1
GATE CSE 2014 Set 2
Numerical
+1
-0
Each of the nine words in the sentence "The Quick brown fox jumps over the lazy dog" is written on a separate piece of paper. These nine pieces of paper are kept in a box. One of the pieces is drawn at random from the box. The expected length of the word drawn is ______________. (Then answer should be rounded to one decimal place.)
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
+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
+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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