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MA242 Final Exam - Real Analysis II 
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MCQs on Real Analysis.

MA242 Final Exam - Real Analysis II 
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25 Questions

1. Let
be a
-form on
, with
and
. Which of the following statements is correct?
2. Let
be
-forms on
. Which of the following statements is correct?
3. Let
, with
. Which of the statements below is correct?
4. The pullback operator connects which of the following two concepts?
5. Let
and
be differential forms on
. Which of the following statements is incorrect?
6. Which of the statements below is incorrect?
7. Let
be a linear transformation with determinant
. Let
,
, and
be Riemann integrable on a rectangle containing
. Which of the statements below is necessarily correct?
8. Let
be the form
. Which of the following answer options is equal to
?
9. Let
and
be continuous functions. Let
. Assume that
. Which of the statements below is correct?
10. Let
be a
-form on
and let
be a curve for which
exists. Which of the following statements is correct?
11. Let
be a function of class
. Write
,
, and
. Given these conditions, which of the statements below is correct?
12. The answer options below are concerned with subsets of
. Which of the statements below is incorrect?
13. Which of the statements below is incorrect?
14. Which of the following answer options is a
-form on
?
15. Consider the function
given by the formula
. Which of the statements below is incorrect?
16. Let
be a function satisfying the homogeneity condition
for some
. Which of the statements below is correct?
17. For the functions
and
, which answer option below results in a Jacobian that is not independent of
?
18. Let
be given. Which of the statements below is incorrect?
19. Let
be Jordan measurable, and
be a function that is integrable on both
and
. Which of the statements below is correct?
20. Let
. Which of the following statements is incorrect?
21. Let
be a function that is continuously differentiable at all points
. Which of the statements below is correct?
22. When the most general Stokes' Theorem is applied to the
-form
to compute the integral
, where
is a smooth curve in
enclosing a region in which
is defined, what is the resulting formula's name?
23. Consider a function
and a point
. Which of the statements below is correct?
24. Consider a closed curve
satisfying
for all
, and let
be the winding number of
. Which of the following statements is correct?
25. Let
and fix
. Each of the derivatives stated in the below answer options is computed at
. Given these conditions, which of the statements below is incorrect?

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