GATE CSE 2020: Revision Quiz 4 for GATE & PSU CS Exams

Question 1

Consider the following DFA

Which of the following two states are equivalent?

Question 2

Consider the following problems:
1. Membership problems for CFGs.
2. Finiteness problem for FSAs.
3. Ambiguity problem for CFGs.
4. Equivalence problem for FSAs.
Which one of the above problems is undecidable?

Question 3

Given that a language L_A= L1 U L2 , where L1 & L2 are two other languages. If L_A is known to be a regular language, then which of the following statements is necessarily TRUE?

Question 4

q1,q2,q3,q4 are different states & L is a language

a. q1 & q2 can never be equivalent
b. q1 & q2 may be equivalent
c. k's place does not matter for being L regular which is correct?

Question 5

Find the true statement from the following?

Question 6

Assume P represents the class of P-problems, NP represents the class of NP-problems and NPC for the class of NP-complete problems. Identify the correct relation from the following?

Question 7

Consider the regular expression: R=(ab|abb)*bbab

Which of the following string in not in the set denoted by R?

Question 8

Let A and B be infinite alphabets and let # be a symbol outside both A and B. Let f be a total functional from A* to B*. We say f is computable if there exists a Turning machine M which given an input x in A*, always halts with f(x) on its tape. Let L_f denote the language

Which of the following statements is true:

Question 9

What is the differentiation of 1/x ?

Question 10

The function, f(x)=2x³-3x²-36x+10, has a local maximum value at ‘x’ equals to.

Question 11

equals

Question 12

Consider the following statements regarding Eigen values :
S1 : Eigen values of A and A^-1 are same.
S2 : Eigen values of A and A^T are same.
S3 : If A is a singular matrix, then atleast one of its Eigen value is 0.
Which option is correct ?

Question 13

A fair six-sided dice is rolled twice. Assume six-sided dice is numbered as 0, 1, 2, 3, 4, 6. Given that the sum of values shown at first and second roll is 6, what is the probability that the value of the first rolled dice is less than or equal to the value of the second rolled dice?

Question 14

Consider a random variable X that takes values +1 and −1 with probability 0.5 each. The values of the cumulative distribution function F(x) at x = −1 and +1 are

Question 15

A point is randomly selected with uniform probability in the X–Y plane within the rectangle with corners at (0,0), (1,0), (1,2) and (0,2). If p is the length of the position vector of the point, the expected value of p² is