Greatest integer function

Q. If $y=3\left[x\right]+1=4[x-1]-10$, then the value of $[x+2y]$ is

Q. If $f\left(x\right)=\cos \left({\pi }^2\right]x+\cos \left(-{\pi }^2\right]x,$ where [x] stands for the greatest integer function, then

1. $f\left(\frac{\pi }{2}\right)=-1$
2. $f\left(\pi \right)=1$
3. $f(-\pi )=0$
4. $f\left(\frac{\pi }{4}\right)=1$

Q.

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

1. $\left[\right[x\left]\right]=\left[x\right]$

2. [x + n ] = [x] + n , n $\in$ I

3. x - 1 < [x] $\le$ x

4. [-x] = -1 - [x] , when x is not an integer

Q.

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

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

2. $[x{]}^x$

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

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

Q. gof(x) is equal to g(x) $\times$ f(x).

1. True
2. False

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

1. $x$
2. $f\left(x\right)$
3. $g\left(x\right)$
4. 1