The solution of the system of equations: x₁ - 3x₂ + 4x₃ = 3 2x₁... | Agrigyan

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Q.86

ICAR AIEEA PG 2024 - Statistical Sciences

MCQ (Single Correct) +4 −1

Which of the following statement is true?

निम्नलिखित में से कौन सा कथन सत्य है?

Every empty set is linearly dependent प्रत्येक रिक्त समुच्चय रैखिकतः आश्रित होता है Every non empty set is linearly independent प्रत्येक अरिक्त समुच्चय रैखिकतः स्वतंत्र होता है Every non empty set is linearly dependent प्रत्येक अरिक्त समुच्चय रैखिकतः आश्रित होता है Single non-zero set is linearly independent एकल अशून्य सदिश का समुच्चय रैखिकतः स्वतंत्र होता है

Q.87

ICAR AIEEA PG 2024 - Statistical Sciences

MCQ (Single Correct) +4 −1

Let $A$ be an $n \times n$ matrix of real number such that $A^2 = A$, then the Eigen values of $A$ are:

मान लीजिए $A$ वास्तविक संख्याओं का एक $n \times n$ आव्यूह है जिससे $A^2 = A$ हो, तो $A$ के आइगेन मान (Eigen values) हैं:

0, 1 0, 1 1, -1 1, -1 1, -1 1, -1 -1, -1 -1, -1

Q.88

ICAR AIEEA PG 2024 - Statistical Sciences

MCQ (Single Correct) +4 −1

Let $\sum_{n=1}^\infty a_n$ be series of real number, then:

मान लीजिए $\sum_{n=1}^\infty a_n$ वास्तविक संख्याओं की एक श्रेणी है, तो:

$\sum_{n=1}^\infty a_n$ is convergent if and only if $\lim_{n \to \infty} |a_n|^{1/n} > 1$ $\sum_{n=1}^\infty a_n$ अभिसारी है यदि और केवल यदि $\lim_{n \to \infty} |a_n|^{1/n} > 1$ $\sum_{n=1}^\infty a_n$ is convergent if and only if $\lim_{n \to \infty} |a_n|^{1/n} = 1$ $\sum_{n=1}^\infty a_n$ अभिसारी है यदि और केवल यदि $\lim_{n \to \infty} |a_n|^{1/n} = 1$ $\sum_{n=1}^\infty a_n$ is convergent if and only if $\lim_{n \to \infty} \left|\frac{a_{n+1}}{a_n}\right| < 1$ $\sum_{n=1}^\infty a_n$ अभिसारी है यदि और केवल यदि $\lim_{n \to \infty} \left|\frac{a_{n+1}}{a_n}\right| < 1$ $\sum_{n=1}^\infty a_n$ is convergent if and only if $\lim_{n \to \infty} \left|\frac{a_{n+1}}{a_n}\right| = 1$ $\sum_{n=1}^\infty a_n$ अभिसारी है यदि और केवल यदि $\lim_{n \to \infty} \left|\frac{a_{n+1}}{a_n}\right| = 1$

Q.89

ICAR AIEEA PG 2024 - Statistical Sciences

MCQ (Single Correct) +4 −1

Let $A = \begin{bmatrix} 2 & 1 & 4 \\ 3 & 2 & 5 \\ 0 & -1 & 1 \end{bmatrix}$ be a matrix, then the rank of $A$ is:

मान लीजिए $A = \begin{bmatrix} 2 & 1 & 4 \\ 3 & 2 & 5 \\ 0 & -1 & 1 \end{bmatrix}$ एक आव्यूह है, तो $A$ की जाति (rank) है:

0 0 1 1 2 2 3 3

Q.90

ICAR AIEEA PG 2024 - Statistical Sciences

MCQ (Single Correct) +4 −1

The solution of the system of equations: $$x_1 - 3x_2 + 4x_3 = 3$$ $$2x_1 - 5x_2 + 7x_3 = 6$$ $$3x_1 - 8x_2 + 11x_3 = 11$$ is given by:

समीकरण निकाय: $$x_1 - 3x_2 + 4x_3 = 3$$ $$2x_1 - 5x_2 + 7x_3 = 6$$ $$3x_1 - 8x_2 + 11x_3 = 11$$ का हल क्या है?

