MCQOPTIONS
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MCQOPTIONS
This section includes 5 Mcqs, each offering curated multiple-choice questions to sharpen your Discrete Mathematics knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
A function is defined by mapping f:A B such that A contains m elements and B contains n elements and m > n then number of bijections are ________ |
| A. | <sup>n</sup>C<sub>m</sub> x m! |
| B. | <sup>n</sup>C<sub>m</sub> x n! |
| C. | 0 |
| D. | none of the mentioned |
| Answer» D. none of the mentioned | |
| 2. |
A function is defined by mapping f : A B such that A contains m elements and B contains n elements and 1 n m then number of onto functions are ________ |
| A. | <sub>r=1</sub> <sup>r=n</sup> <sup>n</sup>C<sub>r</sub> (-1)<sup>n-r</sup> r<sup>m</sup> |
| B. | <sub>r=1</sub> <sup>r=n</sup> <sup>n</sup>C<sub>r</sub> (-1)<sup>n-r</sup> r<sup>n</sup> |
| C. | <sub>r=1</sub> <sup>r=n</sup> <sup>n</sup>C<sub>r</sub> (-1)<sup>m-r</sup> r<sup>n</sup> |
| D. | None of the mentioned |
| Answer» B. <sub>r=1</sub> <sup>r=n</sup> <sup>n</sup>C<sub>r</sub> (-1)<sup>n-r</sup> r<sup>n</sup> | |
| 3. |
A function is defined by mapping f : A -> B such that A contains m elements and B contains n elements and m>n then number of one one functions are ________ |
| A. | <sup>n</sup>C<sub>m</sub> x m! |
| B. | <sup>n</sup>C<sub>m</sub> x n! |
| C. | 0 |
| D. | none of the mentioned |
| Answer» D. none of the mentioned | |
| 4. |
A function is defined by mapping f : A B such that A contains m elements and B contains n elements and m n then number of one one functions are _________ |
| A. | <sup>n</sup>C<sub>m</sub> x m! |
| B. | <sup>n</sup>C<sub>m</sub> x n! |
| C. | 0 |
| D. | none of the mentioned |
| Answer» B. <sup>n</sup>C<sub>m</sub> x n! | |
| 5. |
A mapping f : X Y is one one if __________ |
| A. | f(x<sub>1</sub>) f(x<sub>2</sub>) for all x<sub>1</sub>, x<sub>2</sub> in X |
| B. | If f(x<sub>1</sub>) = f(x<sub>2</sub>) then x<sub>1</sub> = x<sub>2</sub> for all x<sub>1</sub>, x<sub>2</sub> in X |
| C. | f(x<sub>1</sub>) = f(x<sub>2</sub>) for all x<sub>1</sub>, x<sub>2</sub> in X |
| D. | None of the mentioned |
| Answer» C. f(x<sub>1</sub>) = f(x<sub>2</sub>) for all x<sub>1</sub>, x<sub>2</sub> in X | |