The Achievements of S. S. Shrikhande

Description: This quiz is designed to assess your knowledge about the achievements of S. S. Shrikhande, an eminent Indian mathematician. S. S. Shrikhande made significant contributions to various fields of mathematics, including combinatorial designs, finite geometries, and graph theory. His work has had a profound impact on these fields and has been widely recognized by the mathematical community.
Number of Questions: 14
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Tags: combinatorial designs finite geometries graph theory s. s. shrikhande
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S. S. Shrikhande is primarily known for his contributions to which field of mathematics?

  1. Algebra

  2. Analysis

  3. Combinatorial Designs

  4. Number Theory


Correct Option: C
Explanation:

S. S. Shrikhande is renowned for his groundbreaking work in combinatorial designs, a branch of mathematics that deals with the arrangement of objects according to certain rules.

What is the significance of S. S. Shrikhande's work on balanced incomplete block designs (BIBDs)?

  1. It led to the development of new statistical methods.

  2. It provided a framework for error-correcting codes.

  3. It facilitated the construction of efficient experimental designs.

  4. It enabled the design of optimal communication networks.


Correct Option: C
Explanation:

S. S. Shrikhande's research on BIBDs had a significant impact on the field of experimental design, enabling researchers to develop more efficient and reliable experimental designs for various scientific investigations.

Which of the following is a fundamental theorem in combinatorial designs that is attributed to S. S. Shrikhande?

  1. Fisher's Inequality

  2. Hall's Marriage Theorem

  3. Shrikhande's Conjecture

  4. Birkhoff-von Neumann Theorem


Correct Option: C
Explanation:

S. S. Shrikhande is widely recognized for his formulation of Shrikhande's Conjecture, a fundamental problem in combinatorial designs that remains unsolved to this day.

S. S. Shrikhande's work on finite geometries primarily focused on which type of geometric structure?

  1. Affine Geometries

  2. Projective Geometries

  3. Euclidean Geometries

  4. Hyperbolic Geometries


Correct Option: B
Explanation:

S. S. Shrikhande's research in finite geometries centered around projective geometries, a branch of geometry that deals with the properties of geometric figures that are preserved under projection.

What is the significance of S. S. Shrikhande's work on Hadamard matrices?

  1. It led to the development of new encryption algorithms.

  2. It provided a framework for quantum computing.

  3. It facilitated the construction of optimal communication networks.

  4. It enabled the design of efficient error-correcting codes.


Correct Option: D
Explanation:

S. S. Shrikhande's research on Hadamard matrices had a profound impact on the field of coding theory, enabling the design of efficient error-correcting codes that are crucial for reliable data transmission.

Which of the following is a significant result in graph theory that is attributed to S. S. Shrikhande?

  1. Euler's Formula

  2. Hamiltonian Cycle Theorem

  3. Shrikhande's Graph Conjecture

  4. Four Color Theorem


Correct Option: C
Explanation:

S. S. Shrikhande is renowned for his formulation of Shrikhande's Graph Conjecture, a fundamental problem in graph theory that remains unsolved to this day.

S. S. Shrikhande's work on orthogonal arrays had a significant impact on which field of engineering?

  1. Civil Engineering

  2. Mechanical Engineering

  3. Electrical Engineering

  4. Computer Engineering


Correct Option: D
Explanation:

S. S. Shrikhande's research on orthogonal arrays had a profound impact on computer engineering, particularly in the design of efficient experimental designs for computer simulations and optimization algorithms.

Which of the following is a prestigious award that S. S. Shrikhande received in recognition of his contributions to mathematics?

  1. Fields Medal

  2. Abel Prize

  3. Wolf Prize

  4. Ramanujan Prize


Correct Option: C
Explanation:

S. S. Shrikhande was honored with the prestigious Wolf Prize in Mathematics in 1990, recognizing his outstanding achievements in the field.

S. S. Shrikhande's work on association schemes had a significant impact on which area of mathematics?

  1. Algebraic Topology

  2. Differential Geometry

  3. Number Theory

  4. Combinatorics


Correct Option: D
Explanation:

S. S. Shrikhande's research on association schemes had a profound impact on combinatorics, particularly in the study of combinatorial designs and finite geometries.

Which of the following is a fundamental theorem in combinatorial designs that is attributed to S. S. Shrikhande and C. R. Rao?

  1. Fisher's Inequality

  2. Hall's Marriage Theorem

  3. Rao-Shrikhande Theorem

  4. Birkhoff-von Neumann Theorem


Correct Option: C
Explanation:

S. S. Shrikhande, in collaboration with C. R. Rao, formulated the Rao-Shrikhande Theorem, a fundamental result in combinatorial designs that provides necessary conditions for the existence of certain types of designs.

S. S. Shrikhande's work on resolvable block designs had a significant impact on which field of statistics?

  1. Bayesian Statistics

  2. Non-parametric Statistics

  3. Experimental Design

  4. Multivariate Analysis


Correct Option: C
Explanation:

S. S. Shrikhande's research on resolvable block designs had a profound impact on experimental design, enabling researchers to develop more efficient and reliable experimental designs for various scientific investigations.

Which of the following is a fundamental theorem in graph theory that is attributed to S. S. Shrikhande and V. S. Alagar?

  1. Euler's Formula

  2. Hamiltonian Cycle Theorem

  3. Shrikhande-Alagar Conjecture

  4. Four Color Theorem


Correct Option: C
Explanation:

S. S. Shrikhande, in collaboration with V. S. Alagar, formulated the Shrikhande-Alagar Conjecture, a fundamental problem in graph theory that remains unsolved to this day.

S. S. Shrikhande's work on orthogonal arrays had a significant impact on which area of computer science?

  1. Artificial Intelligence

  2. Database Systems

  3. Computer Graphics

  4. Algorithm Design


Correct Option: D
Explanation:

S. S. Shrikhande's research on orthogonal arrays had a profound impact on algorithm design, particularly in the development of efficient algorithms for combinatorial optimization problems.

Which of the following is a prestigious award that S. S. Shrikhande received in recognition of his contributions to mathematics?

  1. Fields Medal

  2. Abel Prize

  3. Wolf Prize

  4. Ramanujan Prize


Correct Option: C
Explanation:

S. S. Shrikhande was honored with the prestigious Wolf Prize in Mathematics in 1990, recognizing his outstanding achievements in the field.

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