DBRAU Kanpur BSc Previous Year Question Papers 2023 |DBRAU Kanpur BSc III Real Analysis Paper 2022
| S.No. | Questions with options |
| 1 | The set of Z of all integers has ________
(a) Unique limit point (b) No limit point (c) Two limit point (d) Three limit point |
| 2 | A denumerable set is equivalent to
(a) R (b) Q (c) Z (d) N |
| 3 | In the following sets, which is the open set?
(a) [2,5] (b) (2,5] (c) [2,5] (d) (1,2) U (4,8) |
| 4 | Which of the following is NOT the neighborhood of 3?
(a) (2,4) (b) {1,2,3,4,5} (c) [2,4] (d) R |
| 5 | Every finite set is
(a) Open (b) Closed (c) Perfect (d) Semi open |
| 6 | A set is said to be of first species if it has only a finite number of __________
(a) Limit points (b) Limit point of R (c) Derived set (d) Closed set |
| 7 | Every infinite bounded set of real numbers has a limit point known as
(a) Hausdorff property (b) Boizano-Weierstrass theorem (c) Archimedean property (d) Completeness property in R |
| 8 | Every ______ of a countable set is _____
(a) Proper set, countable (b) Number, countable (c) Subset, countable (d) Infinite, countable |
| 9 | Which of the following set is countable
(a) The set of real numbers R (b) The set of rational numbers Q (c) The set of complex numbers C (d) The set S=[0,1] |
| 10 | Every Cauchy sequence is
(a) Divergent (b) Unbounded (c) Oscillatory (d) Bounded |
| 11 | The set of all real number is
(a) Closed (b) Open (c) Both open and closed (d) Neither open nor closed |
| 12 | If the set is closed and bounded, then it is
(a) Covering set (b) Compact set (c) Derived set (d) Cluster set |
| 13 | Which one of the following is TRUE?
(a) Every constant function is continuous (b) Every identity function is continuous (c) Every polynomial function is continuous (d) All are true |
| 14 | Borel’s theorem is applicable for
(a) Open interval (a,b) (b) Closed interval [a,b] (c) Both open interval (a,b) and closed interval [a,b] (d) None of these |
| 15 | If repeated limits exist, then ;
(a) They are equal to each other (b) They are not equal to each other (c) They may or may not be equal to each other (d) None of these |
| 16 | A function f(x) is said to be differentiable at x=a, if ;
(a) Only right hand derivative must exist (b) Only left hand derivative must exist (c) Right hand and left hand derivatives at ‘a’ exist and equal (d) Right hand and left hand derivatives at ‘a’ does not exist |
| 17 | Continuity is a condition for differentiability, which is
(a) Necessary and sufficient (b) Necessary but not sufficient (c) Sufficient but not necessary (d) Neither necessary nor sufficient |
| 18 | Every continuous function defined on interval [a,b] is Riemann integrable on
(a) [a,b] (b) (a,b] (c) {a,b} (d) (a,b) |
| 19 | If a function f is monotonic on [a,b], then f is
(a) Riemann integrable on [a,b) (b) Riemann integrable on [a,b] (c) Riemann integrable on (a,b) (d) Riemann integrable on ]a,b[ |
| 20 | A continuous function, which has opposite signs at two points, vanishes between these points
(a) Exactly one time (b) At least one time (c) Does not vanish (d) Exactly three time |
| Published On – 7th June 2022 | |
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