1
GATE CSE 2014 Set 2
Numerical
+1
-0
The security system at an IT office is composed of 10 computers of which exactly four are working. To check whether the system is functional, the officials inspect four of the computers picked at random (without replacement). The system is deemed functional if at least three of the four computers inspected are working. Let the probability that the system is deemed functinal be denoted by p. Then 100p = __________________.
2
GATE CSE 2014 Set 2
Numerical
+2
-0
The probability that a given positive integer lying between 1 and 100 (both inclusive) is NOT divisible by 2, 3 or 5 is _______________
3
GATE CSE 2014 Set 2
MCQ (Single Correct Answer)
+2
-0.6
Which one of the following Boolean expressions is NOT A tautology?
A
$$\left( {\left( {a \to b} \right) \wedge \left( {b \to c} \right)} \right) \to \left( {a \to c} \right)$$
B
$$\left( {a \leftrightarrow c} \right) \to \left( { \sim b \to \left( {a \wedge c} \right)} \right)$$
C
$$\left( {a \wedge b \wedge c} \right) \to \left( {c \vee a} \right)$$
D
$$A \to \left( {b \to a} \right)$$
4
GATE CSE 2014 Set 2
MCQ (Single Correct Answer)
+2
-0.6
Consider the following relation on subsets of the set S integers between 1 and 2014. For two distinct subsets U and V of S we say U < V if the minimum element in the symmetric difference of the two setss is in U.

Consider the following two statements:
S1 There is a subset of S that is larger than every other subset. S2: There is a subset of S that is smaller than every other subset.
Which one of the following is CORRECT?

A
Both S1 and S2 are true
B
S1 is true and S2 is false
C
S2 is true and S1 is false
D
Neither S1 nor S2 is true
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