If the straight line $y=mx+c$ is parallel to the axis of the parabola $y^2=lx$ and intersects the parabola at $\left(\frac{c^2}{8}, c\right)$,then the length of the latus rectum is

At $300 K$ , an ideal dilute solution of a macromolecule exerts osmotic pressure that is expressed in terms of the height $(h)$ of the solution $($density $=1.00 g cm ^{-3} )$ where h is equal to $2.00 cm$ . If the concentration of the dilute solution of the macromolecule is $2.00 g dm ^{-3}$, the molar mass of the macromolecule is calculated to be $X \times 10^4 g mol ^{-1}$. The value of $X$ is $...$ .
Use : Universal gas constant $(R)=8.3 J K ^{-1} mol^{-1}$ and acceleration due to gravity $( g )=10 m s ^{-2}$

$A$ screen is placed $50 \, cm$ from a single slit, which is illuminated with $6000 \, \mathring{A}$ light. If the distance between the first and third minima in the diffraction pattern is $3 \, mm$, the width of the slit is.....$mm$

Consider a solid insulating sphere of radius $R$ with charge density varying as $\rho = \rho_0 r^2$ (where $\rho_0$ is a constant and $r$ is measured from the centre). Consider two points $A$ and $B$ at distances $x$ and $y$ respectively from the centre,such that $x < R$ and $y > R$. If the magnitudes of the electric fields at points $A$ and $B$ are equal,then:

The resistance across $M$ and $N$ in the given figure is

The complex formed by a pair of synapsed homologous chromosomes is called: