1
GATE CSE 1996
+1
-0.3
Two dice are thrown simultaneously. The probability that at least one of them will have 6 facing up is
A
$${1 \over {36}}$$
B
$${1 \over {3}}$$
C
$${25 \over {36}}$$
D
$${11\over {36}}$$
2
GATE CSE 1996
+2
-0.6
The probability that the top and bottom cards of a randomly shuffled deck are both access is
A
$${4 \over {52}}\, \times \,{4 \over {52}}\,$$
B
$${4 \over {52}}\, \times \,{3 \over {52}}\,$$
C
$${4 \over {52}}\, \times \,{3 \over {51}}\,$$
D
$${4 \over {52}}\, \times \,{4 \over {51}}\,$$
3
GATE CSE 1996
+2
-0.6
Let R be a non-emply relation on a collection of sets defined by $${A^R}\,B$$ if and only if $$A\, \cap \,B\, = \,\phi$$. Then, (pick the true statement)
A
R is reflexive and transitive
B
R is symmetric and not transitive
C
R is an equivalence relation
D
R is not reflexive and not symmetric
4
GATE CSE 1996
+2
-0.6
Which one of the following is false?
A
The set of all bijective functions on a finite set forms a group under function composition.
B
The set {1, 2, ..., p - 1} forms a group under multiplication mod p where p is a prime number.
C
The set of all strings over a finite alphabet $$\sum$$ forms a group under concatenation.
D
A subset $$s\, \ne \,\phi$$ of G is a subgroup of the group if and only if for any pair of elements $$a,\,\,b\,\, \in \,\,s,\,\,a\,\,*\,\,{b^{ - 1}}\,\, \in \,s$$.
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