GATE CSE 2005 | GATE CSE Year Wise Previous Years Questions

GATE CSE 2005

MCQ (Single Correct Answer)

-0.6

A random bit string of length n is constructed by tossing a fair coin n times and setting a bit to 0 or 1 depending on outcomes head and tail, respectively. The probability that two such randomly generated strings are not identical is:

$$1/{2^n}$$

1 - 1/n

1/n!

$$1 - \,\,{\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle {{2^n}}$}}$$

GATE CSE 2005

MCQ (Single Correct Answer)

-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?

n + 1

$${2^{n - 1}}\, + \,1$$

GATE CSE 2005

MCQ (Single Correct Answer)

-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?

$$R\, \cup \,S\,,\,R\, \cap \,S$$ are both equivalence relations

$$R\, \cup \,S\,$$ is an equivalence relations

$$R\, \cap \,S$$ is an equivalence relations

Neither $$R\, \cup \,S\,$$ nor $$R\, \cap \,S$$ is an equivalence relation

GATE CSE 2005

MCQ (Single Correct Answer)

-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?

f and g should both be onto functions

f should be onto but g need not be into

g should be onto but f need not be onto

both f and need not be onto

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