1
MCQ (Single Correct Answer)

### GATE CSE 2016 Set 2

Consider the system, each consisting of m linear equations in $n$ variables.
$I.$ $\,\,\,$ If $m < n,$ then all such system have a solution
$II.$ $\,\,\,$ If $m > n,$ then none of these systems has a solution
$III.$ $\,\,\,$ If $m = n,$ then there exists a system which has a solution

Which one of the following is CORRECT?

A
$I$ , $II$ and $III$ are true
B
Only $II$ and $III$ are true
C
Only $III$ is true
D
None of them is true
2
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 _________.

Correct Answer is 1500
3
Numerical

### GATE CSE 2016 Set 2

Suppose that a shop has an equal number of LED bulbs of two different types. The probability of an LED bulb lasting more than $100$ hours given that it is of Type $1$ is $0.7,$ and given that it is of Type $2$ is $0.4.$ The probability that an LED bulb chosen uniformly at random lasts more than $100$ hours is _________.

Correct Answer is 0.55
4
Numerical

### GATE CSE 2016 Set 2

Consider the following expressions:
$\,\,\,\,\,\,\,\,\,\,\,\,\,$ $(i)$ $\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$ false
$\,\,\,\,\,\,\,\,\,\,\,\,$ $(ii)$ $\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$ $Q$
$\,\,\,\,\,\,\,\,\,\,\,$ $(iii)$ $\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$ true
$\,\,\,\,\,\,\,\,\,\,\,\,$ $(iv)$ $\,\,\,\,\,\,\,\,\,\,\,$ $P∨Q$
$\,\,\,\,\,\,\,\,\,\,\,\,\,$ $(v)$ $\,\,\,\,\,\,\,\,\,\,\,\,$ $\neg QVP$

The number of expressions given above that are logically implied by $P \wedge \left( {P \Rightarrow Q} \right)$) is _____________.

Correct Answer is 4

### 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

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