# Tata Institute of Fundamental Research TIFR GS 2024 Mathematics Full Solution with Explanation

The Tata Institute of Fundamental Research (TIFR) conducts an entrance exam for admission to its Ph.D. and integrated Ph.D. programs in Mathematics.

*Key details regarding the TIFR Mathematics Entrance Exam:*

**TIFR Exam - Syllabus and Pattern Syllabus of Mathematics: **

Stage I of the selection process is mainly based on mathematics covered in a reasonable B.Sc. course.

This includes:

**Algebra: **Definitions and examples of groups (finite and infinite, commutative and non-commutative), cyclic groups, subgroups, homomorphisms, quotients. Group actions and Sylow theorems. Definitions and examples of rings and fields. Integers, polynomial rings and their basic properties. Basic facts about vector spaces, matrices, determinants, ranks of linear transformations, characteristic and minimal polynomials, symmetric matrices. Inner products, positive definiteness.

**Analysis:** Basic facts about real and complex numbers, convergence of sequences and series of real and complex numbers, continuity, differentiability and Riemann integration of real valued functions defined on an interval (finite or infinite), elementary functions (polynomial functions, rational functions, exponential and log, trigonometric functions), sequences and series of functions and their different types of convergence.

**Geometry/Topology:** Elementary geometric properties of common shapes and figures in 2 and 3 dimensional Euclidean spaces (e.g. triangles, circles, discs, spheres, etc.). Plane analytic geometry (= coordinate geometry) and trigonometry. Definition and basic properties of metric spaces, examples of subset Euclidean spaces (of any dimension), connectedness, compactness. Convergence in metric spaces, continuity of functions between metric spaces.

**General: **Pigeon-hole principle (box principle), induction, elementary properties of divisibility, elementary combinatorics (permutations and combinations, binomial coefficients), elementary reasoning with graphs, elementary probability theory.

In this blog post, we have meticulously crafted step-by-step solutions for each problem presented in the 2024 exam, accompanied by thorough explanations. Our goal is not only to provide answers but also to elucidate the underlying concepts and methodologies behind each solution. By understanding the reasoning and logic employed in solving these problems, you will not only be better equipped to tackle similar challenges in the future but also deepen your appreciation for the beauty of mathematics.

We invite you to dive into the solutions and explanations provided herein, and to engage actively with the material.

**TIFR GS MATH 2024 Q01 AND Q02 Full Solution with Explanation**

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**TIFR GS MATH 2024 Q03 AND Q04 Full Solution with Explanation**

**TIFR GS MATH 2024 Q05, Q06, Q07 AND Q08 Full Solution with Explanation**

**TIFR GS MATH 2024 Q09 AND Q10 Full Solution with Explanation**

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**TIFR GS MATH 2024 Q13 Full Solution with Explanation**

**TIFR GS MATH 2024 Q14 AND Q15 Full Solution with Explanation**

Feel free to reach out with any questions or thoughts you may have; we're here to support your mathematical journey.

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