GATE-IT-2004

Last Updated : 22 Jun, 2021

Please wait while the activity loads.
If this activity does not load, try refreshing your browser. Also, this page requires javascript. Please visit using a browser with javascript enabled.

If loading fails, click here to try again

Question 1

In a population of N families, 50% of the families have three children, 30% of the families have two children and the remaining families have one child. What is the probability that a randomly picked child belongs to a family with two children?

A	3/23
B	6/23
C	3/10
D	3/5

GATE-IT-2004 General Aptitude
Discuss it

Question 1 Explanation:

x- total families. Given:

50% -3 Children -> (5*x/10) * 3=(1*x/2)*3
30% -2 Children-> (3*x /10) * 2
Rear 20%- 1child -> (2*x/10)*1 =1*x/5

Probability = No of ways it can happen/Total Outcomes =( (3/10)*2 ) / ( (1/2)*3 + (3/10)*2 +1/5 ) = 6/23 So Answer is B

Question 2

In a class of 200 students, 125 students have taken Programming Language course, 85 students have taken Data Structures course, 65 students have taken Computer Organization course; 50 students have taken both Programming Language and Data Structures, 35 students have taken both Data Structures and Computer Organization; 30 students have taken both Data Structures and Computer Organization, 15 students have taken all the three courses.How many students have not taken any of the three courses?

A	15
B	20
C	25
D	35

GATE-IT-2004 General Aptitude
Discuss it

Question 2 Explanation:

P(AUBUC)=P(A)+P(B)+P(C)- P(A\capB)-P(A\capC)- P(B\capC)+P(A\capB\capC)

125 + 85 + 65- 50 - 35 - 30+15 =175

No of students not taking any courses-> 200−175=25 So C is the Answer.

Question 3

Let a(x, y), b(x, y,) and c(x, y) be three statements with variables x and y chosen from some universe. Consider the following statement:

(∃x)(∀y)[(a(x, y) ∧ b(x, y)) ∧ ¬c(x, y)] Which one of the following is its equivalent?

A	(∀x)(∃y)[(a(x, y) ∨ b(x, y)) → c(x, y)]
B	(∃x)(∀y)[(a(x, y) ∨ b(x, y)) ∧¬ c(x, y)]
C	¬ (∀x)(∃y)[(a(x, y) ∧ b(x, y)) → c(x, y)]
D	¬ (∀x)(∃y)[(a(x, y) ∨ b(x, y)) → c(x, y)]

GATE-IT-2004 Linear Algebra
Discuss it

Question 3 Explanation:

Choice (C) is = ¬ (∀x)(∃y)[(a(x, y) ∧ b(x, y)) → c(x, y)] = ¬ (∀x)(∃y)[ a∧ b → c ] = ¬ (∀x)(∃y)[ (ab)' + c] = ∃ x ∀ y[ (ab)' + c]' = ∃ x ∀ y[ abc' ] = ∃ x ∀ y[ a ∧ b ∧ c ¬c] Which is same as the given expression. (∃x)(∀y)[(a(x, y) ∧ b(x, y)) ∧ ¬c(x, y)]

Question 4

Let R₁ be a relation from A = {1, 3, 5, 7} to B = {2, 4, 6, 8} and R₂ be another relation from B to C = {1, 2, 3, 4} as defined below:

An element x in A is related to an element y in B (under R₁) if x + y is divisible by 3.
An element x in B is related to an element y in C (under R₂) if x + y is even but not divisible by 3.

Which is the composite relation R₁R₂ from A to C?

A	R1R2 = {(1, 2), (1, 4), (3, 3), (5, 4), (7, 3)}
B	R1R2 = {(1, 2), (1, 3), (3, 2), (5, 2), (7, 3)}
C	R1R2 = {(1, 2), (3, 2), (3, 4), (5, 4), (7, 2)}
D	R1R2 = {(3, 2), (3, 4), (5, 1), (5, 3), (7, 1)}

GATE-IT-2004 Set Theory & Algebra
Discuss it

Question 4 Explanation:

R1 is a relation from A = {1, 3, 5, 7} to B = {2, 4, 6, 8} . Under R1, an element x in A is related to an element y in B if x + y is divisible by 3.
Thus, R1 = {(1, 2), (1, 8), (3, 6), (5, 4), (7, 2), (7, 8)}
R2 is a relation from B = {2, 4, 6, 8} to C = {1, 2, 3, 4} Under R2, an element y in B is related to an element z in C if y + z is even but not divisible by 3.
Thus, R2 = {(2, 2), (4, 4), (6, 2), (6, 4), (8, 2)}
Then the composition of R1 with R2, denoted R2R1, is the relation from A to C defined by the following property: (x, z) $\epsilon$ R2R1 If and only if there is a y E B such that (x, y) $\epsilon$ R1 and (y, z) $\epsilon$ R2.
Thus, R1R2 = {(1, 2), (3, 2), (3, 4), (5, 4), (7, 2)}

Thus, option (C) is correct.

