For first order decomposition of \(N _2 O _5\) at constant volume, \(p_i\) is initial pressure
and \(p_t\) is pressure at any time \(t\) during the reaction.
Which of the following statement/s is incorrect?
(A) Half life does not depend on initial pressure
(B) Total pressure decreases with time
(C) Rate constant will be the same if initial pressure is doubled
(D) \(k=\frac{2.303}{t} \log \left(\frac{p_t}{p_i}\right)\)
Choose the correct answer from the options given below:

Which of the following pairs of solutions are isotonic?

What is the source of nitrogen in Gabriel synthesis of primary aliphatic amines?

Find the value of \(\text{E}^{\circ}\) in the missing link in the following diagram.
\(Fe ^{3+} \xrightarrow{E_1^{\circ}=0.77 V} Fe ^{2+} \xrightarrow{E_2^{\circ}=-0.44 V} Fe\)
\(Fe ^{3+} \xrightarrow{E_3^{\circ}=?} Fe\)

A reaction takes 30 minutes to complete 50\(\%\) of the reaction and takes 45 minutes to complete 75\(\%\) of the reaction. The order of the reaction is :

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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.
A certain amount of \(N _2 O _5\) decomposes to half of its initial amount in 50 minutes.
If the decomposition is a first order reaction, the rate constant of the reaction is.

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]
Compound \([ F ]\left( C _2 H _4 O _2\right)\) on treatment with chlorine, in the presence of small amount of red phosphorus, gives :

If \(\Delta_1=\left|\begin{array}{lll}x & b & b \\ a & x & b \\ a & a & x\end{array}\right|\) and \(\Delta_2=\left|\begin{array}{ll}x & b \\ a & x\end{array}\right|\) are determinants, then :

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Molar conductivity \(\left(\Lambda_m\right)\) of a solution at a given concentration (c) is the conductance of volume, V of solution, containing one mole of electrolyte kept between the two electrodes with area of cross-section A and at a distance of unit length. It increases with the decrease in concentration and when the concentration approaches zero, the molar conductivity is called limiting molar
conductivity \(\left(\Lambda_m^0\right)\). For a strong electrolyte, \(\Lambda_m\) increases linearly with dilution and is given by \(\Lambda_m=\Lambda_m^0-A c^{1 / 2}\). The value of the constant A for a given solvent depends on the type of electrolyte along with temperature. According to Kohlrausch law, the value of \(\Lambda_m^0\) for an electrolyte is \(\Lambda_m^0=\nu_{+} \lambda_{+}^0+\nu_{-} \lambda_{-}^0\), where \(\nu_{+}\)and \(\nu_{-}\) are the number of cations and anions, respectively, per molecule of the electrolyte and \(\lambda_{+}^0\) and \(\lambda_{-}^0\) are limiting molar conductivities of cation and anion, respectively. Kohlrausch law finds many applications, like determining the solubility of a sparingly soluble salt, determining the degree of dissociation \(\left(\Lambda_m / \Lambda_m^0\right)\), and the dissociation constant of a weak electrolyte.
The plot between \(\Lambda_m\) and \(c^{1 / 2}\) is a straight line with

Arrange the given stages of menstrual cycle in correct sequence.
(A) Luteal phase
(B) Follicular phase
(C) Menstruation
(D) Next cycle begins
Choose the correct answer from the options given below:

In a laboratory population of 80 fruit flies, 8 died in a week, then the death rate of fruit flies is:

Fertilization in human female takes place in -

Read the following passage carefully and answer the given questions.
During anaerobic sludge digestion, bacteria produce a mixture of gases such as methane, hydrogen sulphide and carbon dioxide. These gases form biogas and can be used as source of energy as it is inflammable. The bioactive molecule, cyclosporin A, that is used as an immunosuppressive agent in organ-transplant patients, is produced by the fungus Trichoderma polysporum. You must have noticed that bottled fruit juices bought from the market are clearer as compared to those made at home. This is because the bottled juices are clarified by the use of pectinases and proteases. Statins produced by the yeast Monascus purpureus have been commercialised as blood-cholesterol lowering agents. It acts by competitively inhibiting the enzyme responsible for synthesis of cholesterol. The BOD test measures the rate of uptake of oxygen by micro-organisms in a sample of water and thus, indirectly, BOD is a measure of the organic matter present in the water.
Cyclosporin A, that is used as an immunosuppressive agent in organ-transplant patients, is produced by -