In which of the following sets allotropes of carbon are correctly matched with their uses?
i. graphite - crucibles
ii. activated charcoal - water filters
iii. carbon black - fuel
The correct answer is

2.0 g of \(\mathrm{H}_2\) diffuses through a porous container in 10 minutes. How many grams of \(\mathrm{O}_2\) would diffuse from the same container in the same time under similar conditions?

Match List I with List II

	List-I (defect)		List-II (Examples)
(A)	Frenkel defects	(1)	$\mathrm{FeO}$
(B)	Schottkey defects	(2)	$\mathrm{NaCl}$
(C)	Vacancy defects	(3)	$\mathrm{AgCl}$
(D)	Metal deficiency defects	(4)	Crystals with vacant lattice sites.

Observe the following statements :
a. The thermal stability of hydrides of group 16 elements follow the order :
\(\mathrm{H}_2 \mathrm{O}>\mathrm{H}_2 \mathrm{~S}>\mathrm{H}_2 \mathrm{Se}>\mathrm{H}_2 \mathrm{Te}\)
b. Acidic nature of hydrides of group 16 elements follow the order :
\(\mathrm{H}_2 \mathrm{O}>\mathrm{H}_2 \mathrm{~S}>\mathrm{H}_2 \mathrm{Se}>\mathrm{H}_2 \mathrm{Te}\)
c. The reducing nature of \(\mathrm{H}_2 \mathrm{~S}, \mathrm{H}_2 \mathrm{Se}\) and \(\mathrm{H}_2\) Te follow the order :
\(\mathrm{H}_2 \mathrm{~S} < \mathrm{H}_2 \mathrm{Se} < \mathrm{H}_2 \mathrm{Te}\)
The correct statement are:

If the number average molecular weight and weight average molecular weight of a polymer are 40000 and 60000 respectively, the polydispersity index of the polymer will be

The outer electronic configuration of " \(\mathrm{Pd}\) " is

A chemical \(A\) is used for the preparation of washing soda to recover ammonia. When \(\mathrm{CO}_2\) is bubbled through an aqueous solution of \(A\), the solution tums milky. It is used in white washing due to disinfectant nature. What is the chemical formula of \(A\) ?

The half-lives of two radioactive nuclides \(A\) and \(B\) are 1 and \(2 \mathrm{~min}\) respectively. Equal weights of \(A\) and \(B\) are taken separately and allowed to disintegrate for \(4 \mathrm{~min}\). What will be the ratio of weights of \(A\) and \(B\) disintegrated?

If \(t \in \mathbb{R}-\{-1\}\), then the locus of the point \(\left(\frac{3 a t}{1+t^3}, \frac{3 \mathrm{at}^2}{1+t^3}\right)\) is

If the position vectors of \(\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}\) are \(\bar{i}+2 \bar{j}+2 \bar{k}, 2 \bar{i}-\bar{j}, \bar{i}+\bar{j}+3 \bar{k}\) and \(4 \bar{j}+5 \bar{k}\) respectively, then the quadrilateral \(A B C D\) is a

A \(40 \%\) by mass sucrose solution is heated till, it becomes \(50 \%\) by mass. Calculate the mass of water lost from \(100 \mathrm{~g}\) of the solution is

If $f:R\to R$ and $g:R\to R$ are two functions defined by $f\left(x\right)=ax+b\left(a\ne 0\right)\forall x\in R$ and $g\left(x\right)=c{x}^3+d\left(c\ne 0\right)\forall x\in R$, then ${\left(fog\right)}^{-1}\left(x\right)=$

If $f:[0,2)\to \mathrm{ℝ}$ is defined by $f\left(x\right)=\left\{\begin{array}{ll}1+\frac{2x}{k}& \text{ for }0\le x<1\\ kx& \text{ for }1\le x<2\end{array}\right.$, where $k>0$ and $f$ is such that $\underset{x\to 1^{-}}{\lim }f\left(x\right)=\underset{x\to 1^{+}}{\lim }f\left(x\right),$ then the value of $k^2$ is