What is the PageRank algorithm, and how is it used in link analysis? Describe the concept of "flow of rank" in PageRank. Explain how the PageRank of a web page is calculated using the flow model.

Describe the purpose and functionality of a Bloom filter in data stream processing. How does the Bloom filter efficiently check for element presence? Describe the Flajolet-Martin algorithm for cardinality estimation in data streams.

Compare Apache Spark, Hive, and HBase in terms of functionality, data processing methods, and use cases. When would Spark be preferred over traditional MapReduce, and why?

Explain the Hadoop architecture with a focus on HDFS and the master/slave architecture. How do NameNode and DataNodes work together to store and manage large datasets? Provide a basic example of this storage process.

Discuss the 4 Vs of big data (Volume, Velocity, Variety, and Veracity). Provide a real-world example of each, explaining how these characteristics create challenges in big data management.

Describe the role of statistical hypothesis testing in data analysis. What are Type I and Type II errors, and how do they affect decision-making? Provide an example of hypothesis testing in a real-world scenario.

Explain Exploratory Data Analysis (EDA) and its importance. What are the main steps in performing EDA on a new dataset? Describe two methods for detecting outliers and how handling outliers impacts data analysis.

Define the term data science. Describe its applications in two industries of your choice (e.g., healthcare, finance, e-commerce). What role does the data science lifecycle play in managing data projects?

What is the Agricultural Produce Market Committee (APMC)? Explain the responsibilities and shortcomings of the APMC system

What do you understand by agricultural input marketing? Explain the components of agricultural input marketing strategies.

Discuss the points considered in starting a custom hiring centre. Explain the challenges and opportunities for starting a custom hiring centre.

What do you understand by the cooperatives? Explain the structure of cooperatives in terms of of governance, performance of different types of functions, political and administrative systems and monitoring.

Explain the foodgrains marketing system. Discuss the various schemes under which allocation is made by the Department of Food and Public Distribution.

Explain about the extension efforts made post-independence in India.

Discuss some of the research projects operated/operating at the National level in the agriculture sector.

Suppose you are teaching a child addition of decimal fractions, according to the constructivist model. In this context,

Suppose you are teaching a child addition of decimal fractions, according to the constructivist model. In this context,

i) how would you access her readiness for this topic?

 ii) formulate three questions to draw out her thinking. 

iii) give two errors that this child may make while learning this process. How would you use these errors to her learning?

What is ‘egocentrism’? What did Martin Hughes think about Piaget’s views on egocentrism? What was the experiment which his understanding was based on?

Why do we need to develop the ability of estimating the outcome of arithmetic operations on fractions? Further, give a series of three activities to help a Class 4 child develop the ability to estimate the bigger of two fractions. Explain how the activities form a series.

Explain the following statements briefly. You should include appropriate examples in your explanations.

a) Exploring a mathematical concept is an on-going process.

b) Doing algebra is the essence of mathematical thinking.

c) A teacher should be a scaffold for her learners.

d) Developing spatial understanding is more than about learning some definitions and rules of geometry.

e) Gathering data is one tool for making sense of the world around.

Do you agree with each of the following statements? Give reasons for your answers. a) Mathematics is the study of numbers and calculations.

b) The decimal fraction 0.02 is greater than 0.1.

c) Children learn mainly by imitating adults.

d) Games can play an important role in the mathematics classroom.

e) Children in classes 1 and 2 can handle data.