True or Fa

i. Vendors bank details are available in Vendor Master.

ii. The computer-based application that allows the management of the requests from creation to closure is called Request Tracker.

The quality control team should be a part of the AP team to be most effective.

iv. Degree of certainty of a possible outcome is Risk.

V. The Duality principle of accounting is also called principle of accounting equivalence.

lse:

Fill in the blanks:

i. The activity of placing an order to buy stationery items belong to-------stage.

ii. The average time taken for a transaction to be completed is called ................

Purchase activities consist of and----- process.

iv.  .............. Invoices are raised by the vendor for purchases that were made without raising PO.

V. Measurements taken on an activity to measure its quality is called ...............

If E is a measurable set and f is a simple function such that a , show that

Give an example of an algebra which is not a σ − algebra. Justify your choice of examples.

Let (X,d) be a metric space and A be a subset of X. Show that bdy(A) = Qif and only if A is both open and closed.

Verify the hypothesis and conclusions of the Fatou's lemma for the sequence {f_n} given by

Give an example of a family f₁ of subsets of a set X which has finite intersection property. Justify your choice of example.

 Find  in  where d is the metric given by

Suppose that is given by f(t) = (t,t²) and is given by g(x, y) = (x², xy, y²-x²). Compute the derivative of gof.

Find the directional derivative of the function    defined by

at the point (1,2,-1,-2) in the direction v = (1,0,-2,2).

Is the continuous image of a Cauchy sequence a Cauchy sequence? Justify.

Show that the function f defined by

is not differentiable at (0,0). Does the partial derivatives of f exists at (0,0)? or any at any other point in R²? Justify your answer.

Let F be the function from to defined by

F(x, y) = (x² + y² , xy)

Show that F is differentiable at (2,1) . Find the differential matrix of F.

Find the interior and closure of the set of rationals in with standard metric.

Show that a set A in a metric space is closed if and only if every convergent sequence in A converges to a point of A.

If E is a subset of with standard metric, then show that 

Which of the following subsets of R are compact w.r.t. the metric given against them. Justify your answer.

i) A = (1,0) in of − with standard metric.

ii) A = [4,3] − with discrete metric.

iii) {(x, y) ∈ y > 0} − with standard metric

Prove that if an open set U can be written as the union of pariwise disjoint family V of open connected subsets, then these subsets must be the components of U. Use this theorem to find the components of the set D U E where

Find the Fourier series of  f (t) = t² on [−π,π].

For the equation , x² + y³ + z³ = at which points on its solution set, can we assured that there is a neighbourhood of the point in which the surface given by the equation can be described by an equation of the form z = f (x, y) .