Read the passage given below and answer the question.
Phenols and Alcohol have the same function group (-OH) but phenols are stronger acids than alcohol due the resonance stabilization of phenoxide ion than alkoxide ion (-RO\(^{-}\)). Electron withdrawing groups tend to increase the acidic strength while electron releasing groups tend to decrease it.
Which of the following reagent is used to distinguish between phenol and benzoic acid ?

The correct statements about \(Cr ^{2+}\) and \(Mn ^{3+}\) are : (atomic number of \(Cr =24\) and \(Mn =25\) )
(A) \(Cr ^{2+}\) is a reducing agent
(B) \(Mn ^{3+}\) is an oxidising agent
(C) Both \(Cr ^{2+}\) and \(Mn ^{3+}\) exhibit \(d^4\) electronic configuration
(D) When \(Cr ^{2+}\) is used as reducing agent chromium ion attains \(d^5\) electronic configuration Choose the \(\backslash\) textbf\{correct\} answer from the options given below :

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The speed at which a chemical reaction takes place is called the rate of reaction. The rate of reaction depends on various factors like concentration of the reactants, temperature, etc. The relation between the rate of reaction and the concentration of reacting species is represented by the equation r = k[A]^x[B]^y, where x and y are the order of the reaction with respect to the reactants A and B, respectively. The overall order of the reaction is x + y. The rate of reaction can also be increased by the use of a catalyst which provides an alternate pathway of lower activation energy. It increases the rate of forward and backward reaction to an equal extent. It does not alter the Gibbs energy of the reaction.
The rate of a gaseous reaction is given by r = k[A] [B]. If the volume of the reaction vessel is suddenly reduced to (1/4)th of its initial value, the reaction rate relating to the initial rate will become

Answer the question on the basis of passage given below :
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.
A group-IV element \(X\) shows magnetic moment of 1.73 BM , its oxidation state is?

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The degeneracy of the \(d\) orbitals has been removed due to ligand electron-metal electron repulsions in the octahedral complex to yield three orbitals of lower energy, \(t_{2 g}\) set and two orbitals of higher energy, \(e_g\) set. This splitting of the degenerate levels due to the presence of ligands in a definite geometry is termed as crystal field splitting and the energy separation is denoted by \(\Delta_0\). Thus energy of the two \(e_g\) orbitals will increase by \((3 / 5) \Delta_{\circ}\) and that of three \(t_{2 g}\) will decrease by \((2 / 5) \Delta_0\). The crystal field splitting \(\Delta_{ o }\) depends upon the field produced by the ligand and charge on the metal ion. Some ligands are able to produce strong fields, in which case the splitting will be large, whereas others produce weak fields and consequently result in small splitting of \(d\) orbitals. Relative magnitude of crystal field splitting energy \(\Delta_{\circ}\) and pairing energy, \(P\) (energy required for electron pairing in a single orbital) determine the formation of low spin ( \(\Delta_0>P\) ) or high spin ( \(\Delta_0<P\) ) complex. In tetrahedral coordination entity formation, the \(d\)-orbital splitting is inverted and is smaller as compared to the octahedral field splitting. The crystal field theory attributes the colour of the complex to \(d-d\) transition of the electron. The colour of the coordination compounds depends on the crystal field splitting. In the absence of ligand, crystal field splitting does not occur and hence the substance is colourless.
Choose the correct order of the ligands in their increasing crystal field splitting:

The presence or absence of hydroxyl group on which carbon is ribose sugar differentiate RNA and DNA?

Read the passage carefully and answer the Questions:
Amines are classified as primary \(\left(1^{\circ}\right)\), secondary \(\left(2^{\circ}\right)\) and tertiary \(\left(3^{\circ}\right)\) depending upon the number of hydrogen atoms replaced by alkyl or aryl groups in ammonia molecules. Aliphatic amines are a stronger bases due to \(+I\) effect of an alkyl groups. Intermolecular hydrogen bonding in primary and secondary amines affects the boiling points of amines. The intermolecular association is more in primary amines than in secondary amines as there are more number of hydrogen atoms available for hydrogen bond formation. Nitro compounds are reduced to amines by passing hydrogen gas in the presence of finely divided nickel, palladium or platinum and also by reduction with metals in an acidic medium. Gabriel synthesis is used for the preparation of primary amines. Primary amines react with nitrous acid to give unstable diazonium-salts which can be used to synthesize a variety of compounds.

The reaction is an example of:

Arrange the metal ions of the following compounds in increasing order of oxidation number :
(A) \(\text{TiCl}_3\)
(B) \(\text{CrF}_6\)
(C) \(\text{ZnO}\)
(D) \(\text{Mn}_2\text{O}_7\)
Choose the correct answer from the options given below :

Which one of the following statements is incorrect about ecological pyramids?

Let \(A\) and \(B\) be independent events such that \(P(A)=0.3\) and \(P(B)=0.4\), then
Match List-l with List-ll

List-I	List-II
(A) \(P(A \cap B)\)	(I) 0.3
(B) \(P(A \cup B)\)	(II) 0.4
(C) \(P(A \mid B)\)	(III) 0.12
(D) \(P(B \mid A)\)	(IV) 0.58

Choose the correct answer from the options given below :

A wire of length 10 m and diameter 0.4 mm has a resistance of \( 2 \, \Omega \). The resistivity of the wire is

A total of \(5.0 \times 10^{16}\) electrons per second go through a conductor of area \(2 mm^2\). The current density will be:

The corner points of the feasible region associated with the \(LPP\): Maximise \(Z=p x+q y, p, q>0\) subject to \(2 x+y \leq 10, x+3 y \leq 15, x, y \geq 0\) are \((0,0),(5,0),(3,4)\) and \((0,5)\). If optimum value occurs at both \((3,4)\) and \((0,5)\), then: