Discuss ethical and health perspectives of technology use in education.

Suppose you have to make a presentation on a topic "Securing Digital data and Protecting our privacy online" for secondary school students, mention what all points you will include in your presentation.

 With the help of suitable examples, discuss different tips for protection of software installed in the computer

 With the help of suitable examples, explain ICT use in inclusive classrooms.

How will you use ICT in teaching and assessment? Discuss by selecting a topic of your interest.

Define Open Educational Resource (OER). How are OERs created and shared?

What do you mean by interactivity in educational communication? Explain the different levels of interactivity with suitable examples.

Select a topic on which you would like to write a Self-Learning Material (SLM). Briefly write an SLM by clearly indicating the introductory (first) part, main (middle) part, and concluding (end) part.

 Discuss the pedagogical potential of audio and video programmes in the teaching-learning process.

 What do you mean by learning design? Explain it with a suitable example.

 Construct a field with 125 elements.  

Check whether or not  is a field.  

Find all the units of .  

Which of the following statements are true, and which are false? Give reasons for your answers.  
i) If k is a field, then so is .
ii) If R is an integral domain and I is an ideal of R, then .
iii) In a domain, every prime ideal is a maximal ideal.
iv) If R is a ring with zero divisors, and S is a subring of R, then S has zero divisors.
v) If R is a ring and  is of degree , then f(x) has exactly n roots in R.

Let S be a set, R a ring and f be a 1-1 mapping of S onto R. Define + and  on S by:


.
Show that  is a ring isomorphic to R.  
PART-C (MM: 20 Marks)
(Based on Block 4.)

Is , for any two ideals I and J of a ring R? Give reasons for your answer. 

For an ideal I of a commutative ring R, define
. Show that
i)  is an ideal of R.
ii) .
iii)  in some cases. 

 For an ideal I of a commutative ring R, define
. Show that
i)  is an ideal of R.
ii) .
iii)  in some cases. 

Which of the following statements are true, and which are false? Give reasons for your answers. 
i) For any ring R and .
ii) Every ring has at least two elements.
iii) If R is a ring with identity and I is an ideal of R, then the identity of R/I is the same as the identity of R.
iv) If  is a ring homomorphism, then it is a group homomorphism from (R, +) to (S, +).
v) If R is a ring, then any ring homomorphism from  into R is surjective.

 Use the Fundamental Theorem of Homomorphism for Groups to prove the following theorem, which is called the Zassenhaus (Butterfly) Lemma:
Let H and K be subgroups of a group G and H' and K' be normal subgroups of H and K, respectively. Then
i) 
ii) 

iii)   
The situation can be represented by the subgroup diagram below, which explains the name ‘butterfly’.

PART-B (MM: 30 Marks)
(Based on Block 3.)