Greatest integer function

Q.

Let $S$ be a set of all distinct numbers of the form $\frac{P}{Q}$ , where $p,q\in \left\{1,2,3,4,5,6\right\}$. What is the cardinality of the set $S$?

1. $21$

2. $23$

3. $32$

4. $36$

Q.

Divide the following

$0.5÷10$

Q.

$1.21$($21$ repeating) as a fraction?

Q.

How many real numbers satisfy the condition 0 $\le$$\frac{2}{3}\left[x\right]\le$1

__

Q.

Which of the following functions are identical to f(x) =
$f\left(x\right)=\{\begin{array}{cc}x,& 1\le x<2\\ x^2,& 2\le x<3\end{array}$

(1 $\le$ x < 3)

1. 

2. 

3. 

4. 

Q.

If I < x < I +1, Find [-x], where I is an integr

1. -I

2. -I+1

3. -I-1

4. I-1

Q.

What is the value of [x] + [-x] , where [x] is the greatest integer function

1. -1

2. 0

3. 1

4. 2

Q.

Find the function corresponding to the graph given below, $1\le x\le 3$ ( The function which closely describes the graph )

1. $[x{]}^x$

2. $x^{\left[x\right]}$

3. $\left[x^3\right]$

4. $\left[x^x\right]$

Q. Let g(x)=1 + x - [x] and f(x) =$\{\begin{array}{ccc}-1& x<0& \\ 0,& x=0& \\ 1,& x>0& \end{array}$ then for all x, f[g(x)] is equal to:
(IIT 2001)

1. 1
2. x
3. f(x)
4. g(x)

Q.

Divide the following

$3.2÷100$

Q.

Which of the following is true about [x], greatest integer function ?

1. 

2. 

3. 

4. 

Q.

$\left[\frac{\left[x\right]}{n}\right]=\left[\frac{x}{n}\right]$ Where [] represents greatest integer function.

1. True

2. False

Q. The only number which is neither positive nor negative in a real number set is __________

1. $\pi$
2. 0
3. $\infty$
4. 1

Q.

Subtract$\frac{33}{10}-1\frac{7}{15}$

Q.

Divide the following

$2.11÷1000$

Q.

Divide the following

$62.3÷1000$

Q.

Fill the box

$\frac{4}{13}÷\square =\frac{-4}{7}$