1
GATE CSE 2015 Set 2
Numerical
+2
-0
The number of onto functions (subjective functions) from set $$X = \left\{ {1,2,3,4} \right\}$$ to set $$Y = \left\{ {a,b,c} \right\}$$ is __________________.
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2
GATE CSE 2015 Set 2
Numerical
+2
-0
Let $$X$$ and $$Y$$ denote the sets containing $$2$$ and $$20$$ distinct objects respectively and $$𝐹$$ denote the set of all possible functions defined from $$X$$ to $$Y$$. Let $$f$$ be randomly chosen from $$F.$$ The probability of $$f$$ being one-to-one is ________.
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3
GATE CSE 2015 Set 3
MCQ (Single Correct Answer)
+2
-0.6
Let $$R$$ be a relation on the set of ordered pairs of positive integers such that $$\left( {\left( {p,q} \right),\left( {r,s} \right)} \right) \in R$$ if and only if $$p - s = q - r.$$ Which one of the following is true about $$R$$?
A
Both reflexive and symmetric
B
Reflexive but not symmetric
C
Not reflexive but symmetric
D
Neither reflexive nor symmetric
4
GATE CSE 2014 Set 1
Numerical
+2
-0
Let S denote the set of all functions $$f:\,{\{ 0,\,1\} ^4}\, \to \,\{ 0,\,1\} $$. Denote by N the number of functions from S to the set {0, 1}. The value of $${\log _2}$$ $${\log _2}$$ N is___________________
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