Name a transition element which does not exhibit variable oxidation states

Match List-I with List-II 

List-I	List-II
(A) \(\Lambda _{ m }\) of \(K C l\) increases on dilution	\(I\).  is a linear. Graph
(B) \(\Lambda_m\) of \(CH _3 COOH\) increases on dilution	\(II\) is a non-linear graph
(C) \(\Lambda_m\) of \(K C l\) versus (molarity) \(^{1 / 2}\)	\(III\) due to increased degree of ionisation
(D) \(\Lambda_m\) of \(CH _3 COOH\) versus (molarity) \(^{1 / 2}\)	\(IV\) due to weakening of interionic attractions

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"Answer the question on basis of passage given below :
Carboxylic acids are weaker than mineral acids, but they are stronger acids than alcohols and many simple phenols (\(\text{pKa}\) is ~ 16 for ethanol and 10 for phenol). The higher acidity of carboxylic acids as compared to phenols can be understood similarly. The conjugate base of carboxylic acid, a carboxylate ion, is stabilised by two equivalent resonance structures in which the negative charge is at the more electronegative oxygen atom. The conjugate base of phenol, a phenoxide ion, has non-equivalent resonance structures in which the negative charge is at the less electronegative carbon atom. Further, the negative charge is delocalised over two electronegative oxygen atoms in carboxylate ion whereas it is less effectively delocalised over one oxygen atom and less electronegative carbon atoms in phenoxide ion. Thus, the carboxylate ion is more estabilised than phenoxide ion, so carboxylic acids are more acidic than phenols.
Effect of substituents on the acidity of carboxylic acids: substituents may affect the stabliity of the conjugate base and thus, also affect the acidity of the carboxylic acids. Electron withdrawing group increase the acidity of carboxylic acids by stabilising the conjugate base through delocalisation of the negative charge by inductive and/or resonance effects. Conversely, electron donating groups decrease the acidity by destabilising the conjugate base.
Which of the following compounds would have the smallest value of \(\text{pKa}\)?"

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All transition elements display typical metallic properties like high melting point, boiling point, tensile strength, high malleability and ductility, luster, etc. Their metallic character increases down the group and elements of \(4 d\) and 5d series exhibit higher metallic characters. They show variable oxidation states and forms a number of coloured compounds due to the presence of unpaired electrons which shows d-d transitions and makes them paramagnetic.
Which of the following will be coloured in aqueous medium?

Match List-I with List-II

List-I (Types of solutions)	List-II (Examples)
(A) Gas in Gas solution	(I) Oxygen dissolved in water
(B) Gas in Liquid solution	(II) Copper dissolved in gold
(C) Liquid in Solid solution	(III) Mixture of oxygen and nitrogen gases
(D) Solid in Solid solution	(IV) Amalgam of mercury with sodium

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Arrange the following in increasing order of their molarity when their equal weights are dissolved in 250 mL of water.
(A) glucose \(\left(180 g mol ^{-1}\right)\)
(B) sodium carbonate (106 g mol-1)
(C) sodium hydroxide \(\left(40 g mol ^{-1}\right)\)
(D) acetic acid \(\left(60 g mol ^{-1}\right)\)
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Kinetic studies not only help us to determine the rate of a chemical reaction but also describe the conditions by which the reaction rates can be altered. The factors such as concentration, temperature, pressure and catalyst affect the rate of a reaction. The speed of a reaction or the rate of a reaction can be defined as the change in concentration of a reactant or product in unit time.
Rate \(= \text{k}[\text{A}]^x [\text{B}]^y\)
Here k is the rate constant
\(x + y\) gives the overall order of a reaction, whereas \(x\) and \(y\) represent the order with respect to the reactants A and B, respectively.
Which of the following statements are correct?
(A) Catalysts increase the rate of a chemical reaction.
(B) Catalysts can catalyze both spontaneous and non-spontaneous reactions.
(C) Higher the activation energy for a chemical reaction, lower is the rate of the reaction.
(D) Catalyst increases the potential energy barrier.
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Assume an electric field \( \vec{E} = 30x \, \hat{i} \) exists in space. If \( V_0 \) is the potential at the origin and \( V_A \) is the potential at \( x = 2 \) m, then the potential difference \( V_A - V_0 \) is:

If the lines \(\frac{1-x}{3}=\frac{2 y-4}{4 K}=\frac{z-3}{2}\) and \(\frac{x-1}{3 K}=\frac{1-y}{-1}=\frac{6-z}{5}\) are perpendicular, then the value of \(K\) is :

The function \(f(x)=x^3+3 x^2+4 x+4, x \in R\) (set of real numbers):

A random variable \(X\) has the following probability distribution:

X	0	1	2	3	4	5	6	7
P(X)	0	k	2k	2k	3k	\(k^2\)	\(2 k^2\)	\(7 k^2+k\)

The value of \(P(4 < X < 7)\) is equal to

The electric field intensity produced by the radiations coming from a 200 W bulb at 6 m distance is E . What is the electric field intensity produced by the radiations coming from 100 W bulb at the same distance?

Arrange the following steps in correct sequence for the technique of DNA fingerprinting.
(A) Detection of hybridized DNA fragments by autoradiography
(B) Separation of DNA fragments by electrophoresis
(C) Isolation and digestion of DNA
(D) Transferring of separated DNA fragments and hybridization using labelled VNTR probe
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