\(\text{KMnO}_4\) is a versatile oxidising agent and it can act as a very strong oxidising agent in acidic medium. Identify the correct statement.

Read the passage carefully and answer the questions
The resistance ( \(R\) ) of an object is given by the expression \(R=\rho \frac{l}{A}\)
The inverse of \(R\) is called conductance and the inverse of \(\rho\) is called conductivity or specific conductance represented by \(\kappa\).
The conductivity depends upon the nature of the material (insulator, semiconductor or conductor) and the temperature of the substance.
Similarly, the conductance due to the ions present in the solution. (ionic conductance) depends upon the nature of the electrolyte, size of ions, the nature of the solvent and the temperature.
Molar conductivity ( \(\Lambda _{ m }\) ) of a solution at a given concentration is the conductance of volume \(V\) containing one mole of electrolyte kept between two electrodes of area \(A\) and unit distance apart.
It is given by the expression.\(A_m=\kappa V .\)
Molar conductivity increases with decrease in concentration and when concentration approaches sero, it is called limiting molar conductivity.
The decrease is linear for a strong electrolyte. However, for a weak electrolyte the change is gradual at higher concentrations and sharp near zero concentration.
Using limiting molar conductivity values of strong electrolytes we can calculate the limiting molar conductivity of weak electrolytes using Kohlrausch law of independent migration of ions.
From molar conductivity and limiting molar conductivity we can determine the degree of dissociation \(\left(\frac{\Lambda_m}{\Lambda_m^0}\right)\) and the ionisation constant of a weak acid.
The limiting molar conductivity values for \(HCl , NaCl\) and \(CH _3 COONa\) are \(425.9,126.4\) and \(91.0 S cm ^2 mol^{-1}\), respectively.
Calculate the limiting molar conductivity value for acetic acid.

Arrange the following complexes in increasing order of number of moles of silver chloride precipitated
when one mole of each is reacted with excess of silver nitrate.
(A) \(\left[ Co \left( NH _3\right)_4 Cl _2\right] Cl\)
(B) \(\left[ Co \left( NH _3\right)_5 Cl \right] Cl _2\)
(C) \(\left[ Co \left( NH _3\right)_3 Cl _3\right]\)
(D) \(\left[ Co \left( NH _3\right)_6\right] Cl _3\)
Choose the correct answer from the options given below:

The actual density of a crystal of NaCl is observed to be lower than the expected value. It is caused due to the presence of :

Answer the question on basis of passage given below :
A ketone \([A]\) which undergoes haloform reaction gives compound \([B]\) on reduction. Compound \([B]\) on heating with sulphuric acid gives compound \([C]\) which forms monozonide \([D]\). The compound [D] on hydrolysis in the presence of zinc dust gives compound [E].
Compound [E] on oxidation gives \(C _2 H _4 O _2\) [F]
The boiling point of \([ A ]\) observed is exceptionally high because of :

Match the complexes given in List-I with oxidation state and the type of complexes given in List-II

List-I  (Complex)	List-II  (Oxidation state and type of complex)
(A) \(\left[ Co \left( NH _3\right)_6\right]^{3+}\)	(I) +2 and Inner orbital complex
(B) \(\left[ CoF _6\right]^{3-}\)	(II)  +2 and Outer orbital complex
(C) \(\left[ NiCl _4\right]^{2-}\)	(III) +3 and Outer orbital complex
(D) \(\left[ Ni ( CN )_4\right]^{2-}\)	(IV) +3 and Inner orbital complex

Choose the correct answer from the options given below:

45 g of ethylene glycol (C₂H₆O₂) is mixed with 600 g of water. Calculate the depression in freezing point.
(K_f for water = 1.86 K kg mol^-1)

Which one of the following is an example of man-made ecosystem?

A neutron is absorbed by a \( {}^6_3\text{Li} \) nucleus with subsequent emission of an alpha particle. The energy released in the reaction is
Use mass of \( {}^6_3\text{Li} = 6.015126 \text{ u} \)
Mass of \( {}^4_2\text{He} = 4.002604 \text{ u} \)
Mass of \( {}^1_0\text{n} = 1.008665 \text{ u} \)
Mass of \( {}^3_1\text{H} = 3.016049 \text{ u} \) and \( 1 \text{ u} = 931 \text{ MeV} \)

Which of the following is used to make the bacterial cell as 'Competent cell' to take up DNA?

The unit vector in the xy-plane, making an angle of \(60^{\circ}\) with the positive direction of x-axis is:

Identify the correct statements for the behavior of ethane-1,2-diamine as a ligand.
(A) it is a neutral ligand
(B) it is a bidentate ligand
(C) it is an ambidentate ligand
(D) it is a chelating ligand
Choose the correct answer from the options given below:

Read the passage carefully and answer the Questions
The concentration dependence of the rate of a reaction is called the differential rate equation. It is not always convenient to determine the instantaneous rate, as it is measured by calculating the slope of the tangent at point 't' in the concentration vs time plot. This makes it difficult to determine the rate and hence the order of the reaction. This difficulty is overcome by integrating the differential rate equation. This integrated rate equation gives a direct relation between concentrations at different times and the rate constant. The integrated rate equations are different for the reactions having different reaction orders.
For an integrated first order reaction, a straight line graph is plotted. The incorrect co-ordinates and resulting slope of the graph are