Two unbiased dice are thrown simultaneously. Then the possible number of outcomes will be:
दो निष्पक्ष पासों (Unbiased dice) को एक साथ फेंका जाता है। तो परिणामों की कुल संभव संख्या होगी:
If $C_1$ and $C_2$ are subsets of sample space $S$, then which is correct?
यदि $C_1$ और $C_2$ प्रतिदर्श समष्टि $S$ के उपसमुच्चय (Subsets) हैं, तो कौन-सा कथन सही है?
Two dice are rolled simultaneously. What is the probability that the sum of numbers on the dice is 9?
दो पासे एक साथ फेंके जाते हैं। पासों पर आने वाली संख्याओं का योग 9 होने की प्रायिकता क्या है?
Given $P(A) = p_1$, $P(B) = p_2$, and $P(A \cap B) = p_3$. Then $P(A' \cap B')$ will be:
यदि $P(A) = p_1$, $P(B) = p_2$, और $P(A \cap B) = p_3$ दिया गया है, तो $P(A' \cap B')$ का मान क्या होगा?
If $P(A \cup B) = 5/6$, $P(A \cap B) = 1/3$ and $P(\overline{B}) = 1/2$, then the events $A$ and $B$ are:
यदि $P(A \cup B) = 5/6$, $P(A \cap B) = 1/3$ और $P(\overline{B}) = 1/2$ हो, तो घटनाएं $A$ और $B$ हैं:
सामान्य कृषि, कृषि अर्थशास्त्र एवं प्रसार शिक्षा
8 टॉपिक्स
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
उच्च गणित: बीजगणित, कलन एवं अवकल समीकरण
9 टॉपिक्स
Differential Calculus: Limits, Continuity, Differentiability, Successive Differentiation and Expansion of Functions
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
सांख्यिकीय विधियां, प्रायिकता एवं प्रायोगिक अभिकल्पनाएं
14 टॉपिक्स
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
सक्रिय
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
कंप्यूटर अनुप्रयोग, प्रोग्रामिंग एवं जैव सूचना विज्ञान
10 टॉपिक्स
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
Official PYQ Papers
Previous Year Papers of Statistical Sciences
Practice official shift-wise question papers with answer keys and detailed explanations on the actual exam pattern.
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