2−4x+3=0x^2 - 4x + 3 = 0x2−4x+3=0.
a) 0
b) 1
c) 2
d) 3
Answer: c) 2

Advanced Level CAT Algebra Questions 2026

17. If (x−3)2=0(x - 3)^2 = 0(x−3)2=0, what is the value of x?
a) 3
b) -3
c) 0
d) No real root
Answer: a) 3

18. If x=2x = 2x=2 is a root of the equation x2−kx+4=0x^2 - kx + 4 = 0x2−kx+4=0, find the value of k.
a) 4
b) 5
c) 6
d) 3
Answer: c) 6

19. What is the remainder when x3−4x+5x^3 - 4x + 5x3−4x+5 is divided by x−2x - 2x−2?
a) 5
b) 1
c) 3
d) 9
Answer: d) 9

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20. If the sum of squares of two numbers is 50 and their product is 24, what is the square of their sum?
a) 74
b) 98
c) 100
d) 122
Answer: b) 98

Advanced Level (21–30)

21. The quadratic equation x2+kx+9=0x^2 + kx + 9 = 0x2+kx+9=0 has equal roots. What is the value of k?
a) 3
b) 6
c) ±6
d) ±3
Answer: c) ±6

22. If x4+1x4=194x^4 + \frac{1}{x^4} = 194x4+x41=194 and x+1x=5x + \frac{1}{x} = 5x+x1=5, find the value of x2+1x2x^2 + \frac{1}{x^2}x2+x21.
a) 21
b) 23
c) 19
d) 25
Answer: b) 23

23. The value of (a+b)2−4ab(a + b)^2 - 4ab(a+b)2−4ab is equal to:
a) (a−b)2(a - b)^2(a−b)2
b) (a+b)2(a + b)^2(a+b)2
c) ababab
d) 2a2+2b22a^2 + 2b^22a2+2b2
Answer: a) (a−b)2(a - b)^2(a−b)2

24. If the roots of a quadratic equation differ by 3 and their sum is 7, what is the equation?
a) x2−7x+12=0x^2 - 7x + 12 = 0x2−7x+12=0
b) x2−7x−12=0x^2 - 7x - 12 = 0x2−7x−12=0
c) x2+7x+12=0x^2 + 7x + 12 = 0x2+7x+12=0
d) x2+7x−12=0x^2 + 7x - 12 = 0x2+7x−12=0
Answer: a) x2−7x+12=0x^2 - 7x + 12 = 0x2−7x+12=0

25. If x3−6x2+11x−6=0x^3 - 6x^2 + 11x - 6 = 0x3−6x2+11x−6=0, find the product of its roots.
a) 6
b) -6
c) 11
d) 1
Answer: a) 6

26. What is the maximum value of the function f(x)=−x2+6x+7f(x) = -x^2 + 6x + 7f(x)=−x2+6x+7?
a) 16
b) 9
c) 13
d) 14
Answer: c) 13

27. A quadratic has roots in the ratio 2:3. If their product is 54, find the quadratic equation.
a) x2−15x+54=0x^2 - 15x + 54 = 0x2−15x+54=0
b) x2−13x+54=0x^2 - 13x + 54 = 0x2−13x+54=0
c) x2−10x+54=0x^2 - 10x + 54 = 0x2−10x+54=0
d) x2−12x+54=0x^2 - 12x + 54 = 0x2−12x+54=0
Answer: a) x2−15x+54=0x^2 - 15x + 54 = 0x2−15x+54=0

28. If x+y=12x + y = 12x+y=12 and xy=27xy = 27xy=27, what is the value of x3+y3x^3 + y^3x3+y3?
a) 216
b) 648
c) 936
d) 1080
Answer: b) 648

29. If x−1x=3x - \frac{1}{x} = 3x−x1=3, find the value of x3−1x3x^3 - \frac{1}{x^3}x3−x31.
a) 27
b) 30
c) 35
d) 38
Answer: d) 38

30. If the roots of a quadratic are x=a±bx = a \pm \sqrt{b}x=a±b, and b = 0, what does it imply?
a) No real roots
b) Complex roots
c) Rational but equal roots
d) Rational and distinct roots
Answer: c) Rational but equal roots

Types of Important CAT Algebra Questions

Algebra in CAT can range from straightforward equations to more complex problems involving progressions, inequalities, and functions. Here are some types of important CAT Algebra questions you’ll come across:

• Quadratic Equations
• Progression
• Functions and Graphs
• Inequalities

Tip: If you’re revising concepts before practice, start here: Algebra Topics for CAT.

Importance of CAT Algebra Questions 2026

• CAT Algebra Questions form a crucial part of the Quantitative Aptitude question section of the CAT exam.
• Questions on topics such as linear and quadratic equations, inequalities, functions, and progressions appear consistently every year.
• A clear understanding of algebraic concepts not only enhances accuracy but also helps aspirants solve problems more efficiently within the limited time available during the test.
• Moreover, algebra serves as a foundation for several advanced topics such as number systems, coordinate geometry, and higher mathematics.
• Many algebra problems can be tackled using shortcut methods, substitutions, and mathematical identities, making it ideal for time-saving techniques.
• Given its high weightage and application across various areas, mastering algebra is essential for achieving a competitive CAT exam score..

Important Tips for Solving CAT Algebra Questions 2026

• Carefully read the question: Take a minute to fully comprehend the  CAT Algebra question before attempting to solve it. You can select the most effective approach to solving it if you have clear knowledge.
• Choose the Correct Approach: There are frequently multiple approaches to solving CAT previous year question papers pdf problems. Try a variety of methods to determine which one suits you the best. For instance, factorisation can occasionally be faster than using formulas, and substitution can help simplify complicated equations.
• Stay Calm: Algebra questions for CAT can occasionally be too much to handle. Practice maintaining composure under duress. Breathe deeply and approach every issue with an open mind.
• Learn from Mistakes: After you've practiced, review the CAT previous year question paper PDF to learn from your mistakes. This helps identify your mistakes and teaches you how to steer clear of them in the future.
• Practice Mental Math: In CAT, speed counts. You can save time on the test and perform calculations more quickly if you can improve your mental math skills.

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Conclusion

Here you can find the Important CAT algebra questions 2026 specifically designed to boost your preparation level. It covers essential algebra topics like progressions, equations, functions, maxima/minima, and logarithms, which are frequently tested. 

With over 25 questions divided into easy, medium, and hard levels, this resource aims to help CAT aspirants build their algebra skills and improve their performance in the quantitative aptitude section. 

By practicing these  Algebra CAT Questions, students can gain confidence and increase their chances of achieving a high percentile on the CAT exam.

CAT 2026 Resources for Preparation:

Algebra Topics for CAT	CAT Arithmetic 2027 Syllabus	CAT Important Topics
CAT Previous Year Papers	CAT Sample Papers	CAT Official Mock Test
Arithmetic Questions for CAT	CAT QA Free Resources	CAT DILR Questions