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
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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