During a chemical reaction \(\mathrm{X} \rightarrow \mathrm{Y}\), the rates of reaction starting with initial concentrations of X as \(4.0 \times 10^{-3} \mathrm{M}\) and \(2.0 \times 10^{-3} \mathrm{M}\) are \(4.8 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1} / \mathrm{s}\) and \(1.2 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1} / \mathrm{s}\) respectively. What is the order of reaction with respect to X ?

The number of \(\sigma\) and \(\pi\)-bonds in pent-2-yne is

In the reaction,



\(2 \mathrm{~S}_2 \mathrm{O}_3^{2-}+\mathrm{I}_2 \rightarrow \mathrm{S}_4 \mathrm{O}_6^{2-}+2 \mathrm{I}^{-}\)

In Friedal-Crafts alkylation reaction of phenol with chloromethane, the product formed will be

Which one of the following statements is wrong?

In which one of the case the chemical reaction given in Column I does not match with the name of the reaction given in Column II?
\(\begin{array}{|l|l|l|} \hline \text{S.No.} & \text{Column I - Reactions} & \text{Column II - Name of reaction.} \\ \hline \text{A} & \mathrm{C}_6 \mathrm{H}_5 \mathrm{CHO}+ \text{Conc. NaOH, heat} \rightarrow \mathrm{C}_6 \mathrm{H}_5 \mathrm{CH}_2 \mathrm{OH}+\mathrm{C}_6 \mathrm{H}_5 \mathrm{COONa} & \text{Cannizzaro's reaction} \\ \hline \text{B} & \mathrm{C}_6 \mathrm{H}_5 \mathrm{CH}_3+ \text{ (i) } \mathrm{CrO}_2 \mathrm{Cl}_2 / \mathrm{CS}_2 \text{ (ii) } \mathrm{H}_3 \mathrm{O}^{+} \rightarrow \mathrm{C}_6 \mathrm{H}_5 \mathrm{CHO} & \text{Etard reaction.} \\ \hline \text{C} & \mathrm{C}_6 \mathrm{H}_6+\mathrm{CO} / \mathrm{HCl} \text{ (anh. } \mathrm{AlCl}_3 \rightarrow \mathrm{C}_6 \mathrm{H}_5 \mathrm{CHO} & \text{Kolbe's reaction} \\ \hline \text{D} & \mathrm{RCN}+ \text{ (i) } \mathrm{SnCl}_2+\mathrm{HCl} \text{ (ii) } \rightarrow \mathrm{RCHO} & \text{Stephen's reaction.} \\ \hline \end{array}\)

Match \(\mathrm{A}, \mathrm{B}, \mathrm{C}\) and D with the appropriate functions given.
\(\begin{array}{|l|l|l|l|} \hline & \text { Column I } & & \text { Functions } \\ \hline \text { A } & \text { Oxidoreductase } & \text { P } & \text { Malfunctioning leads to Addison's disease. } \\ \hline \text { B } & \text { Phosphodiester bonds } & \text { Q } & \text { Regulates responses to external stimuli. } \\ \hline \text { C } & \text { Adrenal cortex } & \text { R } & \text { Catalyses glycolysis. } \\ \hline \text { D } & \text { Epinephrine. } & \text { S } & \text { Links nucleotides together. } \\ \hline \end{array}\)

Consider the lines \(L_1\) and \(L_2\) given by the following vector equations:
\(L_1: \vec{r} = (\hat{i} + \hat{j} - \hat{k}) + \lambda(3\hat{i} + t\hat{j})\)    \(L_2: \vec{r} = (4\hat{i} + a\hat{j} - \hat{k}) + \mu(2\hat{i} + 3\hat{k})\)
If \(a = -2\) and the lines intersect, then the value of 't' is:

With the addition of impurities, surface tension of a liquid

Which of the following equations give ionic product of water?
I. \(\mathrm{NH}_{3}(a q)+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{NH}_{4}^{+}(a q)+\mathrm{OH}^{-}(a q)\)
II. \(\mathrm{NH}_{4}^{+}(a q)+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{H}_{3} \mathrm{O}^{+}+\mathrm{NH}_{3}(g)\)
III. \(\mathrm{NH}_{2}^{-}(a q)+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{NH}_{3}(g)+\mathrm{OH}^{-}(a q)\)
IV. \(\mathrm{NH}_{3}(g)+\mathrm{OH}^{-}(a q) \rightleftharpoons \mathrm{NH}_{2}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}\)

The mobility of the charge carriers increases with

In detector, output circuit consists of \(R=10 \mathrm{k} \Omega\) and \(C=100 \mathrm{pF}\). The frequency of carrier signal which it can detect is

Find the geometric progression for which the sum of the first two terms is -4, the fifth term is four times the third term and common ratio is less than zero