The number of molecules with energy greater than the threshold energy for a reaction increases five fold by a rise of temperature from \(27^{\circ}\, C\) to \(42^{\circ}\, C .\) Its energy of activation in \(J / mol\) is.............. (Take in \(\ln 5=1.6094;\left.R =8.314\, J mol ^{-1} K ^{-1}\right)\)

An organic compound undergoes first order decomposition. If the time taken for the \(60 \,\%\) decomposition is \(540\,s\), then the time required for \(90\,\%\) decomposition will be is \(..........s\). (Nearest integer). Given : \(\ln 10=2.3 ; \log 2=0.3\)

The electronic configuration of Einsteinium is _______. (Given atomic number of Einsteinium \(=99\) )

Consider the following elements. Which of the following is/are true about \(\mathrm{A}^{\prime}, \mathrm{B}^{\prime}, \mathrm{C}^{\prime}\) and \(\mathrm{D}^{\prime}\) ? \(A\). Order of atomic radius: \(\mathrm{B}^{\prime}<\mathrm{A}^{\prime}<\mathrm{D}^{\prime}<\mathrm{C}^{\prime}\) \(B\). Order of metallic character: \(\mathrm{B}^{\prime}<\mathrm{A}^{\prime}<\mathrm{D}^{\prime}<\mathrm{C}^{\prime}\) \(C\). Size of the element : \(\mathrm{D}^{\prime}<\mathrm{C}^{\prime}<\mathrm{B}^{\prime}<\mathrm{A}^{\prime}\) \(D\). Order of ionic radius : \(\mathrm{B}^{\prime+}<\mathrm{A}^{\prime+}<\mathrm{D}^{\prime+}<\mathrm{C}^{\prime+}\) Choose the correct answer from the options given below :

In the Hoffmann bromamide degradation reaction, the number of moles of \(NaOH\) and \(Br_2\) used per mole of amine produced are :

A gaseous compound of nitrogen and hydrogen contains \(12.5\%\) (by mass) of hydrogen. The density of the compound relative to hydrogen is \(16\) .The molecular formula of the compound is

A commercially sold conc. \(HCl\) is \(35 \% HCl\) by mass. If the density of this commercial acid is \(1.46\) \(g / mL\), the molarity of this solution is ....\(M\) (Atomic mass : \(Cl =35.5 \,amu , H =1\, amu\) )

The oxide which contains an odd electron at the nitrogen atom is ..... .

If each term of a geometric progression \(a_1, a_2, a_3, \ldots\) with \(a_1=\frac{1}{8}\) and \(a_2 \neq a_1\), is the arithmetic mean of the next two terms and \(S_n=a_1+a_2+\ldots+a_n\), then \(\mathrm{S}_{20}-\mathrm{S}_{18}\) is equal to

Let the line \(\mathrm{L}\) intersect the lines \(\mathrm{x}-2=-\mathrm{y}=\mathrm{z}-1,2(\mathrm{x}+1)=2(\mathrm{y}-1)=\mathrm{z}+1\) and be parallel to the line \(\frac{x-2}{3}=\frac{y-1}{1}=\frac{z-2}{2}\). Then which of the following points lies on \(\mathrm{L}\) ?

The sum \(1+\frac{1+3}{2!}+\frac{1+3+5}{3!}+\frac{1+3+5+7}{4!}+\ldots\) upto \(\infty\) terms, is equal to

Two magnetic dipoles \(X\) and \(Y\) are placed at a separation \(d\), with their axes perpendicular to each other. The dipole moment of \(Y\) is twice that of \(X\). A particle of charge \(q\) is passing through their mid-point \(P\), at angle \(\theta  = 45^o\) with the horizontal line as shown in the figure. What would be the magnitude of force on the particle at that instant ? (\(d\) is much larger than the dimensions of the dipole)

The electron gain enthalpy (in \(kJ/mol\)) of fluorine, chlorine, bromine and iodine, respectively are