Jaypee Institute of Information Technology (JIIT) 2007 B.Tech Information Technology maths - Question Paper

JAYPEE UNIVERSITY OF info AND TECH.

TEST 3

1. Let A and B be finite sets. Suppose A has m elements and B has n elements. State the relationship which must hold ranging from m and n for every of the subsequent to be true:
(a) there exists a one-one (injection) map from A to B.
(b) there exists an onto (surjection) map from A to B.
(c) there exists a bijection (one-one onto) map from A to B.
2. Define floor, ceiling, integer, absolute value, remainder, exponential and logarithmic functions. provide 2 examples for every.
3. Let f(x) = x + 2, g(x) = x – 2, and h(x) = 3x for
obtain
4. Let where State whether these functions are injective, surjective or bijective.



5. Let a and b be positive integers, and suppose Q is described recursively as follows:

obtain (i) Q (2, 5) (ii) Q (12, 5)
(iii) What does this function Q do? obtain Q (5861, 7).
6. Let n denote a positive integer. Suppose a function L is described recursively as follows:

obtain L (25).
7. Consider a recursive function G from set of positive integers to integers,

Is G well defined? Justify.
8. Let x and y be 2 integers and suppose that g(x, y) is described recursively by

obtain g (2, 7), g (5, 3) and g (15, 2).
11. Suppose
12. Prove that
13. Show that
14. Show that
15. Using generating function solve the recurrence relation
16. Using generating function solve the recurrence relation

Earning:   Approval pending.