1
Numerical

### GATE CSE 2016 Set 2

A complete binary min-heap is made by including each integer in $[1,1023]$ exactly once. The depth of a node in the heap is the length of the path from the root of the heap to that node. Thus, the root is at depth $0.$ The maximum depth at which integer $9$ can appear is ___________.

2
Numerical

### GATE CSE 2016 Set 2

The given diagram shows the flowchart for a recursive function $A(n).$ Assume that all statements, except for the recursive calls, have $O(1)$ time complexity. If the worst case time complexity of this function is $O\left( {{n^\alpha }} \right),$ then the least possible value (accurate up to two decimal positions) of $\alpha$ is ____________ .

Correct answer is between 2.2 and 2.4
3
Numerical

### GATE CSE 2016 Set 2

Let ${A_1},{A_2},{A_3},$ and ${A_4}$ be four matrices of dimensions $10 \times 5,\,\,5 \times 20,\,\,20 \times 10,$ and $10 \times 5,\,$ respectively. The minimum number of scalar multiplications required to find the product ${A_1}{A_2}{A_3}{A_4}$ using the basic matrix multiplication method is ______________.

4

### GATE CSE 2016 Set 2

Match the following:

GROUP - 1 GROUP - 2
(P) Lexical analysis (i) Leftmost derivation
(Q) Top down parsing (ii) Type checking
(R) Semantic analysis (iii) Regular expressions
(S) Runtime environments (iv) Activation records

A
$P \leftrightarrow i,\,\,Q \leftrightarrow ii,\,\,R \leftrightarrow iv,\,\,S \leftrightarrow iii$
B
$P \leftrightarrow iii,\,\,Q \leftrightarrow i,\,\,R \leftrightarrow ii,\,\,S \leftrightarrow iv$
C
$P \leftrightarrow ii,\,\,Q \leftrightarrow iii,\,\,R \leftrightarrow i,\,\,S \leftrightarrow iv$
D
$P \leftrightarrow iv,\,\,Q \leftrightarrow i,\,\,R \leftrightarrow ii,\,\,S \leftrightarrow iii$

### Paper Analysis of GATE CSE 2016 Set 2

Subject NameTotal Questions
Algorithms5
Compiler Design3
Computer Networks6
Computer Organization6
Data Structures5
Database Management System4
Digital Logic3
Discrete Mathematics11
Operating Systems3
Theory of Computation6
General Aptitude10