Question Text
Question 1 :
The function $f\left( x \right)=\left[ x \right] ,$  at ${ x }=5$ is:<br/>
Question 2 :
Consider the function<br>$f(x)=\begin{cases}-2\sin x & if & x\le -\dfrac{\pi}{2} \\ A\sin x+B & if & -\dfrac{\pi}{2} < x < \dfrac{\pi}{2} \\ \cos x & if & x \ge \dfrac{\pi}{2}\end{cases}$<br>which is continuous everywhere.<br>The value of B is
Question 4 :
If $\displaystyle f\left( x \right)=\left[ \tan { x }  \right] +\sqrt { \tan { x } -\left[ \tan { x }  \right]  } ,0\le x<\frac { \pi  }{ 2 } $, where $[.]$ denotes thegreatest integer function, then
Question 5 :
If the displacement of a particle moving in straight line is given by $x=3t^2+2t+1$ at time $t$ then  the acceleration of the particle at time $t=3$ is
Question 6 :
The interval in which the function $f(x) = {x^3}$ increases less rapidly than $\,g(x) = 6{x^2} + 15x + 5$ is :
Question 7 :
A man on a wharf 12 mt above the water level pulls in a rope to which a boat is attached at the rate of $1$ mt per second. At what rate is the boat approaching the shore, when there is still $13$ mt rope out ?
Question 8 :
If a ball is thrown vertically upwards and the height 's' reached in time 't' is given by $s = 22 t - 11 t^2$, then the total distance travelled by the ball is
