Experimentally determined molar mass is always lower than the true value in case of:

\(2 N_2 O _5 \rightarrow 4 NO _2+ O _2\)
At a given instant of time, the rate and rate constant are 1.02 \(\times\) 10\(^-\)\(\mathrm{4}\) mol L\(^-\)\(\mathrm{1}\) s\(^-\)\(\mathrm{1}\) and 3.4 \(\times\) 10\(^-\)\(\mathrm{5}\) s\(^-\)\(\mathrm{1}\), respectively.
The concentration of N\(_2\)\(\mathrm{O}\)_5 at that time will be:

Magnetic moment values for \([\text{Fe}(\text{H}_2\text{O})_6]^{3+}\) and \([\text{Fe}(\text{CN})_6]^{3-}\) are

The quantity of charge required to obtain one mole of aluminum from \(\text{Al}_2\text{O}_3\) is :

Answer the question on basis of passage given below:
Organic compounds containing carbon -oxygen double bonds ( \(C = O\) ) are called carbonyl compounds. These are highly polar molecules. Hence, their boiling points are higher than hydrocarbons and ethers. Aldehydes can be prepared from dehydrogenation or oxidation of alcohols and by reduction of acylhalides. Ketones are prepared by oxidation of secondary alcohols or by hydration of alkynes etc. Aldehydes and ketones undergo nucleophilic addition reaction with the number of nucleophiles such as HCN , NaHSO3 ammonia derivatives. Carboxylic acids are prepared by the oxidation of primary alcohols, aldehydes and alkenes, by hydrolysis of nitriles. Carboxylic acids are more acidic than alcohols and phenols.
Which of the following is most reactive towards nucleophilic addition reaction ?

Choose the correct statement about molar conductivity, \(\Lambda_m\)

The unit of molar conductivity is

Answer the question on the basis of passage given below :
Adsorption is a surface phenomenon which can be expressed by means of an empirical relationship know as Freundlich Adsorption isotherm. The relationship given by \(\frac{x}{m} = Kp^{\frac{1}{n}}\ (n > 1)\)
x = Mass of the gas adsorbed
m = Mass of adsorbent
p = Pressure at which adsorption takes place
K and n are constant

Gas	Critical Temperature (in K)
\(\text{C}_2\text{H}_6\)	210
\(\text{SO}_2\)	630
\(\text{Cl}_2\)	243
\(\text{H}_2\)	33

On the basis of given data which one of the following gases shows maximum adsorption on a definite amount of charcoal?

Osmotic pressure of 0.02 M urea solution at \(27^{\circ} C\), is (given \(R=0.0821 atm L mol ^{-1} K^{-1}\) )

Match List-I with List-II

List-I (Electromagnetic Wave Wave)	List-II (Application)
(A) Microwaves	(I) Photographs during foggy season and night vision cameras
(B) X-rays	(II) Radar
(C) Gamma rays	(III) Photographs internal parts of human body
(D) Infrared Rays	(IV) Radiography for malignant tumors in cancer treatment

Choose the correct answer from the options given below:

Answer the question on basis of passage given below :
P block elements are placed in groups 13 to 18 of the periodic table. Their valence shell electronic configuration is \(ns^2 np^{1-6}\). Group 16 of the p block elements are known as the group of chalcogens having \(ns^2 np^4\) as their general electronic configuration. They exhibit number of oxidation states but the stability of \(- 2\) oxidation state decreases down the group. They are sometimes also known as group of chalcogens as the name is derived from the Greek word for brass and points to the association of sulphur and its congeners with copper. Their ionisation enthalpy decreases down the group. Oxygen shows anomalous behaviour due to its small size and high electronegativity.
Match the oxidation state of phosphorous in the following compounds to their counter parts in List II.

List - I (Compounds)	List - II (Oxidation States)
(A) \(H _3 PO _2\)(Hypophosphorous acid)	(I) +3
(B)\(H _4 P _2 O _6\)(Hypophosphoric acid)	(II) +5
(C) \(H _3 PO _3\)(Phosphorous acid)	(III) +1
(D)\(H _3 PO _4\)(Orthophosphoric acid)	(IV) +4

Choose the correct answer from the options given below :

The shortest distance between the following lines :
\(\vec{r}=(\hat{i}+\hat{j}-\hat{k})+s(2 \hat{i}+\hat{j}+\hat{k})\)
\(\vec{r}=(\hat{i}+\hat{j}+2 \hat{k})+t(4 \hat{i}+2 \hat{j}+2 \hat{k})\), where \(s\) and \(t\) are scalars, is :

If in a pond there were 20 lotus plants last year and through reproduction 8 new plants are added, taking the current population to 28, the birth rate would be: