1
GATE CSE 2019
MCQ (Single Correct Answer)
+1
-0.33
Let G be an undirected complete graph on n vertices, where n > 2. Then, the number of different Hamiltonian cycles in G is equal to
A
n!
B
1
C
(n - 1)!
D
$${{\left( {n - 1} \right)!} \over 2}$$
2
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
3
GATE CSE 2019
Numerical
+2
-0.67
Suppose Y is distributed uniformly in the open interval (1,6). The probability that the polynomial 3x2 + 6xY + 3Y + 6 has only real roots is (rounded off to 1 decimal place) _____.
Your input ____
4
GATE CSE 2019
MCQ (Single Correct Answer)
+2
-0.67
Consider the first order predicate formula φ:

∀x[(∀z z|x ⇒ ((z = x) ∨ (z = 1))) ⇒ ∃w (w > x) ∧ (∀z z|w ⇒ ((w = z) ∨ (z = 1)))]

Here 'a|b' denotes that 'a divides b', where a and b are integers.

Consider the following sets:

S1. {1, 2, 3, ..., 100}
S2. Set of all positive integers
S3. Set of all integers

Which of the above sets satisfy φ?
A
S1 and S3
B
S1, S2 and S3
C
S2 and S3
D
S1 and S2
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