Chapter 1

Question 1

Rational number

Answer 1

rational number is a number that can be put in the form p/q where p, q belongs to Z, q≠0.
The numbers 16, 3.7,4, etc., are rational numbers.16 can be reduced to the formwhere p,qeZ, and q ≠0 because16=4=4/

Question 2

Irrational numbers

Answer 2

Irrational numbers are those numbers that can not be put into the form p/q where p,q belongs to Z and q≠0.
The numbers /2, /3, are irrational numbers.

Question 3

Terminating decimals

Answer 3

A decimal which has only a finite number of digits in itsdecimal part, is called a terminating decimal. Thus 202.04,0.0000415, 100000.41237895are examples of terminating decimals.

Question 4

Recurring decimals

Answer 4

This is another type of rational numbers. In general,arecurring or periodic decimal is a decimal in which one or more digits repeatindefinitely

Question 5

Closure property of addition

Answer 5

For all a,b belong to R
A+b belong to R

Question 6

Associative law of addition

Answer 6

For all a,b,c belong to R
(A+b)+c=a+(b+c)

Question 7

Identity element of addition

Answer 7

For all a belong to R
A+0=0+a=a
0 is called additive identity element

Question 8

Inverse element of addition

Answer 8

For all a belong to R and there exists -a belong to R
A+(-a)=-a+a=0

Question 9

Commutative property of addition

Answer 9

For all a,b belong to R
A+b=b+a

Question 10

Closure law of multiplication

Answer 10

For all a,b belong to R
A×b belong to R

Question 11

Associative law of multiplication

Answer 11

For all a, b , c belong to R
A×(b×c)=(a+b)×c

Question 12

Identify element of multiplication

Answer 12

For all a belongs to R
A×1=1×a=a
So 1 is called multiplication identity element

Question 13

Inverse element of multiplication

Answer 13

For all a belongs to R
There exists 1/a
Belongs to R
A(1/a)=(1/a)a=1

Question 14

Commutative property of multiplication

Answer 14

For all a b belong to R
Ab=ba

Question 15

Multiplication addition law

Answer 15

For all a,b &c belong to R
a(b+c)=ab+ac
This is called distributivity of multiplication over addition

Question 16

Reflexive property of equality

Answer 16

For all al belong to R
A=a

Question 17

Symmetric property of equality

Answer 17

For all a b belong to R
A=b or b=a

Question 18

Transitive law of equality

Answer 18

For all a b belong to R
A=b and b=c this means a=c

Question 19

Additive property of equality

Answer 19

For all a b belong to R
A=b this means a+c=b+c
C belong to R

Question 20

Multiplication property of equality

Answer 20

For all a b belong to R
A=b this means
Ac=bc
C belong to R

Question 21

Cancellation property w.r.t addition of equality

Answer 21

For all a b c belong to R
A+c=b+c
This means a=b

Question 22

Cancellation property w.r.t multiplication of equality

Answer 22

For all a b c belong to R
Ac=bc
This means a=b

Question 23

Trichotomy property of inequality

Answer 23

For all a b belong to R
A=b , a<b,a>b

Question 24

Transitive property of inequality

Answer 24

For all a b c belong to R
A>b or b>c that means a>c
A<b or b<c this means a<c

Question 25

Additive identity of inequality

Answer 25

For all a b c belong to R A>b means a+c>b+c Ab and c>d means a+c>b+d A

Question 26

Multiplicative property of inequality

Answer 26

A) for all a b c belong to R and c>0 i) a>b means ac>bc ii)ab means acbc C)for all a b c d belong to R and a b c d are all positive i) a>b and c>d means ac >bd ii) a

Question 27

complex numbers

Answer 27

Numbers of the form of x+iy where x,y belong to the real numbers and i=√-1 are called complex numbers

Question 28

Conjugate of complex no.

Answer 28

Complex no. Of the form (a+b>) and (a-bi) which have same real parts and whose imaginary parts differ in signs only are called conjugate of each other. 5+6i and 5-6i

Question 29

Ordered pairs

Answer 29

Members of a cartesian product are ordered pairs

Question 30

Cartesian plane

Answer 30

The cartesian product R×R where R is set of real numvers called cartesian plane

Question 31

Real plane / coordinate plane

Answer 31

The geometrical plane on which coordinate system has been specified is called real or coordinate plane

Question 32

Coordinates Abscissa Ordinate

Answer 32

If a point "A" on the coordinate corresponds to the ordered pair (a,b) the a,b are called coordinates of A. a is called x coordinate or abscissa and b is called y coordinate or ordinate

Question 33

Argand diagram

Answer 33

The figure representing one or more complex numbers on the complex plane is called argand diagram X axis represent real no. Y axis represent imaginary no.

Question 34

Modules of complex no. Value

Answer 34

The real no. /(x² + y²) is called modules of complex no. a+ib.

Question 35

Modules of complex no def

Answer 35

The modules of complex no is the distance from the origin of the point representing the number Denoted as |x+yi| or |(x,y)| As complex no. =z Then z=x+iy = (x,y) Then |z| = /(x²+y²)

Question 36

Polar form of complex no.

Answer 36

Polar form of complex no. z= x+iy is given by x+iy= rcos (theta)+i r sin(theta) Where r= modulus of z =|z|= √(x²+y²) and theta = argument of z = amplitude of z = tan-¹ y/x

Question 37

(a+b)³

Answer 37

a³+b³+3ab(a+b)