CAT Algebra Questions with Solutions Practice for 2025 Exam

Overview: Algebra is one of the important topic 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.

Download FREE Study Material for CAT Exam 2025 by SuperGrads

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.

Continue reading to know The types of CAT algebra questions that are commonly found on the CAT exam, important strategies for answering them, and practice tips that will help you succeed will all be covered in this article.  Let's explore CAT algebra together and give you the resources you need to succeed.

Read more: VARC Syllabus for CAT 2025

Read More: How to Prepare for Data Interpretation for CAT Exam

Importance of CAT Algebra Questions 2025

CAT Algebra Questions form a crucial part of the Quantitative Aptitude section of the CAT exam. Questions from topics like 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.

Types of CAT Algebra Questions 2025

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

• Linear Equations
• Quadratic Equations
• Progression
• Functions and Graphs
• Inequalities

Read more: CAT Geometry Formulas with Explanation

Easy Level CAT Algebra Questions 2025

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

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

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

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

Practise with: CAT Trigonometry Question with Solutions

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
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

Check: How to prepare for Quantitative Aptitude for CAT exam

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

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

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

10. If x=5+3x = \sqrt{5} + \sqrt{3}x=5+3, then what is the rationalised form of 1x\frac{1}{x}x1?
a) 5−3\sqrt{5} - \sqrt{3}5−3
b) 5−32\frac{\sqrt{5} - \sqrt{3}}{2}25−3
c) 5−3(5+3)(5−3)\frac{\sqrt{5} - \sqrt{3}}{(\sqrt{5} + \sqrt{3})(\sqrt{5} - \sqrt{3})}(5+3)(5−3)5−3
d) 3−5\sqrt{3} - \sqrt{5}3−5

Read More: SuperGrads CAT Toppers Interview

Moderate Level CAT Algebra Questions 2025

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

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

Read more: CAT Mensuration Questions with Answers

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

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

Know More | How Many Times CAT Exam is Conducted in a Year

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

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

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

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

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

Check: Venn Diagram Practice Questions for CAT 2025

20. If the sum of the 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 

Check: CAT Syllabus for 3 Sections

Advanced Level CAT Algebra Questions 2025

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

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

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

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
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

Click Here: Download CAT Arithmetic questions PDF with Solutions

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

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

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

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

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

Important Tips for Solving CAT Algebra Questions 2025

• Carefully read the question: Take a minute to fully comprehend the question before attempting to solve it. You can select the most effective approach to solving it if you have a clear knowledge.
• Choose the Correct Approach: There are frequently multiple approaches to solving algebraic problems. Try a variety of methods to determine which one suits you the best. For instance, factorization can occasionally be faster than formulas, and substitution can help make complicated equations simpler.
• Stay Calm: CAT algebra problems 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, go back and examine your errors. This helps in identifying your mistakes and teaching 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.

Find: DILR Topics in CAT 2025

Conclusion

Here you can find the CAT algebra questions 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 questions, students can gain confidence and increase their chances of achieving a high percentile on the CAT exam.

Explore: Practice with CAT Previous Year Papers with Solutions