Engineering-Mathematics |Gate-2020| Previous Year Questions| Set-1

Set-15 GATE-2006 Engineering-Mathematics

Engineering-Mathematics |Gate-2020|

1. Let G be a group of 35 elements. Then the largest possible size of a subgroup of G other than G itself is ______. [GATE -2020]

a. 7
b. 8
c. 9
d. 10

Answer : a)


2. Let R be the set of all binary relations on the set {1,2,3}. Suppose a relation is chosen from R at random. The probability that the chosen relation is reflexive (round off to 3 decimal places) is _____. [GATE -2020]

a. 0.129
b. 0.126
c. 0.127
d. 0.125

Answer : d)


3. Consider the functions

I . e-x
II . x2 –sin x
III . √ x3 +1

Which of the above functions is/are increasing everywhere in [0,1]? [GATE -2020]

a. I and III only
b. III only
c. II only
d. I and III only

Answer : b)


4. For n > 2, let a {0,1}n be a non-zero vector. Suppose that x is chosen uniformly at random from {0,1}n. Then, the probability that

 is an odd number  is ____. [GATE -2020]

a. 0.5
b. 0.6
c. 0.7
d. 0.8

Answer : a)
Engineering-Mathematics |Gate-2020|


5. Graph G is obtained by adding vertex s to K3,4 and making s adjacent to every vertex of K3,4. The minimum number of colours required to edge-colour G is _____. [GATE -2020]

a. 5
b. 6
c. 7
d. 8

Answer : c)


6. Which one of the following predicate formulae is NOT logically valid?
Note that W is a predicate formula without any free occurrence of x. [GATE -2020]

a.

b.

c.

d.

Answer : b)


7. The number of permutations of the characters in LILAC so that no character appears in its original position, if the two L’s are indistinguishable, is _______. [GATE -2020]

a. 12
b. 13
c. 14
d. 15

Answer: a)


8. Let A and B be two n×n matrices over real numbers. Let rank(M) and det(M) denote the rank and determinant of a matrix M, respectively. Consider the following statements,

I. rank(AB) = rank(A) rank(B)
II. det(AB) = det(A) det(B)
III. rank(A + B) ≤ rank(A) + rank(B)
IV. det(A + B) ≤ det(A) + det(B)
Which of the above statements are TRUE? [GATE -2020]

a. I and II only
b. I and IV only
c. III and IV only
d. II and III only

Answer : d)


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