CS and IT Gate 2025 Set-1 Questions with Answer

Ques 27 GATE 2025 SET-1

Consider a relational schema team(name, city, owner), with functional dependencies {name→city, name→owner}.
The relation team is decomposed into two relations, t1(name, city) and t2(name, owner). Which of the following statement(s) is/are TRUE?

The relation team is NOT in BCNF.

The relations t1 and t2 are in BCNF.

The decomposition constitutes a lossless join.

The relation team is NOT in 3NF.

(a) is the correct answer.

Ques 28 GATE 2025 SET-1

Consider the following database tables of a sports league.

An instance of the table and an SQL query are given.

The value returned by the given SQL query is ______ (Answer in integer)

(26) is the correct answer.

Ques 29 GATE 2025 SET-1

Let X be a 3-variable Boolean function that produces output as '1' when at least two of the input variables are '1'. Which of the following statement(s) is/are CORRECT, where a, b, c, d, e are Boolean variables?

X(a,b,X(c,d,e))=X(X(a,b,c),d,e)

X(a,b,X(a,b,c))=X(a,b,c)

X(a,b,X(a,c,d))=(X(a,b,a) AND X(c,d,c))

X(a,b,c)=X(a,X(a,b,c),X(a,c,c))

(b) is the correct answer.

Ques 30 GATE 2025 SET-1

Consider the following four variable Boolean function in sum-of-product form
F(b₃,b₂,b₁,b₀)=Σ(0,2,4,8,10,11,12)
where the value of the function is computed by considering b₃b₂b₁b₀ as a 4-bit binary number, where b₃ denotes the most significant bit and b₀ denotes the least significant bit. Note that there are no don't care terms. Which ONE of the following options is the CORRECT minimized Boolean expression for F?

b̅₁b̅₀+b̅₂b̅₀+b₁b̅₂b₃

b̅₁b̅₀+b̅₂b̅₀

b̅₂b̅₀+b₁b₂b₃

b̅₀b̅₂+b̅₃

(a) is the correct answer.

Ques 31 GATE 2025 SET-1

Consider a finite state machine (FSM) with one input X and one output f. represented by the given state transition table. The minimum number of states required to realize this FSM is ______ (Answer in integer)

Present state	Next state		Output f
	X=0	X=1	X=0	X=1
A	F	B	0	0
B	D	C	0	0
C	E	F	0	0
D	G	A	1	0
E	D	C	0	0
F	F	B	1	1
G	H	G	1	0
H	A	G	1	0

(5) is the correct answer.

Ques 32 GATE 2025 SET-1

Consider the given sequential circuit designed using D-Flip-flops. The circuit is initialized with some value (initial state). The number of distinct states the circuit will go through before returning back to the initial state is ______ (Answer in integer)

(4) is the correct answer.

Ques 33 GATE 2025 SET-1

g(.) is a function from A to B, f(.) is a function from B to C, and their composition defined as f(g(.)) is a mapping from A to C.
If f(.) and f(g(.)) are onto (surjective) functions, which ONE of the following is TRUE about the function g(.)?

g(.) must be an onto (surjective) function.

g(.) must be a one-to-one (injective) function.

g(.) must be a bijective function, that is, both one-to-one and onto.

g(.) is not required to be a one-to-one or onto function.

(a) is the correct answer.

Ques 34 GATE 2025 SET-1

Let S be the set of all ternary strings defined over the alphabet {a, b, c}. Consider all strings in S that contain at least one occurrence of two consecutive symbols, that is, "aa", "bb" or "cc". The number of such strings of length 5 that are possible is ______ (Answer in integer)

(153) is the correct answer.

Ques 35 GATE 2025 SET-1

Which of the following predicate logic formulae/formula is/are CORRECT representation(s) of the statement: "Everyone has exactly one mother"?
The meanings of the predicates used are:
mother(y, x): y is the mother of x
noteq(x, y): x and y are not equal

∀x∃y∃z(mother(y,x)&land;¬mother(z,x))

∀x∃y[mother(y,x)&land;∀z(noteq(z,y)→¬mother(z,x))]

∀x∀y[mother(y,x)→∃z(mother(z,x)&land;¬noteq(z,y))]

∀x∃y[mother(y,x)&land;¬∃z(noteq(z,y)&land;mother(z,x))]

(b) is the correct answer.

Ques 36 GATE 2025 SET-1

A={0,1,2,3,...} is the set of non-negative integers. Let F be the set of functions from A to itself. For any two functions, f₁, f₂∈F we define
(f₁⊙f₂)(n)=f₁(n)+f₂(n)
for every number n in A. Which of the following is/are CORRECT about the mathematical structure (F, ⊙)?

(F,⊙) is an Abelian group.

(F, ) is an Abelian monoid.

(F,⊙) is a non-Abelian group.

(F, ) is a non-Abelian monoid.

(a) is the correct answer.

Ques 37 GATE 2025 SET-1

Consider the given system of linear equations for variables x and y, where k is a real-valued constant. Which of the following option(s) is/are CORRECT?
x+ky=1
kx+y=-1

There is exactly one value of k for which the above system of equations has no solution.

There exist an infinite number of values of k for which the system of equations has no solution.

There exists exactly one value of k for which the system of equations has exactly one solution.

There exists exactly one value of k for which the system of equations has an infinite number of solutions.

(a) is the correct answer.

Ques 38 GATE 2025 SET-1

Consider the given function f(x)

If the function is differentiable everywhere, the value of b must be ______ (rounded off to one decimal place)

(2.0) is the correct answer.

Ques 39 GATE 2025 SET-1

Let A be a 2×2 matrix as given.

What are the eigenvalues of the matrix A¹³ ?

1,-1

2√2, -2√2

4√2, 4√2

64√2, -64√2

(d) is the correct answer.

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