Real Analysis Questions and answers

  1. Elementary Mathematics
    1. Quadratic Equations
    2. Simplification
    3. Area and perimeter
    4. Volume and surface area
    5. Geometry
    6. Trigonometry
    7. Polynomials
    8. Height and Distance
    9. Simple and Decimal fraction
    10. Indices and Surd
    11. Logarithms
    12. Trigonometric ratio
    13. Straight lines
    14. Triangle
    15. Circles
    16. Quadrilateral and parallelogram
    17. Loci and concurrency
    18. Statistics
    19. Rectangular and Cartesian products
    20. Rational expression
    21. Set theory
    22. Factorisation
    23. LCM and HCF
    24. Clocks
    25. Real Analysis
31). \(Q \times Q\) is
A). uncountable
B). countable
C). finitgset
D). infinite set
32). (0, 1] is
A). countable
B). uncountable
C). finite
D). none of these
33). The set of irrational numbers lying in the interval (0, 1] is
A). countable
B). finite
C). uncountable
D). none of these
34). The set \(P_{n}\) of all polynomials with integer coefficients is
A). countable
B). uncountable
C). finite
D). none of these
35). R is equivalent
A). (0, 1)
B). (0, 1]
C). [0, 1]
D). none of these


36). Which of the following is not true?
A). Cantor set is measurable and its measure zero
B). Cantor set is equivalent to [0, 1]
C). Cantor set is uncountable
D). Cantor set is countable
37). R with usual metric {0} is
A). open
B). closed
C). half-open
D). none of these
38). Which of the following is not true?
A). Q is not open in R
B). Z is not open in R
C). Any open interval (a, b) is o
D). [0, 1) is open in R
39). Let M be any non-empty set Define \[d(x,y)=\begin{cases}0\text{ if }x=y\\1\text{ if }x\ne y\end{cases}\] This metric is called
A). Stanaard Metric
B). Discrete Metric
C). Absolute Metric
D). Bounded Metric
40). Which of the following is not correct?
A). In a discrete metric space every-subset is open
B). \(\phi\) is open 3
C). Union of any family of open set is open
D). Arbitrary intersection of ope'nI sets is open
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