If $f(x)$ satisfies the relation $f(x)=e^x+\int_0^1\left(y+x e^x\right) f(y) d y$, then $e+f(0)$ is equal to $\_\_\_\_$ .

The fifth harmonic of a closed organ pipe is found to be in unison with the first harmonic of an open pipe. The ratio of lengths of closed pipe to that of the open pipe is $5 / x$. The value of $x$ is $\_\_\_\_$

In case of vertical circular motion of a particle by a thread of length $r$ if the tension in the thread is zero at an angle $30^{\circ}$ shown in figure, the velocity at the bottom point $(A)$ of the circular path is (g = gravitational acceleration)

The velocity $(v)$ - Distance $(x)$ graph is shown in figure. Which graph represents acceleration(a) versus distance ( $x$ ) variation of this system?