1
GATE CSE 2016 Set 2
MCQ (Single Correct Answer)
+2
-0.6
Consider a set $$U$$ of $$23$$ different compounds in a Chemistry lab. There is a subset $$S$$ of $$U$$ of $$9$$ compounds, each of which reacts with exactly $$3$$ compounds of $$U.$$ Consider the following statements:

$$\,\,\,\,\,\,\,{\rm I}.\,\,\,\,\,$$ Each compound in $$U \ S$$ reacts with an odd number of compounds.
$$\,\,\,\,\,{\rm I}{\rm I}.\,\,\,\,\,$$ At least one compound in $$U \ S$$ reacts with an odd number of compounds.
$$\,\,\,{\rm I}{\rm I}{\rm I}.\,\,\,\,\,$$ Each compound in $$U \ S$$ reacts with an even number of compounds.

Which one of the above statements is ALWAYS TRUE?

A
Only $${\rm I}$$
B
Only $${\rm II}$$
C
Only $${\rm III}$$
D
None
2
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
3
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 ________.
Your input ____
4
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 __________________.
Your input ____
GATE CSE Subjects
Software Engineering
Web Technologies
EXAM MAP