100+ CAT Algebra Questions with Answers PDF Download here

Q: What kind of algebra questions appear on the CAT exam?

The CAT exam includes algebra questions covering various topics such as equations, progressions (arithmetic and geometric), functions, maxima and minima, and logarithms. You'll find a mix of easy, moderate, and challenging questions.

Q: Where can I find algebra practice questions for CAT?

You can get the algebra practice questions here in this blog for the CAT exam. It is divided into different difficulty levels. Additionally, you can find more algebra CAT questions PDF resources online, including sample papers and previous year question papers.

Q: Are previous year algebra questions CAT important for preparation?

Yes, absolutely! Solving algebra previous year questions from CAT can help you analyse the difficulty level. It gives you a clear idea of the exam pattern, the types of questions asked, and the difficulty level.

Q: How many algebra questions can I expect in the CAT exam?

Typically, you can expect around 10-12 questions from algebra in the CAT exam. This makes it an important topic to master. Regularly practising algebra questions CAT will significantly boost your chances of scoring well in the quantitative aptitude section.

Q: Do CAT Algebra questions require more computation or are they more conceptual?

In general, CAT algebra questions are less computationally demanding and more conceptual. They assess your comprehension of fundamental algebraic concepts as well as your capacity for rational problem-solving and simplification as opposed to laborious computations.

Author : Lalita Vishwakarma

November 25, 2025

Overview: Algebra is one of the important topics of the quantitative aptitude section. Practising CAT Algebra questions can help you ace the exam with a high percentile. Continue reading to get all these questions.

Algebra includes key topics such as progressions, equations, functions, maxima and minima, and logarithms.

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 25+ Algebra CAT questions divided into three difficulty levels, like easy, medium and hard.

Please continue reading to know the types of CAT 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's CAT algebra questions PDF together and give you the resources you need to succeed.

Read more: VARC Syllabus for CAT 2026

What are the CAT Algebra questions 2026?

CAT Algebra questions are a part of the Quantitative Ability section in the CAT exam 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 Algebra Questions PDF below

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CAT Quadratic Questions PDF
CAT Inequalities Questions PDF
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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

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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

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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

Check: How to prepare for Quantitative Aptitude for CAT exam

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

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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

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:

Click Here: Download CAT Arithmetic questions PDF with Solutions

Importance of CAT Algebra Questions 2026

CAT Algebra Questions form a crucial part of the Quantitative Aptitude 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 score in the CAT exam.

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 algebra questions 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 practised, review the CAT's previous year algebra questions 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.

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