Read the passage carefully and answer the Questions
\(KMnO _4\) is prepared by the fusion of \(MnO _2\) with an alkali metal hydroxide and an oxidizing agent like \(KNO _3\) to give a dark-green manganate ion which disproportionate to give permanganate as follows.
\(\begin{array}{l}2 MnO _2+4 KOH + O _2 \rightarrow 2 K_2 MnO _4+2 H _2 O \\ 3 K_2 MnO _4+4 H ^{+} \rightarrow 2 KMnO _4+ MnO _2+2 H _2 O \end{array}\)
On heating \(K _2 MnO _4\) decomposes at 513 K to give \(K _2 MnO _4\). Permanganate ion is tetrahedral and diamagnetic
Acidified \(KMnO _4\) acts a strong oxidizing agent which oxidizes oxalic acid, ferrous ions, nitrite ion and iodides.
When one mole of \(KMnO _4\) is used for the oxidation of oxalic acid, how many moles of \(CO _2\) will be produced?

Which of the following is the best reducing agent to convert RCOOH into \(RCH _2 OH\) ?

Out of the following which will be see-saw shaped?
A. \(\text{XeO}_2\text{F}_2\)
B. \(\text{SF}_4\)
C. \(\text{BrF}_3\)
D. \(\text{XeO}_4\)
Choose the correct answer from the options given below:

Identify the optically active compounds from the following:
(A) \([\text{Co(en)}_3\text{]}^{3+}\)
(B) \(\text{trans-[Co(en)}_2\text{Cl}_2\text{]}^{+}\)
(C) \(\text{cis-[Co(en)}_2\text{Cl}_2\text{]}^{+}\)
(D) \([\text{Cr(NH}_3\text{)}_5\text{Cl}]\)
Choose the correct answer from the options given below:

The resistance of 1N solution of four different electrolytes are given below. Arrange them in increasing order of their equivalent conductance values if the same conductivity cell was used to measure the resistance of all the electrolytic solutions:
(A) 250 ohm
(B) 150 ohm
(C) 50 ohm
(D) 280 ohm
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Which of the following is a characteristic of Sy2 reaction?
(A). Concentration of both reactants determines the reaction rate.
(B). Proceeds with inversion of configuration.
(C). The transition state involves central carbon bonded to five species.
(D). Occurs in polar protic solvent
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Colligative properties are applicable to:

There are two values of a for which the determinant, \(\Delta = \begin{vmatrix} 1 & -2 & 5 \\ 0 & a & -1 \\ 0 & 4 & 2a \end{vmatrix} = 86\), then the sum of these values of a is:

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

Match List - I with List - II.

List - I (Electromagnetic waves)	List - II (Uses)
(A) Radio waves	(I) Aircraft navigation
(B) Ultraviolet rays	(II) Physical therapy
(C) Infrared waves	(III) Television communication systems
(D) Microwaves	(IV) Kill germs in water purifiers

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The direction cosines of a line equally inclined with the co-ordinate axes are :

If \(A=\left[\begin{array}{ll}2 & 3 \\ 1 & 4\end{array}\right]\) and \(B=\left[\begin{array}{cc}1 & -2 \\ 1 & 3\end{array}\right]\), then which of the following are incorrect?
(A) \(|A|=5\)
(B) \(\operatorname{Adj} A=\left[\begin{array}{ll}4 & 3 \\ 1 & 2\end{array}\right]\)
(C) \(A(\operatorname{Adj} A)=25 I\)
(D) \(|3 B|=45\)
(E) \((A B)^{-1}=B^{-1} A^{-1}\)
Choose the correct answer from the options given below:

Answer the question on basis of passage given below:
Organic compounds containing carbon -oxygen double bonds ( \(C = O\) ) are called carbonyl compounds. These are highly polar molecules. Hence, their boiling points are higher than hydrocarbons and ethers. Aldehydes can be prepared from dehydrogenation or oxidation of alcohols and by reduction of acylhalides. Ketones are prepared by oxidation of secondary alcohols or by hydration of alkynes etc. Aldehydes and ketones undergo nucleophilic addition reaction with the number of nucleophiles such as HCN , NaHSO3 ammonia derivatives. Carboxylic acids are prepared by the oxidation of primary alcohols, aldehydes and alkenes, by hydrolysis of nitriles. Carboxylic acids are more acidic than alcohols and phenols.
Which of the following is most reactive towards nucleophilic addition reaction ?