## PPSC Test MathMatics MCQs 2019 Withfull Book Download in PDF

**NUMBER SYSTEMS BASIC RULES**

• The closure property of real numbers under addition states that the sum of two real numbers Is also a real number.

• The commutative property of real numbers under addition states that the sum of NO real numbers is independent of the order In which they are added.

• The associative property of real numbers under addition states that

a+(b+c)=(a+b)+c ‘Va,b,ceR.

• For each a e R there exists an element – a e R such that a +(-a) = 0 = -a +a . The

element -a Is called the additive inverse of the real number 8.

• The closure property of real numbers under multiplication states that the product of two real numbers is also a real number.

• The commutative property of real numbers under multipfteation states that the product of two real numbers is Independent of the order in which they are multiplied.

• The associative property of real numbers under multiplication states that

a(bc) = (ab)c ‘V a,b,c e R.

• The left distributive law for multiplication over addition states that

a(b+c)=ab+ac rta,b,ce R.

• The right distributive law for multiplication over addition states that

(a+b)c = ac+bc rta,b,c e R .

• The trichotomy property of real numbers states that for real numbers a and b, exactly one of the following

• If a< band c <d, then a+ c < b +d. This is known as additivity.

**Multiple Choice Questions**

**1. Ois**

(a) an odd integer (b) an irrational number

(c) a natural number (d) an even integer

**2. 3is**

(a) an odd integer (b) an irrational number

(c) a rationalnumber (d) a negative integer

**3. J3 is**

(a) an irrational number (b) a rational number

(c) a natural number (d) a negative Integer

**8. Every odd Integer is also**

**9. .Every even integer is also**

**10. If n is a prime,then fn Is**

**11. If n is a perfect square, then fn is**

**12. 1r is**

**13. Every recurring decimal or terminating decimal represents the**

**14. Every non-repeating non-terminating decimal is**

**15. The addiUve identity of real numbers is**

**31. The set {0} has**

**32. Which of the following sets has closure property with respect to addition?**

**69 Z is a group under**

**70 The action of wearing soc:Ks and shoes**

**71 The set of all non-singular matrices of order 2 fonns a non-abelian group under**

**72 A closed set with respect to some binary operation is called the**

**73 A non-empty set which is closed with respect to some binary operation is called the semi· group If**

**DIFFERENTIATION**

**ANALYTIC GEOMETRY**

**VECTORS**