# GATE CSE 1990

 Question 1
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Two NAND gates having open collector outputs are tied together as shown in below figure. The logic function Y, implemented by the circuit is,
 A Y=ABC + DE B $Y=\overline{ABC + DE}$ C Y=ABC.DE D $Y=\overline{ABC.DE}$
Digital Logic   Boolean Algebra
Question 1 Explanation:
 Question 2
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Indicate which of the following statements are true:
A relational database which is in 3NF may still have undesirable data redundancy because there may exist:
 A Transitive functional dependencies B Non-trivial functional dependencies involving prime attributes on the right-side. C Non-trivial functional dependencies involving prime attributes only on the left-side. D Non-trivial functional dependencies involving only prime attributes.
Database Management System   Normal Form
Question 2 Explanation:
 Question 3
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The number of rooted binary trees with n nodes is,
 A Equal to the number of ways of multiplying (n+1) matrices. B Equal to the number of ways of arranging n out of 2 n distinct elements. C Equal to $\frac{1}{(n+1)}\binom{2n}{n}$. D Equal to n!.
Data Structure   Binary Tree
Question 3 Explanation:
 Question 4
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The total external path length, EPL, of a binary tree with n external nodes is, $\Sigma _w=Iw$, where $I_{w}$ is the path length of external node w),
 A $\leq n^{2}$ always. B $\geq n \log_{2}$ n always. C Equal to $n^{2}$ always. D O(n) for some special trees.
Data Structure   Binary Tree
Question 4 Explanation:
 Question 5
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The complexity of comparision based sorting algorithms is:
 A $\Theta (n \log n)$ B $\Theta (n)$ C $\Theta \left(n^2\right)$ D $\Theta (n\sqrt n)$
Algorithm   Sorting
Question 5 Explanation:
 Question 6
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Recursive languages are:
 A A proper superset of context free languages. B Always recognizable by pushdown automata. C Also called type 0 languages. D Recognizable by Turing machines.
Theory of Computation   Recursive Language
Question 6 Explanation:
 Question 7
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It is undecidable whether:
 A An arbitrary Turing machine halts after 100 steps. B A Turing machine prints a specific letter. C A Turing machine computes the products of two numbers D None of the above.
Theory of Computation   Undecidability
Question 7 Explanation:
 Question 8
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Let $R_{1}$ and $R_{1}$ be regular sets defined over the alphabet $\Sigma$ Then:
 A $R_{1} \cap R_{2}$ is not regular. B $R_{1} \cup R_{2}$ is regular. C $\Sigma^{*}-R_{1}$ is regular. D $R_{1}^{*}$ is not regular.
Theory of Computation   Regular Grammar
Question 8 Explanation:
 Question 9
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The number of ways in which 5 A's, 5 B's and 5 C's can be arranged in a row is:
 A $15!/(5!)^{3}$ B 15! C $\left(\frac{15}{5}\right)$ D $15!(5!3!).$
Discrete Mathematics   Combination
Question 9 Explanation:
 Question 10
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Indicate which of the following well-formed formulae are valid:
 A $\left(P\Rightarrow Q\right) {\wedge} \left(Q \Rightarrow R\right) \Rightarrow \left(P \Rightarrow R\right)$ B $\left(P\Rightarrow Q\right) \Rightarrow \left( \neg P \Rightarrow \neg Q\right)$ C $\left(P{\wedge} \left(\neg P \vee \neg Q\right)\right) \Rightarrow Q$ D $\left(P \Rightarrow R\right) \vee \left(Q \Rightarrow R\right) \Rightarrow \left(\left(P \vee Q \right) \Rightarrow R\right)$
Discrete Mathematics   Propositional Logic
Question 10 Explanation:
There are 10 questions to complete.