Which of the following is an unsuitable habitat for algae?

The normal to the curve $x = a(1 + \cos \theta)$,$y = a \sin \theta$ at $\theta$ always passes through which fixed point?

Which of the following is a bad conductor of electricity?

The integral $\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \sec^{\frac{2}{3}} x \operatorname{cosec}^{\frac{4}{3}} x \, dx$ is equal to

If $f(x) = \frac{x^2-10x+25}{x^2-7x+10}$ and $f$ is continuous at $x = 5$,then $f(5)$ is equal to

$A$ soap bubble,having a radius of $1 \ mm$,is blown from a detergent solution having a surface tension of $2.5 \times 10^{-2} \ N/m$. The pressure inside the bubble is equal to the pressure at a point $Z_0$ below the free surface of water in a container. Taking $g = 10 \ m/s^2$ and the density of water $\rho = 10^3 \ kg/m^3$,the value of $Z_0$ is: (in $cm$)