11). Which of the four statements given below is different from the other?
| A). \( \Large f:A \rightarrow B \) |
| B). \( \Large f:x \rightarrow f \left(x\right) \) |
| C). f is a mapping from A to B |
| D). f is a function from A to B |
|
12). Which of the following is correct?
| A). \( \Large A \cap B \subset A \cup B \) |
| B). \( \Large A \cap B \subseteq A \cup B \) |
| C). \( \Large A \cup B \subset A \cap B \) |
| D). None of these |
|
13). Let \( \Large f:N \rightarrow R:f \left(x\right)=\frac{ \left(2x-1\right) }{2} \) and \( \Large g:Q \rightarrow R:g \left(x\right)=x+2 \) be two functions then \( \Large \left(gof\right) \left(\frac{3}{2}\right) \)
| A). 3 |
| B). 1 |
| C). \( \Large \frac{7}{2} \) |
| D). None of these |
|
14). If N be the set of all natural numbers, consider \( \Large f:N \rightarrow N:f \left(x\right)=2x \forall x \epsilon N \), then f is:
| A). one-one onto |
| B). one-one into |
| C). many-one |
| D). one of these |
|
15). N is the set of natural numbers. The relation R is defined on \( \Large N \times N \) as follows: \( \Large \left(a,\ b\right)R \left(c,\ d\right) \Leftrightarrow a+d=b+c \) is:
| A). reflexive |
| B). symmetric |
| C). transitive |
| D). all of these |
|
16). Let \( \Large A = \{ 2,\ 3,\ 4,\ 5 \} \) and
\( \Large R = \{ \left(2,\ 2\right),\ \left(3,\ 3\right),\ \left(4,\ 4\right),\ \left(5,\ 5\right),\
\left(2,\ 3\right),\ \left(3,\ 2\right),\) \( \Large \ \left(3,\ 5\right),\ \left(5,\ 3\right) \} \) be a relation in A, Then R is:
| A). reflexive and transitive |
| B). reflexive and symmetric |
| C). reflexive and anti-symmetric |
| D). none of the above |
|
17). For real numbers x and y, we write
\( \Large x R y \Leftrightarrow x^{2}-y^{2}+\sqrt{3} \)
is an irrational number. Then the relation R is:
| A). reflexive |
| B). symmetric |
| C). transitive |
| D). none of these |
|
18). \( \Large f \left(x\right)=\frac{1}{2}-\tan \frac{ \pi x}{2},\ -1 < x < 1\ and\ g \left(x\right) \) \( \Large =\sqrt{ \left(3+4x-4x^{2}\right) } \) then dom \( \Large \left(f + g\right) \) is given by:
| A). \( \Large \left[ \frac{1}{2}, 1 \right] \) |
| B). \( \Large \left[ \frac{1}{2}, -1 \right] \) |
| C). \( \Large \left[ -\frac{1}{2}, 1 \right] \) |
| D). \( \Large \left[ -\frac{1}{2}, -1 \right] \) |
|
19). If \( \Large R \subset A \times B\ and\ S \subset B \times C \) be two relations, then \( \Large \left(SOR\right)^{-1} \) is equal to:
| A). \( \Large S^{-1}OR^{-1} \) |
| B). \( \Large R^{-1}OS^{-1} \) |
| C). SOR |
| D). ROS |
|
20). If \( \Large A = \{ x:x\ is\ multiple\ of\ 4 \} \) and \( \Large B = \{ x:x\ is\ multiples\ of 6 \} \) then \( \Large A \subset B \) consists of all multiples of:
| A). 16 |
| B). 12 |
| C). 8 |
| D). 4 |
|
