The point on the curve \(y^2=x\), where the tangent line makes an angle of \(\frac{\pi}{4}\) with x axis is

If \(a_{i j}\) represents the element of \(i^{\text {th }}\) row and \(j^{\text {th }}\) column and \(A_{i j}\) is the corresponding cofactor, then for the matrix \(A=\left[\begin{array}{ccc}1 & -1 & 0 \\ 2 & 0 & 1 \\ 3 & 4 & 2\end{array}\right]\) the value of \(a_{11} A_{21}+a_{12} A_{22}+a_{13} A_{23}\) is:

\(\int\left(\frac{1}{\log _e x}-\frac{1}{\left(\log _e x\right)^2}\right) d x\) is equal to

\(\int \sin^3 x dx\) is equal to:

If \(y=x^x, \frac{d y}{d x}\) will be:

If \(\tan ^{-1}(2 x)+\tan ^{-1}(3 x)=\frac{\pi}{4}\), then number of solution(s) of the given equation is :

If \(A\) is a square matrix of order 2 , then \(|\operatorname{adj} A|\) is equal to:

Match List - I with List - II.

List – I	List – II
(A) Polyvinyl chloride	(I) Phenol formaldehyde
(B) Urea-formaldehyde	(II) Ethyleneglycol and phthalic acid
(C) Glyptal	(III) Vinyl chloride
(D) Bakelite	(IV) Urea-formaldehyde

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With reference to transition metals which of the following statements are correct?
A. Electronic configuration is represented by ( \(n -2\) ) d1-10 ns1-2
B. They exhibit catalytic property
C. Some of them form interstitial compounds
D. In \(Ni ( CO ) 4\) and \(Fe ( CO ) 5\), the oxidation state of Ni and Fe are +4 and + 5 respectively.
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Carboxylic acids are the organic compounds which comprise of carboxyl functional group, -COOH. These are generally found in nature, some higher members are known as fatty acids as they occur in natural fats as esters of glycerol. They can be prepared from oxidation of alcohols and aldehydes, hydrolysis of nitriles and amides and Grignard reagents. They are stronger acids than simple phenols and alcohols. but weaker than mineral acids. Substituents affect the acidity of aliphatic and aromatic carboxylic acids. They undergo reactions involving cleavage of -OH and C-OH bond. Carboxylic acids having an alpha hydrogen get halogenated in the presence of red phosphorus to form alpha halo carboxylic acids. The reaction is known as Hell Volhard Zelinsky reaction. Besides these aromatic carboxylic acids undergo electrophilic substitution reactions. They are versatile and are employed in the manufacture of various useful compounds. For example, methanoic acid is used in rubber, textile, dyeing, leather and electroplating industries. Higher fatty acids are used in the manufacture of soaps and detergents. Esters of Benzoic acid are used in perfumery.
The reagents needed for the preparation of Benzoic acid from ethyl benzene is :

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Aldehydes and ketones are important organic compounds prepared mainly by oxidation of alcohols. Primary alcohols give aldehyde and secondary alcohols yield ketones. Aldehydes can also be formed by partial reduction of acid chlorides, reduction of esters or by Gattermann-Koch reaction. Ketones are prepared by Friedel-Craft's acylation, hydration of alkyne and reaction of Grignard's reagent with nitriles. Chemically, aldehydes and ketones are reactive in nature due to the carbonyl group and undergo nucleophilic addition reactions. Aldehydes are more reactive than ketones and can be oxidized to carboxylic acids, while both can be reduced to alcohols or hydrocarbons and exhibit condensation reaction
The correct IUPAC name of Vanillin is

Observe the figures and answer the question.

Identify the parts of the embryonal axis of a dicot embryo:
A. Epicotyle
B. Plumule
C. Radicle
D. Scutellum
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The probability that a student is not a swimmer is \(\frac{1}{5}\). Then, the probability that out of 5 students, 4 are swimmers is