If u = (x³ + y³/3x + 4y), then the value of x( u/ x) + y( u/ y)... | Agrigyan

All Subjects General Agriculture, Economics & Extension Mathematics Statistical Methods & Experimental Designs Computer Applications & Bioinformatics

Q.111

ICAR AIEEA PG 2024 - Statistical Sciences

MCQ (Single Correct) +4 −1

If $\ln u = \frac{x^3 + y^3}{3x + 4y}$, then the value of $x\frac{\partial u}{\partial x} + y\frac{\partial u}{\partial y}$ is given by:

यदि $\ln u = \frac{x^3 + y^3}{3x + 4y}$ हो, तो $x\frac{\partial u}{\partial x} + y\frac{\partial u}{\partial y}$ का मान है:

$u \ln\frac{u}{2}$ $u \ln\frac{u}{2}$ $\frac{u}{2}\ln u$ $\frac{u}{2}\ln u$ $2u \ln u$ $2u \ln u$ $\frac{u}{2}\ln\frac{u}{2}$ $\frac{u}{2}\ln\frac{u}{2}$

Q.112

ICAR AIEEA PG 2024 - Statistical Sciences

MCQ (Single Correct) +4 −1

The solution of the initial value problem $\frac{dy}{dx} = -6xy; y(0) = 7$ is given by:

प्रारंभिक मान समस्या (initial value problem) $\frac{dy}{dx} = -6xy; y(0) = 7$ का हल है:

$7e^{-3x^2}$ $7e^{-3x^2}$ $3e^{-7x^2}$ $3e^{-7x^2}$ $7e^{-x^2}$ $7e^{-x^2}$ $3e^{-x^2}$ $3e^{-x^2}$

Q.113

ICAR AIEEA PG 2024 - Statistical Sciences

MCQ (Single Correct) +4 −1

The formula to solve simple nonlinear equation $f(x) = 0$ by Newton's Raphson Method is given by:

न्यूटन-रैफसन विधि (Newton-Raphson Method) द्वारा सरल अरैखिक समीकरण $f(x) = 0$ को हल करने का सूत्र है:

$x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}$ $x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}$ $x_{n+1} = x_n - \frac{f'(x_n)}{f(x_n)}$ $x_{n+1} = x_n - \frac{f'(x_n)}{f(x_n)}$ $x_{n+1} = f(x_n) - \frac{f''(x_n)}{f'(x_n)}$ $x_{n+1} = f(x_n) - \frac{f''(x_n)}{f'(x_n)}$ $x_{n+1} = f(x_n) - \frac{f'(x_n)}{f''(x_n)}$ $x_{n+1} = f(x_n) - \frac{f'(x_n)}{f''(x_n)}$

Q.114

ICAR AIEEA PG 2024 - Statistical Sciences

MCQ (Single Correct) +4 −1

If $A$ is any real number and $r$ is positive rational number, then the value of $\lim_{x \to +\infty} \frac{A}{x^r}$ is given by:

यदि $A$ कोई वास्तविक संख्या है और $r$ एक धनात्मक परिमेय संख्या है, तो $\lim_{x \to +\infty} \frac{A}{x^r}$ का मान है:

$e$ $e$ -1 -1 0 0 1 1

Q.115

ICAR AIEEA PG 2024 - Statistical Sciences

MCQ (Single Correct) +4 −1

If the interval of differencing being unity and $\Delta$ be the forward difference operator, then the value of $\Delta\left(\frac{2^x}{x!}\right)$ is given by:

यदि अंतरण अंतराल इकाई (unity, $h=1$) हो और $\Delta$ अग्रगामी अंतर संकारक (forward difference operator) हो, तो $\Delta\left(\frac{2^x}{x!}\right)$ का मान होगा:

$\frac{2^x(x + 1)!}{(1 - x)}$ $\frac{2^x(x + 1)!}{(1 - x)}$ $\frac{2^x(1 - x)}{(x + 1)!}$ $\frac{2^x(1 - x)}{(x + 1)!}$ $\frac{3^x(1 - x)}{(x - 2)!}$ $\frac{3^x(1 - x)}{(x - 2)!}$ $\frac{3^x(1 + x)}{(x + 1)!}$ $\frac{3^x(1 + x)}{(x + 1)!}$

General Agriculture, Economics & Extension

8 Topics

Agronomy, Agro-Climatic Zones, Cropping Systems, Tillage and Soil Fertility Management Major Plant Diseases, Insect Pests, Weeds and Integrated Pest Management (IPM) Plant Physiology, Mineral Nutrition, Genetics and Plant Breeding Fundamentals Historical Milestones, Agricultural Research Infrastructure and ICAR Institutes Micro & Macro Economics: Demand, Supply, Production Costs and Market Structures Agricultural Marketing, Market Intermediaries, Price Policy, MSP and Buffer Stocking Agricultural Finance, Credit Institutions (NABARD, RRBs, Commercial Banks) and KCC Extension Education Principles, Rural Development Programs and Community Reconstruction

Mathematics

9 Topics

Differential Calculus: Limits, Continuity, Differentiability, Successive Differentiation and Expansion of Functions Active Sequences and Series: Arithmetic, Geometric, Harmonic Progressions and Infinite Series Convergence Matrices and Determinants: Matrix Operations, Rank, Inverse, Systems of Linear Equations and Eigenvalues Sets, Relations, Functions, Mathematical Induction and Theory of Equations Integral Calculus: Definite and Indefinite Integrals, Reduction Formulas and Areas Under Curves Differential Equations: First Order Ordinary Differential Equations, Linear Differential Equations with Constant Coefficients Applications of Derivatives: Tangents, Normals, Maxima-Minima, Mean Value Theorems and Indeterminate Forms Numerical Methods: Interpolation, Numerical Differentiation, Integration (Trapezoidal, Simpson) and Root Finding Coordinate Geometry: Straight Lines, Circles, Parabola, Ellipse and Hyperbola in Two Dimensions

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

10 Topics

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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