Let the degree and order of the differential equation \(2 x^3 \frac{d y}{d x}-5\left(\frac{d^2 y}{d x^2}\right)^2=6\left(\frac{d y}{d x}\right)^3\) be \(m\) and \(n\) respectively. Then
(A) \(m=2\)
(B) \(n=3\)
(C) \(m=3\)
(D) \(m n=4\)

The area bounded by \(x = 1, x = 2, xy = 1\) and x-axis is :

A person started keeping aside 10,000 each year for his child's college education in a sinking fund. The amount he will receive after 6 years, if the rate of interest is \(10 \%\) p.a., is: [Use \((1.1)^{\wedge} 6=1.771\) ]

The domain of \(y = \cos^{-1}(x^2 - 4)\) is:

The number of all possible matrices of order \(3 \times 4\) with each entry 1, 2 or 3 are:

The interval in which \(f(x)=2 x^3-9 x^2+12 x+1\) is decreasing is:

If R and S are two equivalence relations on a set A, then

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:

Arrange the following ligands in decreasing order of field strength in spectrochemical series.
(A) Br\(^-\)
(B) H\(_2\)\(\mathrm{O}\)
(C) OH\(^-\)
(D) CO
Choose the correct answer from the options given below:

The value of \(\int(5 x-2)^3 d x\) is:

Read the passage carefully and answer the questions
Replacement of a hydrogen atom in a hydrocarbon by an alkoxy or carboxyl group yields a class of compounds known as ethers. Ethers are classified as symmetrical or unsymmetrical on the basis of groups attached to the oxygen atoms. Diethyl ether, a symmetrical ether, has been widely used as an inhalation anesthetic. Ethers can be prepared by acid catalyzed intermolecular dehydration of alcohols and Williamson's synthesis. Acid catalyzed dehydration of alcohols is not generally preferred as it gives a mixture of elimination and substitution products. In Williamson's synthesis, an alkyl halide is allowed to react with sodium alkoxide. Ethers containing substituted Alkyl groups may also be prepared by this method. The C-O bond in ether is weakly polar and is cleaved under drastic conditions with excess of hydrogen halides. In electrophilic substitution, the alkoxy group deactivates the aromatic ring and directs the incoming group to ortho and para positions.
The major product in the reaction of anisole with bromine in ethanoic acid, is :

Which of the following contribute to increase in population density?

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: