question 1

Let A = {15,16,17,18,0}, then the number of subsets of A containing 15 and 0 is

- 1
- 2
- 4
- 8
- none of these

question 2

In a group of 50 persons, everyone takes either tea or coffee. If 35 take tea and 25 take coffee, then the number of persons who take tea only is

- 10
- 25
- 35
- 40
- none of these

question 3

In a town of 10,000 families, it was found that 40% families buy newspaper A, 20% buy newspaper B, 10% buy newspaper C, 5% buy A & B, 3% buy B & C, and 4% buy A & C. If 2% families buy all the newspapers, then the number of families which buy none of A, B & C is

- 3300
- 1400
- 4000
- 1200
- none of these

question 4

If f : R→R is given by f(x) = 3x - 5, then f^{ -1}(x) is

- 3x - 5
- (3x - 5)
^{-1} - (x + 5) / 3
- does not exist
- cannot be determined

question 5

The domain of the the real valued function is

- (1, 2)
- (-2, 2)
- (- ∞, - 2) ∪ (2, ∞)
- (- ∞, - 2) ∪ (1, ∞)
- (- ∞, ∞) - {1, ± 2}

question 6

The domain of the definition of the function is

- (1, ∞)
- [1, ∞)
- (- ∞, - 1) ∪ (1, ∞)
- set of all reals different from 1
- none of these

question 7

The number of surjections from A = {1, 2, 3, ..., n}, n ≥ 2 onto B = {a, b} is

^{n}P_{2}^{n}C_{2}- 2
^{n}- 2 - 2
^{n}- 1 - none of these

question 8

Set A has 3 elements and set B has 4 elements. The number of injections that can be defined from A to B is

- 144
- 12
- 24
- 64
- none of these

question 9

If b^{2} - 4ac = 0 and a > 0, the domain of the function y = log {ax^{3} +
(a + b)x^{2} + (b + c)x + c} is

- R
- R - {- b / 2a}
- (0, ∞)
- none of these

question 10

The range of the function is

- R
- [3, ∞)
- (1/3, 3)
- [1/3, 3]
- none of these

syllabus

**Sets** – Introduction and Definition; Representation of sets, Roster method, Set
–Builder method; Different types of sets – Empty set, Singleton set, Finite set,
Infinite set, Equivalent sets, Equal sets; Cardinal number of a finite set;
Subsets, Results on subsets; Power set; Universal set; Venn Diagrams,
Representing sets using Venn Diagrams, Solving real world problems using Venn
Diagram; Operations on sets - Union, Intersection, Difference, Symmetric
difference and Complement of sets; Disjoint sets; Laws of Algebra of sets and
proofs – Idempotent laws, Identity laws, Commutative laws, Associative laws,
Distributive laws and De Morgan's laws; Results on Number of elements in sets.

**Cartesian Product of sets**, Ordered pair, Equality of ordered pairs, Graphical
representation of Cartesian Product of sets; Results and Theorems on Cartesian
Products; **Relation**, Total Number of Relations, Domain of a Relation, Range of a
relation, Relation on a set, Inverse Relation; Types of Relations – Void
Relation, Universal Relation, Identity Relation, Reflexive Relation, Symmetric
Relation, Transitive Relation, Antisymmetric Relation and Equivalence
Relation; Prove Equivalence of a relation by checking Reflexivity, Symmetry and
Transitivity; Results and Theorems on Relations.

**Functions**, Definition of Function; Domain, Co-domain and Range of a Function;
Description or Representation of Function; Equal Functions; Function as a
Relation; Standard Functions and their Graps – Constant Function, Identity
Function, Modulus Function, Greatest Integer Function, Exponential Function,
Logarithmic Function, Trigonometric Functions, Inverse Trigonometric Functions,,
Hyperbolic Functions, Inverse Hyperbolic Functions; Kinds of Functions, One-One
Function or Injection, Many-One Function, Onto Function or Surjection, Into
Function, Bijection or One-One Onto Function; Proving Injectivity, Surjectivity
and Bijectivity; Composition of Functions, Properties of Composition of
Functions; Inverse of a Function, Properties of Inverse of a Function.