Test: Real Analysis - 3 - Mathematics MCQ

countable collection of disjoint open intervals

uncountable collection of disjoint open intervals

countable collection of disjoint closed intervals.

uncountable collection of disjoint closed intervals

it contains all of its points of closure

it contains all of its accumulation point

 (a) is true, (b) is false 

Both (a) and (b) are true

closed set

open set

null set

None of these

10

T2

15

None of these

Supremum 

Minimum

Infimum 

Maximum

field axiom

ordered axiom

None of these

completeness axiom 

diverges 

Converges 

oscillates 

None of these

sup A = sup S + sup T

sup A > sup S + sup T

sup A < sup S + sup T

sup A ≠ sup S + sup T

maximal element only

minimal element only

Both maximal and minimal element

None of the above

uncountable

countable

infinite

bounded

there doesn’t exist a decreasing function on (a, b) that is continuous only at points in (a, b) ∼ C.

there doesn’t exist an increasing function on (a, b)that is continuous only at points in (a, b) ∼ C.

there is an increasing function on (a, b) that is continuous only at points in (a, b) ∼ C.

None of the above options

0

1

φ

2

closed set

open set

null set

None of these

{1, 2, 3}

{1, 3, 5, 7, 9}

{1, 2, 5, 9}

{1, 5, 7, 9, 11}

f has neither minimum nor a maximum at x = 2

f does not have a critical point at 2 

f has a minimum at 2 

f has a maximum at 2 

Both statements A and B are true.

Both statements A and B are false.

A is true but R is false

None of the above

upper bound

lower bound

maximal element

None of these

Point where function has maximum value

Point where function has minimum value

Point where function has zero value

Point where function neither have maximum value nor minimum value