The limiting molar conductivities for \(\mathrm{H}^{+}, \mathrm{Na}^{+}, \mathrm{Cl}^{-}, \mathrm{CH}_3 \mathrm{COO}^{-}\)are \(349.6,50.1,76.3,40.9 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}\), respectively, in water at 298 K.
Match List-l and List-II

List-I	List-II
Electrolyte	\(\Lambda_m^o\)
(A) HCl	(I) \(390.5 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}\)
(B) NaCl	(II) \(126.4 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}\)
(C) \(\mathrm{CH}_3 \mathrm{COONa}\)	(III) \(425.9 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}\)
(D) \(\mathrm{CH}_3 \mathrm{COOH}\)	(IV) \(91.0 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}\)

Choose the correct answer from the options given below:

The standard Gibbs energy of the following reaction is \(-610 kJ mol ^{-1}\)
\(Mg(s)+2 Ag^{+}(aq) \rightarrow Mg^{2+}(aq)+2 Ag(s)\)
What is the standard EMF for the cell correspondng to the above reaction?
Given: Faraday's constant \(=96500 C mol ^{-1}\)

Arrange the following gases in the increasing order of their solubility in water at 298 K and atmospheric pressure.
(A) \(CH _4\left(K_{ H }=0.413 kbar \right)\)
(B) \(HCHO \left( K _{ H }=1.83 \times 10^{-5} kbar \right)\)
(C) \(He \left( K _{ H }=144.97 kbar \right)\)
(D) \(CO _2\left(K_{ H }=1.67 kbar \right)\)
Choose the correct answer from the options given below:

Answer the question on the basis of passage given below :
Aldehydes and ketones represent two essential classes of organic compounds which are extensively used in the synthesis of a wide variety of other organic molecules. Due to the inherent polarity of the central carbonyl group, these substances readily undergo nucleophilic addition reactions. Broadly speaking, these addition reactions can be categorized into two types: one in which simple addition of the nucleophilic reagent occurs across the \(> C = O\) bond, and the second type where the initial addition is subsequently followed by the elimination of a water molecule. A variety of ammonia derivatives, including hydroxylamine, hydraaine, phenylhydraxine, 2,4-dinitroplhemylhdrasine, and semicarbaside, all belong to this second category of reactions. These specific derivatives are fundamentally used for the identification and definitive characterization of aldehydes and ketones. Significantly, both types of nucleophilic addition reactions are strongly influenced by both steric and electronic factors. As a general rule, aliphatic aldehydes exhibit higher reactivity compared to aromatic aldehydes. The aliphatic aldehydes demonstrate the ability to reduce both Fehling's solution and Tollen's reagent, whereas aromatic aldehydes are limited to reducing only Tollen's reagent. In a similar manner to aldehydes, aromatic ketones are observed to be less reactive than aliphatic ketones towards all nucleophilic addition reactions. In a separate context, phenols and carboxylic acids both exhibit acidic properties in nature. Both classes of compounds readily dissolve in NaOH solution and cause blue litmus to turn red. However, carboxylic acids stand out as much stronger acids than phenols and thus can decompose sodium bicarbonate \(\left( NaHCO _3\right)\) with the distinct evolution of \(CO _2\) gas, a reaction which phenols do not undergo. It is important to note that both electron- donating and electron- withdrawing substituents significantly influence the acid strength of both aliphatic as well as aromatic carboxylic acids. Furthermore, unlike all other common aliphatic acids, formic acid uniquely possesses reducing properties and simultaneously does not display the typical reactions characteristic of the allyl group.
Which of the following statement(s) is/are correct?
A. Aldehydes give positive test with Tollen's reagent.
B. Ketones give positive test with Fehling's solution
C. Ketones do not react with Fehling's solution.
D. Aldehydes with Schiff's reagent restore pink colour
E. Ketones with Schiff's reagent restore pink colour.
Choose the correct answer from the options given below:

Helium and element ' \(X\) ' have outer electron configuration of ns2. Identify the element ' \(X\) '.

\(\Delta_o\) for a complex \([ML_6]^{3-}\) is \(18000\) \(cm^{-1}\). \(\Delta_t\) for \([ML_4]\) would be :

Insulin is the example of

Identify the correct statements in the context of paramagnetic substances.
(A) In external magnetic field B, individual atomic dipole moment points in opposite direction of B.
(B) Susceptibility is small and positive.
(C) In non-uniform magnetic field, the paramagnetic bar will tend to move from weak field to strong.
(D) Examples of paramagnetic substances are Aluminium, Sodium and oxygen.
Choose the correct answer from the options given below:

Which of the following statements are correct.
A. Every polynomial function is continuous.
B. Every constant function is continuous.
C. Modulus function is not continuous.
D. Identity function on real numbers is not continuous.
E. Every differentiable function is continuous.
Choose the correct answer from the options given below:

A surface of area \( \vec{A} = 2\hat{i} - 3\hat{k} \) exists in a region of electric field \( \vec{E} = a\hat{i} + b\hat{j} \). The net flux passing through the surface is

A double stranded DNA fragment has 500 Adenine bases. If total number of base pairs in this fragment is 2500, then what will be the number of guanine bases?

RNAi takes place in all eukaryotic organisms as a method of

The derivative of \(\frac{\tan ^{-1} x}{1+\tan ^{-1} x}\) with respect to \(\tan ^{-1}\) is :