Focal length of a convex lens will be maximum for

The diameter of the objective lens of a telescope is $250 \ cm$. For light of wavelength $600 \ nm$ coming from a distant object,the limit of resolution of the telescope is close to:

$\lim _{x \rightarrow \infty} \left(\frac{x+a}{x+b}\right)^{x}$ is equal to

$A$ charged particle of mass $m$ and charge $q$ is released from rest in a uniform electric field $E$. Neglecting the effect of gravity,the kinetic energy of the charged particle after $t$ seconds is:

Which of the following is false?

$A$ magnetic needle lying parallel to a magnetic field is turned through $60^{\circ}$. The work done on it is $W$. The torque required to maintain the magnetic needle in the position mentioned above is