$x_1 = 3, x_2 = 0, x_3 = 2$ $x_1 = 3, x_2 = 0, x_3 = 2$ $x_1 = 0, x_2 = 0, x_3 = 0$ $x_1 = 0, x_2 = 0, x_3 = 0$ $x_1 = 1, x_2 = 0, x_3 = 2$ $x_1 = 1, x_2 = 0, x_3 = 2$ No solution exists कोई हल मौजूद नहीं है

General Agriculture, Economics & Extension

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Statistical Methods & Experimental Designs

14 Topics

Theoretical Discrete Probability Distributions: Bernoulli, Binomial, Poisson, Geometric and Hypergeometric Design of Experiments: Principles of Experimentation, CRD, RBD, Latin Square Design (LSD) and Factorial Experiments Probability Theory: Classical, Axiomatic Definitions, Addition, Multiplication Theorems and Bayes Theorem Small Sample Tests: Students t-test, Snedecors F-test, Chi-Square Test of Goodness of Fit and Contingency Tables Measures of Central Tendency: Arithmetic Mean, Geometric Mean, Harmonic Mean, Median and Mode Theoretical Continuous Probability Distributions: Uniform, Normal, Exponential, Beta and Gamma Distributions Sampling Theory: Census vs Sample Survey, Sampling Errors, SRSWOR, SRSWR, Stratified, Systematic and Cluster Sampling Measures of Dispersion: Range, Quartile Deviation, Mean Deviation, Standard Deviation and Coefficient of Variation Testing of Hypotheses: Null and Alternative Hypotheses, Type I and II Errors, Significance Level, Large Sample Tests (Z-test) Collection, Classification and Tabulation of Data, Frequency Distributions and Graphical Representations Regression Analysis: Simple and Multiple Linear Regression, Least Squares Principle, Properties and R-Squared Random Variables, Probability Mass and Density Functions, Expectation and Moment Generating Functions Correlation Analysis: Simple, Partial, Multiple Correlation, Pearson Coefficient and Rank Correlation Moments, Skewness (Karl Pearson, Bowley) and Kurtosis

Computer Applications & Bioinformatics

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Computer Networks and Internet: Topologies (LAN, WAN, MAN), OSI Model, TCP/IP, Protocols (HTTP, FTP) and Web Computer Architecture and Hardware: Generations of Computers, CPU, Memory Hierarchy (RAM, ROM, Cache), Input-Output System Software and Operating Systems: Functions of OS, DOS Commands, Windows OS, Linux/Unix Architecture Application Software: Word Processing, Spreadsheets (MS Excel Formulas, Functions, Charts), DBMS Basics Number Systems and Boolean Algebra: Binary, Octal, Hexadecimal Conversions, Logic Gates and Truth Tables Sequence Alignment and Computational Genomics: Pairwise and Multiple Alignment (BLAST, FASTA, Clustal), Scoring Matrices Cyber Security and Data Protection: Computer Viruses, Malware, Firewalls, Cryptography Basics and IPR Programming Fundamentals: Algorithms, Flowcharts, Control Structures, Loops, Functions, Arrays and Pointers in C/C++ Object-Oriented Programming and Modern Languages: Concepts of OOP (Classes, Objects, Inheritance), Python and R Introduction to Bioinformatics: Scope, Biological Databases (NCBI, GenBank, EMBL, UniProt, PDB) and Data Retrieval

ICAR AIEEA PG 2024 - Statistical Sciences

120 Questions Bilingual

ICAR AIEEA PG Statistical Science 14 July 2023 Shift-1 Paper

120 Questions Bilingual

ICAR AIEEA PG Statistical Sciences 09 July 2023 (Shift 1) Paper

120 Questions Bilingual

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