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Sodium dichromate \(Na _2 Cr _2 O _7\) and Potassium dichromate \(K _2 Cr _2 O _7\) are strong oxidizing agents; in acidic solution, its oxidising action can be represented as follows :
\(Cr _2 O _7^{2-}+14 H ^{+}+6 e^{-} \rightarrow 2 Cr ^{3+}+7 H _2 O \left( E ^{\circ}=1.33 V\right)\)
The chromates and dichromates are interconvertible in aqueous solution depending upon pH of the solution.
The chromate ion is tetrahedral whereas the dichromate ion consists of two tetrahedra sharing one corner with \(Cr - O - Cr\) bond angle of \(126^{\circ}\)
Potassium permanganate is prepared by fusion of \(MnO _2\) with an alkali metal hydroxide and an oxidising agent like \(KNO _3\).
This produces the dark green \(K _2 MnO _4\) which disproportionates in a neutral or acidic solution to give permanganate. It is a strong oxidizing agent. Hydrogen ion concentration of the solution plays
an important part in the reduction of permanganate to manganate, manganese dioxide and manganese(II) salt.
Potassium permanganate forms dark purple (almost black) crystals which are isostructural with those of \(KClO _4\).
The salt is not very soluble in water \((6.4 g / 100 g\) of water at 293 K ), but when heated it decomposes at 513 K.
Potassium dichromate is used in the leather industry because of its nature as

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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?

Select the correct formula for the coordination compound "Dichloridobis(ethane-1,2-diamine)cobalt(III) chloride"

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Alcohols are versatile compounds as they can act as both nucleophile and electrophile. They undergo reactions based on cleavage of O-H and C-O bonds. The cleavage of O-H bond reflects the acidic character of alcohols. However they are weaker acids than water, phenol and carboxylic acids. Alkoxide ion formed by loss of proton from the OH group of alcohols reacts with water to form the corresponding conjugate acid - base pair. They act as Bronsted base due to presence of unshared electron pairs on oxygen.Both alcohols and phenol react with carboxylic acids, acid chlorides and anhydrides to form esters. The introduction of acetyl group in alcohols or phenol is known as acetylation. Alcohols react with hydrogen halides to form alkyl halides which form the basis of Lucas test. They also undergo acid catalyzed dehydration to form alkenes. Alcohols can be easily oxidized with variety of oxidizing agents. The nature of the product depends on the type of oxidizing agent and the nature of alcohol.
Pyridinium chlorochromate is used for:

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Living systems are made up of various complex bio-molecules like carbohydrates, proteins, nucleic acids, lipids etc. Proteins and carbohydrates are essential constituents of our food. Carbohydrates are primarily produced by plants and form a very large group of naturally occurring organic compounds. Some common examples are cane sugar, glucose, starch etc.
Carbohydrates are stored in animals as:

According to Alexander Zaitsev the most preferred product for dehydrohalogenation of 2-Bromopentane will be :

Identify the incorrect statement about the \(H _2- O _2\) fuel cell from the following:

Which of the following statements are correct?
(A) The electric field and magnetic field vectors of an electromagnetic wave are perpendicular to each other and also perpendicular to the direction of propagation of wave.
(B) Short waves are reflected from ionosphere.
(C) Electric field vector, E and magnetic field vector B have the same frequency.
(D) The line integral of magnetic field induction over a closed path is not zero.
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Nearly all the transition elements display typical metallic properties such as high tensile strength, ductility, malleability, high thermal and electrical conductivity and metallic lustre. The transition metals (with the exception of Zn, Cd and Hg) are very hard and have low volatility. Their melting and boiling points are high. They have high enthalpies of atomization. lons of the same charge in a given series show progressive decrease in radius with increasing atomic number. However, the variation within a series is quite small. The filling of 4f before 5d orbital results in a regular decrease in atomic radii called Lanthanoid contraction which essentially compensates for the expected increase in atomic size with increasing atomic number. The net result of the lanthanoid contraction is that the second and the third d series exhibit similar radii (e.g., Zr 160 pm, Hf 159 pm) and have very similar physical and chemical properties. There is an increase in ionisation enthalpy along each series of the transition elements from left to right. The first ionisation enthalpy, in general, increases, but the magnitude of the increase in the second and third ionisation enthalpies for the successive elements, is much higher along a series. One of the notable features of a transition elements is the great variety of oxidation states these may show in their compounds.
Atomic number of Fe, Co, Ni and Cu are 26, 27, 28 and 29 respectively. Which among them is expected to possess the highest value for the second ionization enthalpy?

Which of the following is not correct about the Central Limit Theorem?

Let \(R\) be the set of all real numbers and \(f: R \rightarrow\) Range \(f\) be given by \(f(x)=3 x^2+1\). Then \(f^{-1}\{1,2\}\) is :

Match List-l with List-ll

List-l (Disease)	List-II (Characteristic symptoms)
(A) Malaria	(I) Inflammation of lower limb
(B) Filariasis	(II) Cycles of fever
(C) Ringworms	(III) Blood clots and excess mucus in stools
(D) Amoebiasis	(IV) Scaly lesions on nails

Choose the correct answer from the options given below:

A 50 W, 100 V bulb is to be used on a 200 V, 50 Hz a.c. supply. Calculate the inductance of inductor used so that the bulb glows with normal brightness.