{"id":3327,"date":"2026-07-13T11:54:42","date_gmt":"2026-07-13T06:24:42","guid":{"rendered":"https:\/\/www.catmock.com\/blog\/?p=3327"},"modified":"2026-07-13T14:48:59","modified_gmt":"2026-07-13T09:18:59","slug":"top-modern-math-questions-to-practice-for-cat-2026","status":"publish","type":"post","link":"https:\/\/www.catmock.com\/blog\/top-modern-math-questions-to-practice-for-cat-2026\/","title":{"rendered":"Top Modern Math Questions to Practice for CAT 2026"},"content":{"rendered":"\n

As the countdown to CAT 2026 (29 November 2026)<\/strong> begins, every study session becomes more valuable. This is the ideal time to strengthen topics that can give you a competitive advantage without requiring months of preparation.<\/p>\n\n\n\n

Modern Math<\/strong> is one such opportunity. While most aspirants dedicate the bulk of their preparation to Arithmetic and Algebra, topics like Permutation & Combination, Probability, Set Theory, Progressions, and Functions<\/strong> are often postponed until the final phase of preparation\u2014or skipped altogether.<\/p>\n\n\n\n

Ironically, this is what makes Modern Math so rewarding. It generally accounts for 3\u20135 questions<\/strong> in the CAT Quant section, and these questions are usually straightforward for candidates with solid conceptual understanding. Since many test-takers neglect this area, even a few extra correct answers can translate into a meaningful jump in your Quant score<\/strong> and, ultimately, your overall percentile<\/strong>.<\/p>\n\n\n\n

If you’re looking for a high-impact topic to focus on before CAT 2026, this deserves a place in your revision plan.<\/p>\n\n\n\n

Table of Contents<\/strong><\/h1>\n\n\n\n

\u2022 Why Modern Mathematics is Important for CAT 2026<\/p>\n\n\n\n

\u2022 Important Modern Math Topics<\/p>\n\n\n\n

\u2022 Top Modern Math Questions with Solutions<\/p>\n\n\n\n

\u2022 Common Mistakes to Avoid<\/p>\n\n\n\n

\u2022 How to Prepare Modern Mathematics for CAT 2026<\/p>\n\n\n\n

\u2022 Practice 600+ Modern Math Questions with CATMOCK Bhandara<\/p>\n\n\n\n

\u2022 FAQs<\/p>\n\n\n\n

\n\n\n\n

Why Modern Mathematics is Important for CAT 2026<\/strong><\/h1>\n\n\n\n

Modern Math covers Permutation & Combination, Probability, Set Theory, Functions & Graphs, Logarithms, and Sequences & Series. Individually, none of these topics carry huge weightage. Together, though, they show up in almost every CAT paper, and their concepts quietly support Logical Reasoning and Data Interpretation questions too\u2014a strong grip on sets and counting principles makes a surprising number of LRDI sets easier to crack.<\/p>\n\n\n\n

Modern Math is also one of the most “learnable” parts of Quant. Unlike Arithmetic, where speed comes from years of number sense, Modern Math rewards structured practice\u2014once you’ve internalised the core counting and probability principles, most questions follow a small number of recurring patterns. That makes it a genuinely efficient use of your remaining prep time.<\/p>\n\n\n\n

Important Modern Math Topics<\/strong><\/h1>\n\n\n\n

Here’s how the topic typically breaks down in a CAT paper, based on trends from recent years:<\/p>\n\n\n\n

Modern Math Topic<\/strong><\/td>Avg. Questions in CAT<\/strong><\/td>Difficulty Level<\/strong><\/td>Prep Priority<\/strong><\/td><\/tr><\/thead>
Permutation & Combination<\/td>1\u20132<\/td>Moderate\u2013High<\/td>High<\/td><\/tr>
Probability<\/td>1<\/td>Moderate<\/td>Medium<\/td><\/tr>
Set Theory & Venn Diagrams<\/td>1<\/td>Low\u2013Moderate<\/td>High (also helps LRDI)<\/td><\/tr>
Functions & Graphs<\/td>1<\/td>Moderate<\/td>Medium<\/td><\/tr>
Logarithms<\/td>0\u20131<\/td>Low<\/td>Low\u2013Medium<\/td><\/tr>
Sequences & Series<\/td>1<\/td>Moderate<\/td>Medium<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Nothing here needs the same formula-heavy grind as Arithmetic. But Permutation & Combination and Set Theory consistently reward focused practice, since a large share of aspirants either skip them or panic through them under time pressure.<\/p>\n\n\n\n

Top Modern Math Questions with Solutions<\/strong><\/h1>\n\n\n\n
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Note:<\/strong> These questions below aren’t reproduced from any specific CAT paper\u2014they’re written to reflect the exact patterns that have repeatedly shown up across recent CAT exams, worked through step by step so you can see the logic, not just the final answer.<\/p>\n<\/blockquote>\n\n\n\n

1. Permutation & Combination<\/strong><\/h2>\n\n\n\n

Q1. A committee of 4 members is to be formed from 6 men and 4 women such that the committee has at least 2 women. In how many ways can this be done?<\/strong><\/p>\n\n\n\n

This needs three cases based on how many women are on the committee: exactly 2, exactly 3, or all 4.<\/p>\n\n\n\n

Case 1 (2 women, 2 men): C(4,2) \u00d7 C(6,2) = 6 \u00d7 15 = 90<\/p>\n\n\n\n

Case 2 (3 women, 1 man): C(4,3) \u00d7 C(6,1) = 4 \u00d7 6 = 24<\/p>\n\n\n\n

Case 3 (4 women, 0 men): C(4,4) \u00d7 C(6,0) = 1 \u00d7 1 = 1<\/p>\n\n\n\n

Total ways = 90 + 24 + 1 = 115<\/p>\n\n\n\n

Answer: 115 ways<\/strong><\/p>\n\n\n\n

2. Probability<\/strong><\/h2>\n\n\n\n

Q2. Two dice are rolled together. Find the probability that the sum of the numbers is either 7 or 11.<\/strong><\/p>\n\n\n\n

Total possible outcomes when two dice are rolled = 6 \u00d7 6 = 36.<\/p>\n\n\n\n

Ways to get a sum of 7: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) \u2192 6 ways<\/p>\n\n\n\n

Ways to get a sum of 11: (5,6),(6,5) \u2192 2 ways<\/p>\n\n\n\n

Favourable outcomes = 6 + 2 = 8<\/p>\n\n\n\n

Probability = 8\/36 = 2\/9<\/p>\n\n\n\n

Answer: 2\/9<\/strong><\/p>\n\n\n\n

3. Set Theory & Venn Diagrams<\/strong><\/h2>\n\n\n\n

Q3. In a survey of 100 students, 45 read Physics, 50 read Chemistry, and 20 read both subjects. How many students read neither?<\/strong><\/p>\n\n\n\n

Use the formula: |P \u222a C| = |P| + |C| \u2212 |P \u2229 C|<\/p>\n\n\n\n

|P \u222a C| = 45 + 50 \u2212 20 = 75<\/p>\n\n\n\n

Students reading neither = Total \u2212 |P \u222a C| = 100 \u2212 75 = 25<\/p>\n\n\n\n

Answer: 25 students<\/strong><\/p>\n\n\n\n

4. Functions & Graphs<\/strong><\/h2>\n\n\n\n

Q4. If f(x) = 3x \u2212 2 and g(x) = x\u00b2 + 1, find the value of f(g(2)).<\/strong><\/p>\n\n\n\n

First evaluate the inner function: g(2) = 2\u00b2 + 1 = 4 + 1 = 5<\/p>\n\n\n\n

Now apply f to this result: f(5) = 3(5) \u2212 2 = 15 \u2212 2 = 13<\/p>\n\n\n\n

Answer: 13<\/strong><\/p>\n\n\n\n

5. Logarithms<\/strong><\/h2>\n\n\n\n

Q5. If log\u2082x + log\u2084x + log\u2088x = 11, find the value of x.<\/strong><\/p>\n\n\n\n

Let log\u2082x = a. Using the change-of-base rule, log\u2084x = a\/2 and log\u2088x = a\/3.<\/p>\n\n\n\n

So the equation becomes: a + a\/2 + a\/3 = 11<\/p>\n\n\n\n

Taking LCM: (6a + 3a + 2a)\/6 = 11 \u2192 11a\/6 = 11 \u2192 a = 6<\/p>\n\n\n\n

Since log\u2082x = 6, x = 2\u2076 = 64<\/p>\n\n\n\n

Answer: x = 64<\/strong><\/p>\n\n\n\n

6. Sequences & Series<\/strong><\/h2>\n\n\n\n

Q6. The sum of the first n terms of an AP is given by S\u2099 = 3n\u00b2 + 5n. Find the 10th term of the series.<\/strong><\/p>\n\n\n\n

The nth term of a series can be found using a\u2099 = S\u2099 \u2212 S\u2099\u208b\u2081<\/p>\n\n\n\n

S\u2081\u2080 = 3(10)\u00b2 + 5(10) = 300 + 50 = 350<\/p>\n\n\n\n

S\u2089 = 3(9)\u00b2 + 5(9) = 243 + 45 = 288<\/p>\n\n\n\n

a\u2081\u2080 = S\u2081\u2080 \u2212 S\u2089 = 350 \u2212 288 = 62<\/p>\n\n\n\n

Answer: 62<\/strong><\/p>\n\n\n\n

Common Mistakes to Avoid<\/strong><\/h1>\n\n\n\n