Questions and answers for exam Preparation

MCQs

Total Questions : 65 | Page 5 of 7 pages

A binary operation `oplus` on a set of integers is defined as `x``oplus` `y` = `x^2` + `y^2`. Which one of the
following statements is `TRUE` about`oplus` ?

Commutative but not associative
Both commutative and associative
Associative but not commutative
Neither commutative nor associative

Discuss Question

Answer: Option A. -> Commutative but not associative

`x``oplus` `y` = `x^2` + `y^2` = `y^2` + `x^2` = `y``oplus` `x`

`:.` commutative

Not associative, since, for example

( 1`oplus` 2 ) `oplus` 3 `ne` 1 `oplus` ( 2`oplus` 3 )

Question 42.

1 `x` `x^2`

Which one of the following does `NOT` equal 1 `y` `y^2` ?

1 `z` `z^2`

1 `x`(`x` + 1) `x` + 1; 1 y(y + 1) y + 1; 1 z(z + 1) z + 1;
1 x + 1 `x^2` + 1; 1 y + 1 `y^2` + 1; 1 z + 1 `z^2` + 1;
0 x - y `x^2` - `y^2`; 0 y - z `y^2` - `z^2`; 1 z `z^2`
2 x + y `x^2` + `y^2`; 2 y + z `y^2` + `z^2`; 1 z `z^2`

Discuss Question

Answer: Option A. -> 1 `x`(`x` + 1) `x` + 1; 1 y(y + 1) y + 1; 1 z(z + 1) z + 1;

If matrix B is obtained from matrix A by replacing the `1^(th)` row by itself plus k times

the `m^(th)` row, for1 `ne` m then det(B)=det(A). With this property given matrix is

equal to the matrices
given in options (B),(C) and (D).

Question 43.

Suppose p is number of cars per minute passing through a certain road junction between 5
PM and 6PM, and p has a Poisson distribution with mean 3. What is the probability of
observing fewer than 3 cars during any given minute in this interval?

8 /(2`e^3`)
9 /(2`e^3`)
17 /(2`e^3`)
26 /(2`e^3`)

Discuss Question

Answer: Option C. -> 17 /(2`e^3`)

P(p < 3) = P(p = 0) +P(p = 1) + P(p = 2)

=`(e^(-lambda) lambda^0)/(0!)` + `(e^(-lambda) lambda^1)/(1!)` + `(e^(-lambda) lambda^2)/(2!)` (where `lambda` = 3)

= `e^(-3)` + `e^(-3)` x 3 + `(e^(-3) xx 9)/2`

= `e^(-3)` `(1 + 3 +9/2)` = `17/(2e^3)`

Question 44.

The smallest integer than can be represented by an 8 - bit number in 2's complement form is

-256
-128
-127
0

Discuss Question

Answer: Option B. -> -128

`-` `2^(8 - 1)` = -128 . Range is -`2^((n - 1))` to + `2^((n - 1))` - 1

Question 45.

In the following truth table, V = 1 if and only if the input is valid.

Inputs Outputs

`D_0` `D_1` `D_2` `D_3` `X_0` `X_1` V

0 0 0 0 X X 0

1 0 0 0 0 0 1

X 1 0 0 0 1 1

X X 1 0 1 0 1

X X X 1 1 1 1

What function does the truth table represent?

Priority encoder
Decoder
Multiplexer
Demultiplexer

Discuss Question

Answer: Option A. -> Priority encoder

4 to 2 priority encoder.

Question 46.

Which one of the following is the tightest upper bound that represents the number of swaps
required to sort n numbers using selection sort?

O(log n)
O(n)
O(n log n)
O(`n^2`)

Discuss Question

Answer: Option B. -> O(n)

The maximum number of swaps that takes place in selection sort on n numbers is n

Question 47.

Consider the languages `L_1` = `Phi` and `L_2` = {a} . Which one of the following represents `L_1``L_2`*`U``L_1`* = ?

{`in`}
`Phi`
a*
{`epsi`, a}

Discuss Question

Answer: Option A. -> {`in`}

Concatenation of empty language with any language will give the empty language and `L_1`* = `Phi`* = `in` . Hence `L_1``L_2`*`U``L_1`* = {`in` }

Question 48.

What is the maximum number of reduce moves that can be taken by a

bottom-up parser for a
grammar with no epsilon- and unit-production

(i.e., of type A and A a `rightarrow` `in` `rightarrow` ) to parse a
string with n tokens?

n/2
n - 1
2n - 1
`2^n`

Discuss Question

Answer: Option B. -> n - 1

To have maximum number of reduce moves, all the productions will be of the typeA`rightarrow` `alpha` `beta`

(where `alpha` and `beta` could be terminals or non-terminals). Consider the following illustration
then:

Input String :`a_1``a_2``a_3`........`a_(n - 2)` `a_(n - 1)` `a_n`

`uparrow`

`a_1``a_2``a_3`........`a_(n - 2)` A

`uparrow`

`a_1``a_2``a_3`................A n - 1 moves

`.`

`a_1` `a_2`

Question 49.

A scheduling algorithm assigns priority proportional to the waiting time of a process. Every

process starts with priority zero(the lowest priority). The scheduler re-evaluates the process

priorities every T time units and decides the next process to schedule. Which one of the

following is TRUE if the processes have no I/O operations and all arrive at time zero?

This algorithm is equivalent to the first-come-first-serve algorithm
This algorithm is equivalent to the round-robin algorithm
This algorithm is equivalent to the shortest-job-first algorithm
This algorithm is equivalent to the shortest-remaining-time-first algorithm

Discuss Question

Answer: Option B. -> This algorithm is equivalent to the round-robin algorithm

The given scheduling definition takes two parameters, one is dynamically assigned

processpriority and the other is 'T' time unit to re-evaluate the process priorities.

This dynamically assigned priority will be deciding processes order in ready queue

of round robin algorithm whose time quantum is same as â€˜Tâ€™ time units. As all the

processes are arriving at the same time, they will be given same priority but soon

after first 'T` time burst
remaining processes will get higher priorities

Question 50.

Which one of the following is the tightest upper bound that represents the time complexity of
inserting an object into a binary search tree of n nodes?