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Most Important Algebra Questions for CAT 2026
Algebra is one of the major areas of the CAT Quantitative Aptitude section and requires a combination of conceptual clarity, question selection and efficient problem-solving. CAT Algebra questions are rarely about simply remembering a formula. Aspirants need to identify the underlying relationship, translate the information into mathematical form and choose an efficient approach.
If you have already completed the concepts from the CAT 2026 syllabus, these questions can be used as focused practice before moving to CAT Algebra PYQs, Quant sectional tests and full-length CAT mock tests.
The objective should not be to simply complete all 100+ questions. Track which questions you solve correctly, which take too long and which concepts repeatedly lead to mistakes. This makes the question bank a diagnostic error logΒ toolΒ rather than just another practice set.
Download 100+ CAT Algebra Questions PDF
Aspirants can download the 100+ CAT Algebra Questions PDF and use it for topic-wise practice and revision. The PDF is particularly useful if you want to practise Algebra separately before attempting mixed Quant tests.
While solving the PDF, mark questions using three categories:
- Comfortable: Solved correctly with a clear approach.
- Slow: Solved correctly but required excessive time.
- Weak: Incorrect, unattempted or conceptually unclear.
Revisit the second and third categories during revision. This is considerably more useful than repeatedly solving questions you already know.
For additional practice, aspirants can also use CAT free study material and topic-wise CAT Quant questions after completing this set.
CAT Algebra Questions for CAT 2026
CAT Algebra questions below should ideally be attempted only after learning the fundamental concepts. Avoid checking the solution immediately after getting stuck.
Give yourself enough time to identify the underlying concept and try an alternative approach. Once you check the solution, compare it with your method and determine whether there was a shorter or more reliable approach.
Important Algebra Questions for CAT 2026
Once you have completed these practice questions, move to CAT Algebra previous year questions. PYQs are important because they show how Algebra concepts have actually been tested in CAT rather than only providing additional practice.
Most Important Algebra Topics for CAT 2026
CAT Algebra covers several interconnected concepts. Aspirants should avoid preparing each chapter as an isolated formula list because a single question may combine ideas from equations, inequalities, functions or other areas.
Question 1
A value of $$c$$ for which the minimum value of $$f(x)=x^{2}-4cx+8c$$ is greater than the maximum value of $$g(x)=-x^{2}+3cx-2c$$, is
correct answer:- 2
Question 2
Let $$3\leq x\leq6$$ and $$\left[x^{2}\right] =\left[x\right]^{2}$$ , where $$[x]$$ is the greatest integer not exceeding $$x$$ . If set $$S$$ represents all feasible values of $$x$$, then a possible subset of $$S$$ is
correct answer:- 1
Question 3
Stocks A, B and C are priced at rupees 120, 90 and 150 per share, respectively. A trader holds a portfolio consisting of 10 shares of stock A, and 20 shares of stocks B and C put together. If the total value of her portfolio is rupees 3300, then the number of shares of stock B that she holds, is
correct answer:- 15
Question 4
If a, b and c are positive real numbers such that $$a > 10 \geq b \geq c$$ and $$\cfrac{\log_8 (a + b)}{\log_2c} + \cfrac{\log_{27} (a - b)}{\log_3c} = \cfrac{2}{3}$$, then the greatest possible integer value of a is
correct answer:- 14
Question 5
A function f maps the set of natural numbers to whole numbers, such that f(xy) = f(x)f(y) + f(x) + f(y) for all x, y and f(p) = 1 for every prime number p. Then, the value of f(160000) is
correct answer:- 1
Question 6
The roots $$\alpha, \beta$$ of the equation $$3x^2 + \lambda x - 1 = 0$$, satisfy $$\cfrac{1}{\alpha^2} + \cfrac{1}{\beta^2} = 15$$.
