Integrated Pest Management $(IPM)$ is based on which of the following?

If $f(x) = \sin x + \cos x$,then $f\left(\frac{\pi}{4}\right) f^{(iv)}\left(\frac{\pi}{4}\right)$ is equal to

Which of the following features of genetic codes allow bacteria to produce human insulin by recombinant $\text{DNA}$ technology?

$A$ small fish $0.4\, m$ below the surface of a lake is viewed through a simple converging lens of focal length $3\, m$. The lens is kept at $0.2\, m$ above the water surface such that the fish lies on the optical axis of the lens. The image of the fish seen by the observer will be at (given $\mu_{water} = 4/3$):

$\lim _{x \rightarrow 0} x^2 \sin \left(\frac{\pi}{x}\right)$ is equal to

$A$ metal $M$ which is not affected by strong acids like conc. $HNO_3$,conc. $H_2SO_4$ and conc. solutions of alkalies like $NaOH$,$KOH$ forms $MCl_3$ which finds use for toning in photography. The metal $M$ is