__TEST DATE: 20-12-2018__
1.
In mathematical logic, which of the following
are statements?

(i) There
will be snow in January.

(ii) What is
the time now?

(iii) Today
is Sunday.

(iv) You
must study Discrete mathematics

Choose the
correct answer from the code given below:

**Code:**

(1) i and
iii

(2) i and ii

(3) ii and
iv

(4) iii and
iv

Answer: 1

2. Match
the List-I with List-II and choose the correct answer from the code given
below:

**List I List II**

(a) Equivalence (i) p⇒q

(b) Contrapositive (ii) p⇒q : q⇒p

(c) Converse (iii) p⇒q : ∼q⇒∼p

(d)
Implication (iv) p⇔q

**Code:**

(1) (a)-(i),
(b)-(ii), (c)-(iii), (d)-(iv)

(2) (a)-(ii),
(b)-(i), (c)-(iii), (d)-(iv)

(3) (a)-(iii),
(b)-(iv), (c)-(ii), (d)-(i)

(4) (a)-(iv),
(b)-(iii), (c)-(ii), (d)-(i)

Answer: 4

3. A
box contains six red balls and four green balls. Four balls are selected at
random from the box. What is the probability that two of the selected balls
will be red and two will be green?

(1)

^{1}/_{14}
(2)

^{3}/_{7}
(3)

^{1}/_{35}
(4)

^{1}/_{9}
Answer: 2

4. A
survey has been conducted on methods of commuter travel. Each respondent was
asked to check Bus, Train and Automobile as a major method of travelling to
work. More than one answer was permitted. The results reported were as follows:

Bus 30
people; Train 35 people; Automobile 100 people; Bus and Train 15 people; Bus
and Automobile 15 people; Train and Automobile 20 people; and all the three
methods 5 people. How many people completed the survey form?

(1) 120

(2) 165

(3) 160

(4) 115

Answer: 1

5. Which
of the following statements are true?

(i) Every
logic network is equivalent to one using just NAND gates or just NOR gates.

(ii) Boolean
expressions and logic networks correspond to labelled acyclic diagraphs.

(iii) No two
Boolean algebras with n atoms are isomorphic.

(iv) Non-zero
elements of finite Boolean algebras are not uniquely expressible as joins of
atoms.

Choose the
correct answer from the code given below:

**Code:**

(1) i and iv
only

(2) i, ii
and iii only

(3) i and ii
only

(4) ii, iii,
and iv only

Answer: 3

6. The
relation ≤ and > on a boolean algebra are defined as:

x≤y
if and only if x∨y=y

x<y
means x≤y but x≠y

x≥y
means y≤x and

x>y
means y<x

Considering
the above definitions, which of the following is

**not**true in the boolean algebra?
(i) If x≤y
and y≤z, then x≤z

(ii) If x≤y
and y≤x, then x=y

(iii) If
x<y and y<z, then x≤y

(iv) If
x<y and y<z, then x<y

Choose the
correct answer from the code given below:

**Code:**

(1) (i) and (ii)
only

(2) (ii) and
(iii) only

(3) (iii)
only

(4) (iv)
only

Answer: 3

7. The
boolean expression A’⋅B
+ A⋅B’ + A⋅B is equivalent to

(1) A’⋅B

(2) (A + B)’

(3) A⋅B

(4) A + B

Answer: 4

8. In
PERT/CPM, the merge event represents .............. of two or more events.

(1) completion

(2) beginning

(3) splitting

(4) joining

Answer: 1

9. Use
Dual Simplex Method to solve the following problem:

Maximize
z = −2x

_{1 }− 3x_{2}
subject
to:

x

_{1 }+ x_{2 }≥ 2
2x

_{1 }+ x_{2 }≤ 10
x

_{1 }+ x_{2 }≤ 8
x

_{1}, x_{2 }≥ 0
(1) x

_{1}= 2, x_{2}= 0, and z = −4
(2) x

_{1}= 2, x_{2}= 6, and z = −22
(3) x

_{1}= 0, x_{2}= 2, and z = −6
(4) x

_{1}= 6, x_{2}= 2, and z = −18
Answer: 1

10. In
computers, subtraction is generally carried out by

(1) 9’s
complement

(2) 1’s
complement

(3) 10’s
complement

(4) 2’s
complement

Answer: 4

11. Consider
the following boolean equations:

(i) wx + w(x+y)
+ x(x+y) = x + wy

(ii) (wx’(y+xz’)
+ w’x’)y = x’y

What can you
say about the above equations?

