During bromination of phenol, Lewis acid is not necessary required because of :

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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.
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Given below are four statements with reference to a catalyst. Choose the incorrect statement(s)
(A) A catalyst lowers the potential energy barrier, thus decreasing the activation energy.
(B) A catalyst lowers the Gibbs energy \((\Delta G)\) of the reaction.
(C) A small amount of catalyst converts a large amount of reactants into products.
(D) A catalyst can catalyze non-spontaneous reactions also.
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\(\left[ Cu ( en )_2\right]^{2+}\) is more stable than \(\left[ Cu \left( NH _3\right)_4\right]^{2+}\) because

Which of the following is not correct about the order of a reaction?

Ambidentate ligand among the following is
A. NCS
B. \(\text{C}_2\text{O}_4^{2-}\)
C. SCN
D. \(\text{H}_2\text{NCH}_2\text{CH}_2\text{NH}_2\)
E. \(\text{NO}_2\)
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When we consider an inert electrode in a cell; which statement is not suitable for it?
(A) It provides surface either for oxidation or for reduction reaction.
(B) It does not participate in the cell reaction.
(C) It provides surface for redox reaction.
(D) It provides surface for conduction of electrons.
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Electrons in an experiment are accelerated by a voltage of 36 kV. If the voltage is increased to 144 kV, then the de-broglie wavelength associated with the electron would

The area enclosed between \(y^2=4 x\) and \(x^2=4 y\) is:

The order of the differential equation \(\left[1+\left(\frac{d y}{d x}\right)^2\right]^2=\left(\frac{d^3 y}{d x^3}\right)\) is:

Arrange the following electromagnetic waves in increasing order of their wavelengths.
(A) Visible Light
(B) Microwave
(C) X rays
(D) Infra-red rays
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Match List-I (Name of the Base) with List-II (Structure)

List-I (Name of the Base)	List-II (Structure)
(A). Adenine (A)	(I).
(B). Cytosine (C)	(II).
(C). Thymine (T)	(III).
(D). Guanine (G)	(IV).

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An object is placed at 5 cm in front of a concave mirror with a radius of curvature of 20 cm. The distance of the image from mirror and its nature are