CS and IT GATE 2025 SET-2 Questions with Answer

Ques 27 Databases

Consider the following relational schema along with all the functional dependencies that hold on them.
R1(A,B,C,D,E):{D→E,EA→B,EB→C}
R2(A,B,C,D):{A→D,A→B,C→A}
Which of the following statement(s) is/are TRUE?

R1 is in 3NF

R2 is in 3NF

R1 is NOT in 3NF

R2 is NOT in 3NF

Ques 28 Databases

Consider the database transactions T1 and T2, and data items X and Y. Which of the schedule(s) is/are conflict serializable?

R1(X), W2(X), W1(Y), W2(Y), R1(X), W1(X), COMMIT(T2), COMMIT(T1)

W2(X) R1(X) W2(Y) W1(Y) R1(X) COMMIT(T2) W1(X) COMMIT(T1)

R1(X) W2(X) W1(Y) W2(Y) R1(X) W1(X) COMMIT(T1) COMMIT(T2)

W2(X) R1(X) W1(Y) W2(Y) R1(X) COMMIT(T2) W1(X) COMMIT(T1)

Ques 29 Databases

Consider the following relational schema:
Students (rollno: integer, name: string, age: integer, cgpa: real)
Courses (courseno: integer, cname: string, credits: integer)
Enrolled (rollno: integer, courseno: integer, grade: string)
Which of the following options is/are correct SQL query/queries to retrieve the names of the students enrolled in course number (i.e., courseno) 1470?

SELECT S.name FROM Students S WHERE EXISTS (SELECT * FROM Enrolled E WHERE E.courseno =1470 AND E.rollno = S.rollno);

SELECT S.name FROM Students S WHERE SIZEOF (SELECT * FROM Enrolled E WHERE E.courseno =1470 AND E.rollno = S.rollno) > 0;

SELECT S.name FROM Students S WHERE 0 < (SELECT COUNT(*) FROM Enrolled E WHERE E.courseno =1470 AND E.rollno = S.rollno);

SELECT S.name FROM Students S NATURAL JOIN Enrolled E WHERE E.Courseno =1470;

Ques 30 Databases

In a B⁺ tree where each node can hold at most four key values, a root to leaf path consists of the following nodes: A=(49,77,83,-), B=(7,19,33,44), C=(20*,22*,25*,26*)
*-marked keys signify that these are data entries in a leaf. Assume that a pointer between keys k₁ and k₂ points to a subtree containing keys in [k₁,k₂), and that when a leaf is created, the smallest key in it is copied up into its parent.
The record with key value 23 is inserted into the B⁺ tree.
The smallest key value in the parent of the leaf that contains 25* is ______ (Answer in integer)

Ques 31 Digital Logic

Consider the following logic circuit diagram.

Which is/are the CORRECT option(s) for the output function F?

X Y̅

X̅ + Y̅ + X Y̅

X̅ Y̅ + X̅ + X Y̅

X + Y̅

Ques 32 Digital Logic

In a 4-bit ripple counter, if the period of the waveform at the last flip-flop is 64 microseconds, then the frequency of the ripple counter in kHz is ______ (Answer in integer)

Ques 33 Digital Logic

Given the following Karnaugh Map for a Boolean function F(w,x,y,z):

Which one or more of the following Boolean expression(s) represent(s) F?

w̅x̅y̅z̅+wx̅y̅z̅+w̅x̅yz̅+wx̅yz̅+xz

w̅x̅y̅z̅+w̅x̅yz̅+wx̅yz+xz

w̅x̅y̅z̅+wx̅y̅z̅+wx̅y̅z+xz

x̅z̅+xz

Ques 34 Digital Logic

Which of the following Boolean algebraic equation(s) is/are CORRECT?

A̅BC+A B̅C̅+A̅B̅C̅+A B̅C+ABC=BC+B̅C̅+A̅B̅

AB+A̅C+BC=AB+A̅C

(A+C)(A̅+B)=AB+A̅C

(A+B̅+D̅)(C+D)(A̅+C+D)(A+B+D̅)=A̅D+C̅D̅

Ques 35 Discrete Mathematics

Let P(x) be an arbitrary predicate over the domain of natural numbers.
Which ONE of the following statements is TRUE?

(P(0)&land;(∀x[P(x)⇒P(x+1)]))⇒(∀x P(x))

(P(0)&land;(∀x[P(x)⇒P(x-1)]))⇒(∀x P(x))

(P(1000)&land;(∀x[P(x)⇒P(x-1)]))⇒(∀x P(x))

(P(1000)&land;(∀x[P(x)⇒P(x+1)]))⇒(∀x P(x))

Ques 36 Engineering Mathematics

If then which ONE of the following is A⁸?

Ques 37 Engineering Mathematics

The value of x such that x>1 satisfying the equation ∫₁^xt ln t dt=1/4 is

√e

e²

e-1

Ques 38 Engineering Mathematics

Let L, M, and N be non-singular matrices of order 3 satisfying the equations
L²=L^-1, M=L⁸ and N=L².
Which ONE of the following is the value of the determinant of (M-N)?

Ques 39 Engineering Mathematics

Consider a system of linear equations PX=Q where P∈ℜ^3×3 and Q∈ℜ^3×1. Suppose P has an LU decomposition, P=LU where

Which of the following statement(s) is/are TRUE?

The system PX=Q can be solved by first solving LY=Q and then UX=Y

If P is invertible, then both L and U are invertible.

If P is singular, then at least one of the diagonal elements of U is zero.

If P is symmetric, then both L and U are symmetric.

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CS and IT GATE 2025 SET-2 Questions with Answer