The plates of a parallel plate capacitor are charged up to $100 \, V$. $A$ $2 \, mm$ thick dielectric plate is inserted between the plates. To maintain the same potential difference,the distance between the capacitor plates is increased by $1.6 \, mm$. The dielectric constant of the plate is:

If $\int \sec ^2 x \operatorname{cosec}^4 x \, dx = -\frac{1}{3} \cot ^3 x + k \tan x - 2 \cot x + C$, then $k$ is equal to

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 $( g )=10 m s ^{-2}$

If $\int(1-\cos x) \operatorname{cosec}^2 x \, dx = f(x) + c$, then $f(x)$ is equal to

When a $p-n$ diode is reverse biased,then

$A$ complex has a composition corresponding to the formula $CoBr_2Cl \cdot 4NH_3$. What is the structural formula if conductance measurements show two ions per formula unit? Silver nitrate solution gives an immediate precipitate of $AgCl$ but no $AgBr$.