The value of $$(\alpha^3 + \beta^3)^2$$, is
correct answer:- 2
Question 7
If $$x$$ and $$y$$ are positive real numbers such that $$\log_{x}(x^2 + 12) = 4$$ and $$3 \log_{y} x = 1$$, then $$x + y $$ equals
correct answer:- 3
Question 8
If $$\sqrt{5x+9} + \sqrt{5x - 9} = 3(2 + \sqrt{2})$$, then $$\sqrt{10x+9}$$ is equal to
correct answer:- 3
Question 9
If $$x$$ and $$y$$ are real numbers such that $$x^{2} + (x - 2y - 1)^{2} = -4y(x + y)$$, then the value $$x - 2y$$ is
correct answer:- 2
Question 10
For any natural number n, suppose the sum of the first n terms of an arithmetic progression is $$(n + 2n^2)$$. If the $$n^{th}$$ term of the progression is divisible by 9, then the smallest possible value of n is
correct answer:- 3
Question 11
Let $$0 \leq a \leq x \leq 100$$ and $$f(x) = \mid x - a \mid + \mid x - 100 \mid + \mid x - a - 50\mid$$. Then the maximum value of f(x) becomes 100 when a is equal to
correct answer:- 3
Question 12
Let a, b, c be non-zero real numbers such that $$b^2 < 4ac$$, and $$f(x) = ax^2 + bx + c$$. If the set S consists of all integers m such that f(m) < 0, then the set S must necessarily be
correct answer:- 3
Important Algebra topics for CAT 2026 include:
CAT Algebra Topic | What to Focus On |
Formation of equations, simultaneous equations and word problems | |
Roots, coefficients, nature of roots and applications | |
Linear and quadratic inequalities, intervals and modulus | |
Domain, range, types and relationships between functions | |
Properties, equations and restrictions | |
Simplification and exponent relationships | |
Polynomials | Roots, coefficients, factor theorem and remainder theorem |
AP, GP, terms, sums and patterns | |
Maxima and Minima | Algebraic optimisation and possible values |
Students should check the complete CAT Quant important topics 2026 alongside these Algebra topics instead of preparing Algebra in isolation. Arithmetic, Geometry, Number Systems and Modern Mathematics must also receive adequate preparation time.
How to Practise CAT Algebra Questions Effectively?
A common mistake is measuring preparation through the number of questions completed. Solving 200 questions without analysing errors may produce less improvement than solving 100 questions and carefully revisiting the difficult ones.
A better CAT Algebra practice cycle is:
Begin with the concept and basic examples. Then attempt topic-wise CAT Algebra questions followed by PYQs. Once multiple Quant topics are covered, start attempting CAT Quant sectional tests under the actual sectional time constraint.
After every sectional test, identify whether your problem was conceptual knowledge, question selection, calculation, accuracy or time management.
As preparation progresses, include CAT mock tests as well. A full mock tests something that a topic-wise question bank cannot: whether you can recognise and select a solvable Algebra question while simultaneously managing VARC, DILR and the rest of Quant.
CAT Algebra Formulas for Quick Revision
Formula revision can help before CAT sectional tests and mocks, but Algebra should not be prepared entirely through memorisation.
Use a CAT Quant formula PDF to revise important identities, equations, logarithmic properties, progressions, indices and other frequently used results. Against every formula, try to recall at least one question in which it can be applied.
This converts passive CAT formula revision into active recall.
If you repeatedly forget a formula during tests, add it to a short personal revision sheet rather than repeatedly revising every formula you already know.
CAT Algebra Preparation Resources for CAT 2026
Different resources should be used at different stages of preparation. Aspirants who are still learning concepts can begin with the CAT 2026 syllabus, concept lessons and free CAT study material.
Once the basics are clear, move to topic-wise questions, CAT Algebra PYQs and CAT previous year papers. CAT Sectional tests should then be introduced to develop speed and question selection.
Full-length CAT 2026 mock tests become increasingly important as the exam approaches because Algebra ultimately has to be solved as part of the complete QA section.
Students who need structured concept coverage, practice and testing can also explore the CAT 2026 Course. Aspirants beginning preparation closer to the examination can use a CAT crash course for a more compressed revision and practice schedule.
Aspirants looking to strengthen their concepts specifically in the QA section can use a CAT Quant Course for structured topic-wise learning, practice questions and Quant-focused preparation.
100+ Most Important Algebra Questions for CAT 2026: Conclusion
The most important Algebra questions for CAT 2026 are valuable only when they are used as part of a structured preparation process. Start with conceptual understanding, solve topic-wise questions, analyse mistakes and then validate your preparation using CAT Algebra PYQs.
As your accuracy improves, move from isolated Algebra practice to Quant sectional tests, CAT previous year papers and full-length mocks. This progression helps develop the two abilities that matter most during CAT: knowing how to solve a question and knowing which question is worth attempting.
Keep an error log for difficult Algebra questions and revisit it during revision. By the final phase of preparation, your goal should be to recognise familiar Algebra structures quickly and solve the right questions accurately under time pressure.
