GATE CSE 1987

## GATE CSE

Solve the recurrence equations
T (n) = T (n - 1) + n
T (1) = 1

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What is the generating function G (z) for the sequence of Fibonacci numbers?

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Let P be a quicksort program to sort numbers in ascending order. Let t1 and t2 be the time taken by the program for the

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Find a solution to the following recurrence equation
T(n) = T(n - 1)+ n
T(1) = 1

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In a circular linked list organization,insertion of a record involves modification of :

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If the no of leaves in a tree is not a power of 2,then the tree is not a binary tree.

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It is possible to construct a binary tree uniquely whose pre-order and post-order traversals are given.

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State whether the following statement are TRUE or FALSE:
(a) The union of two equivalence relations is also an equivale

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(a) How many binary relations are there on a set A with n elements?
(b) How many one - to - one functions are there from

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(a) Solve the recurrence equations
$$\,\,\,\,\,\,\,\,\,T\left( n \right) = T\left( {n - 1} \right) + n$$
$$\,\,\,\,\,\,

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A square matrix is singular whenever:

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If a, b and c are constants, which of the following is a linear inequality?

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A critical region is:

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On receiving an interrupt from an $${\rm I}/O$$ device the $$CPU$$:

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Give the regular expression over $${\left\{ {0,\,\,1} \right\}}$$ to denote the set of proper non-null substrings of the

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Give minimal $$DFA$$ that performs as a Mod-$$3$$ $$1's$$ counter, i.e., outputs a $$1$$ each time the number of $$1's$$

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A context-free grammar is ambiguous if:

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FORTRAN is:

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