If $x^2+px+1$ is a factor of the expression $ax^3+bx+c$,then

The plates of a parallel plate capacitor are charged up to $200 \ V$. $A$ dielectric slab of thickness $4 \ mm$ is inserted between its plates. Then,to maintain the same potential difference between the plates of the capacitor,the distance between the plates is increased by $3.2 \ mm$. The dielectric constant of the dielectric slab is:

The solution of $\frac{dy}{dx} = (\frac{x}{y})^{-1/3}$ is

Which type of mouthparts is present on the lateral side of the pre-oral cavity in cockroach?

What is the correct order of spin only magnetic moment (in $BM$) of $Mn^{2+}, Cr^{2+}$ and $V^{2+}$?

If the point $P(1,3)$ undergoes the following transformations successively:
$(i)$ Reflection with respect to the line $y=x$.
(ii) Translation through $3$ units along the positive direction of the $X$-axis.
(iii) Rotation through an angle of $\frac{\pi}{6}$ about the origin in the clockwise direction.
Then,the final position of the point $P$ is