GATE CSE 2019

Question 1
A certain processor uses a fully associative cache of size 16 kB, The cache block size is 16 bytes. Assume that the main memory is byte addressable and uses a 32-bit address. How many bits are required for the Tag and the Index fields respectively in the addresses generated by the processor?
A
24 bits and 0 bits
B
28 bits and 4 bits
C
24 bits and 4 bits
D
28 bits and 0 bits
Computer Organization   Cache Memory
Question 2
The chip select logic for a certain DRAM chip in a memory system design is shown below. Assume that the memory system has 16 address lines denoted by A_{15} \; to \; A_0. What is the range of address (in hexadecimal) of the memory system that can get enabled by the chip select (CS) signal?
A
C800 to CFFF
B
CA00 to CAFF
C
C800 to C8FF
D
DA00 to DFFF
Computer Organization   Memory Chip Design
Question 3
Which one of the following kinds of derivation is used by LR parsers?
A
Leftmost
B
Leftmost in reverse
C
Rightmost
D
Rightmost in reverse
Compiler Design   Parsing
Question 4
In 16-bit 2's complement representation, the decimal number -28 is:
A
1111 1111 0001 1100
B
0000 0000 1110 0100
C
1111 1111 1110 0100
D
1000 0000 1110 0100
Digital Logic   Number System
Question 5
Let U=\{1,2,,...n\}. Let A=\{(x,X)|x\in X,X\subseteq U\}. Consider the following two statements on |A|.

I. |A|=n2^{n-1}
II. |A|=\sum_{k=1}^{n}k\binom{n}{k}

Which of the above statements is/are TRUE?
A
Only I
B
Only II
C
Both I and II
D
Neither I nor II
Discrete Mathematics   Set Theory
Question 6
Which one of the following is NOT a valid identity?
A
(x\oplus y)\oplus z=x\oplus (y\oplus z)
B
(x+ y)\oplus z=x\oplus (y+z)
C
x\oplus y=x+y, \; if \; xy=0
D
x\oplus y=(xy+x'y')'
Digital Logic   Boolean Algebra
Question 7
If L is a regular language over \Sigma =\{a,b\}, which one of the following languages is NOT regular ?
A
L\cdot L^R=\{xy|x \in L,y^R \in L\}
B
\{ww^R|w \in L\}
C
Prifix(L)={x \in \Sigma ^*|\exists y \in \Sigma ^* such that xy \in L}
D
Suffix(L)={y \in \Sigma ^*|\exists x \in \Sigma ^* such that xy \in L}
Theory of Computation   Regular Language
Question 8
Consider Z = X - Y where X, Y and Z are all in sign-magnitude form. X and Y are each represented in n bits. To avoid overflow, the representation of Z would require a minimum of:
A
n bits
B
n-1 bits
C
n+1 bits
D
n+2 bits
Digital Logic   Number System
Question 9
Let X be a square matrix. Consider the following two statements on X.

I. X is invertible
II. Determinant of X is non-zero

Which one of the following is TRUE?
A
I implies II; II does not imply I
B
II implies I; I does not imply II
C
I does not imply II; II does not imply I
D
I and II are equivalent statements
Engineering Mathematics   Linear Algebra
Question 10
Let G be an arbitrary group. Consider the following relations on G:

R1: \forall a,b \in G, aR_1b if and only if \exists g \in G such that a=g^{-1}bg
R2: \forall a,b \in G, aR_2b if and only if a=b^{-1}

Which of the above is/are equivalence relation/relations?
A
R1 and R2
B
R1 only
C
R2 only
D
Neither R1 nor R2
Discrete Mathematics   Relation
There are 10 questions to complete.

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