Please comment below if you find anything wrong in the above post.

Question 5

What is the maximum number of edges in an acyclic undirected graph with n vertices?

A	n-1
B	n
C	n + 1
D	2n-1

GATE-IT-2004 Top MCQs on Graph Data Strcuture with Answers
Discuss it

Question 5 Explanation:

n * (n - 1) / 2 when cyclic. But acyclic graph with the maximum number of edges is actually a spanning tree and therefore, correct answer is n-1 edges.

Question 6

What values of x, y and z satisfy the following system of linear equations?

$begin{bmatrix}1&2&3\ 1&3&4\ 2&2&3 end{bmatrix} begin{bmatrix}x\y\zend{bmatrix} = begin{bmatrix}6\8\12end{bmatrix}$

A	x=6, y=3, z=2
B	x=12, y=3, z=-4
C	x=6, y=6, z=-4
D	x=12, y=-3, z=0

GATE-IT-2004 Linear Algebra
Discuss it

Question 6 Explanation:

1 * x + 2 * y + 3 * z = 6

1 * x + 3 * y + 4 * z = 8

2 * x + 2 * y + 3 * z = 12

Put x =6 , y = 6 and z = -4

The above three equation are satisfied.

Question 7

Which one of the following regular expressions is NOT equivalent to the regular expression (a + b + c) *?

A	(a* + b* + c)
B	(abc)
C	((ab)* + c)
D	(ab + c)

GATE-IT-2004 Regular languages and finite automata
Discuss it

Question 7 Explanation:

C- (ab)* + c*)* will always give strings with "ab" together.Whereas (a+b+c)* would generate language where a,b,c may not be always together. A,B,D may generate same language as (a+b+c)* So, Answer is (C)

Question 8

What is the minimum number of NAND gates required to implement a 2-input EXCLUSIVE-OR function without using any other logic gate?

A	3
B	4
C	5
D	6

GATE-IT-2004 Digital Logic & Number representation Logic functions and Minimization
Discuss it

Question 8 Explanation:

Pic Courtesy: http://www.electronics-tutorials.ws/logic/logic_7.html Other way around: x XOR y = x’y+xy’ = x’y+xy’+xx’+yy’ = (x+y) (x’+y’) Using NAND gates F= (x+y)(xy)’ = x. (xy)’ + y. (xy)’ Taking compliment F’= ( x. (xy)’ + y. (xy)’ )’ = (x. (xy)’)’. (y. (xy)’) Compliment again F=( (x. (xy)’)’. (y. (xy)’) )’ So Answer is B

Question 9

Which one of the following statements is FALSE?

A	There exist context-free languages such that all the context-free grammars generating them are ambiguous
B	An unambiguous context free grammar always has a unique parse tree for each string of the language generated by it.
C	Both deterministic and non-deterministic pushdown automata always accept the same set of languages
D	A finite set of string from one alphabet is always a regular language.

GATE-IT-2004 Context free languages and Push-down automata
Discuss it

Question 9 Explanation:

A) For real-world programming languages, the reference CFG is often ambiguous, due to issues such as the dangling else problem. //Wikipedia

B) A string is ambiguous if it has two distinct parse trees;The grammar is unambiguous,if a string has distinct parse trees.

C) Deterministic pushdown automata can recognize all deterministic context-free languages while nondeterministic ones can recognize all context-free languages

Therefore it's FALSE

D)Properties of Regular Language:

The set of regular languages over an alphabet $\Sigma$ is closed under operations union, concatenation and Kleene star.
Finite languages are regular

So Answer is C

Question 10

What is the minimum size of ROM required to store the complete truth table of an 8-bit x 8-bit multiplier?

A	32 K x 16 bits
B	64 K x 16 bits
C	16 K x 32 bits
D	64 K x 32 bits

GATE-IT-2004 Computer Organization and Architecture CPU control design and Interfaces
Discuss it

Question 10 Explanation:

Input to ROM - 2 lines ,8 bit each. Possible combinations in ROM - (2^8)x(2^8) Size of truth table = (2^8)*(2^8)=2^16=64 KB Maximum output size = 16 bit So, Answer is B

There are 88 questions to complete.

1 2 3 4 5 6 7 8 9

My Personal Notes

A	(a* + b* + c)
B	(abc)
C	((ab)* + c)
D	(ab + c)

Table of Contents

GATE-IT-2004

GATE-IT-2004

GATE CS & IT 2024

Data Structures and Algorithms - Self Paced

Complete Interview Preparation - Self Paced