GATE 2019 CS Computer Science and information technology

#### Show Answer With Best Explanation

Explanation:
SMTP: SMTP stands for Simple Mail Transfer Protocol and is a TCP/IP protocol used in `sending e-mail` . It’s a set of communication rules that allow software to send email over the Internet.

POP3(Post Office Protocol 3) and IMAP(Intractive Mail Access Protocol): POP3 and IMAP are two different protocols used to `access email`. POP3 and IMAP function very differently and each has its own advantages. POP3 is useful in checking emails from a computer that is in a specific location. IMAP is the better option when we need to check our emails from multiple locations, such as at work, from home, or on the road, using different computers.

MIME(Multipurpose Internet Mail Extensions): MIME is an Internet Standard that extends the format of e-mail to support-
• Text in character sets other than ASCII
• Non-Text Attachments.
• Message bodies with multiple parts

So, Option(IV) is correct.

#### Show Answer With Best Explanation

Explanation:
Fermat’s Little Theorem:
If p is a prime and a is an integer then
ap-1 ≡ 1 (mod p) , if p does not divide a
else
ap ≡ a (mod p)

Caculation:
351 mod 5
here, p=5, a=3 and p does not divide
≡ 34*12 +3 mod 5
≡ ((34)12 mod 5) * (33 mod 5)
≡ (112 mod 5) * (33 mod 5) {* 35-1 ≡ 1 mod 5 *}
≡ 27 mod 5
≡ 2

#### Show Answer With Best Explanation

Explanation:
Given,
IP addresses of M = 100.10.5.2
IP addresses of N = 100.10.5.5
IP addresses of P = 100.10.5.6

Logic to solve,
We will find Network Id by X-ORing of IP Address of Machine with Subnet Mask. Same Network Id of Machine belong to same Subnet.

`Machine M`:
100. 10 . 5 .0000 0010
255.255.255.1111 1100
——————————-
(100.10.5.0)

`Machine N`:
100. 10 . 5 .0000 0101
255.255.255.1111 1100
———————————
(100.10.5.4)

`Machine P`:
100. 10 . 5 .0000 0110
255.255.255.1111 1100
———————————-
(100.10.5.4)

Machine N and P belong to same subnet.

So, Option(II) is correct.

#### Show Answer With Best Explanation

Explanation:
Given,
n = 3007
ϕ(n) = 2880

Calculation,
Let p and q be two prime number such that n=p*q = 3007
ϕ(n) = ϕ(p*q) = ϕ(p)* ϕ(q) = (p-1)*(q-1) = 2880
=> pq -p-q-1 =2880
=> 3007-p-q-1 =2880
=> p+q =128 ————(1)
=> pq =3007 ————(2)
put value of q in eq(1)
=> p+(3007/p) =128
=> p2 -128p + 3007 =0

The prime factor of n greater than 50 is 97.