Advance Real Analysis MCQs deal with For Monotonic Decreasing Function, An Interval Has Partitions, Norm Is Defined As The length Of Subinterval, For Monotonic Increasing Function. V (F, A, B) =F (B) – F (A), The Least Upper Bound Of [0, 1], The Greatest Lower Bound Of [0, 1], The Norm Of P Is Denoted By, Many Partitions May Have Same, If F Is Integrable Then |F| Is, A Sequence In Which Every Term Is A Function Of X On Set E Called, In Fundamental Theorem Of Calculus F On[A,B], In Fundamental Theorem Of Calculus F’=, (X) =0 If X=0 And I(X) =1 If X=0. I(X) Is Called, If P And P* Be Two Partitions Of [A,B] Then P* Is Called Refinement Of P If, Continuous Function Defined On A:

# Advance Real Analysis MCQs

## If P and P* be two partitions of [a,b] then P* is called refinement of P if.

A. P* = P

B. P = P*

C. P= P*

D. None

**View Answer**

**B. P = P***

## (x) =0 if x=0 and I(x) =1 if x=0. I(x) is called.

A. Unity function

B. Union function

C. Unit step function

D. Constant function

**View Answer**

**C. Unit step function**

## In fundamental theorem of calculus F’=.

A. F+g

B. f

C. g

D. l

**View Answer**

**B. f**

## In fundamental theorem of calculus F on[a,b].

A. Constant

B. Integrable

C. Differentiable

D. None

**View Answer**

**C. Differentiable**

## If total variation of f is finite then f is called.

A. Function with unbounded variation

B. Function having no variation

C. Function

D. Function of bounded variation

**View Answer**

**D. Function of bounded variation**

## A real value monotone function on [a,b] is a.

A. Function of bounded variation

B. Function of unbounded variation

C. Undefined function

D. All above

**View Answer**

**A. Function of bounded variation**

## A sequence in which every term is a function of x on set E called.

A. Sequence of set E

B. Sequence of x

C. Sequence of function

D. Unique sequence

**View Answer**

**C. Sequence of function**

## If f is integrable then |f| is.

A. Differentiable

B. Undefined

C. Integrable

D. All above

**View Answer**

**C. Integrable**

## Many partitions may have same.

A. Upper sum

B. Lower sum

C. Norm

D. Lower and upper sum

**View Answer**

**C. Norm**