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

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 inputs [1 2 3 4] and [5 4 3 2 1], respectively. Which of the following holds?

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

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

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

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

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

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

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

A square matrix is singular whenever:

(a) Solve the recurrence equations
$$\,\,\,\,\,\,\,\,\,T\left( n \right) = T\left( {n - 1} \right) + n$$
$$\,\,\,\,\,\,\,\,\,T\left( 1 \right) = 1T$$
(b) What is the generating function?
$$\,\,\,\,\,\,\,\,\,G\left( z \right)$$ for the sequence of Fibonacci numbers?

(a) How many binary relations are there on a set A with n elements?

(b) How many one - to - one functions are there from a set A with n elements onto itself

A critical region is:

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

FORTRAN is:

A context-free grammar is ambiguous if:

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

Give the regular expression over $${\left\{ {0,\,\,1} \right\}}$$ to denote the set of proper non-null substrings of the string $$0110$$.