Class XII A Test 1

R is a relation on the set Z of integers and it is given by $\left(x,y\right)\in R\ \Longleftrightarrow\left|x-y\right|\le1$  .Then ,   R is

• reflexive and transitive

• reflexive and symmetric

• symmetric and transitive

• an equivalence relation

R is a relation from {11,12,13} to {8,10,12} defined by y = x - 3 . Then,  $R^{-1}$  is

• { (8,11) , (10,13) }

• { (11,8) , (13,10) }

• { (10,13) , (8,11) , (8,10) }

• none of these

Let A = { 1,2,3 } and R = { (1,2) , (2,3) , (1,3)} be a relation on A. Then , R is

• neither reflexive nor transitive

• neither symmetric nor transitive

• transitive

• none of these

If R is a relation on the set A={1,2,3} given by R = {(1,1),(2,2),(3,3)}, then R is

• reflexive

• symmetric

• transitive

• equivalence

The maximum number of equivalence relation on the set A={1,2,3} is

• 1

• 2

• 3

• 5

The function $f:\ Z\rightarrow Z$  given by  $f\left(x\right)=x^2+x$  for all  $x\in Z$  is

• one-one but not onto

• many-one but not onto

• one-one and onto

• many-one and onto

The function $f:Q\rightarrow Q$  given by f(x) = 2x - 3 for all  $x\in Q$  is

• one-one but not onto

• onto but not one-one

• bijection

• none of the above

The function $f:\ \left[0,\infty\right)\rightarrow R$  given by  $f\left(x\right)=\frac{x}{x+1}$  is

• one-one and onto

• one-one but not onto

• onto but not one-one

• neither one-one nor onto

Find the principal values of $\tan^{-1}\left\{\sin\left(-\frac{\pi}{2}\right)\right\}$  

•  $\frac{\pi}{4}$  

•  $-\frac{\pi}{4}$  

•  $\frac{3\pi}{2}$  

•  $-\frac{3\pi}{2}$  

Find the principal values of  $\cot^{-1}\left(-\sqrt{3}\right)$  

•  $\frac{5\pi}{6}$  

•  $-\frac{5\pi}{6}$  

•  $\frac{\pi}{6}$  

•  $-\frac{\pi}{6}$