1
GATE CSE 2006
MCQ (Single Correct Answer)
+2
-0.6
Given a set of elements N = {1, 2, ....., n} and two arbitrary subsets $$A\, \subseteq \,N\,$$ and $$B\, \subseteq \,N\,$$, how many of the n! permutations $$\pi $$ from N to N satisfy $$\min \,\left( {\pi \,\left( A \right)} \right) = \min \,\left( {\pi \,\left( B \right)} \right)$$, where min (S) is the smallest integer in the set of integers S, and $${\pi \,\left( S \right)}$$ is the set of integers obtained by applying permutation $${\pi}$$ to each element of S?
A
$$\left( {n - \left| {A\, \cup \,B} \right|} \right)\,\left| A \right|\,\left| B \right|$$
B
$$\left( {{{\left| A \right|}^2} + {{\left| B \right|}^2}} \right)\,{n^2}$$
C
$$n!{{\left| {A\, \cap \,B} \right|} \over {\left| {A\, \cup B} \right|}}$$
D
$$\,{{{{\left| {A\, \cap \,B} \right|}^2}} \over {\left( {\matrix{ n \cr {\left| {A\, \cup \,B} \right|} \cr } } \right)}}$$
2
GATE CSE 2005
MCQ (Single Correct Answer)
+2
-0.6
Let A be a set with n elements. Let C be a collection of distinct subsets of A such that for any two subsets $${S_1}$$ and $${S_2}$$ in C, either $${S_1}\, \subset \,{S_2}$$ or $${S_2}\, \subset \,{S_1}$$. What is the maximum cardinality of C?
A
n
B
n + 1
C
$${2^{n - 1}}\, + \,1$$
D
n!
3
GATE CSE 2005
MCQ (Single Correct Answer)
+2
-0.6
Let f: $$\,B \to \,C$$ and g: $$\,A \to \,B$$ be two functions and let h = fog. Given that h is an onto function which one of the following is TRUE?
A
f and g should both be onto functions
B
f should be onto but g need not be into
C
g should be onto but f need not be onto
D
both f and need not be onto
4
GATE CSE 2005
MCQ (Single Correct Answer)
+2
-0.6
Let R and S be any two equivalence relations on a non-emply set A. Which one of the following statements is TRUE?
A
$$R\, \cup \,S\,,\,R\, \cap \,S$$ are both equivalence relations
B
$$R\, \cup \,S\,$$ is an equivalence relations
C
$$R\, \cap \,S$$ is an equivalence relations
D
Neither $$R\, \cup \,S\,$$ nor $$R\, \cap \,S$$ is an equivalence relation
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