MCQOPTIONS
Saved Bookmarks
MCQOPTIONS
This section includes 18 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 bijection is a function which is many-one and onto. |
| A. | True |
| B. | False |
| Answer» C. | |
| 2. |
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. | nCm x m! |
| B. | nCm x n! |
| C. | 0 |
| D. | none of the mentioned |
| Answer» D. none of the mentioned | |
| 3. |
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. | r=1∑r=n nCr (-1)n-r rm |
| B. | r=1∑r=n nCr (-1)n-r rn |
| C. | r=1∑r=n nCr (-1)m-r rn |
| D. | None of the mentioned |
| Answer» B. r=1∑r=n nCr (-1)n-r rn | |
| 4. |
Set A has 3 elements and set B has 4 elements then number of injections defined from A to B are? |
| A. | 12 |
| B. | 24 |
| C. | 36 |
| D. | 48 |
| Answer» C. 36 | |
| 5. |
Onto function are known as injection. |
| A. | True |
| B. | False |
| Answer» C. | |
| 6. |
For an onto function range is equivalent to codomain. |
| A. | True |
| B. | False |
| Answer» B. False | |
| 7. |
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. | nCm x m! |
| B. | nCm x n! |
| C. | 0 |
| D. | none of the mentioned |
| Answer» D. none of the mentioned | |
| 8. |
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. | nCm x m! |
| B. | nCm x n! |
| C. | 0 |
| D. | none of the mentioned |
| Answer» B. nCm x n! | |
| 9. |
A mapping f : X → Y is one one if __________ |
| A. | f(x1) ≠ f(x2) for all x1, x2 in X |
| B. | If f(x1) = f(x2) then x1 = x2 for all x1, x2 in X |
| C. | f(x1) = f(x2) for all x1, x2 in X |
| D. | None of the mentioned |
| Answer» C. f(x1) = f(x2) for all x1, x2 in X | |
| 10. |
An injection is a function which is? |
| A. | many-one |
| B. | one-one |
| C. | onto |
| D. | none of the mentioned |
| Answer» C. onto | |
| 11. |
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 | |
| 12. |
State_True_or_False.$ |
| A. | |
| B. | True |
| Answer» C. | |
| 13. |
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>‚àë<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>‚àë<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>‚àë<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>‚Äö√Ñ√∂‚àö‚Ć‚àö¬¥<sup>r=n</sup> <sup>n</sup>C<sub>r</sub> (-1)<sup>n-r</sup> r<sup>n</sup> | |
| 14. |
Set A has 3 elements and set B has 4 elements then number of injections defined from A to B are? |
| A. | 12 |
| B. | 24 |
| C. | 36 |
| D. | 48 |
| Answer» C. 36 | |
| 15. |
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 | |
| 16. |
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! | |
| 17. |
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. | |
| 18. |
An injection is a function which is : |
| A. | many-one |
| B. | one-one |
| C. | onto |
| D. | none of the mentioned |
| Answer» C. onto | |