1
GATE CSE 2020
Numerical
+1
-0.33
Let G be a group of 35 elements. Then the largest possible size of a subgroup of G other than G itself is ______.
Your input ____
2
GATE CSE 2020
Numerical
+1
-0.33
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 _____.
Your input ____
3
GATE CSE 2019
MCQ (Single Correct Answer)
+1
-0.33
Let G be an arbitrary group. Consider the following relations on G :

R1: ∀a,b ∈ G, aR1b if and only if ∃g ∈ G such that a = g-1bg

R2: ∀a,b ∈ G, aR2b if and only if a = b-1

Which of the above is/are equivalence relation/relations?
A
R1 only
B
Neither R1 nor R2
C
R1 and R2
D
R2 only
4
GATE CSE 2019
MCQ (Single Correct Answer)
+1
-0.33
Let U = {1, 2 ,..., n}. Let A = {(x, X) | x ∈ X, X ⊆ U}. Consider the following two statements on |A|.

I. |A| = n2n–1

II. |A| = $$\sum\limits_{k = 1}^n {k\left( {\matrix{ n \cr k \cr } } \right)} $$

Which of the above statements is/are TRUE?
A
Neither I nor II
B
Only II
C
Both I and II
D
Only I
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