ECAT Mathematics Chapter 1 Number System

The polar form of complex number x ≠ I y =

• r cos θ+ r sin θ A
• r cos θ+ is sin θ B
• cos θ+ r sin θ C
• i cos θ+ i sin θ D

If in a set of real no a is additive identity then

• a+a = 2a A
• a+a = 1 B
• a+a = 0 C
• None of these D

The set {1,2,3,4......} is called

• Set of natural numbers A
• Set of whole numbers B
• Set of rational number C
• Set of irrational numbers D

• 15 A
• 15 i B
• -15 i C
• -15 D

The multiplicative inverse of -3i is

• 3i A
• -3i B
• -1/3i C
• 1/3 i D

The value of x, and y, when (x + iy)²= 5 + 4i

• X = 2, y = 1 A
• X = -2, y = 1 B
• X = 2, y = -1 C
• X = 2, y = 2 D

A subset of set of complex number whose elements are of the form (a,0) is called

• Real number A
• Complex number B
• Rational number C
• Irrational number D

In R the right cancellation property w.r.t. addition is

• 
  A
• 
  B
• 
  C
• 
  D

In polar form of complex number r =

• 
  A
• 
  B
• 
  C
• 
  D

∀ z ∈ C, multipliucative is

• (1,1) A
• (1,0) B
• (0,1) C
• None of these D

∀a,b,c∈R and c>0,then

• a>b ⇒ ac < bc A
• a>b ⇒ ac > bc B
• a<b ⇒ ac > bc C
• None of these D

2.333....is a

• Irrational no A
• Complex no B
• Rational no C
• None of these D

If z₁ = (a,b), z₂=(c,d), then z₁ z₂ = -------------------

• (ac,bd) A
• (ac+bd, ad-bc) B
• (ac-bd , ad+bc) C
• (ac-bd , ad-bc) D

The equation |x + 4| = x has solution

• x = -2 A
• x = 2 B
• x = -4 C
• x = 4 D

Name the property used in 1000 x 1 = 1000

• additive inverse A
• multiplicative inverse B
• additive identity C
• multiplicative identity D

• 
  A
• 
  B
• 
  C
• 
  D

• -8 A
• 8 B
• 8i C
• 32 D

If ∀a,b ε R,then a +b  ε  R is a property

• Closure law of addition A
• Associative law of addition B
• Additive inverse C
• Additive identity D

The square root of 2i - 20i is

• +-(5 - 2i) A
• +-(5 + 2i) B
• (5 - 2i) C
• None of these D

If z=(x,y) then z has no multiplicative inverse when

• x ≠ 0, y = 0 A
• x = 0, y = 0 B
• x = 0, y ≠ 0 C
• None of these D

• 
  A
• 
  B
• 
  C
• 
  D

The conjugate of √5 i is

• √5 A
• -√5 i B
• i C
• 5i D

• 0 A
• 1 B
• -1 C
• None of these D

• Associative law of addition A
• Commutative law of addition B
• Additive identity C
• Closure law of addition D

• additive property A
• multiplicative property B
• additive inverse C
• additive identity D

The decimal fraction in which we have finite number of digits in its decimal part is called.

• recurring decimal fraction A
• Non terminating faction B
• Non recurring fraction C
• terminating decimal fraction D

The multiplicative inverse of 4 is

• -4 A
• -1/4 B
• 1/4 C
• 1 D

Every natural number is

• A prime number A
• An irrational number B
• An integer C
• An even number D

Which of the following sets has closure property w.r.t. addition

• { 0 } A
• { 1 } B
• { 0, -1} C
• { 1, -1} D

If in a set of real no a is multiplicative identity then

• a,a = a² A
• a,a = 1 B
• a,a = 0 C
• None of these D