(1) (i) is
true and (ii) is false

(2) (i) is
false and (ii) is true

(3) Both (i)
and (ii) are true

(4) Both (i)
and (ii) are false

Answer: 3

12. Consider
the graph shown below:

Use
Kruskal’s algorithm to find the minimum spanning tree of the graph. The weight
of this minimum spanning tree is

(1) 17

(2) 14

(3) 16

(4) 13

Answer: 3

13. Consider
the following statements:

(i) Auto
increment addressing mode is useful in creating self-relocating code.

(ii) If auto
increment addressing mode is included in an instruction set architecture, then
an additional ALU is required for effective address calculation.

(iii) In
auto incrementing addressing mode, the amount of increment depends on the size
of the data item accessed.

Which of the
above statements is/are true?

Choose the
correct answer from the code given below:

**Code:**

(1) (i) and
(ii) only

(2) (ii) and
(iii) only

(3) (iii)
only

(4) (ii)
only

Answer: 3

14. A
computer uses a memory unit with 256 K words of 32 bits each. A binary instruction
code is stored in one word of memory. The instruction has four parts: an
indirect bit, an operation code and a register code part to specify one of 64
registers and an address part. How many bits are there in the operation code,
the register code part and the address part?

(1) 7,6,18

(2) 6,7,18

(3) 7,7,18

(4) 18,7,7

Answer: 1

15. Consider
the following x86 – assembly language instructions:

MOV
AL, 153

NEG
AL

The contents
of the destination register AL (in 8-bit binary notation), the status of Carry
Flag (CF) and Sign Flag (SF) after the execution of above instructions, are

(1) AL = 0110
0110; CF = 0;SF = 0

(2) AL = 0110
0111; CF = 0;SF = 1

(3) AL = 0110
0110; CF = 1;SF = 1

(4) AL = 0110
0111; CF = 1;SF = 0

Answer: 4

16. The
decimal floating point number −40.1 represented using IEEE−754 32-bit
representation and written in hexadecimal form is

(1) 0xC2206666

(2) 0xC2206000

(3) 0xC2006666

(4) 0xC2006000

Answer: 1

17. Find
the Boolean expression for the logic circuit shown below:

(1-NAND gate,
2-NOR gate, 3-NOR gate)

(1) AB’

(2) A’B

(3) AB

(4) A’B’

Answer: 3

18. Consider
a disk pack with 32 surfaces, 64 tracks and 512 sectors per pack. 256 bytes of
data are stored in a bit serial manner in a sector. The number of bits required
to specify a particular sector in the disk is

(1) 18

(2) 19

(3) 20

(4) 22

Answer: 3

19. Consider
a system with 2 level cache. Access times of Level 1 cache, Level 2 cache and
main memory are 0.5 ns, 5 ns and 100 ns respectively. The hit rates of Level 1
and Level 2 caches are 0.7 and 0.8 respectively. What is the average access
time of the system ignoring the search time within the cache?

(1) 35.20 ns

(1) 7.55 ns

(1) 20.75 ns

(1) 24.35 ns

Answer: 2

20. If
a graph (G) has no loops or parallel edges, and if the number of vertices (n)
in the graph is n≥3, then graph G is Hamiltonian if

(i) deg(v) ≥

^{n}/_{3}for each vertex v
(ii) deg(v) +
deg(w) ≥ n whenever v and w are not connected by an edge

(iii) E(G) ≥

^{1}/_{3}(n−1)(n−2)+2
Choose the
correct answer from the code given below:

**Code:**

(1) (i) and
(iii) only

(2) (ii)
only

(3) (ii) and
(iii) only

(4) (iii)
only

Answer: 2

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