What is the use of potassium dichromate $(K_2Cr_2O_7)$?

An integrating factor of the differential equation $(1-x^2) \frac{dy}{dx} + xy = \frac{x^4}{(1+x^5)} (\sqrt{1-x^2})^3$ is

Which of the following cations cannot give the borax bead test?

$A$ thin semi-circular ring of radius $r$ has a positive charge $q$ distributed uniformly over it. The net electric field $\vec{E}$ at the center $O$ is:

$A$ projectile is projected with velocity $k v_e$ in the vertically upward direction from the ground into space. ($v_e$ is the escape velocity and $k < 1$). If air resistance is considered to be negligible,then the maximum height from the centre of the Earth to which it can go will be: ($R =$ radius of Earth)

When ${}_{92}U^{238}$ changes into ${}_{82}Pb^{206}$,the number of $\alpha$ and $\beta^-$ particles emitted are: