NPTEL Computational Number Theory and Algebra Assignment 1 Answer

Next Week Assignment Answers

CHECK HERE OTHERS NPTEL ASSIGNMENTS ANSWERS 

BELOW YOU CAN GET YOUR NPTEL Computational Number Theory and Algebra Assignment 1 Answer 2022? :

1 point

Which of the following pair of integers are coprime?

108, 45

1243,110

110,100

8,1

1 point

Which of the following equals gcd(108,48)?

gcd(48,1)

gcd(108,1)

gcd(48,12)

gcd(108,6)

ans – d

1 point

Which of the following is false?

nlogn=O(n2)nlog⁡n=O(n2)

n=o(n)n=o(n)

nlogn=Ω(n)nlog⁡n=Ω(n)

123456⋅n2=O(n2)123456⋅n2=O(n2)

ans –  d

1 point

Probabilistic algorithms are good?

In lectures, you learned about the class BPPBPP of randomized algorithms, which are efficient (i.e, run in time polynomial in the size of the input) but make errors with ‘low’ probability (less than 1/2). Here, you will learn that randomized algorithms are ‘good’ (as asked in self-assessment). One reason is that they are often very simple in comparison to the deterministic algorithms. The other reason is, although they make errors, they are as good as (or even better than) their deterministic counterparts in practice.

You saw an example of a randomized algorithm in Assignment-0 which finds an even integer from an array AA of 2n2n consecutive integers in just one query with probability 1/2 while the best deterministic algorithm needs at least n+1n+1 queries. Think about the situation when AA has 22 million entries (around n=220n=220 ). Let us run the algorithm log2nlog2⁡n times until we get the answer (i.e, just 2020 queries). What is the probability that the algorithm gets at least one even number in log2nlog2⁡n queries?

1−1n1−1n (around 0.99999990.9999999).

1n1n (around 0.00000010.0000001).

1313

1212

ans –  d

1 point

In lectures, you have learned about some mathematical objects: rings, fields and domains. Based on this answer the following question.

Let,

Mn(R)Mn(R) be the set of all n×nn×n matrices over reals with matrix addition and multiplication operations,

GLn(R)GLn(R) be the set of all n×nn×n invertible matrices over reals with only matrix multiplication operation

and ZZ be the ring of all numbers of the form a+b−5−−−√a+b−5, where aa and bb are integers.

Which of the following statements is/are true?

1. Mn(R)Mn(R)is not a domain as it has zero-divisors.
2. GLn(R)GLn(R)forms a group under matrix multiplication.
3. Every number in ZZ has a unique factorisation.

Only 1.

Only 2.

Only 1 and 2.

All of 1, 2 and 3.

ans –  d

1 point

You learned in lectures that an isomorphism is a one to one map that preserves the structure of two sets. Let ZZ be the set of integers and EE be the set of even integers. Which of the following is/are true?

1. The map φ:Z→Eφ:Z→Edefined as φ(n)=2nφ(n)=2nis an isomorphism.
2. Any infinite cyclic group is isomorphic to (Z,+)(Z,+).

Only 1.

Only 2.

Both 1 and 2.

None of 1 and 2.

ans –  d

Yhaa You have done it but next? if YOU Want to your Others NPTEL Computational Number Theory and Algebra Assignment 1 Answer Then Follow US HEREand Join Telegram.