Sudo GATE 2020 Mock I (27 December 2019)

Question 51

In a language in which operations are associated right-to-left instead of left-to-right (i.e., a+b+c = a+(b+c)), the value of the expression

7 - (16/(3+1)*2) - 4 

is ___________ .

• 3
• -5
• 7
• 9

Question 52

Which of the following option is false?

• If there are no SR conflicts in LR(1) then LALR(1) will never have SR conflicts.
• Recursive decent parser is a top-down parser.
• Removing left recursion and left factoring to suffice to convert a CFG to an LL(1) grammar.
• CLR can handle all deterministic context-free languages.

Question 53

Which of the following matrices has similar eigenvalues ?

• Only A and B
• Only B and C
• Only A and C
• None of these

Question 54

A computer responds to an interrupt request signal by pushing onto a full descending stack the contents of PC and the current PSW (program status word), assume that each one will need one word. It then reads a new PSW from memory from a location given by an interrupt address symbolized by IAD. The first address of the service program is taken from memory at location IAD+1. Note: TR (temporary register could be used). Consider the following statements: I. Sequence of micro-operations for the return from interrupt instruction:

SP ← SP-1
M[SP] ← PC
SP ← SP-1
M[SP] ← PSW
TR ← IAD
PSW ← M[TR]
TR ← TR + 1
PC ← M[TR]
Go to fetch phase. 

II. Sequence of micro-operations for the interrupt cycle:

PSW ← M[SP]
SP ← SP+1
PC ← M[SP]
SP ← SP+1

Which of the following option is correct?

• Only statement I is correct.
• Only statement II is correct.
• Both statement I and II are correct.
• Neither statement I nor II is correct.

Question 55

Assume that multiplying a matrix M₁ of dimension a×b with another matrix M₂ of dimension bxc requires abc scalar multiplications. Computing the product of n matrices M₁M₁M₃ ... M_n can be done by parenthesizing in different ways. Define M_iM_i+1 as an explicitly computed pair for a given parenthesization if they are directly multiplied. For example, in the matrix multiplication chain M₁M₂M₃M₄M₅M₆ using parenthesization (M₁(M₂M₃))(M₄(M₅M₆)), M₂M₃ and M₅M₆ are only explicitly computed pairs. Consider a matrix multiplication chain A₁A₂A₃A₄, where matrices A₁, A₂, A₃ and A₄ are of dimensions 5x40,40×6,6x20 and 20×5 respectively. In the parenthesization of A₁A₂A₃A₄ that minimizes the total number of scalar multiplications, the explicitly computed pairs is/are

• A₁A₂ and A₃A₄
• A₂A₃ only
• A₃A₄ only
• A₁A₂ and A₂A₃

Question 56

There 1,000 multicast groups are ongoing at the same time and choose their multicast group addresses at random. What is the probability that they interfere with each other ?

• 0.002
• 0.998
• 0.02
• 0.08

Question 57

Which of the following problems is decidable?

• I. Given a TM M and a string y, does M ever write the symbol # on its tape on input y?
• II. Given a context free grammar G over {a, b}, does G generate all the strings of the language {a, b}^*of length ≤ 381?
• III. Given a TM M, are there infinitely many TMs M′accepting the same recursive enumerable set A = L(M)?
• IV. Given a TM M and a string y, does M accept y?

• I and II
• II and III
• I, II and III
• II and IV

Question 58

Which of the following statement(s) is/are correct regarding IPv4 Header.

1. The maximum possible value of time to live (TTL) in IPv4 is 256.
2. The maximum value of fragment offset is 65,535.
3. The maximum number of IPv4 router address addresses that can be listed in the record route (RR) option field is 38.

• 1 and 2 only
• 1 and 3 only
• 2 and 3 only
• None of these.

Question 59

Consider the following statements regarding implementations of half-adder and half-subtractor:

1. Total 5 NAND gates are required to implement half adder and 5 NAND gates are required to implement half subtractor.
2. Total 5 NAND gates are required to implement half adder and 5 NOR gates are required to implement half subtractor.
3. Total 5 NOR gates are required to implement half adder and 5 NAND gates are required to implement half subtractor.
4. Total 5 NOR gates are required to implement half adder and 5 NOR gates are required to implement half subtractor.

• Only 1, 2 and 3 are correct
• Only 2 and 3 are correct
• Only 1 and 4 are correct
• All 1, 2, 3, and 4 are correct

Question 60

In an RSA Cryptosystem, Suppose n = 101*113, e1 = 8765, and e2 = 7653. Note: 101 and 113 are primes. Which of the following option is not correct ?

• Value of e1 as public key is not valid.
• Value of e2 as public key is not valid.
• Value of private key d is 9517.
• Decrypted message of cipher-text c = 3233 is 10101.