# 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 1 Explanation:
 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 2 Explanation:
 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 3 Explanation:
 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 4 Explanation:
 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 5 Explanation:
 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 6 Explanation:
 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 7 Explanation:
 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 8 Explanation:
 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 9 Explanation:
 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
Question 10 Explanation:
There are 10 questions to complete.