Real Analysis Questions and answers

Topics
  1. Elementary Mathematics
    1. Area and perimeter
    2. Circles
    3. Clocks
    4. Factorisation
    5. Geometry
    6. Height and Distance
    7. Indices and Surd
    8. LCM and HCF
    9. Loci and concurrency
    10. Logarithms
    11. Polynomials
    12. Quadratic Equations
    13. Quadrilateral and parallelogram
    14. Rational expression
    15. Real Analysis
    16. Rectangular and Cartesian products
    17. Set theory
    18. Simple and Decimal fraction
    19. Simplification
    20. Statistics
    21. Straight lines
    22. Triangle
    23. Trigonometric ratio
    24. Trigonometry
    25. Volume and surface area
1). In a discrete metric space M any open Ball is
A). non empty subset of M
B). empty
C). either a singleton set or the whole space
D). none of these
2). A metric space M is separable if there exists a
A). dense subset in M
B). countable dense subset in M
C). uncountable Idense subset in M
D). none of these
3). Let M be an uncountable discrete metric space. Then M is
A). separable
B). not separable
C). empty
D). none of these
4). Any discrete metric space is
A). not complete
B). complete
C). finite
D). none of these
5). Any subspace of a complete metric space is
A). complete
B). closed
C). need not be complete
D). none of these


6). Any subset A of a complete metric space is complete if and only if
A). A is closed
B). A is open
C). A is finite
D). A is countable
7). A complete metric space is of
A). first category
B). second category
C). both (A) and (B)
D). none of these
8). R is of
A). second category
B). first category
C). third category
D). none of these
9). Any discrete metricspace is
A). first category
B). second category
C). third category
D). none of these
10). Any discrete metric space having more than one point is
A). connected
B). finite
C). null set
D). disconnected
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