Which among the following is a haloalkyne?

If $\int e^x \left( \frac{1-\sin x}{1-\cos x} \right) dx = f(x) + \text{constant}$,then $f(x)$ is equal to

Observe the following statements:
$I. f(x) = a x^{41} + b x^{-40} \Rightarrow \frac{f^{\prime \prime}(x)}{f(x)} = 1640 x^{-2}$
$II. \frac{d}{d x} \tan ^{-1}\left(\frac{2 x}{1-x^2}\right) = \frac{1}{1+x^2}$
Which of the following is correct?

The $P-V$ diagram of a system undergoing thermodynamic transformation is shown in figure. The work done on the system in going from $A$ $\rightarrow B$ $\rightarrow C$ is $50 \ J$ and $20 \ cal$ heat is given to the system. The change in internal energy between $A$ and $C$ is ...... $J$. (Take $1 \ cal = 4.2 \ J$)

Which polymer is used as a lubricant and an electrical insulator?

For the parabola $y^2+6y-2x+5=0$:
$(I)$ The vertex is $(-2,-3)$
$(II)$ The directrix is $y+3=0$
Which of the following is correct?